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Volumetric Properties and Viscosity of Fluid Mixtures at High Pressures: Lubricants and Ionic
Liquids
James Scott Dickmann
Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in
partial fulfillment of the requirements for the degree of
Doctor of Philosophy
In
Chemical Engineering
Erdogan Kiran, Chair
Richey M. Davis
Stephen M. Martin
Hongliang Xin
April 26, 2019
Blacksburg, VA
Keywords: Viscosity, Density, Lubricants, Ionic liquids, High pressure, Viscometer, Modeling,
Compressibility, Solubility parameter
Volumetric Properties and Viscosity of Fluid Mixtures at High Pressures: Lubricants and
Ionic Liquids
James Dickmann
Abstract
The present thesis explores the volumetric and transport properties of complex fluid
mixtures under pressure in order to develop a better, more holistic understanding of the
relationship between the volumetric properties, derived thermodynamic properties, and viscosity.
To accomplish this broad objective, two different categories of fluid mixtures were examined
using a combination of experimental data and models. These included base oils and their
mixtures with polymeric additives, used in lubricants and ionic liquids, with cosolvent addition,
for use in biomass and polymer processing. Experimental density data were collected using a
variable-volume view-cell at pressures up to 40 MPa and temperatures up to 398 K. A unique
high pressure rotational viscometer was developed to study the effect of pressure, temperature,
and shear rate on viscosity while also allowing for the simultaneous examination of phase
behavior. Viscosity data were collected at pressures up to 40 MPa, temperatures up to 373 K,
and shear rates up to 1270 s-1. Experimental density and viscosity data were fit to a pair of
coupled model equations, the Sanchez-Lacombe equation of state and the free volume theory
respectively. From density, derived thermodynamic properties, namely isothermal
compressibility, isobaric thermal expansion coefficient, and internal pressure, were calculated.
By generating these models, viscosity could be viewed in terms of density, allowing for a direct
link with thermodynamic properties.
In the first part of the study, the effect of composition on density, thermodynamic
properties, and viscosity was examined for base oils used in automotive lubricants. Six different
base oils, four mineral oils and two synthetic oils, were studied to develop a better understanding
on how the thermodynamic properties, particularly isothermal compressibility and internal
pressure, vary with the concentration of cyclic molecules in the oil stock. Isothermal
compressibility was found to decrease with cycloalkane content, while internal pressure
increased. Additionally, the effect of two different polymeric additives on the volumetric
properties and viscosity of a base oil composed of poly(α olefins) was examined. Both additives
are polymethacrylate based, one with amine functionality, and are used as viscosity index
modifiers in engine oils and automatic transmission fluids. The polymer with amine
functionality was found to have a significant effect on internal pressure, seen as a large drop at
high polymer concentration (7 mass percent), due to the addition of repulsive intermolecular
interactions.
In the second part of the study, six ionic liquids with the 1-alkyl-3-methylimidazolium
cation and their mixtures with ethanol were examined. Two anions were used, chloride and
acetate. The effect of ethanol addition on the derived thermodynamic properties and viscosity
was studied in terms of chain length of the alkyl group on the cation. In addition, a method of
estimating Hildebrand solubility parameter was employed, allowing for solubility parameter to
be put in terms of pressure, temperature, and composition. The effect of cosolvent addition on
the thermodynamic properties was changed by the length of the alkyl group on the cation. As the
cation became bulkier, anion-cation interactions weakened, allowing for an increase in the anion-
cosolvent interactions.
Volumetric Properties and Viscosity of Fluid Mixtures at High Pressures: Lubricants and
Ionic Liquids
James Dickmann
General Audience Abstract
The present thesis aims to understand both the density and viscosity of various fluid
mixtures at high pressures and temperatures through both experiments and modeling. By
studying these properties simultaneously, a more holistic view of a fluid can be developed to
predict its usefulness for a specific application. This is especially important in the case of fluid
mixtures, where, in addition to temperature and pressure, composition needs to be taken into
account. To accomplish the experimental portion of this work, a new high pressure rotational
viscometer was developed to measure viscosity as a function of temperature and pressure in
conjunction with a preexisting technique for measuring density. This experimental data was
used to create models, allowing for a better understanding of the effect of temperature, pressure,
and composition on both density and viscosity along with certain thermodynamic properties.
In the first part of the study, oils and additives used to make lubricants with automotive
applications, such as engine oils and automatic transmission fluids, were studied. By studying
the properties of these mixtures under pressure, a better understanding of how properties key to
lubricant effectiveness are related to temperature, pressure, and composition can be developed.
In the second part of the study, ionic liquids, salts with melting points below 100oC, and
their mixtures with ethanol were studied. Ionic liquids have unique properties and have been
studied for use in batteries, polymer processing, biomass processing, and gas capture. Due to the
wide range of potential ionic liquids with various properties that can be made, these salts have
been described as tailorable solvents. By adding an additional solvent, the resulting mixture can
be tuned through temperature, pressure, and composition. Using the set of tools employed in the
present work, important properties for process design were calculated. In particular, the
Hildebrand solubility parameter was estimated as a function of temperature, pressure, and
composition. The solubility parameter is a useful tool in predicting whether or not a material
will dissolve in the solvent of choice.
v
Acknowledgments
A number of people have been instrumental in the completion of the body of work found
in the current thesis. I would like to express my appreciation to my advisor Dr. Erdogan Kiran
for his help in the work presented in the present thesis. His help and reassurance through both
the successes and failures in the long road of developing the high pressure rotational viscometer
were instrumental in getting it to the place it is today. His consistent encouragement has been
key in getting me this far in my professional life. I would also like to thank Mrs. Gunin Kiran
for her encouragement and the many wonderful meals she provided for the lab group over the
years.
I would like to offer a special thanks to Dr. John Hassler. His help in coding in Python®
and in troubleshooting the viscometer, especially the software and electronics involved, has
made a major impact on this work. Additionally, without his early groundwork on the use of
Python® for the Sanchez-Lacombe equation of state, the modeling section of this work would
not have been possible. My grateful thanks are also extended to Michael Vaught and Kevin
Holshouser, without whom, the viscometer would never be completed.
In addition, I would like to acknowledge the Afton Chemical Corp for sponsoring much
of this research, especially Dr. Mark Devlin, whose interactions always provided an excellent
learning opportunity into a field I was not as familiar with.
I wish to extend my thanks to the other members of the Supercritical Fluids Lab that I
have worked alongside over the past six years: Mary McCorkill and Katrina Avery for their help
in generating the final series of experimental results, Dr. Joon-Hyuk Yim for working alongside
of me on parts of the ionic liquid research, Michael Williams and Joseph Sarver for agreeing to
help edit this thesis, Dr. Heather Grandelli, Dr. Sulamith Frerich, and Shinya Takahashi for
training me at the start of my degree, and Daniel Aube, KwangHae Noh, Mai Ngo, Macy
Lupton, Lauren Pironis, Jenna Sumey, Carter Berry, Scott Holahan, Josh Rasco, and Morgan
Whitfield for their continued support over the course of this work.
Finally, I would like to thank my parents, Norb and Marion Dickmann, who have been
there every step of the way in my journey to finish this thesis.
vi
Table of Contents
Chapter I Introduction and Survey of the Literature 1
I.1 A Brief Description of the Scope of the Thesis 1
I.2 A Brief Overview of the Literature 3
I.2.1 Experimental Determination of Viscosity at High Pressure 7
I.2.1.A Falling Body/Rolling Ball Viscometers 7
I.2.1.B Capillary Viscometers 8
I.2.1.C Vibrating Wire Viscometers 9
I.2.1.D Oscillating Quartz Viscometers 9
I.2.1.E Oscillating Piston Viscometers 10
I.2.1.F Rotational Viscometers 10
I.2.1.G Other 11
I.2.1.H Density and High Pressure Viscosity 11
I.2.1.I Limitations 12
I.2.2 Modeling of Pressure Effects on Viscosity 13
I.2.2.A Modeling Viscosity of Gases 13
I.2.2.B Free Volume Theory 15
I.2.2.C Friction Theory 16
I.2.2.D Scaling Factors 16
I.2.2.E Molecular Dynamics Simulations 17
I.2.2.F Other models 17
I.2.2.G Modeling of Density and Phase Behavior 18
I.2.2.H Limitations 19
I.2.3 Oils, Lubricants, and Fuels 19
I.2.3.A Lubricants 20
I.2.3.B Fuels 21
I.2.3.C Oil Recovery 21
I.2.4 Ionic Liquids 22
I.2.5 Gas Expanded Liquids 23
I.2.6 Polymers 24
vii
I.2.6.A Plasticizers 24
I.2.6.B Foams 25
I.2.7 Geological Effects 25
I.3 A Brief Rationale for the Present Study 26
I.4 References 27
Chapter II Experiments 35
II.1 Variable-Volume View-Cell 35
II.2 High Pressure Rotational Viscometer 39
III.3 References 60
Chapter III Analysis and Modeling 51
III.1 Volumetric properties and lattice fluid models 51
III.2 Modeling mixtures 53
III.3 Derived thermodynamic properties 55
III.4 Viscosity and free volume 56
III.5 Statistical analysis of model fits 57
III.6 References 58
Chapter IV Base Oils 60
IV.1 Introduction 70
IV.1.1 Objectives 61
IV.2 Materials and Methods 61
IV.3 Results and Discussion 64
IV.3.1 PVT Data and Modeling 64
IV.3.2 Derived Thermodynamic Properties 66
IV.3.3 Viscosity and Modelling 73
IV.4 Conclusions 77
IV.5 References 77
Chapter V Base Oil Additives 79
V.1 Introduction 79
V.1.1 Objectives 79
V.2 Materials and Methods 80
V.3 Results and Discussion 81
viii
V.3.1 Viscosity Index Modifiers 81
V.3.2 Automatic Transmission Fluids 92
V.4 Conclusions 96
V.5 References 97
Chapter VI Ionic Liquids 98
VI.1 Introduction 98
VI.1.1 Objectives 98
VI.2 Materials and Methods 99
VI.2.1 Synthesis 101
VII.3 Results and Discussion 103
VI.3.1 1-Alkyl-3-methylimidazolium Chlorides and their Mixtures with
Ethanol
103
VI.3.1.A Derived Thermodynamic Properties of [RMIM]Cl + Ethanol 109
VI.3.2 1-Alkyl-3-methylimidazolium Acetates and their Mixtures with
Ethanol
118
VI.3.2.A Derived Thermodynamic Properties of [RMIM]Ac + Ethanol 121
VI.3.2.B Viscosity of [RMIM]Ac + Ethanol 128
VI.3.3 Hildebrand Solubility Parameters of Ionic Liquids 130
VI.4 Conclusions 135
VI.5 References 136
Chapter VII Conclusions 138
VII.1 Future Work 139
VII.2 References 140
Appendix A: Publications Represented in the Present Thesis 141
Appendix B: Calibration and Verification of Density and Viscosity Measurements 142
Appendix C: Density, Derived Thermodynamic Properties, and Viscosity of Base
Oils
151
Appendix D: Density, Derived Thermodynamic Properties, and Viscosity of
Mixtures of Base Oils with Additives and Automatic Transmission Fluids
166
Appendix E: Density, Derived Thermodynamic Properties, and Viscosity of Ionic
Liquids and Their Mixtures with Ethanol
191
ix
List of Tables
Table I.1. Base oil categories as laid out by the American Petroleum Institute
guidelines.
20
Table II.1. Cannon Instrument Company calibration standards used to calibrate the
high pressure rotational viscometer.
45
Table IV.1. Characteristics of the base oils studied. 62
Table IV.2. Sanchez-Lacombe parameters of base oils. 65
Table IV.3. Parameters for the free volume theory of viscosity. 75
Table V.1. S-L parameters for mixtures of PAO 4 with Polymer 1. 83
Table V.2. S-L parameters for mixtures of PAO 4 with Polymer 2. 84
Table V.3. Parameters for the free volume theory of viscosity for mixtures of PAO 4
and viscosity index modifier Polymer 1.
90
Table V.4. Parameters for the free volume theory of viscosity for mixtures of PAO 4
and viscosity index modifier Polymer 2.
91
Table V.5. Tait equation parameters for automatic transmission fluids. 93
Table VI.1. Melting Points of the ILs used in this study. 101
Table VI.2. S-L EOS characteristic parameters for ethanol, [EMIM]Cl, [PMIM]Cl,
[BMIM]Cl, and [HMIM]Cl.
104
Table VI.3. Comparison of Root Mean Squared Deviations (RSME) for different
models of the binary interaction parameter used in mixing rules for the S-L EOS.
106
Table VI.4. S-L EOS characteristic parameters for [EMIM]Cl + ethanol mixtures. 106
Table VI.5. S-L EOS characteristic parameters for [PMIM]Cl + ethanol mixtures. 107
Table VI.6. S-L EOS characteristic parameters for [BMIM]Cl + ethanol mixtures. 107
Table VI.7. S-L EOS characteristic parameters for [HMIM]Cl + ethanol mixtures. 107
Table VI.8. S-L EOS characteristic parameters for [EMIM]Ac and [BMIM]Ac. 119
Table VI.9. Comparison of Root Mean Squared Deviations (RSME) for different
models of the binary interaction parameter used in mixing rules for the S-L EOS for
[EMIM]Ac and [BMIM]Ac.
120
Table VI.10. S-L EOS characteristic parameters for [EMIM]Ac + ethanol mixtures. 120
Table VI.11. S-L EOS characteristic parameters for [BMIM]Ac + ethanol mixtures. 121
x
Table VI.12. Parameters for the free volume theory of viscosity. 129
Table VI.13. Solubility parameters of ionic liquids at 298 K and 0.1 MPa. 135
xi
List of Figures
Figure I.1. Journal articles published every year from 2000-2018 using search terms
Viscosity + High Pressure on Web of Science.
4
Figure I.2. Journal articles published every year from 2000-2018 using search terms
Viscosity + High Pressure + Lubricant on Web of Science.
4
Figure I.3. Journal articles published every year from 2000-2018 using search terms
Viscosity + High Pressure + Ionic Liquid on Web of Science.
5
Figure I.4. Journal articles published every year from 2000-2018 using search terms
Viscosity + High Pressure + Polymer on Web of Science.
5
Figure I.5. Journal articles published every year from 2000-2018 using search terms
Viscosity + High Pressure + Supercritical Fluid on Web of Science.
6
Figure II.1. External diagram of the variable-volume view-cell. 36
Figure II.2. Internal diagram of the variable-volume view-cell. 37
Figure II.3. Dimensions of the variable-volume view-cell. 37
Figure II.4. Evaluation of a sample run of ethanol in the variable-volume view-cell at
a fixed temperature of 298 K.
38
Figure II.5. Comparison of experimental (circles) data for a validation run to
literature values (diamonds).
39
Figure II.6. External diagram of the high pressure rotational viscometer. 41
Figure II.7. Internal diagram of the high pressure rotational viscometer. 41
Figure II.8. Internal geometries of the high pressure rotational viscometer. 42
Figure II.9. Torque versus time (left) and average torque versus rotational speed
(right) for Cannon Instrument Company calibration standard N14 at 298 K and
ambient pressure.
46
Figure II.10. Torque versus time for Cannon Instrument Company calibration
standard N14 at 298 K and ambient pressure.
46
Figure II.11. Viscosity versus average corrected torque/rotational speed for Cannon
Instrument Company calibration standard N14.
47
Figure II.12. Viscosity versus average corrected torque/rotational speed for all
calibration standards in Table III.1.
47
xii
Figure II.13. Viscosity versus time for a validation run at ambient pressure for a
silicone oil (Canon Instruments S60).
48
Figure II.14. Evaluation of a sample run in the high pressure rotational viscometer,
involving a base oil composed of poly(alpha olefins) at 298 K and 500 rpm.
49
Figure III.1. Two-dimensional representation of the lattice fluid model. 53
Figure IV.1. Composition of base oils IIA (left) and IIB (right). 62
Figure IV.2. Composition of base oils IIIA (left) and IIIB (right). 63
Figure IV.3. Composition of base oils PAO 4 (left) and PAO 8 (right). 63
Figure IV.4. Examples of the primary poly(α-olefins) found in PAO 4 and PAO 8, a
trimer (A) and tetramer (B) of 1-decene.
64
Figure IV.5. Density versus pressure for the base oil IIB at isotherms 298, 323, 348,
373, and 398 K.
65
Figure IV.6. Density versus pressure for six base oils at 323 K (left) and 373 K
(right).
66
Figure IV.7. Isothermal compressibility versus pressure (left) and isobaric thermal
expansion coefficient versus temperature (right) for IIB as calculated from the S-L
EOS.
67
Figure IV.8. Internal pressure versus pressure for IIB calculated from the S-L EOS. 67
Figure IV.9. Isothermal compressibility versus pressure for six base oils at 323 K
(left) and 373 K (right).
68
Figure IV.10. Isothermal compressibility versus mass percent cycloparaffin content
at 373 K and 10 MPa for all base oils.
69
Figure IV.11. Isobaric thermal expansion coefficient versus temperature for six base
oils at 10 MPa (left) and 40 MPa (right).
70
Figure IV.12. Isobaric thermal expansion coefficient versus mass percent
cycloparaffin content at 373 K and 10 MPa for all base oils.
70
Figure IV.13. Internal pressure versus pressure for six base oils at 323 K (left) and
373 K (right).
71
Figure IV.14. Internal pressure versus mass percent cycloparaffin content at 373 K
and 10 MPa for all base oils.
72
xiii
Figure IV.15. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the
298 K run).
73
Figure IV.16. Viscosity versus pressure (left) and average shear stress at 10 MPa
versus shear rate (right) for IIB at 323 K
74
Figure IV.17. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the
298 K run). Free volume correlation fit is represented by black dots.
76
Figure IV.18. Viscosity versus pressure for six base oils at 323 K and 500 rpm. Free
volume correlation fit is represented by black dots.
76
Figure V.1. Structure of viscosity index modifier Polymer 1. 80
Figure V.2. Structure of viscosity index modifier Polymer 2. 81
Figure V.3. Density versus pressure for PAO 4 and its mixtures with viscosity index
modifier Polymer 1 at 323 K.
82
Figure V.4. Density versus pressure for PAO 4 and its mixtures with viscosity index
modifier Polymer 2 at 323 K.
83
Figure V.5. Isothermal compressibility versus pressure for PAO 4 and its mixtures
with viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.
85
Figure V.6. Isothermal compressibility versus mass percent polymer at 323 K and 10
MPa for mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.
85
Figure V.7. Isobaric thermal expansion coefficient versus temperature for PAO 4
and its mixtures with viscosity index modifiers Polymer 1 (left) and Polymer 2 (right)
at 10 MPa.
86
Figure V.8. Isobaric thermal expansion coefficient versus mass percent polymer at
323 K and 10 MPa for mixtures of PAO 4 with viscosity index modifiers Polymer 1
and Polymer 2.
87
Figure V.9. Internal pressure versus pressure for PAO 4 and its mixtures with
viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.
88
Figure V.10. Internal pressure versus mass percent polymer at 323 K and 10 MPa for
mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.
88
Figure V.11. Viscosity versus pressure for mixtures of PAO 4 with viscosity index
modifiers Polymer 1 (left) and Polymer 2 (right) at 298 K and 500 rpm.
89
xiv
Figure V.12. Viscosity versus pressure for mixtures of PAO 4 with viscosity index
modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K and 500 rpm.
90
Figure V.13. Density versus pressure for an experimental and a commercial ATF at
323 K (left) and 373 K (right). Tait equation fits are shown as black diamonds.
93
Figure V.14. Isothermal compressibility versus pressure for an experimental and a
commercial ATF at 323 K (left) and 373 K (right).
94
Figure V.15. Isobaric thermal expansion coefficient versus temperature for an
experimental and a commercial ATF at 10 MPa (left) and 40 MPa (right).
94
Figure V.16. Internal pressure versus pressure for an experimental and a commercial
ATF at 323 K (left) and 373 K (right).
95
Figure V.17. Viscosity versus pressure for an experimental ATF (left) and a
commercial ATF (right).
95
Figure V.18. Viscosity versus pressure for an experimental and a commercial ATF at
323 K and 500 rpm.
96
Figure VI.1. 1-Alkyl-3-methylimidazolium cation and the chloride and acetate
anions. R is an alkyl group (ranging in length from 2 to 6 in the present thesis).
99
Figure VI.2. Route of synthesis for 1-alkyl-3-methylimidazolium chloride. R
represents either a propyl or hexyl group.
102
Figure VI.3. FTIR comparison of the synthesized [HMIM]Cl to commercial
[HMIM]Cl (purity 97 %) and spectra from the Bio-Rad database.
102
Figure VI.4. Density versus pressure for ILs [EMIM]Cl (top left), [PMIM]Cl (top
right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right).
105
Figure VI.5. Density versus pressure for mixtures of [EMIM]Cl (top left), [PMIM]Cl
(top right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right) with ethanol at
348 K.
108
Figure VI.6. Isothermal compressibility versus pressure for 50% [EMIM]Cl + 50%
ethanol (left) and various concentrations of [EMIM]Cl + ethanol at 348 K (right).
109
Figure VI.7. Isothermal compressibility versus pressure for 50% [PMIM]Cl + 50%
ethanol (left) and various concentrations of [PMIM]Cl + ethanol at 348 K (right).
110
Figure VI.8. Isothermal compressibility versus pressure for 50% [BMIM]Cl + 50%
ethanol (left) and various concentrations of [BMIM]Cl + ethanol at 348 K (right).
110
xv
Figure VI.9. Isothermal compressibility versus pressure for 50% [HMIM]Cl + 50%
ethanol (left) and various concentrations of [HMIM]Cl + ethanol at 348 K (right).
111
Figure VI.10. Isothermal compressibility versus mass percent IL for mixtures of
[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.
111
Figure VI.11. Isobaric expansivity versus temperature for 50% [EMIM]Cl + 50%
ethanol (left) and various concentrations of [EMIM]Cl + ethanol at 10 MPa (right).
112
Figure VI.12. Isobaric expansivity versus temperature for 50% [PMIM]Cl + 50%
ethanol (left) and various concentrations of [PMIM]Cl + ethanol at 10 MPa (right).
113
Figure VI.13. Isobaric expansivity versus temperature for 50% [BMIM]Cl + 50%
ethanol (left) and various concentrations of [BMIM]Cl + ethanol at 10 MPa (right).
113
Figure VI.14. Isobaric expansivity versus temperature for 50% [HMIM]Cl + 50%
ethanol (left) and various concentrations of [HMIM]Cl + ethanol at 10 MPa (right).
114
Figure VI.15. Isobaric thermal expansion coefficient versus mass percent IL for
mixtures of [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K
and 10 MPa.
114
Figure VI.16. Internal pressure versus pressure for 50% [EMIM]Cl + 50% ethanol
(left) and various concentrations of [EMIM]Cl + ethanol at 348 K (right).
116
Figure VI.17. Internal pressure versus pressure for 50% [PMIM]Cl + 50% ethanol
(left) and various concentrations of [PMIM]Cl + ethanol at 348 K (right).
116
Figure VI.18. Internal pressure versus pressure for 50% [BMIM]Cl + 50% ethanol
(left) and various concentrations of [BMIM]Cl + ethanol at 348 K (right).
117
Figure VI.19. Internal pressure versus pressure for 50% [HMIM]Cl + 50% ethanol
(left) and various concentrations of [HMIM]Cl + ethanol at 348 K (right).
117
Figure VI.20. Internal pressure versus mass percent IL for mixtures of [EMIM]Cl,
[PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.
118
Figure VI.21. Density versus pressure for ILs [EMIM]Ac (left) and [BMIM]Ac
(right).
119
Figure VI.22. Density versus pressure for mixtures of [EMIM]Ac (left) and
[BMIM]Ac (right) with ethanol at 348 K.
121
Figure VI.23. Isothermal compressibility versus pressure for 50% [EMIM]Ac + 50%
ethanol (left) and various concentrations of [EMIM]Ac + ethanol at 348 K (right).
122
xvi
Figure VI.24. Isothermal compressibility versus pressure for 50% [BMIM]Ac + 50%
ethanol (left) and various concentrations of [BMIM]Ac + ethanol at 348 K (right).
123
Figure VI.25. Isothermal compressibility versus mass percent IL for mixtures of
[EMIM]Ac and [BMIM]Ac + ethanol at 348 K and 10 MPa.
123
Figure VI.26. Isobaric expansivity versus temperature for 50% [EMIM]Ac + 50%
ethanol (left) and various concentrations of [EMIM]Ac + ethanol at 10 MPa (right).
124
Figure VI.27. Isobaric expansivity versus temperature for 50% [BMIM]Ac + 50%
ethanol (left) and various concentrations of [BMIM]Ac + ethanol at 10 MPa (right).
125
Figure VI.28. Isobaric thermal expansion coefficient versus mass percent IL for
mixtures of [EMIM]Ac and [BMIM]Ac + ethanol at 348 K and 10 MPa.
125
Figure VI.29. Internal pressure versus pressure for 50% [EMIM]Ac + 50% ethanol
(left) and various concentrations of [EMIM]Ac + ethanol at 348 K (right).
127
Figure VI.30. Internal pressure versus pressure for 50% [BMIM]Ac + 50% ethanol
(left) and various concentrations of [BMIM]Ac + ethanol at 348 K (right).
127
Figure VI.31. Internal pressure versus mass percent IL for mixtures of [EMIM]Ac
and [BMIM]Ac + ethanol at 348 K and 10 MPa.
128
Figure VI.32. Viscosity versus pressure for [EMIM]Ac from 298-373 K (left) and
mixtures of [EMIM]Ac with ethanol at 323 K and 500 rpm (right).
129
Figure VI.33. Viscosity versus pressure for [BMIM]Ac from 298-373 K (left) and
mixtures of [BMIM]Ac with ethanol at 323 K and 500 rpm (right).
130
Figure VI.34. Solubility parameter versus pressure for mixtures of [EMIM]Cl (top
left), [PMIM]Cl (top right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right)
with ethanol at 348 K.
132
Figure VI.35. Solubility parameter versus pressure for mixtures of [EMIM]Ac (left)
and [BMIM]Ac (right) with ethanol at 348 K.
133
Figure VI.36. Solubility parameter versus mass % IL for mixtures of [EMIM]Cl,
[PMIM]Cl, [BMIM]Cl and [HMIM]Cl with ethanol at 298 K and (left) and 348 K
and (right) and 10 MPa.
133
Figure VI.37. Solubility parameter versus mass % IL for mixtures of [EMIM]Ac and
[BMIM]Ac with ethanol at 298 K and (left) and 348 K and (right) and 10 MPa.
134
xvii
Figure VI.38. Solubility parameter versus temperature at ambient pressure as
estimated in the current work using the S-L EOS and estimated through
chromatographic techniques in the literature.
134
1
I. Introduction and Survey of the Literature
I.1 A Brief Description of the Scope of the Thesis
The broad aim of this thesis is to investigate the thermodynamic and transport properties
of complex fluid mixtures under pressure. With this in mind, the present study has been
designed with the objectives of generating fundamental volumetric data, reliable viscosity data,
and descriptive models. Experiments were carried out to examine the effect of pressure and
temperature on density, and pressure, temperature, and shear rate on viscosity for a range of fluid
mixtures. The primary focus has been on two categories of mixtures, namely base oils and their
mixtures with polymeric additives which are of high significance as lubricants, and ionic liquids
and their mixtures with organic solvents which are of high significance in applications such as
biomass processing. Modeling in the form of the free volume theory of viscosity paired with the
Sanchez-Lacombe equation of state was employed in conjunction with experimentally
determined data to aid in the development of a more holistic understanding of how viscosity
relates to density, and with it, to the derived thermodynamic properties. With a complete
understanding of the interconnection between these thermodynamic properties and viscosity, a
better understanding of how these mixtures function as both lubricants and solvents can be
developed.
While there is extensive literature on viscosity determination techniques and viscosity
data at ambient conditions, there is still a need for a greater understanding of the effect of
pressure on the viscosity of fluids. This applies to both the design of experimental systems to
collect viscosity data at high pressure conditions and the models used to analyze and, if possible,
carry out predictions. A major effort in the present study was devoted the development of a
novel high pressure rotational viscometer. This new instrument combines the ability to collect
viscosity data across a range of pressures and temperatures with the ability to control and
measure the shear rate while at the same time assessing the phase-state of the system. The
viscometer design incorporates features for assessment of density along with viscosity which is
expected to be put into operation in future studies. In the present study, an independent
variable-volume view-cell was used to collect density data at the same temperature and pressure
2
conditions where viscosity determinations were carried out. The experimental systems are
described in Chapter II.
The research completed in this thesis can be divided into two different areas of focus:
oils for use in automotive lubricants and ionic liquids as specialty solvents for polymeric
systems.
In the first focus area, base oils and their mixtures with select additives were studied.
These oils and additives are all constituents in automotive lubricants: engine oils and automatic
transmission fluids. The effects of both pressure and temperature on viscosity and density were
studied and modeled. In addition, the derived thermodynamic properties isothermal
compressibility, isobaric thermal expansion coefficient, and internal pressure were calculated.
By looking at these oils holistically, relating viscosity to density and thermodynamic properties
related to intermolecular interactions, a better understanding of how these mixtures function as
effective lubricants can be determined. These are discussed in detail in Chapters IV and V of the
thesis.
In the second focus area, ionic liquids were studied to determine the effect of cation ion
modification and anion choice on the solvent properties of these molten salts. A series of ionic
liquids with varying length alkyl functional groups on the imidazolium cation were used to study
the effect of modifications on the viscosity and density across a range of pressures and
temperatures. The effects of two different anions were studied, chloride and acetate. Viscosity
and density data were collected and modeled for mixtures of these ionic liquids with ethanol.
This in turn allowed for the estimation of Hildebrand solubility parameters as a function of
pressure, temperature, and composition. Knowing both the solubility parameter and viscosity
across a range of pressures, temperatures, and compositions allows for the determination of the
usefulness of these mixtures as solvents, especially for use with polymeric systems, such as the
dissolution and separation of lignocellulosic materials.
In the following sections, a brief overview of the literature is presented. Viscosity is of
particular interest due to its effects in mass transfer, heat transfer, flow behavior, and
elastohydrodynamic lubrication.1-5 There is a growing demand for high pressure viscosity data
and for their modeling. Since a major effort in the present thesis was devoted to the development
of a new instrument to measure this particular fluid property and its importance in the relevant
fields of interest, the primary emphasis of the next section is on the review of the current
3
literature with regards to the viscosity of fluids under high pressure conditions. While density
determinations at high pressure is also a major part of this thesis, the method that was employed
in this study is the same as used previously which is described in detail in Chapter II. The
modeling of density is described in Chapter III. More extensive literature background on
automotive lubricants and ionic liquids are included in the chapters relevant to these areas of
focus.
I.2 A Brief Overview of the Literature
With growth in fields such as lubricant design, diesel fuel and engine optimization, oil
recovery, ionic liquids, and polymer processing, interest in viscosity data of complex and
polymeric mixtures at high pressures has increased, especially after 1991. This trend can easily
be seen in the literature. Searching the Web of Science for the keywords viscosity and high
pressure yielded a total of 14,020 publications covering the period from 1920 to 2018. Of these
13881 have been published since 1990. While 24 articles had appeared in 1990, there was a
drastic increase in the number of publications in 1991, up to 159. This increase continued, with
311 articles published in 2000, all the way up to 1090 in 2018. Figure I.1 shows the increase in
articles published per year from 2000-2018. Figures I.2 – I.5 show the publication trends from
2000-2018 by narrowing the search topics with an additional term: lubricant, ionic liquids,
polymer, or supercritical fluid. A search of high pressure viscosity for lubricants showed an
increase from 13 articles in 2000 to 35 articles in 2018. Replacing lubricant with ionic liquid
showed a dramatic increase from 4 articles published in 2000, to 75 in 2018. Articles involving
polymeric systems showed an increase from 43 articles in 2000 to 102 articles in 2018. Finally,
adding the parameter supercritical fluid to a search of high pressure viscosity showed an increase
from 7 articles published in 2000 to 36 articles in 2018.
4
Figure I.1. Journal articles published every year from 2000-2018 using search terms Viscosity +
High Pressure on Web of Science.
Figure I.2. Journal articles published every year from 2000-2018 using search terms Viscosity +
High Pressure + Lubricant on Web of Science.
0
200
400
600
800
1000
1200
20
00
20
02
20
04
20
06
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18
Pap
ers
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bli
shed
Year
Viscosity + High Pressure
0
10
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60
Pap
ers
Pu
bli
shed
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Viscosity + High Pressure +
Lubricant
5
Figure I.3. Journal articles published every year from 2000-2018 using search terms Viscosity +
High Pressure + Ionic Liquid on Web of Science.
Figure I.4. Journal articles published every year from 2000-2018 using search terms Viscosity +
High Pressure + Polymer on Web of Science.
0
20
40
60
80
100
120
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ers
Pu
bli
shed
Year
Viscosity + High Pressure +
Ionic Liquid
0
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120
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ers
Pu
bli
shed
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Viscosity + High Pressure +
Polymer
6
Figure I.5. Journal articles published every year from 2000-2018 using search terms Viscosity +
High Pressure + Supercritical Fluid on Web of Science.
A close examination of the articles cited in the Web of Science shows that interest in
viscosity at high pressure conditions covers a wide range of applications, including but not
limited to food processing and pasteurization,6,7 estimating the properties of molten rock in the
Earth’s mantle,8,9 and oil recovery and CO2 sequestration.4,10-15 There are also distinct trends that
have been displayed over the past few years. Areas of particular interest that have been noted in
more recent publications include lubricants and fuels used in the automotive industry,1,16-27 ionic
liquids for such applications as high pressure CO2 or SO2 capture,28-41 gas expanded liquids as
tunable solvents,42-48 and polymer processing (including polymer foams).49-67
The following sections provide a brief overview of the literature on the methods of
viscosity measurement, analysis, and select areas of interest:
I.2.1 Experimental Determination of Viscosity at High Pressures
I.2.2 Modeling of Pressure Effects on Viscosity
I.2.3 Oils, Lubricants, and Fuels
I.2.4 Ionic Liquids
I.2.5 Gas Expanded Liquids
0
5
10
15
20
25
30
35
40
Pap
ers
Pu
bli
shed
Year
Viscosity + High Pressure +
Supercritical Fluid
7
I.2.6 Polymers, Foams, and Plasticizers
I.2.7 Geological Effects
I.2.1 Experimental Determination of Viscosity at High Pressure
A variety of experimental techniques have been employed in the literature to determine
viscosity as a function of both temperature and pressure. Due to the difficulties involved with
performing measurements under high pressure conditions, all techniques employed have
different advantages and limitations. While not an exhaustive list, the most common techniques
are described below.
I.2.1.A Falling Body/Rolling Ball Viscometers
Falling body viscometers are commonly used in high pressure applications in the
literature.3,4,30,32,39,43,44,54,68-71 The concept is simple. A sinker is allowed to fall through a fluid in
a tube. Based on the geometry of the system, and the viscosity of the fluid being measured, the
sinker will reach a terminal velocity. If the density of both the sinker (ρs) and fluid (ρf) are
known, and the terminal velocity (Vt) can be measured, viscosity can be determined from:
𝜂 = 𝐶(𝜌𝑠 − 𝜌𝑓)1
𝑉𝑡 I.1
where C is a constant that needs to be experimentally determined.43,44,68 To determine terminal
velocity, an accurate method of measuring sinker position in real time is needed. This has been
accomplished through a variety of means: visually under a microscope,9 using x-ray scattering
paired with a high speed camera,8 or magnetic detectors such as a linear variable differential
transformer (LVDT).68 These viscometers can be designed to operate in the range of hundreds of
MPa16 with some implementations for determining viscosities of magmatic melts reaching up to
7.5 GPa.9 While these instruments have simple operating principles and incredibly high pressure
ranges, they do have drawbacks. Due to the design, it is difficult to control the shear rate applied
to the measured fluid, often limiting these instruments to low shear or Newtonian conditions. In
addition, for highly viscous fluids, fall times can be extremely long, leading to difficulties in
8
measuring the terminal velocity.56 Rolling ball viscometers operate on a similar principle by
measuring the fall time of a ball submerged in the measured fluid rolling down an incline due to
gravitational forces and relating it to viscosity through a relation to sinker and fluid density, such
as equation I.1.34,72 One challenge with rolling ball viscometers is ensuring that no skidding or
sliding occurs.
I.2.1.B Capillary Viscometers
Another technique employed in the literature involves using capillary viscometers that
determine viscosity by measuring the pressure drop of a fluid at a steady flow rate through a
long, narrow tube.52,73-76 When fluid through a cylindrical tube is fully developed and laminar,
viscosity, η, can be determined from the Hagen-Poiseuille equation:
𝜂 =𝜋𝑟4Δ𝑃
8𝐿𝑞 I.2
where r is the radius of the tube, ΔP is the pressure drop across the capillary, L is the length of
the capillary, and q is the flow rate.73 The difficulty of the design for high pressure instruments
is having a steady flow rate in an instrument with high pressure requirements. Due to the
requirement of laminar flow, only conditions in which the measured fluid flow exhibits low
Reynolds numbers are valid for measurement. Additionally, depending on the design of the
instrument, end effects may need to be taken into account.75,76 Examples of this style instrument
operating up to 0.6 GPa have been reported in the literature.74
In addition to standard capillary viscometers, capillary dies and slit rheometers can be
used in conjunction with extruders to determine the viscosity of polymer melts.53,55,59,61,64,67
These systems seem useful in measuring the viscosity of polymers in the presence of a
supercritical or compressible fluid, such as CO2, as a plasticizer or foaming agent, but have their
short comings. Due to the pressure differential across the capillary, it can be difficult to
determine the actual concentration or homogeneity of plasticizer in the melt.64 To reduce this
pressure differential, many of these instruments include a counter pressure chamber at the end of
the die. This counter pressure chamber allows for greater control of the pressure differential
9
involved with the viscosity determination while also preventing the compressible fluid from
separating out of the polymer being measured.67
I.2.1.C Vibrating Wire Viscometers
Vibrating wire viscometers use a submerged wire that is exposed to a permanent
magnetic field. By passing a sinusoidal current through the wire, the wire is vibrated.1,25,26,77,78
By measuring the voltage applied to the wire, viscosity can be determined. There are
instruments in the literature capable of reaching pressures into the GPa range.78 These
instruments can be complex to calibrate and utilize, requiring the correct wire chosen for the
viscosity range being measured. A limitation of this style instrument is that while shear rates can
be varied by changing the frequency of vibration, the shear rates are not necessarily defined with
any degree of accuracy.
I.2.1.D Oscillating Quartz Viscometers
Another design based on vibrational effects utilizes a piezoelectric sensor submerged in
the fluid being measured. By comparing the frequency dampening by the fluid, viscosity can be
determined:
𝑓0 − 𝑓𝑟𝑒𝑠 = 𝑘(𝜋𝑓𝑟𝑒𝑠𝜂𝜌𝑓) I.3
where f0 is the oscillation of the quartz, fres is the frequency of oscillation while the quartz is
submerged, k is a constant, and ρf is the density of the fluid.3 Similar to the vibrating wire
viscometer, the effect of shear rate can be determined by varying the voltage applied to the
crystal. This allows for the determination of Newtonian versus non-Newtonian behavior of a
fluid.
10
I.2.1.E Oscillating Piston Viscometers
Oscillating piston viscometers operate by measuring the time it takes for a magnetically
driven piston to move a specified distance through the fluid being measured. The viscosity range
that can be resolved depends on the magnetic field used in the experiment.42 They have been
employed in high pressure conditions,29,35,42 up to 300 bar at temperatures up to 110oC. These
instruments are known for requiring a small amount of fluid to assess viscosity. At high pressure
conditions, such viscometers are known to be capable of performing measurements up to 10,000
mPa s.42
I.2.1.F Rotational Viscometers
Rotational viscometers use a rotating element compared to a fixed element with the
measured fluid in between, such as parallel plates or concentric cylinders, to determine
viscosity.12,13,18,57,58,65,79 There are commercial instruments available of this type, but many of
them are limited to pressures below 20 MPa, with at least one example capable of reaching
pressures up to 40 MPa.13 Viscosity is calculated by determining torque and shear rate. Shear
rate is easily controlled and determined, though the viscosity range that can be effectively
measured is affected by the geometry of the instrument.18 These instruments often have a lower
viscosity limit that can be effectively measured. With moving parts that need to be coupled to a
torque transducer and/or motor, a layer of complexity is added into instrument design,
particularly involving sealing at high pressures. The instrument either needs to be sealed across
moving parts, or some form of magnetic coupling needs to be employed. Either method adds in
frictional effects that need to be compensated for in the viscosity determinations. For many
magnetically coupled designs, the inner rotating shaft needs to be set on sapphire bearings. The
lubrication effects need to be considered in the final calculations. This can be done in one of two
ways. One approach is to add a drop of the fluid to the bearings and perform a calibration run to
get a baseline to eliminate in the viscosity calculations.13 This approach is limited to single
phase or saturated fluids. Another approach is to perform an ambient pressure scan across a
range of shear rates of the fluid being measured at the temperature of interest. Resulting torque
versus shear rate data can be fit and the intercept taken as the baseline to be eliminated from final
11
calculations.18 In the present thesis, viscosity measurements were carried out using a specially
designed rotational viscometer which will be described in more detail in Chapter II.
I.2.1.G Other
A variety of other methods of determining viscosity have been described in the literature.
These are usually custom designed and of limited implementation. An acoustic levitation
method was used to study the viscosity of squalene + CO2 at pressures up to 16 MPa and
temperatures up to 433 K.13 A sound wave is sent through the CO2 medium to a reflector. The
waves from the source interfere with those coming back from the reflector, causing pressure
zones in which a drop of squalene is levitated. A high speed camera allows for the oscillations in
the drop to be observed and converted to both viscosity and interfacial tension.13 An instrument
using a magnetically levitated sphere was developed to look at samples of viscosities up to 100
Pa s and pressures up to 42 MPa.60 A sphere is held in place by an electromagnet while the outer
cylinder is moved, inducing flow around the sphere. By comparing the current needed to keep
the sphere in place during fluid flow compared to a stationary fluid phase, viscosity is
determined.60 Another unique instrument, a torsional vibrating viscometer uses measurements of
the damping of oscillations of a cylinder submerged in a fluid to calculate viscosity. This
method is similar to quartz or vibrating wire viscometers. One particular example was capable
of measurements up to 15 MPa and 373 K.63
I.2.1.H Density and High Pressure Viscosity
In addition to generating high pressure viscosity data, many techniques either directly
integrate, or are run in conjunction with, a method for determining density. Additionally, there
are several models utilized in the literature, discussed in Section I.3, that require knowledge of
density effects to describe how viscosity varies with pressure. Many of the techniques used in
determining viscosity (such as falling body viscometers) also require knowledge of the density of
the fluid at the specific temperature and pressure of each run. To determine density at these high
pressure conditions, a variety of techniques are employed, such as vibrating tube
densitometers30,80 and variable-volume methods.3,18 Variable-volume methods involving bellows
12
based apparatuses or movable pistons operate on the principle of a closed system in which the
internal volume can be changed as a function of temperature and pressure. By knowing the mass
loaded and having a method to determine the position of the piston or bellows, and with it the
volume, density can be determined.18 A detailed description of a variable-volume view-cell
employed in the present thesis is provided in Chapter II.
I.2.1.I Limitations
Each experimental design comes with its limitations. As with any high pressure
instrument, seal design plays an important role in determining the pressure and temperature
range of operation. While certain designs, such as falling body viscometers, have specific
implementations that can reach incredibly high pressures (in the range of GPas), not every such
instrument found in the literature are designed for such applications. Some designs, such as
rotational viscometers, have pressure limitations due to the need for specialty sealing
arrangements to compensate for moving parts. Additionally, design has an impact on the
viscosity range that can be accurately resolved, with some viscometers being capable of allowing
modifications from run to run to change the measurable range. In falling body viscometers, this
may be achieved by using sinkers of different densities. Oscillating piston viscometers have
limited viscosity ranges based off a replaceable magnet in the system. Other designs require
implementing methods to provide and control a consistent flow rate, such as capillary type
viscometers. One major limitation common to most high pressure viscometer implementations is
the lack of ability to accurately control and measure the shear rate. Falling body viscometers are
simple and allow for measurements up to high pressures, but it is difficult to control shear rate,
often limiting these instruments to studying fluids at low shear or Newtonian conditions.
Methods based on vibrations, such as vibrating wire or oscillating quartz viscometers, can
provide a range of shear rates, allowing for the detection of the presence of non-Newtonian
behavior. While shear rate can be varied, it appears that accurate shear rates are not reported
using this method in the literature. Rotational viscometers, in spite of their limitations in
pressure and viscosity ranges, are the most suitable viscometers for the assessment of shear rates
and their effect on viscous behavior under high pressure conditions.
13
I.2.2 Modeling of Pressure Effects on Viscosity
Experimental techniques for the determination of viscosity data at high pressure are
subject to limitations as described in the previous sections. Additionally, due to time and cost, it
would be impossible to generate this data for every possible pure component and mixture
experimentally. Many of the fluids utilized in high pressure scenarios, particularly fuels and
lubricants, are not pure components. They are complex mixtures composed of many species.
While there is no replacement for experimental data, there are several models available in the
literature that provide descriptions of viscous behavior with a possibility of predictions. For
gases at low pressures, theoretical models derived from kinetic theory can be used.10,81 For
dense or liquid fluids, however, modeling is not as simple. In these situations, empirical or semi-
empirical models have been used, including free volume theory, friction theory, and density
scaling approaches.10,37-41,82,83 In addition to experimental data, molecular dynamics simulations
have been used to provide estimations of the needed viscosity data.21,45-48,84
I.2.2.A Modeling Viscosity of Gases
Many models utilized in the determination of viscosity of fluids at high pressures,
especially free volume and friction theory, include a term to represent the dilute gas viscosity at
the zero density limit (η0). From the kinetic theory of gases, an equation has been derived:
𝜂0 =𝑘𝐵𝑇
⟨𝑣⟩
𝑓𝜂(𝑛)
𝔖
I.4
where T is temperature, kB is Boltzmann’s constant, ⟨𝑣⟩ is the average relative thermal speed, 𝔖
is the generalized cross section, and fη(n) is a correction factor.81 While theoretically derived, this
form requires specific knowledge of intermolecular interactions that may not be readily available
for all fluids. By modeling a fluid as a collection of rigid, non-attractive spheres, a more specific
equation was proposed:
𝜂0 = 26.69√𝑀𝑇
𝜎2
I.5
14
where M is molecular weight and σ is the sphere diameter.10 Chapman-Enskog theory adds
collision effects to the above model. Further modification by Chung et al.85 results in a model
that puts the zero density limit viscosity in terms of temperature and critical point values of the
species in question:10,14,41
𝜂0 = 40.785√𝑀𝑇
𝑉𝑐2/3Ω∗𝑇∗𝐹𝑐
I.6
𝑇∗ = 𝑇/𝑇𝑐 I.7
where TC and VC are the critical temperature and volume respectively, Ω* is the collision
integral, and FC is a correction factor:10,14,41
Ω∗ =1.16145
𝑇∗+
0.52487
𝑒0.77320𝑇∗ +
2.1678
𝑒2.43787𝑇∗
−6345 × 10−4(𝑇∗)0.014784 sin[18.0323(𝑇∗)−0.76830 − 7.2731]
I.8
𝐹𝑐 = 1 − 0.2756𝜔 + 0.059035𝜇𝑟4 + 𝜅′ I.9
where κ’ corrects for hydrogen bonding, ω is the accentric factor, and μr is a reduced dipole
moment calculated from the dipole moment μ:10,14,41
𝜇𝑟 =131.3𝜇
√𝑉𝑐𝑇𝑐 I.10
The viscosities calculated for η0 are very low, in the μPa s range. For many studies, the specific
model used for calculating the zero density limit viscosity is often the weakest part of the model,
or is neglected all together, due to the negligible effect that η0 has on overall viscosity for many
dense fluids at high pressure conditions.18,41
15
I.2.2.B Free Volume Theory
Viscosity is often interpreted in terms of and linked to free volume.82 This concept of
relating the viscosity to the spacing between molecules allows for the linking of viscosity to
density. An early approach to relating viscosity to density is given by the Doolittle equation:82,86
𝜂 = 𝐴𝑒𝑥𝑝 (𝐵
1−𝑉0𝜌) I.11
where ρ is density, V0 is close packed volume of the fluid, and A and B are constants. This
approach is empirical in nature and has been applied to high pressure systems, including those
involving polymeric materials.57,87 This equation has been expanded by Allal et al.82 to add more
physical significance to the model. The full form of the free volume theory is thus represented
by the equation:82
𝜂 = 𝜂0 +𝜌𝜄(𝛼𝜌+
𝑃𝑀
𝜌)
√3𝑅𝑇𝑀𝑒𝐵(
𝛼𝜌+𝑃𝑀𝜌
𝑅𝑇)
3 2⁄
I.12
where η0 is the dilute gas viscosity at the zero density limit (as previously described), R is the gas
constant, M is molecular weight, T is temperature, ι is the characteristic molecular length, α is
related to the energy barrier molecules must overcome to diffuse, and B is a dimensionless
parameter that represents free volume effects. The use of this model requires coupling with an
equation of state to generate the required density values. Studies in the literature have coupled
the above equation with a variety of equations of state, such as PC-SAFT (perturbed-chain
statistical associating fluid theory)14,41 and Sanchez-Lacombe.18 A limitation of this model is the
need for experimental data to determine the parameters ι, α, and B.10 Free volume theory and its
implementation in this thesis will be discussed in greater detail in Chapter III.
16
I.2.2.C Friction Theory
As with the free volume theory, friction theory divides viscosity into two contributions,
viscosity at the zero density limit (η0) and in the dense state (ηf):10,83,88
𝜂(𝑇, 𝑃) = 𝜂0(𝑇) + 𝜂𝐹(𝑇, 𝑃) I.13
The viscosity term for dense states is then related to the attractive (pa) and repulsive (pr) pressure
contributions as predicted by a Van der Waals based model:
𝜂𝐹 = 𝜅𝑎𝑝𝑎 + 𝜅𝑟𝑝𝑟 + 𝜅𝑟𝑟𝑝𝑟2 I.14
where κa, κr, and κrr are friction coefficients paired with the attractive pressure (pa), repulsive
pressure (pr), and square of the repulsive pressure (pr2) contributions respectively. These three
coefficients are functions of temperature.83,88 The pressure terms are generally calculated from
cubic equations of state, such as Peng-Robinson or Soave-Redlich-Kwong, though in principle
this model can be paired with any EOS, including SAFT (statistical associating fluid theory).10,83
It should be noted that the friction coefficients are determined by fitting with experimental data
in conjunction with the EOS of choice. This leads to the coefficients used being dependent on
the EOS used.10
I.2.2.D Scaling Factors
One more approach to relate viscosity to density effects is through the use of scaling
factors. Viscosity can be expressed in terms of a function (f) that combines both temperature and
density:
𝜂(𝑇, 𝜌) = 𝑓(𝑇𝜌−𝛾) I.15
where γ is a scaling factor.37-40,89 The value of gamma is chosen in such a way that causes the
viscosity data to superimpose into one master curve. The effectiveness of the model is then
17
dependent on the function (f) chosen. The value of gamma is useful in assessing the types of
intermolecular forces, with lower values representing stronger attractive effects, such as
hydrogen bonding.37 It is known that for certain fluids, such as water, this method does not work
across a wide range of temperatures and pressures as there is no value of gamma that causes all
values of viscosity to collapse into a single curve.37 In these cases, modifications to the model
may be needed, such as using a reduced value of viscosity instead.37 This scaling parameter
approach is not only useful for modeling viscous effects, it has been used in the literature to also
model relaxation times, diffusion coefficients, thermal conductivities, and electrical
conductivities.37
I.2.2.E Molecular Dynamics Simulations
While these empirical models for liquid and dense fluids require some experimental data
to fit to the necessary equations, molecular dynamics simulations offer a potential supplement by
providing estimations of viscosity data when experiments have not been performed. Such
simulations have been performed for a number of high pressure systems, especially CO2 and CO2
expanded systems.46-48,84 The quality of the results of a molecular dynamics simulation can vary
depending on the simplifications used to reduce computing time. Due to this, viscosity
predictions by such modeling are often only accurate to within an order of magnitude.10 With
such a disparity, predictive values from molecular dynamics simulations still need a way to
validate the reasonableness of the results, such as with experimental data.
I.2.2.F Other models
There are a number of other models available to describe viscosity under high pressure
conditions. Eyring’s absolute rate theory models Newtonian fluids in similar terms as a chemical
reaction:10
𝜂 =ℎ𝑁𝑎
𝑉𝑒
𝐹
𝑅𝑇 I.16
18
where h is Planck’s constant, Na is Avogadro’s number, V is molar volume, R is the gas
constant, and F is the molar free energy of activation of flow. This basic model has been
modified to model both binary mixtures of organic solvents and ionic liquids among other
applications.36,90
One work attempted to use a semi-theoretical approach to do predictive modeling with a
rough hard sphere model in conjunction with an artificial neural network to examine viscosity at
high pressure for biodiesels and their constituents.24
I.2.2.G Modeling of Density and Phase Behavior
Three of the viscosity models described above are dependent on either density or values
dependent on an equation of state: free volume theory, friction theory, and density scaling
approaches. Understanding how viscosity is related to fluid density is important in
understanding how viscosity is in turn related to pressure. As pressure changes, so do the
intermolecular interactions, affecting viscosity. Due to this, many studies by necessity
incorporate density modeling by equations of state such as SAFT models14,41 or lattice fluid
models, such as the Sanchez-Lacombe equation of state,18 in their analysis. Also important in
the determination of viscosity are compositional effects. Utilizing equations of state allows for
the modeling of phase composition in situations where phase separation can occur, such as the
use of compressible fluids as plasticizers in polymer processing64 or in the case of gas expanded
liquids.42 Another benefit of modeling density effects through an equation of state alongside
viscosity is that other properties can also be determined: isothermal compressibility, isobaric
thermal expansion coefficient, and internal pressure. These derived thermodynamic properties
can aid in providing a complete picture of the intermolecular forces affecting a fluid system.
These properties, such as compressibility, are also useful for determining the effectiveness of a
fluid as a lubricant, for which viscosity plays an important role.17,18 Modeling of density data by
the Sanchez-Lacombe equation of state and the calculation of derived thermodynamic properties
has been a major component of the present research and is described in greater detail in Chapter
III.
19
I.2.2.H Limitations
The empirical or semi-empirical nature of the models employed in the literature requires
experimental viscosity data to be used for any fitting parameters to be determined. There have
been cases where it has been possible to use data from an analogous species as a starting point
for the determination of model parameters where high pressure data of the material in question
are not available.42 This is especially relevant for situations where there are several similar
species in a series, such as alkanes or ionic liquids with the same anion and a cation that varies
by alkyl chain length. It is difficult to effectively model viscous effects for dense fluids as a
function of temperature without experimental data. Additionally, most of these models do not
take into account shear effects. For non-Newtonion fluids, either zero shear viscosity needs to be
determined, or some modification must be done to account for the shear rate. Due to the above
reasons, there is currently no effective way to replace experimental data. Many of the models
require coupling with an equation of state to model density. This adds an additional requirement
to either generate, or have available in the literature, accurate density data at high pressures.
Finally, many of these models require assumptions to be made that may not hold true, such as
that each molecule can be treated as a hard sphere, which reduce the physical significance of the
models.
I.2.3 Oils, Lubricants, and Fuels
Crude oil and oil derivatives are used in a variety of applications that require exposure to
high pressure conditions. While studies have been performed on model systems, the entire story
is more complex, with crude oils and their derivative fuels and mineral oils being composed of a
multitude of components.14,18 Even synthetic derivatives are blends of different components,
such as poly(α-olefins) of varying lengths.17,18 Specific applications where high pressure
viscosity data for these mixtures of hydrocarbons are needed include lubricant development,
engine design to incorporate specific fuel mixtures (such as diesel and natural gas), and CO2
assisted oil recovery. Two review articles on fluid properties under high pressure conditions of
hydrocarbons have been published at the end of 2017: on pure hydrocarbons and their viscosity
models by Baled et al.,10 and more generally (including experimentation) by Mallepally et al.4
20
I.2.3.A Lubricants
There is a need in the automotive industry to increase fuel efficiency. One suggested
approach to solve this issue is to improve the effectiveness of the lubricants used: both engine
oils and automatic transmission fluids.91 By using lower viscosity oils in the formulation of
these lubricants, fuel efficiency can be increased.17,92,93 Under standard operating conditions,
these oils are exposed to high pressures (in the GPa range) and shear rates (up to 105 s-1).17,94,95
While it is known that using low viscosity lubricants improves fuel efficiency,
elastohydrodynamic lubrication effects occur at these extreme conditions. There is a need in
understanding the effect of pressure on viscosity, along with other parameters, such as isothermal
compressibility.17,18 Each engine oil is composed of a base oil (the majority component) and 10
or more additives.18 Base oils are fit into a series of categories, with Group I-III oils all being
mineral oils, with each category dependent on composition and viscosity index (a measure of the
temperature dependence of viscosity). Group IV oils are synthetic oils. Group V oils do not fit
into the other four groups based on hydrocarbons.18 These classifications are laid out in Table
I.1. Additives include viscosity index modifiers, detergents, dispersants, friction modifiers, and
anti-wear modifiers.96-98
Table I.1. Base oil categories as laid out by the American Petroleum Institute guidelines.18
Sulfur Content Saturates Viscosity Index Additional Information
Group I > 0.03% < 90% 80-120 Group II < 0.03% > 90% 80-120 Group III < 0.03% > 90% > 120 Group IV 0% 100% NA Synthetic oils composed of PAOs
Group V NA NA NA All oils that don't fit into Groups I-IV
Recent publications have studied the effect of pressure on viscosity using both
experimental and modeling techniques. Mixtures of polyalkylene glycol with CO2 were modeled
under high pressure conditions. By adding a compressible fluid, an adaptive lubricant is made
that can have its lubricant effectiveness easily modified by pressure in response to changing
pressure conditions.19 Another area of importance is examining the effect of additive, such as
graphene, for the formation of nanoliquids.21 Actual experimentation has also been run on
21
hydraulic oils and their constituents22 and the base oil stocks that make up the majority of a
lubricant.99
I.2.3.B Fuels
Recent work dealing with hydrocarbons for fuel purposes involves studying viscosity of
these mixtures at high pressures.1,23,25,100 A number of fuels either need to be stored at high
pressures, such as natural gas, or are exposed to high pressure situations during operation, such
as diesel. Mixtures simulating natural gas, both with and without CO2, were studied by a
vibrating wire viscometer.1,25 In addition to natural gas, there is a need for high pressure data for
rocket fuel. Using a capillary viscometer, viscosity for the fuel RP-1 was studied up to 60 MPa
and higher than standard temperatures of 744 K.23 In diesel engines, viscosity has a significant
effect on fuel atomization during fuel injection.20 With new fuel blends based around high
viscosity biodiesels gaining more notice, having actual data to design engines and injectors for
these new fuel types is necessary. Both model and experimental data have been generated to
help fill the blanks in the literature.20,100
I.2.3.C Oil Recovery
A final area involving the effect of pressure on the viscosity of hydrocarbon based fluids
is oil recovery. There is a need to modify the transport properties of crude oil that has yet to be
extracted from reservoirs, especially the reduction of viscosity.101 Supercritical CO2 has found
use in enhanced oil recovery.11,13,102 One way an understanding of these systems has been
accomplished is by studying CO2 solubility and its effect on viscosity for model hydrocarbons
such as squalene (C30H50).13 Understanding both solubility and viscosity at operating conditions
is necessary due to the challenges associated with enhanced oil recovery. Low density and
viscosity CO2 can displace the oil in an unfavorable way, causing oil recovery to decrease,
instead of increasing as desired. By adding viscosity thickeners, this effect can be mitigated.102
One potential side effect to operating oil wells at higher pressures involves the phase behavior
with water contamination in the oil. As pressure increases, water miscibility in the oil increases,
further complicating the determination of the viscous behavior of the recovered product.12 There
22
are attempts in the literature to model oil/solvent mixtures using a cubic model103 and free
volume theory.14
I.2.4 Ionic Liquids
Ionic liquids (ILs) are a class of salts with melting points below 100oC.104 These molten
salts owe their low melting points due to their composition, a bulky, often asymmetrical organic
cation matched with an anion that is often also organic, which prevents packing. Known for
their negligible vapor pressure and interesting solvent capabilities, there has been interest in the
literature in using ILs as replacements for volatile organic compounds.104-106 The choice of
cation, anion, and any functional groups associated with the cation is critical in determining the
physical properties of the salt used.107,108 It has been estimated that there are potentially 1012
possible combinations of ions that would form an ionic liquid.104 Due to this, these materials are
often considered to be designer solvents.107,108 Additionally, cosolvents can be used to modify
solvent capabilities and add compressibility to the fluid, allowing for pressure to be used as a
tuning parameter.109 Due to their unique properties, these fluids have been investigated for use
in polymer processing and synthesis,110-114 CO2 or SO2 capture,28,34,35 battery electrolytes,115 and
biomass processing.116-118
There has been much work in the literature to characterize ionic liquids and determine
their physical properties, including viscosity. Many of these molten salts have much higher
viscosities than the volatile organic solvents they are meant to replace, making it crucial to
understand how ionic liquid structure affects viscosity when designing one for a particular
process. In spite of the large number of publications on viscosity, very few record viscosity data
at high pressure conditions. This is especially surprising due to the interest in using ionic liquids
under high pressure conditions for CO2 capture. A few examples of ionic liquids with high
pressure viscosity data are available in the literature. Harris et al.30 used a falling body
viscometer to study triethylpentylphosphonium bis(trifluoromethanesulfonyl)imide (273-363 K,
up to 243 MPa). Gacino et al.33 used a falling body viscometer to study 1-ethyl-3-
methylimidazolium ethylsulfate and two pyrrolidinium based salts with the anion
bis(trifluoromethanesulfonyl)imide (313-363 K, up to 150 MPa). Ahosseini and Scurto29 used an
oscillating piston viscometer to study imidazolium based ionic liquids with the anions
23
bis(trifluoromethanesulfonyl)imide, tetrafluoroborate, and hexafluorophosphate (298-343 K, up
to 126 MPa). There are some examples of viscosity data for mixtures of ionic liquids with CO2
as well: imidazoliums with the hexaflurophosphate34 and bis(trifluoromethanesulfonyl)imide35
anions. To help remedy this lack of experimental data, there has been an emphasis on the
effective modeling of pressure and temperature effects on the viscosity of ionic liquids. There
are a number of examples of the utilization of density scaling methods available in the
literature.37-40 Additionally, free volume theory paired with ePC-SAFT (electrolyte PC-SAFT)
was used to model a wide range of ionic liquids by Sun et al.41 By examining broad trends
affiliated with ionic liquids, especially those with similar structures, it was shown that it is
possible to improve the predictive properties of some of these model fits without a full set of
high pressure data. Anion effects appear to be dominant in determining the viscosity of an ionic
liquid.41 Also, with the same anion and same cation type, viscosity changes with the addition or
adjustment of functional groups on the cation. An example of this is that viscosity increases with
alkyl chain length.41 With the same anion, minor variations in the cation, such as alkyl chain
length, can be modeled using free volume theory using high pressure data from just a small
sample size of ionic liquids.41
I.2.5 Gas Expanded Liquids
A class of mixtures referred to as gas expanded liquids have been gaining popularity in
the literature. By combining a liquid with a compressible gas, such as CO2, the volume can be
increased with pressure as increasing amounts of CO2 are dissolved in the liquid. The resulting
mixture properties then become adjustable with pressure. Some examples of gas expanded
liquids utilizing CO2 as the compressible fluid portion in the literature include alkanes
(methane,48 n-hexane, n-decane, and n-tetradecane42), alkyl acetates,47 ethanol,44 acetone,43 and
acetonitrile.45,46 These mixtures have properties between pure liquids and supercritical fluids.42-
48 Common experimental techniques for measuring the viscosity in these systems include falling
body43,44 and oscillating piston viscometers.42 Due to the wide range of possible combinations of
liquids to compressible gases, combined with the fact that these are binary mixtures compared to
other complex fluids such as mineral oils or diesel fuels, a number of molecular dynamics
simulations have been run to provide estimations of the viscosities of these mixtures.47,48
24
I.2.6 Polymers
Polymer processing requires knowledge of transport properties and flow behavior at high
shear rates and potentially high pressures. Polymeric materials are highly viscous due to their
high molecular weights and entanglement effects.55 The viscosity of polymers is affected by
more than the standard intermolecular interactions as the long chain nature of these
macromolecules allow for the mers that make up the polymer to interact with each other on the
same chain. This leads to elastic effects and non-Newtonian behavior.55 Modeling in terms of
free volume is especially important for polymeric systems as an increase in molecular spacing
leads to an increase in chain mobility (decrease in viscosity). Increasing free volume, thereby
decreasing viscosity and increasing processability, in polymer melts can be accomplished by
decreasing pressure, increasing temperature, or adding a plasticizer.56,87 To reduce the
temperature requirements needed to examine polymer melts, many studies have employed model
systems. Polydimethylsiloxane in particular is commonly used to model melt conditions and
validate viscometers due to its ability to exist as a melt at room temperature conditions.61
In addition to techniques utilized for low molecular weight systems, such as oscillating
quartz and rotational viscometers, capillary die rheometers are used in the literature for
examining polymer melts.53,55,59,61,64,67 Polymer viscosity data is needed at operating conditions,
especially at high shear rates, making it advantageous to incorporate the measurement device
directly into an extruder or injection molder.53
I.2.6.A Plasticizers
While increasing temperature is one method to decrease viscosity in polymer melts, this
is not an effective solution for every situation. The temperature requirements to reduce the
viscosity of many biocompatible polymers (such as poly(lactic acid)) to processable levels is
high enough to lead to degradation of the polymer, or any drug molecules that may be
impregnated into the polymer.55-65 For situations where viscosity needs to be decreased without
increasing temperature, plasticizers can be used. Due to its cost, nontoxicity, solubility in
polymer, and ease of removal, supercritical CO2 has been considered as a potential plasticizer in
the literature.55-65 One potential downside of using CO2 is the time of uptake. Adding an
25
additional plasticizer can help overcome this difficulty. In the case of poly(lactic acid), adding
poly(ethylene glycol) can further reduce viscosity and increase the rate at which CO2 is sorbed
into the polymer melt.65
I.2.6.B Foams
Polymers are extensively used in the production of foams.57,66 In certain industries, such
as the production of automobiles, there is a need for lightweight parts that still meet standards for
strength.57 These components are often injected molded. For these systems, it is necessary to
maintain the pressure during extrusion to keep the blowing agent in solution until the actual
injection. This adds an extra layer of complexity in accurately determining the viscosity of the
polymer solution. The inclusion of a counter pressure chamber to maintain high pressure
conditions at the end of the capillary can help keep the foaming agent in solution during
measurement.57
I.2.7 Geological Effects
One particular field that benefits from high pressure and temperature instrumentation is
geology. Due to the need to study highly viscous melts at temperatures above 1000oC and
pressures in the range of GPas, the instrumentation involved pushes the limits of what high
pressure viscometers found in the literature are capable of. Understanding viscosity at these
extreme conditions allows for the development of a better understanding of phenomena below
the Earth’s crust, where direct observation is impossible.8,9 Two recent studies show the current
capabilities of experimentation in this field. Stagno et al.8 measured viscosities of sodium
carbonate melts at temperatures as high at 1700oC and pressure up to 4.6 GPa. Viscosities for
sodium carbonate at these conditions went as high as 0.0073 Pa s. Additionally, Persikov et al.9
determined viscosities for haplokimberlitic and basaltic melts at temperatures up to 1950oC and
7.5 GPa. Viscosities were in a range up to 1.5 Pa s. Both studies employed falling body
techniques to determine viscosity.
26
I.3 A Brief Rationale for the Present Study
Over the past two decades, there has been a significant increase in the literature on high
pressure viscosity determination and modelling. There is, however, much room for further
growth. Modeling endeavors have grown with increasing need to generate data when
experiments cannot be run. That being said, due to the nature of the available models and their
limitations, experimental data cannot be replaced. However, experimental apparatuses are also
limited in some fashion. While this is not likely to change due to the nature of high pressure
instrumentation, these limitations can be mitigated somewhat by understanding the appropriate
use cases of the fluids being measured and the design of new instrumentation. There is a need
for improved instruments capable of shear rate control and determination during the
measurement process. Rotational viscometers are capable of providing this shear rate control,
but at the cost of pressure limitations. The development of rotational viscometers that can reach
higher pressures than most commercial instruments, incorporates the ability to measure density,
and allows for the observation of phase behavior would be very useful and has been a primary
focus in this thesis. Since most semi-empirical descriptions of viscosity (free volume theory,
friction theory, and density scaling) involve density, having methods of generating PVT data in
the same study, preferably simultaneously with the viscosity determinations, is important.
Without this capability, studies are either limited in their description of the system being
measured, or are limited to systems with well defined PVT data and models.
Two particular fields that could greatly benefit from further expansion of available high
pressure viscosity data are those of automotive lubricants and ionic liquids. Lubricant oils are
complex mixtures, leading to difficulties in accurately modeling these fluids without detailed
experimental data. Additionally, these lubricants include additives, including polymeric
modifiers, whose effects on the system as a whole need to be characterized. By determining both
viscosity and density as a function of temperature and pressure, a holistic understanding of the
flow behavior, film formation, and thermodynamics can be produced. In the case of ionic
liquids, high pressure viscosity and density measurements allows for the simultaneous
determination of the transport behavior and solvent capabilities through PVT data. This
information is needed if ionic liquids are to be successfully used as replacements for traditional
solvents in any sort of chemical engineering applications.
27
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35
II. Experiments
II.1 Variable-Volume View-Cell
A variable-volume view-cell was used to generate density data across a range of
temperatures and pressures. The details of this instrument have been previously published.1-5
However, for completeness, a description of the instrument and how it was used in the present
thesis is provided below. Figures II.1 and II.2 are diagrams of the apparatus. The instrument
uses a pair of sapphire windows to allow for visual or optical observation of the phase behavior.
Real time measurements of phase behavior are possible by utilizing an optical sensor in
conjunction with a light source. By passing light through the sample and measuring the
transmittance, the temperature and pressure at which phase separation or miscibility occurs can
be determined. The variable-volume portion allows for the control and measurement of volume
in the cell. With knowledge of the volume and mass loaded, density is determined.
The variable-volume portion consists of a piston with a back-pressure fluid, ethanol,
controlling the piston movement. Pressure in the back-pressure line is controlled by a motorized
pressure generator, allowing for steady pressure scans (typical runs are performed at a pressure
scan rate of 0.5 MPa/s) at a constant temperature. Piston position, and with it, volume in the cell,
is measured using a linear variable differential transformer (LVDT), manufactured by TE
Connectivity (model HR2000). This LVDT monitors the position of a magnetic core attached to
the piston. This system allows for the determination of volume in the cell to within ± 0.1 cm3
across a range of 11 to 23 cm3. Temperature in the cell is measured by a J-type thermocouple (±
1.1 K) while pressure is measured by a Dynisco diaphragm pressure transducer (model
#TPT432A-10M-6/18, up to 70 MPa, ± 0.07 MPa). Density is determined to within ± 1%.
Heating of the cell is achieved by four electric cartridge heaters (75 W heaters from ProTherm
Industries, model #TD25030AA) controlled by an Omega Engineering CN76000 temperature
controller. Figure II.3 shows the inner dimensions of the variable-volume view-cell. Mixing in
the cell is achieved with a magnetic stir bar.
In a typical experiment, the cell is loaded with 12-15 g of sample. For mixtures, each
constituent is loaded separately until the desired composition is reached. Components with low
volatility at ambient conditions (such as solids or liquids with high boiling points) are loaded into
36
the apparatus with a syringe before the cell is closed. Once the cell is closed, vacuum is pulled
on the internal volume to eliminate the effects of air on the density measurements. Volatile
components are pumped into the closed cell from a secondary container. The mass of all
constituents loaded is measured by a Mettler PM6100 balance (± 0.005 g). Once the variable-
volume view-cell is loaded, isothermal pressure scans are performed at temperatures of 298, 323,
348, 373, and 398 K across a range of 10-40 MPa.
Figure II.4 shows a typical run in the variable-volume view-cell, performed for ethanol at
298 K. The voltage of the LVDT and pressure are recorded with time. The LVDT reading is
directly related to piston position, and with it volume. With the mass loaded into the instrument
known, density is determined. Once density has been calculated across the isotherm, it can be
related to pressure. In the present thesis, this process was repeated for four more isotherms up to
398 K.
The variable-volume view-cell was validated with a series of additional ethanol runs.
The density of ethanol at the conditions evaluated has been also reported in the literature.6-10
Figure II.5 shows a comparison of an ethanol validation run compared to select points from the
literature.6 The experimental density of ethanol fell within ± 1% of the literature values, with the
average deviation determined to be 0.50 %. Further information on the validation of the
variable-volume view-cell can be found in Appendix B.
Figure II.1. External diagram of the variable-volume view-cell.
Thermocouple
Pressure Transducer
PGN
LVDT
Sapphire Window
37
Figure II.2. Internal diagram of the variable-volume view-cell.
Figure II.3. Dimensions of the variable-volume view-cell.
30.6 mm
12.9 mm 36.9 mm
15.7 mm
92.6 mm
Thermocouple
Pressure Transducer
PGN
LVDT
Magnetic Core Piston
Stir Bar
Magnetic
Stir Plate
38
Figure II.4. Evaluation of a sample run of ethanol in the variable-volume view-cell at a fixed
temperature of 298 K. Pressure (top left) and LVDT readings (top right) are collected
simultaneously during the run. LVDT reading relates to piston position, and with it, volume and
density (bottom left). Once density is determined, it can be related to pressure along the
isotherm (bottom right).
0
5
10
15
20
25
30
35
40
45
0 20 40 60 80 100
Pre
ssu
re (
MP
a)
Time (s)
Ethanol
298 K
0.2
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0 20 40 60 80 100
LV
DT
Rea
din
g (
V)
Time (s)
Ethanol
298 K
0.76
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0 20 40 60 80 100
Den
sity
(g/c
m3)
Time (s)
Ethanol
298 K
0.76
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
Ethanol
298 K
39
Figure II.5. Comparison of experimental (circles) data for a validation run to literature values
(diamonds). Literature values used were from Abdulagatov et al.6
II.2 High Pressure Rotational Viscometer
A high pressure rotational viscometer was developed in the present thesis to examine
viscosity as a function of temperature, pressure, and shear rate. A detailed description of this
instrument and how it was used in the present thesis is provided below. The system has been
described in our recent publication.5 The operation of rotational viscometers is dependent on the
geometry of the instrument. Examples of potential inner geometries of rotational viscometers
include coaxial cylinders, cone and plate, and parallel plate.11-13 This particular instrument is
based on the coaxial cylinder geometry, with the viscosity determined by the flow of fluid
between two concentric cylinders. Depending on design, either the inner (Searle) or outer
(Couette) cylinder can act as the rotating element.11-14 For this instrument, a Searle type design
was used, with the inner rotating shaft driven by a motor combined with a torque transducer.
The outer cylinder is built into the main body of the high pressure cell as a cylindrical cavity.
Figures II.6 and II.7 show the layout of this instrument. To avoid having to seal across
moving parts, the inner shaft is magnetically coupled to the torque transducer/motor. A
Thermofisher Haake Viscotester 550 (± 0.00015 N m) has been modified to serve as both the
torque transducer and motor. While this arrangement allows for the operation of the viscometer
0.65
0.67
0.69
0.71
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
Ethanol
298 K
323 K
348 K
373 K
398 K
40
at high pressures, the use of magnetic coupling adds a number of complications in the
determination of viscosity. Rotating a magnetic field over the steel portions of the high pressure
cell induces eddy currents in the system. This in turn creates a magnetic field that is picked up
by the torque transducer. The effect of this magnetic term needs to be taken into account in
calibrating the instrument. There is also a limit in the viscosity that can be reached before the
magnets decouple. In the present system, if the torque required to maintain a constant rotational
speed is too high, above 0.02 N m, the inner rotating shaft ceases to move. In addition to the
magnetic effects, the unusual geometry of the high pressure cell further modifies the
interpretation of the final results. Figure II.8 shows the measurements and proportions of the
instrument. The cylindrical cavity in the main body is not fully cylindrical for its full length due
to the presence of the sapphire windows and variable volume portions of the cell. However,
these irregular portions are small compared to the portions that are indeed cylindrical, with the
overall length being 136.9 mm and the length of the irregular portions being 41 mm, making the
interactive length 95.9 mm.
In addition to serving as a viscometer, this instrument is also a variable-volume view-cell.
Two pairs of sapphire windows allow for visual observations of the phase behavior inside the
viscometer. Additionally, there are two variable-volume portions, with movable pistons that
allows for the control of the volume and pressure in the cell. LVDTs (TE Connectivity XS-A
1003) are used to measure the position of both pistons. Here also, ethanol was used as the back-
pressure fluid. A 60,000 psi pressure generator from High Pressure Equipment Company was
used to control the pressure of the back pressure line. Using two pistons insures that the internal
volume range of the cell is wide enough to allow for the instrument to be usable in performing
measurements on compressible fluids. Additionally, the arrangement of the two pistons, one on
either side, allows for viscous multicomponent fluids to be forced back and forth across the
rotating shaft, ensuring proper mixing. Temperature and pressure are measured by a J-type
thermocouple (± 1.1 K) and an Omega PX91N0-60KSV pressure transducer (full range of 400
MPa, ± 0.4 MPa). Heating for the instrument was performed by four electric heating cartridges
(150 W heaters from ProTherm Industries, model #TD25060AA) controlled by an Omega
Engineering CN78000 temperature controller.
41
Figure II.6. External diagram of the high pressure rotational viscometer.
Figure II.7. Internal diagram of the high pressure rotational viscometer.
Torque
Transducer/Motor
LVDT
PGN PGN
LVDT
Sapphire
Windows
Pressure
Transducer
J Thermocouple
LVDT
Coupling
Magnets
Hole
LVDT
Piston
Magnetic Core
Thermocouple
Sapphire
bearings
42
Figure II.8. Internal geometries of the high pressure rotational viscometer.
To calculate viscosity, shear stress and shear rate are needed, which are calculated from
torque and rotational speed according to the following relationships:14
𝜏 =𝑀𝑇
2𝜋𝑟𝑖2𝐻
II.1
=2𝑟𝑜
2
(𝑟𝑜2−𝑟𝑖
2)Ω II.2
where τ is the shear stress, is the shear rate, ri is the inner radius, ro is the outer radius, H is
height, MT is measured torque, and Ω is rotational speed. Viscosity is then calculated from the
shear stress and shear rate:11-12
𝜂 =𝜏
II.3
However, due to the effects of the friction, magnetic fields and the inner geometry, equation II.3
cannot be simply used in conjunction with equations II.1 and II.2. During operation, the inner
rotating shaft sits in between two sapphire bearings, one at each end, to keep the shaft centered.
The friction addition from these physical contact points change depending on the fluid in the cell,
54.0 mm
20.5 mm 152.4 mm
23.8 mm
18.9 mm
23.6 mm
18.7 mm
136.9 mm
14.1 mm 16.7 mm
43
due to lubrication effects. For each fluid and temperature, a correction factor needs to be
determined. Additionally, the magnetic eddy currents and nonuniform geometry requires the use
of an empirical fit determined through calibration with fluids of known viscosity. For a
Newtonian fluid, viscosity is calculated from rotational speed and measured torque using
equation:
𝜂 = 𝐴 (𝐶𝑇
Ω) − 𝐵 II.4
where η is viscosity, CT is the corrected torque, Ω is rotational speed, and A and B are constants.
Constants A and B were determined with silicone and mineral oil standards from the Cannon
Instrument Company shown in Table II.1.
For each calibration standard, ambient pressure runs were performed at temperatures at
which the standards had been characterized by the manufacturer (298 K, 323 K, 353 K, and 373
K for two oils, 273 K and 313 K for the rest). All of these standards were Newtonian in nature.
The viscosity and density at each temperature at which a calibration run was performed can be
found in Table II.1. At each rotational speed, from 100-800 rpm, torque was measured for one
minute. The average torque at each rotational speed was plotted versus rotational speed to
determine the y-intercept. Figure II.9 shows this process for a mineral oil based calibration
standard N14 at 298 K and ambient pressure. The calculated y-intercept for each temperature
and each standard was used as the correction factor to compensate for friction and lubrication
effects pertaining to mechanical contact of the rotating shaft with the sapphire bearings. The
correction factor was subtracted from the measured torque values to determine the corrected
torque. Figure II.10 shows this correction process at 500 rpm and the corrected torque for all
rotational values for calibration standard N14 at 298 K and ambient pressure. Finally, the known
viscosity can be compared to average corrected torque/rotational speed (ACT/Ω). The constants
for equation II.4 were determined by through a linear fit of viscosity versus ACT/Ω for all
calibration standards. Figure II.11 shows the comparison of viscosity and ACT/Ω for standard
N14 at all measured temperatures (298 K, 323 K, 353 K, and 373 K), ambient pressure, and all
rotational speeds. Figure II.12 shows the final calibration curve using all calibration standards in
Table II.1. Plots of the measured torque and torque corrections for each calibration standard at
each temperature can be found in Appendix B.
44
Comparing data collected at ambient pressures to oil standards, the uncertainty was found
to be ± 5% for runs at 300 rpm or above at viscosities above 3 cP. Figure II.13 shows an
example of a validation run using silicone oil S60 from Canon Instrument Company at ambient
pressure at rotational speeds of 300-800 rpm. This was a separate run from those performed for
the calibration of the instrument. With the calibration and validation completed at ambient
pressures, a similar procedure can be used to determine the viscosity of fluids at high pressure
conditions. For each individual experiment at each temperature, a correction run is completed.
Once the temperature in the viscometer has come to a stable equilibrium, a run at each rotational
speed up to 800 rpm, or when the rotating shaft decoupled, was completed at ambient pressure.
As with the calibration runs, average torque for each one minute run was plotted versus
rotational speed. The y-intercept of the resulting linear fit is subtracted from the measured
torque to calculate the corrected torque for each run at that temperature for the loaded fluid.
Once the correction run is completed, pressure scans at each rotational speed can be done across
the isotherm. The full process for converting measured torque to viscosity for an experimental
run is shown in Figure II.14 for an oil (a base oil composed of poly(alpha olefins)) at 298 K and
500 rpm.
Once calibrations are done, typical viscosity measurements were performed at constant
temperatures of 298, 323, 348, and 373 K across a pressure range of 10-40 MPa. The pressure
scan rate was typically 0.3 MPa/s. Runs were performed at rotational speeds ranging from 300-
800 rpm. Unlike the variable-volume view-cell, the high pressure viscometer is not operational
at 398 K, with 373 K being the maximum operating temperature. Additionally, at low rotational
speeds, below 300 rpm, there was an instability leading to high scatter of the data (± 3 mPa s).
This limitation was ignored for certain runs at high viscosities (above 80 mPa s) where
decoupling of the magnets occurred at 300 rpm and above. For typical experiments, shear rates
were estimated to range from 480 to 1270 s-1.
45
Table II.1. Cannon Instrument Company calibration standards used to calibrate the high
pressure rotational viscometer. Viscosity and density values are specific to the actual sample
used, with values provided by the manufacturer.
Standard T (K) η (mPa s) ρ (g/cm3) Oil Type
N14 298 21.68 0.8103 Mineral
323 8.909 0.7944
353 4.127 0.7752
373 2.774 0.7624
S60 298 102.0 0.8619 Silicone
323 29.03 0.8468
353 10.16 0.8282
373 6.052 0.8158
RT50 298 46.65 0.9592 Silicone
313 35.05 0.9459
RT100 298 90.33 0.9625 Silicone
313 67.91 0.9491
46
Figure II.9. Torque versus time (left) and average torque versus rotational speed (right) for
Cannon Instrument Company calibration standard N14 at 298 K and ambient pressure.
Figure II.10. Torque versus time for Cannon Instrument Company calibration standard N14 at
298 K and ambient pressure. The friction correction for the 500 rpm run is shown on the left
while the corrected torque for all rotational speeds is shown on the right.
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Torq
ue
(N m
)
Times (s)
N14
298 K
0.1 MPa
100 rpm
200 rpm
300 rpm
400 rpm
500 rpm
600 rpm
700 rpm
800 rpm
0
0.005
0.01
0.015
0.02
0.025
0.03
0 200 400 600 800 1000
Aver
age
Torq
ue
(N m
)
Rotational Speed (rpm)
N14
298 K
0.1 MPa
AT = 2.1391E-05Ω + 0.0022050
R2 = 0.9999
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
N14
298 K
0.1 MPa
500 rpm
Measured Torque
Corrected Torque
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
N14
298 K
0.1 MPa
100 rpm
200 rpm
300 rpm
400 rpm
500 rpm
600 rpm
700 rpm
800 rpm
47
Figure II.11. Viscosity versus average corrected torque/rotational speed for Cannon Instrument
Company calibration standard N14 at 0.1 MPa.
Figure II.12. Viscosity versus average corrected torque/rotational speed for all calibration
standards in Table II.1. The final calibration curve used to determine the constants in equation
II.4 is represented by the dashed line.
0
5
10
15
20
25
0.00001 0.000015 0.00002 0.000025
Vis
cosi
ty (
mP
a s
)
ACT/Ω (N m min)
N14
0.1 MPa
298 K
323 K
353 K
373 K
0
20
40
60
80
100
120
0 0.00002 0.00004 0.00006
Vis
cosi
ty (
mP
a s
)
ACT/Ω (N m min)
η = 2.6600E6ACT/Ω - 31.497
R2 = 0.997
48
Figure II.13. Viscosity versus time for a validation run at ambient pressure for a silicone oil
(Canon Instruments S60). Blue circles represent collected data and orange lines are the actual
values as specified by the manufacturer.
0
20
40
60
80
100
120
140
0 20 40 60 80
Vis
cosi
ty (
mP
a s
)
Time (s)
Silicone Oil S60
300-800 rpm
298 K
(300 rpm)
323 K
348 K373 K
49
Figure II.14. Evaluation of a sample run in the high pressure rotational viscometer, involving a
base oil composed of poly(alpha olefins) at 298 K and 500 rpm. Torque values are compared to
rotational speeds at low pressures to generate a correction plot (top left). This base line is then
subtracted from the torque values from a run (top right). Corrected torque is then converted to
viscosity (bottom).
y = 2E-05x + 0.0004R² = 0.9998
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0 200 400 600 800
Torq
ue
(N m
)
Rotational Speed (rpm)
PAO 4
298 K
0.012
0.013
0.014
0.015
0.016
0.017
0.018
0 10 20 30 40 50
Torq
ue
(N m
)
Pressure (MPa)
PAO 4
298 K
500 rpm
Torque
Correction
Original
Corrected
30
35
40
45
50
55
60
65
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4
298 K
500 rpm
50
II.3 References
1. H.E. Grandelli, E. Kiran, High pressure density, miscibility and compressibility of
poly(lactide-co-glycolide) solutions in acetone and acetone + CO2 binary fluid mixtures,
Journal of Supercritical Fluids, 75 (2013) 159-171.
2. J.M. Milanesio, J.C. Hassler, E. Kiran, Volumetric Properties of Propane, n-Octane, and
Their Binary Mixtures at High Pressures, Ind. Eng. Chem. Res., 52 (2013) 6592-6609.
3. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric
Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Industrial &
Engineering Chemistry Research, 52 (2013) 17725-17734.
4. J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and
estimation of the solubility parameters of ionic liquid plus ethanol mixtures with the
Sanchez-Lacombe and Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol
and [EMIM]Cl plus ethanol mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.
5. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and
Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &
Engineering Chemistry Research, 57 (2018) 17266-17275.
6. I.M. Abdulagatov, F.Sh. Aliyev, M.A. Talibov, J.T. Safarov, A.N. Shahverdiyev, E.P.
Hassel, High-pressure densities and derived volumetric properties (excess and partial
molar volumes, vapor-pressures) of binary methanol + ethanol mixtures, Thermochimica
Acta, 476 (2008) 51-62.
7. D. Pecar, V. Dolecek, Volumetric properties of ethanol-water mixtures under high
temperatures and pressures, Fluid Phase Equilibria, 230 (2005) 36-44.
8. Y. Takiguchi, M. Uematsu, Densities for liquid ethanol in the temperature range from
310 K to 480 K at pressures up to 200 MPa, J. Chem. Thermodynamics, 28 (1996) 7-16.
9. H. Pohler, E. Kiran, Volumetric Properties of Carbon Dioxide + Ethanol at High
Pressures, J. Chem. Eng. Data, 42 (1997) 384-388.
10. C.K. Zeberg-Mikkelsen, L. Lugo, J. Garcia, J. Fernandez, Volumetric properties under
pressure for the binary system ethanol + toluene, Fluid Phase Equilibria, 235 (2005) 139-
151.
11. W.H. Deen, Analysis of Transport Phenomena, second ed., Oxford University Press, New
York, 2011.
12. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., John Wiley
& Sons, New York, 2002.
13. S. Bair, High Pressure Rheology for Quantitative Elastohydrodynamics, first ed.,
Elsevier, New York, 2007.
14. A. Blanco, C. Negro, E. Fuente, J. Tijero, Rotor selection for a Searle-type device to
study the rheology of paper pulp suspensions, Chemical Engineering and Processing, 46
(2007) 37-44.
51
III. Analysis and Modeling
III.1 Volumetric properties and lattice fluid models
In addition to determination through experimental means, density at high pressure
conditions can be modelled. By utilizing a model to fit collected density data, it is possible to
generate a better understanding of both the temperature and pressure effects on density and
calculate derived thermodynamic properties. There are a number of methods used in the
literature to model PVT data, ranging from empirical fits1-4 to detailed equations of state.3-8
A common method used to fit experimental density data is the semi-empirical Tait
equation:9,10
𝜌0
𝜌= 1 −
1
1+𝐾0′ ln [1 +
𝑃
𝐾0(1 + 𝐾0
′)] III.1
where ρ is density, ρ0 is reference density, K0 is the bulk modulus, and K0’ is the pressure
derivative of the bulk modulus. Temperature dependence is added to the Tait equation through
the modulus and reference density terms:10
𝐾0 = 𝐾00exp(−𝛽𝐾𝑇) III.2
𝜌0 = 𝜌𝑅 (1 − 𝑎𝜌(𝑇 − 𝑇𝑅)) III.3
where K00, βK, and aρ are constants and ρR is the density at reference temperature TR. It is
assumed that K0’ is temperature independent. This model has been employed in the analysis of a
wide range of systems, including lubricants10,11 and ionic liquids.12,13 While the Tait equation is
commonly employed, it has its limitations.4 This semi-empirical equation is often modified for
the model to fit the data, adding extra required parameters, and its terms have limited physical
significance. Instead, in this thesis study we employed a lattice fluid model, the Sanchez-
Lacombe equation of state (S-L EOS). In the S-L EOS, the fluid is modeled as fitting into a
lattice, where each lattice site is occupied by either a molecule or polymer segment, or a vacant
site.14,15 Figure III.1 shows a two-dimensional representation of the model. The S-L EOS is
represented by the equation:14,15
52
2 + + (ln(1 − ) + (1 −1
𝑟) ) = 0 III.4
where , , and are reduced values of density, pressure, and temperature, while r represents
the number of lattice sites a molecule fills:
=𝜌
𝜌∗, =
𝑃
𝑃∗, =
𝑇
𝑇∗,𝑟 =
𝑀𝑊𝑃∗
𝑅𝑇∗𝜌∗ III.5
where ρ is density, P is pressure, T is temperature, MW is molecular weight, R is gas constant,
and ρ*, T*, and P* are the characteristic parameters of the S-L EOS. The equation can also be
put in terms of intermolecular effects represented by molecular segment interaction parameter
(ε*) and close-packed volume of each segment (ν*):
𝑇∗ =𝜀∗
𝑘 𝑃∗ =
𝜀∗
𝑣∗ III.6
where k is Boltzmann’s constant.14,15 From its earliest use, the S-L EOS has been employed in
literature to model both molecular solvents14 and polymers.15 This thesis includes some of the
first work on the application of the S-L EOS for the modeling of ionic liquids.16 In recent years,
the use of this model to describe ionic liquids has increased.13,17
53
Figure III.1. Two-dimensional representation of the lattice fluid model.
III.2 Modeling mixtures
Equations III.4 – 5 can simply be fit to data for a single component system. The S-L
EOS is not limited to single component systems, however. In order to model multicomponent
systems, mixing rules must be used.15 The S-L parameters for a multicomponent mixture can be
calculated based on concentration:
𝑃𝑚𝑖𝑥∗ = ∑ ∑ 𝜙𝑖𝜙𝑗𝑃𝑖𝑗
∗𝑗𝑖 III.7
where ϕi is the close pack volume fraction, calculated from mass fraction of the components (wj)
and characteristic density of each component (𝜌𝑗∗):
𝜙𝑖 =
𝑤𝑖𝜌𝑖∗
∑ (𝑤𝑗
𝜌𝑗∗)𝑗
III.8
The term 𝑃𝑖𝑗∗ is a cross parameter:
54
𝑃𝑖𝑗∗ = (1 − 𝑘𝑖𝑗) ∗ √𝑃𝑖
∗𝑃𝑗∗
III.9
where 𝑃𝑗∗ is the characteristic pressure for a component and kij is an empirical interaction
parameter. Once 𝑃𝑚𝑖𝑥∗ has been calculated, 𝑇𝑚𝑖𝑥
∗ can be calculated:
𝑇𝑚𝑖𝑥∗ = 𝑃𝑚𝑖𝑥
∗ ∑ 𝜙𝑖0
𝑖𝑇𝑖∗
𝑃𝑖∗
III.10
where 𝑇𝑖∗ is the characteristic temperature of a single component and 𝜙𝑖
0 is the average close
packed mer volume fraction:
𝜙𝑖0 =
𝜙𝑖𝑃𝑖∗
𝑇𝑖∗
∑ 𝜙𝑗
𝑃𝑗∗
𝑇𝑗∗𝑗
III.11
Once 𝑃𝑚𝑖𝑥∗ and 𝑇𝑚𝑖𝑥
∗ have been calculated, 𝜌𝑚𝑖𝑥∗ and rmix need to be determined in order to use
equations III.4 and 5 to model a mixture. A value for rmix can be calculated using the equation:
1
𝑟𝑚𝑖𝑥= ∑
𝜙𝑗
𝑟𝑗𝑗 III.12
In conjunction with an average molecular weight:
1
𝑀𝑊𝑚𝑖𝑥= ∑
𝑤𝑖
𝑀𝑊𝑖𝑖 III.13
the parameter 𝜌𝑚𝑖𝑥∗ can be calculated using equations III.12 in conjunction with the equation for r
in equation III.5 to derive:
1
𝜌𝑚𝑖𝑥∗ = ∑
𝑤𝑖
𝜌𝑖∗𝑖 III.14
55
Once the pure component values have been determined for the S-L EOS, equations III.7 – III.14
can be used to determine S-L characteristic parameters for a mixture at a fixed composition. By
utilizing mixing rules, density can be modeled in terms of composition, in addition to
temperature and pressure.15,18
IV.3 Derived thermodynamic properties
Once PVT data have been fit to a model equation, derived thermodynamic properties can
be determined. Isothermal compressibility and isobaric thermal expansion coefficient can be
determined from the partial derivatives of density with respect of pressure (compressibility) and
temperature (expansion):16,19
𝜅𝑇 = −1
𝑉(𝜕𝑉
𝜕𝑃)𝑇=
1
𝜌(𝜕𝜌
𝜕𝑃)𝑇
III.15
𝛽𝑃 =1
𝑉(𝜕𝑉
𝜕𝑇)𝑃= −
1
𝜌(𝜕𝜌
𝜕𝑇)𝑃
III.16
Using the S-L EOS in conjunction with these equations leads to:16
𝜅𝑇 =2
𝑃([1
−1+1
𝑟]−2)
III.17
𝛽𝑃 =1+2
𝑇([1
−1+1
𝑟]−2)
III.18
Once isothermal compressibility and thermal expansion coefficient have been calculated, internal
pressure can be calculated. Internal pressure is a measure of the overall attractive and repulsive
interactions in the system:1,20-23
𝜋 = (𝜕𝑈
𝜕𝑉)𝑇= 𝑇 (
𝜕𝑃
𝜕𝑇)𝑉− 𝑃 = 𝑇 (
𝛽𝑃
𝜅𝑇) − 𝑃 III.19
56
With an understanding of the intermolecular interactions, it is possible to estimate solvent
capabilities of a fluid or mixture. It has indeed been suggested in the literature that the
Hildebrand solubility parameter can be estimated using internal pressure.23,24 Used as an
estimate of the miscibility of two different species, the solubility parameter provides a method of
determining the effectiveness of a solvent for a particular process before experimentation has
been carried out. The solubility parameter is defined as the square root of the cohesive energy
density (CED) and traditionally requires knowledge on the heat of vaporization of a species:
𝜎 = 𝐶𝐸𝐷1 2⁄ = (𝑈
𝑉)1 2⁄
= (∆𝐻𝑣−𝑅𝑇
𝑉)1 2⁄
III.20
where U is internal energy, V is volume, ΔHv is heat of vaporization, R is gas constant, and T is
temperature.25 While heat of vaporization is readily measurable for volatile organic solvents,
this is not the case for many materials with low or negligible volatilities, such as polymers, ionic
liquids, or base oils. While internal pressure is not directly equivalent to cohesive energy
density, it can be used as a substitute for many substances:23,24
𝜎 ≅ √𝜋 III.21
Thus, by utilizing internal pressure, PVT data can be used to estimate the Hildebrand solubility
parameter of both pure components and mixtures as a function of temperature and pressure.
III.4 Viscosity and free volume
Viscosity can be modeled alongside density and the derived thermodynamic properties.
As previously discussed in Chapter I, one possible approach is to examine viscosity through the
lens of free volume, and with it, density. An early approach to relating viscosity to free volume
and density is the empirical Doolittle equation (Equation I.11).26,27 A later model by Allal et
al.,27,28 shown in equation I.12, provides a more detailed relationship of density and free volume
effects on viscosity. In this study, equation I.12 was further simplified. All experiments in this
study were carried out on dense liquids, both lubricants and ionic liquids. The term η0,
representing the gas viscosity at infinite dilution, is small compared to the overall viscosities of
57
these fluids. For the experiments carried out in the high pressure rotational viscometer described
in Chapter II, it was assumed that η >> η0, allowing for the equation to be simplified to three
parameters:
𝜂 =𝜌𝜄(𝛼𝜌+
𝑃𝑀𝑊
𝜌)
√3𝑅𝑇𝑀𝑊𝑒𝐵(
𝛼𝜌+𝑃𝑀𝑊𝜌
𝑅𝑇)
3 2⁄
III.22
where ι is the characteristic molecular length, α relates to intermolecular energy, and B
represents free volume effects. Once the parameters ι, α, and B, which are treated at constants,
have been calculated, viscosity can be calculated in conjunction with an EOS for determining
density, such as the S-L EOS (Equation III.4).29
IV.5 Statistical analysis of model fits
Python® programs were written to fit density data of both pure components and mixtures
to the S-L EOS (Equations III.4 and III.5) and viscosity data to equation III.22. For both density
and viscosity models, root mean squared deviation (RMSE), percent absolute deviation (%
AAD), and bias (ℬ) were evaluated:
𝑅𝑀𝑆𝐸 = √∑(𝑥𝑐,𝑖−𝑥𝑖)
2
𝑛
III.23
𝑑𝑖 = (1 −𝑥𝑐,𝑖
𝑥) ∗ 100% III.24
%𝐴𝐴𝐷 =1
𝑛∑|𝑑𝑖| III.25
ℬ =1
𝑛∑𝑑𝑖 III.26
Equations III.23 – 26 allow for the determination of the quality of fit these models provide to the
experimental data collected as described in Chapter II.
58
III.6 References
1. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric
Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Industrial &
Engineering Chemistry Research, 52 (2013) 17725-17734.
2. C.C. Sampson, X. Yang, J. Xu, M. Richter, Measurement and correlation of the (p, ρ, T)
behavior of liquid propylene glycol at temperatures from (272.7 to 393.0) K and
pressures up to 91.4 MPa, J. Chem. Thermodynamics, 131 (2019) 206-218.
3. I. Abala, F.E.M. Alaoui, Y. Chhiti, A.S. Eddine, N.M. Rujas, F. Aguilar, Experimental
density and PC-SAFT modeling of biofuel mixtures (DBE + 1-Heptanol) at temperatures
from (298.15 to 393.15) K and at pressures up to 140 MPa, J. Chem. Thermodynamics,
131 (2019) 269-285.
4. R. Mohammadkhani, A. Paknejad, H. Zarei, Thermodynamic Properties of Amines under
High Temperature and Pressure: Experimental Results Correlating with a New Modified
Tait-like Equation and PC-SAFT, Ind. Eng. Chem. Res., 57 (2018) 16978-16988.
5. J.A. Sarabando, P.J.M. Magano, A.G.M. Ferreira, J.B. Santos, P.J. Carvalho, S. Mattedi,
I.M.A. Fonseca, M. Santos, Influence of temperature and pressure of the density and
speed of sound of N-ethyl-2-hydroxyethylammonium propionate ionic liquid, J. Chem.
Thermodynamics, 131 (2019) 303-313.
6. M. Ebrahiminejadhasanabadi, W.M. Nelson, P. Naidoo, A.H. Mohammadi, D.
Ramjugernath, Experimental measurement of carbon dioxide solubility in 1-
methypyrrolidin-2-one (NMP) + 1-butyl-3-methyl-1H-imidazol-3-ium tetrafluoroborate
([bmim][BF4]) mixtures using a new static-synthetic cell, Fluid Phase Equilibria, 477
(2018) 62-77.
7. J. Hekayati, A. Roost, J. Javanmardi, Volumetric properties of supercritical carbon
dioxide from volume-translated and modified Peng-Robinson equations of state, Korean
J. Chem. Eng., 33(2016) 3231-3244.
8. M.R. Curras, M.M. Mato, P.B. Sanchez, J. Garcia, Experimental densities of 2,2,2-
trifluoroethanol with 1-butyl-3-methylimidazolium hexafluorophosphate at high
pressures and modelling with PC-SAFT, J. Chem. Thermodynamics, 113 (2017) 29-40.
9. J.H. Dymond, The Tait equation: 100 years on, International Journal of Thermophysics,
9 (1996) 941-951.
10. W. Habchi, S. Bair, Quantitative Compressibility Effects in Thermal Elastohydrodynamic
Circular Contacts, J. Tribology, 135 (2013) 011502-1 – 011502-10.
11. I. Krupka, P. Kumar, S. Bair, M.M. Khonsari, M. Hartl, The Effect of Load (Pressure) for
Quantitative EHL Film Thickness, Tribol. Lett., 37 (2010) 613-622.
12. Y. Hiraga, S. Hagiwara, Y. Sato, R.L. Smith, Measurement and Correlation of High-
Pressure Densities and Atmospheric Viscosities of Ionic Liquids: 1-Butyl-1-
methylpyrrolidinium Bis(trifluoromethylsulfonyl)imide), 1-Allyl-3-methylimidazolium
Bis(trifluoromethylsulfonyl)imide, 1-Ethyl-3-methylimidazolium Tetracyanoborate, and
1-Hexyl-3-methylimidazolium Tetracyanoborate, J. Chem. Eng. Data, 63 (2018) 972-
980.
13. Y. Hiraga, M. Goto, Y. Sato, R.L. Smith, Measurement of high pressure densities and
atmospheric pressure viscosities of alkyl phosphate anion ionic liquids and correlation
59
with the ε*-modified Sanchez-Lacombe equation of state, J. Chem. Thermodynamics,
104 (2017) 73-81.
14. I.C. Sanchez, R.H. Lacombe, An Elementary Molecular Theory of Classical Fluids. Pure
Fluids, J. Phys. Chem., 80 (1976) 2352–2362.
15. I.C. Sanchez, R.H. Lacombe, Statistical Thermodynamics of Polymer Solutions,
Macromolecules, 11 (1978) 1145-1156.
16. J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and
estimation of the solubility parameters of ionic liquid plus ethanol mixtures with the
Sanchez-Lacombe and Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol
and [EMIM]Cl plus ethanol mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.
17. H. Machida, Y. Sato, R.L. Smith, Simple modification of the temperature dependence of
the Sanchez-Lacombe equation of state, Fluid Phase Equilibria, 297 (2010) 205-209.
18. Y. Hiraga, K. Koyama, Y. Sato, R.L. Smith, High pressure densities for mixed ionic
liquids having different functionalities: 1-butyl-3-methylimidazolium chloride and 1-
butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, J. Chem.
Thermodynamics, 108 (2017) 7-17.
19. K.G. Nayar, M.H. Sharqawy, L.D. Banchik, J.H. Lienhard V, Thermophysical properties
of seawater: A review and new correlations that include pressure dependence,
Desalination, 390 (2016) 1-24.
20. B.O. Ahrstrom, S. Lindqvist, E. Hoglund, K.G. Sundin, Modified split Hopkinson
pressure bar method for determination of the dilation –pressure relationship of lubricants
used in elastohydrodynamic lubrication, Proceedings of the Institution of Mechanical
Engineers Part J – Journal of Engineering Tribology, 216 (2002) 63-73.
21. A.Vadakkepatt, A. Martini, Confined fluid compressibility predicted using molecular
dynamic simulation, Tribology International, 44 (2011) 330-335.
22. S. Verdier, S.I. Anderson, Internal pressure and solubility parameter as a function of
pressure, Fluid Phase Equilibria, 231(2005) 125-137.
23. E. Zorebski, Internal pressure as a function of pressure, Molecular and Quantum
acoustics, 27 (2006) 327-336.
24. M.M. Alavianmehr, S.M. Hosseini, A.A. Mohsenipour, J. Moghadasi, Further property of
ionic liquids: Hildebrand solubility parameter from new molecular thermodynamic
model, Journal of Molecular Liquids, 218 (2016) 332-341.
25. S.H. Lee, S.B. Lee, The Hildebrand solubility parameters, cohesive energy densities and
internal energies of 1-alkyl-3-methylimidazolium-based room temperature ionic liquids,
Chem. Commun., (2005) 3469-3471.
26. A.K. Doolittle, Studies in Newtonian Flow. II. The Dependence of the Viscosity of
Liquids on Free-Space, J. Appl. Phys., 1951, 22, 1471-1475
27. A. Allal, C. Boned, A. Baylaucq, Free-Volume Viscosity Model for Fluids in the Dense
and Gaseous States, Phys. Rev. E, 2001, 64, 1-10
28. M. Yoshimura, C. Boned, A. Baylaucq, G. Galliero, H. Ushiki, Influence of the Chain
Length on the Dynamic Viscosity at High Pressure of Some Amines: Measurements and
Comparison Study of Some Models, J. Chem. Thermodyn., 2009, 41, 291-300.
29. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and
Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &
Engineering Chemistry Research, 57 (2018) 17266-17275.
60
IV. Base Oils
IV.1 Introduction
In this chapter, we discuss the volumetric properties and viscosity of several mineral and
synthetic base oils used in the manufacturing of automotive lubricants. There is a growing need
in the automotive industry to increase fuel efficiency. One way this can be accomplished is by
the choice of the lubricant used as engine oils and automatic transmission fluids.1 A reduction in
viscosity of the lubricant used often leads to an improvement in the lubricant effectiveness and
fuel efficiency.2-4 These lubricants operate under conditions that expose them to very high
pressures, in the range of GPas, and shear rates, in the range of 105 s-1. It is thus important to
understand the effect of pressure and shear on the flow behavior of these fluids.2,5,6 As described
in Chapter I in section I.2.3, while much work has been done at ambient pressures, there is a
growing need to understand the effect of pressure on both viscosity and thermodynamic
properties.
These engine oils and transmission fluids are complex mixtures, primarily composed of a
base oil, which itself is generally made up of many hydrocarbon-based constituents. In addition
to the base oil, these automotive lubricants contain a number of additives, often ten or more.
These additives allow for the lubricants to be tailored to meet the requirements needed for
effective use by modifying physical properties, like the temperature dependence of viscosity,
controlling the formation of deposits on mechanical parts, and reducing wear. These additives
include viscosity index modifiers, detergents, dispersants, friction modifiers and anti-wear
additives.7-10 Given that they are the primary components in automotive lubricants,
understanding the properties of base oils is necessary for the development of a successful
lubricant. The system for classifying these base oils as laid out by the American Petroleum
Institute was presented in Chapter I in Table I.1.
One of the major defining traits of these oils is the viscosity index. Viscosity index is a
measure of the temperature dependence of viscosity as compared to known standards at 40oC and
100oC.11 As viscosity index increases, the effect of temperature on viscosity decreases. Group I-
III oils are mineral oils and are categorized by viscosity index. Group I oils are generally made
by a solvent extraction of crude oil. Group II oils are group I oils that have been hydrotreated to
61
remove sulfur containing and aromatic compounds, leading to an increase in viscosity index. By
further treating the mineral oil, both opening the rings of cycloalkanes through hydrocracking
and further increasing viscosity index, Group III oils are made.12 Group IV and V oils are not
defined by viscosity index. Instead, Group IV oils are all synthetic oils composed of poly(α-
olefins), while Group V oils are anything that does not fit into Groups I-IV.
IV.1.1 Objectives
To gain a greater understanding of these oils, density and viscosity measurements were
carried out as a function of temperature, pressure, and in the case of viscosity also as a function
of shear rate for six base oils including two Group II, two Group III, and two Group IV oils. The
data were collected over a pressure and temperature range of 10-40 MPa and 298-398 K
respectively for density measurements and a range of 10-40 MPa and 298-373 K for viscosity
measurements.
The objective was to use the data to develop and test a holistic model to describe both
density and viscosity, while also allowing for the evaluation of the thermodynamic properties, of
these base oils. Density data were fit to the Sanchez-Lacombe equation of state, and the
thermodynamic properties isothermal compressibility, isobaric thermal expansion coefficient,
and internal pressure were calculated as a function of temperature and pressure. Viscosity data
were modeled by the free volume theory in conjunction with the Sanchez-Lacombe models
developed to describe the volumetric behavior.
IV.2 Materials and Methods
The base oils that were explored were provided by Afton Chemical Corp. They were
used as received. Basic properties for all six oils can be found in Table IV.1. These include the
kinematic viscosity at 373 K, viscosity index, and average molecular weight. The kinematic
viscosities and viscosity indexes were indicated to be as specified by the manufacturers of these
oils using ASTM tests D445 and D2270 respectively.
Figures IV.1-3 show the compositions of all six oils, which were provided by Afton
Chemical Corp based on GC-MS analysis. The technique is described in the literature.13 All six
62
oils fall into the base oil categories as laid out by the American Petroleum Institute guidelines,
described in Table I.1. Oils IIA and IIB are Group II oils composed of approximately 30 wt%
paraffins, 60 wt% cycloalkanes, and the remainder aromatic compounds. Oils IIIA and IIIB are
Group III oils composed of approximately 50 wt% paraffins, 45 wt% cycloalkanes, with the
remainder aromatics. Oils PAO 4 and PAO 8 are both Group IV oils, which are synthetic oils
composed solely of poly(α-olefins).
Table IV.1. Characteristics of the base oils studied.14
Kinematic Viscosity at 373 K
(cSt)
Viscosity
Index
Average Molecular Weight (g/mol)
IIA 4.1 103 354
IIB 6.4 103-109 445
IIIA 3.1 112 333
IIIB 6.5 131 474
PAO 4 4.1 126 489
PAO 8 7.9 139 526
Figure IV.1. Composition of base oils IIA (left) and IIB (right).14
0
10
20
30
40
50
60
70
80
90
100
Mass
Per
cen
t
IIA
0
10
20
30
40
50
60
70
80
90
100
Mass
Per
cen
t
IIB
63
Figure IV.2. Composition of base oils IIIA (left) and IIIB (right).14
Figure IV.3. Composition of base oils PAO 4 (left) and PAO 8 (right).14
0
10
20
30
40
50
60
70
80
90
100M
ass
Per
cen
t
IIIA
0
10
20
30
40
50
60
70
80
90
100
Mass
Per
cen
t
IIIB
0
10
20
30
40
50
60
70
80
90
100
Mass
Per
cen
t
PAO 4
0
10
20
30
40
50
60
70
80
90
100
Mass
Per
cen
t
PAO 8
64
Figure IV.4. Examples of the primary poly(α-olefins) found in PAO 4 and PAO 8, a trimer (A)
and tetramer (B) of 1-decene.
IV.3 Results and Discussions
The findings that are presented in the following sections are also described in our recent
publication in the journal Industrial & Engineering Chemistry Research.14
IV.3.1 PVT Data and Modeling
Density data were collected experimentally (oils IIA, IIB, IIIA, and IIIB) in the present
study and in an earlier study also conducted in our lab (oils PAO 4 and PAO 8).2 Figure IV.5
shows an example of the full range of data collected for oil IIB. The experimental data was fit to
the Sanchez-Lacombe equation of state (S-L EOS) laid out in equations III.4 and III.5. Table
IV.2 includes the parameters for the S-L EOS along with the root mean square deviation
(RSME), percent absolute average deviation (% AAD), and bias (% ℬ) for all six oils. The %
AAD was found to range from 0.130 to 0.204 %. A visual comparison of the S-L model fits to
the experimental data for oil IIB is show in Figure IV.4. The experimental density data and S-L
model fits for the remaining five oils are included in Appendix C. Figure IV.6 compares the
densities and S-L fits of all six oils at both 323 and 373 K. The Group II oils (IIA and IIB) were
found to have higher densities than the other four oils, with oil IIB having the highest densities
across the full range of temperatures and pressures represented in this study. Oil III B has
A) B)
65
slightly higher densities than the remaining three oils, which all had similar values in the
measured range.
Table IV.2. Sanchez-Lacombe parameters of base oils
IIA IIB IIIA IIIB PAO 4 PAO 8
P* (MPa) 506.42 501.44 488.06 499.53 433.62 418.46
T* (K) 553.4 556.03 538.91 548.92 544.10 548.24
ρ* (g/cm3) 0.95617 0.96258 0.91726 0.91979 0.91160 0.90929
MW (g/mol) 354 445 333 474 489 526
RMSE (g/cm3) 0.00140 0.00176 0.00157 0.00156 0.00198 0.00198
% AAD 0.130 0.171 0.160 0.156 0.201 0.204
% ℬ -0.00000860 -0.104 -0.000579 0.0000785 -0.000177 0.000285
Figure IV.5. Density versus pressure for the base oil IIB at isotherms 298, 323, 348, 373, and
398 K. Sanchez-Lacombe EOS fits are represented by black dots.
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
IIB
298 K
323 K
348 K
373 K
398 K
66
Figure IV.6. Density versus pressure for six base oils at 323 K (left) and 373 K (right).
Sanchez-Lacombe EOS fits are represented by black dots.
IV.3.2 Derived Thermodynamic Properties
Once the density data were fit to the S-L equation of state, the derived thermodynamic
properties isothermal compressibility, isobaric thermal expansion coefficient, and internal
pressure were calculated using equations III.17-19. Figures IV.7 and IV.8 show the calculated
thermodynamic properties for oil IIB across the temperature and pressure range in which the
density measurements were made. The thermodynamic properties across the full range of
temperatures and pressures examined in this study for the remaining five oils can be found in
Appendix C. For all six oils, the same trends with regards to temperature and pressure were
seen. Isothermal compressibility was found to increase with temperature and decrease with
pressure. Isobaric thermal expansion coefficient was also seen to increase with temperature and
decrease with pressure. Internal pressure had inverse trends, decreasing with temperature and
increasing with pressure.
0.77
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
323 K
IIB IIA
IIIA
IIIB
PAO 4
PAO 8
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
373 K
IIBIIA
IIIA
IIIB
PAO 4
PAO 8
67
Figure IV.7. Isothermal compressibility versus pressure (left) and isobaric thermal expansion
coefficient versus temperature (right) for IIB as calculated from the S-L EOS.
Figure IV.8. Internal pressure versus pressure for IIB calculated from the S-L EOS.
A comparison of the isothermal compressibilities of all six oils displays identifiable
trends. Figure IV.9 compares the compressibilities for the six oils in this study at two selected
temperatures, 323 and 373 K. The Group IV oils (PAOs) were found to have the highest
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
IIB
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
IIB
300
320
340
360
380
400
420
440
460
480
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
IIB
68
compressibilities followed by the Group III oils, then the Group II oils. The order of the oils was
found to be PAO 8 ≈ PAO 4 > IIIA > IIIB > IIA > IIB, with the differences between IIIB, IIA,
and IIB being relatively low. A similar trend was reported in Guimarey et al.,15 with the poly(α-
olefin) based oil (Group IV) they studied being more compressible than the reference Group III
oil in the study.
The differences in isothermal compressibility across these oils can be attributed to
composition. Figure IV.10 shows a comparison of compressibility versus cyclic molecule
content in the base oil. Group II oils have the highest content of cycloalkanes, followed by
Group III oils (Figures IV.1 and IV.2). Group IV oils have no cyclic molecule content as they
are synthetic oils. Given the trend, Group IV > Group III > Group II, it appears that isothermal
compressibility increases with decreasing cycloalkane content, indicating that these cyclic
molecules potentially pack in a manner that reduces compression effects compared to noncyclic
paraffins.
Figure IV.9. Isothermal compressibility versus pressure for six base oils at 323 K (left) and 373
K (right).
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
IIB
IIA
IIIB
IIIA
PAO 4
PAO 8
323 K
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
IIB
IIA
IIIB
IIIA
PAO 4PAO 8
373 K
69
Figure IV.10. Isothermal compressibility versus mass percent cycloparaffin content at 373 K
and 10 MPa for all base oils.
When comparing the thermal expansion coefficients for the oils studied, there were no
clear trends to be found. While oil IIIA had noticeably higher values for the expansion
coefficient, the other five oils had similar values. Figure IV.11 shows a comparison of thermal
expansion coefficient versus temperature for all six oils at two selected pressures, 10 and 40
MPa, while Figure IV.12 shows expansion coefficient versus composition. Unlike isothermal
compressibility, there is no clear effect of the cycloalkane content on the thermal expansion
coefficient.
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
0 20 40 60 80
κT
(1/M
Pa)
Mass % Cycloalkanes
373 K
10 MPa
70
Figure IV.11. Isobaric thermal expansion coefficient versus temperature for six base oils at 10
MPa (left) and 40 MPa (right).
Figure IV.12. Isobaric thermal expansion coefficient versus mass percent cycloparaffin content
at 373 K and 10 MPa for all base oils.
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
IIB
IIA
IIIAIIIB
PAO 4
PAO 8
10 MPa
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
250 300 350 400 450
βP
(1/K
)
Temperature (K)
IIB
IIAIIIA
IIIBPAO 4
PAO 8
40 MPa
0.0009
0.00092
0.00094
0.00096
0.00098
0.001
0.00102
0.00104
0.00106
0.00108
0.0011
0 20 40 60 80
βP
(1/K
)
Mass % Cycloalkanes
373 K
10 MPa
71
With isothermal compressibility and isobaric thermal expansion coefficient determined,
internal pressure can be calculated using equation III.19. Figure IV.13 compares internal
pressure of all six oils at both 323 and 373 K. As shown in equations III.19, the internal pressure
is proportional to the inverse of isothermal compressibility. Due to this, the trends associated
with internal pressure were also found to be inverted. Base oil IIA was found to have the highest
values across the range of temperatures and pressures examined in this study. The overall order
of the oils studied in terms of internal pressure was found to be IIA > IIB > IIIB > IIIA > PAO 4
> PAO 8. The group IV oils, PAO 4 and PAO 8, had much lower values of internal pressure
than the other four oils. Figure IV.14 shows the effect of composition on internal pressure.
Internal pressure was shown to increase with cycloalkane content.
Figure IV.13. Internal pressure versus pressure for six base oils at 323 K (left) and 373 K
(right).
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
IIB
IIA
IIIA
IIIB
PAO 4
PAO 8
323 K
300
310
320
330
340
350
360
370
380
390
400
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
IIB
IIA
IIIA
IIIB
PAO 4
PAO 8
373 K
72
Figure IV.14. Internal pressure versus mass percent cycloparaffin content at 373 K and 10 MPa
for all base oils.
The isothermal compressibility and internal pressure were found to be dependent on oil
composition, specifically cycloalkane content. This compositional effect was not found in the
isobaric thermal expansion coefficient. Isothermal compressibility is proportional to the partial
derivative of density with respect to pressure, while thermal expansion coefficient is related to
the partial derivative of density with respect to temperature (equations III.17 and III.18). The
effect of composition appears to change the sensitivity of the density of these base oils with
respect to pressure. The ring structures potentially allow for more efficient packing, reducing the
effect of pressure on density of the Group II and Group III oils, and with it, isothermal
compressibility. Given that lubricants operate by forming thin films under high pressure and
shear conditions, the change in the effect of pressure potentially affects this film formation.
Being inversely related to compressibility, internal pressure has also been shown to be affected
by the amount of cycloalkanes in the oil. Internal pressure is a measure of the overall effect of
the attractive and repulsive intermolecular forces. As internal pressure increases, attractive
forces become more dominant. As the amount of cyclic content increases, the more efficient
packing in the oil causes an increase in attractive intermolecular forces versus repulsive forces.
250
270
290
310
330
350
370
390
410
0 20 40 60 80
Inte
rnal
Pre
ssu
re (
MP
a)
Mass % Cycloalkanes
373 K
10 MPa
73
IV.3.3. Viscosity and Modelling
Viscosity data for all six base oils were collected in the high pressure rotational
viscometer described in Chapter II. Due to the high viscosities at 298 K, decoupling occurred for
several oils. At 298 K, viscosity data were collected for oils PAO 4 and IIIA from 300-800 rpm,
for oil IIA from 300-700 rpm, and for oils IIB, IIIB, and PAO 8 from 100-400 rpm. Figure
IV.15 shows the viscosity for oil IIB at 500 rpm (except at 298 K, where 300 rpm data were
shown). For all six oils, viscosity was shown to decrease with temperature and increase with
pressure. Figure IV.16 compares viscosity versus pressure collected at all rotational speeds and
shear stress to shear rate for oil IIB at 323 K. The isothermal viscosity data overlapped for all
rotational speeds, showing Newtonian behavior. All six oils were found to be Newtonian in
behavior in the measured range of shear rates.
Figure IV.15. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the 298 K run).
0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
298 K
(300 rpm)
323 K
348 K373 K
IIB
500 rpm
74
Figure IV.16. Viscosity versus pressure (left) and average shear stress at 10 MPa versus shear
rate (right) for IIB at 323 K. All data points at rotational speeds from 300 to 800 rpm are
represented in the figure on the left. The linearity of shear stress versus shear rate shows the oil
is Newtonian in behavior.
With viscosity data collected, and the Newtonian behavior of the six oils studied in the
measured range confirmed, the temperature and pressure effects were modeled. Free volume
theory, described in detail in Chapter III and represented by equation III.22, was used. Due to
the Newtonian behavior of the oils studied, only the viscosity data for the 500 rpm runs were
fitted to the model equation. The exception to this were oils IIB, IIIB, and PAO 8 at 298 K as
the 500 rpm data could not be generated due to decoupling. For these oils at 298 K, 300 rpm
data were used (500 rpm data was used for all other temperatures). The fitted parameters are
shown in Table IV.3 for all six oils, along with values for root mean squared deviation (RSME),
percent absolute average deviation (% AAD), and the bias (% ℬ). Figure IV.17 shows the free
volume theory fit for oil IIB compared to the experimental data at all temperatures and 500 rpm.
The viscosity and free volume fits for the remaining five oils can be found in Appendix C. With
the exception of oils IIA and IIIA, the % AAD for each of the studied oils was below 10 %. Oils
IIA and IIIA had lower viscosities than the other four, with the 373 K values falling below the
threshold of sensitivity of the viscometer used, 3 mPa s. The high level of error in the low
temperature measurements could account for the high values of % AAD involved in the model
20
25
30
35
40
45
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
IIB
323 K
300-800 RPM
R² = 0.9995
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 500 1000 1500
Sh
ear
Str
ess
(N/m
2)
Shear Rate (1/s)
IIB
323 K
10 MPa
75
for these two oils. Figure IV.18 compares both the data and their fits at 323 K and 500 rpm for
all six oils studied.
Unlike isothermal compressibility and internal pressure, there is no clear trend relating
viscosity to the concentration of cyclic compounds in the oils. The viscosity is more closely
related to molecular weight for the oils studied, indicating that there are differences in what
intermolecular interactions influence the derived thermodynamic properties compared to viscous
effects. These differences indicate that it is necessary to examine both viscosity and the
volumetric effects simultaneously as both viscosity and compressibility are useful in the design
of lubricants for mechanical systems such as automobiles.
Table IV.3. Parameters for the free volume theory of viscosity.
IIA IIB IIIA IIIB PAO 4 PAO 8
L (cm) X 105 8.09 2.49 18.7 12.2 31.8 10.3
α (MPa*cm6/g*mol) 413600 1089000 447200 638600 728400 936200
B X 103 4.44 1.17 3.480 2.46 1.57 1.44
RMSE (mPa s) 0.845 1.21 0.735 0.922 1.06 1.79
% AAD 28.8 10.0 25.3 5.07 8.98 5.53
% ℬ -23.5 8.15 -20.5 -0.885 5.28 4.15
76
Figure IV.17. Viscosity versus pressure for base oil IIB at 500 rpm (300 rpm for the 298 K run).
Free volume correlation fit is represented by black dots.
Figure IV.18. Viscosity versus pressure for six base oils at 323 K and 500 rpm. Free volume
correlation fit is represented by black dots.
0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
298 K
(300 rpm)
323 K
348 K373 K
IIB
500 rpm
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4
PAO 8
IIA
IIB
IIIA
IIIB
323 K
500 rpm
77
IV.4 Conclusions
Density data for six base oils were collected across a range of temperatures and pressures
and modeled using the Sanchez-Lacombe equation of state. Absolute average deviations were
found to be in range of 0.130 to 0.204 %. Both isothermal compressibility and internal pressure
were found to be concentration dependent, specifically affected by the concentration of cyclic
compounds in the base oils. This dependency was not seen in the thermal expansion
coefficients. These trends appear to indicate that pressure effects are particularly impacted by
the packing of these cycloalkanes compared to chained paraffins.
All six base oils were found to be Newtonian in nature in the measured range. The
viscosity data were then fit to the free volume theory in conjunction with the Sanchez-Lacombe
equation of state. For all but two of the oils, the absolute average deviations for the free volume
theory fits of the viscosity were found to be below 10 %. For oils IIA and IIIA, absolute average
deviation was around 25 % due to the low viscosities of these two oils at 373 K compared to the
sensitivity of the instrument. Viscosity was found not to be driven by the same concentration
effects as isothermal compressibility and internal pressure, indicating that the intermolecular
interactions driving viscosity are more complex.
IV.5 References
1. R.I. Taylor, R.C. Coy, Improved Fuel Efficiency by Lubricant Design: A Review, Proc.
Inst. Mech. Eng. J., 2000, 214, 1-15.
2. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric
Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Ind. Eng. Chem. Res.,
2013, 52, 17725-17734.
3. G.D. Yadav, N.S. Doshi, Development of a Green Process for Poly-α-olefin Based
Lubricants, Green Chem., 2002, 4, 528-540.
4. P.W. Michael, J.M. Garcia, S.S. Bair, M.T. Devlin, A. Martini, Lubricant Chemistry and
Rheology Effects on Hydraulic Motor Starting Efficiency, Tribol. Trans. 2002, 55,
549−557.
5. R. Feng, K.T. Ramesh, On the Compressibility of Elastohydrodynamic Lubricants, J.
Tribology, 1993, 115, 557-559.
6. K.T. Ramesh, The Short-Time Compressibility of Elastohydrodynamic Lubricants, J.
Tribology, 1991, 113, 361-371.
7. E.H. Okrent, The Effect of Lubricant Viscosity and Composition on Engine Friction and
Bearing Wear, ASLE Trans., 1961, 4, 97-108.
78
8. K. Inoue, H. Watanabe, Interactions of Engine Oil Additives, ASLE Transactions, 1982,
26, 189-199.
9. J.J. Rodgers, N.E. Gallopoulos, Friction Characteristics of Some Automatic Transmission
Fluid Components, ASLE Trans., 1966, 10, 102-114.
10. M. Nobelen, S. Hoppe, C. Fonteix, F. Pla, M. Dupire, B. Jacques, Modeling of the
Rheological Behavior of Polyethylene/Supercritical CO2 Solutions, Chem. Eng. Sci.,
2006, 61, 5334-5345.
11. J.W. Robinson, Y. Zhou, J. Qu, R. Erck, L. Cosimbescu, Effects of Star-Shaped
Poly(alkyl methacrylate) Arm Uniformity on Lubricant Properties, J. Appl. Polym. Sci.,
2016, 133, 1-11.
12. N. Chandak, A. George, A.A. Hamadi, M. Berthod, Optimization of Hydrocracker Pilot
Plant Operation for Base Oil Production, Catal. Today, 2016, 271, 199-206.
13. I. Dzidic, H.A. Peterson, P.A. Wadsworth, H.V. Hart, Townsend Discharge Nitric Oxide
Chemical Ionization Gas Chromatography/Mass Spectrometry for Hydrocarbon Analysis
of the Middle Distillates. Anal. Chem., 1992, 64, 2227.
14. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and
Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &
Engineering Chemistry Research, 57 (2018) 17266-17275.
15. M.J.G. Guimarey, M.J.P. Comunas, E.R. Lopez, A. Amigo, J. Fernandez, Volumetric
Behavior of Some Motor and Gear-Boxes Oils at High Pressure: Compressibility
Estimation at EHL Conditions, Ind. Eng. Chem. Res., 2017, 56, 10877-10885.
79
V. Base Oils with Additives
V.1 Introduction
In this chapter, we discuss the volumetric properties and viscosity of a base oil modified
by the addition of polymeric additive along with two automatic transmission fluids (ATFs). As
discussed in Chapter I and Chapter IV, the choice of lubricants in automotive applications can
have a significant effect on fuel efficiency.1 Engine oils and ATFs are not simple fluids. These
lubricants are composed of a base oil with a number of additives meant to fulfill specific roles
they have been tailored to, including detergents, dispersants, friction modifiers, and anti-wear
additives.2-4 One particular class of additive is the viscosity index modifier.
As stated earlier, the viscosity index is an empirical measure of the effect of temperature
on viscosity. The higher the viscosity index, the less effect temperature has on viscosity. With
the viscosity of a lubricant being important in determining fuel efficiency,5-7 it is important to
lower the viscosity range across the temperatures at which the engine or transmission operate at
to ensure uniform performance. Viscosity index is calculated by comparing the kinematic
viscosities of an oil at 313 K and 373 K to known standards:
𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦𝐼𝑛𝑑𝑒𝑥 = 100𝜈𝑉𝐼0−𝜈313
𝜈𝑉𝐼0−𝜈𝑉𝐼100 V.1
where ν313 is the kinematic viscosity of the measured oil at 313 K, νVI 0 is the kinematic viscosity
at 313 K of an oil standard with a viscosity index of 0 and the same kinematic viscosity as the
measured oil at 373 K, and νVI 100 is the kinematic viscosity at 313 K of an oil standard with a
viscosity index of 100 and the same kinematic viscosity as the measured oil at 373 K.8
V.1.1 Objectives
To understand the effect of viscosity index modifying polymers on the properties of base
oils, density measurements were carried out over a pressure range of 10-40 MPa and a
temperature range of 298-398 K on mixtures of base oil PAO 4 with two polymeric additives, up
to 7.12 mass percent. Alongside the density measurements, viscosity measurements were carried
80
out across a pressure range of 10-40 MPa, a temperature range of 298-373 K, and rotational
speeds from 300-800 rpm. Additionally, densities and viscosities were determined for two fully
formulated automatic transmission fluids.
The objective was again to use the collected data to apply a holistic approach, described
in Chapter IV, to describe the density, derived thermodynamic properties, and viscosity. To
accomplish this, following the methodology described in Chapter III, density data were fit to the
Sanchez-Lacombe equation of state (S-L EOS) while viscosity data were fit to a coupled model,
the free volume theory. Using the S-L EOS fits, the derived thermodynamic properties were
calculated. By examining all these properties simultaneously, the effect of polymeric additives
on base oils could be assessed. Finally, the density of two ATFs was modeled. Due to an
incomplete description of the compositions of the ATFs, instead of the S-L EOS, the Tait
equation was used in modeling these lubricants.
V.2 Materials and Methods
Mixtures of synthetic base oil PAO 4, composed completely of poly(α-olefins), with
viscosity index modifiers were provided by Afton Chemical Corp. These mixtures were used as
received. These mixtures were made using two different viscosity index modifiers. These
viscosity index modifiers were indicated to be both polymethacrylate based polymers. Both
additives have alkyl chains of varying length coming off the methacrylate mers. The difference
between the two additives is the existence of amine end-groups on some of these alkyl chains for
Polymer 1 (3-4% of these chains contain a N(CH3)2 group), while Polymer 2 had no amine
functionality at all. Figures V.1 and V.2 shows the structure of these two additives.
Figure V.1. Structure of viscosity index modifier Polymer 1.
81
Figure V.2. Structure of viscosity index modifier Polymer 2.
In addition to mixtures of a base oil with an individual additive, fully formulated
automatic transmission fluids were studied. Two ATFs were provided by Afton Chemical Corp,
one experimental and one commercial. They were used as received.
V.3 Results and Discussion
V.3.1 Viscosity Index Modifiers
Experimental density data for mixtures of base oil PAO 4 with two polymer additives at
concentrations up to 7 mass % (4 mixtures with each polymer) were analyzed. Figures V.3 and
V.4 compare the densities of PAO 4 and its mixtures with both viscosity index modifiers at 323
K. Densities for PAO 4 were determined experimentally in a previous study conducted in our
lab.5 Additionally, these mixtures were treated as pseudo-single component fluids and modeled
with the Sanchez-Lacombe equation of state. The S-L EOS parameters, and derived
thermodynamic properties, for base oil PAO 4 were calculated in our previous publication in
Industrial & Engineering Chemistry Research.9 To effectively model these mixtures, knowledge
of the molecular weight is needed. As all mixtures were composed of concentrations of > 90
mass % PAO 4, the average molecular weight of the pure base oil (MW of 489 g/mol) was used
in all fits. Tables V.1 and V.2 show the calculated S-L parameters for these mixtures along with
root mean squared deviation (RSME), percent absolute average deviation (% AAD), and bias (%
ℬ). The S-L EOS fits for all these mixtures were found to have % AADs less than 0.3 For all
82
mixtures, both with Polymer 1 and Polymer 2, a small reduction of density is seen. The densities
of these mixtures are within 1 % of each other, the error associated with these measurements,
making it difficult to determine a trend in the effect of polymer concentration on density. The
experimental densities and resulting S-L EOS fits for all mixtures can be found in Appendix D.
Figure V.3. Density versus pressure for PAO 4 and its mixtures with viscosity index modifier
Polymer 1 at 323 K.
0.78
0.79
0.8
0.81
0.82
0.83
0.84
0.85
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
Polymer 1
323 K PAO 4
0.71 %
7.12 %
1.42 %
2.85 %
83
Figure V.4. Density versus pressure for PAO 4 and its mixtures with viscosity index modifier
Polymer 2 at 323 K.
Table V.1. S-L parameters for mixtures of PAO 4 with Polymer 1
PAO 4 0.71 % 1.42 % 2.85 % 7.12 %
P* (MPa) 433.62 447.50 455.80 473.49 311.29
T* (K) 544.10 530.08 529.95 523.17 576.05
ρ* (g/cm3) 0.91160 0.89343 0.90072 0.90447 0.88624
RMSE (g/cm3) 0.00198 0.00185 0.00206 0.00284 0.00213
% AAD 0.201 0.195 0.212 0.298 0.221
% ℬ -0.000177 -0.000260 -0.00086 -0.0283 -0.00066
0.79
0.795
0.8
0.805
0.81
0.815
0.82
0.825
0.83
0.835
0.84
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
Polymer 2
323 KPAO 4
0.70 %
1.40 %
2.80 %
7.01 %
84
Table V.2. S-L parameters for mixtures of PAO 4 with Polymer 2
PAO 4 0.70 % 1.40 % 2.80 % 7.01 %
P* (MPa) 433.62 496.64 547.29 460.72 402.04
T* (K) 544.10 516.55 469.18 535.53 522.81
ρ* (g/cm3) 0.91160 0.90588 0.89350 0.89927 0.90184
RMSE (g/cm3) 0.00198 0.00190 0.00182 0.00166 0.00266
% AAD 0.201 0.190 0.182 0.167 0.277
% ℬ -0.000177 0.0362 -0.00066 -0.00027 -0.00089
Once the density data were fit to the S-L equation of state, the derived thermodynamic
properties for these mixtures were calculated using equations III.17-19. The thermodynamic
properties across the full range of temperatures and pressures examined in this study for the
mixtures of PAO 4 with viscosity index modifiers can be found in Appendix D.
As with the pure base oils from Chapter IV, isothermal compressibility was found to
increase with temperature and decrease with pressure. Additionally, compressibility was found
to be influenced by composition. Figure V.5 shows a comparison of isothermal compressibility
versus pressure at 323 K for all mixtures. Figure V.6 shows isothermal compressibility versus
mass % polymer at 323 K and 10 MPa. Compressibility was found to be slightly high in
mixtures with Polymer 1 up to concentrations of 2.85 mass % polymer. Isothermal
compressibility was found to increase upon addition of around 7 mass % polymer for both
additives.
85
Figure V.5. Isothermal compressibility versus pressure for PAO 4 and its mixtures with
viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.
Figure V.6. Isothermal compressibility versus mass percent polymer at 323 K and 10 MPa for
mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.
As with the pure base oils, isobaric thermal expansion coefficient for these mixtures was
found to increase with temperature and decrease with pressure. Thermal expansion coefficient
0.0005
0.00055
0.0006
0.00065
0.0007
0.00075
0.0008
0.00085
0.0009
0.00095
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
Polymer 1
323 K
7.12%
0.71%
2.85%
1.42%
PAO 4
0.0005
0.00055
0.0006
0.00065
0.0007
0.00075
0.0008
0.00085
0.0009
0.00095
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
Polymer 2
323 K
7.01%
0.70%
2.80%
1.40%
PAO 4
0.0007
0.00075
0.0008
0.00085
0.0009
0.00095
0 2 4 6 8
κT
(1/M
Pa)
Mass % Polymer
323 K
10 MPa
Polymer 1
Polymer 2
86
was found to be affected by polymer composition. Figure V.7 shows isobaric thermal expansion
coefficient versus temperature at 10 MPa for mixtures of PAO 4 with Polymer 1 and Polymer 2.
Figure V.8 shows thermal expansion coefficient versus mass percent polymer of both additives.
The thermal expansion coefficient showed an initial increase upon the addition of a small amount
of either polymer (0.7 mass %). For Polymer 1, expansivity continued to increase with polymer
concentration up to 2.85 mass % polymer, then dropped at the high concentration mixture (7
mass %). For Polymer 2, After the initial increase in expansivity, as polymer concentration
increased thermal expansion coefficient stabilized at a value between the pure PAO 4 and 0.70
mass % polymer mixture.
Figure V.7. Isobaric thermal expansion coefficient versus temperature for PAO 4 and its
mixtures with viscosity index modifiers Polymer 1 (left) and Polymer 2 (right) at 10 MPa.
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
250 300 350 400 450
βP
(1/K
)
Temperature (K)
Polymer 1
10 MPa
PAO 4
7.12%
2.85%
0.71%
1.42%
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
250 300 350 400 450
βP
(1/K
)
Temperature (K)
Polymer 2
10 MPa
PAO 4
7.01%
2.80%
0.70%
1.40%
87
Figure V.8. Isobaric thermal expansion coefficient versus mass percent polymer at 323 K and
10 MPa for mixtures of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.
The internal pressure for these mixtures was found to decrease with temperature and
increase with pressure. As with isothermal compressibility and thermal expansion coefficient,
internal pressure was found to be affected by polymer composition. Figure V.9 shows internal
pressure versus pressure at 323 K for mixtures of PAO 4 with both additives Polymer 1 and
Polymer 2. Figure V.10 shows internal pressure versus mass percent polymer of both additives.
For mixtures with Polymer 1, internal pressure increased with additive concentration up to 2.85
mass % polymer. Internal pressure decreased to significantly lower than the pure base oil value
upon the addition of 7 mass % polymer. For mixtures with polymer 2, internal pressure initially
increased with polymer addition (0.7 mass % polymer). After that initial increase, internal
pressure decreased with increasing concentration of Polymer 2. Additionally, the internal
pressures were found to be higher for mixtures with Polymer 2 than those with Polymer 1,
indicating that the overall attractive intermolecular interactions were stronger in the mixtures
with Polymer 2. This could indicate that the addition of the amine groups on Polymer 1 adds
additional repulsive interactions into the lubricant system.
0.0007
0.00075
0.0008
0.00085
0.0009
0.00095
0.001
0 2 4 6 8
βP
(1/K
)
Mass % Polymer
323 K
10 MPaPolymer 1
Polymer 2
88
Figure V.9. Internal pressure versus pressure for PAO 4 and its mixtures with viscosity index
modifiers Polymer 1 (left) and Polymer 2 (right) at 323 K.
Figure V.10. Internal pressure versus mass percent polymer at 323 K and 10 MPa for mixtures
of PAO 4 with viscosity index modifiers Polymer 1 and Polymer 2.
Viscosity data for mixtures of base oil PAO 4 with two polymer additives at
concentrations up to 7 mass % were collected across a range of 10-40 MPa and 300-800 rpm at
250
270
290
310
330
350
370
390
410
430
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
Polymer 1
323 K
7.12%
PAO 40.71%
1.42%
2.85%
250
270
290
310
330
350
370
390
410
430
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
Polymer 1
323 K
7.01%
PAO 4
0.70%
1.40% 2.80%
250
275
300
325
350
375
400
0 2 4 6 8
Inte
rnal
Pre
ssu
re (
MP
a)
Mass % Polymer
323 K
10 MPaPolymer 2
Polymer 1
89
isotherms of 298, 323, 348, and 373 K. All mixtures of PAO 4 with Polymer 1 and Polymer 2
were Newtonian in nature. Figures V.11 and V.12 compare the viscosities of these mixtures at
both 298 and 323 K and 500 rpm. At 298 K, there is a decrease in viscosity with the addition of
these polymeric additives at lower concentrations (below 2.85 mass %), with viscosity
decreasing by approximately 3.5 mPa s at all concentrations for Polymer 1 and 5 mPa s at
concentrations of 0.70 and 1.40 mass %, and 3 mPa s at a concentration of 2.80 mass %, for
Polymer 2. At temperatures of 323 K and above, this decrease in viscosity was not readily seen.
For the mixtures involving high concentrations of polymer, above 7 mass %, the viscosity
increased at all temperatures, with an increase of 20 mPa s for Polymer 1 and 16 mPa s for
Polymer 2 at 298 K. In addition, viscosity data was fit to the free volume theory (equation
III.22) in conjunction with the Sanchez-Lacombe equation of state. As with the S-L EOS fits,
these mixtures were treated as pseudo-single component. Tables V.3 and V.4 show the fitted
parameters for the free volume theory along with RSME, % AAD, and % ℬ. The full range of
viscosity data and corresponding free volume theory fits for the mixtures studied in this chapter
can be found in Appendix D.
Figure V.11. Viscosity versus pressure for mixtures of PAO 4 with viscosity index modifiers
Polymer 1 (left) and Polymer 2 (right) at 298 K and 500 rpm.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4 + Polymer 1
298 K
500 rpm 7.12 %
0.71 %
1.42 %2.85 %
PAO 4
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4 + Polymer 2
298 K
500 rpm 7.01 %
0.70 %1.40 %2.80 %
PAO 4
90
Figure V.12. Viscosity versus pressure for mixtures of PAO 4 with viscosity index modifiers
Polymer 1 (left) and Polymer 2 (right) at 323 K and 500 rpm.
Table V.3. Parameters for the free volume theory of viscosity for mixtures of PAO 4 and
viscosity index modifier Polymer 1.
PAO 4 0.71 % 1.42 % 2.85 % 7.12 %
L (cm) X 105 31.8 18.8 67.2 43.8 44.8
α (MPa*cm6/g*mol) 728000 779000 596000 715000 830000
B X 103 1.57 1.56 1.94 1.77 1.31
RMSE (mPa s) 1.06 0.417 1.24 0.586 0.795
% AAD 8.98 5.17 12.4 4.69 4.64
% ℬ 5.28 0.565 2.01 1.73 -0.34
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4 + Polymer 1
323 K
500 rpm7.12 %
0.71 %
1.42 %
2.85 %
PAO 4
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4 + Polymer 2
323 K
500 rpm
7.01 %
0.70 %1.40 %
2.40 %
PAO 4
91
Table V.4. Parameters for the free volume theory of viscosity for mixtures of PAO 4 and
viscosity index modifier Polymer 2.
PAO 4 0.70 % 1.40 % 2.80 % 7.01 %
L (cm) X 105 31.8 48.1 80.5 39.7 55.6
α (MPa*cm6/g*mol) 728000 621000 571000 611000 728000
B X 103 1.57 1.89 2.01 2.02 1.57
RMSE (mPa s) 1.06 0.573 1.07 0.537 0.901
% AAD 8.98 5.67 8.87 6.21 5.36
% ℬ 5.28 0.582 5.14 -2.91 2.99
The addition of these viscosity index modifiers has an effect on volumetric,
thermodynamic, and transport properties of the original base oils they are added to. Of particular
interest is the increase in isothermal compressibility at higher polymer concentrations. Knowing
how pressure effects the change in density, and volume, is important for understanding film
formation of these mixtures under lubrication conditions. Additionally, isobaric thermal
expansion coefficient and internal pressure were found to initially increase with a small amount
of polymer additive, with both properties dropping as polymer concentration increased. Internal
pressure is a measure of the overall intermolecular interactions. The higher values of internal
pressure for mixtures with Polymer 1 versus Polymer 2 can be attributed to the lack of amine
groups. The alkyl chains interact with the poly(α-olefins) of the pure base oil, while the amine
groups disrupt these interactions to a degree. Additionally, isobaric thermal expansion
coefficient (equation III.18) is proportional to the partial derivative of density with regards to
temperature. The initial addition of polymer causes a change in the effect of temperature on the
fluid. At higher concentrations, the thermal expansion coefficient drops as the polymer
interactions start to become more dominant.
This is the inverse of viscosity, which decreases at 298 K at low concentrations. These
additives are meant to change the viscosity index, a measure of the effect of temperature on
viscosity. These oils are selected due to their low viscosities at higher temperatures, leading to
an increase fuel efficiency. Even so, these oils need to operate over a range of temperatures,
making it necessary to reduce the effect of temperature on viscosity. By reducing viscosity at
92
low temperature conditions while keeping them constant at higher temperatures, viscosity index
can be increased without changing the performance at high temperature conditions the base oil
was selected for. At higher concentrations, in the case of this study above 7 mass %, polymeric
interactions take over leading to an increase in viscosity at all temperatures. The addition of
these additives has a particular effect on the effect of temperature on these fluids.
V.3.2 Automatic Transmission Fluids
The effect of temperature and pressure on the volumetric properties and viscosity of two
ATFs, an experimental blend and a commercial sample, was analyzed. The use of the S-L EOS
requires knowledge of the molecular weights of the constituents. These ATFs are composed of a
base oil (already a complex mixture) and numerous additives. Without a detailed description of
the composition of these ATFs, it is difficult to employ the S-L EOS. Due to the complexity of
these fluids, the Tait equation (equations III.1-3) were used instead of the S-L EOS in the
modeling of these ATFs. Figure V.13 shows density versus pressure for these ATFs at 323 and
373 K. Table V.5 shows the Tait equation parameters along with RSME, % AAD, and % ℬ.
The commercial ATF was shown to have higher densities than the experimental blend at the
temperatures and pressures in which measurements were carried out. The % AADs of both fits
were found to be approximately 0.1 %.
Utilizing the Tait equation fits, isothermal compressibility, isobaric thermal expansion
coefficient, and internal pressure were calculated. Figures V.14-16 show comparisons of the
derived thermodynamic properties of both ATFs. Isothermal compressibility was found to be
similar for both samples. The experimental ATF was found to have higher values of isobaric
thermal expansion coefficient and internal pressure. The full densities, Tait equation fits, and
derived thermodynamic properties for both ATFs can be found in Appendix D.
Figures V.17 and V.18 show viscosity versus pressure for these ATFs. Both the
experimental and commercial ATF samples were found to exhibit Newtonian behavior. The
commercial ATF was found to have higher viscosities than the experimental one, though at 323
K, this difference was within the 5 % error associated with the viscosity measurement. Due to
lack of compositional information, these viscosities were not modeled with the free volume
theory. Select viscosities are tabulated in Appendix D.
93
Figure V.13. Density versus pressure for an experimental and a commercial ATF at 323 K (left)
and 373 K (right). Tait equation fits are shown as black diamonds.
Table V.5. Tait equation parameters for automatic transmission fluids
Experimental
ATF
Commercial
ATF
aρ (1/K) 0.000934 0.000884
ρR (g/cm3) 0.860 0.870
Tr (K) 298 298
K0' 10.0 10.0
K00 (MPa) 9070 8270
βK (1/K) 0.00586 0.00561
RSME 0.00114 0.000972
% AAD 0.111 0.0936
% ℬ -0.000740 0.00400
0.84
0.845
0.85
0.855
0.86
0.865
0.87
0.875
0.88
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
323 KCommercial ATF
Experimental ATF
0.8
0.81
0.82
0.83
0.84
0.85
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
373 KCommercial ATF
Experimental ATF
94
Figure V.14. Isothermal compressibility versus pressure for an experimental and a commercial
ATF at 323 K (left) and 373 K (right).
Figure V.15. Isobaric thermal expansion coefficient versus temperature for an experimental and
a commercial ATF at 10 MPa (left) and 40 MPa (right).
0.0005
0.00055
0.0006
0.00065
0.0007
0.00075
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
323 K
Commercial ATF
Experimental ATF
0.00065
0.0007
0.00075
0.0008
0.00085
0.0009
0.00095
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
373 KExperimental ATF
Commercial ATF
0.0008
0.00082
0.00084
0.00086
0.00088
0.0009
0.00092
0.00094
0.00096
0.00098
0.001
250 300 350 400 450
Isob
ari
c E
xp
an
sivit
y (
1/K
)
Temperature (K)
10 MPa Experimental ATF
Commercial ATF
0.00075
0.00077
0.00079
0.00081
0.00083
0.00085
0.00087
0.00089
250 300 350 400 450
Isob
ari
c (1
/K)
Pressure (MPa)
40 MPa
Experimental ATF
Commercial ATF
95
Figure V.16. Internal pressure versus pressure for an experimental and a commercial ATF at
323 K (left) and 373 K (right).
Figure V.17. Viscosity versus pressure for an experimental ATF (left) and a commercial ATF
(right).
350
360
370
380
390
400
410
420
430
440
450
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
323 KExperimental ATF
Commercial ATF
350
360
370
380
390
400
410
420
430
440
450
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
373 K
Experimental ATF
Commercial ATF
0
20
40
60
80
100
120
0 10 20 30 40 50
Vis
cosi
ty (
cP)
Pressure (MPa)
Experimental ATF
500 RPM
298 K (400 RPM)
323 K
348 K
373 K0
20
40
60
80
100
120
0 10 20 30 40 50
Vis
cosi
ty (
cP)
Pressure (MPa)
Commercial ATF
500 RPM
298 K (400 RPM)
323 K
348 K
373 K
96
Figure V.18. Viscosity versus pressure for an experimental and a commercial ATF at 323 K and
500 rpm. Viscosity data are shown on the left, while error bars, showing that both ATFs have
similar viscosities within the measurement error, are shown on the right.
V.4 Conclusions
Isothermal compressibility was found to increase at higher polymer concentrations
(around 7 mass % polymer). Isobaric thermal expansion coefficient and internal pressure
initially increased with the addition of a small amount of polymer (around 0.7 mass %), followed
by an eventual drop in both properties as polymer concentration increased. Internal pressure was
found to be higher for mixtures with Polymer 2 than additive Polymer 1. This could be due to
the presence of a small number of amine functional groups disrupting carbon-carbon interactions
between the poly(α-olefins) of the base oil used and the polymeric additives in the case of
Polymer 1. Viscosity was found to initially drop at 298 K, while staying the same within the
error associated with the viscosity measurements at higher temperatures (323 K and above), for
concentrations below 3 mass % polymer. This should correspond with an increase in viscosity
index. At 7 mass % polymer, for both additives, viscosity increased at all temperatures as the
polymer chains interact with each other instead of just the base oil at these higher concentrations.
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
323 K
500 rpmCommercial ATF
Experimental ATF
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
323 K
500 rpmCommercial ATF
Experimental ATF
97
For the automatic transmission fluids, the Tait equation was used model density. A
comparison of the derived thermodynamic properties revealed that while there were differences
in isobaric thermal expansion coefficient and internal pressure, both of these transmission fluids
had similar isothermal compressibilities and viscosities. Knowledge of compressibility and
viscosity is needed for the design of effective lubricants.
V.5 References
1. R.I. Taylor, R.C. Coy, Improved Fuel Efficiency by Lubricant Design: A Review, Proc.
Inst. Mech. Eng. J., 2000, 214, 1-15.
2. E.H. Okrent, The Effect of Lubricant Viscosity and Composition on Engine Friction and
Bearing Wear, ASLE Trans., 1961, 4, 97-108.
3. K. Inoue, H. Watanabe, Interactions of Engine Oil Additives, ASLE Transactions, 1982,
26, 189-199.
4. J.J. Rodgers, N.E. Gallopoulos, Friction Characteristics of Some Automatic Transmission
Fluid Components, ASLE Trans., 1966, 10, 102-114.
5. H.E. Grandelli, J.S. Dickmann, M.T. Devlin, J.C. Hassler, E. Kiran, Volumetric
Properties and Internal Pressure of Poly(alpha-olefin) Base Oils, Ind. Eng. Chem. Res.,
2013, 52, 17725-17734.
6. G.D. Yadav, N.S. Doshi, Development of a Green Process for Poly-α-olefin Based
Lubricants, Green Chem., 2002, 4, 528-540.
7. P.W. Michael, J.M. Garcia, S.S. Bair, M.T. Devlin, A. Martini, Lubricant Chemistry and
Rheology Effects on Hydraulic Motor Starting Efficiency, Tribol. Trans. 2002, 55,
549−557.
8. J.W. Robinson, Y. Zhou, J. Qu, R. Erck, L. Cosimbescu, Effects of Star-Shaped
Poly(alkyl methacrylate) Arm Uniformity on Lubricant Properties, J. Appl. Polym. Sci.,
2016, 133, 1-11.
9. J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and
Viscosity of Base Oils Used in Automotive Lubricants and Their Modeling, Industrial &
Engineering Chemistry Research, 57 (2018) 17266-17275.
98
VI. Ionic Liquids
VI.1 Introduction
Ionic liquids (ILs) are a class of salts with melting points below 100oC that are known for
their unique properties, such as negligible vapor pressure, electrochemical properties, and
potential thermal stability.1-3 The choice of cation and anion, along with the modification of any
functional groups on the ions, has a significant effect on the physical and solvent properties of
these salts. The properties associated with these fluids, specifically the low melting points but
also including viscosity and solubility parameter, are attributed to the structure of the ions, with
the cations being composed of bulky, often asymmetric, organic structures that inhibit the
association between the cation and ion, preventing crystallization.1 It has been estimated that
there are at least 1012 possible combinations of cation and anion that can form an IL.1 Due to the
number of possible ion pairs alongside the wide range of variation of the physical and solvent
properties of these materials, ILs have been described as designer solvents.4,5
The negligible vapor pressures and designer nature of these potential solvents has led to
increasing interest in using these ILs as replacements for volatile organic compounds.1 More
specifically, there has been growing body of work in the literature on the utilization of ILs in a
wide range of applications, including polymer processing and synthesis, CO2 capture, lithium ion
batteries, and biomass processing.6-17 In addition to utilizing ILs as a designer solvent, it can be
beneficial to add a cosolvent as a parameter to tune the solvent properties of the IL.18 The
addition of a cosolvent also adds the potential to increase the compressibility of a system,
allowing for the use of pressure as an additional tuning parameter. Due to the range of possible
options, effectively choosing an IL and cosolvent for a process requires knowledge of the
volumetric properties and viscosity of these mixtures across a range of temperatures and
pressures.
VI.1.1 Objectives
To determine the effect of cation and anion choice, along with the addition of a
cosolvent, on the solvent properties of ILs, density measurements were carried out in the
99
variable-volume view-cell on a series of ILs and their mixtures with ethanol. These ILs were
composed of four different variants of 1-alkyl-3-methylimidazolium with two different anions,
chloride and acetate. In addition to the density measurements, viscosity measurements were
carried out on two different ILs and select mixtures of ethanol. Figure VI.1 shows the structures
of the 1-alkyl-3-methylimidazolium cation and chloride and acetate anions that have been
studied.
The density data was modeled as a function of temperature, pressure, and composition
with the Sanchez-Lacombe equation of state (S-L EOS), while the free volume model was used
to describe viscosity. The S-L EOS fits were used to calculate derived thermodynamic
properties, which were in turn used to estimate the Hildebrand solubility parameter. The
solubility parameter was described in terms of alkyl chain length on the cation, anion, along with
temperature, pressure, and ethanol concentration. Finally, the effect of temperature, pressure,
ethanol concentration, and alkyl chain length on viscosity was examined.
Figure VI.1. 1-Alkyl-3-methylimidazolium cation and the chloride and acetate anions. R is an
alkyl group (ranging in length from 2 to 6 in the present thesis).
VI.2 Materials and Methods
ILs 1-ethyl-3-methylimidazolium chloride ([EMIM]Cl, ≥ 95 % purity), 1-ethyl-3-
methylimidazolium acetate ([EMIM]Ac, ≥ 95 % purity), 1-butyl-3-methylimidazolium chloride
([BMIM]Cl, ≥ 95 % purity), and 1-butyl-3-methylimidazolium acetate ([BMIM]Ac, ≥ 95 %
purity) were purchase from Sigma Aldrich. The ILs [EMIM]Ac and [BMIM]Ac were used as
received. [EMIM]Cl and [BMIM]Cl were dried for 48 hours at 343 K in a vacuum oven before
use. ILs 1-propyl-3-methylimidazolium chloride ([PMIM]Cl) and 1-hexyl-3-imidazolium
100
chloride ([HMIM]Cl) were synthesized for use in this study. Ethanol at 100% purity was
purchased from Decon Labs, Inc. 1-Methylimidazole, 1-chloropropane, 1-chlorohexane, and
ethyl acetate were used in the synthesis of ILs. 1-Methylimidazole (≥ 99 % purity), 1-
chloropropane (≥ 98 % purity), and 1-chlorohexane (≥ 99 % purity) were purchased from Sigma-
Aldrich. Ethyl acetate of purity 99.9 % was purchased from Fisher Scientific. Table VI.1 shows
the melting points of these ILs. The melting points were provided by Ionic Liquids Technologies
GmbH and Sigma-Aldrich.
Density data for these six ILs, ethanol, and mixtures of IL with ethanol were collected in
the variable-volume view-cell. Experiments were run from 10-40 MPa along isotherms of 298,
323, 348, 373, and 398 K. Viscosity data for [EMIM]Ac and [BMIM]Ac and their mixtures with
ethanol were collected in the high pressure rotational viscometer from 10-40 MPa at isotherms of
298, 323, 348, and 373 K. Due to restrictions arising from the decoupling of the magnetic
coupling, at certain temperatures, low rotational speeds were used. For [EMIM]Ac, runs were
performed at 100 and 200 rpm at 298 K, 300-800 rpm for all other temperatures. For
[BMIM]Ac, runs were performed at 50 rpm at 298 K, 100-300 rpm at 323 K, and 300-800 rpm at
348 and 373 K. Experimental details on the collection of density and viscosity can be found in
Chapter II. Experimental density data of the pure ILs and ethanol were fit to the S-L EOS.
Mixing rules were employed alongside the pure component values of the equation of state to
model mixtures with ethanol. With the S-L EOS parameters determined, derived thermodynamic
properties isothermal compressibility, isobaric thermal expansion coefficient, and internal
pressure were calculated. Additionally, the free volume theory was used to fit viscosity of the
pure ILs. The use of these models and the resulting calculations are described in further detail in
Chapter III.
101
Table VI.1. Melting Points of the ILs used in this study.
Ionic Liquid Melting Point (K)
[EMIM]Cl 360
[PMIM]Cl 333
[BMIM]Cl 338
[HMIM]Cl 198
[EMIM]Ac 303
[BMIM]Ac 253
VI.2.1 Synthesis
[PMIM]Cl and [HMIM]Cl were synthesized by reacting 1-methylimidazole with 1-
chloroalkane. Ethyl acetate was used as the reaction medium. Figure VI.2 shows the route of
synthesis for [RMIM]Cl, where R represents a propyl or hexyl group. The reaction was carried
out at the boiling point of ethyl acetate (350 K) for 48 hours in a reflux set up. Ice water was
circulated through the reflux column, which was open to the atmosphere. A magnetic stir bar
provided mixing during the reaction. Both [PMIM]Cl and [HMIM]Cl are insoluble in ethyl
acetate. As the reaction progressed, two phases were formed as the IL separated out of the ethyl
acetate. After the reaction was completed, leftover ethyl acetate was removed using a separation
funnel. To remove any unreacted reagents from the IL phase, clean ethyl acetate was added to
the IL and mixing applied. Again, a separation funnel was used to remove the ethyl acetate
phase. This wash step was repeated 5 times. Once the ethyl acetate washing was completed, the
resulting IL was dried in the vacuum oven for 48 hours at 343 K, then stored in a desiccant
chamber.
To determine if the IL was successfully synthesized, and to test for purity, FTIR was run
on the final products. A commercial sample of [HMIM]Cl was purchased from Sigma-Aldrich
(97 % purity) and dried at 343 K for 48 hours in a vacuum oven. The spectra for the synthesized
[HMIM]Cl was compared to both the commercial sample and a reference spectra from Bio-
Rad,19 as seen in Figure VI.3. The commercial sample from Sigma Aldrich was found to have
additional peaks not seen in the synthesized or reference spectra, at 1264, 1095, and 1017 cm-1,
102
indicating that the commercial sample had some unknown impurity not present in the
synthesized sample used in this study. According the Bio-Rad FTIR database, the presence of
these unknown peaks may be attributed to a catalyst.19 The FTIR spectra for [PMIM]Cl can be
found in Appendix E.
Figure VI.2. Route of synthesis for 1-alkyl-3-methylimidazolium chloride. R represents either
a propyl or hexyl group.
Figure VI.3. FTIR comparison of the synthesized [HMIM]Cl to commercial [HMIM]Cl (purity
97 %) and spectra from the Bio-Rad database.19
Commercial
Synthesized
Bio-Rad
103
VI.3 Results and Discussion
VI.3.1 1-Alkyl-3-methylimidazolium Chlorides and their Mixtures with Ethanol
The experimental densities for four ILs with the chloride anion, ethanol, and mixtures of
IL + ethanol (25, 50, and 75 mass percent IL) were compared. Due to the high melting point of
[EMIM]Cl (356 K), data was only collected at 348 K and above for both the pure IL and 75 mass
percent IL mixture with ethanol. While [PMIM]Cl and [BMIM]Cl both have melting points well
above room temperature, density data was collected across the full temperature range, though the
pure [BMIM]Cl run was limited to a pressure of 28 MPa at 298 K. Although the measurement
range for these three ILs included temperatures below the melting point, these ILs are capable of
existing as subcooled melts. This allows for the collection of liquid densities below their melting
points. The density data for the IL [EMIM]Cl and its mixtures with ethanol along with the S-L
EOS parameters for the IL and ethanol have been previously reported in our publication in The
Journal of Supercritical Fluids.18 The S-L EOS characteristic parameters for [EMIM]Cl,
[PMIM]Cl, [BMIM]Cl, and [HMIM]Cl can be found in Table VI.2, along with root mean
squared deviation (RSME), percent absolute average deviation (% AAD), and bias (% ℬ).
Figure VI.4 shows the density data and corresponding S-L EOS fits for both ILs. The % AADs
for [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl were found to be 0.130 %, 0.170 %,
0.145 %, and 0.165 % respectively.
To model the mixtures of IL + ethanol, mixing rules were employed. The mixing rules
employed are described in Chapter III by equations III.7-14. Interaction parameter kij was
determined for all four IL + ethanol systems. Using a constant kij produced reasonable results
for the mixtures involving [EMIM]Cl. However, the RSME of the overall fits to the mixture
data increased with increasing alkyl chain length, from 0.00370 g/cm3 to 0.00906 g/cm3. Due to
this increased error, a concentration dependent kij was used:
𝑘𝑖𝑗 = 𝑘𝐴𝜙𝑖 − 𝑘𝐵 VI.1
where kA and kB are constants and ϕi is the close packed volume fraction of component i as
described by equation III.8. In the case of the present work, kij is represented in terms of the
104
close packed volume fraction of the IL. The constants needed to determine kij can be found in
Table VI.3. Using this concentration dependent kij in conjunction with the mixing rules
described in Chapter III reduces the RSME for [HMIM]Cl by 64% from 0.00906 to 0.00322
g/cm3. The S-L EOS parameters, along with RSME, % AAD, and % ℬ, calculated using mixing
rules for each mixture of [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl with ethanol can be
found in Tables VI.4-7. Figure VI.5 shows density versus pressure for all four ILs and their
mixtures with ethanol at 348 K, along with the corresponding S-L EOS fits. Density was found
to increase with increasing IL concentration. The full range of densities for all mixtures of
[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl with ethanol can be found in Appendix E.
Table VI.2. S-L EOS characteristic parameters for ethanol, [EMIM]Cl, [PMIM]Cl, [BMIM]Cl,
and [HMIM]Cl
Ethanol [EMIM]Cl [PMIM]Cl [BMIM]Cl [HMIM]Cl
P* (Mpa) 464.54 612.51 410.51 440.25 377.06
T* (K) 549.03 623.35 709.66 714.79 699.82
rho* (g/cm3) 0.88699 1.1834 1.1566 1.1181 1.0990
MW (g/mol) 46.07 146.62 160.65 174.69 202.71
RSME (g/cm3) 0.00138 0.00173 0.00231 0.00186 0.00212
% AAD 0.151 0.130 0.170 0.145 0.165
% ℬ -0.00774 -0.00173 0.00198 0.000429 0.00202
105
Figure VI.4. Density versus pressure for ILs [EMIM]Cl (top left), [PMIM]Cl (top right),
[BMIM]Cl (bottom left), and [HMIM]Cl (bottom right). S-L EOS fits are represented by black
diamonds.
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[EMIM]Cl
348 K
373 K
398 K
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.1
1.11
1.12
1.13
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[PMIM]Cl298 K
323 K
348 K
373 K
398 K
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.1
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
BMIM]Cl
348K
373K
398K
323 K
298 K
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[HMIM]Cl 298 K
323 K
348 K
373 K
398 K
106
Table VI.3. Comparison of Root Mean Squared Deviations (RSME) for different models of the
binary interaction parameter used in mixing rules for the S-L EOS.
IL Mixing Rule Fit Parameter Parameter Value RSME (g/cm3)
[EMIM]Cl Constant Parameter kij 0.03383 0.00370
Volume Fraction
Dependent kij*
kA 0.07612 0.00310
kB 0.00248
[PMIM]Cl Constant Parameter kij -0.030331 0.00538
Volume Fraction
Dependent kij*
kA 0.06019 0.00479
kB -0.64970
[BMIM]Cl Constant Parameter kij -0.09405 0.00628
Volume Fraction
Dependent kij*
kA 0.26520 0.00397
kB -0.20947
[HMIM]Cl Constant Parameter kij -0.17651 0.00906
Volume Fraction
Dependent kij*
kA 0.79783 0.00322
kB -0.46194
*Equation VI.1
Table VI.4. S-L EOS characteristic parameters for [EMIM]Cl + ethanol mixtures.
Mass % IL 25 50 75
P* (Mpa) 489.47 516.26 552.24
T* (K) 560.42 570.72 587.12
rho* (g/cm3) 0.94624 1.0140 1.0922
r 6.0596 7.2780 9.4776
RSME (g/cm3) 0.00400 0.00324 0.00251
% AAD 0.406 0.269 0.216
% ℬ -0.102 0.180 -0.0262
107
Table VI.5. S-L EOS characteristic parameters for [PMIM]Cl + ethanol mixtures.
Mass % IL 25 50 75
P* (Mpa) 498.10 505.62 479.43
T* (K) 623.21 692.21 726.91
rho* (g/cm3) 0.94189 1.0040 1.0749
r 5.8222 6.5788 7.7244
RSME (g/cm3) 0.00663 0.00602 0.00485
% AAD 0.673 0.594 0.380
% ℬ 0.673 -0.507 0.378
Table VI.6. S-L EOS characteristic parameters for [BMIM]Cl + ethanol mixtures.
Mass % IL 25 50 75
P* (Mpa) 482.45 474.28 451.65
T* (K) 604.59 637.23 660.29
rho* (g/cm3) 0.93532 0.98923 1.0497
r 5.9627 6.9574 8.5600
RSME (g/cm3) 0.00309 0.00422 0.00506
% AAD 0.318 0.374 0.443
% ℬ -0.204 0.0720 -0.102
Table VI.7. S-L EOS characteristic parameters for [HMIM]Cl + ethanol mixtures.
Mass % IL 25 50 75
P* (Mpa) 486.18 446.19 383.91
T* (K) 622.53 629.45 610.71
rho* (g/cm3) 0.93194 0.98169 1.0371
r 5.9940 7.0387 8.7322
RSME (g/cm3) 0.00329 0.00345 0.0619
% AAD 0.322 0.344 6.21
% ℬ -0.0808 -0.215 6.21
108
Figure VI.5. Density versus pressure for mixtures of [EMIM]Cl (top left), [PMIM]Cl (top
right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right) with ethanol at 348 K. S-L EOS
fits are represented by black diamonds.
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[EMIM]Cl
348 K
ethanol
25%
50%
75%
IL
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[PMIM]Cl
348 KIL
75% IL
50% IL
25% IL
ethanol
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
IL
75%
50%
25%
ethanol
[BMIM]Cl
348 K
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[HMIM]Cl
348 K
IL
ethanol
50%
25%
75%
109
VI.3.1.A Derived Thermodynamic Properties of [RMIM]Cl + Ethanol
With the S-L EOS parameters determined for all four ILs and their mixtures with ethanol,
the derived thermodynamic properties isothermal compressibility, isobaric thermal expansion
coefficient, and internal pressure were calculated. The full range of derived thermodynamic
properties for [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, [HMIM]Cl and their mixtures with ethanol can
be found in Appendix E.
Figures VI.6-9 show isothermal compressibility versus pressure for the ILs and their
mixtures with ethanol. Compressibility was found to increase with temperature and decrease
with pressure for all ILs and their mixtures with ethanol. For [EMIM]Cl, isothermal
compressibility was found to decrease with increasing IL concentration. For the remaining three
ILs, this trend was more complicated. Figure VI.10 shows isothermal compressibility versus
mass % IL for all four ILs at 348 K and 10 MPa. For mixtures of [PMIM]Cl with ethanol,
compressibility goes through a minimum at 75 mass % IL in a parabolic fashion. For mixtures
of [BMIM]Cl and [HMIM]Cl with ethanol, the apparent trend starts to look like a third order
polynomial. This is especially visible for [HMIM]Cl, with a minimum at 50 mass % IL and a
maximum at 75 mass % IL.
Figure VI.6. Isothermal compressibility versus pressure for 50% [EMIM]Cl + 50% ethanol
(left) and various concentrations of [EMIM]Cl + ethanol at 348 K (right).
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
50% [EMIM]Cl
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
[EMIM]Cl
348 K
ethanol
25%
50%
75%
IL
110
Figure VI.7. Isothermal compressibility versus pressure for 50% [PMIM]Cl + 50% ethanol
(left) and various concentrations of [PMIM]Cl + ethanol at 348 K (right).
Figure VI.8. Isothermal compressibility versus pressure for 50% [BMIM]Cl + 50% ethanol
(left) and various concentrations of [BMIM]Cl + ethanol at 348 K (right).
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
50% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
[PMIM]Cl
348 Kethanol
25% IL
50% IL
75% IL
IL
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298K
323K
348K
373K
398K
50% [BMIM]Cl
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
[BMIM]Cl
348Kethanol
25%
50%
75%
IL
111
Figure VI.9. Isothermal compressibility versus pressure for 50% [HMIM]Cl + 50% ethanol
(left) and various concentrations of [HMIM]Cl + ethanol at 348 K (right).
Figure VI.10. Isothermal compressibility versus mass percent IL for mixtures of [EMIM]Cl,
[PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
50% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
[HMIM]Cl
348 Kethanol
25%
50%IL
75%
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 20 40 60 80 100
κT
(1/M
Pa)
Mass % IL
348 K
10 MPa
[HMIM]Cl
[BMIM]Cl
[PMIM]Cl
[EMIM]Cl
112
Figures VI.11-14 show isobaric thermal expansion coefficient versus temperature for
mixtures of 50 mass % IL with ethanol at all isotherms and all mixtures at 348 K for both
[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl. Thermal expansion coefficient was found
to increase with temperature and decrease with pressure for the ILs and their mixtures with
ethanol. Thermal expansion coefficient was found to be higher for [EMIM]Cl than the other
three ILs. As with isothermal compressibility, the addition of ethanol affected the expansivity of
these ILs. Figure VI.15 shows isobaric thermal expansion coefficient versus mass % IL for both
ILs at 348 K and 10 MPa. For [EMIM]Cl, the coefficient was found to decrease with increasing
IL concentration in a near linear manner. For [BMIM]Cl, expansivity decreased with IL
concentration, but the linearity was less than clear. [PMIM]Cl went through a minimum at 75
mass % IL, while [HMIM]Cl went through a minimum at 50 mass % IL then a maximum at 75
mass % IL, before dropping to the pure IL value.
Figure VI.11. Isobaric expansivity versus temperature for 50% [EMIM]Cl + 50% ethanol (left)
and various concentrations of [EMIM]Cl + ethanol at 10 MPa (right).
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
0.0015
0.0016
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
50% [EMIM]Cl
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0.0022
250 300 350 400 450
βP
(1/K
)
Temperature (K)
[EMIM]Cl
10 MPa ethanol
25%
50%
75%
IL
113
Figure VI.12. Isobaric expansivity versus temperature for 50% [PMIM]Cl + 50% ethanol (left)
and various concentrations of [PMIM]Cl + ethanol at 10 MPa (right).
Figure VI.13. Isobaric expansivity versus temperature for 50% [BMIM]Cl + 50% ethanol (left)
and various concentrations of [BMIM]Cl + ethanol at 10 MPa (right).
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
250 300 350 400 450
βP
(1/K
)
Temperature (K)
50% [PMIM]Cl
10 MPa
20 MPa
30 MPa
40 MPa
0
0.0005
0.001
0.0015
0.002
0.0025
250 300 350 400 450
βP
(1/K
)
Temperature (K)
[PMIM]Cl
10 MPaethanol
25%
50%
75%IL
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Pressure (MPa)
50% [BMIM]Cl
10 MPa
20 MPa
30 MPa
40 MPa
0
0.0005
0.001
0.0015
0.002
0.0025
250 300 350 400 450
βP
(1/K
)
Temperature (K)
ethanol
25%
50%
75%
IL
[BMIM]Cl
348K
114
Figure VI.14. Isobaric expansivity versus temperature for 50% [HMIM]Cl + 50% ethanol (left)
and various concentrations of [HMIM]Cl + ethanol at 10 MPa (right).
Figure VI.15. Isobaric thermal expansion coefficient versus mass percent IL for mixtures of
[EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
50% [HMIM]Cl10 MPa
20 MPa
30 MPa
40 MPa
0
0.0005
0.001
0.0015
0.002
0.0025
250 300 350 400 450
Isob
ari
c E
xp
an
sivit
y (
1/K
)
Temperature (K)
[HMIM]Cl
10 MPaethanol
25%
50%
IL
75%
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 20 40 60 80 100
βP
(1/K
)
Mass % IL
348 K
10 MPa
[EMIM]Cl
[PMIM]Cl
[BMIM]Cl
[HMIM]Cl
115
Internal pressure was found to decrease with temperature while increasing with pressure.
Figures VI.16-19 show internal pressures across a range of temperatures and pressures for
mixtures of 50 mass % IL with ethanol for [EMIM]Cl, [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl
along with internal pressures at 348 K for all four ILs and their mixtures with ethanol. Trends
were seen with regards to the effect of ethanol on internal pressure. For mixtures of [EMIM]Cl
with ethanol, internal pressure increased with increasing mass % IL. For mixtures of [PMIM]Cl
with ethanol, internal pressure followed a parabolic trend with a maximum at 50 mass % IL.
Both [BMIM]Cl, and [HMIM]Cl went through a maximum at 50 mass % IL and 25 mass % IL
respectively, before dropping to a minimum at 75 mass % IL, then settling at the pure IL value.
The difference between the maximum and minimum was more pronounced in the case of
[HMIM]Cl. The comparison between both ILs on the effect of IL concentration on internal
pressure at 348 K and 10 MPa is shown in Figure VI.20.
The changing effect of ethanol on internal pressure appears to be dependent on the alkyl
chain length on the cation. The length of the alkyl functional group on the imidazolium cation
leads to a further dissociation of the acetate anion. This can be seen by the general trend of
decreasing melting point with increasing alkyl chain length, as seen in Table VI.1, with melting
point dropping from 360 K for [EMIM]Cl to 206 K for [HMIM]Cl. This could provide an
explanation of the unusual effect the addition of a polar cosolvent has on the derived
thermodynamic properties of [PMIM]Cl, [BMIM]Cl, and [HMIM]Cl. As the interaction
between the constituent ions weaken, the negatively charged anion has a greater potential to
interact with the ethanol cosolvent through hydrogen bonding. Additionally, as the alkyl chain
length increases, the potential for the cation to interact with the ethyl group on the alcohol
increases. This potentially allows for the formation of short range order in the liquid phase,
explaining the concentration dependence on both the thermodynamics and the interaction
parameter needed to employ the mixing rules for the S-L EOS.
116
Figure VI.16. Internal pressure versus pressure for 50% [EMIM]Cl + 50% ethanol (left) and
various concentrations of [EMIM]Cl + ethanol at 348 K (right).
Figure VI.17. Internal pressure versus pressure for 50% [PMIM]Cl + 50% ethanol (left) and
various concentrations of [PMIM]Cl + ethanol at 348 K (right).
300
320
340
360
380
400
420
440
460
480
500
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
50% [EMIM]Cl
300
350
400
450
500
550
600
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
[EMIM]Cl
348 K
IL
75%
50%
25%
ethanol
350
370
390
410
430
450
470
490
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
50% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
300
325
350
375
400
425
450
475
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
[PMIM]Cl
348 K
ethanol
25% IL
50% IL
75% IL
IL
117
Figure VI.18. Internal pressure versus pressure for 50% [BMIM]Cl + 50% ethanol (left) and
various concentrations of [BMIM]Cl + ethanol at 348 K (right).
Figure VI.19. Internal pressure versus pressure for 50% [HMIM]Cl + 50% ethanol (left) and
various concentrations of [HMIM]Cl + ethanol at 348 K (right).
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
50% [BMIM]Cl298K
323K
348K
373K
398K
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
[BMIM]Cl
348K
IL75%
50%
25%
ethanol
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
50% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
300
325
350
375
400
425
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
[HMIM]Cl
348 K
ethanol
25% IL
50% IL
IL
75%
118
Figure VI.20. Internal pressure versus mass percent IL for mixtures of [EMIM]Cl, [PMIM]Cl,
[BMIM]Cl, and [HMIM]Cl + ethanol at 348 K and 10 MPa.
VI.3.2 1-Alkyl-3-methylimidazolium Acetates and their Mixtures with Ethanol
The experimental densities for two ILs with the acetate anion and their mixtures with
ethanol were compared. The density data for the IL [EMIM]Ac and its mixtures with ethanol
along with the S-L EOS parameters for the IL and ethanol have been previously reported in our
publication in The Journal of Supercritical Fluids.18 The S-L EOS characteristic parameters for
[EMIM]Ac and [BMIM]Ac can be found in Table VI.8, along with RSME, % AAD, and % ℬ.
Figure VI.21 shows the density data and corresponding S-L EOS fits for both ILs. The % AADs
for [EMIM]Ac and [BMIM]Ac were found to be 0.258 % and 0.190 % respectively. Density
was found to decrease as the alkyl functional group changed from ethyl to butyl. Additionally,
mixing rules were employed in the fitting of the mixture data to the S-L EOS. A concentration
dependent interaction parameter, kij, was used as described in equation VI.1. The constants
needed to determine kij can be found in Table VI.9. The S-L EOS parameters calculated using
mixing rules for each mixture with ethanol studied in the present thesis can be found in Tables
VI.10 and 11. Figure VI.22 shows the densities as a function of pressure for both ILs and their
mixtures with ethanol at 348 K, along with the corresponding S-L EOS fits. Density was found
200
250
300
350
400
450
500
550
600
0 20 40 60 80 100
Inte
rnal
Pre
ssu
re (
MP
a)
Mass % IL
348 K
10 MPa
[EMIM]Cl
[PMIM]Cl
[BMIM]Cl
[HMIM]Cl
119
to increase with increasing IL concentration. The full range of densities for all mixtures of
[BMIM]Ac with ethanol can be found in Appendix E.
Table VI.8. S-L EOS characteristic parameters for [EMIM]Ac and [BMIM]Ac
[EMIM]Ac [BMIM]Ac
P* (Mpa) 614.59 528.62
T* (K) 557.54 590.64
rho* (g/cm3) 1.1897 1.138
MW (g/mol) 170.21 198.26
RSME (g/cm3) 0.00329 0.00241
% AAD 0.258 0.190
% ℬ 0.000312 -0.00218
Figure VI.21. Density versus pressure for ILs [EMIM]Ac (left) and [BMIM]Ac (right). S-L
EOS fits are represented by black diamonds.
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
298 K[EMIM]Ac
323 K
348 K
373 K
398 K
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[BMIM]Ac
298K
323K
348K
373K
398K
120
Table VI.9. Comparison of Root Mean Squared Deviations (RSME) for different models of the
binary interaction parameter used in mixing rules for the S-L EOS for [EMIM]Ac and
[BMIM]Ac.
IL Mixing Rule Fit Parameter Parameter Value RSME (g/cm3)
[EMIM]Ac Constant Parameter kij -0.02439 0.00820
Volume Fraction
Dependent kij*
kA 0.19329 0.00718
kB -0.10101
[BMIM]Ac Constant Parameter kij -0.17989 0.0114
Volume Fraction
Dependent kij*
kA 0.58770 0.00481
kB -0.49625
*Equation VI.1
Table VI.10. S-L EOS characteristic parameters for [EMIM]Ac + ethanol mixtures.
Mass % IL 5 15 25 50 75
P* (Mpa) 473.46 489.53 503.39 530.89 558.56
T* (K) 553.25 558.89 561.12 555.59 545.92
rho* (g/cm3) 0.89842 0.92219 0.94725 1.0163 1.0962
r 5.4833 5.9268 6.4484 8.2674 11.516
RSME (g/cm3) 0.00642 0.00825 0.0034 0.00789 0.0078
% AAD 0.772 1.00 0.359 0.785 0.741
% ℬ -0.772 -1.00 -0.135 0.783 -0.643
121
Table VI.11. S-L EOS characteristic parameters for [BMIM]Ac + ethanol mixtures.
Mass % IL 5 14.9 25 50 75
P* (MPa) 481.55 509.72 528.86 539.81 520.64
T* (K) 569.56 599.93 619.23 623.32 591.95
ρ* (g/cm3) 0.89641 0.91668 0.93834 0.99662 1.0626
r 5.435 5.7992 6.2413 7.8143 10.81
RSME (g/cm3) 0.00302 0.00746 0.00507 0.00614 0.00911
% AAD 0.257 0.855 0.505 0.617 0.932
% ℬ 0.188 -0.784 -0.00542 -0.0579 -0.932
Figure VI.22. Density versus pressure for mixtures of [EMIM]Ac (left) and [BMIM]Ac (right)
with ethanol at 348 K. S-L EOS fits are represented by black diamonds.
VI.3.2.A Derived Thermodynamic Properties of [RMIM]Ac + Ethanol
With the S-L EOS parameters determined for both ILs and their mixtures with ethanol,
the derived thermodynamic properties isothermal compressibility, isobaric thermal expansion
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
[EMIM]Ac
348 KIL
75%
50%
25%
15%5%
ethanol
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
IL
75%
50%
25%
14.9%
5%
ethanol
[BMIM]Ac
348 K
122
coefficient, and internal pressure were calculated. The full range of derived thermodynamic
properties for the ILs and their mixtures with ethanol can be found in Appendix E.
Figures VI.23 and 24 show isothermal compressibility versus pressure for mixtures of 50
mass % IL with ethanol at all isotherms and all mixtures at 348 K for both [EMIM]Ac and
[BMIM]Ac. Compressibility was found to increase with temperature and decrease with pressure
for both ILs and all mixtures with ethanol. Both ILs were found to have similar values of
isothermal compressibility, with differences in compressibility ranging from around 1.0 %
difference at 298 K and 10 MPa, up to a maximum of 5.5 % difference at 398 K and 40 MPa,
with [EMIM]Ac having slightly high values. In spite of the similarities of the two ILs in their
pure states, differences begin to appear when these ILs are mixed with a cosolvent, in this case
ethanol. For [EMIM]Ac, isothermal compressibility was found to decrease with increasing IL
concentration. For [BMIM]Ac, this trend was only visible up to 50 mass % IL. Figure VI.25
shows isothermal compressibility versus mass % IL for both ILs at 348 K and 10 MPa. For
mixtures of [BMIM]Ac with ethanol, compressibility goes through a local minimum at 50 mass
% IL. Compressibility increases again to the 75 mass % IL point before dropping to the value
for the pure IL.
Figure VI.23. Isothermal compressibility versus pressure for 50% [EMIM]Ac + 50% ethanol
(left) and various concentrations of [EMIM]Ac + ethanol at 348 K (right).
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
50% [EMIM]Ac
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
[EMIM]Ac
348 K
ethanol
5%
15%
25%50%
75%
IL
123
Figure VI.24. Isothermal compressibility versus pressure for 50% [BMIM]Ac + 50% ethanol
(left) and various concentrations of [BMIM]Ac + ethanol at 348 K (right).
Figure VI.25. Isothermal compressibility versus mass percent IL for mixtures of [EMIM]Ac
and [BMIM]Ac + ethanol at 348 K and 10 MPa.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298K
323K
348K
373K
398K
50% [BMIM]Ac
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
[BMIM]Ac
348 Kethanol
5%
14.9%
25%
50%75%
IL
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 20 40 60 80 100
κT
(1/M
Pa)
Mass % IL
348 K
10 MPa
[EMIM]Ac
[BMIM]Ac
124
Figures VI.26 and 27 show isobaric thermal expansion coefficient versus temperature for
a mixture of 50 mass % IL with ethanol at all isotherms and all mixtures at 348 K for both
[EMIM]Ac and [BMIM]Ac. As with isothermal compressibility, thermal expansion coefficient
was found to increase with temperature and decrease with pressure for both ILs and their
mixtures with ethanol. However, thermal expansion coefficient was found to be higher for
[EMIM]Ac than [BMIM]Ac. Additionally, the addition of ethanol affected the expansivity of
these ILs. For [EMIM]Ac, the coefficient was found to decrease with increasing IL
concentration. For [BMIM]Ac, this trend was only visible up to 50 mass % IL. Figure VI.28
shows isobaric thermal expansion coefficient versus mass % IL for both ILs at 348 K and 10
MPa. For mixtures of [BMIM]Ac with ethanol, thermal expansion coefficient goes through a
local minimum at 50 mass % IL and a local maximum at 75 mass % IL before dropping to the
value for the pure IL.
Figure VI.26. Isobaric expansivity versus temperature for 50% [EMIM]Ac + 50% ethanol (left)
and various concentrations of [EMIM]Ac + ethanol at 10 MPa (right).
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
0.0015
0.0016
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
50% [EMIM]Ac
0
0.0005
0.001
0.0015
0.002
0.0025
250 300 350 400 450
βP
(1/K
)
Temperature (K)
[EMIM]Ac
10 MPaethanol
5%
15%
25%50%
75%
IL
125
Figure VI.27. Isobaric expansivity versus temperature for 50% [BMIM]Ac + 50% ethanol (left)
and various concentrations of [BMIM]Ac + ethanol at 10 MPa (right).
Figure VI.28. Isobaric thermal expansion coefficient versus mass percent IL for mixtures of
[EMIM]Ac and [BMIM]Ac + ethanol at 348 K and 10 MPa.
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
50% [BMIM]Ac 10 MPa
20 MPa
30 MPa
40 MPa
0
0.0005
0.001
0.0015
0.002
0.0025
250 300 350 400 450
βP
(1/K
)
Temperature (K)
ethanol
5%
14.9%25%
50%75%
IL
[BMIM]Ac
10 MPa
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 20 40 60 80 100
βP
(1/K
)
Mass % IL
348 K
10 MPa
[EMIM]Ac
[BMIM]Ac
126
Internal pressure was found to decrease with temperature while increasing with pressure.
Figures VI.29 and 30 show internal pressures across a range of temperatures and pressures for
mixtures of 50 mass % IL with ethanol for [EMIM]Ac and [BMIM]Ac along with internal
pressures at 348 K for both ILs and all mixtures with ethanol. Internal pressure was found to be
higher for [EMIM]Ac than [BMIM]Ac, indication stronger attractive interactions in the pure
[EMIM]Ac system. As with the chloride anion containing ILs, this could be explained by
disruption of the cation – anion interaction by the alkyl functional groups. As the alkyl chain
increases from an ethyl to butyl group, the ability of the anion to associate with the cation
decreases, causing a decrease in melting point and density ([EMIM]Ac melts above 303 K while
[BMIM]Ac has a melting point below 253 K as seen in Table VI.1).
With regards to mixtures with ethanol, differing trends were seen between the two ILs.
For mixtures of [EMIM]Ac with ethanol, internal pressure increased with increasing mass % IL.
For mixtures of [BMIM]Ac with ethanol, internal pressure followed a trend similar to a third
order polynomial, going through a maximum at 50 mass % IL and a minimum at 75 mass % IL.
The comparison between both ILs on the effect of IL concentration on internal pressure at 348 K
and 10 MPa is shown in Figure VI.31.
As the acetate anion dissociates with increasing alkyl chain length, the effect of the
addition of a polar cosolvent on the derived thermodynamic properties of [BMIM]Ac changes.
Isothermal compressibility and internal pressure were found to have both a maximum (75 and 50
mass % IL respectively) and a minimum (50 and 75 mass % IL respectively) as the concentration
of [BMIM]Ac increased. As the interaction between the constituent ions weaken, the negatively
charged anion has a greater potential to interact with the ethanol cosolvent through hydrogen
bonding, potentially leading to the formation of short range order in the liquid phase.
127
Figure VI.29. Internal pressure versus pressure for 50% [EMIM]Ac + 50% ethanol (left) and
various concentrations of [EMIM]Ac + ethanol at 348 K (right).
Figure VI.30. Internal pressure versus pressure for 50% [BMIM]Ac + 50% ethanol (left) and
various concentrations of [BMIM]Ac + ethanol at 348 K (right).
300
320
340
360
380
400
420
440
460
480
500
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
50% [EMIM]Ac
250
300
350
400
450
500
550
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
[EMIM]Ac
348 K
ethanol
5%15%25%
50%
75%
IL
350
370
390
410
430
450
470
490
510
530
550
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
50% [BMIM]Ac
298K
323K
348K
373K
398K
300
320
340
360
380
400
420
440
460
480
500
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
[BMIM]Ac
348 K
IL
75%
50%
25%
14.9%
5%
ethanol
128
Figure VI.31. Internal pressure versus mass percent IL for mixtures of [EMIM]Ac and
[BMIM]Ac + ethanol at 348 K and 10 MPa.
VI.3.2.B Viscosity of [RMIM]Ac + Ethanol
Viscosity data were collected for both [EMIM]Ac and [BMIM]Ac and their mixtures
with ethanol, up to 10 mass % ethanol with [EMIM]Ac and up to 25 mass % ethanol with
[BMIM]Ac. The high pressure rotational viscometer has a lower limit of 3 cP. Due to the
significant effect of both temperature and ethanol addition on viscosity, the range of
concentrations studied in the current work was limited compared to the density measurements.
For the pure ILs, viscosity was fit to the free volume theory. The parameters for the free volume
theory for both ILs can be found in Table VI.12, along with RSME, % AAD, and % ℬ.
Viscosity was found to be very temperature dependent, with a viscosity drop of approximately
75 % when temperature was increased from 298 to 323 K. Additionally, Viscosity was found to
decrease with the addition of ethanol. Adding 10 mass % ethanol caused a decrease in viscosity
of approximately 40 % in [EMIM]Ac and 70 % in [BMIM]Ac. This significant difference in the
effect of ethanol on viscosity may be due to the stronger interaction between the cosolvent and
anion, leading to further dissociation between the anions and cations. Figures VI.32 and 33 show
the viscosity versus pressure of [EMIM]Ac and [BMIM]Ac across the full range of temperatures
250
300
350
400
450
500
550
0 20 40 60 80 100
Inte
rnal
Pre
ssu
re (
MP
a)
Mass % IL
348 K
10 MPa
[BMIM]Ac
[EMIM]Ac
129
studied and their mixtures with ethanol at 323 K. The full range of values for viscosity for both
ILs and their mixtures with ethanol can be found in Appendix E.
Table VI.12. Parameters for the free volume theory of viscosity.
[EMIM]Ac [BMIM]Ac
L (cm) X 105 2.2402 0.3535
α (MPa*cm6/g*mol) 1470000 1490000
B X 103 0.50737 0.7203
RSME (mPa s) 4.00 8.30
% AAD 13.2 13.9
% ℬ 8.47 12.1
Figure VI.32. Viscosity versus pressure for [EMIM]Ac from 298-373 K (left) and mixtures of
[EMIM]Ac with ethanol at 323 K and 500 rpm (right).
0
50
100
150
200
250
0 10 20 30 40 50
Vis
cosi
ty (
cP)
Pressure (MPa)
[EMIM]Ac
500 RPM298 K (200 RPM)
323 K
348 K373 K
0
10
20
30
40
50
60
0 10 20 30 40 50
Vis
cosi
ty (
cP)
Pressure (MPa)
[EMIM]Ac
323 K
500 rpmIL
95% IL
90% IL
130
Figure VI.33. Viscosity versus pressure for [BMIM]Ac from 298-373 K (left) and mixtures of
[BMIM]Ac with ethanol at 323 K and 500 rpm (right).
VI.3.3 Hildebrand Solubility Parameters of Ionic Liquids
With internal pressure calculated, Hildebrand solubility parameter was estimated using
equation III.21. Due to their negligible vapor pressure, the heat of vaporization of ILs cannot be
easily determined, rendering it difficult to calculate the solubility parameter. Figures VI.34 and
35 show solubility parameter versus pressure for mixtures of all six ILs with ethanol at 348 K.
As with internal pressure, solubility parameter was found to increase with pressure and decrease
with temperature. Looking at ILs with the chloride anion at temperatures of both 298 K and 323
K and a pressure of 10 MPa (Figure VI.36), solubility parameter was found to increase with
increasing IL concentration in mixtures of [EMIM]Cl with ethanol. This contrasts with
[PMIM]Cl, which follows a parabolic trend with a maximum at 50 mass % IL. [BMIM]Cl and
showed a maximum at 50 mass % IL and minimum at 75 mass % IL. [HMIM]Cl showed a
minimum at 75 mass % IL. For mixtures of [EMIM]Ac and ethanol, solubility parameter
decreased with increasing IL concentration, while mixtures of [BMIM]Ac with ethanol showed a
maximum at 50 mass % IL and a minimum at 75 mass % IL (Figure VI.37). Values of the
Hildebrand solubility parameter were calculated from the S-L EOS for [EMIM]Ac at ambient
pressure in the temperature range from 313 to 393 K and compared to literature values from Yoo
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
[BMIM]Ac
500 RPM298 K (50 RPM)
323 K (300 rpm)
348 K373 K
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
[BMIM]Ac
323 K
500 RPMIL (300 RPM)
5%
10%
25%
131
et al (Figure VI.36).20 These values were estimated through the use of a chromatographic
technique using mixtures of ILs with solvents with known solubility parameters. The estimates
from the S-L EOS were found to be on average 5 % lower than the those calculated using the
chromatographic technique. In addition, values of the Hildebrand solubility parameter at 298 K
and ambient pressures (0.1 MPa) were estimated using the S-L EOS. Based on these
extrapolated values, the solubility parameter overall decreases with increasing alkyl chain length
on the cation. Also, with the same cation, switching from the chloride anion to acetate causes a
drop in solubility parameter. Table VI.13 shows the extrapolated values for solubility parameter
at 298 K and 0.1 MPa.
132
Figure VI.34. Solubility parameter versus pressure for mixtures of [EMIM]Cl (top left),
[PMIM]Cl (top right), [BMIM]Cl (bottom left), and [HMIM]Cl (bottom right) with ethanol at
348 K.
15
16
17
18
19
20
21
22
23
24
25
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
[EMIM]Cl
348 K
ethanol
25%
50%
75%
IL
17
18
19
20
21
22
23
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
[PMIM]Cl
348 K
ethanol
IL
25%
50%
75%
17.5
18
18.5
19
19.5
20
20.5
21
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
[BMIM]Cl
348 K
ethanol
50%
25%
75%IL
17
17.5
18
18.5
19
19.5
20
20.5
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
[HMIM]Cl
348 K 25%
50%
IL
ethanol
75%
133
Figure VI.35. Solubility parameter versus pressure for mixtures of [EMIM]Ac (left) and
[BMIM]Ac (right) with ethanol at 348 K.
Figure VI.36. Solubility parameter versus mass % IL for mixtures of [EMIM]Cl, [PMIM]Cl,
[BMIM]Cl and [HMIM]Cl with ethanol at 298 K and (left) and 348 K and (right) and 10 MPa.
15
16
17
18
19
20
21
22
23
24
25
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
[EMIM]Ac
348 K
ethanol
5%
25%15%
50%
75%
IL
17
18
19
20
21
22
23
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
[BMIM]Ac
348 K
IL
75%
50%25%
14.9%
5%
ethanol
16
17
18
19
20
21
22
23
24
0 20 40 60 80 100
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Mass % IL
298 K
10 MPa
[PMIM]Cl
[BMIM]Cl
[HMIM]Cl
[EMIM]Cl
16
17
18
19
20
21
22
23
24
0 20 40 60 80 100
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Mass % IL
348 K
10 MPa
[PMIM]Cl
[BMIM]Cl
[HMIM]Cl
[EMIM]Cl
134
Figure VI.37. Solubility parameter versus mass % IL for mixtures of [EMIM]Ac and
[BMIM]Ac with ethanol at 298 K and (left) and 348 K and (right) and 10 MPa.
Figure VI.38. Solubility parameter versus temperature at ambient pressure as estimated in the
current work using the S-L EOS and estimated through chromatographic techniques in the
literature.20
17
18
19
20
21
22
23
24
25
0 20 40 60 80 100
Solu
bit
ilit
y P
ara
met
er (
MP
a0
.5)
Mass % IL
298 K
10 MPa
[BMIM]Ac
[EMIM]Ac
15
16
17
18
19
20
21
22
23
24
25
0 20 40 60 80 100
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Mass % IL
348 K
10 MPa
[BMIM]Ac
[EMIM]Ac
20
20.5
21
21.5
22
22.5
23
23.5
24
250 300 350 400 450
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Temperature (K)
[EMIM]Ac
0.1 MPa
Literature
Values
Current
Work
135
Table VI.13. Solubility parameters of ionic liquids at 298 K and 0.1 MPa.
Ionic Liquid Solubility Parameter (MPa0.5)
[EMIM]Cl 23.1
[PMIM]Cl 19.3
[BMIM]Cl 20.0
[HMIM]Cl 18.4
[EMIM]Ac 22.6
[BMIM]Ac 21.2
VI.4 Conclusions
Changing alkyl chain length on the cation not only effects the physical properties of the
pure ionic liquid, but the interaction of the IL with a polar cosolvent. Increasing alkyl chain
length caused further dissociation of the anion from the cation, allowing for hydrogen bonding
with to occur between the anion and ethanol. Additionally, the longer alkyl chain on the cation
could increase the interaction with the ethyl group of the added alcohol. Due to these
interactions, modifications to the mixing rules used in conjunction with the S-L EOS was
required. By making the binary interaction parameter concentration dependent, the root mean
squared deviation of the fits of the mixture data decreased by up to 64 %. For ILs with the
chloride anion, these changing IL + cosolvent interactions could also be seen in the effect of
ethanol on the derived thermodynamic properties, especially internal pressure. Internal pressure
increased with increasing IL concentration for mixtures with [EMIM]Cl. For [PMIM]Cl, this
trend changed to a parabolic effect, with a maximum at 50 mass %. Both [BMIM]Cl and
[HMIM]Cl showed both a maximum and minimum (maximum at 50 and 25 mass %
respectively, minimum at 75 mass %). These complex interactions and their effects on internal
pressure could also be seen in ILs with the acetate anion and their mixtures with ethanol.
The viscosity of ionic liquid was found to drastically decrease with ethanol concentration.
Adding 10 mass % ethanol to [EMIM]Ac resulted in a decrease in viscosity of 40 %, while a
similar addition of ethanol caused a drop of 70 % in [BMIM]Ac. Increasing the alkyl chain
136
length both increases the viscosity of the pure IL and increases the effect of cosolvent addition
on viscosity.
Hildebrand solubility parameter for the six ILs and their mixtures with ethanol were
estimated as a function of temperature, pressure, and IL concentrations. Estimates of the
solubility parameter for [EMIM]Ac was found to be within 5 % of literature values. In addition,
solubility parameter was found to decrease with increasing alkyl chain length and by changing
the anion from chloride to acetate. Additionally, these estimations followed the same trends as
internal pressure. Due to the existence of both minimum and maximums in solubility parameter
as concentration is adjusted, it may be possible to create specific solvent mixtures adequately
tuned to a particular process that neither pure ethanol or the pure IL could effectively handle.
VI.5 References
1. S.A. Forsyth, J.M. Pringle, D.R. MacFarlane, Ionic Liquids-An Overview, Aust. J. Chem.
57 (2004) 113-119.
2. W. Ye, X. Li, H. Zhu, X. Wang, S. Wang, H. Wang, T. Sun, Green fabrication of
cellulose/graphene composite in ionic liquid and its electrochemical and photothermal
properties, Chemical Engineering Journal, 299 (2016) 45-55.
3. V.S. Rao, T.V. Krishna, T.M. Mohan, P.M. Rao, Thermodynamic and volumetric
behavior of green solvent 1-butyl-3-methylimidazolium tetrafluoroborate with aniline
from T=(293.15 to 323.15) K at atmospheric pressure, The Journal of Chemical
Thermodynamics, 100 (2016) 165-176.
4. T. Vancov, A.S. Alston, T. Brown, S. McIntosh, Use of ionic liquids in converting
lignocellulosic materials to biofuels, Renewable Energy, 45 (2012) 1-6.
5. F. Endres, S.Z. El Abedin, Air and water stable ionic liquids in physical chemistry, Phys.
Chem. Chem. Phys. 8 (2006) 2101-2116.
6. M.E. Zakrzewska, E.B. Lukasik, R.B. Lukasik, Solubility of carbohydrates in ionic
liquids, Energy & Fuels, 24 (2010) 737-745.
7. P. Kubisa, Ionic liquids as solvents for polymerization processes – progress and challenges,
Progress In Polymer Science, 34 (2009) 1333-1347.
8. T. Ueki, M. Watanabe, Polymers in ionic liquids. Dawn of neoteric solvents and innovative
materials, Bulletin of the Chemical Society of Japan, 85 (2012) 33-50.
9. H.Q.N. Gunarante, R. Langrick, A.V. Puga, K.R. Seddon, K. Whiston, Production of
polyetheretherketone in ionic liquid media, Green Chemistry, 15 (2013) 1166-1172.
10. N. Byrne, A. Leblais, B. Fox, Preparation of polyacrylonitrile polymer composite
precursors for carbon fiber using ionic liquid co-solvent solutions, J. Materials Chemistry
A, 2 (2014) 3424-3429.
11. H. Wang, G. Gurau, R.D. Rogers, Ionic liquid processing of cellulose, Chemical Society
Reviews, 41 (2012) 1519-1537.
137
12. M.M. Hossain, L. Aldous, Ionic liquids for lignin processing: Dissolution, isolation and
conversion, Australian Journal of Chemistry, 65 (2012) 1465-1477.
13. M. Isik, H. Sardon, D. Mecerreyes, Ionic liquids and cellulose: Dissolution, chemical
modification and preparation of new cellulose materials, International J. Molecular
Science, 15 (2014) 11922-11940.
14. M.M. Alavianmehr, S.M. Hosseini, A.A. Mohsenipour, J. Moghadasi, Further property of
ionic liquids: Hildebrand solubility parameter from new molecular thermodynamic
model, Journal of Molecular Liquids, 218 (2016) 332-341.
15. S.H. Lee, S.B. Lee, The Hildebrand solubility parameters, cohesive energy densities and
internal energies of 1-alkyl-3-methylimidazolium-based room temperature ionic liquids,
Chem. Commun., (2005) 3469-3471.
16. D.R. MacFarlane, N. Tachikawa, M. Forsyth, J.M. Pringle, P.C. Howlett, G.D. Elliot,
J.H. Davis Jr., M. Watanabe, P. Simon, C.A. Angell, Energy applications of ionic liquids,
Energy Environ. Sci., 7 (2014) 232-250.
17. J.L. Allen, D.W. McOwen, S.A. Delp, E.T. Fox, J.S. Dickmann, S.D. Han, Z.B. Zhou,
T.R. Jow, W.A. Henderson, N-Alkyl-N-methylpyrrolidinium difluoro(oxalate)borate
ionic liquids: Physical/electrochemical properties and Al corrosion, Journal of Power
Sources, 237 (2013) 104-111.
18. J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and
estimation of the solubility parameters of ionic liquid plus ethanol mixtures with the
Sanchez-Lacombe and Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol
and [EMIM]Cl plus ethanol mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.
19. Bio-Rad Laboratories, Inc. SpectraBase; SpectraBase Compound ID=FM76x1IROU9
http://spectrabase.com/compound/FM76x1IROU9 (accessed Mar 03, 2019).
20. B. Yoo, W. Afzal, J.M. Prausnitz, Solubility Parameters for Nine Ionic Liquids, Ind. Eng.
Chem. Res., 51 (2012) 9913–9917.
138
VII. Conclusions
In the present thesis, it has been shown that through both experimentation and modeling
approaches, a more holistic view allowing the examination of density, viscosity, and derived
thermodynamics simultaneously can be developed for complex fluid mixtures. A novel high
pressure rotational viscometer was built and validated, allowing for the collection of viscosity
data of base oils, oil and additive mixtures, and ionic liquids across a range of temperatures,
pressures, and shear rates while also allowing for the assessment of phase behavior. This high
pressure viscosity data was used in conjunction with density data to show that models could be
generated to look at both properties, along with the derived thermodynamic properties isothermal
compressibility, isobaric thermal expansion coefficient, and internal pressure. The Sanchez-
Lacombe equation of state was shown to accurately model density for a variety of mixtures
involving low molecular weight constituents. More specifically, this equation of state was
successfully used with base oils used in the formulation of automotive lubricants and, for the first
time, ionic liquids useful in the processing of biomass. Additionally, it was shown that the
Sanchez-Lacombe equation of state could be coupled with the free volume theory to model
viscosity, linking viscosity to density and the derived thermodynamic processes. For all
mixtures studied, the collection of high pressure density and viscosity data and subsequent
generation of holistic models allowed for the examination of how the composition of these
mixtures change their intermolecular interactions and, as a result, their volumetric properties and
viscosity.
In both lubricant and ionic liquid systems, the derived thermodynamic properties,
particularly isothermal compressibility and internal pressure, were found to be affected by
compositional effects. In the case of lubricants, the internal pressure was found to increase with
increasing cycloalkane concentration in base oils. Additionally, the addition of polymeric
additives caused changes in internal pressure that differed based in the functionality of polymer.
The addition of a small number of amine groups to the polymethacrylate base polymer added
more repulsive interactions, causing a subsequent drop in internal pressure in these mixtures
compared to the non-amine functionalized additive. The effect of cosolvent addition on ionic
liquids was found to change with cation modification. As the alkyl chain length increased on the
1-alkyl-3-methylimidazlium cation, the association with the anion further decreased. With the
139
greater opportunity for anion-cosolvent interactions, the overall trends for internal pressure
change from a near linear increase with increasing ionic liquid addition, to going through a
maximum, to even going through both a minimum and a maximum as fluid concentration
changes.
The ability to effectively model these trends creates opportunities for improving these
systems for their desired use cases. In the case of lubrication, understanding the effect of
composition on compressibility is useful in creating engine oils and automatic transmission
fluids that can effectively form films during the high pressure and high shear conditions they are
exposed to while in mechanical systems. In the case of ionic liquids, Hildebrand solubility
parameter can be estimated from these derived thermodynamic properties, allowing for the
tuning of these mixtures for task specific applications. Understanding the formation of short
range order between an ionic liquid with its cosolvent can lead to potentially better solvents than
either pure fluid, or cost savings as the amount on ionic liquid needed for a specialty process is
reduced. Additionally, the effectiveness of both lubricants and solvents requires knowledge of
the viscosity, showing the necessity of having a holistic understanding of all the properties of
these mixtures under high pressure conditions.
VII.1 Recommendations for Future Work
While the current study has looked at the volumetric properties, derived thermodynamic
properties, and viscosity of a number of complex mixtures and related them back to composition,
the research can be further expanded in the future. The following are some recommendations:
1. In addition to the work on determining the effect of viscosity index modifying polymers
on base oil properties carried out in the present study, other additives, in particular
dispersants, can be explored. Dispersants are known to form micellar structures in the
fluid phase. How the properties of oils are altered with respect to isothermal
compressibility, internal pressure, and viscosity in the presence of micelle forming
additives should be explored.
2. Data on volumetric properties and viscosity do not tell the whole story with regards to the
physical interactions between base oils and certain additives. In the case of the viscosity
index modifiers, there are still unanswered questions regarding how, for example, the
140
amine groups on polymethacrylate based additives effect both solvent – polymer and
polymer – polymer interactions. It would be useful to know what causes the significant
drop in internal pressure at the higher (~ 7 wt%) concentrations of polymer in the mixtures
with the amine containing polymer additive compared to the mixtures with the additive
that only contains alkyl group functionality. This drop appears to be due to an increase in
repulsive intermolecular interactions as these nitrogen containing groups are introduced to
a purely paraffinic fluid. However, this effect is not seen until high concentrations,
suggesting that short-range order between the polymer chains may form at these
conditions. In addition to the lubricants, the present findings suggest that short-range
order also forms in the case of the ionic liquid + ethanol mixtures. It may be possible to
further elucidate the formation of short – ranged structures in the bulk fluid using either
spectroscopy or light/x-ray scattering techniques. Of particular interest for this type of
study would be the use of Raman spectroscopy due to its previous use in the literature in
detecting the presence of aggregates in the bulk fluid phase of ternary mixtures at high
pressures.1
3. Ionic liquid structure has an impact on the interaction of the constituent ions with the
cosolvent. By varying alkyl chain length, the cation – anion interactions decrease, leading
to greater interactions with the cosolvent. In the current study, the 1-alkyl-3-
methylimidazolium cation was used. Further functionalization of the cation can be carried
out. Adding an additional alkyl group to the imidazolium cation can lead to further
dissociation of the anion. There is potential to further develop an understanding of the
solvent – anion interactions by studying 1-alkyl-2,3-dimethylimidazolium chloride ionic
liquids and their mixtures with ethanol. Adding further asymmetry to the cation should
have the effect of increasing solvent – anion interactions, allowing the further
confirmation and examination of the trends seen in the present thesis.
VII.2 References
1. N. Grimaldi, P.E. Rojas, S. Stehle, A. Cordoba, R. Schweins, S. Sala, S. Luelsdorf, D.
Pina, J. Veciana, J. Faraudo, A. Triolo, A.S. Braeuer, N. Ventosa, Pressure-Responsive,
Surfactant-Free CO2-Based Nanostructured Fluids, ACS Nano, 11 (2017) 10774-10784.
141
Appendix A: Publications Based on the Present Thesis
J.S. Dickmann, J.C. Hassler, E. Kiran, Modeling of the volumetric properties and estimation of
the solubility parameters of ionic liquid plus ethanol mixtures with the Sanchez-Lacombe and
Simha-Somcynsky equations of state: [EMIM]Ac plus ethanol and [EMIM]Cl plus ethanol
mixtures, Journal of Supercritical Fluids, 98 (2015) 86-101.
J.S. Dickmann, J.C. Hassler, E. Kiran, High Pressure Volumetric Properties and Viscosity of
Base Oils Used in Automotive Lubricants and Their Modeling, Industrial & Engineering
Chemistry Research, 57 (2018) 17266-17275.
142
Appendix B: Calibration and Verification of Density and Viscosity Measurements
In this section, the results of the verification and calibration of the experimental systems
have been reported.
Table B.1 shows the comparison of literature values to the results of a verification run
using ethanol in the variable-volume view-cell.
Figures B.1-B.12 show the collected torque values, both measured and corrected, for all
oil standards used in the calibration of the high pressure rotational viscometer. For a complete
list of these standards, see Table II.1.
This Appendix has been organized into three sections:
B.1 Verification Results of the Variable-Volume View-Cell for Density Determinations
B.2 Torque Values of Calibrations Standards ( N14, S60, RT50, RT 100) as Determined
with the High Pressure Rotational Viscometer
B.3 References
143
B.1 Verification Results of the Variable-Volume View-Cell for Density Determinations
Table B.1. Comparison of literature values with verification run for densities of ethanol in the
variable-volume view-cell.1
T (K) P (MPa) literature ρ (g/cm3) Average ρ (g/cm3) % Deviation
298 10 0.79398 0.78545 1.074
298 20 0.80179 0.79513 0.831
298 30 0.80896 0.80330 0.700
298 40 0.81562 0.81165 0.487
323 10 0.77347 0.76965 0.494
323 20 0.78237 0.77765 0.603
323 30 0.79046 0.78563 0.612
323 40 0.79788 0.79410 0.474
348 10 0.75137 0.74740 0.528
348 20 0.76167 0.75728 0.576
348 30 0.77087 0.76666 0.546
348 40 0.77922 0.77540 0.490
373 10 0.72705 0.72673 0.044
373 20 0.73918 0.73756 0.219
373 30 0.7498 0.74728 0.336
373 40 0.7593 0.75635 0.389
398 10 0.69993 0.70470 -0.681
398 20 0.71452 0.71738 -0.401
398 30 0.72697 0.72913 -0.298
398 40 0.73788 0.73975 -0.253
144
B.2 Torque Values of Calibrations Standards ( N14, S60, RT50, RT 100) as Determined with the
High Pressure Rotational Viscometer
Figure B.1. Torque versus time at 298 K for N14, both raw (left) and corrected (right) values.
Figure B.2. Torque versus time at 323 K for N14, both raw (left) and corrected (right) values.
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Torq
ue
(N m
)
Times (s)
N14
298 K
0.1 MPa
100 rpm
200 rpm
300 rpm
400 rpm
500 rpm
600 rpm
700 rpm
800 rpm
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80C
orr
ecte
d T
orq
ue
(N m
)
Times (s)
N14
298 K
0.1 MPa
100 rpm
200 rpm
300 rpm
400 rpm
500 rpm
600 rpm
700 rpm
800 rpm
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
N14
323 K
0.1 MPa
800
700
600500
400
300
200
100
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
N14
323 K
0.1 MPa
800
700
600
500
400300
200
100
145
Figure B.3. Torque versus time at 353 K for N14, both raw (left) and corrected (right) values.
Figure B.4. Torque versus time at 373 K for N14, both raw (left) and corrected (right) values.
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
N14
353 K
0.1 MPa
800
700
600500
400
300
200
100
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
N14
353 K
0.1 MPa
800
700
600
500
400300
200
100
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
N14
373 K
0.1 MPa
100
200
300
400
500
600
700
800
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
N14
373 K
0.1 MPa
100
200
300
400
500
600
700
800
146
Figure B.5. Torque versus time at 298 K for S60, both raw (left) and corrected (right) values.
Figure B.6. Torque versus time at 323 K for S60, both raw (left) and corrected (right) values.
0
0.004
0.008
0.012
0.016
0.02
0.024
0.028
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
S60
298 K
0.1 MPa
300
250
200
150
100
50
0
0.004
0.008
0.012
0.016
0.02
0.024
0.028
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
S60
298 K
0.1 MPa
250
150
300
200
50
100
0
0.004
0.008
0.012
0.016
0.02
0.024
0.028
0.032
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
S60
323 K
0.1 MPa
800
700
600500
400
300
200
100
0
0.004
0.008
0.012
0.016
0.02
0.024
0.028
0.032
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
S60
323 K
0.1 MPa
800
700
600
500
400300
200
100
147
Figure B.7. Torque versus time at 353 K for S60, both raw (left) and corrected (right) values.
Figure B.8. Torque versus time at 373 K for S60, both raw (left) and corrected (right) values.
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0.024
0.026
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
S60
353 K
0.1 MPa
800
700
600500
400
300
200
100
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0.024
0.026
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
S60
353 K
0.1 MPa
800
700
600
500
400300
200
100
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
S60
373 K
0.1 MPa
800
700
600500
400
300
200
100
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
S60
373 K
0.1 MPa
800
700
600
500
400300
200
100
148
Figure B.9. Torque versus time at 298 K for RT50, both raw (left) and corrected (right) values.
Figure B.10. Torque versus time at 313 K for RT50, both raw (left) and corrected (right) values.
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
RT50
298 K
0.1 MPa
600
500
400
300
200
100
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
RT50
298 K
0.1 MPa
600
500
400
300
200
100
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
RT50
313 K
0.1 MPa800
700
600500
400
300
200
100
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
RT50
313 K
0.1 MPa
800
700
600
500
400
300
200
100
149
Figure B.11. Torque versus time at 298 K for RT100, both raw (left) and corrected (right)
values.
Figure B.12. Torque versus time at 313 K for RT100, both raw (left) and corrected (right)
values.
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
RT100
298 K
0.1 MPa
400
300
200
100
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
RT100
298 K
0.1 MPa
400
300
200
100
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Torq
ue
(N m
)
Time (s)
RT100
313 K
0.1 MPa
600
500
400
300
200
100
0
0.005
0.01
0.015
0.02
0.025
0.03
0 20 40 60 80
Corr
ecte
d T
orq
ue
(N m
)
Time (s)
RT100
313 K
0.1 MPa
600
500
400
300
200
100
150
B.3 References
1. I.M. Abdulagatov, F.Sh. Aliyev, M.A. Talibov, J.T. Safarov, A.N. Shahverdiyev, E.P.
Hassel, High-pressure densities and derived volumetric properties (excess and partial
molar volumes, vapor-pressures) of binary methanol + ethanol mixtures, Thermochimica
Acta, 476 (2008) 51-62.
151
Appendix C: Density, Derived Thermodynamic Properties, and Viscosity of Base Oils
In this section, the full range of density, derived thermodynamic properties, and viscosity
for base oils IIA, IIIA, IIIB, PAO 4, and PAO 8 have been reported.
Figures C.1-C.5 show density, isothermal compressibility, isobaric thermal expansion
coefficient, and internal pressure of all five base oils from 10-40 MPa and 298-398 K.
Figures C.6-C.10 show viscosity versus pressure for all five base oils from 10-40 MPa
and 298-373 K.
Tables C.1-C.5 include select data for density as calculated from the Sanchez-Lacombe
equation of state, derived thermodynamic properties, and viscosity as calculated from the free
volume theory.
This Appendix has been organized into three sections:
C.1 PVT data and thermodynamic properties for IIA, IIIA, IIIB, PAO 4, and PAO 8
C.2 Viscosity data for IIA, IIIA, IIIB, PAO 4, and PAO 8
C.3 Select tabulated data for IIA, IIIA, IIIB, PAO 4, and PAO 8
152
C.1 PVT data and thermodynamic properties for IIA, IIIA, IIIB, PAO 4, and PAO 8
Figure C.1. PVT data and thermodynamic properties for IIA: Density (top left), isothermal
compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal
pressure (bottom right).
0.77
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
IIA298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
IIA
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
IIA
300
320
340
360
380
400
420
440
460
480
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
IIA
153
Figure C.2. PVT data and thermodynamic properties for IIIA: Density (top left), isothermal
compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal
pressure (bottom right).
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0.87
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure, MPa
IIIA298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
IIIA
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
IIIA
300
320
340
360
380
400
420
440
460
480
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
IIIA
154
Figure C.3. PVT data and thermodynamic properties for IIIB: Density (top left), isothermal
compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal
pressure (bottom right).
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0.87
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
IIIB298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
IIIB
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
IIIB
300
320
340
360
380
400
420
440
460
480
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
IIIB
155
Figure C.4. PVT data and thermodynamic properties for PAO 4: Density (top left), isothermal
compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal
pressure (bottom right).
0.73
0.75
0.77
0.79
0.81
0.83
0.85
0.87
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
PAO 4298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
PAO 4
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
PAO 4
290
310
330
350
370
390
410
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
PAO 4
156
Figure C.5. PVT data and thermodynamic properties for PAO 8: Density (top left), isothermal
compressibility (top right), isobaric thermal expansion coefficient (bottom left), and internal
pressure (bottom right).
0.75
0.77
0.79
0.81
0.83
0.85
0.87
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
PAO 8
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
SS8
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
PAO 8
280
300
320
340
360
380
400
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
PAO 8
157
C.2 Viscosity data for IIA, IIIA, IIIB, PAO 4, and PAO 8
Figure C.6. Viscosity versus pressure for IIA at 500 rpm (left) and 323 K (right).
Figure C.7. Viscosity versus pressure for IIIA at 500 rpm (left) and 323 K (right).
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
IIA
500 RPM 298 K
323 K
348 K
373 K0
5
10
15
20
25
30
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)Pressure (MPa)
IIA
323 K
300-800 RPM
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
IIIA
500 RPM 298 K
323 K
348 K
373 K
0
2
4
6
8
10
12
14
16
18
20
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
IIIA
323 K
300-800 RPM
158
Figure C.8. Viscosity versus pressure for IIIB at 500 rpm (left) and 323 K (right).
Figure C.9. Viscosity versus pressure for PAO 4 at 500 rpm (left) and 323 K (right).
0
20
40
60
80
100
120
140
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
IIIB
500 RPM 298 K
(300 RPM)
323 K
348 K
373 K
0
10
20
30
40
50
60
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
IIIB
323 K
300-800 RPM
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4
500 rpm298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 4
323 K
300-800 RPM
159
Figure C.10. Viscosity versus pressure for PAO 8 at 500 rpm (left) and 323 K (right).
0
50
100
150
200
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 8
500 RPM298 K
(200 RPM)
348 K373 K
323 K
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
PAO 8
323 K
300-800 RPM
160
C.3 Select tabulated data for IIA, IIIA, IIIB, PAO 4, and PAO 8
Table C.1. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for base oil IIA.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.8773 0.0005165 0.0007563 426.3 47.86
298 15 0.8795 0.0004934 0.0007343 428.5 53.22
298 20 0.8816 0.0004720 0.0007135 430.5 59.09
298 25 0.8837 0.0004520 0.0006939 432.5 65.52
298 30 0.8856 0.0004333 0.0006753 434.4 72.55
298 35 0.8875 0.0004158 0.0006576 436.3 80.25
298 40 0.8893 0.0003994 0.0006407 438.1 88.65
323 10 0.8601 0.0006385 0.0008297 409.7 14.51
323 15 0.8627 0.0006080 0.0008043 412.3 16.08
323 20 0.8653 0.0005799 0.0007805 414.7 17.78
323 25 0.8678 0.0005539 0.0007581 417.1 19.63
323 30 0.8701 0.0005298 0.0007370 419.4 21.64
323 35 0.8724 0.0005073 0.0007171 421.5 23.83
323 40 0.8745 0.0004864 0.0006982 423.6 26.20
348 10 0.8416 0.0007800 0.0009018 392.4 5.33
348 15 0.8448 0.0007399 0.0008725 395.4 5.90
348 20 0.8479 0.0007032 0.0008452 398.2 6.50
348 25 0.8508 0.0006696 0.0008197 401.0 7.16
348 30 0.8536 0.0006387 0.0007958 403.6 7.87
348 35 0.8563 0.0006101 0.0007734 406.1 8.63
348 40 0.8588 0.0005836 0.0007522 408.6 9.46
373 10 0.8221 0.0009445 0.0009734 374.4 2.28
373 15 0.8259 0.0008919 0.0009394 377.9 2.51
373 20 0.8295 0.0008443 0.0009080 381.1 2.77
373 25 0.8329 0.0008010 0.0008790 384.3 3.04
373 30 0.8362 0.0007615 0.0008520 387.3 3.33
373 35 0.8393 0.0007253 0.0008268 390.2 3.65
373 40 0.8423 0.0006919 0.0008032 393.0 3.99
398 10 0.8017 0.0011365 0.0010451 356.0 -
398 15 0.8061 0.0010675 0.0010055 359.9 -
398 20 0.8103 0.0010057 0.0009695 363.7 -
398 25 0.8142 0.0009501 0.0009364 367.2 -
398 30 0.8180 0.0008999 0.0009059 370.6 -
398 35 0.8216 0.0008542 0.0008776 373.9 -
398 40 0.8250 0.0008124 0.0008513 377.0 -
161
Table C2. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for base oil IIB.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.8847 0.0005097 0.0007415 423.55 99.55
298 15 0.8869 0.0004869 0.0007199 425.66 107.44
298 20 0.8890 0.0004657 0.0006996 427.69 115.76
298 25 0.8910 0.0004459 0.0006803 429.65 124.53
298 30 0.8930 0.0004275 0.0006620 431.53 133.78
298 35 0.8948 0.0004102 0.0006447 433.34 143.52
298 40 0.8966 0.0003940 0.0006281 435.08 153.77
323 10 0.8676 0.0006290 0.0008128 407.40 26.16
323 15 0.8703 0.0005990 0.0007880 409.91 28.22
323 20 0.8729 0.0005714 0.0007648 412.31 30.39
323 25 0.8753 0.0005458 0.0007429 414.62 32.66
323 30 0.8776 0.0005221 0.0007222 416.84 35.05
323 35 0.8799 0.0005000 0.0007027 418.98 37.56
323 40 0.8820 0.0004794 0.0006842 421.03 40.18
348 10 0.8494 0.0007670 0.0008827 390.49 8.54
348 15 0.8526 0.0007277 0.0008541 393.42 9.22
348 20 0.8556 0.0006919 0.0008275 396.22 9.93
348 25 0.8585 0.0006589 0.0008026 398.90 10.67
348 30 0.8613 0.0006286 0.0007793 401.48 11.45
348 35 0.8640 0.0006005 0.0007574 403.95 12.26
348 40 0.8665 0.0005745 0.0007368 406.33 13.10
373 10 0.8302 0.0009268 0.0009517 372.99 3.30
373 15 0.8339 0.0008756 0.0009187 376.36 3.57
373 20 0.8375 0.0008291 0.0008882 379.58 3.84
373 25 0.8409 0.0007869 0.0008600 382.66 4.13
373 30 0.8441 0.0007482 0.0008337 385.61 4.43
373 35 0.8472 0.0007128 0.0008092 388.43 4.75
373 40 0.8502 0.0006802 0.0007862 391.15 5.07
398 10 0.8100 0.0011125 0.0010204 355.04 -
398 15 0.8143 0.0010455 0.0009822 358.89 -
398 20 0.8185 0.0009856 0.0009473 362.55 -
398 25 0.8224 0.0009316 0.0009153 366.04 -
398 30 0.8262 0.0008826 0.0008857 369.38 -
398 35 0.8297 0.0008381 0.0008583 372.57 -
398 40 0.8331 0.0007974 0.0008327 375.63 -
162
Table C.3. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for base oil IIIA.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.8365 0.0005734 0.0008003 405.91 26.37
298 15 0.8388 0.0005464 0.0007759 408.18 28.84
298 20 0.8411 0.0005213 0.0007529 410.37 31.50
298 25 0.8432 0.0004981 0.0007312 412.46 34.35
298 30 0.8453 0.0004765 0.0007108 414.48 37.41
298 35 0.8473 0.0004564 0.0006914 416.42 40.69
298 40 0.8492 0.0004376 0.0006730 418.28 44.22
323 10 0.8191 0.0007097 0.0008772 389.23 9.66
323 15 0.8220 0.0006737 0.0008488 391.93 10.54
323 20 0.8247 0.0006408 0.0008224 394.52 11.48
323 25 0.8273 0.0006105 0.0007976 396.99 12.49
323 30 0.8297 0.0005825 0.0007744 399.37 13.56
323 35 0.8321 0.0005566 0.0007525 401.65 14.71
323 40 0.8344 0.0005326 0.0007318 403.84 15.93
348 10 0.8006 0.0008685 0.0009529 371.82 4.15
348 15 0.8040 0.0008209 0.0009200 374.98 4.53
348 20 0.8072 0.0007778 0.0008895 377.99 4.92
348 25 0.8103 0.0007385 0.0008612 380.86 5.34
348 30 0.8132 0.0007024 0.0008349 383.61 5.79
348 35 0.8160 0.0006693 0.0008102 386.25 6.27
348 40 0.8187 0.0006388 0.0007871 388.79 6.77
373 10 0.7810 0.0010541 0.0010283 353.86 2.02
373 15 0.7850 0.0009913 0.0009899 357.49 2.20
373 20 0.7888 0.0009349 0.0009548 360.95 2.39
373 25 0.7924 0.0008840 0.0009225 364.25 2.59
373 30 0.7958 0.0008379 0.0008926 367.39 2.81
373 35 0.7991 0.0007958 0.0008649 370.41 3.04
373 40 0.8022 0.0007573 0.0008391 373.29 3.27
398 10 0.7605 0.0012718 0.0011040 335.49 -
398 15 0.7652 0.0011887 0.0010592 339.64 -
398 20 0.7696 0.0011152 0.0010187 343.57 -
398 25 0.7738 0.0010496 0.0009818 347.31 -
398 30 0.7777 0.0009906 0.0009480 350.87 -
398 35 0.7815 0.0009374 0.0009168 354.27 -
398 40 0.7851 0.0008891 0.0008880 357.51 -
163
Table C.4. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for base oil IIIB.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.8432 0.0005262 0.0007589 419.77 87.64
298 15 0.8453 0.0005025 0.0007367 421.93 97.08
298 20 0.8474 0.0004804 0.0007157 424.01 107.38
298 25 0.8494 0.0004598 0.0006959 426.01 118.60
298 30 0.8513 0.0004406 0.0006771 427.93 130.81
298 35 0.8532 0.0004227 0.0006593 429.78 144.11
298 40 0.8549 0.0004059 0.0006423 431.56 158.57
323 10 0.8266 0.0006494 0.0008311 403.40 26.60
323 15 0.8292 0.0006181 0.0008055 405.97 29.37
323 20 0.8317 0.0005892 0.0007816 408.43 32.37
323 25 0.8341 0.0005626 0.0007590 410.78 35.61
323 30 0.8364 0.0005379 0.0007378 413.05 39.12
323 35 0.8386 0.0005149 0.0007177 415.23 42.92
323 40 0.8407 0.0004935 0.0006987 417.33 47.02
348 10 0.8089 0.0007919 0.0009018 386.30 9.79
348 15 0.8120 0.0007508 0.0008722 389.29 10.78
348 20 0.8150 0.0007133 0.0008448 392.15 11.86
348 25 0.8178 0.0006790 0.0008192 394.89 13.01
348 30 0.8205 0.0006473 0.0007953 397.51 14.26
348 35 0.8231 0.0006182 0.0007728 400.04 15.59
348 40 0.8256 0.0005911 0.0007516 402.46 17.03
373 10 0.7901 0.0009571 0.0009715 368.62 4.18
373 15 0.7938 0.0009033 0.0009374 372.07 4.60
373 20 0.7973 0.0008548 0.0009060 375.35 5.05
373 25 0.8006 0.0008107 0.0008769 378.49 5.54
373 30 0.8038 0.0007704 0.0008499 381.49 6.06
373 35 0.8068 0.0007335 0.0008247 384.37 6.61
373 40 0.8097 0.0006996 0.0008011 387.13 7.20
398 10 0.7705 0.0011491 0.0010409 350.54 -
398 15 0.7748 0.0010788 0.0010015 354.46 -
398 20 0.7789 0.0010160 0.0009655 358.19 -
398 25 0.7827 0.0009596 0.0009325 361.75 -
398 30 0.7864 0.0009086 0.0009020 365.14 -
398 35 0.7899 0.0008622 0.0008739 368.39 -
398 40 0.7932 0.0008199 0.0008477 371.50 -
164
Table C.5. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for base oil PAO 4.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.8345 0.0006138 0.0007690 363.34 38.50
298 15 0.8370 0.0005820 0.0007432 365.52 41.76
298 20 0.8393 0.0005528 0.0007191 367.60 45.22
298 25 0.8416 0.0005260 0.0006964 369.58 48.89
298 30 0.8438 0.0005011 0.0006752 371.49 52.78
298 35 0.8458 0.0004781 0.0006551 373.31 56.91
298 40 0.8478 0.0004567 0.0006361 375.06 61.29
323 10 0.8178 0.0007573 0.0008417 349.00 15.14
323 15 0.8208 0.0007155 0.0008120 351.58 16.40
323 20 0.8237 0.0006774 0.0007845 354.03 17.72
323 25 0.8264 0.0006427 0.0007588 356.38 19.13
323 30 0.8290 0.0006107 0.0007348 358.62 20.61
323 35 0.8315 0.0005814 0.0007123 360.76 22.17
323 40 0.8339 0.0005542 0.0006911 362.81 23.81
348 10 0.8001 0.0009233 0.0009127 334.02 6.90
348 15 0.8037 0.0008685 0.0008785 337.02 7.47
348 20 0.8071 0.0008191 0.0008471 339.88 8.07
348 25 0.8103 0.0007744 0.0008180 342.60 8.70
348 30 0.8134 0.0007337 0.0007911 345.19 9.36
348 35 0.8163 0.0006965 0.0007659 347.66 10.05
348 40 0.8190 0.0006624 0.0007424 350.03 10.78
373 10 0.7813 0.0011158 0.0009828 318.56 3.52
373 15 0.7856 0.0010441 0.0009434 322.02 3.82
373 20 0.7896 0.0009803 0.0009074 325.29 4.12
373 25 0.7933 0.0009230 0.0008745 328.40 4.44
373 30 0.7969 0.0008714 0.0008442 331.36 4.78
373 35 0.8003 0.0008247 0.0008162 334.18 5.13
373 40 0.8035 0.0007820 0.0007902 336.87 5.49
398 10 0.7617 0.0013394 0.0010525 302.76 -
398 15 0.7667 0.0012457 0.0010069 306.69 -
398 20 0.7713 0.0011634 0.0009658 310.40 -
398 25 0.7756 0.0010905 0.0009286 313.92 -
398 30 0.7797 0.0010254 0.0008946 317.26 -
398 35 0.7836 0.0009669 0.0008634 320.43 -
398 40 0.7873 0.0009140 0.0008347 323.46 -
165
Table C.6. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for base oil PAO 8.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.8340 0.0006204 0.0007538 352.06 119.96
298 15 0.8366 0.0005875 0.0007278 354.19 131.98
298 20 0.8389 0.0005573 0.0007035 356.22 144.89
298 25 0.8412 0.0005295 0.0006808 358.16 158.75
298 30 0.8434 0.0005039 0.0006594 360.02 173.61
298 35 0.8455 0.0004801 0.0006393 361.79 189.54
298 40 0.8475 0.0004581 0.0006203 363.49 206.60
323 10 0.8177 0.0007649 0.0008251 338.43 35.56
323 15 0.8208 0.0007216 0.0007953 340.95 39.06
323 20 0.8237 0.0006824 0.0007676 343.35 42.81
323 25 0.8264 0.0006465 0.0007419 345.64 46.80
323 30 0.8290 0.0006137 0.0007179 347.83 51.06
323 35 0.8315 0.0005835 0.0006954 349.91 55.59
323 40 0.8339 0.0005557 0.0006742 351.91 60.43
348 10 0.8003 0.0009316 0.0008947 324.18 12.83
348 15 0.8040 0.0008751 0.0008604 327.13 14.09
348 20 0.8074 0.0008243 0.0008289 329.92 15.43
348 25 0.8106 0.0007784 0.0007998 332.57 16.85
348 30 0.8137 0.0007367 0.0007729 335.10 18.36
348 35 0.8166 0.0006986 0.0007478 337.51 19.96
348 40 0.8194 0.0006636 0.0007243 339.81 21.66
373 10 0.7820 0.0011245 0.0009631 309.47 5.40
373 15 0.7862 0.0010508 0.0009237 312.85 5.93
373 20 0.7902 0.0009854 0.0008878 316.05 6.49
373 25 0.7940 0.0009268 0.0008550 319.09 7.09
373 30 0.7976 0.0008740 0.0008248 321.97 7.71
373 35 0.8010 0.0008263 0.0007968 324.72 8.38
373 40 0.8042 0.0007828 0.0007709 327.34 9.08
398 10 0.7627 0.0013480 0.0010310 294.42 -
398 15 0.7677 0.0012521 0.0009855 298.27 -
398 20 0.7723 0.0011680 0.0009446 301.90 -
398 25 0.7767 0.0010935 0.0009076 305.33 -
398 30 0.7808 0.0010272 0.0008738 308.58 -
398 35 0.7847 0.0009676 0.0008429 311.67 -
398 40 0.7884 0.0009139 0.0008143 314.62 -
166
Appendix D: Density, Derived Thermodynamic Properties, and Viscosity of Mixtures of
Base Oils with Additives and Automatic Transmission Fluids
In this section, the full range of density, derived thermodynamic properties, and viscosity
for mixtures of PAO 4 with two methacrylate based polymeric additives and two automatic
transmission fluids have been reported.
Figures D.1-D.8 show density, isothermal compressibility, isobaric thermal expansion
coefficient, and internal pressure of mixtures of PAO 4 with both polymeric additives up to 7
mass percent from 10-40 MPa and 298-398 K.
Figures D.9-D.16 show viscosity versus pressure for all mixtures from 10-40 MPa and
298-373 K.
Figures D.17 and D.18 show density and the derived thermodynamic properties for both
ATFs.
Tables D.1-D.10 include select data for density as calculated from the Sanchez-Lacombe
equation of state, derived thermodynamic properties, and viscosity as calculated from the free
volume theory.
This Appendix has been organized into four sections:
D.1 Density and Derived Thermodynamic Properties of Mixtures of PAO4 + Viscosity
Index Modifiers
D.2 Viscosity of Mixtures of PAO 4 + Viscosity Index Modifiers
D.3 Density and Derived Thermodynamic Properties of ATFs
D.4 Select Tabulated Data for Mixtures of PAO 4 + Viscosity Index Modifiers and ATFs
167
D.1 Density and Derived Thermodynamic Properties of Mixtures of PAO4 + Viscosity Index
Modifiers
Figure D.1. PVT data and thermodynamic properties for a mixture of PAO 4 + 0.71 mass %
Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
0.71% Polymer 1
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50κ
T(1
/MP
a)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
0.71% Polymer 1
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
0.71% Polymer 1
250
270
290
310
330
350
370
390
410
430
450
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
0.71% Polymer 1
168
Figure D.2. PVT data and thermodynamic properties for a mixture of PAO 4 + 1.42 mass %
Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
1.42% Polymer 1
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
1.42% Polymer 1
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
1.42% Polymer 1
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
1.42% Polymer 1
169
Figure D.3. PVT data and thermodynamic properties for a mixture of PAO 4 + 2.85 mass %
Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
2.85% Polymer 1
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
2.85% Polymer 1
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
2.85% Polymer 1
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
2.85% Polymer 1
170
Figure D.4. PVT data and thermodynamic properties for a mixture of PAO 4 + 7.12 mass %
Polymer 1: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
7.12% Polymer 1
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K323 K
298 K
7.12% Polymer 1
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
7.12% Polymer 1
200
210
220
230
240
250
260
270
280
290
300
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
7.12% Polymer 1
171
Figure D.5. PVT data and thermodynamic properties for a mixture of PAO 4 + 0.70 mass %
Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
0.70% Polymer 2
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
0.70% Polymer 2
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
0.70% Polymer 2
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
0.70% Polymer 2
172
Figure D.6. PVT data and thermodynamic properties for a mixture of PAO 4 + 1.40 mass %
Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
1.40% Polymer 2
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
1.40% Polymer 2
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
1.40% Polymer 2
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
1.40% Polymer 2
173
Figure D.7. PVT data and thermodynamic properties for a mixture of PAO 4 + 2.80 mass %
Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
2.80% Polymer 2
298 K
323 K
348 K
373 K
398 K
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
2.80% Polymer 2
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
2.80% Polymer 2
300
320
340
360
380
400
420
440
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
2.80% Polymer 2
174
Figure D.8. PVT data and thermodynamic properties for a mixture of PAO 4 + 7.01 mass %
Polymer 2: Density (top left), isothermal compressibility (top right), isobaric thermal expansion
coefficient (bottom left), and internal pressure (bottom right).
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
7.01% Polymer 2
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
7.01% Polymer 2
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
7.01% Polymer 2
250
270
290
310
330
350
370
390
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
7.01% Polymer 2
175
D.2 Viscosity of Mixtures of PAO 4 + Viscosity Index Modifiers
Figure D.9. Viscosity versus pressure for a mixture of PAO 4 + 0.71 mass % Polymer 1 at 500
rpm (left) and 323 K (right).
Figure D.10. Viscosity versus pressure for a mixture of PAO 4 + 1.42 mass % Polymer 1 at 500
rpm (left) and 323 K (right).
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
0.71% Polymer 1298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)Pressure (MPa)
0.71% Polymer 1
300-800 rpm
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
1.42% Polymer 1298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
1.42% Polymer
300-800 rpm
176
Figure D.11. Viscosity versus pressure for a mixture of PAO 4 + 2.85 mass % Polymer 1 at 500
rpm (left) and 323 K (right).
Figure D.12. Viscosity versus pressure for a mixture of PAO 4 + 7.12 mass % Polymer 1 at 500
rpm (left) and 323 K (right).
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
2.85% Polymer 1298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
2.85% Polymer 1
300-800 rpm
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50
Vis
cosi
ty (
cP)
Pressure (MPa)
7.12% Polymer 1
298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50
Vis
cosi
ty (
cP)
Pressure (MPa)
7.12% Polymer 1
300-800 RPM
177
Figure D.13. Viscosity versus pressure for a mixture of PAO 4 + 0.70 mass % Polymer 2 at 500
rpm (left) and 323 K (right).
Figure D.14. Viscosity versus pressure for a mixture of PAO 4 + 1.40 mass % Polymer 2 at 500
rpm (left) and 323 K (right).
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
0.70% Polymer 2
298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
0.70% Polymer 2
300-800 rpm
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
1.40% Polymer 2298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
1.40% Polymer 2
300-800 rpm
178
Figure D.15. Viscosity versus pressure for a mixture of PAO 4 + 2.80 mass % Polymer 2 at 500
rpm (left) and 323 K (right).
Figure D.16. Viscosity versus pressure for a mixture of PAO 4 + 7.01 mass % Polymer 2 at 500
rpm (left) and 323 K (right).
0
10
20
30
40
50
60
70
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
2.80% Polymer 2298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
2.80% Polymer 2
300-800 rpm
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
7.01% Polymer 2
298 K
323 K
348 K
373 K
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50
Vis
cosi
ty (
cP)
Pressure (MPa)
7.01% Polymer 2
300-800 rpm
179
D.3 Density and Derived Thermodynamic Properties of ATFs
Figure D.17. PVT data and thermodynamic properties for an experimental ATF: Density (top
left), isothermal compressibility (top right), isobaric thermal expansion coefficient (bottom left),
and internal pressure (bottom right).
0.77
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0 10 20 30 40 50κ
T(1
/MP
a)
Pressure (MPa)
298 K
323 K
348K
373K
398K
0.00075
0.0008
0.00085
0.0009
0.00095
0.001
250 300 350 400 450
Isob
ari
c E
xp
an
sivit
y (
1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
350
370
390
410
430
450
470
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
180
Figure D.18. PVT data and thermodynamic properties for a commercial ATF: Density (top
left), isothermal compressibility (top right), isobaric thermal expansion coefficient (bottom left),
and internal pressure (bottom right).
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
298 K
323 K
348 K
373 K
398
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298 K
323 K
348K
373K
398K
0.0007
0.00075
0.0008
0.00085
0.0009
0.00095
250 300 350 400 450
Isob
ari
c E
xp
an
sivit
y (
1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
340
350
360
370
380
390
400
410
420
430
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
181
D.4 Select Tabulated Data for Mixtures of PAO 4 + Viscosity Index Modifiers and ATFs
Table D.1. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 0.71 mass % Polymer 1.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.81282 0.000636 0.000812 370.391 32.87341
298 15 0.815343 0.000604 0.000786 372.6943 35.82478
298 20 0.817747 0.000574 0.000761 374.8948 38.9718
298 25 0.820039 0.000546 0.000737 377 42.32589
298 30 0.82223 0.000521 0.000715 379.0166 45.89911
298 35 0.824324 0.000497 0.000694 380.9504 49.70417
298 40 0.826331 0.000475 0.000674 382.8068 53.75453
323 10 0.79572 0.000786 0.000888 354.9708 12.15951
323 15 0.798766 0.000743 0.000857 357.6936 13.23238
323 20 0.801659 0.000704 0.000828 360.2891 14.37013
323 25 0.804411 0.000668 0.000802 362.7673 15.5762
323 30 0.807034 0.000635 0.000777 365.1371 16.85416
323 35 0.809538 0.000605 0.000753 367.4064 18.20778
323 40 0.811932 0.000577 0.000731 369.5823 19.64102
348 10 0.777523 0.00096 0.000962 338.921 5.268102
348 15 0.78115 0.000903 0.000927 342.0906 5.730682
348 20 0.784583 0.000852 0.000894 345.1036 6.218834
348 25 0.787838 0.000805 0.000863 347.9735 6.7338
348 30 0.790933 0.000763 0.000835 350.7123 7.27687
348 35 0.793879 0.000725 0.000809 353.3303 7.849387
348 40 0.79669 0.000689 0.000784 355.8366 8.452754
373 10 0.758343 0.001162 0.001036 322.4063 2.57946
373 15 0.762617 0.001087 0.000994 326.0505 2.807398
373 20 0.766644 0.001021 0.000956 329.5032 3.04684
373 25 0.77045 0.000961 0.000922 332.7826 3.298312
373 30 0.774055 0.000907 0.00089 335.9045 3.562356
373 35 0.777479 0.000859 0.000861 338.8825 3.839533
373 40 0.780736 0.000814 0.000833 341.7281 4.130422
398 10 0.738284 0.001398 0.001109 305.5761 -
398 15 0.743277 0.0013 0.001061 309.7233 -
398 20 0.747959 0.001213 0.001017 313.6373 -
398 25 0.752364 0.001137 0.000978 317.3427 -
398 30 0.756523 0.001069 0.000942 320.8603 -
398 35 0.760459 0.001008 0.00091 324.2075 -
398 40 0.764193 0.000953 0.000879 327.3994 -
182
Table D.2. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 1.42 mass % Polymer 1.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.819331 0.00062622 0.000814 377.1491 36.04737
298 15 0.821834 0.00059468 0.000787 379.4576 39.26547
298 20 0.824221 0.00056567 0.000762 381.6648 42.69662
298 25 0.826499 0.00053891 0.000739 383.7778 46.35321
298 30 0.828678 0.00051415 0.000717 385.8033 50.24834
298 35 0.830762 0.00049116 0.000697 387.7469 54.39583
298 40 0.83276 0.00046977 0.000677 389.6139 58.81026
323 10 0.80207 0.00077347 0.000889 361.4261 13.1858
323 15 0.805093 0.00073171 0.000859 364.1552 14.34245
323 20 0.807966 0.00069366 0.000831 366.7587 15.56903
323 25 0.810701 0.00065884 0.000804 369.2464 16.8692
323 30 0.81331 0.00062687 0.000779 371.6269 18.24682
323 35 0.815802 0.0005974 0.000756 373.908 19.70594
323 40 0.818186 0.00057014 0.000734 376.0965 21.25079
348 10 0.783702 0.00094461 0.000964 345.0614 5.660301
348 15 0.787302 0.0008895 0.000928 348.2387 6.154336
348 20 0.790711 0.00083981 0.000896 351.2613 6.675699
348 25 0.793947 0.00079478 0.000866 354.1427 7.225707
348 30 0.797026 0.00075378 0.000838 356.8942 7.805735
348 35 0.799959 0.00071627 0.000812 359.5262 8.417214
348 40 0.802759 0.00068183 0.000788 362.0474 9.061636
373 10 0.764341 0.00114396 0.001037 328.223 2.750142
373 15 0.768583 0.00107136 0.000996 331.8765 2.991661
373 20 0.772584 0.0010067 0.000959 335.3407 3.245391
373 25 0.776368 0.00094871 0.000925 338.6337 3.511887
373 30 0.779956 0.00089641 0.000893 341.7708 3.791721
373 35 0.783365 0.00084897 0.000864 344.7651 4.085485
373 40 0.786611 0.00080575 0.000837 347.6283 4.393791
398 10 0.744092 0.00137675 0.001111 311.0631 -
398 15 0.749049 0.0012812 0.001063 315.2213 -
398 20 0.753702 0.00119724 0.00102 319.1491 -
398 25 0.758083 0.00112284 0.000981 322.8706 -
398 30 0.762222 0.00105643 0.000946 326.4059 -
398 35 0.766143 0.00099677 0.000914 329.7724 -
398 40 0.769865 0.00094286 0.000884 332.9846 -
183
Table D.3. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 2.85 mass % Polymer 1.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.819855 0.000627 0.000839 389.0425 36.31646
298 15 0.822365 0.000596 0.000813 391.4277 39.56122
298 20 0.82476 0.000568 0.000788 393.711 43.0226
298 25 0.827049 0.000541 0.000765 395.8994 46.71332
298 30 0.829239 0.000517 0.000743 397.9994 50.64679
298 35 0.831338 0.000494 0.000722 400.0167 54.83718
298 40 0.833352 0.000473 0.000702 401.9566 59.29944
323 10 0.802042 0.000775 0.000918 372.3206 13.1811
323 15 0.805073 0.000734 0.000887 375.1399 14.33889
323 20 0.807957 0.000697 0.000858 377.8324 15.56738
323 25 0.810706 0.000662 0.000831 380.408 16.87032
323 30 0.813331 0.000631 0.000806 382.8751 18.25164
323 35 0.815841 0.000602 0.000783 385.2416 19.71545
323 40 0.818244 0.000575 0.000761 387.5142 21.2661
348 10 0.783099 0.000948 0.000994 354.9411 5.620786
348 15 0.786712 0.000894 0.000959 358.2235 6.112384
348 20 0.790137 0.000845 0.000926 361.3495 6.631497
348 25 0.793392 0.0008 0.000895 364.3323 7.179466
348 30 0.79649 0.00076 0.000867 367.1835 7.757685
348 35 0.799445 0.000722 0.00084 369.9132 8.367608
348 40 0.802268 0.000688 0.000816 372.5305 9.010751
373 10 0.763144 0.001151 0.001071 337.0821 2.715188
373 15 0.767406 0.001078 0.001029 340.8575 2.954352
373 20 0.771429 0.001014 0.000991 344.4407 3.205774
373 25 0.775237 0.000957 0.000956 347.8499 3.470016
373 30 0.778851 0.000905 0.000924 351.1005 3.747656
373 35 0.782288 0.000857 0.000895 354.2059 4.039294
373 40 0.785563 0.000814 0.000867 357.1775 4.345549
398 10 0.742283 0.001388 0.001147 318.905 -
398 15 0.747269 0.001292 0.001098 323.2038 -
398 20 0.751953 0.001209 0.001054 327.2679 -
398 25 0.756367 0.001134 0.001015 331.1215 -
398 30 0.76054 0.001068 0.000979 334.7852 -
398 35 0.764495 0.001008 0.000945 338.2765 -
398 40 0.768253 0.000954 0.000915 341.6103 -
184
Table D.4. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 7.12 mass % Polymer 1.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.822226 0.000721 0.000672 267.9444 37.55771
298 15 0.825093 0.000672 0.000643 269.816 41.11807
298 20 0.827779 0.000629 0.000615 271.5757 44.89652
298 25 0.830301 0.000589 0.00059 273.2335 48.90472
298 30 0.832676 0.000554 0.000566 274.7984 53.15497
298 35 0.834914 0.000521 0.000544 276.278 57.66021
298 40 0.837029 0.000491 0.000524 277.6791 62.43408
323 10 0.807853 0.000887 0.000738 258.6586 14.19729
323 15 0.811315 0.000824 0.000704 260.8804 15.5272
323 20 0.81455 0.000768 0.000673 262.9651 16.93026
323 25 0.817582 0.000718 0.000645 264.926 18.41001
323 30 0.820429 0.000673 0.000619 266.7748 19.97013
323 35 0.82311 0.000632 0.000594 268.5212 21.61449
323 40 0.82564 0.000595 0.000572 270.174 23.34713
348 10 0.792447 0.001078 0.000802 248.8871 6.266918
348 15 0.796564 0.000997 0.000763 251.4804 6.853501
348 20 0.800399 0.000925 0.000728 253.9073 7.469044
348 25 0.803981 0.000862 0.000697 256.1854 8.114852
348 30 0.807339 0.000806 0.000668 258.3296 8.792274
348 35 0.810494 0.000755 0.000641 260.3524 9.502703
348 40 0.813465 0.000709 0.000616 262.2648 10.24759
373 10 0.776108 0.001296 0.000864 238.7301 3.119198
373 15 0.780947 0.001192 0.00082 241.7159 3.413765
373 20 0.785433 0.001102 0.000781 244.5013 3.721332
373 25 0.789611 0.001022 0.000746 247.1093 4.042473
373 30 0.793515 0.000952 0.000714 249.5589 4.377767
373 35 0.797175 0.00089 0.000684 251.866 4.727808
373 40 0.800614 0.000834 0.000657 254.0442 5.0932
398 10 0.75893 0.001547 0.000926 228.279 -
398 15 0.76456 0.001413 0.000876 231.6783 -
398 20 0.769755 0.001299 0.000832 234.8377 -
398 25 0.774574 0.0012 0.000792 237.787 -
398 30 0.779062 0.001113 0.000757 240.5504 -
398 35 0.783257 0.001037 0.000724 243.1479 -
398 40 0.78719 0.000969 0.000695 245.5964 -
185
Table D.5. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 0.70 mass % Polymer 2.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.818367 0.000619 0.000863 405.319 35.55873
298 15 0.820845 0.00059 0.000837 407.7765 38.71976
298 20 0.823213 0.000563 0.000812 410.1327 42.09336
298 25 0.825479 0.000538 0.000789 412.3945 45.69211
298 30 0.827652 0.000514 0.000767 414.5681 49.52932
298 35 0.829737 0.000492 0.000746 416.6592 53.61904
298 40 0.831739 0.000472 0.000727 418.6727 57.9761
323 10 0.800091 0.000767 0.000943 387.4177 12.85681
323 15 0.803084 0.000727 0.000913 390.3212 13.98001
323 20 0.805936 0.000691 0.000884 393.0984 15.17241
323 25 0.808659 0.000658 0.000857 395.759 16.4377
323 30 0.811262 0.000628 0.000833 398.3112 17.77978
323 35 0.813755 0.0006 0.000809 400.7627 19.20274
323 40 0.816144 0.000574 0.000787 403.12 20.71085
348 10 0.780675 0.000939 0.001022 368.8424 5.464581
348 15 0.784243 0.000886 0.000986 372.2221 5.939854
348 20 0.787632 0.000839 0.000953 375.4456 6.442013
348 25 0.790856 0.000796 0.000923 378.5259 6.972379
348 30 0.793931 0.000757 0.000895 381.4744 7.53233
348 35 0.796867 0.00072 0.000868 384.3011 8.123302
348 40 0.799675 0.000687 0.000843 387.0147 8.746796
373 10 0.760238 0.001141 0.0011 349.7837 2.632185
373 15 0.76445 0.001071 0.001059 353.6706 2.862757
373 20 0.768433 0.001009 0.001021 357.3653 3.105296
373 25 0.772209 0.000953 0.000986 360.8856 3.360356
373 30 0.775796 0.000902 0.000953 364.2466 3.628507
373 35 0.779212 0.000856 0.000924 367.4614 3.91034
373 40 0.782471 0.000814 0.000896 370.5417 4.206466
398 10 0.738889 0.001378 0.001179 330.4139 -
398 15 0.743821 0.001285 0.00113 334.8401 -
398 20 0.748461 0.001204 0.001086 339.0308 -
398 25 0.752841 0.001131 0.001046 343.0099 -
398 30 0.756986 0.001066 0.00101 346.7979 -
398 35 0.76092 0.001008 0.000976 350.4119 -
398 40 0.764663 0.000955 0.000945 353.867 -
186
Table D.6. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 1.40 mass % Polymer 2.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.812691 0.000609 0.000814 388.1513 32.81357
298 15 0.815109 0.000579 0.000788 390.4645 35.70653
298 20 0.817417 0.000552 0.000764 392.6787 38.79116
298 25 0.819623 0.000526 0.000742 394.8009 42.07869
298 30 0.821734 0.000503 0.00072 396.8373 45.581
298 35 0.823756 0.000481 0.0007 398.7935 49.31066
298 40 0.825697 0.00046 0.000681 400.6743 53.28089
323 10 0.79556 0.000753 0.00089 371.9596 12.13465
323 15 0.798479 0.000713 0.00086 374.6943 13.18409
323 20 0.801257 0.000677 0.000833 377.3063 14.29703
323 25 0.803906 0.000644 0.000807 379.8051 15.47684
323 30 0.806435 0.000613 0.000783 382.1988 16.72705
323 35 0.808854 0.000585 0.00076 384.495 18.05137
323 40 0.81117 0.000559 0.000738 386.7 19.45369
348 10 0.777329 0.000919 0.000964 355.1078 5.256254
348 15 0.780806 0.000867 0.00093 358.2917 5.707876
348 20 0.784104 0.00082 0.000898 361.3246 6.184511
348 25 0.787238 0.000777 0.000869 364.2193 6.687379
348 30 0.790224 0.000738 0.000841 366.9867 7.217747
348 35 0.793071 0.000702 0.000816 369.6365 7.776941
348 40 0.795792 0.000669 0.000792 372.1773 8.366342
373 10 0.758114 0.001113 0.001038 337.7687 2.573158
373 15 0.762212 0.001044 0.000998 341.4301 2.795314
373 20 0.766083 0.000983 0.000962 344.9067 3.028723
373 25 0.769749 0.000928 0.000928 348.2155 3.273901
373 30 0.773229 0.000878 0.000897 351.3713 3.531381
373 35 0.77654 0.000832 0.000869 354.3868 3.801713
373 40 0.779695 0.000791 0.000842 357.273 4.085468
398 10 0.738018 0.00134 0.001111 320.0988 -
398 15 0.742807 0.001249 0.001065 324.2665 -
398 20 0.747309 0.001169 0.001023 328.2091 -
398 25 0.751555 0.001098 0.000985 331.9494 -
398 30 0.755571 0.001035 0.00095 335.5068 -
398 35 0.75938 0.000978 0.000918 338.898 -
398 40 0.763001 0.000926 0.000889 342.1371 -
187
Table D.7. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 2.80 mass % Polymer 2.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa) η (mPa s)
298 10 0.820019 0.000604 0.000796 383.0934 36.40073
298 15 0.822435 0.000574 0.000771 385.3541 39.60047
298 20 0.82474 0.000546 0.000747 387.5171 43.01048
298 25 0.826942 0.000521 0.000724 389.5891 46.64297
298 30 0.829048 0.000497 0.000703 391.5764 50.51085
298 35 0.831066 0.000475 0.000683 393.4843 54.62771
298 40 0.833 0.000455 0.000664 395.318 59.00795
323 10 0.803106 0.000745 0.000871 367.4541 13.36148
323 15 0.806023 0.000706 0.000841 370.1282 14.5136
323 20 0.808798 0.00067 0.000814 372.6811 15.73482
323 25 0.811443 0.000637 0.000789 375.1223 17.02879
323 30 0.813967 0.000606 0.000765 377.4598 18.39929
323 35 0.81638 0.000578 0.000742 379.701 19.85032
323 40 0.81869 0.000552 0.000721 381.8524 21.38607
348 10 0.785093 0.000909 0.000944 351.1554 5.75266
348 15 0.788567 0.000857 0.00091 354.2699 6.245392
348 20 0.791861 0.000811 0.000879 357.2355 6.765165
348 25 0.79499 0.000768 0.00085 360.0647 7.313281
348 30 0.79797 0.000729 0.000823 362.7685 7.891097
348 35 0.800811 0.000693 0.000798 365.3564 8.500026
348 40 0.803525 0.00066 0.000774 367.8369 9.141544
373 10 0.766093 0.0011 0.001016 334.3643 2.802136
373 15 0.770186 0.001032 0.000977 337.9466 3.043234
373 20 0.774051 0.000971 0.000941 341.347 3.296427
373 25 0.777711 0.000916 0.000908 344.5822 3.562263
373 30 0.781184 0.000867 0.000878 347.6668 3.841308
373 35 0.784487 0.000822 0.000849 350.6131 4.134146
373 40 0.787634 0.000781 0.000823 353.4322 4.441382
398 10 0.746208 0.001323 0.001088 317.2318 -
398 15 0.750989 0.001234 0.001042 321.3102 -
398 20 0.755483 0.001155 0.001001 325.1671 -
398 25 0.759721 0.001084 0.000964 328.8252 -
398 30 0.763729 0.001021 0.00093 332.3035 -
398 35 0.767528 0.000965 0.000898 335.6183 -
398 40 0.771139 0.000913 0.000869 338.7835 -
188
Table D.8. Density, isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and dynamic viscosity for a selection of temperatures and pressures as calculated by the
S-L EOS and free volume model for PAO 4 + 7.01 mass % Polymer 2.
T (K) P (MPa) ρ (g/cm3) κT
(1/MPa)
βP (1/K) π (MPa) η (mPa s)
298 10 0.818058 0.000729 0.000833 330.8096 35.40306
298 15 0.820957 0.000687 0.000803 333.1588 38.78146
298 20 0.823704 0.000649 0.000774 335.3917 42.38607
298 25 0.82631 0.000615 0.000748 337.5178 46.22989
298 30 0.828788 0.000583 0.000723 339.5452 50.32662
298 35 0.831148 0.000554 0.0007 341.4812 54.69071
298 40 0.833397 0.000527 0.000678 343.3323 59.33741
323 10 0.800413 0.0009 0.000911 316.6931 12.90971
323 15 0.803912 0.000845 0.000875 319.4676 14.1282
323 20 0.807214 0.000796 0.000843 322.0981 15.42103
323 25 0.81034 0.000751 0.000813 324.5972 16.79207
323 30 0.813304 0.00071 0.000785 326.976 18.24533
323 35 0.81612 0.000673 0.000759 329.244 19.78506
323 40 0.818799 0.000639 0.000735 331.4098 21.41568
348 10 0.781656 0.0011 0.000986 302.024 5.527238
348 15 0.785821 0.001027 0.000945 305.2511 6.049505
348 20 0.789737 0.000962 0.000908 308.3011 6.600837
348 25 0.79343 0.000905 0.000874 311.1911 7.18262
348 30 0.796921 0.000852 0.000843 313.9357 7.796295
348 35 0.800229 0.000805 0.000814 316.5475 8.443359
348 40 0.80337 0.000762 0.000787 319.0376 9.125372
373 10 0.761906 0.001333 0.001061 286.9542 2.679491
373 15 0.766811 0.001237 0.001013 290.6614 2.93569
373 20 0.771402 0.001153 0.000971 294.1522 3.204859
373 25 0.775714 0.001078 0.000932 297.4495 3.487589
373 30 0.779775 0.001012 0.000897 300.5726 3.784483
373 35 0.783613 0.000953 0.000865 303.538 4.096163
373 40 0.787246 0.000899 0.000835 306.3596 4.423269
398 10 0.741271 0.001605 0.001136 271.6214 -
398 15 0.747 0.001478 0.00108 275.8366 -
398 20 0.752333 0.001369 0.001031 279.7886 -
398 25 0.757317 0.001274 0.000988 283.5081 -
398 30 0.761994 0.00119 0.000948 287.0204 -
398 35 0.766396 0.001116 0.000912 290.3469 -
398 40 0.770554 0.001049 0.000879 293.5053 -
189
Table D.9. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the Tait equation
for an experimental ATF.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)
298 10 0.865318 0.000594 0.0009 441.4847
298 15 0.867854 0.000577 0.000884 441.6019
298 20 0.870325 0.000561 0.000869 441.6752
298 25 0.872736 0.000546 0.000855 441.706
298 30 0.875088 0.000531 0.000841 441.6955
298 35 0.877387 0.000518 0.000828 441.6448
298 40 0.879633 0.000505 0.000816 441.5553
323 10 0.845892 0.000681 0.000917 424.8183
323 15 0.848729 0.000659 0.000899 425.7044
323 20 0.851485 0.000638 0.000882 426.5349
323 25 0.854164 0.000619 0.000866 427.3118
323 30 0.85677 0.0006 0.000851 428.0368
323 35 0.859309 0.000583 0.000837 428.7117
323 40 0.861783 0.000567 0.000824 429.3381
348 10 0.82654 0.00078 0.000935 406.8522
348 15 0.82971 0.000751 0.000914 408.5746
348 20 0.832775 0.000724 0.000895 410.2272
348 25 0.835744 0.000699 0.000878 411.8128
348 30 0.838622 0.000676 0.000861 413.3338
348 35 0.841416 0.000655 0.000846 414.7926
348 40 0.844132 0.000634 0.000832 416.1914
373 10 0.807271 0.000892 0.000953 388.202
373 15 0.810804 0.000855 0.00093 390.8322
373 20 0.814204 0.00082 0.000909 393.3753
373 25 0.817484 0.000788 0.000889 395.8352
373 30 0.820652 0.000759 0.000871 398.2153
373 35 0.823716 0.000732 0.000855 400.5189
373 40 0.826684 0.000707 0.000839 402.7491
398 10 0.788092 0.001019 0.000971 369.3576
398 15 0.792018 0.00097 0.000946 372.9713
398 20 0.79578 0.000926 0.000922 376.477
398 25 0.799391 0.000886 0.000901 379.8801
398 30 0.802864 0.000849 0.000882 383.1854
398 35 0.806212 0.000816 0.000864 386.3974
398 40 0.809443 0.000785 0.000847 389.5202
190
Table D.10. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the Tait equation
for a commercial ATF.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)
298 10 0.875381 0.000604 0.00085 409.1594
298 15 0.87799 0.000586 0.000834 408.8845
298 20 0.880531 0.00057 0.00082 408.5673
298 25 0.883009 0.000554 0.000806 408.2093
298 30 0.885427 0.00054 0.000793 407.8117
298 35 0.887788 0.000526 0.00078 407.3757
298 40 0.890095 0.000512 0.000769 406.9022
323 10 0.85682 0.000689 0.000865 395.5996
323 15 0.859727 0.000666 0.000847 396.0235
323 20 0.862548 0.000645 0.000831 396.3944
323 25 0.86529 0.000625 0.000816 396.7142
323 30 0.867957 0.000606 0.000801 396.9846
323 35 0.870553 0.000589 0.000788 397.2072
323 40 0.873084 0.000572 0.000775 397.3835
348 10 0.838331 0.000784 0.00088 380.6305
348 15 0.841563 0.000755 0.000861 381.8126
348 20 0.844688 0.000728 0.000843 382.9285
348 25 0.847713 0.000703 0.000826 383.9809
348 30 0.850647 0.000679 0.00081 384.9721
348 35 0.853494 0.000658 0.000795 385.9046
348 40 0.856261 0.000637 0.000781 386.7802
373 10 0.81992 0.000892 0.000896 364.8114
373 15 0.823505 0.000854 0.000874 366.8141
373 20 0.826958 0.00082 0.000854 368.7348
373 25 0.830288 0.000788 0.000836 370.5772
373 30 0.833504 0.000759 0.000819 372.3446
373 35 0.836615 0.000732 0.000803 374.04
373 40 0.839629 0.000707 0.000788 375.6664
398 10 0.801592 0.001013 0.000912 348.5938
398 15 0.805562 0.000964 0.000888 351.4831
398 20 0.809366 0.000921 0.000866 354.2714
398 25 0.813019 0.000881 0.000846 356.9638
398 30 0.816534 0.000845 0.000827 359.5649
398 35 0.819922 0.000812 0.00081 362.0787
398 40 0.823193 0.000781 0.000794 364.509
191
Appendix E: Density, Derived Thermodynamic Properties, and Viscosity of Ionic Liquids
and Their Mixtures with Ethanol
In this section, the full range of density, derived thermodynamic properties, and viscosity
for mixtures of PAO 4 with two methacrylate based polymeric additives and two automatic
transmission fluids have been reported.
Figures E.1-E.8 show densities of mixtures of ionic liquids with ethanol from 10-40 MPa
and 298-398 K.
Figures E.9-E.24 show the derived thermodynamic properties for all mixtures from 10-40
MPa and 298-398 K.
Figures D.25 and D.29 show viscosity values for mixtures of ionic liquids with ethanol
from 10-40 MPa and 298-373 K.
Tables E.1-E.28 include select data for density as calculated from the Sanchez-Lacombe
equation of state and derived thermodynamic properties.
This Appendix has been organized into four sections:
E.1 Density of Ionic Liquid + Ethanol Mixtures
E.2 Derived Thermodynamic Properties of Ionic Liquid + Ethanol Mixtures
E.3 Viscosities of Ionic Liquid + Ethanol Mixtures
E.4 Select Tabulated Data for Ionic Liquid + Ethanol Mixtures
192
E.1 Density of Ionic Liquid + Ethanol Mixtures
Figure E.1. Density data for 25 mass % IL + Ethanol: [EMIM]Cl (top left), [PMIM]Cl (top
right), [BMIM]Cl (bottom left), [HMIM]Cl (bottom right).
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
25% [EMIM]Cl
298 K
323 K
348 K
373 K
398 K
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
25% [PMIM]Cl298 K
323 K
348 K
373 K
398 K
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
25% [BMIM]Cl298K
323K
348K
373K
398K
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
25% [HMIM]Cl298 K
323 K
348 K
373 K
398 K
193
Figure E.2. Density data for 50 mass % IL + Ethanol: [EMIM]Cl (top left), [PMIM]Cl (top
right), [BMIM]Cl (bottom left), [HMIM]Cl (bottom right).
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
50% [EMIM]Cl
298 K
323 K
348 K
373 K
398 K
0.86
0.88
0.9
0.92
0.94
0.96
0.98
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
50% [PMIM]Cl298 K
323 K
348 K
373 K
398 K
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
50% [BMIM]Cl298K
323K
348K
373K
398K
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
50% [HMIM]Cl298 K
323 K
348 K
373 K
398 K
194
Figure E.3. Density data for 75 mass % IL + Ethanol: [EMIM]Cl (top left), [PMIM]Cl (top
right), [BMIM]Cl (bottom left), [HMIM]Cl (bottom right).
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
75% [EMIM]Cl
348 K
373 K
398 K
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
75% [PMIM]Cl298 K
323 K
348 K
373 K
398 K
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
75% [BMIM]Cl
298K
323K
348K
373K
398K
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
75% [HMIM]Cl 298 K
323 K
348 K
373 K
398 K
195
Figure E.4. Density data for 5 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).
Figure E.5. Density data for 15 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).
0.68
0.7
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
5% [EMIM][Ac]
298 K
323 K
348 K
373 K
398 K
0.7
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
5% [BMIM]Cl298K
323K
348K
373K
398K
0.7
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
15% [EMIM][Ac]
298 K
323 K
348 K
373 K
398 K
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
15% [BMIM]Ac298K
323K
348K
373K
398K
196
Figure E.6. Density data for 25 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).
Figure E.7. Density data for 50 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
25% [EMIM][Ac]
298 K
323 K
348 K
373 K
398 K
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
25% [BMIM]Ac298K
323K
348K
373K
398K
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
50% [EMIM][Ac]
298 K
323 K
348 K
373 K
398 K
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
50% [BMIM]Ac298K
323K
348K
373K
398K
197
Figure E.8. Density data for 75 mass % IL + Ethanol: [EMIM]Ac (left) and [BMIM]Ac (right).
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
75% [EMIM][Ac]
298 K
323 K
348 K
373 K
398 K
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
0 10 20 30 40 50
Den
sity
(g/c
m3)
Pressure (MPa)
75% [BMIM]Ac
298K
323K
348K
373K
398K
198
E.2 Derived Thermodynamic Properties of Ionic Liquid + Ethanol Mixtures
Figure E.9. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 25 mass % [EMIM]Cl + ethanol.
0
0.0005
0.001
0.0015
0.002
0.0025
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K323 K
298 K
25% [EMIM]Cl
0.0007
0.0009
0.0011
0.0013
0.0015
0.0017
250 300 350 400 450
βP
(1/K
)Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
25% [EMIM]Cl
250
270
290
310
330
350
370
390
410
430
450
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
25% [EMIM]Cl
15
16
17
18
19
20
21
22
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
25% [EMIM]Cl
199
Figure E.10. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 75 mass % [EMIM]Cl + ethanol.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
75% [EMIM]Cl
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
75% [EMIM]Cl
300
350
400
450
500
550
600
650
700
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
348 K373 K
398 K
75% [EMIM]Cl
15
16
17
18
19
20
21
22
23
24
25
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
348 K
373 K
398 K
75% [EMIM]Cl
200
Figure E.11. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 25 mass % [PMIM]Cl + ethanol.
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
25% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
250 300 350 400 450
βP
(1/K
)
Temperature (K)
25% [PMIM]Cl
10 MPa
20 MPa
30 MPa
40 MPa
350
370
390
410
430
450
470
490
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
25% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
17
17.5
18
18.5
19
19.5
20
20.5
21
21.5
22
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
25% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
201
Figure E.12. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 75 mass % [PMIM]Cl + ethanol.
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
75% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
250 300 350 400 450
βP
(1/K
)
Temperature (K)
75% [PMIM]Cl
10 MPa
20 MPa
30 MPa
40 MPa
350
370
390
410
430
450
470
490
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
75% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
19
19.5
20
20.5
21
21.5
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
75% [PMIM]Cl
298 K
323 K
348 K
373 K
398 K
202
Figure E.13. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 25 mass % [BMIM]Cl + ethanol.
0
0.0005
0.001
0.0015
0.002
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
348K
373K
398K
25% [BMIM]Cl
323 K
298 K
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
250 300 350 400 450
βP
(1/K
)
Pressure (MPa)
25% [BMIM]Cl 10 MPa
20 MPa
30 MPa
40 MPa
300
320
340
360
380
400
420
440
460
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
25% [BMIM]Cl
298K
323K
348K
373K
398K
17
18
19
20
21
22
23
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
25% [BMIM]Cl
298K
323K
348K
373K
398K
203
Figure E.14. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 75 mass % [BMIM]Cl + ethanol.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298K
323K
348K
373K
398K
75% [BMIM]Cl
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
250 300 350 400 450
Isob
ari
c E
xp
an
sivit
y (
1/K
)
Pressure (MPa)
75% [BMIM]Cl
10 MPa
20 MPa
30 MPa
40 MPa
320
340
360
380
400
420
440
460
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
75% [BMIM]Cl
298K
323K
348K
373K
398K
18
18.5
19
19.5
20
20.5
21
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
75% [BMIM]Cl
298K
323K
348K
373K
398K
204
Figure E.15. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 25 mass % [HMIM]Cl + ethanol.
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
25% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
250 300 350 400 450
βP
(1/K
)
Temperature (K)
25% [HMIM]Cl10 MPa
20 MPa
30 MPa
40 MPa
320
340
360
380
400
420
440
460
480
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
25% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
18
18.5
19
19.5
20
20.5
21
21.5
22
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
25% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
205
Figure E.16. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 75 mass % [HMIM]Cl + ethanol.
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
75% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
250 300 350 400 450
βP
(1/K
)
Temperature (K)
75% [HMIM]Cl10 MPa
20 MPa
30 MPa
40 MPa
260
280
300
320
340
360
380
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
75% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
16
16.5
17
17.5
18
18.5
19
19.5
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
75% [HMIM]Cl
298 K
323 K
348 K
373 K
398 K
206
Figure E.17. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 5 mass % [EMIM]Ac + ethanol.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
5% [EMIM][Ac]
0.0007
0.0009
0.0011
0.0013
0.0015
0.0017
0.0019
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
250
270
290
310
330
350
370
390
410
430
450
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
5% [EMIM][Ac]
15
16
17
18
19
20
21
22
23
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
5% [EMIM][Ac]
207
Figure E.18. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 15 mass % [EMIM]Ac + ethanol.
0
0.0005
0.001
0.0015
0.002
0.0025
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
15% [EMIM][Ac]
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
250
270
290
310
330
350
370
390
410
430
450
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
15% [EMIM][Ac]
15
16
17
18
19
20
21
22
23
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
15% [EMIM][Ac]
208
Figure E.19. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 25 mass % [EMIM]Ac + ethanol.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
25% [EMIM][Ac]
0.0007
0.0009
0.0011
0.0013
0.0015
0.0017
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
25% [EMIM][Ac]
300
350
400
450
500
550
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K
323 K
348 K
373 K
398 K
25% [EMIM][Ac]
15
16
17
18
19
20
21
22
23
24
25
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
298 K323 K
348 K373 K
398 K
25% [EMIM][Ac]
209
Figure E.20. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 75 mass % [EMIM]Ac + ethanol.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
398 K
373 K
348 K
323 K
298 K
75% [EMIM][Ac]
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
0.0015
250 300 350 400 450
βP
(1/K
)
Temperature (K)
10 MPa
20 MPa
30 MPa
40 MPa
300
350
400
450
500
550
600
650
700
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
298 K323 K348 K
373 K
398 K
75% [EMIM][Ac]
15
16
17
18
19
20
21
22
23
24
25
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
298 K323 K348 K
373 K
398 K
75% [EMIM][Ac]
210
Figure E.21. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 5 mass % [BMIM]Ac + ethanol.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298K
323K
348K
373K
398K
5% [BMIM]Ac
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
250 300 350 400 450
βP
(1/K
)
Pressure (MPa)
5% [BMIM]Ac 10 MPa
20 MPa
30 MPa
40 MPa
250
270
290
310
330
350
370
390
410
430
450
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
5% [BMIM]Ac
298K
323K
348K
373K
398K
15
16
17
18
19
20
21
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
5% [BMIM]Ac298K
323K
348K
373K
398K
211
Figure E.22. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 15 mass % [BMIM]Ac + ethanol.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298K
323K
348K
373K
398K
15% [BMIM]Ac
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
0.0014
0.0015
250 300 350 400 450
βP
(1/K
)
Pressure (MPa)
15% [BMIM]Ac 10 MPa
20 MPa
30 MPa
40 MPa
270
290
310
330
350
370
390
410
430
450
470
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
15% [BMIM]Ac298K
323K
348K
373K
398K
16
17
18
19
20
21
22
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
15% [BMIM]Ac
298K
323K
348K
373K
398K
212
Figure E.23. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 25 mass % [BMIM]Ac + ethanol.
0
0.0005
0.001
0.0015
0.002
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298K
323K
348K373K
398K
25% [BMIM]Ac
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
0.0013
250 300 350 400 450
βP
(1/K
)
Pressure (MPa)
25% [BMIM]Ac 10 MPa
20 MPa
30 MPa
40 MPa
340
360
380
400
420
440
460
480
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
25% [BMIM]Ac298K
323K
348K
373K
398K
17
18
19
20
21
22
23
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
25% [BMIM]Ac
298K
323K
348K
373K
398K
213
Figure E.24. Isothermal compressibility, isobaric thermal expansion coefficient, internal
pressure, and solubility parameter for a mixture of 75 mass % [BMIM]Ac + ethanol.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0 10 20 30 40 50
κT
(1/M
Pa)
Pressure (MPa)
298K
323K
348K
373K
398K
75% [BMIM]Ac
0.0006
0.0007
0.0008
0.0009
0.001
0.0011
0.0012
250 300 350 400 450
βP
(1/K
)
Temperature (K)
75% [BMIM]Ac10 MPa
20 MPa
30 MPa
40 MPa
350
370
390
410
430
450
470
490
510
530
550
0 10 20 30 40 50
Inte
rnal
Pre
ssu
re (
MP
a)
Pressure (MPa)
75% [BMIM]Ac
298K
323K
348K
373K
398K
17
18
19
20
21
22
23
0 10 20 30 40 50
Solu
bil
ity P
ara
met
er (
MP
a0
.5)
Pressure (MPa)
75% [BMIM]Ac
298K
323K348K
373K
398K
214
E.3 Viscosities of Ionic Liquid + Ethanol Mixtures
Figure E.25. Viscosity versus pressure for a mixture of 95 mass % [EMIM]Ac + ethanol at 500
rpm.
Figure E.26. Viscosity versus pressure for a mixture of 90 mass % [EMIM]Ac + ethanol at 500
rpm.
0
20
40
60
80
100
120
140
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
95% [EMIM]Ac
500 RPM
298 K (300 RPM)
323 K
348 K
373 K
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
90% [EMIM]Ac
500 RPM
298 K
323 K
348 K
298 K
215
Figure E.27. Viscosity versus pressure for a mixture of 95 mass % [BMIM]Ac + ethanol at 500
rpm.
Figure E.28. Viscosity versus pressure for a mixture of 90 mass % [BMIM]Ac + ethanol at 500
rpm.
0
50
100
150
200
250
300
350
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
95% [BMIM]Ac
500 RPM
298 K (150 RPM)
323 K
348 K373 K
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
90% [BMIM]Ac
500 RPM
298 K
323 K
348 K373 K
216
Figure E.29. Viscosity versus pressure for a mixture of 75 mass % [BMIM]Ac + ethanol at 500
rpm.
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50
Vis
cosi
ty (
mP
a s
)
Pressure (MPa)
75% [BMIM]Ac
500 RPM
298 K
323 K
348 K
217
E.4 Select Tabulated Data for Ionic Liquid + Ethanol Mixtures
Table E.1. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
[EMIM]Cl.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)
348 10 1.068247 0.00053 0.000776 499.1067
348 15 1.071023 0.000508 0.000755 501.7042
348 20 1.073694 0.000488 0.000735 504.2091
348 25 1.076265 0.000469 0.000716 506.627
348 30 1.078743 0.000451 0.000699 508.9629
348 35 1.081134 0.000435 0.000682 511.2214
348 40 1.083442 0.000419 0.000666 513.4067
373 10 1.046798 0.000646 0.000847 479.2654
373 15 1.050109 0.000617 0.000823 482.3013
373 20 1.053284 0.000591 0.0008 485.2228
373 25 1.056335 0.000566 0.000779 488.0374
373 30 1.059268 0.000543 0.000759 490.7518
373 35 1.062093 0.000522 0.000739 493.3723
373 40 1.064814 0.000502 0.000721 495.9043
398 10 1.023921 0.000782 0.000921 458.5459
398 15 1.027835 0.000744 0.000892 462.0581
398 20 1.031577 0.00071 0.000866 465.429
398 25 1.035161 0.000678 0.000841 468.669
398 30 1.038599 0.000649 0.000818 471.7873
398 35 1.041901 0.000621 0.000796 474.7919
398 40 1.045077 0.000596 0.000775 477.6903
218
Table E.2. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
25 mass % [EMIM]Cl + ethanol.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)
298 10 0.853326 0.00071521 0.000979 398.0595
298 15 0.856297 0.00067589 0.000943 400.8366
298 20 0.859118 0.00064011 0.00091 403.4817
298 25 0.861801 0.0006074 0.000878 406.0053
298 30 0.864356 0.00057737 0.000849 408.4167
298 35 0.866794 0.00054972 0.000822 410.7241
298 40 0.869124 0.00052417 0.000797 412.9347
323 10 0.83131 0.00092766 0.001114 377.7842
323 15 0.835054 0.00087075 0.001068 381.1946
323 20 0.838588 0.00081973 0.001026 384.4285
323 25 0.841934 0.00077372 0.000988 387.5021
323 30 0.845108 0.00073199 0.000953 390.4292
323 35 0.848125 0.00069398 0.00092 393.2217
323 40 0.850998 0.00065921 0.00089 395.8902
348 10 0.807011 0.00120016 0.001262 356.0223
348 15 0.811695 0.00111658 0.001204 360.167
348 20 0.816086 0.00104306 0.001151 364.0745
348 25 0.820217 0.00097786 0.001104 367.7696
348 30 0.824115 0.0009196 0.00106 371.2734
348 35 0.827803 0.00086722 0.001021 374.6036
348 40 0.8313 0.00081987 0.000984 377.7754
373 10 0.780329 0.00155726 0.001431 332.8696
373 15 0.786176 0.00143199 0.001355 337.8766
373 20 0.791607 0.00132444 0.001287 342.561
373 25 0.796677 0.00123101 0.001228 346.9624
373 30 0.801428 0.00114904 0.001174 351.1129
373 35 0.805896 0.0010765 0.001126 355.0393
373 40 0.810112 0.00101184 0.001082 358.7638
398 10 0.751084 0.00203808 0.00163 308.3863
398 15 0.758399 0.00184509 0.001527 314.4226
398 20 0.765112 0.00168454 0.001439 320.0133
398 25 0.771315 0.0015487 0.001363 325.2229
398 30 0.777078 0.00143216 0.001296 330.1017
398 35 0.78246 0.001331 0.001236 334.6902
398 40 0.787507 0.00124231 0.001183 339.0211
219
Table E.3. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
50 mass % [EMIM]Cl + ethanol.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)
298 10 0.922728 0.000603 0.000885 427.5271
298 15 0.925443 0.000573 0.000856 430.0466
298 20 0.928033 0.000546 0.000828 432.4574
298 25 0.930509 0.00052 0.000803 434.7673
298 30 0.932877 0.000497 0.000779 436.9832
298 35 0.935145 0.000475 0.000756 439.1112
298 40 0.937321 0.000455 0.000734 441.1569
323 10 0.901282 0.000771 0.000998 407.8847
323 15 0.904667 0.000729 0.000962 410.9544
323 20 0.907884 0.000691 0.000928 413.882
323 25 0.910946 0.000656 0.000898 416.6789
323 30 0.913867 0.000624 0.000869 419.355
323 35 0.916656 0.000595 0.000842 421.9192
323 40 0.919325 0.000568 0.000817 424.3793
348 10 0.877776 0.00098 0.001118 386.8862
348 15 0.881956 0.000921 0.001074 390.5801
348 20 0.885908 0.000868 0.001033 394.0877
348 25 0.889652 0.00082 0.000995 397.4262
348 30 0.893208 0.000777 0.000961 400.6099
348 35 0.896593 0.000737 0.000929 403.6516
348 40 0.89982 0.000701 0.000899 406.5624
373 10 0.852193 0.001245 0.00125 364.6633
373 15 0.857327 0.00116 0.001194 369.0701
373 20 0.862147 0.001085 0.001143 373.2318
373 25 0.866688 0.001018 0.001098 377.1739
373 30 0.870979 0.000959 0.001056 380.9178
373 35 0.875044 0.000905 0.001018 384.4819
373 40 0.878904 0.000857 0.000983 387.8817
398 10 0.824471 0.001584 0.001399 341.3239
398 15 0.830763 0.00146 0.001326 346.5535
398 20 0.83662 0.001353 0.001263 351.4575
398 25 0.842098 0.00126 0.001206 356.075
398 30 0.847242 0.001178 0.001155 360.4382
398 35 0.852088 0.001105 0.00111 364.5735
398 40 0.856668 0.00104 0.001068 368.5033
220
Table E.4. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
75 mass % [EMIM]Cl + ethanol.
T (K) P (MPa) ρ (g/cm3) κT (1/MPa) βP (1/K) π (MPa)
348 10 0.962059 0.000766 0.000965 428.5136
348 15 0.965654 0.000727 0.000933 431.7221
348 20 0.96908 0.000691 0.000903 434.791
348 25 0.972351 0.000658 0.000875 437.7312
348 30 0.975479 0.000627 0.000848 440.5519
348 35 0.978474 0.000599 0.000824 443.2615
348 40 0.981346 0.000573 0.000801 445.8676
373 10 0.937957 0.000952 0.001066 407.3119
373 15 0.942305 0.000898 0.001026 411.0966
373 20 0.946429 0.000849 0.00099 414.7032
373 25 0.950351 0.000805 0.000957 418.147
373 30 0.954087 0.000765 0.000926 421.4414
373 35 0.957653 0.000728 0.000897 424.598
373 40 0.961063 0.000694 0.00087 427.627
398 10 0.912088 0.001182 0.001173 385.1539
398 15 0.917317 0.001107 0.001125 389.583
398 20 0.92225 0.00104 0.001081 393.7841
398 25 0.926916 0.00098 0.001041 397.7795
398 30 0.931343 0.000927 0.001005 401.588
398 35 0.935552 0.000878 0.000971 405.2259
398 40 0.939562 0.000834 0.00094 408.7073
221
Table E.5. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
[PMIM]Cl.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 1.103534 0.000372 0.000479 373.6855
298 15 1.105536 0.000353 0.000462 375.0424
298 20 1.10744 0.000336 0.000446 376.3356
298 25 1.109254 0.000319 0.000431 377.5692
298 30 1.110983 0.000304 0.000417 378.7473
298 35 1.112633 0.00029 0.000403 379.8731
298 40 1.114209 0.000276 0.000391 380.9499
323 10 1.089579 0.000465 0.000539 364.294
323 15 1.092048 0.000441 0.00052 365.947
323 20 1.094394 0.000418 0.000502 367.5211
323 25 1.096626 0.000397 0.000484 369.0217
323 30 1.098752 0.000378 0.000468 370.4539
323 35 1.100779 0.00036 0.000453 371.8222
323 40 1.102714 0.000343 0.000439 373.1307
348 10 1.074192 0.000572 0.000599 354.0777
348 15 1.077184 0.000541 0.000577 356.0529
348 20 1.080021 0.000512 0.000556 357.9311
348 25 1.082716 0.000485 0.000537 359.7196
348 30 1.08528 0.000461 0.000518 361.4249
348 35 1.087721 0.000438 0.000501 363.0529
348 40 1.090049 0.000417 0.000485 364.6088
373 10 1.05744 0.000696 0.000659 343.1203
373 15 1.061016 0.000655 0.000633 345.445
373 20 1.064399 0.000619 0.00061 347.6512
373 25 1.067605 0.000585 0.000588 349.7487
373 30 1.070649 0.000554 0.000567 351.7458
373 35 1.073543 0.000526 0.000548 353.6502
373 40 1.0763 0.0005 0.00053 355.4686
398 10 1.03938 0.000839 0.00072 331.5
398 15 1.043609 0.000787 0.00069 334.2033
398 20 1.047597 0.00074 0.000663 336.7625
398 25 1.051367 0.000698 0.000638 339.1905
398 30 1.054938 0.000659 0.000615 341.4983
398 35 1.058326 0.000624 0.000594 343.6955
398 40 1.061547 0.000592 0.000574 345.7908
222
Table E.6. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
25 mass % [PMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.873888 0.000502 0.000739 428.7741
298 15 0.876029 0.000477 0.000714 430.8778
298 20 0.878073 0.000455 0.000691 432.8904
298 25 0.880026 0.000434 0.00067 434.8183
298 30 0.881894 0.000415 0.000649 436.6669
298 35 0.883684 0.000397 0.00063 438.4412
298 40 0.8854 0.00038 0.000612 440.1457
323 10 0.856837 0.000641 0.000838 412.205
323 15 0.859516 0.000608 0.000809 414.7867
323 20 0.862064 0.000577 0.000781 417.2501
323 25 0.864493 0.000549 0.000755 419.6043
323 30 0.86681 0.000523 0.000731 421.857
323 35 0.869025 0.000498 0.000708 424.0154
323 40 0.871144 0.000476 0.000687 426.0858
348 10 0.837965 0.000813 0.000944 394.2478
348 15 0.841279 0.000766 0.000908 397.3716
348 20 0.844417 0.000724 0.000874 400.3419
348 25 0.847396 0.000685 0.000843 403.1717
348 30 0.850229 0.00065 0.000814 405.8722
348 35 0.852929 0.000618 0.000788 408.4534
348 40 0.855505 0.000588 0.000763 410.9242
373 10 0.817252 0.001027 0.00106 374.9977
373 15 0.82132 0.000961 0.001014 378.7404
373 20 0.825152 0.000902 0.000973 382.2828
373 25 0.828772 0.00085 0.000935 385.6442
373 30 0.8322 0.000802 0.000901 388.841
373 35 0.835453 0.000759 0.000869 391.8873
373 40 0.838547 0.00072 0.000839 394.7955
398 10 0.794636 0.001297 0.001188 354.5303
398 15 0.799613 0.001203 0.00113 358.9856
398 20 0.804269 0.001121 0.001079 363.1779
398 25 0.808639 0.001048 0.001033 367.1359
398 30 0.812756 0.000984 0.000991 370.8838
398 35 0.816646 0.000927 0.000953 374.442
398 40 0.82033 0.000875 0.000918 377.8277
223
Table E.7. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
50 mass % [PMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.950522 0.000359 0.000558 453.1684
298 15 0.952193 0.000343 0.000541 454.7629
298 20 0.953794 0.000329 0.000525 456.2933
298 25 0.955329 0.000315 0.00051 457.7633
298 30 0.956802 0.000302 0.000495 459.1764
298 35 0.958217 0.00029 0.000482 460.5357
298 40 0.959578 0.000278 0.000468 461.8445
323 10 0.936484 0.000454 0.000632 439.8814
323 15 0.938562 0.000433 0.000612 441.8357
323 20 0.940549 0.000413 0.000593 443.7088
323 25 0.942452 0.000395 0.000576 445.5059
323 30 0.944275 0.000378 0.000559 447.2317
323 35 0.946025 0.000362 0.000543 448.8904
323 40 0.947705 0.000347 0.000528 450.4861
348 10 0.920929 0.000566 0.000708 425.3906
348 15 0.923474 0.000538 0.000684 427.7443
348 20 0.925901 0.000512 0.000662 429.9957
348 25 0.92822 0.000488 0.000642 432.1521
348 30 0.930438 0.000466 0.000622 434.2198
348 35 0.932562 0.000446 0.000604 436.2047
348 40 0.934598 0.000427 0.000586 438.1118
373 10 0.903887 0.000699 0.000787 409.792
373 15 0.906967 0.000662 0.000759 412.5893
373 20 0.909895 0.000628 0.000733 415.2582
373 25 0.912685 0.000597 0.000709 417.8085
373 30 0.915347 0.000568 0.000686 420.2492
373 35 0.917891 0.000542 0.000665 422.5878
373 40 0.920324 0.000517 0.000645 424.8315
398 10 0.885367 0.000859 0.00087 393.1714
398 15 0.889065 0.000809 0.000837 396.4628
398 20 0.892568 0.000764 0.000806 399.5928
398 25 0.895893 0.000724 0.000777 402.5753
398 30 0.899055 0.000686 0.000751 405.4222
398 35 0.902068 0.000652 0.000726 408.1442
398 40 0.904943 0.000621 0.000703 410.7505
224
Table E.8. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
75 mass % [PMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 1.026939 0.000316 0.000474 437.5741
298 15 1.028525 0.000302 0.00046 438.9269
298 20 1.030044 0.000289 0.000446 440.224
298 25 1.031499 0.000276 0.000432 441.4687
298 30 1.032894 0.000265 0.00042 442.6639
298 35 1.034233 0.000254 0.000408 443.8123
298 40 1.035519 0.000243 0.000396 444.9165
323 10 1.014044 0.000397 0.000537 426.6544
323 15 1.016011 0.000379 0.00052 428.3115
323 20 1.017893 0.000362 0.000504 429.899
323 25 1.019693 0.000346 0.000488 431.4213
323 30 1.021418 0.000331 0.000474 432.8823
323 35 1.023072 0.000317 0.00046 434.2855
323 40 1.02466 0.000304 0.000447 435.6343
348 10 0.99975 0.000491 0.000599 414.7111
348 15 1.002147 0.000467 0.00058 416.7021
348 20 1.004435 0.000445 0.000561 418.6069
348 25 1.006622 0.000425 0.000544 420.4313
348 30 1.008713 0.000406 0.000527 422.1805
348 35 1.010717 0.000388 0.000512 423.8592
348 40 1.012638 0.000372 0.000497 425.4717
373 10 0.984105 0.0006 0.000663 401.8328
373 15 0.986986 0.00057 0.00064 404.1893
373 20 0.98973 0.000541 0.000619 406.4397
373 25 0.992347 0.000515 0.000599 408.5915
373 30 0.994845 0.000491 0.00058 410.6518
373 35 0.997235 0.000469 0.000563 412.6268
373 40 0.999522 0.000448 0.000546 414.5218
398 10 0.967144 0.000728 0.000728 388.1013
398 15 0.970573 0.000688 0.000702 390.858
398 20 0.973828 0.000652 0.000677 393.4843
398 25 0.976925 0.000619 0.000654 395.9904
398 30 0.979875 0.000588 0.000633 398.3856
398 35 0.98269 0.00056 0.000613 400.6779
398 40 0.98538 0.000534 0.000594 402.8744
225
Table E.9. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
[BMIM]Cl.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 1.068676 0.000333 0.00046 402.1893
298 15 1.070414 0.000317 0.000445 403.4984
298 20 1.072074 0.000303 0.000431 404.7504
298 25 1.07366 0.000289 0.000418 405.9489
298 30 1.075177 0.000276 0.000405 407.097
298 35 1.076629 0.000264 0.000393 408.1977
298 40 1.078021 0.000253 0.000381 409.2536
323 10 1.055693 0.000415 0.000517 392.4761
323 15 1.057832 0.000395 0.0005 394.0686
323 20 1.059873 0.000376 0.000484 395.5907
323 25 1.061822 0.000359 0.000469 397.0469
323 30 1.063685 0.000343 0.000454 398.4415
323 35 1.065468 0.000327 0.000441 399.7781
323 40 1.067175 0.000313 0.000428 401.0602
348 10 1.041395 0.000509 0.000573 381.9173
348 15 1.043982 0.000483 0.000554 383.8169
348 20 1.046445 0.00046 0.000536 385.6304
348 25 1.048795 0.000438 0.000519 387.3637
348 30 1.051038 0.000417 0.000502 389.0223
348 35 1.053181 0.000398 0.000487 390.611
348 40 1.055233 0.00038 0.000472 392.1342
373 10 1.025853 0.000617 0.000629 370.6028
373 15 1.028937 0.000584 0.000607 372.8339
373 20 1.031867 0.000554 0.000587 374.9603
373 25 1.034656 0.000526 0.000567 376.9901
373 30 1.037315 0.000501 0.000549 378.93
373 35 1.039852 0.000477 0.000532 380.7864
373 40 1.042278 0.000455 0.000516 382.5648
398 10 1.009128 0.00074 0.000686 358.6168
398 15 1.012763 0.000699 0.00066 361.2049
398 20 1.016208 0.000661 0.000637 363.6667
398 25 1.01948 0.000626 0.000615 366.0123
398 30 1.022593 0.000594 0.000594 368.2508
398 35 1.025559 0.000565 0.000575 370.3901
398 40 1.028389 0.000538 0.000557 372.4372
226
Table E.10. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
25 mass % [BMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.860406 0.000577 0.00081 408.2557
298 15 0.862828 0.000547 0.000782 410.5571
298 20 0.865133 0.00052 0.000755 412.7539
298 25 0.867331 0.000495 0.000731 414.8536
298 30 0.869429 0.000472 0.000707 416.8631
298 35 0.871435 0.00045 0.000685 418.7884
298 40 0.873354 0.00043 0.000665 420.635
323 10 0.842021 0.00074 0.000919 390.9947
323 15 0.845054 0.000699 0.000884 393.8163
323 20 0.847929 0.000661 0.000852 396.5011
323 25 0.850661 0.000626 0.000822 399.0601
323 30 0.853261 0.000595 0.000795 401.5032
323 35 0.85574 0.000566 0.000769 403.839
323 40 0.858105 0.000539 0.000744 406.0751
348 10 0.821712 0.000943 0.001036 372.3611
348 15 0.825471 0.000884 0.000993 375.7757
348 20 0.829017 0.000831 0.000953 379.011
348 25 0.83237 0.000784 0.000917 382.0835
348 30 0.835549 0.000741 0.000884 385.0074
348 35 0.838569 0.000702 0.000853 387.7952
348 40 0.841442 0.000667 0.000825 390.4575
373 10 0.799443 0.001198 0.001164 352.4522
373 15 0.804075 0.001114 0.00111 356.5479
373 20 0.808415 0.00104 0.001061 360.4074
373 25 0.812496 0.000975 0.001017 364.0555
373 30 0.816345 0.000917 0.000977 367.5132
373 35 0.819986 0.000864 0.00094 370.7982
373 40 0.823437 0.000817 0.000906 373.9258
398 10 0.775133 0.001527 0.001309 331.3425
398 15 0.780827 0.001404 0.001239 336.229
398 20 0.786119 0.001299 0.001178 340.8013
398 25 0.791058 0.001208 0.001123 345.0976
398 30 0.795688 0.001128 0.001074 349.1491
398 35 0.800043 0.001057 0.00103 352.9817
398 40 0.804153 0.000994 0.00099 356.6169
227
Table E.11. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
50 mass % [BMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.923176 0.000477 0.000677 413.0553
298 15 0.925326 0.000454 0.000655 414.9811
298 20 0.927376 0.000432 0.000633 416.8227
298 25 0.929336 0.000412 0.000614 418.5856
298 30 0.931209 0.000394 0.000595 420.275
298 35 0.933003 0.000376 0.000577 421.8955
298 40 0.934721 0.00036 0.00056 423.4513
323 10 0.906703 0.000604 0.000764 398.4461
323 15 0.909373 0.000572 0.000737 400.7957
323 20 0.911912 0.000544 0.000712 403.0376
323 25 0.914333 0.000517 0.000689 405.1797
323 30 0.916642 0.000492 0.000667 407.2292
323 35 0.918849 0.00047 0.000646 409.1923
323 40 0.92096 0.000449 0.000626 411.0747
348 10 0.888564 0.000757 0.000854 382.6634
348 15 0.891835 0.000714 0.000821 385.4857
348 20 0.894936 0.000675 0.000792 388.1708
348 25 0.897881 0.00064 0.000764 390.73
348 30 0.900684 0.000607 0.000739 393.1731
348 35 0.903355 0.000578 0.000715 395.5087
348 40 0.905905 0.00055 0.000692 397.7447
373 10 0.868781 0.000942 0.000949 365.8134
373 15 0.872751 0.000883 0.00091 369.1644
373 20 0.876497 0.000831 0.000874 372.3407
373 25 0.880042 0.000784 0.000842 375.3583
373 30 0.883403 0.000741 0.000811 378.2309
373 35 0.886597 0.000703 0.000784 380.9705
373 40 0.889637 0.000667 0.000758 383.5876
398 10 0.84735 0.001168 0.001051 347.9889
398 15 0.85214 0.001088 0.001003 351.9342
398 20 0.856635 0.001017 0.00096 355.6563
398 25 0.860866 0.000955 0.000921 359.1784
398 30 0.864861 0.000898 0.000886 362.5196
398 35 0.868642 0.000848 0.000853 365.6966
398 40 0.87223 0.000802 0.000823 368.7235
228
Table E.12. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
75 mass % [BMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.988827 0.000428 0.000589 400.7704
298 15 0.990891 0.000407 0.00057 402.4452
298 20 0.99286 0.000387 0.000551 404.0462
298 25 0.99474 0.00037 0.000534 405.578
298 30 0.996537 0.000353 0.000517 407.0451
298 35 0.998257 0.000337 0.000502 408.4514
298 40 0.999905 0.000323 0.000487 409.8007
323 10 0.97348 0.000537 0.000662 388.4271
323 15 0.976028 0.000509 0.000639 390.463
323 20 0.978453 0.000484 0.000618 392.406
323 25 0.980765 0.00046 0.000598 394.2627
323 30 0.982972 0.000439 0.000579 396.039
323 35 0.985081 0.000419 0.000561 397.7402
323 40 0.987099 0.0004 0.000544 399.3712
348 10 0.956622 0.000665 0.000736 375.0908
348 15 0.959719 0.000629 0.000709 377.5232
348 20 0.962659 0.000595 0.000684 379.8397
348 25 0.965455 0.000565 0.000661 382.0492
348 30 0.968118 0.000537 0.000639 384.1597
348 35 0.970658 0.000511 0.000619 386.1782
348 40 0.973084 0.000487 0.0006 388.1111
373 10 0.938306 0.000816 0.000811 360.865
373 15 0.942027 0.000768 0.00078 363.7328
373 20 0.945548 0.000725 0.000751 366.4564
373 25 0.948885 0.000685 0.000724 369.0479
373 30 0.952056 0.000649 0.000699 371.5182
373 35 0.955073 0.000617 0.000676 373.8767
373 40 0.957949 0.000586 0.000654 376.1316
398 10 0.918571 0.000995 0.00089 345.8443
398 15 0.923004 0.000932 0.000853 349.1908
398 20 0.927181 0.000875 0.000819 352.358
398 25 0.931126 0.000824 0.000788 355.3628
398 30 0.934861 0.000778 0.000759 358.2196
398 35 0.938405 0.000736 0.000732 360.9411
398 40 0.941775 0.000698 0.000708 363.5381
229
Table E.13. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
[HMIM]Cl.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 1.048114 0.000403 0.000478 342.9323
298 15 1.050172 0.000381 0.00046 344.28
298 20 1.052122 0.000361 0.000443 345.5601
298 25 1.053973 0.000342 0.000427 346.7772
298 30 1.055732 0.000325 0.000412 347.9356
298 35 1.057405 0.000309 0.000398 349.0394
298 40 1.058998 0.000294 0.000384 350.0919
323 10 1.034919 0.000502 0.000536 334.3522
323 15 1.037448 0.000474 0.000515 335.9879
323 20 1.039841 0.000448 0.000496 337.5402
323 25 1.042111 0.000424 0.000478 339.0152
323 30 1.044266 0.000402 0.000461 340.4186
323 35 1.046314 0.000382 0.000445 341.7553
323 40 1.048263 0.000363 0.00043 343.03
348 10 1.020424 0.000616 0.000593 325.0519
348 15 1.023476 0.000579 0.000569 326.9989
348 20 1.026359 0.000546 0.000548 328.844
348 25 1.029088 0.000516 0.000528 330.5954
348 30 1.031676 0.000489 0.000509 332.2603
348 35 1.034134 0.000463 0.000491 333.845
348 40 1.03647 0.00044 0.000474 335.3554
373 10 1.004702 0.000745 0.000649 315.1125
373 15 1.008334 0.000699 0.000623 317.3948
373 20 1.011757 0.000657 0.000598 319.5536
373 25 1.01499 0.00062 0.000576 321.5992
373 30 1.018051 0.000585 0.000555 323.5417
373 35 1.020952 0.000554 0.000535 325.3886
373 40 1.023708 0.000525 0.000517 327.1473
398 10 0.987816 0.000894 0.000707 304.6098
398 15 0.992092 0.000835 0.000676 307.2525
398 20 0.99611 0.000783 0.000648 309.7462
398 25 0.999895 0.000735 0.000623 312.1047
398 30 1.003469 0.000693 0.000599 314.34
398 35 1.006852 0.000654 0.000577 316.4625
398 40 1.010058 0.000618 0.000557 318.4813
230
Table E.14. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
25 mass % [HMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.863198 0.000524 0.000751 417.098
298 15 0.865405 0.000498 0.000726 419.2337
298 20 0.86751 0.000474 0.000702 421.2749
298 25 0.869518 0.000452 0.000679 423.2282
298 30 0.871438 0.000431 0.000658 425.0993
298 35 0.873276 0.000412 0.000638 426.8936
298 40 0.875035 0.000394 0.000619 428.616
323 10 0.846091 0.000669 0.000851 400.7298
323 15 0.84885 0.000633 0.00082 403.3476
323 20 0.851472 0.0006 0.000792 405.8425
323 25 0.853966 0.00057 0.000765 408.2242
323 30 0.856345 0.000542 0.00074 410.501
323 35 0.858615 0.000517 0.000716 412.6804
323 40 0.860785 0.000493 0.000694 414.7691
348 10 0.827185 0.000848 0.000958 383.0212
348 15 0.830595 0.000798 0.00092 386.185
348 20 0.833819 0.000753 0.000885 389.1894
348 25 0.836876 0.000712 0.000853 392.0483
348 30 0.83978 0.000674 0.000823 394.7736
348 35 0.842543 0.00064 0.000795 397.376
348 40 0.845178 0.000609 0.00077 399.8648
373 10 0.806462 0.001071 0.001074 364.0697
373 15 0.810644 0.001 0.001026 367.8559
373 20 0.814578 0.000937 0.000984 371.4344
373 25 0.818288 0.000881 0.000945 374.8257
373 30 0.821797 0.000831 0.000909 378.0472
373 35 0.825123 0.000786 0.000876 381.1138
373 40 0.828283 0.000744 0.000846 384.0386
398 10 0.783865 0.001352 0.001202 343.9539
398 15 0.788979 0.001251 0.001143 348.4558
398 20 0.793752 0.001164 0.00109 352.6851
398 25 0.798227 0.001087 0.001042 356.6725
398 30 0.802435 0.001018 0.000999 360.4436
398 35 0.806406 0.000957 0.00096 364.0198
398 40 0.810163 0.000903 0.000924 367.4192
231
Table E.15. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
50 mass % [HMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.914281 0.00052 0.000693 387.0189
298 15 0.916599 0.000493 0.000669 388.9843
298 20 0.918805 0.000468 0.000646 390.8584
298 25 0.920906 0.000445 0.000624 392.6478
298 30 0.922909 0.000424 0.000604 394.3582
298 35 0.924822 0.000404 0.000585 395.995
298 40 0.926651 0.000386 0.000567 397.5628
323 10 0.897592 0.000659 0.000781 373.019
323 15 0.90047 0.000622 0.000752 375.4144
323 20 0.903198 0.000589 0.000725 377.6933
323 25 0.905791 0.000558 0.0007 379.8646
323 30 0.908258 0.00053 0.000676 381.9366
323 35 0.910609 0.000504 0.000654 383.9165
323 40 0.912852 0.00048 0.000633 385.8105
348 10 0.879235 0.000825 0.000873 357.9178
348 15 0.88276 0.000776 0.000838 360.7929
348 20 0.886089 0.000731 0.000805 363.5194
348 25 0.889241 0.00069 0.000776 366.1102
348 30 0.892231 0.000653 0.000748 368.5767
348 35 0.895074 0.000619 0.000723 370.9287
348 40 0.89778 0.000588 0.000699 373.1749
373 10 0.859234 0.001028 0.000969 341.8186
373 15 0.863511 0.00096 0.000927 345.2299
373 20 0.867531 0.000899 0.000888 348.4519
373 25 0.871321 0.000845 0.000853 351.5031
373 30 0.874903 0.000797 0.000821 354.3993
373 35 0.878297 0.000753 0.000791 357.1539
373 40 0.881518 0.000713 0.000764 359.7787
398 10 0.837586 0.001276 0.001073 324.812
398 15 0.842745 0.001182 0.001021 328.8257
398 20 0.847565 0.001101 0.000975 332.5977
398 25 0.852085 0.001028 0.000933 336.1545
398 30 0.856338 0.000964 0.000895 339.5181
398 35 0.86035 0.000907 0.000861 342.7074
398 40 0.864146 0.000855 0.000829 345.7381
232
Table E.16. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
75 mass % [HMIM]Cl + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.963378 0.000612 0.000701 331.2972
298 15 0.966243 0.000576 0.000674 333.2712
298 20 0.968951 0.000543 0.000648 335.1415
298 25 0.971513 0.000513 0.000624 336.9164
298 30 0.973943 0.000486 0.000601 338.6035
298 35 0.976249 0.000461 0.00058 340.2091
298 40 0.978442 0.000437 0.00056 341.7392
323 10 0.945645 0.00077 0.000785 319.213
323 15 0.949177 0.000722 0.000752 321.602
323 20 0.952503 0.000678 0.000722 323.8599
323 25 0.955642 0.000639 0.000694 325.9982
323 30 0.958611 0.000603 0.000668 328.027
323 35 0.961424 0.00057 0.000644 329.9551
323 40 0.964094 0.00054 0.000621 331.7903
348 10 0.926277 0.000958 0.000871 306.2716
348 15 0.930571 0.000893 0.000832 309.1176
348 20 0.934598 0.000835 0.000796 311.7985
348 25 0.938385 0.000783 0.000764 314.3305
348 30 0.941955 0.000737 0.000734 316.7272
348 35 0.94533 0.000694 0.000706 319.0005
348 40 0.948525 0.000656 0.000681 321.1607
373 10 0.90533 0.001183 0.00096 292.5759
373 15 0.910498 0.001096 0.000913 295.9255
373 20 0.915319 0.001019 0.000871 299.0679
373 25 0.919834 0.000951 0.000834 302.0254
373 30 0.924075 0.00089 0.000799 304.8168
373 35 0.928069 0.000836 0.000768 307.4579
373 40 0.931842 0.000787 0.000739 309.9623
398 10 0.882839 0.001455 0.001054 278.2194
398 15 0.889014 0.001336 0.000998 282.1254
398 20 0.89474 0.001234 0.000948 285.7712
398 25 0.900073 0.001145 0.000904 289.188
398 30 0.90506 0.001067 0.000864 292.4016
398 35 0.90974 0.000997 0.000828 295.433
398 40 0.914144 0.000935 0.000795 298.3004
233
Table E.17. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
[EMIM]Ac.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 1.088334 0.000452 0.000795 514.3214
298 15 1.090747 0.000434 0.000775 516.6046
298 20 1.093073 0.000418 0.000756 518.8104
298 25 1.095317 0.000403 0.000738 520.943
298 30 1.097484 0.000388 0.00072 523.0064
298 35 1.099578 0.000374 0.000704 525.0041
298 40 1.101603 0.000362 0.000688 526.9396
323 10 1.065811 0.000564 0.000878 493.2547
323 15 1.068755 0.00054 0.000854 495.9835
323 20 1.071587 0.000518 0.000832 498.6148
323 25 1.074312 0.000498 0.000811 501.1544
323 30 1.076939 0.000479 0.000791 503.6078
323 35 1.079472 0.000461 0.000772 505.9799
323 40 1.081918 0.000444 0.000754 508.2751
348 10 1.041581 0.000696 0.000962 471.0821
348 15 1.045127 0.000664 0.000934 474.2956
348 20 1.048528 0.000635 0.000908 477.3866
348 25 1.051792 0.000608 0.000883 480.3636
348 30 1.054929 0.000583 0.00086 483.2339
348 35 1.057949 0.00056 0.000839 486.0042
348 40 1.060858 0.000538 0.000818 488.6806
373 10 1.015752 0.000853 0.001047 448.0086
373 15 1.019984 0.000811 0.001014 451.749
373 20 1.024026 0.000772 0.000984 455.3364
373 25 1.027893 0.000736 0.000955 458.7823
373 30 1.0316 0.000704 0.000928 462.0969
373 35 1.035157 0.000674 0.000903 465.2893
373 40 1.038576 0.000646 0.00088 468.3676
398 10 0.988417 0.001041 0.001136 424.2199
398 15 0.99343 0.000984 0.001096 428.5341
398 20 0.998198 0.000932 0.00106 432.657
398 25 1.002742 0.000885 0.001027 436.6049
398 30 1.007081 0.000843 0.000996 440.3918
398 35 1.011232 0.000803 0.000967 444.0301
398 40 1.01521 0.000768 0.00094 447.5306
234
Table E.18. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for 5
mass % [EMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.804804 0.000803 0.00105 379.9313
298 15 0.807943 0.000755 0.001008 382.9009
298 20 0.810912 0.000712 0.00097 385.7199
298 25 0.813726 0.000674 0.000934 388.4012
298 30 0.816398 0.000638 0.000902 390.956
298 35 0.81894 0.000606 0.000871 393.3943
298 40 0.821362 0.000576 0.000842 395.7249
323 10 0.782484 0.001052 0.001202 359.1497
323 15 0.78647 0.000982 0.001149 362.8183
323 20 0.790216 0.00092 0.0011 366.2823
323 25 0.793746 0.000864 0.001056 369.5619
323 30 0.797081 0.000814 0.001015 372.6744
323 35 0.800241 0.000769 0.000978 375.6346
323 40 0.80324 0.000728 0.000943 378.4554
348 10 0.757717 0.00138 0.001375 336.774
348 15 0.762755 0.001274 0.001304 341.267
348 20 0.767448 0.001182 0.001241 345.4793
348 25 0.771838 0.001102 0.001185 349.4432
348 30 0.77596 0.001031 0.001135 353.1858
348 35 0.779843 0.000967 0.001089 356.7294
348 40 0.783511 0.000911 0.001047 360.093
373 10 0.730327 0.001822 0.001577 312.8664
373 15 0.736697 0.001657 0.001481 318.3483
373 20 0.742564 0.001519 0.001399 323.4388
373 25 0.748 0.001401 0.001327 328.1915
373 30 0.753062 0.001299 0.001263 332.649
373 35 0.757798 0.00121 0.001206 336.8459
373 40 0.762244 0.001132 0.001155 340.8104
398 10 0.700017 0.00244 0.001823 287.4366
398 15 0.708123 0.002175 0.00169 294.1321
398 20 0.715473 0.001962 0.001579 300.2694
398 25 0.722198 0.001785 0.001485 305.9403
398 30 0.728395 0.001637 0.001403 311.2139
398 35 0.734142 0.00151 0.001332 316.1442
398 40 0.739499 0.0014 0.001269 320.7741
235
Table E.19. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
15 mass % [EMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.830447 0.000728 0.000994 396.9745
298 15 0.833391 0.000688 0.000957 399.7935
298 20 0.836183 0.000651 0.000923 402.4776
298 25 0.838839 0.000618 0.000891 405.0375
298 30 0.841367 0.000587 0.000861 407.4829
298 35 0.843778 0.000558 0.000834 409.8221
298 40 0.846082 0.000532 0.000808 412.0627
323 10 0.808682 0.000947 0.001132 376.4381
323 15 0.812396 0.000888 0.001085 379.9044
323 20 0.815901 0.000835 0.001043 383.1897
323 25 0.819217 0.000788 0.001003 386.3106
323 30 0.822361 0.000745 0.000967 389.2814
323 35 0.825348 0.000706 0.000934 392.1147
323 40 0.828192 0.00067 0.000902 394.8213
348 10 0.784632 0.001228 0.001286 354.3814
348 15 0.78929 0.001141 0.001225 358.6011
348 20 0.793653 0.001065 0.001171 362.5762
348 25 0.797753 0.000998 0.001122 366.3329
348 30 0.80162 0.000938 0.001077 369.893
348 35 0.805277 0.000884 0.001037 373.2749
348 40 0.808742 0.000835 0.000999 376.4947
373 10 0.758185 0.001599 0.001462 330.8941
373 15 0.764015 0.001468 0.001382 336.0024
373 20 0.769424 0.001356 0.001312 340.7765
373 25 0.774467 0.001259 0.00125 345.258
373 30 0.779188 0.001174 0.001194 349.4808
373 35 0.783626 0.001099 0.001145 353.4727
373 40 0.78781 0.001032 0.001099 357.2572
398 10 0.729139 0.002103 0.00167 306.0268
398 15 0.736459 0.001899 0.001562 312.2024
398 20 0.743164 0.001731 0.001469 317.913
398 25 0.74935 0.001589 0.00139 323.2273
398 30 0.755091 0.001467 0.00132 328.1988
398 35 0.760446 0.001362 0.001259 332.87
398 40 0.765461 0.00127 0.001204 337.2757
236
Table E.20. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
25 mass % [EMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.855787 0.000678 0.000957 410.8726
298 15 0.858614 0.000642 0.000923 413.5914
298 20 0.861303 0.000609 0.000892 416.1859
298 25 0.863865 0.000579 0.000862 418.6656
298 30 0.86631 0.000552 0.000835 421.039
298 35 0.868647 0.000526 0.000809 423.3133
298 40 0.870883 0.000502 0.000785 425.4955
323 10 0.834234 0.000875 0.001085 390.4375
323 15 0.837784 0.000824 0.001043 393.7672
323 20 0.841144 0.000778 0.001004 396.9317
323 25 0.844331 0.000736 0.000968 399.9456
323 30 0.847361 0.000698 0.000935 402.8211
323 35 0.850246 0.000663 0.000904 405.5692
323 40 0.852999 0.000631 0.000875 408.1996
348 10 0.810509 0.001127 0.001225 368.5459
348 15 0.814932 0.001052 0.001171 372.5791
348 20 0.819092 0.000986 0.001123 376.3919
348 25 0.823015 0.000927 0.001079 380.0064
348 30 0.826726 0.000874 0.001038 383.4413
348 35 0.830245 0.000826 0.001001 386.7126
348 40 0.833589 0.000783 0.000967 389.834
373 10 0.784542 0.001452 0.001383 345.3087
373 15 0.790035 0.001342 0.001313 350.1609
373 20 0.795157 0.001246 0.001252 354.7164
373 25 0.799955 0.001162 0.001196 359.0095
373 30 0.804464 0.001088 0.001147 363.0688
373 35 0.808717 0.001022 0.001102 366.9178
373 40 0.812739 0.000963 0.00106 370.5766
398 10 0.756831 0.001868 0.001557 321.7948
398 15 0.7639 0.001696 0.001462 328.0519
398 20 0.7704 0.001553 0.00138 333.8683
398 25 0.776431 0.00143 0.001309 339.337
398 30 0.782032 0.001325 0.001247 344.4566
398 35 0.787263 0.001233 0.001191 349.2788
398 40 0.792165 0.001153 0.001141 353.8292
237
Table E.21. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
50 mass % [EMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.920358 0.000612 0.000915 435.3855
298 15 0.923109 0.000582 0.000885 437.9922
298 20 0.925736 0.000555 0.000858 440.4893
298 25 0.92825 0.00053 0.000832 442.8843
298 30 0.930657 0.000506 0.000807 445.1842
298 35 0.932965 0.000485 0.000785 447.3951
298 40 0.93518 0.000464 0.000763 449.5226
323 10 0.898298 0.000781 0.001027 414.7645
323 15 0.901718 0.000739 0.000991 417.9285
323 20 0.904971 0.000702 0.000958 420.9495
323 25 0.908071 0.000667 0.000927 423.8385
323 30 0.911031 0.000635 0.000898 426.6057
323 35 0.91386 0.000606 0.000871 429.2597
323 40 0.916569 0.000579 0.000845 431.8085
348 10 0.874227 0.000991 0.001147 392.8342
348 15 0.878438 0.000932 0.001102 396.6275
348 20 0.882422 0.000879 0.001062 400.2337
348 25 0.886202 0.000831 0.001024 403.6696
348 30 0.889795 0.000788 0.000989 406.9498
348 35 0.893218 0.000748 0.000957 410.0869
348 40 0.896485 0.000712 0.000927 413.0918
373 10 0.848148 0.001255 0.001278 369.7462
373 15 0.853303 0.001171 0.001222 374.2544
373 20 0.858148 0.001096 0.001171 378.517
373 25 0.862719 0.00103 0.001125 382.5594
373 30 0.867041 0.000971 0.001084 386.4029
373 35 0.871141 0.000917 0.001045 390.0656
373 40 0.875038 0.000869 0.00101 393.5631
398 10 0.820021 0.001593 0.001423 345.6292
398 15 0.826317 0.00147 0.001351 350.9568
398 20 0.832186 0.001364 0.001288 355.9598
398 25 0.837681 0.001271 0.001232 360.6768
398 30 0.842847 0.00119 0.001181 365.1394
398 35 0.84772 0.001118 0.001135 369.3738
398 40 0.85233 0.001053 0.001094 373.4021
238
Table E.22. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
75 mass % [EMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.993053 0.000566 0.00089 458.3899
298 15 0.995804 0.000541 0.000864 460.933
298 20 0.99844 0.000517 0.000839 463.3768
298 25 1.00097 0.000495 0.000816 465.7278
298 30 1.0034 0.000475 0.000794 467.9918
298 35 1.005737 0.000456 0.000773 470.1741
298 40 1.007986 0.000438 0.000753 472.2794
323 10 0.96999 0.000715 0.000991 437.3455
323 15 0.973378 0.00068 0.000959 440.4063
323 20 0.976614 0.000648 0.000929 443.3395
323 25 0.97971 0.000618 0.000902 446.1543
323 30 0.982675 0.000591 0.000876 448.8591
323 35 0.985519 0.000565 0.000852 451.4611
323 40 0.988251 0.000542 0.000829 453.967
348 10 0.945036 0.000897 0.001095 415.133
348 15 0.949165 0.000848 0.001057 418.768
348 20 0.95309 0.000804 0.001021 422.2391
348 25 0.956831 0.000764 0.000989 425.5599
348 30 0.960402 0.000727 0.000958 428.742
348 35 0.963816 0.000693 0.00093 431.7958
348 40 0.967086 0.000662 0.000903 434.7304
373 10 0.918253 0.001119 0.001206 391.9362
373 15 0.923246 0.001051 0.001159 396.2099
373 20 0.927968 0.000991 0.001116 400.2733
373 25 0.932446 0.000936 0.001077 404.1457
373 30 0.936703 0.000887 0.001041 407.844
373 35 0.940758 0.000842 0.001007 411.3826
373 40 0.944628 0.000801 0.000976 414.7743
398 10 0.889674 0.001396 0.001325 367.9192
398 15 0.895685 0.0013 0.001267 372.9071
398 20 0.901332 0.001216 0.001215 377.6238
398 25 0.906656 0.001141 0.001168 382.0981
398 30 0.911691 0.001075 0.001125 386.3539
398 35 0.916466 0.001016 0.001085 390.4117
398 40 0.921005 0.000962 0.001049 394.289
239
Table E.23. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
[BMIM]Ac.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 1.055047 0.000445 0.000693 454.3626
298 15 1.057344 0.000426 0.000673 456.3435
298 20 1.05955 0.000408 0.000655 458.2494
298 25 1.06167 0.000392 0.000637 460.0848
298 30 1.063709 0.000376 0.000621 461.8537
298 35 1.065672 0.000362 0.000605 463.5598
298 40 1.067563 0.000348 0.00059 465.2065
323 10 1.035976 0.000552 0.000766 438.0853
323 15 1.038776 0.000528 0.000744 440.4565
323 20 1.041459 0.000504 0.000723 442.7343
323 25 1.044032 0.000483 0.000703 444.9246
323 30 1.046502 0.000463 0.000684 447.0329
323 35 1.048877 0.000444 0.000666 449.0641
323 40 1.051162 0.000427 0.000648 451.0227
348 10 1.015386 0.000678 0.00084 420.8441
348 15 1.01875 0.000645 0.000813 423.6374
348 20 1.021964 0.000615 0.000789 426.3149
348 25 1.02504 0.000587 0.000766 428.8847
348 30 1.027987 0.000561 0.000744 431.3542
348 35 1.030814 0.000537 0.000724 433.73
348 40 1.033529 0.000515 0.000705 436.0179
373 10 0.993379 0.000825 0.000913 402.7994
373 15 0.997377 0.000782 0.000883 406.0484
373 20 1.001185 0.000743 0.000854 409.1545
373 25 1.004817 0.000707 0.000828 412.1289
373 30 1.008288 0.000673 0.000803 414.9813
373 35 1.011611 0.000643 0.00078 417.7205
373 40 1.014795 0.000615 0.000759 420.3543
398 10 0.970043 0.000998 0.000989 384.0975
398 15 0.974756 0.000941 0.000953 387.8385
398 20 0.979226 0.00089 0.00092 391.4037
398 25 0.983476 0.000843 0.000889 394.8082
398 30 0.987524 0.000801 0.000861 398.0653
398 35 0.991388 0.000762 0.000835 401.1864
398 40 0.995082 0.000726 0.000811 404.1816
240
Table E.24. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for 5
mass % [BMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.80975 0.000723 0.000978 392.9433
298 15 0.8126 0.000683 0.000941 395.7137
298 20 0.815301 0.000646 0.000906 398.3492
298 25 0.817867 0.000612 0.000874 400.8607
298 30 0.820309 0.000581 0.000845 403.2579
298 35 0.822636 0.000553 0.000817 405.5492
298 40 0.824857 0.000526 0.000791 407.7422
323 10 0.788836 0.000943 0.001118 372.9074
323 15 0.792443 0.000884 0.00107 376.3261
323 20 0.795844 0.00083 0.001027 379.5632
323 25 0.799059 0.000783 0.000988 382.6355
323 30 0.802104 0.00074 0.000951 385.5576
323 35 0.804995 0.0007 0.000918 388.3421
323 40 0.807745 0.000664 0.000887 391
348 10 0.765633 0.001227 0.001274 351.2926
348 15 0.770172 0.001139 0.001213 355.4701
348 20 0.774418 0.001062 0.001158 359.4011
348 25 0.778406 0.000994 0.001108 363.1122
348 30 0.782163 0.000933 0.001064 366.6258
348 35 0.785713 0.000879 0.001023 369.9605
348 40 0.789074 0.00083 0.000985 373.1327
373 10 0.740004 0.001604 0.001455 328.1681
373 15 0.745708 0.001471 0.001373 333.2468
373 20 0.750993 0.001357 0.001302 337.9865
373 25 0.755914 0.001258 0.001239 342.4303
373 30 0.760516 0.001172 0.001183 346.6128
373 35 0.764837 0.001096 0.001133 350.5626
373 40 0.768907 0.001028 0.001087 354.3035
398 10 0.711718 0.002121 0.001671 303.5592
398 15 0.718915 0.001911 0.001559 309.7296
398 20 0.725494 0.001738 0.001465 315.4248
398 25 0.731554 0.001593 0.001384 320.7164
398 30 0.737171 0.001469 0.001313 325.6597
398 35 0.742403 0.001362 0.00125 330.2987
398 40 0.747298 0.001269 0.001194 334.669
241
Table E.25. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
15 mass % [BMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.840878 0.000569 0.000837 428.9056
298 15 0.843211 0.00054 0.000809 431.2896
298 20 0.845437 0.000514 0.000783 433.5693
298 25 0.847562 0.00049 0.000758 435.752
298 30 0.849595 0.000468 0.000735 437.8444
298 35 0.851541 0.000447 0.000713 439.8524
298 40 0.853406 0.000428 0.000692 441.7813
323 10 0.822293 0.000732 0.000952 410.1567
323 15 0.825223 0.000692 0.000917 413.0849
323 20 0.828006 0.000655 0.000885 415.8757
323 25 0.830654 0.000622 0.000855 418.54
323 30 0.833179 0.000592 0.000827 421.0876
323 35 0.835588 0.000564 0.0008 423.5269
323 40 0.837892 0.000538 0.000776 425.8655
348 10 0.801738 0.000936 0.001075 389.9068
348 15 0.805382 0.000879 0.001032 393.459
348 20 0.808824 0.000828 0.000992 396.8298
348 25 0.812085 0.000782 0.000955 400.0356
348 30 0.81518 0.00074 0.000921 403.0907
348 35 0.818124 0.000702 0.00089 406.0074
348 40 0.820929 0.000667 0.000861 408.7964
373 10 0.779156 0.001196 0.001213 368.2516
373 15 0.783665 0.001114 0.001157 372.526
373 20 0.787895 0.001041 0.001107 376.559
373 25 0.791878 0.000977 0.001062 380.376
373 30 0.79564 0.000919 0.001021 383.9981
373 35 0.799201 0.000868 0.000983 387.4433
373 40 0.802581 0.000821 0.000948 390.7271
398 10 0.752154 0.001587 0.001409 343.1703
398 15 0.757875 0.001459 0.001332 348.4106
398 20 0.763188 0.001348 0.001265 353.313
398 25 0.768147 0.001252 0.001205 357.9194
398 30 0.772795 0.001169 0.001152 362.2637
398 35 0.777167 0.001094 0.001104 366.3737
398 40 0.781291 0.001028 0.00106 370.2732
242
Table E.26. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
25 mass % [BMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.868371 0.000487 0.000756 452.9301
298 15 0.870437 0.000464 0.000732 455.0879
298 20 0.872414 0.000443 0.00071 457.1574
298 25 0.874308 0.000424 0.000689 459.1444
298 30 0.876124 0.000406 0.000669 461.0539
298 35 0.877868 0.000389 0.00065 462.8907
298 40 0.879543 0.000373 0.000632 464.659
323 10 0.851058 0.000621 0.000856 435.0497
323 15 0.853639 0.00059 0.000827 437.6921
323 20 0.8561 0.000562 0.000801 440.2199
323 25 0.858452 0.000536 0.000775 442.6414
323 30 0.860701 0.000511 0.000752 444.9638
323 35 0.862855 0.000489 0.00073 447.1937
323 40 0.86492 0.000468 0.000709 449.3372
348 10 0.831946 0.000787 0.000962 415.7291
348 15 0.835133 0.000743 0.000927 418.9203
348 20 0.83816 0.000704 0.000895 421.9626
348 25 0.841041 0.000669 0.000864 424.8681
348 30 0.843787 0.000636 0.000836 427.6474
348 35 0.846409 0.000606 0.00081 430.3099
348 40 0.848917 0.000578 0.000785 432.8637
373 10 0.811019 0.000992 0.001078 395.0775
373 15 0.814927 0.000932 0.001034 398.8938
373 20 0.818618 0.000877 0.000994 402.516
373 25 0.822115 0.000828 0.000957 405.9621
373 30 0.825435 0.000784 0.000924 409.2473
373 35 0.828593 0.000744 0.000892 412.385
373 40 0.831603 0.000707 0.000863 415.3868
398 10 0.788226 0.001252 0.001205 373.183
398 15 0.793001 0.001166 0.00115 377.7177
398 20 0.797481 0.00109 0.0011 381.9976
398 25 0.801699 0.001022 0.001056 386.0496
398 30 0.805683 0.000962 0.001015 389.8962
398 35 0.809456 0.000908 0.000978 393.5566
398 40 0.813038 0.000859 0.000943 397.0472
243
Table E.27. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
50 mass % [BMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.926811 0.000438 0.000701 466.8361
298 15 0.928798 0.000419 0.00068 468.84
298 20 0.930704 0.000401 0.000661 470.7663
298 25 0.932535 0.000385 0.000642 472.6194
298 30 0.934293 0.000369 0.000625 474.4038
298 35 0.935985 0.000355 0.000608 476.1233
298 40 0.937613 0.000341 0.000592 477.7815
323 10 0.909727 0.000554 0.000788 449.7843
323 15 0.912189 0.000528 0.000764 452.2222
323 20 0.914545 0.000504 0.000741 454.5608
323 25 0.916802 0.000482 0.000719 456.8066
323 30 0.918966 0.000461 0.000698 458.9657
323 35 0.921043 0.000442 0.000679 461.0434
323 40 0.92304 0.000424 0.000661 463.0447
348 10 0.89098 0.000693 0.000878 431.4375
348 15 0.893991 0.000658 0.000849 434.3585
348 20 0.896862 0.000626 0.000822 437.153
348 25 0.899605 0.000596 0.000796 439.8303
348 30 0.902228 0.000569 0.000772 442.3988
348 35 0.90474 0.000544 0.00075 444.8659
348 40 0.907149 0.00052 0.000728 447.2382
373 10 0.870599 0.000861 0.000974 411.9254
373 15 0.874249 0.000813 0.000938 415.3858
373 20 0.877714 0.00077 0.000905 418.6849
373 25 0.881011 0.00073 0.000875 421.8363
373 30 0.884154 0.000695 0.000847 424.8514
373 35 0.887155 0.000661 0.000821 427.7407
373 40 0.890025 0.000631 0.000796 430.5133
398 10 0.848591 0.001067 0.001076 391.3622
398 15 0.852987 0.001001 0.001032 395.4276
398 20 0.85714 0.000942 0.000993 399.2871
398 25 0.861073 0.00089 0.000957 402.9598
398 30 0.864807 0.000842 0.000923 406.4624
398 35 0.86836 0.000799 0.000893 409.8091
398 40 0.871747 0.000759 0.000864 413.0124
244
Table E.28. Density, isothermal compressibility, isobaric thermal expansion coefficient, and
internal pressure for a selection of temperatures and pressures as calculated by the S-L EOS for
75 mass % [BMIM]Ac + ethanol.
T (K) P
(MPa)
ρ
(g/cm3)
κT
(1/MPa)
βP (1/K) π (MPa)
298 10 0.981295 0.000486 0.000741 444.0145
298 15 0.98363 0.000465 0.000719 446.1304
298 20 0.985868 0.000444 0.000698 448.1621
298 25 0.988013 0.000425 0.000678 450.1149
298 30 0.990073 0.000408 0.00066 451.9935
298 35 0.992052 0.000391 0.000642 453.8025
298 40 0.993956 0.000376 0.000625 455.5457
323 10 0.962257 0.000611 0.000826 426.953
323 15 0.965129 0.000581 0.0008 429.5051
323 20 0.967872 0.000554 0.000776 431.9505
323 25 0.970497 0.000529 0.000753 434.2965
323 30 0.973011 0.000506 0.000731 436.5497
323 35 0.975423 0.000484 0.00071 438.7162
323 40 0.977738 0.000464 0.000691 440.8014
348 10 0.941559 0.000759 0.000914 408.7832
348 15 0.945045 0.000719 0.000882 411.8153
348 20 0.948363 0.000683 0.000853 414.7126
348 25 0.951528 0.00065 0.000827 417.4854
348 30 0.954552 0.000619 0.000801 420.143
348 35 0.957445 0.000591 0.000778 422.6934
348 40 0.960216 0.000565 0.000755 425.144
373 10 0.919266 0.000937 0.001004 389.6551
373 15 0.923457 0.000883 0.000967 393.2159
373 20 0.92743 0.000835 0.000932 396.6068
373 25 0.931205 0.000791 0.000901 399.8423
373 30 0.9348 0.000751 0.000871 402.9352
373 35 0.938229 0.000714 0.000844 405.8964
373 40 0.941505 0.000681 0.000819 408.736
398 10 0.895422 0.001152 0.001099 369.7037
398 15 0.900428 0.001079 0.001054 373.8488
398 20 0.905149 0.001014 0.001013 377.7794
398 25 0.909615 0.000956 0.000976 381.5162
398 30 0.91385 0.000903 0.000942 385.077
398 35 0.917875 0.000856 0.00091 388.4768
398 40 0.921709 0.000812 0.000881 391.7288
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