harshit agarwal thesis.pdf
TRANSCRIPT
2014
By
Thesis
UNDER THE SUPERVISION OF
SUBMITTED TO THE
UNIVERSITY OF LUCKNOW
FOR THE DEGREE OF
Doctor of PhilosophyIn
PHYSICS
Prof. Manisha Gupta
DEPARTMENT OF PHYSICSUNIVERSITY OF LUCKNOW
LUCKNOW 226 007INDIA
ULTRASONIC, VISCOMETRIC AND VOLUMETRIC
STUDIES OF SOME MOLECULAR SPECIES
EXHIBITING COMPLEX FORMATION IN SOLUTION
Harshit Agarwal
CONDENSED MATTER PHYSICS LAB
M.Sc.
CONTENTS
Page No. Acknowledgement Certificate I Certificate II List of Published and Communicated Papers List of Conference / Seminar Papers Abstract
i iii iv v
vi ix
Chapter 1 General Discussion
1-22
1.1 Introduction 1 1.2 Ultrasonics 4 1.3 Viscometry 7 1.4 Volumetry 9 1.5 Refractometry 10 1.6 Excess Parameters 11 1.7 Objective and Scope of the Study 12 References 15
Chapter 2 Experimental Techniques and Evaluation of
Excess Parameters
23-57
2.1 Ultrasonic Velocity Measurement 23 2.1.1 Principle of Interferometry Technique 23 2.1.2 Experimental Set-up 24 2.2 Viscosity Measurement 26 2.3 Density Measurement 29 2.4 Refractive Index Measurement 30 2.4.1 Principle of Abbe’s Refractometer 31 2.4.2 Calibration and Mode of Operation 33 2.5 Temperature Maintenance 33 2.6 Preparation of Mixtures 34 2.7 Evaluation of Thermo-acoustic and Excess
Parameters 34
2.7.1 Isentropic Compressibility 34 2.7.2 Acoustic Impedance 35 2.7.3 Intermolecular Free Length 35 2.7.4 Gibb’s Free Energy of Activation of
Viscous Flow 37
2.7.5 Free Volume (Vf) and Internal Pressure 37 2.7.6 Effective Debye Temperature and
Pseduo-Grünrisen Parameter 39
2.7.7 Excess / Deviation Parameters 41
2.8 Curve Expert 1.3 Linear Regression Polynomial Equation
42
2.9 Estimation of Ultrasonic Velocity 44 2.9.1 Mixing Rules for Ultrasonic Velocity 44 2.9.2 Collision Factor Theory (CFT) 45 2.9.3 Flory Statistical Theory (FST) 45 2.10 Estimation of Viscosity 48 2.11 Density Models 50 2.11.1 Modified Rackett Model and Hankinson
Brobst-Thomson(HBT) Model for Density
50
2.11.2 Mixing Rules for Both the Modified Rackett and Hankinson equations
51
2.12 Semi Empirical Relations for Prediction of Refractive Index
52
References 54
Chapter 3 Studies on Molecular Interaction Between N,N-dimethylacetamide (DMA) with 1-Propanol, Methanol and Water from Density, Viscosity and Refractive Index Measurements at 293.15, 303.15 and 313.15K
58-75
3.1 Introduction 58 3.2 Chemicals 59 3.3 Results 60 3.4 Discussion 60 3.5 Conclusion 63 References 73
Chapter 4 Thermoacoustical Studies in Binary Liquid
Mixtures of N,N-dimethylacetamide (DMA) + 1-Propanol, + Methanol and + Water at Three Temperatures
76-97
4.1 Introduction 76 4.2 Results 77 4.3 Discussion 78 4.3.1 Excess Parameters 78 4.3.2 Thermacoustical Parameters 79 4.3.3 Semi-empirical Relations 80 4.4 Conclusion 81 References 95
Chapter 5 Studies on Molecular Association in Binary Liquid Mixtures of Poly(propylene glycol)monobutylether340 (PPGMBE 340) with Toluene, Benzene and Benzyl alcohol form Density, Viscosity and Refractive Index Data at 293.15, 303.15 and 313.15 K
98-120
5.1 Introduction 98 5.2 Chemicals 100 5.3 Results 100 5.4 Discussion 101 5.4.1 Excess Parameters 101 5.4.2 Thermophysical Parameters 106 5.5 Conclusion 107 References 119
Chapter 6 Thermoacoustical Studies in Binary Liquid
Mixtures of Poly(propylene glycol) monobutyl ether 340 (PPGMBE340) with Toluene, Benzene and Benzyl alcohol at Three Temperatures
121-137
6.1 Introduction 121 6.2 Results 122 6.3 Discussion 122 6.4 Conclusion 125 References 137
Chapter 7 Theoretical Calculations of Some
Thermophysical Parameters for Binary Liquid Mixtures of PPGMBE340 with Toluene, Benzene and Benzyl alcohol
138-153
7.1 Introduction 138 7.2 Calculation of Surface Tension and Other
Thermophysical Parameters 138
7.3 Results 140 7.4 Discussion 140 7.5 Conclusion 142 References 153
i
ACKNOWLEDGEMENT
“Man Proposes – God Disposes”
First of all I bow my head to ALMIGHTY GOD who always blessed
and directed me to move on the right path.
I am highly grateful to my supervisor Prof. (Mrs.) Manisha Gupta,
Department of Physics, University of Lucknow, Lucknow, for her analytical,
scientific, encouraging and kind guidance throughout the research work. I
have looked back at her indepth scientific knowledge and invaluable visionary
approach which has helped me to take corrective measures.
It is an honour for me to thank Prof. J. P. Shukla, Former Head,
Department of Physics, University of Lucknow, for his valuable guidance,
critical and fruitful discussions throughout the work. I am also grateful to
Prof. (Mrs.) A. Shukla for her affection and encouragement.
I, gratefully acknowledge Prof. (Mrs.) Kirti Sinha, Head, Department
of Physics, University of Lucknow, for providing all necessary departmental
facilities.
I am thankful to my seniors and coworkers namely Dr. Isht Vibhu, Dr.
Amit Misra, Dr. Rishabh Dev Singh, Dr. Shashi Singh, Dr. Divya Shukla,
Dr. Vijay Kumar Misra, Dr. Shahla Parveen and Dr. Rahul Singh, Dr.
Kaushlendra Pratap Singh, Dr. V. K. Shukla, Dr. Maimoona Yasmin, Mr.
Sudir Kumar and Miss Sangeeta Sagar for their help and sincere support
during the entire course of work.
I am highly obliged and grateful to Dr. Nisheeth Rastogi, Assistant
Professor, Department of Chemistry, Lucknow Christian Degree College,
Lucknow, for his critical comments and help in preparing this manuscript.
ii
I always experienced the presence of my parents, Prof. D. K. Agarwal
and Smt. Vinita Agarwal standing behind me by all means. The immense
knowledge, of my father and extensive discussions with him has provided a
colourful scientific lustre to the thesis.
The valuable and judicious scientific suggestions, motivation and
incredible support of my elder brother Dr. Abhinav Agarwal, Postdoctoral
Associate at the University of Louisville, Louisville USA, cannot be ignored
at any stage. My brother in law Mr. Amit Agarwal and sister Dr. Akriti
Agarwal have always encouraged me, whenever, I felt bore during the tenure
of research which is most creditable.
Date (Harshit Agarwal)
iii
CERTIFICATE I
This is to certify that all the regulations necessary for the
submission of Ph.D. thesis of Mr. Harshit Agarwal have been fully
observed.
Date (Prof. Kirti Sinha)
Head
0522-2740410 (O) Department of Physics University of Lucknow Lucknow-226007 (U.P.) India
Dr. Kirti Sinha Ph. D. (L.U.)
Professor and Head
iv
CERTIFICATE II
Certified that this work on "ULTRASONIC,
VISCOMETRIC AND VOLUMETRIC STUDIES OF SOME
MOLECULAR SPECIES EXHIBITING COMPLEX
FORMATION IN SOLUTION" has been carried out by Mr.
Harshit Agarwal under my supervision and the work has not been
submitted elsewhere for the award of degree.
Date (Prof. Manisha Gupta) Supervisor
0522-2740410 (O) Department of Physics University of Lucknow Lucknow-226007 (U.P.) India
Dr. Manisha Gupta Ph. D. (L.U.)
Professor
v
LIST OF PUBLISHED AND COMMUNICATED PAPERS
1. Thermoacoustical Properties of PEG with Alkoxy Ethanols
K. P. Singh, H. Agarwal, V. K. Shukla, M. Yasmin, M. Gupta and J. P. Shukla, J.
Pure Appl. Ultrason., 31(2009)124.
2. Ultrasonic Velocities, Densities, and Refractive Indices of Binary Mixtures of
Polyethylene Glycol 250 Dimethyl Ether with 1-Propanol and with 1-Butanol
K. P. Singh, H. Agarwal, V. K. Shukla, I. Vibhu, M. Gupta and J. P. Shuka, J.
Solution Chem., 39 (2010) 1749.
3. Determination of Ultrasonic Velocities and Excess Parameters of Polymer
Solutions by Means of Piezoelectric Sensor-Transducer
M. Yasmin, H. Agarwal, V. K. Shukla, S. Kumar, M. Gupta and J. P. Shukla,
Lucknow J. Sci., 8(1) (2011) 293.
4. Molecular interactions in Binary Mixtures of Formamide with Alkoxyalcohols at
Varying Temperatures
M. Yasmin, R. Singh, H. Agarwal, V. K. Shukla, S. Kumar, M. Gupta and J. P.
Shukla, Lucknow J. Sci., 8(2), (2011), 324.
5. Study of Molecular Interactions in Binary Mixtures of Formamide with 2-
Methoxyethanol and 2- Ethoxyethanol at Varying Temperatures
R. Singh, M. Yasmin, H. Agarwal, V. K. Shukla, M. Gupta and J. P. Shukla, Phy.
Chem. Liq., 51 (2013) 606-620
6. Study of Density, Viscosity, Refractive Index and Their Excess Parameters for
Binary Liquid Mixtures, N,N-dimethylacetamide with 1-Propanol, Methanol and
Water at 293.15, 303.15 and 313.15 K
H. Agarwal, V. K. Shukla, S. Kumar, M. Yasmin, S. Sagar and M. Gupta, J.
Chem. Eng. Data, Communicated 2014
7. Study of Molecular interaction in Binary Liquid Mixtures of Poly (propylene
glycol) monobutyl ether 340(PPGMBE 340) with Toluene, Benzene and Benzyl
alcohol from Density, Viscosity, Refractive Index Measurements at 293.15, 303.15
and 313.15 K
H. Agarwal and M. Gupta, J. Solution. Chem., Communicated 2014
vi
LIST OF CONFERENCE / SEMINAR PAPERS
1. Acoustical and Thermodynamical Study of Binary Liquid Mixtures, K. P. Singh,
H. Agarwal, R. D. Singh, V. K. Shukla, M. Yasmin and J. P, Shukla
95th Session of Indian Science Congress, Visakhapatnam, Jan 3-7, 2008.
2. Ultrasonic Velocity, Density and Refractive Index and Derived Properties of 2 –
Butoxyethnol with Polymers, S. Parveen, S. Singh, D. Shukla, K. P. Singh, H.
Agarwal, V. K. Shukla, M. Yasmin, M. Gupta and J.P.Shukla
Polychar -16, World Forum for Advanced Materials, Lucknow, Feb 17 -21, 2008.
3. Thermoacoustical Properties of PEG with Alkoxy Ethanols, K. P. Singh, H.
Agarwal, V. K. Shukla, M. Yasmin, M. Gupta and J. P. Shukla
17th National Symposium on Ultrasonics, B.H.U. (NSU-XVII) Dec. 4-6, 2008.
4. Ultasonic Velocity, Effective Debye Temperatures, Pseudo- Gruneisen Parameter
and Excess Properties of Binary Mixtures of Benzaldehyde with Methanol and
Ethanol, H. Agarwal, K. P. Singh, V. K. Shukla, S. Singh, M. Gupta and J. P. Shukla
96th Session of Indian Science Congress, Shillong, Jan 3-7, 2009.
5. Thermoacostic Properties of 1-Propanol with Poly (ethylene glycol) Dimethyl
Ether 150 and 250 at Varying Temperatures, H. Agarwal, M. Yasmin, K. P.
Singh, V. K. Shukla, S. Gupta, M. Gupta and J.P.Shukla
National Conference on Recent Trends in Material Sciences (NCRTMS),
Amritsar, Feb. 10-11, 2009.
6. Thermodynamic Properties of Binary Liquid Mixtures of THF with Methanol and
o-Cresol-An Experimental and Theoretical Study, M. Yasmin, K. P.Singh, H.
Agarwal, V. K. Shukla, S. Parveen, M. Gupta and J.P.Shukla
National Conference on Recent Developments in Science and Technology,
Aligarh, Feb. 15-16, 2009.
7. Volumetric, Ultrasonic and Optical Study of Molecular Interactions in Liquid
Mixtures of 1-Propanol with Poly (ethylene glycol) Dimethyl Ether 150 and 250 at
Varying Temperatures, K. P. Singh, H.Agarwal, M. Yasmin, V. K. Shukla, S.
Gupta, M. Gupta and J. P. Shukla
MR-09, IIT Bombay, May 7-9, 2009.
vii
8. Validity of Various Thermodynamical Relations and Non Linearity Parameter in
Investigation of Molecular Interactions in the Binary Mixtures of Polymers with
Alcohols, M. Yasmin, K. P. Singh, H. Agarwal, V. K. Shukla, M. Gupta and
J.P.Shukla
18th National Symposium on Ultrasonics, , Vellore, Dec 21-23, 2009.
9. Thermo-acoustical Properties of Polyethylene Glycol 250 Dimethyl Ether with 1-
Propanol and 1-Butanol at Varying Temperatures, K. P. Singh, H. Agarwal, M.
Yasmin, V. K. Shukla, R. Singh, M. Gupta and J.P. Shukla
97th Session of Indian Science Congress, Thiruvananthapuram, Jan. 3-7, 2010.
10. Thermo-acoustic Studies on Binary Liquid Mixtures of N,N-
dimethylacetamide with Methanol, 1-propanol and Water at 293, 303 and
313K, H. Agarwal, V. K. Shukla, K. P. Singh, M. Gupta and J. P. Shukla
98th Session of Indian Science Congress, Chennai, Jan. 3-7, 2011.
11. Determination of Ultrasonic Velocities and Excess Parameters of Polymer
Solutions by Means of Piezoelectric Sensor-Transducer, M. Yasmin, H. Agarwal,
V. K. Shukla, S. Kumar, M. Gupta and J. P. Shukla
16th National Seminar on Physics and Technology of Sensors, Lucknow, Feb. 11 –
13, 2011.
12. Molecular Interaction in Binary Mixtures of Acetonitrile with 2-Ethoxyethanol and
2-Butoxyethanol at 293, 303 and 313K, R. Singh, H. Agarwal, V. K. Shukla, M.
Gupta and J. P. Shukla
Advancement and Futuristic Trends in Material Science, M. J. P. Rohilkhand
University, Bareilly, March 26-27, 2011.
13. Molecular Interaction in Binary Mixtures of Acetonitrile with 2-Ethoxyethanol and
2-Butoxyethanol at 293, 303 and 313K, R. Singh, H. Agarwal, V. K. Shukla, M.
Gupta and J. P. Shukla Advancement and Futuristic Trends in Material Science, M. J. P. Rohilkhand
University, Bareilly, March 26-27, 2011. 14. Thermodynamic Properties of Binary Mixtures of Poly(propylene
glycol)monobutyl ether Mn-340 with Benzene /Toluene at Varying Temperatures,
H. Agarwal, V. K.Shukla, M. Gupta and J. P. Shukla
100th Session of Indian Science Congress, Kolkata, January 3-7, 2013.
viii
15. Molecular Interactions in Binary Mixtures of Polypropylene Glycol Monobutyl
Ethers (PPGMBE) with 1-Butanol and 2-(Methylamino) Ethanol (MAE), S.
Kumar, S. Sagar, H. Agarwal, V. K. Shukla, M. Yasmin, M. Gupta and J. P. Shukla
101st Session of Indian Science Congress, Jammu, January 3-7, 2014.
16. Study of Ultrasonic Velocity, Density, Viscosity and Their Excess Parameters for
the Binary Mixtures of Poly(ethylene glycol) Methyl Ether Methacrylate 300
(PEGMEM 300) with 2-Methoxyethanol and 2-Ethoxyethanol, V. K. Shukla, H.
Agarwal and M. Gupta
International Symposium on Advances in Biological and Material Sciences
(ISABMS-2014), Lucknow, July 15, 2014.
ix
ABSTRACT
The present thesis deals with the molecular interaction studies
amounting to complex formation in binary solutions of N,N-
dimethylacetamide (DMA) with 1-propanol, methanol and water and
poly(propylene glycol)monobutyl ether (Mn-340) (PPGMBE 340)
with toluene, benzene and benzyl alcohol using volumetric,
viscometric, refractometric and ultrasonic velocity techniques through
their excess and other parameters to evaluate the effect of various
factors namely polarity, molecular size and heteromolecular hydrogen
bonding etc. and influence of temperature on molecular interactions.
The thesis has been divided into seven chapters:
Chapter 1 comprises of the review of the latest literature on
the ultrasonic, viscometric, volumetric, and refractometric studies
with their excess parameters along with the objective and scope of the
present work.
Chapter 2 describes the details of the experimental techniques
used for the measurement of ultrasonic velocity, viscosity, density
and refractive index. Evaluation of thermophysical parameters,
calculation of excess / deviation parameters, standard deviation in
excess parameters from Curve Expert 1.3 linear regression
polynomial equation, theoretical estimation of ultrasonic velocity,
viscosity, refractive index and density models are discussed in brief.
Chapter 3 reports the experimental data of the density ( ρ ),
viscosity (η) and refractive index (n) for binary solutions of N,N-
dimethylacetamide (DMA) with1-propanol, methanol and water at
varying concentrations and temperatures. Using these data, excess
x
molar volume (VmE), deviation in viscosity (∆η), deviation in molar
refraction (ΔRm) and excess Gibbs’s free energy of activation for
viscous flow (ΔG*E) have been evaluated along with their standard
deviation. The results have been interpreted in terms of strength of
intermolecular interaction resulting complex formation in these
mixtures.
Chapter 4 presents the data of density (ρm) and ultrasonic
velocity (um) for the binary mixtures of DMA with 1-propanol,
methanol and water over the entire range of composition at 293.15,
303.15 and 313.15 K. The intermolecular interactions present in the
mixtures have been investigated through deviation in ultrasonic
velocity (Δu), excess acoustic impedance (ZE) and excess
intermolecular free length (LfE). Derived parameters such as
isentropic compressibility (Ks), effective Debye temperature (ϴD) and
specific heat ratio (γ) at varying concentrations of DMA have also
been calculated using experimental data for all the three systems.
Various semi-empirical mixing rules proposed by Nomoto, Vandeal,
Junjie, CFT and Flory’s statistical theory (FST) for the estimation of
ultrasonic velocity of liquid mixtures have also been applied to these
binary mixtures. HBT and Rackett density models have been used to
compare the experimental and theoretically calculated values.
In Chapter 5, a polymer namely Poly (propylene glycol)
monobutyl ether 340 (PPGMBE 340) has been selected for the study
of molecular interaction in its binary solution with toluene, benzene
and benzyl alcohol from density, viscosity and refractive index data.
The excess molar volume (VmE), deviation in viscosity (∆η) and
deviation in molar refraction (ΔRm) and many other derived
parameters such as optical dielectric constant (ε), polarizability (α)
xi
and interaction parameter (d) at varying concentrations of
PPGMBE340 have also been calculated. Results have been analyzed
in the light of molecular interactions between like and unlike
molecules with respect of their polarities.
Chapter 6 is the further extension of the work on same binary
systems used in Chapter 5 employing other techniques namely
volumetric and ultrasonic. Deviation in ultrasonic velocity (Δu),
deviation in isentropic compressibility (ΔKsE), excess acoustic
impedance (ZE), excess intermolecular free length (LfE) and excess
molar enthalpy (HmE) of binary systems PPGMBE340 with toluene,
benzene and benzyl alcohol over whole composition range and
varying temperatures have been calculated and examined in terms of
various physical, chemical and structural interactions.
Chapter 7 is based on theoretical computation and deals with
the calculations of many thermophysical parameters like surface
tension (σ), non-linearity parameter (B/A), relaxation time (τ) and
molecular association (MA), van der Waal’s constant (b), relaxation
strength (r), molecular radius (rm), geometrical volume (B), molar
surface area (Y) and collision factor (S) for the binary mixtures of
PPGMBE 340 with toluene, benzene and benzyl alcohol at three
different temperatures. Surface tension and other thermophysical
parameters have been interpreted on the basis of molecular interaction
in the three systems. These findings gave a strong theoretical
coverage to the experimental results of Chapters 5 and 6.
CHAPTER 1 General Discussion
1.1 Introduction 1.2 Ultrasonics 1.3 Viscometry 1.4 Volumetry 1.5 Refractometry 1.6 Excess Parameters 1.7 Objective and Scope of the Study
References
1
1.1 INTRODUCTION
Research is not a scope but it is an intellectual exercise. The
properties of condensed matter are determined by the strength of
interactions between its constituent atoms, ions or molecules. The
properties of matter in the liquid phase are qualitatively described by
two characteristics;
(i) Lack of shear rigidity, common in gases and
(ii) Very low compressibility, common in solids.
At temperature and pressure above the critical point, the liquid
phase does not exist at all. At lower temperature near freezing point,
the structural concepts of the solid phase are applicable; while at
higher temperature, near the boiling point, the statistical concepts of
the kinetic theory of gases are more useful. Both of these approaches
are only approximations to more accurate description of the liquid
phase [1, 2].
There are various theories or models proposed to describe the
liquid state whose applicability and validity varies with the nature of
liquids. Regular solution theory gives good results in non-polar
liquids [3, 4] and is based on the assumption of no excess entropy
and no volume change on mixing.
The lattice theory, initially proposed by Eyring and
coworkers [5] requires molecule to be more or less bound to one
position in space. Further, the concept of “hole” or vacant sites in
the lattice is required to account for the fluidity of liquids [6, 7].
With this hole concept, Eyring and coworkers [5] concluded that a
liquid possesses dual characteristics of gas and solid; solid-voids
2
experience gas like freedom while remaining part of the liquid
exhibits solid like rigidity. Free “volume” or “cell” model [5, 7-9]
of the liquid state implies some amount of organization of structure
in it and assumes a molecule to be confined to small region of the
liquid constrained by the repulsive fields of its neighbors. The basic
assumption of free volume theory that there is probability of
occurrence of empty neighboring sites, where molecules can jump
[10], has been found very valuable to study viscosity of liquid and
liquid mixtures. The description of the free energy required for the
transition of a molecule to a new equilibrium position is given by the
absolute rate theory [11].
The physical properties of any medium can be described either
macroscopically or microscopically. On a macroscopic scale, matter
is treated as a “continuum” which possesses certain properties,
clearly defined by well-known measuring operations without any
knowledge of the internal structure. The microscopic point of view,
on the other hand, deals with detailed knowledge of the internal
structure and composition of the matter.
The physiochemical behavior and intermolecular interactions
in mixtures have been a subject of active interest. Fascinating
progress in the study of molecular interactions in liquid mixtures has
taken place and a number of theories [12-17] have been proposed, in
this regard.
The advantage of this progress, into the variation of
macroscopic physical properties of the mixtures is twofold. Firstly,
this offers an indirect but convenient way to ascertain the nature or /
and possibilities of microscopic interactions between like as well as
unlike molecular species. Secondly, this provides experimental
3
background to develop, test and modify the theories for precise
prediction of the properties of mixtures; in varying ambience and
composition, often needed in condensed matter physics [18-20],
chemistry [21, 22], chemical engineering [23-25] and industry
[26,27].
Liquids and especially liquid mixtures are widely used in
processing and product formulation in many industrial applications.
Properties of mixtures are useful for designing vehicles in the
transportation of process equipments in chemical industry [28, 29].
Thermodynamic properties of a mixture depend on
intermolecular forces operating between the constituent molecules in
the mixture. To interpret and correlate thermodynamic properties of
solutions, the knowledge / nature of intermolecular forces is required
for protic, aprotic, hydrogen and non-hydrogen bonded, electron
donating and electron accepting liquids.
Two types of binary systems were selected for the present
study:
(i) Binary systems of N,N-dimethylacetamide (DMA) + 1-
propanol, + methanol and + water
(ii) Binary systems of Poly(propyleneglycol)monobutylether (Mn-
340)(PPGMBE340) + benzene, + toluene and + benzyl
alcohol
Thermodynamic and transport properties like ultrasonic
velocity, viscosity, refractive index and density were used as a tool
for the study of interaction in binary solutions. The various excess
and thermophysical parameters were evaluated such as excess molar
volume, inter molecular free length, excess Gibb’s free energy of
activation, specific heat ratio, effective Debye temperature etc.
4
Though a large number of sophisticated techniques like NMR,
FTIR, X-ray, vapour pressure, dielectric constant etc. are available
to study the molecular interactions and its relationship with
ambience parameters. Even then the ultrasonic, volumetric,
viscometric and refractometric techniques are being used because of
their less demanding experimental requirements.
1.2 ULTRASONICS
In the last two three decades, to study the physicochemical
behavior and molecular interactions in liquid mixtures, the
ultrasonic velocity technique has been extensively used [30-36].
The mechanical longitudinal waves which are generated
through the crystal are propagated through the matter - solid, liquid
or gas. These waves may be divided roughly into the following
classes according to their frequency:
(i) Infrasonic waves (below 20 Hz.)
(ii) Audible or sonic waves (between 20Hz to 20 kHz.)
(iii) Ultrasonic waves (between 20 kHz. to 1GHz)
(iv) Hypersonic waves (above 1GHz)
The term ‘ultrasonic’ is used to describe a vibrating wave of a
frequency above that the upper frequency limit of the human ear; it
generally embraces all frequencies above 20 kHz [37]. Also, high
amplitude ultrasonic waves are sometimes referred to as “sonic”
[17].
There are a number of ways in which ultrasonic waves can be
generated. The method chosen depends upon the power output
necessary and the frequency range to be covered. It was Galton, who
in 1883 modified the edge-tone generator so as to generate the sound
5
waves of frequency above than the audible range of human ear. In
Galton’s apparatus, a jet of air debounces from a narrow slit to fall
upon the sharp edge of an object which faces the slit. The jet is set in
pendulation, the frequency of which can be increased by raising the
velocity of efflux and reducing the separation of slit from edge.
Some ultrasonic generators which use a spark plug or an arc of
direct current to produce vibrations are based on thermal principles
and are not commonly used in the present days.
The simplest method of generating high frequency ultrasonics is
piezoelectric crystal transducers. The piezoelectric is a phenomenon
resulting from a coupling between the electric and mechanical properties
of a material. It is a phenomenon, exhibited by certain crystals which
distort in shape when electric stresses are applied to them in certain
directions. The commonly used crystals for ultrasonic wave generation
are quartz, rouchelle salt, ammonium dihydrogen phosphate, lithium
sulphate, dipotassium tertrate, potassium dihydrogen phosphate.
Magnetostrictive transducers are also commonly employed for the
generation of ultrasonic waves. This designates the effect by which
magnetic materials suffer a change in length owing to a molecular
rearrangement, when the magnetic field in which they are placed,
changes the strength. When a ferromagnetic rod is subjected to an
alternating magnetic field parallel to its length it can be set in
oscillations at one of its natural frequencies, hence ultrasonic waves are
produced.
The modern technique for producing ultrasonic wave is Laser
Beam Ultrasonic (LBU). Laser-ultrasonic uses lasers to generate
and detect ultrasonic waves. It is a non-contact technique used to
characterize a material, to measure its thickness and to detect flaws.
6
LBU is operated by first generating ultrasound in a sample using a
pulsed laser. When the laser pulse strikes the sample, ultrasonic
waves are generated through a thermo elastic process or by ablation.
Its accuracy and flexibility have made it an attractive new option in
the non-destructive testing market. Well established applications of
laser ultrasonics are composite inspections for the aerospace
industry and on-line hot tube thickness measurements for the
metallurgical industry.
The important physical effects of ultrasonic are cavitation,
local heating and the production of fog. Cavitation is a generic term
applied to a number of ultrasonic effects characterized by the
formation and collapse of bubbles in a liquid. The results of
cavitation may be spectacular and many ultrasonic effects are
ascribed to the accompanying cavitation [38, 39]. It has been found
that at 4MHz. sound energy transforms into heat with a constant
ratio [40]. Heating effects become greater with increase of frequency
because of increased absorption. Fog production is resulted by the
jet of liquid thrown up when intense waves hit an interface between
a liquid and air. Ultrasonic waves can bring about a degassing
action, i.e. the expulsion of gases from liquids or solids. There are so
many biological effects, chemical effects, electro chemical effects
which have been exploited in numerous applications of ultrasonics.
Medical applications of ultrasound usually do not involve
measurement of sound velocity but instead depend on the relative
invariance of sound velocity in human tissue. Many medical devices
measure the reflected signal and display the spatial variation of its
amplitude, often using the time domain to give depth to the image.
7
Over the years, ultrasonic technique [41-44] has been found to
be one of the most powerful tools for studying the structural and
other physico-chemical properties of liquids and liquid mixtures.
Boyle [45] initiated the study of propagation of ultrasonic wave in
liquids. Lagemann and Dunbar [46] were the first to point out the
sound velocity approach for qualitative determination of the degree
of association in liquids. Ultrasonic studies [47-49] at low amplitude
provide valuable information regarding the structure and interactions
taking place in pure liquids and multicomponent liquid mixtures.
Ultrasonic velocity and density data permit the direct estimation of
isentropic compressibility; intermolecular free length and few more
related parameters which cannot be deduced easily by any other
method. Apart from this, ultrasonic velocity has also been found to
be an important property for testing the validity of various liquid
state models. Many workers have examined the validity of various
theories [50-55] by ultrasonic velocity and density measurements.
1.3 VISCOSITY
Viscosity is a transport property that is generally defined as
the resistance to flow under applied shear stress. Fluids are classified
either as Newtonian or non-Newtonian fluids. Newtonian fluids are
fluids that obey Newton’s law of viscosity, whereas non-Newtonian
fluids do not. According to Newton’s law of viscosity, the absolute
viscosity is the proportionality constant in an equation that relates
the shear stress to the shear rate or velocity gradient viz;
τ = η 𝑑𝑣𝑑𝑥
8
The shear stress, τ, is the force applied to the fluid per unit
area, the velocity gradient dv/dx is the measure of the shearing
experienced by the liquid and is thus called shear strain (γ). η is a
constant for a given material and is called viscosity. Thus, viscosity
may be defined mathematically as,
η = 𝜏𝛾 = 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠
𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛
The viscosity of pure components as well as those of liquid
mixtures has attracted the attention of many researchers over the
years. In spite of all the earlier efforts, complete description of the
viscosity of multi-component liquid mixtures remains insufficient,
attributing to the difficulty of understanding the structure of the
liquids. Thus more accurate and precise viscosity data, especially for
liquid mixtures are required to have a clear knowledge of structure
of the liquid / liquid mixtures.
Accurate viscosity data are needed for the design of most of
fluid flow equipment. The pharmaceutical industry relies on
viscosity measurement to qualify the flow behavior of materials for
a variety of applications.
Viscometric data has various applications in material
characterization or finger-printing, standard testing methods to
check for differences between batches, indirect way of measuring
quality, product formulation, quality control, process control, design,
optimization and operation of process equipment.
Viscometry is one of the most widely utilized methods for the
characterization of polymer molecular weight, since it provides the
easiest and most rapid means of obtaining molecular weight related
9
data and requires a minimum amount of instrumentation. A most
obvious characteristic of polymer solutions is their high viscosity,
even when the amount of added polymer is small [56].
Considerable work has been done in our laboratory [57-64] to
establish an extensive database that contains accurate density and
viscosity of liquid and liquid mixtures at different compositions and
temperatures. Extensive experimental data on viscosity together with
the study of ultrasonic velocity and density, has led to the
determination of Gibb’s free energy, free volume, internal pressure
and enthalpy etc. [65, 66].
1.4 VOLUMETRY
Density / specific gravity, an intensive property of the matter,
is defined as the mass per unit volume. The relative density is the
ratio of the weight of a given volume of the substance to the weight
of an equal volume of water at the same temperature and the density
of the substance is equal to the relative density multiplied by the
density of water at that temperature.
Density describes the degree of compactness of a substance or
in other words, how closely packed together the atoms or molecules
in a substance are. An extensive and exhaustive study of density
gives an insight into the nature of strength and possibilities of
microscopic interactions and it provides an experimental
background to develop, test and then modify theories for the liquid
mixtures and their transport properties. Liquid densities are needed
in many engineering problems such as process calculations,
simulations, pipe designing and metering calculations.
10
Molar volume (Vm) can be easily calculated from the
experimental data of density and mole fraction provides an efficient
and convenient tool to study the interactions at molecular level.
Positive and negative values of excess molar volume (VmE) show the
deviations of molar volume from ideality. This has been interpreted
by several research workers [67,68] as a commulative manifestation
of three effects such as physical, chemical and structural.
1.5 REFRACTOMETRY
Refractometry is the study of the variation of refractive index
and molar refraction of the medium in different environment.
Refractive index of any medium is a quantitative measure of the
response of constituents molecules of the medium to the
electromagnetic waves and is defined as the ratio of the velocity of
electromagnetic wave in vacuum to that in the medium. H. A.
Lorentz, on the basis of electromagnetic theory of light and L. V.
Lorenz, on the basis of wave theory of light, independently deduced
following relationship between the refractive index (n) and density
(ρ) viz:
=
+
−ρ1
2n1n
2
2 Constant
This constant is called specific refraction.
The molar refraction ( mR ) is a derived quantity and is defined
as,
m2
2
m V2n1nR
+−
=
11
Where n is the refractive index of the medium and mV is the molar
volume of the medium.
The study of the variations of refractive index of a liquid with
temperature and with mixing of different solutes in varying
concentration gives valuable inferences about the structure of liquids
or liquid mixtures.
There are many semi-empirical rules [69-77] for evaluating
the refractive indices of binary and ternary liquid mixtures.
Extensive survey of literature reveals that enormous amount of the
work has been done to measure or to evaluate the refractive index of
liquids and liquid mixtures [44, 78-80].
1.6 EXCESS PARAMETERS
The values of excess parameters for binary mixtures describe
the deviation of a solution from ideality. The excess values AE for
any parameters, can be computed using the relation,
AE = Amix – ∑ 𝑥 𝑖 𝑛𝑖=1 𝐴𝑖
where Amix represent the parameter of the mixture, Ai represent the
physical parameter of the pure component i.
The excess parameters have been interpreted by many
workers [81-83] as a cumulative manifestation of three effects-
(1) Physical; this is due to non-specific physical interactions.
(2) Chemical; this occurs due to breaking up of the liquid order of
associated species.
12
(3) Structural; this takes place due to geometrical fitting of
molecules into the voids created by bigger molecules and also
due to differences in molar and free volumes of the components.
The literature survey reveals that the study of intermolecular
forces in solutions is mostly done in terms of excess thermodynamic
functions. These functions are found to be sensitive towards the
intermolecular forces as well as the size and shape of the molecules
[84-94].
Variation of the excess molar volume, deviation in viscosity
and the excess molar refraction with temperature and mole fraction
have been employed by number of workers [85-87] for studying the
molecular interactions in liquid mixtures. Many more derived
parameters such as Gibb’s activation energy of viscous flow,
internal pressure, free volume etc. can also be computed with the
help of experimental data of sound velocity, density and viscosity.
Excess values of these derived parameters reflect the variation in
nature of molecular units and also provide significant inferences
about the nature of the interactions [85, 91-103].
1.7 OBJECTIVE AND SCOPE OF THE STUDY
In our laboratory a huge amount of work has been done on
molecular interactions / complex formation in binary solutions
during the last two decades. In continuation of that, in the present
study, two liquids N,N-dimethylacetamide (DMA), highly exploited,
and poly(propylene glycol)monobutyl ether 340 (PPGMBE 340),
almost untouched, were selected for molecular interaction or
complex formation studies in their binary solutions with other
13
liquids, in the light of polarity (dipole moment), molecular size /
chain length, hydrogen bonding and along with the thermal effect.
The density, viscosity, refractive index and ultrasonic velocity
techniques will be employed as tools for this study. Excess
properties namely EmV , u∆ , η∆ , mR∆ , sk∆ , EZ , E
fL , Eiπ , E*G∆ ,
EfV , E
mH and derived parameters will also be calculated to have a
deep insight to the findings. Due to lack of work on PPGMBE340,
in order to provide strength to our findings on molecular interaction
in this polymer, thermophysical parameters will also be calculated
theoretically and taken into consideration.
It is pertinent to mention here that DMA is selected due to the
fact that it is very important organic specie, acting as a good reaction
medium as well as catalyst for many reactions. It is very versatile
polar aprotic liquid with high dielectric constant (ε=37.78) and
dipole moment (μ=3.7D), but practically unassociated. Three liquids
namely 1-propanol, methanol and water used for the preparation of
binary solutions with DMA are polar aprotic liquids having
significant dielectric constant and dipole moment in the order 1-
propanol < methanol < water as given below:
Liquid Structure Dielectric
Constant
Dipole
Moment
N,N
Dimethylacetamide
37.78
3.72D
1-Propanol
20.1
1.68D
14
Methanol
33
1.70D
Water
80 1.85D
On the other hand, poly(propylene glycol)monobutyl ether 340
(PPGMBE340) is one of the synthetic polymers among other polyalkylene
glycols. Poly (propylene glycol)monobutyl ether 340 is used extensively as
lubricant for automobile engine in cold climates [104-107]. The fluid shows
the expected low carbon and low sludge, as well as cleans engine parts and
satisfactory cranking at low temperature down to -60oF. PPGMBE340 does
not readily crystallize. Instead, it becomes too thick to flow at a temperature
known as the pour point. The pour point for this polymer is very low (-
56oC). Even at temperature below its pour point, it does not crystallize but
form a glasslike solid. Due to the extraordinary properties of PPGMBE340
in automobile industry, it is also selected as one of the components of binary
solutions with two non-polar aromatic liquids toluene and benzene and one
polar aromatic liquid benzyl alcohol in order to investigate the effect of
polarity and aromaticity on molecular interaction in binary solutions.
It is expected that this study will give a deep inview on the role of
various factors like polarity (dipole moment), molecular size, hydrogen
bonding, etc. governing the molecular interactions amounting to the
complex formation and temperature sensitivity towards the strength of the
complexation between different molecular species.
The detailed study on molecular interactions in binary solutions in
future may be helpful for the selection of binary mixtures as better lubricants
and engine oil to enhance the longevity of engine in different industries.
15
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CHAPTER 2 Experimental Techniques and Evaluation of
Excess Parameters
2.1 Ultrasonic Velocity Measurement 2.1.1 Principal of Interferometry Technique
2.1.2 Experimental Set-up 2.2 Viscosity Measurement 2.3 Density Measurement 2.4 Refractive Index Measurement 2.4.1 Principle of Abbe’s Refractometer 2.4.2 Calibration and Mode of Operation 2.5 Temperature Maintenance 2.6 Preparation of Mixtures 2.7 Evaluation of Thermo-acoustic and Excess Parameters 2.7.1 Isentropic Compressibility 2.7.2 Acoustic Impedance 2.7.3 Intermolecular Free Length 2.7.4 Gibb’s Free Energy of Activation of Viscous Flow 2.7.5 Free Volume (Vf) and Internal Pressure 2.7.6 Effective Debye Temperature and Pseduo-Grünrisen Parameter 2.7.7 Excess / Deviation Parameters 2.8 Curve Expert 1.3 Linear Regression Polynomial Equation 2.9 Estimation of Ultrasonic Velocity 2.9.1 Mixing Rules for Ultrasonic Velocity 2.9.2 Collision Factor Theory (CFT)
2.9.3 Flory Statistical Theory (FST) 2.10 Estimation of Viscosity 2.11 Density Models 2.11.1 Modified Rackett Model and Hankinson-Brobst- Thomson (HBT) Model for Density 2.11.2 Mixing Rules for Both the Modified Rackett and Hankinson Equations 2.12 Semi Empirical Relations for Prediction of Refractive
Index
References
23
The present chapter reports a systematic description of
experimental measurements of ultrasonic velocity, viscosity, density
and refractive index at varying temperatures viz. 293.15, 303.15 and
313.15 K and at atmospheric pressure. A brief description of
apparatuses and their principles of working have been summarized.
The thermodynamic and excess parameters evaluated using
experimental data are reported in this chapter.
2.1 ULTRASONIC VELOCITY MEASUREMENT
Mainly there are three techniques used to measure ultrasonic
velocity in liquids viz. echo-pulse, optical diffraction and
interferometry technique. In the present work ultrasonic velocity is
measured using interferometry technique, a modified version of
Owens and Simmons [1] has recently being used by many workers
[2-5], for the measurement of ultrasonic velocity in liquids.
2.1.1 Principle of Interferometry Technique
An ultrasonic interferometer is a simple and direct device to
determine the ultrasonic velocity in liquids with a high degree of
accuracy. A single crystal interferometer was first devised by Pierre
[6] to measure sound velocity in liquids. The working of such
devices can be illustrated with the help of schematic diagram (Fig.
2.1), where T represents a transducer, usually an X-cut quartz
crystal, whose surfaces are silver or gold polished to provide
metallic contacts to a radio frequency electronic oscillator, ‘O’.
When the frequency of driving oscillator (O) coincides with the
natural frequency of piezoelectric transducer T, it vibrates with
Figure2.1 Principle of the Ultrasonic Interferometer: T, Transducer Silvered on Opposite Faces; R, Movable Reflector; O, Oscillator
24
appreciable amplitude. These vibrating surfaces of the crystal
generate a plane mechanical wave of the same frequency, which
travels through the medium towards a plane reflecting plate R,
maintained parallel to the crystal surface. The reflector R can be
moved normal to the crystal and along the direction of the sound
wave. When the distance between the reflector and the crystal is an
integral number of half the wavelength, standing waves are set-up in
the medium between the crystal and the reflector. The reflected
wave arriving back at the crystal is then 180o out of phase with the
vibration of the crystal. The resulting decrease in the amplitude of
the crystal vibration is accompanied by a corresponding decrease in
the alternating current through the crystal. The distance moved by
the reflector between two successive current minima (or maxima) is
equal to λ/2 (Fig. 2.2), where λ is the wavelength of the mechanical
wave in the medium between crystal and reflector. Once the
wavelength is known, the ultrasonic velocity (u) in the liquid can be
obtained using the following relation:
Ultrasonic velocity(u)= frequency (f) × wavelength (ʎ) (2.1)
2.1.2 Experimental Set-up
A variable path fixed frequency interferometer (Model F81,
Mittal Enterprises, New Delhi) Fig. 2.3 was used for the present
study, consisting of a high frequency generator and a measuring cell.
2.1.2a High Frequency Generator
The circuit diagram of ultrasonic interferometer is shown in
Fig. 2.4. This is a high frequency crystal controlled oscillator based
on modified Pierre circuit operating in the megahertz region. It is
used to excite the piezoelectric transducer which is a quartz crystal
Figure2.2 Position of Reflector versus Crystal Current Curve
Figure2.3 Ultrasonic Interferometer
Figu
re2.
4 C
ircu
it D
iagr
am o
f Ultr
ason
ic In
terf
erom
eter
25
fixed at the bottom of the measuring cell to produce ultrasonic
waves at its resonant frequency in the experimental liquid filling the
cell. The oscillator is provided with a micro-ampere meter and two
trimmer condensers marked A and B on the backside of the
generator assembly. These are used to adjust or tune the instrument
so that sufficient deflection in anode current can be observed. Two
controls, one for the adjustment of micro-ampere meter and the
other for controlling the gain, are provided. The detailed technical
specifications are given below:
(a) Main voltage- 220V, 50Hz
(b) Measuring frequency- 2 MHz
(c) Glow lamp- 6.3 V, 0.3 A
(d) Fuse- 150 mA
2.1.2b Measuring Cell
Measuring cell is a double walled cylindrical metallic
container (Fig. 2.5) attached vertically into a slot on a heavy metal
base which works as the coupler between piezoelectric crystal and
the high frequency generator. Piezoelectric crystal is fixed at the
base of this measuring cell. Outer wall has provision for circulation
of water or any other liquid for maintaining the temperature of the
experimental liquid, filled in this cell. A quartz crystal of a particular
natural frequency of vibration, which acts as piezoelectric transducer
is fixed at the bottom of the cell. A movable metallic reflector plate,
attached to a micrometre screw arrangement and kept parallel to the
crystal, is housed inside the cell. A digital screen is also attached
with cell to give direct micrometer reading. The measuring cell can
be easily dismantled into three pieces viz. metal base, container and
reflector such that the experimental liquid can be easily poured into
Figure2.5 Measuring Cell of Ultrasonic Interferometer
26
the cell. The transducer is coupled to the high frequency oscillator
by a coaxial cable. The detailed technical specifications are as
under:
(a) Maximum displacement of the reflector -25 mm
(b) Liquid cell capacity-12 mL
(c) Least count of micrometer-0.001 mm
The calibration of ultrasonic interferometer was done by
measuring the velocity in AR grade benzene (C6H6) and carbon tetra
chloride (CCl4). Our measured values of ultrasonic velocity at
293.15, 303.15 and 313.15 K agree closely with the literature values
of C6H6 and CCl4. The temperature was maintained by circulating
water around the liquid cell from thermostatically microprocessor
controlled Brookfield temperature controller TC-502 (see section
2.5) and covering the measuring cell along with its base with a
specially made thermocol jacket with a window for noting down
micrometre readings using digital display which directly gives the
reading of current maxima or minima. The uncertainty in the
measurement of speed of sound is found to be 0.1m/sec.
2.2 VISCOSITY MEASUREMENT
The viscosity has been measured using Brookfield Cone /
Plate LVDV-II+ Pro programmable viscometer (Brookfield
Engineering Laboratories, Inc., USA) with complete control by PC
using Brookfield Rheocalc32 Software (Fig. 2.6). The temperature is
measured by RTD temperature sensor.
2.2.1 Principle of Operation
The principle of operation of the LVDV-II + Pro is to drive a
spindle (which is immersed in the test fluid) through a calibrated
Figure2.6 LVDV II + Pro Viscometer Supplied by Brookfield Engineering Laboratories, USA
27
spring. The viscous drag of the fluid against the spindle is measured
by the spring deflection, which in turn measured by a rotary
transducer. Cone/plate geometry offers absolute viscosity
determinations with precise shear rate and shear stress information
readily available. Cone/plate geometry is particularly suitable for
advanced rheological analysis of non-Newtonian fluids. The
measurement range of a DV-II + Pro is determined by the rotational
speed of the spindle rotating in the container and the full scale
torque of the calibrated spring. The viscometer is of the rotational
variety. It measures the torque required to rotate an immersed
spindle in the fluid. The spindle is driven by a motor through a
calibrated spring. By utilizing a multiple speed transmission and
interchangeable spindles, a variety of viscosity ranges can be
measured. For a given viscosity, the viscous drag, or resistance to
flow, is proportional to the spindle’s speed of rotation and is related
to the spindle size and shape. The drag will increase as the spindle
size / rotational speed increases.
2.2.2 Experimental Set-up
The stepper drive motor is located at the top of the instrument
inside housing. The viscometer case contains a calibrated beryllium-
copper spring, one end of which is attached to the pivot shaft; the
other end is connected directly to the dial. The dial is driven by the
motor driven shaft and in turn drives the pivot shaft through the
calibrated spring. The relative angular position of the pivot shaft is
detected by a rotary variable displacement transducer (RVDT) and is
read out on a digital display. Below the main case, is the pivot cup
through which the lower end of the pivot shaft protrudes. A jewel
bearing inside the pivot cup rotates the transducer; the pivot shaft is
28
supported on this bearing by the pivot point. The lower end of the
pivot shaft comprises the spindle coupling to which the
Viscometer’s spindles are attached.
2.2.3 Electronic Gap Setting
The gap between the cone and plate is adjusted by moving the
plate (build into the sample cup) up towards the cone until the pin in
the centre of the cone touches the surface of the plate, and then by
lowering the plate 0.0005 inch. This gap setting is required because
most of the fluids are dependent on shear rate and the spindle
geometry conditions. The specification of the viscometer spindle
and chamber geometry will affect the viscosity readings. The faster
the spindle, higher is the shear rate. The shear rate of a measurement
is given by the rotational speed of the spindle, the size and shape of
the container and therefore, on the distance between the container
wall and the spindle surface.
2.2.4 Software
Rheocalc 32 is a control programme which operates the
LVDV-II + Pro in external control via a PC as well as a data
gathering program which collects the data output from DV-II + Pro
and provides the capability to perform graphical analysis and data
file management. Important features and benefits in Rheocalc32
enhance operator versatility in performing viscosity tests. It is
compatible with Windows 95, 98, ME, 2000 and NT operating
systems. Its 32 bit operation makes the performance rapid.
2.2.5 Specifications
Each spindle has a two digit entry code which is entered via
the keypad on the LVDV-II + Pro. The entry code allows the
LVDV-II + Pro to calculate viscosity, shear rate and shear stress
29
value. Each spindle has two constants which are used in these
calculations. The Spindle Multiplier Constant (SMC) is used for
viscosity and shear stress calculations and the Shear Rate Constant
(SRC), used for shear rate and shear stress calculations. For spindle
CPE-40 (entry code 40) SMC value is 0.327 and SRC is 7.5, while
for spindle CPE- 52 (entry code 52) SMC is 9.922 and SRC is 2.
The spring torque constant TK is 0.09373. Using these constants, the
full scale viscosity range is calculated using following equations,
Full Scale Viscosity Range (cp) =TK×SMC×100/RPM×Torque (2.2)
Shear Rate (1 / sec) = SRC × RPM (2.3)
Shear Stress (Dynes / cm2) = TK × SMC × SRC × Torque (2.4)
The experimental assembly allows measurement of viscosities
in the range of 0.15 to 3065 cp (with CPE-40) and 4.6 to 92,130 cp
(with CPE-52) with an accuracy of +1.0% of full scale range and
repeatability of +0.2%. These viscosity ranges are for operational
speeds 0.1 through 200 rpm. Apparatus requires only 0.5mL of the
liquid for measurement of viscosity.
The apparatus measures fluid absolute viscosity directly in cp.
The apparatus was calibrated by two viscosity standards
(Polydimethylsiloxane, with viscosity 4.6 and 485 cp) provided by
the Brookfield Engineering Laboratories. The viscosity standards are
Newtonian, and therefore, have the same viscosity regardless to the
spindle speed.
2.3 DENSITY MEASUREMENT
The density of each liquid and liquid mixture has been
measured using a dilatometer. The dilatometer consists of a long
tube graduated in 0.01 mL scale, fitted to a bulb of about 8 mL
30
capacity. To minimize the loss of liquid due to evaporation, Teflon
cap was used for closing the open end of the capillary stem, with a
small orifice to ensure that the pressure inside the capillary was
equal to the atmospheric pressure. A certain mass of solution was
allowed to expand at the desired temperature and reading was taken
when thermal equilibrium was maintained. The weight of empty,
well cleaned and dried dilatometer was taken accurately by
electronic balance OHAUS (AR 2140) (see section 2.6) and then the
liquid was introduced into the bulb of the dilatometer with the help
of hypodermic syringe having a needle long enough to reach the
bottom of the bulb so as to avoid the undesired sticking of the
solution to the inner wall of the dilatometer stem. Filled dilatometer
was again weighed accurately. For maintaining the temperature,
filled dilatometer was kept inside a double wall glass jacket having
provisions of water circulation. The temperature was controlled by
circulating water around the glass jacket using microprocessor based
digital controller bath having precessions of + 0.010C (Model TC-
502) (see section 2.5). Temperature of the dilatometer was
maintained for about half an hour to attain thermal equilibrium
between the contents of the dilatometer and the water circulating
around it. The density of the experimental liquid, at the given
temperature, is calculated using the values of its mass and volume.
2.4 REFRACTIVE INDEX MEASUREMENT
Refractive index of the liquid under investigation was
measured using an Abbe’s refractometer supplied by the Optics
Technologies, New Delhi, measuring refractive index in the range of
1.300 to 1.700 with uncertainty less than + 0.001 unit.
31
2.4.1 Principle of Abbe’s Refractometer
The working of the Abbe’s refractometer can be understood
with the help of Fig. 2.7. Abbe’s refractometer is based on accurate
measurement of critical angle. The critical angle for a boundary
separating two optical media is defined as the smallest angle of
incidence in the medium of greater refractive index, for which the
light is total internally reflected [7]. Fig. 2.8 shows the schematic
diagram of the Abbe’s refractometer. A light-beam from a
monochromatic source, a sodium lamp in the present work,
illuminates the face AB. P and Q are right-angled prisms each of
refractive index higher than that of the experimental liquid. A thin
layer of the experimental liquid is introduced between them using a
hypodermic glass syringe. The prism Q and mirror M simply
provide a convenient method of passing light from the liquid into
prism P. The light ray incident on face AB of the prism P at an angle
θi is refracted at an angle θr and strikes at the face AC at an angle ψi.
φi is the angle of emergence from the face AC. If θc is the critical
angle for the interface between the prism and liquid, then
plc nn θ sin = , (2.5)
where, ln = refractive index of the liquid, and
pn = refractive index of the prism-material.
For grazing incidence on the face AB (i.e. θi ≈ 90o), the light
will be refracted at an angle θi = θc (due to principle of reversibility)
[10] and thus emerges from the face AC at an angle φc (say). For any
other incidence, i.e. θi < 90o, the light will be refracted at an angle
less than θc and therefore will emerge from the face AC at an angle
Figure 2.7 Abbe’s Refractometer
Figure2.8 Working of Abbe’s Refractometer
32
greater than φc. Thus, no light ray will emerge at an angle of
emergence less than φc. Hence, along the line in the plane, across the
field of view of telescope T, the intensity will show a sudden rise at
the point corresponding to the angle of emergence φc; a line of
demarcation will appear, the right hand side of which will appear
brighter.
If α is the angle of the prism, then
cpl sinnn θ=
=
p
lc n
nsinθ
( )cp sinn ψα −= �from ∆AMN, 𝜃𝑐 = 𝛼 − cψ � (2.6)
cpcp sincosncossinn ψαψα −=
cc22
pl sincossinnsinn φαφα −−= (2.7)
=
pc
c
n1
sinsin
,laws'Snellfromφψ
Thus by knowing the value of φc, one can measure the value
of refractive index of the liquid with respect to air [8]. To measure
φc, telescope T is adjusted to bring the demarcation line on the cross-
wire. The telescope is then swung round using the Gauss eyepiece
until it is set with its axis perpendicular to face AC. The angle turned
through by the telescope T is obviously φc. Usually Telescope is
carried on an arm attached to a scale which is calibrated to read
directly the refractive index of the liquid.
33
2.4.2 Calibration and Mode of Operation
The prism chamber and the scale of the Abbe’s refractometer
are mounted on the same axis and rotate together when the milled
head is operated (Fig. 2.8). There is a provision for circulating water
from the water bath around the prism chamber in order to maintain
the desired temperature of the prism chamber and hence that of
experimental liquid.
A small quantity of the experimental liquid is introduced
between the two prisms. The reflector fitted on the base of the
instrument is adjusted in such a way that a beam of light passes
through the opening at the bottom of the lower prism. The eyepiece
of telescope is focused on the cross-wire in its focal plane. The
prism chamber is rotated by operating the milled head until the
cross-wire coincides with the line of demarcation between bright
and dark halves of the field of view. At this position, the reading on
the scale gives the direct value of refractive index of the liquid. The
calibration of the refractometer was verified by measuring the
refractive indices of standard liquids - benzene and carbon tetra
chloride. Refractive indices were found to be 1.501 and 1.461
respectively which are very close to the respective literature values
of 1.5011 and 1.4607 [9].
2.5 TEMPERATURE MAINTENANCE
The temperature was maintained using programmable
temperature controller (Model TC-502), supplied by Brookfield
Engineering Laboratories, Inc., USA (Fig. 2.9). It has a pump of
variable speeds for water circulation in water jackets of the
Figure2.9 Temperature Controller Model TC 502 Supplied by Brookfield Laboratories, USA
34
apparatus. The temperature controllers cover the temperature
measurement range of -20 to 200oC, with an accuracy of + 0.01oC.
2.6 PREPARATION OF MIXTURES
Binary liquid mixtures have been prepared in thoroughly
cleaned and dried narrow-mouthed tight stoppered glass bottles. The
two liquids mixed by mass weighted on an electronic balance
OHAUS AR-2104 (OHAUS Corp. Pine Brook, NJ, USA; Fig. 2.10)
with an accuracy of 1 x 10-4g. The possible error in the estimation of
mole fraction is less than + 0.0001.
The masses of the component liquids required for preparing
the mixture of a known composition were calculated and the liquids
weight and mix to prepare binary mixture. Extreme care was taken
to minimize the preferential evaporation during the process.
2.7 EVALUATION OF THERMO-ACOUSTIC AND EXCESS
PARAMETERS
2.7.1 Isentropic Compressibility (KS)
The study of sound propagation, both in the hydrodynamic
treatment and relaxation process yields that in the limit of low
frequencies; sound velocity u in a fluid medium is expressed as
s
2 Pu
∂∂
=ρ
, (2.8)
which gives rise to the well-known Laplace’s equation,
ρκ s
2 1u = (2.9)
Figure2.10 Electronic Weighing Balance (Model OHUAS AR2140)
35
⇒ ρ
κ 2s u1
= , (2.10)
where P, ρ and sκ are pressure, density and isentropic
compressibility of the medium respectively.
The importance of the isentropic compressibility in
determining the physicochemical behavior of liquid mixtures has
been reported by earlier workers [10-12].
2.7.2 Acoustic Impedance (Z)
The acoustic impedance represents a characteristic of the
medium that is closely akin to electrical impedance. It is determined
by all the elastic properties of the material and is defined as,
Z = ρ u (2.11)
Singh et al. [13] has used the deviation of acoustic impedance
from ideal behavior by mole fractional addition as a measure of
intermolecular interaction.
2.7.3 Intermolecular Free Length (Lf)
In the analysis of propagation of sound wave through a
loosely packed medium, a simple model that envisages the
molecules as rigid billiard-balls was developed by many workers
[14-17]. Let L be the average distance between the centers of the
molecules and the distance between the surfaces of two neighboring
molecules, be called as intermolecular free length, fL . The
mechanical momentum of a sound wave is transferred from one
molecule to the next with gas kinetic mechanism with velocity νm,
such that
36
ρ
ν om
P3= (2.12)
where, Po = pressure in the space unoccupied by matter, called
available or free volume.
Since the molecules are assumed to be rigid, they must travel
only the fraction Lf /L of any distance over which momentum is
transmitted. A part of the path of the sound wave is thus short-
circuited by the molecule i.e. in the time interval Δt between two
collisions the molecules have travelled a distance Lf = νmΔt, but the
momentum is transferred over a greater distance L = uΔt [18]. The
distance Lf is directly related to available volume per mole Va and is
given as
YV2L a
f = (2.13)
where, Va = VT – Vo ,
1/32 ) = οΑΝπ V (36 Y , (2.14)
3.0
cTo T
T1V V
−= , (2.15)
where Vo, VT, Tc, and NA are molar volume at absolute zero
temperature, molar volume at absolute temperature T, critical
temperature of the liquid and Avogadro’s number respectively.
Jacobson [19] has shown that if Tc for a liquid is not available,
then the intermolecular free length can be estimated from the
experimental density and ultrasonic velocity data using the relation
2/1f uKL
ρ= (2.16)
37
or sf K L κ= (2.17)
where, K is temperature dependent empirical constant, proposed by
Jacobson, having values 618, 631 and 642 at 293.15K, 303.15K and
313.15K, respectively.
A number of workers [20-23] have reported the importance of
intermolecular free length in the study of molecular interactions.
2.7.4 Gibb’s Free Energy of Activation of Viscous Flow (∆G*)
The absolute rate theory [24] based Eyring’s kinematic
viscosity model gives the relation
∆
=RT
*G exp N A hVη (2.18)
where η, V, NA, h, R, T and ΔG* are kinematic viscosity, molar
volume, Avagadro’s constant, Plank’s constant, universal gas
constant, absolute temperature and Gibb’s activation energy of flow
respectively.
Many workers [25-27] have discussed the importance of
excess value of ∆G* in the study of molecular interactions.
2.7.5 Free Volume (Vf) and Internal Pressure (πi)
Internal pressure is a fundamental liquid property, which is a
resultant of the attractive and repulsive forces among the constituent
molecules of a liquid. The relationship among applied pressure (P),
molar volume (V), temperature (T), and molar internal energy (U) is
given by the thermodynamic relation
PTP T
VU
VT−
∂∂
=
∂∂
(2.19)
38
The isothermal internal energy volume coefficient (∂U/∂V)T is
often called internal pressure πi. So, the above equation can be
written as
PTP T
Ti −
∂∂
=π (2.20)
Since externally applied pressure is negligible as compared to
the internal pressure πi, it can be written as
V
i TP T
∂∂
=π (2.21)
or T
iT
βαπ = (2.22)
where PT
V V1
∂∂
=α and T
T PV
V1
∂∂
−=β
From the work of Eyring, Hirschfelder and Kincaid [16, 28],
the free volume in liquids is given as
2
3
Tf V
1VU PbRT V
∂∂
+= (2.23)
where, b is packing factor in liquid and is equal to 1.78 for closely
packed hexagonal structure. For, negligible values of P
2
3
f V1
TVUbRT V
∂∂
≅ (2.24)
or [ ] 23
i f V1bRT V π= (2.25)
Suryanarayan and Kuppusami [29, 30] proposed the following
relation for free volume in liquids,
39
2/3
f kMuV
=
η (2.26)
solving these equations, one gets
6/7
3/22/1
i M
Uk bRT ρηπ
= . (2.27)
Here, M is the effective molecular mass; k is a dimensionless
temperature-independent constant having a value of 4.28 Χ 109, η is
the viscosity in poise, ρ is the density in g cm-3, u is the sound
velocity in cm.s-1, T is the absolute temperature.
With the help of internal pressure, excess molar enthalpy of
the binary mixture was calculated using the following relation,
discussed by Rajendran [31].
mim22i211iiE
m VVxVxH πππ −+= (2.28)
Here πi1, πi2, and V1, V2 represent internal pressure and volume of
pure liquids. πim and Vm are internal pressure and molar volume of
mixtures.
2.7.6 Effective Debye Temperature and Pseduo-Grünrisen Parameter
The effective Debye temperature θD can be evaluated by using
the following expression [32]
3/1
3l
3l
m
D
u2
u1V4
N9kh
+
=
π
θ (2.29)
where lu and ut are the propagation velocities for longitudinal and
transverse modes respectively. Vm, the molar volume and h, k and N
40
are Planck’s constant, Boltzmann’s constant and Avogadro’s
number respectively.
The two wave velocities may be expressed in terms of density
( mρ ), the instantaneous adiabatic compressibility ( sk ) and
Poisson’s ratio (σ) for liquids exhibiting the quasi-crystalline
properties, as follows:
( ) ( )( )
( )
−+
+
−+
=+2/32/3
2/3ms3
t3l 213
12213
1ku2
u1
σσ
σσρ (2.30)
where,
−=
p
m2
Ts CVT
kα
β
where α , βT and PC represents the coefficient of linear expression,
the isothermal compressibility and the specific heat at constant
pressure respectively.
Poisson’s ratio can be obtained from the knowledge of the
bulk modulus KT, and the modulus of rigidity GT, which arise from
the change in lattice spacing corresponding to the solid – like
character of the liquid. The Poisson’s ratio is given by
2A62A3
+−
=σ (2.31)
and γ34
GKA
T
T == (2.32)
where γ is specific heat ratio.
The pseudo-Grüneisen parameter and non-linearity parameter
( AB ) have been defined in terms of specific heat ratio as:
T
1α
γΓ −= (2.33)
41
2.7.7 Excess / Deviation Parameters
Excess parameters, associated with a liquid mixture, are a
quantitative measure of deviation in the behaviour of the liquid
mixtures from ideality. The excess / deviations parameters of molar
volume EmV , ultrasonic velocity Δu, viscosity Δη, molar refraction
ΔRm, isentropic compressibility ΔKs, acoustic impedance ZE,
intermolecular free length LfE, internal pressure E
iπ , free energy of
activation for viscous flow E*G∆ , free volume EfV and molar
enthalpy EmH have been calculated from following relations:
+−
+=
2
22
1
11
m
2211Em
MxMxMxMxVρρρ
(2.34)
)uxux(uu 2211m +−=∆ (2.35)
)( 2211 ηηηη xxm +−=∆ (2.36)
idm
texpmm RRR −=∆ (2.37)
where
+
+−
=m
22112m
2mtexp
mMxMx
2n1nR
ρ
and
+−
+
+−
= 22
222
22
11
121
21id
mM
2n1nM
2n1nR φ
ρφ
ρ
+−=∆
222
2
121
1
m2
ms u
xu
xu
1kρρρ
(2.38)
)uxux()u(Z 222111mmE ρρρ +−= (2.39)
42
+−=21
222
2
21
121
1
21
m2
m
Ef
)u(
Kx
)u(
Kx
)u(
KL
ρρρ
(2.40)
+−=67
21
2
32
221
221
2
67
21
1
32
121
121
1
67
21
m
32
m21
m21
Eim
Mu
bRTkx
Mu
bRTkx
Mu
bRTk ρηρηρηπ (2.41)
−
=∆
2m2
1m11
2m2
mmE*
VVlnx
VVlnRTG
ηη
ηη (2.42)
2/3
2
222
1
11123
+−
=
kuMx
kuMx
kuM
Vm
meffEf ηηη
(2.43)
mim22i211i1Em VVxVxH πππ −+= (2.44)
where M1, M2; 1ρ , 2ρ 1u , 2u ; 1η , 2η ; 1φ , 2φ ; 1iπ , 2iπ and V1, V2
denote molecular weight, density, ultrasonic velocity, viscosity,
volume fraction, internal pressure and molar volume respectively of
the pure components. mρ , mu , mη , imπ and Vm represent density,
ultrasonic velocity, viscosity, internal pressure and molar volume of
the mixtures respectively. K, R, T and k denote Jacobson constant,
gas constant, absolute temperature and dimensionless temperature
independent constant having a value of 4.28×109.
2.8 CURVE EXPERT 1.3 LINEAR REGRESSION
POLYNOMIAL EQUATION
The values of EmV , u∆ , η∆ , mR∆ , sk∆ , EZ , E
fL , Eiπ ,
E*G∆ , EfV and E
mH for each mixture were fitted to the Curve
Expert 1.3 software for calculating polynomial coefficient ai and
standard deviation.
43
Curve Expert 1.3 linear regression equation consists of a
linear combination of a particular set of functions XA are called
linear models, and linear regression can be used to minimize the
difference between the model and data. The general form of this
kind of model is
𝑦(𝑘) = ∑𝑎𝑘𝑋𝑘(𝑥) (2.45)
where Xk(x) are fixed function of x that are called the basis
functions, and ak one the free parameters. “Linear” refers only to
dependence of the model on parameters ak; the functions Xk(x) may
be nonlinear. Minimization of the above linear model is performed
with respect to the merit function,
𝑆(𝑎) = ∑ �𝑦𝑖 ∑ 𝑎𝑘𝑋𝑘(𝑥𝑖)𝑛𝑝𝑘=1 �
2𝑛𝑖=1 (2.46)
The minimum of the above occurs where the derivative of S
with respect to the parameters disappears. Substituting the linear
model into this function, taking the first derivative, and setting this
equal to zero gives the normal equations that can be solved directly
for the parameters ak.
In Curve Expert, the linear regression polynomial equation is,
𝑦 = 𝑎 + 𝑏𝑥 + 𝑐𝑥2 + 𝑑𝑥3 + ⋯⋯⋯ (2.47)
The standard deviation ( )EYσ with no. of co-efficients (p) is
given by,
( ) ( ) 2/12caltexpE
pnYY
Y
−
−Σ=σ (2.48)
where n is the number of measurements.
44
2.9 ESTIMATION OF ULTRASONIC VELOCITY
The theoretical evaluation of sound velocity in liquid mixtures
is of considerable interest. The theoretical evaluation of sound
velocity based on molecular models in liquid mixtures has been used
to correlate with the experimental findings and to know the
thermodynamics of the mixtures. The comparison of theoretical and
experimental results also provides better understanding about the
validity of the various thermodynamic, empirical, semi empirical
and statistical theories.
2.9.1 Mixing Rules for Ultrasonic Velocity
Nomoto [33], assuming the linearity of the molar sound
velocity and the additivity of the molar volumes in liquid solutions,
gave the following relation
3
2211
22113
m
mm VxVx
RxRxVR
u
++
=
= (2.49)
Van Dael and Vangeel [34] proposed the following ideal
mixing relation for predicting speed of sound of a binary liquid
mixture
+=
+ 2
22
2211
12m2211 uM
xuM
xu1
MxMx1
(2.50)
Zhang Junjie [35] gave following relation for the ultrasonic
velocity in a binary mixture
( )
++
+=
222
22211
112211
2211m
uρVx
uρVx
MxMx
VxVxu (2.51)
45
2.9.2 Collision Factor Theory (CFT)
Schaaffs’ relation [36], which is based on the Collision Factor
Theory (CFT), for predicting ultrasonic velocity in pure liquids, has
been extended to the binary liquid mixtures by Nutsch-Kuhnkies
[37] and is given as
( ) ( )m
22112211m V
BxBxSxSxuu
++= ∞ (2.52)
where M, ρ, n, φ , w, u, R and x represent molecular weight, density,
refractive index, volume fraction, weight fraction, ultrasonic
velocity, molar sound velocity and mole fraction of mixtures
respectively. Symbols 1, 2 and m, in suffix represent pure
components and mixtures respectively.
In the eqn. 2.52, S and B respectively are ‘collision factor’ and
‘actual volume’ of the molecules per mole and are given as
Bu
uVS∞
= and A3 Nπr
34B
=
where, ∞u = 1600 m/s, is an empirical constant,
NA = Avogadro number
32
21
RTMu1
MuRT1V
N163r
−
+−=
π, is the
molecular radius of the given component.
2.9.3 Flory Statistical Theory
Flory Statistical Theory [38] is an important method for
theoretical evaluation of surface tension of mixture. Patterson and
Rastogi [39] studied this theory for the evaluation of surface tension
using reduced parameters. The values of surface tension thus
46
obtained, have been utilized to calculate ultrasonic velocity using
critical data of temperature, pressure, volume and reduced
parameters, employing the Auerbach relation (eq. 2.53).
The following relation to calculate characteristic surface
tension was used,
3/1*3/2*3/1* TPk=σ (2.53)
where k , *P and *T are the Boltzmann constant, characteristic
pressure and temperature respectively. Here,
T
2* V~ T P
βα
= (2.54)
where α is the thermal expansion coefficient and Tβ is the
isothermal compressibility, given by the following equation,
3/12/19/1
3
uT10X6.75
ρα
−= (2.55)
23/49/4
3
uT10X71.1
ρβ
−= (2.56)
The reduced volume V~ for a pure substance in terms of
thermal expansion coefficient is given as,
( )
3
T13T1V~
+
+=α
α (2.57)
The characteristic temperature *T is given as
−=
1V~V~T*T
3/1
3/4 (2.58)
47
The characteristic and reduced parameters have been used to
evaluate the surface tension of binary liquid mixtures, and are given
by the following relations,
*22
*11
* VxVxVm += (2.59)
}VxVx{
VV~ *
22*11
mm
+= (2.60)
1221*22
*11 XPP*P θψψψ −+= (2.61)
+
=
*2
*22
*1
*11
*
TP
TP
P*Tψψ
(2.62)
where ψ , 2θ and 12X are the segment fraction, the site fraction and
the interaction parameter respectively and these are expressed as,
*22
*11
*11
1VxVx
Vx+
=ψ (2.63)
12 1 ψψ −=
+
=3/1
*1
*2
12
22
VV
ψψ
ψθ (2.64)
and
22/1
*1
*2
6/1
*1
*2*
112 PP
VV1PX
−= (2.65)
Priogogine and Saraga [40] gave the equation for reduced
surface tension viz;
48
( )
−
−−−= −
1V~5.0V~n
V~1V~V~MV~~
3/1
3/1
2
3/13/5 σ (2.66)
where M is the fraction of nearest neighbors that a molecule loses on
moving from the bulk of the liquid to the surface.
Thus the surface tension of a liquid mixture is given by the
relation,
( )V~~*m σσσ = (2.67)
The values of surface tension obtained by Flory theory have
been used to evaluate ultrasonic velocity, from well-known
Auerbach relation [41],
3/2
m4
mm 103.6
u
Χ=
− ρσ (2.68)
2.10 ESTIMATION OF VISCOSITY
Bingham [42] proposed the following relation for ideal
viscosity of a binary mixture
2211m xx ηηη += (2.69)
This relation assumes that no changes in the volume of the
mixture on mixing the components have taken place.
The Additive relation, based on Arrhenius model and
Eyring’s model [43] for the viscosity of pure liquids can be
modified for binary mixtures as,
222111mm V ln xV ln xV ln ηηη += (2.70)
According to Kendall-Munroe [44], the viscosity of a binary
mixture is given by,
ln x ln x ln 2211m ηηη += (2.71)
49
and it assumes logarithmic additivity of viscosity.
Hind and Ubbelohde [45] gave the following relation for
predicting viscosity of a binary mixture, taking into consideration
the molecular interactions
12212221
21m xx2xx ηηηη ++= (2.72)
Frenkel [46], using the Eyring’s model, developed the
following logarithmic relation for non-ideal binary liquid mixtures
12212221
21m lnxx2 lnx lnx ln ηηηη ++= (2.73)
which takes into account the molecular interaction.
The Sutherland-Wassiljewa [47] equation for viscosity of
liquid mixtures is
∑∑
=i
jjij
iim xA
x ηη (2.74)
where Aij is the Wassiljewa coefficient which is independent of
composition. Thus, viscosity of multicomponent mixtures can be
predicted from values of Aij deduced from the measurement of
binary mixtures and is given as,
28/3
jMiM
2/1
j
i141
ijA
+=
η
η
Grunberg and Nissan Model [48] proposed their parabolic
type equation for correlating the viscosity of mixtures with only one
adjustable parameter,
lnη = x1 lnη1 + x2 lnη2 + x1 x2 G12
where G12 is the only interaction parameter in the equation.
50
2.11 DENSITY MODELS
2.11.1 Modified Rackett Model and Hankinson- Brobst- Thomson
(HBT) Model for Density
Due to strong dependence of design and optimization of
chemical processes on computer calculations, the availability of
accurate, simple and tested method, as well as related parameters is
of increasing relevance. In this case, consideration was given to the
Rackett equation of state and HBT model in order to analyze how
accurate densities are predicted. According to Rackett model [49]
the density could be described as,
( )[ ]7/2rT11
RAc
c ZRTMP −+−
=ρ (2.75)
The Hankinson equation of state [50] for density could be
described as,
]V1[VV
M)(
RSRK)o(
R* δω
ρ−
= (2.76)
where
3/4rr
3/2r
3/1r
)o(R )T1(d)T1(c)T1(b)T1(a1V −+−+−+−+=
0.25< rT <0.95
and
00001.1T
)hTgTfTe(V
r
3r
2rr)(
R −+++
=δ
0.25< rT < 1.0
where values of the constants are
a = -1.52816 e = -0.296123,
b = 1.43907 f = 0.386914
51
c = -0.81446 g = -0.0427258,
d = 0.190454, h = -0.0480645
where ZRA is a unique constant for each compound, Tr is the reduced
temperature, Tc and Pc are the pseudo critical properties of mixture,
M is the average weight in mixture, *V is the characteristic volume,
SRKω is the acentric factor respectively.
2.11.2 Mixing Rules for Both the Modified Rackett and
Hankinson equations
The modified Rackett equation for mixtures [51]
7/2)rT1(1(
RAmi ci
ciim Z
PTx
RV −+
∑= (2.77)
where R represents gas constant.
∑=i
RAiiRAm ZxZ
where cm
r TTT = and the Chueh-Prausnitz rules [52] are
recommended for
cijji j
icm TT φφ∑ ∑= (2.78)
∑
=
icii
ciii Vx
Vxφ (2.79)
2/1cjciijcij )TT)(k1(T −= (2.80)
( )
( )33/1cj
3/1ci
2/1cjci
ijVV
VV8k1
+=− (2.81)
Mixing rules recommended [53] for the Hankinson-Brobst-
Thomson equations are,
52
*m
i jcij
*ijji
cmV
TVxxT
∑ ∑= (2.82)
∑
∑
∑+=
i
3/1*ii
i i
3/2*ii
*ii
*m Vx Vx3Vx
41V (2.83)
( ) 2/1cj
*jci
*icij
*ij TVTVTV = (2.84)
∑=i
SRKiiSRKm x ωω (2.85)
2.12 SEMI EMPIRICAL RELATIONS FOR PREDICTION
OF REFRACTIVE INDEX
The Lorentz-Lorenz (L-L) relation [54] given below for
refractive index is based on the change in the molecular
polarizability with volume fraction
2
222
22
1
121
21
m2m
2m w
2n1nw
2n1n1
2n1n
ρρρ
+
−+
+
−=
+
− (2.86)
Gladstone-Dale (G-D) equation [55] for predicting the
refractive index of a binary mixture is as follows,
( ) ( ) ( )1n1n1n 2211m −+−=− φφ (2.87)
Wiener (W) relation [56] may be represented as,
221
22
21
22
21
21
2
22φ
+−
=
+−
nnnn
nnnn
m
m (2.88)
Heller’s (H) relation [57] is given by,
22
2
1
1m
2m1m
23
nnn
φ
+
−=
− (2.89)
where 1
2
nn
m =
53
Arago-Biot (A-B) [58], assuming volume additively,
proposed the following relation for refractive index of binary
mixtures,
2211 nnnm φφ += (2.90)
Newton (N) [59] gave the following equation,
( ) ( ) ( )111 222
211
2 −+−=− nnnm φφ (2.91)
Eykman’s (Eyk) relation [60] may be represented as,
222
22
111
21
mm
2m xV
4.0n1nxV
4.0n1nV
4.0n1n
+−
+
+−
=
+−
(2.92)
Oster’s relation (OS) [61] for binary mixtures can be given
as,
( )( )=
+−m2
m
2m
2m V
n12n 1n ( )( ) ( )( )
2222
22
22
1121
21
21 xV
n12n 1nxV
n12n 1n
+−+
+− (2.93)
where symbols have their usual meaning.
54
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CHAPTER 3 Studies on Molecular Interaction Between N,N-dimethylacetamide (DMA) with 1-
Propanol, Methanol and Water from Density, Viscosity and Refractive Index Measurements
at 293.15, 303.15 and 313.15 K
3.1 Introduction 3.2 Chemicals 3.3 Results 3.4 Discussion 3.5 Conclusion
References
58
3.1 INTRODUCTION
In recent years [1-6], researchers are taking considerable
interest in theoretical and experimental investigations of excess
thermodynamic properties of binary mixtures. The interaction
between molecules can be established from the study of
characteristic departure from ideal behavior of physical properties
viz; density, viscosity, refractive index, excess Gibb’s free energy of
activation etc. [7,8].
N,N-dimethylacetamide (DMA), a clear liquid, miscible in all
proportions with water as well as most of the organic solvents
including alcohols, ethers, ketones etc. DMA is a dipolar aprotic
solvent with boiling point (438.2 K), significant dipole moment
(3.72D) greater than water and medium dielectric constant (37.78) at
298.15 K [9]. The good water solubility and excellent solvent power
particularly for high molecular weight polymers and resins make
DMA as a common solvent in man- made fiber and polyurethane
production. DMA is also used as a solvent for production of X-ray
and photo-resistant stripping compounds. It acts as a good reaction
medium as well as a catalyst for many reactions. It is also used as a
plasticizer for cosmetic and pharmaceutical intermediates and a
good extraction agent for gases and oils.
Alcohol molecules are highly associated through H-bonding,
though they have low values of dipole moment and dielectric
constant. The solution properties of binary mixtures of DMA with
alkanols have been the subject of intensive research [10-13], owing
59
to their importance as super solvent for chemical reactions and many
industrial processes.
A rigorous literature survey on molecular interaction studies
on binary liquid mixtures in DMA [9, 14-21] reveals that no
systematic detailed study has been made on density, viscosity and
refractive index with excess properties for binary mixtures namely
DMA + 1-propanol, DMA + methanol and DMA + water. In the
present study, molecular association in the binary mixtures of DMA
with 1-propanol, methanol and water at three temperatures 293.15,
303.15 and 313.15 K over the entire range of composition has been
reported. Values of excess molar volume (VmE), deviation in
viscosity (∆η), deviation in molar refraction (ΔRm) and excess
Gibbs’s free energy of activation for viscous flow (ΔG*E) have been
evaluated and fitted to Curve Expert 1.3 linear regression
polynomial equation. The results have been discussed in terms of
molecular association occurring between the constituent molecules
of the mixture.
3.2 CHEMICALS
N, N-dimethylacetamide (grade analytical standard, mass
fraction ≥ 0.999), anhydrous 1-propanol (mass fraction ≥ 0.997) and
methanol (mass fraction ≥ 0.998) were supplied by Sigma-Aldrich
Pvt. Ltd. All these solvents were stored under moisture free
conditions to avoid the alterations of their specifications. Deionized
water (conductivity < 10-6 mho) was used. The measured density,
viscosity and refractive index of pure liquids along with their
literature values are given in Table 3.1 and are in good agreement.
60
3.3 RESULTS
The values of density, viscosity and refractive index for the
mixtures DMA + 1-propanol, DMA + methanol and DMA + water
over the entire range of composition at three temperatures, 293.15,
303.15 and 313.15 K were determined experimentally. These values
are reported in Tables 3.2 to 3.4 along with the calculated values of
excess molar volume (VmE), deviation in viscosity (∆η), deviation in
molar refraction (ΔRm) and excess Gibbs’s free energy of activation
for viscous flow (ΔG*E). Table 3.5 displays the values of the
polynomial coefficient ia and standard deviations evaluated by Curve
Expert 1.3 software.
3.4 DISCUSSION
The values of excess parameters for binary mixtures can be
explained by different types of intermolecular interactions between
the component molecules on the basis of non-specific van der
Waal’s forces, hydrogen bonding, dipole-dipole interactions, donor-
acceptor interaction between unlike molecules and fitting of smaller
molecules into the voids created by bigger molecules.
In Fig. 3.1, variation of excess molar volume (VmE) for all the
three systems as a function of mole fraction of DMA at 293.15,
303.15 and 313.15 K is shown. Examination of curves reveals that
the values of VmE are negative for all the three systems and varies in
a manner; 1-propanol < methanol < water. Negative values of VmE
are an indication of presence of strong intermolecular interaction in
these systems due to the formation of hydrogen bonds between
oxygen atom of >C=O group of DMA and hydrogen atom of –OH
61
of alcohols and water molecules. This contribution is found to be
most significant for DMA + water system and is least for DMA + 1-
propanol. The higher negative values of VmE amongst all three
systems show that DMA is more interactive with water molecules
than methanol or 1-propanol molecules.
In Fig. 3.2(a), for DMA + 1-propanol mixture, deviation in
viscosity (∆η) is found to be negative over entire composition range
at all three temperatures. At a particular mole fraction the absolute
values of ∆η decreases as temperature is raised. An increase in
temperature decreases the self-association of molecules of pure
component and increases hetero association between unlike
molecules results in less negative values of ∆η. Similar temperature
dependence has been reported by Marigliano et al. [22] for
formamide + alcohol mixture. Many workers [9, 23-27] have
reported similar behavior where negative values of ∆η indicate
dispersive forces and some workers [28, 29] have suggested that
negative ∆η values may also be due to difference in size of
component molecules. For DMA + methanol system (Fig. 3.2b),
both positive and negative values of ∆η were obtained, the increase
in positive value of ∆η up to a mole fraction of 0.5 clearly indicates
very strong interaction through intermolecular hydrogen bonding
between DMA and methanol molecules. The fall in positive value of
∆η from a mole fraction of 0.5 to around 0.7 indicates lesser
interaction between DMA and methanol through intermolecular
hydrogen bonding. Hydrogen bonding interaction becomes almost
negligible after the inflection point at around 0.7 mole fraction and
thereafter negative ∆η values are observed indicating intermolecular
interaction through weak dispersive forces. The positive values of
62
∆η for DMA + water system (Fig. 3.2c) at all the concentrations of
the mixture indicates the formation of strong hydrogen bonding
between DMA and water molecules perhaps due to the smaller size
of water. Collective comparison of Fig. 3.2 (a), (b) and (c) supports
the size dependent hydrogen bond interaction, since water is the
smallest molecule and 1-propanol is the largest molecule clearly
indicating the size dependent interaction between DMA +
water/alcohol molecules. It seems that as the size from water
molecule to the 1-propanol increases the percent of hetero-molecular
hydrogen bond interaction decreases.
Fig. 3.3 (a), (b) and (c) represents the variation ΔRm versus
mole fraction for DMA + 1-propanol, + methanol, + water
respectively. The highest negative values of ΔRm for DMA + water
system suggest the strongest hetero-intermolecular interaction in the
system and the order of interaction is
DMA + water > DMA + methanol > DMA + 1-propanol
These results of ΔRm support our findings based on VmE and Δη.
Like deviation in viscosity, excess Gibb’s free energy of
activation (∆G*E) is negative for DMA + 1-propanol mixture (Fig.
3.4a) and positive for DMA + water mixture (Fig. 3.4c) over entire
range of composition at all the three temperatures. In DMA +
methanol mixture (Fig. 3.4b) ∆G*E values are positive in methanol
rich region but slightly negative in amide rich region. These positive
values of ∆G*E indicates strong interaction in DMA + water and
DMA + methanol mixtures, whereas negative ∆G*E values for DMA
+ 1-propanol mixture is due to the predominance of dispersive
forces.
63
3.5 CONCLUSION
Excess molar volume (VmE), deviation in viscosity (∆η), molar
refraction deviation (ΔRm) and excess Gibbs’s free energy of
activation for viscous flow (ΔG*E) were calculated from
experimentally measured density, viscosity and refractive index data
at three temperatures and atmospheric pressure and correlated with
Curve Expert 1.3 linear regression polynomial equation. The
observed negative values of VmE, ΔRm and positive values of ∆η and
ΔG*E indicate the presence of strong interaction in DMA + water and
DMA + methanol systems. The order of interaction was found to be
DMA + water > DMA + methanol > DMA + 1-propanol. This order
clearly indicates the size dependent hetero-inter molecular hydrogen
bonding interactions.
64
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure3.1 Excess molar volume (Vm
E) against mole fraction of DMA (x1): ■, 293 K; ▲, 303 K; ◆, 313 K. (a) DMA + 1-Propanol, (b) DMA + Methanol and (c) DMA + Water
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.000 0.2 0.4 0.6 0.8 1
x1
293K303K313K
V mE (c
m3 .m
ol-1
)
-0.80
-0.60
-0.40
-0.20
0.000 0.2 0.4 0.6 0.8 1
x1
293K303K313K
V mE(c
m3 .m
ol-1
)
-2.00
-1.50
-1.00
-0.50
0.000 0.2 0.4 0.6 0.8 1
x1
293K303K313K
V mE(c
m3 .m
ol-1
)
65
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure3.2 Deviation in viscosity (Δη) against mole fraction of DMA (x1): ■, 293 K; ▲, 303 K; ◆, 313 K. (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water
-0.50
-0.40
-0.30
-0.20
-0.10
0.000 0.2 0.4 0.6 0.8 1
x1
293K303K313K∆η
(cp)
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0 0.2 0.4 0.6 0.8 1
x1
293K303K313K∆η
(cp)
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
293K303K313K
∆η(c
p)
x1
66
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure3.3 Molar refraction deviation (∆Rm) against mole fraction of DMA (x1): ■, 293 K; ▲, 303 K; ◆, 313 K. (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water
-0.50
-0.40
-0.30
-0.20
-0.10
0.000 0.2 0.4 0.6 0.8 1
x1
293K303K313K
ΔRm
-3.50
-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.000 0.2 0.4 0.6 0.8 1
293K303K313K
x1
ΔRm
-10.00
-8.00
-6.00
-4.00
-2.00
0.000 0.2 0.4 0.6 0.8 1
x1
293K303K313K
ΔRm
67
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure3.4 Excess Gibbs’s free energy of activation for viscous flow (∆G*E) against mole fraction of DMA (x1): ■, 293 K; ▲, 303 K; 313K. (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water.
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0 0.2 0.4 0.6 0.8 1
293K303K313K
x1
ΔG*E
(KJ.
mol
-1)
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 0.2 0.4 0.6 0.8 1
293K303K313K
x1
ΔG*E
(KJ.
mol
-1)
0.00
1.00
2.00
3.00
4.00
5.00
0 0.2 0.4 0.6 0.8 1
x1
293K303K313K
ΔG*E
(KJ.
mol
-1)
68
Table 3.1 Density (ρ), Viscosity (η) and Refractive index (n) of Pure Liquids at Temperatures, (293.15, 303.15, 313.15) K and Comparison with their Literature Data Density ρ
(gm.cm-3) Viscosity η
(cp) Refractive index n
Component Temp.(K) Expt. Lit. Expt. Lit. Expt. Lit.
DMA 293.15 0.9398 0.939824[15] 1.0119 1.437 1.438[31]
0.9410[15]
0.9422[30]
303.15 0.9315 0.930769[15] 0.8710 0.8784[9] 1.432
0.9320[15] 0.871[16]
0.93169[16]
313.15 0.9234 0.921912[15] 0.7685 0.7685[9] 1.427
0.9229[15]
1-Propanol 293.15 0.8038 0.8032[32] 2.2030 2.203[32] 1.386 1.385[34]
303.15 0.7957 0.7956[32] 1.7190 1.719[32] 1.381 1.381[35]
313.15 0.7874 0.7975[33] 1.3630 1.363[32] 1.378 1.378[35]
Methanol 293.15 0.7915 0.79151[36] 0.5820 0.587[36] 1.328
0.79154[37] 0.582[37]
303.15 0.7820 0.78206[36] 0.5100 0.510[36] 1.323 1.324[35]
0.78191[38] 0.512[39]
0.7819[22] 0.504[22]
313.15 0.7727 0.77272[36] 0.4480 0.447[36] 1.319 1.320[35]
0.7725[22] 0.448[37]
0.77260[37] 0.447[39]
Water 293.15 0.9982 0.99820[40] 1.002 1.0050[41] 1.333 1.3330[40]
303.15 0.9956 0.99565[40] 0.797 0.8007[41] 1.332 1.3319[40]
313.15 0.9922 0.99222[40] 0.653 0.6560[41] 1.331 1.3306[40]
69
Table 3.2 Experimental Values of Density (ρm), Viscosity (ηm), Refractive Index (nm), Excess Molar Volume (Vm
E), Viscosity Deviation (∆η), Molar Refraction Deviation (∆Rm) and Excess Gibbs’s Free Energy of Activation for Viscous Flow ( ΔG*E) along with Mole Fraction for Binary Mixture (DMA + 1-Propanol) at 293.15, 303.15 and 313.15 K.
X1 ρm
(g.cm-3)
ηm (cp)
nm VmE
(cm3.mol-1) ∆η
(cp) ∆Rm ∆G*E
(KJ.mol-1)
293.15 K 0.0000 0.0999 0.1998 0.2998 0.3998 0.4999 0.5998 0.7998 0.8997 1.0000
0.8038 0.8224 0.8385 0.8535 0.8675 0.8807 0.8937 0.9184 0.9297 0.9398
2.2030 1.7846 1.5922 1.4629 1.3421 1.2366 1.1777 1.0891 1.0520 1.0119
1.386 1.390 1.397 1.403 1.409 1.414 1.419 1.428 1.432 1.437
0 -0.2001 -0.2384 -0.2385 -0.2065 -0.1552 -0.1419 -0.1403 -0.1095 0
0 -0.2994 -0.3728 -0.3830 -0.3847 -0.3710 -0.3109 -0.1613 -0.0794 0
0 -0.2746 -0.3409 -0.3945 -0.3972 -0.3987 -0.3718 -0.2669 -0.1825 0
0 -0.3246 -0.4102 -0.4240 -0.4418 -0.4495 -0.3794 -0.1954 -0.0935 0
303.15 K 0.0000 0.0999 0.1998 0.2998 0.3998 0.4999 0.5998 0.7998 0.8997 1.0000
0.7957 0.8143 0.8303 0.8451 0.8590 0.8722 0.8853 0.9100 0.9212 0.9315
1.7190 1.4311 1.2881 1.2118 1.1024 1.0380 0.9960 0.9279 0.9006 0.8710
1.381 1.385 1.392 1.398 1.404 1.409 1.414 1.423 1.428 1.432
0 -0.2082 -0.2410 -0.2248 -0.1848 -0.1343 -0.1318 -0.1320 -0.0913 0
0 -0.2032 -0.2615 -0.2530 -0.2776 -0.2571 -0.2144 -0.1129 -0.0555 0
0 -0.2323 -0.2356 -0.2513 -0.2333 -0.2366 -0.2246 -0.1767 -0.0815 0
0 -0.2918 -0.3827 -0.3618 -0.4259 -0.4041 -0.3377 -0.1783 -0.0852 0
313.15 K 0.0000 0.0999 0.1998 0.2998 0.3998 0.4999 0.5998 0.7998 0.8997 1.0000
0.7874 0.8063 0.8223 0.8369 0.8507 0.8637 0.8766 0.9011 0.9126 0.9234
1.3630 1.2097 1.1169 1.0696 0.9724 0.9192 0.8984 0.8418 0.8175 0.7685
1.378 1.381 1.388 1.394 1.399 1.405 1.410 1.419 1.423 1.427
0 -0.2416 -0.2746 -0.2376 -0.1853 -0.1120 -0.0871 -0.0607 -0.0457 0
0 -0.0939 -0.1273 -0.1152 -0.1529 -0.1466 -0.1080 -0.0457 -0.0106 0
0 -0.3131 -0.3643 -0.3973 -0.4290 -0.3715 -0.3334 -0.2083 -0.1223 0
0 -0.1640 -0.2194 -0.1787 -0.2740 -0.2684 -0.1790 -0.0542 0.0150 0
70
Table 3.3 Experimental Values of Density (ρm), Viscosity (ηm), Refractive Index (nm), Excess Molar Volume (Vm
E), Viscosity Deviation (∆η), Molar Refraction Deviation (∆Rm) and Excess Gibbs’s Free Energy of Activation for Viscous Flow ( ΔG*E) along with Mole Fraction for Binary Mixture (DMA + Methanol) at 293.15, 303.15 and 313.15 K.
X1 ρm
(g.cm-3)
ηm (cp)
nm VmE
(cm3.mol-1) ∆η
(cp) ∆Rm ∆G*E
(KJ.mol-1)
293.15 K 0.0000 0.0999 0.2000 0.3999 0.4984 0.5998 0.6993 0.8026 0.8982 1.0000
0.7915 0.8277 0.8552 0.8916 0.9041 0.9147 0.9234 0.9307 0.9364 0.9398
0.5820 0.6320 0.6827 0.7790 0.8235 0.8600 0.8930 0.9240 0.9513 1.0119
1.328 1.353 1.371 1.398 1.408 1.416 1.422 1.427 1.432 1.437
0 -0.3393 -0.5781 -0.7232 -0.7045 -0.6562 -0.5874 -0.4677 -0.3354 0
0 0.0071 0.0147 0.0251 0.0272 0.0202 0.0104 -0.0030 -0.0168 0
0 -1.6352 -2.6497 -3.2877 -3.1458 -2.8060 -2.3281 -1.6933 -0.9501 0
0 0.1416 0.2468 0.3485 0.3514 0.3059 0.2367 0.1419 0.0390 0
303.15 K 0.0000 0.0999 0.2000 0.3999 0.4984 0.5998 0.6993 0.8026 0.8982 1.0000
0.7820 0.8181 0.8451 0.8819 0.8947 0.9054 0.9144 0.9219 0.9277 0.9315
0.5100 0.5520 0.5940 0.6730 0.7110 0.7420 0.7670 0.7900 0.8055 0.8710
1.323 1.348 1.366 1.394 1.403 1.411 1.418 1.423 1.427 1.432
0 -0.3322 -0.5350 -0.6817 -0.6715 -0.6177 -0.5608 -0.4457 -0.3110 0
0 0.0059 0.0118 0.0186 0.0211 0.0155 0.0046 -0.0097 -0.0288 0
0 -1.5061 -2.4646 -3.0640 -2.9796 -2.6673 -2.1827 -1.5809 -0.9116 0
0 0.1425 0.2474 0.3430 0.3484 0.3045 0.2257 0.1209 -0.0053 0
313.15 K 0.0000 0.0999 0.2000 0.3999 0.4984 0.5998 0.6993 0.8026 0.8982 1.0000
0.7727 0.8092 0.8355 0.8724 0.8856 0.8962 0.9054 0.9131 0.9193 0.9234
0.4480 0.4830 0.5190 0.5891 0.6229 0.6490 0.6734 0.6890 0.7071 0.7685
1.319 1.343 1.362 1.390 1.398 1.406 1.413 1.418 1.422 1.427
0 -0.3533 -0.5082 -0.6381 -0.6445 -0.5693 -0.5158 -0.4044 -0.2952 0
0 0.0030 0.0069 0.0129 0.0152 0.0088 0.0013 -0.0162 -0.0288 0
0 -1.6300 -2.5813 -3.1655 -3.0970 -2.7544 -2.2449 -1.6174 -0.9312 0
0 0.1340 0.2396 0.3410 0.3469 0.2969 0.2242 0.0976 -0.0175 0
71
Table 3.4 Experimental Values of Density (ρm), Viscosity (ηm), Refractive Index (nm), Excess Molar Volume (Vm
E), Viscosity Deviation (∆η), Molar Refraction Deviation (∆Rm) and Excess Gibbs’s Free Energy of Activation for Viscous Flow ( ΔG*E) along with Mole Fraction for Binary Mixture (DMA + Water) at 293.15, 303.15 and 313.15 K.
X1 ρm
(g.cm-3)
ηm (cp)
nm VmE
(cm3.mol-1) ∆η
(cp) ∆Rm ∆G*E
(KJ.mol-1)
293.15 K 0.0000 0.0999 0.1998 0.2999 0.3998 0.5000 0.6975 0.7949 0.9000 1.0000
0.9982 1.0000 0.9994 0.9961 0.9865 0.9739 0.9597 0.9533 0.9464 0.9398
1.002 2.930 4.634 4.918 4.072 3.340 1.840 1.475 1.219 1.012
1.333 1.379 1.405 1.419 1.427 1.431 1.435 1.436 1.436 1.437
0 -0.5868 -1.1219 -1.5447 -1.6260 -1.3977 -1.1217 -0.8691 -0.4830 0
0 1.9270 3.6300 3.9130 3.0660 2.3331 0.8311 0.4651 0.2081 0
0 -5.4224 -7.4664 -8.0344 -7.7523 -6.9606 -4.6796 -3.2945 -1.6907 0
0 2.9975 4.3101 4.5406 4.1035 3.5946 1.9492 1.2724 0.6359 0
303.15 K 0.0000 0.0999 0.1998 0.2999 0.3998 0.5000 0.6975 0.7949 0.9000 1.0000
0.9956 0.9932 0.9924 0.9866 0.9771 0.9686 0.9511 0.9438 0.9374 0.9315
0.797 2.089 3.138 3.356 2.871 2.295 1.470 1.220 1.034 0.871
1.332 1.377 1.401 1.415 1.422 1.427 1.430 1.431 1.431 1.432
0 -0.5411 -1.1000 -1.4509 -1.5394 -1.5389 -1.0882 -0.7651 -0.4174 0
0 1.2844 2.3262 2.5365 2.0445 1.4612 0.6213 0.3639 0.1702 0
0 -5.3557 -7.4185 -7.9653 -7.7102 -6.9530 -4.6632 -3.2624 -1.6717 0
0 2.7199 3.8870 4.1215 3.7436 3.1414 1.8304 1.2201 0.6221 0
313.15 K 0.0000 0.0999 0.1998 0.2999 0.3998 0.5000 0.6975 0.7949 0.9000 1.0000
0.9922 0.9866 0.9851 0.9776 0.9680 0.9598 0.9420 0.9352 0.9284 0.9234
0.653 1.615 2.342 2.474 2.229 1.839 1.259 1.067 0.924 0.769
1.331 1.374 1.398 1.411 1.418 1.422 1.425 1.426 1.426 1.427
0 -0.5110 -1.0759 -1.3788 -1.4654 -1.4825 -1.0066 -0.7192 -0.3325 0
0 0.9502 1.6654 1.7859 1.5299 1.1281 0.5254 0.3223 0.1670 0
0 -5.4464 -7.4982 -8.0250 -7.7424 -6.9946 -4.6693 -3.2671 -1.6574 0
0 2.5671 3.6304 3.8202 3.5497 3.0041 1.8187 1.2401 0.6751 0
72
Table 3.5 Coefficients ia of Curve Expert 1.3 linear regression polynomial equation for Excess Parameters and their Standard Deviation for the Systems DMA + 1-Propanol, DMA + Methanol and DMA + Water at three temperatures Functions a1 a2 a3 a4 a5 σ(YE)
DMA + 1-Propanol T=293.15 K Vm
E(cm3.mol-1) -0.0019 -2.7974 10.3011 -13.8667 6.3645 0.0081 ηE(cp) -0.0174 -3.1715 8.3915 -8.3535 3.1590 0.0282 ∆Rm -0.0108 -3.1054 8.6892 -10.3679 4.7960 0.0189 ∆G*E(KJ.mol-1) -0.0216 -3.2493 7.7897 -7.0447 2.5357 0.0361 T=303.15 K Vm
E(cm3.mol-1) -0.0050 -2.8394 10.7807 -14.6660 6.7340 0.0105 ηE(cp) -0.0117 -2.1567 5.6077 -5.4832 2.0491 0.0211 ∆Rm -0.0183 -2.3489 7.6043 -9.7329 4.5084 0.0306 ∆G*E(KJ.mol-1) -0.0192 -2.9483 7.0317 -6.2987 2.2424 0.0369 T=313.15 K Vm
E(cm3.mol-1) -0.0077 -3.2075 12.0454 -15.4444 6.6187 0.0132 ηE(cp) -0.0074 -0.8359 1.3914 -0.3562 -0.1887 0.0169 ∆Rm -0.0162 -3.3449 9.2659 -10.0926 4.1921 0.0288 ∆G*E(KJ.mol-1) -0.0178 -1.1896 0.9408 1.9931 -1.7183 0.0419
DMA + Methanol T=293.15 K Vm
E(cm3.mol-1) 0.0089 -4.6857 11.0749 -11.7817 5.3720 0.0202 ηE(cp) 0.0012 -0.0211 0.7067 -1.5541 0.8649 0.0038 ∆Rm
0.0031 -20.3031 41.3232 -32.2236 11.2009 0.0075 ∆G*E(KJ.mol-1) 0.0032 1.3859 -0.2904 -3.2699 2.1656 0.0095 T=303.15 K Vm
E(cm3.mol-1) 0.0045 -4.3661 10.2599 -10.9069 5.0001 0.0146 ηE(cp) 0.0022 -0.0725 0.9117 -1.9000 1.0544 0.0068 ∆Rm 0.0026 -18.5914 36.6298 -27.2042 9.1583 0.0161 ∆G*E(KJ.mol-1) 0.0065 1.2314 0.6657 -5.0875 3.1712 0.0205 T=313.15 K Vm
E(cm3.mol-1) -0.0023 -4.3417 10.7049 -11.6181 5.2481 0.0215 ηE(cp) 0.0020 -0.1066 0.9799 -1.9622 1.0832 0.0061 ∆Rm -0.0079 -0.1976 40.1674 -31.0736 10.6765 0.0261 ∆G*E(KJ.mol-1) 0.0068 1.0663 1.5418 -6.5823 3.9547 0.0209
DMA + Water T=293.15 K Vm
E(cm3.mol-1) 0.0439 -8.5174 13.8936 -7.0029 1.5601 0.0961 ηE(cp) -0.1577 33.6014 -93.8688 87.5647 -27.0823 0.2677 ∆Rm -0.1243 -66.2275 179.5525 -183.0507 69.9332 0.2055 ∆G*E(KJ.mol-1) 0.0263 38.9811 -107.9595 106.4839 -37.5455 0.0719 T=303.15 K Vm
E(cm3.mol-1) 0.0257 -6.9623 6.1435 5.2908 -4.5181 0.0450 ηE(cp) -0.0967 21.9662 -62.3313 60.0138 -19.5212 0.1635 ∆Rm -1.2300 -65.3446 175.8656 -177.8814 67.5653 0.2053 ∆G*E(KJ.mol-1) 0.0158 35.8636 -101.4766 103.3124 -37.7320 0.0336 T=313.15 K Vm
E(cm3.mol-1) 0.0229 -6.5455 4.9527 7.0597 -5.4994 0.0432 ηE(cp) -0.0554 15.3968 -42.9074 40.9669 -13.3799 0.0911 ∆Rm -0.1325 -66.2452 179.3324 -182.2330 69.3677 0.2213 ∆G*E(KJ.mol-1) 0.0244 33.3978 -94.6918 97.7223 -36.4664 0.0421
73
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41th edition 1960, p. 2181.
CHAPTER 4 Thermoacoustical Studies in Binary Liquid
Mixtures of N, N-dimethylacetamide (DMA) + 1-Propanol, + Methanol and + Water at Three
Temperatures
4.1 Introduction 4.2 Results 4.3 Discussion 4.3.1 Excess Parameters 4.3.2 Thermophysical Parameters 4.3.3 Semi-empirical Relations 4.4 Conclusion
References
76
4.1 INTRODUCTION
The study of molecular association in organic binary mixtures
having alcohol as one of the components is of particular interest,
since alcohols are strongly self-associated liquids having a three
dimensional network of hydrogen bonds [1] and can be associated
with any of other group having some degree of polarity [2]. Since
the ultrasonic velocity measurements are highly sensitive to
molecular interactions and can be used to provide qualitative
information about the physical nature and strength of molecular
interaction in the liquid mixtures [3-5].
An extensive survey of literature [6-15] reveals that thermo-
acoustical studies for binary mixtures of N,N-dimethylacetamide
(DMA) with 1-propanol, methanol and water are lacking. Therefore,
in the present chapter, ultrasonic velocity technique is selected to
study these mixtures systematically.
The intermolecular interactions present in the mixtures have
been investigated through deviation in ultrasonic velocity (Δu),
excess acoustic impedance (ZE) and excess intermolecular free
length (LfE). These excess parameters have been fitted to Curve
Expert 1.3 linear regression polynomial equation. Derived
parameters such as isentropic compressibility (Ks), effective Debye
temperature (ϴD) and specific heat ratio (γ) at varying concentrations
of DMA have also been calculated using experimental data for all
the three systems. The results have been interpreted on the basis of
strength of intermolecular interaction occurring between constituent
molecules of the mixtures.
77
Various semi empirical mixing rules proposed by Nomoto,
Vandeal, Junjie, CFT and Flory’s statistical theory (FST) for the
estimation of ultrasonic velocity of liquid mixtures have also been
applied to these binary mixtures. HBT (and Rackett) density models
have been applied to compare the experimental and theoretically
calculated values of density because these theories are successfully
used by many workers [16-19]. The results have been discussed in
terms of average percentage deviation (APD).
The main purpose of this chapter is to reconfirm the results
obtained in previous chapter that molecular interactions are based on
the hydrocarbon chain length of alcohols, using ultrasonic technique.
4.2 RESULTS
The experimental and literature values of ultrasonic velocity
for pure liquids viz. DMA, 1-propanol, methanol and water are
given in Table 4.1, which are in close agreement. The values of
density and ultrasonic velocity for DMA + 1-propanol, DMA +
methanol and DMA + water mixtures over the entire range of
composition at three temperatures, 293.15, 303.15 and 313.15 K are
reported in Table 4.2. The calculated excess parameters like
deviation in ultrasonic velocity (Δu), excess acoustic impedance (ZE)
and excess intermolecular free length (LfE) are presented in Table
4.3. Table 4.4 displays the values of the Curve Expert 1.3 linear
regression polynomial coefficient, ia evaluated by Curve Expert 1.3
software along with standard deviations. The parameters isentropic
compressibility (Ks), pseudo-Grüneisen parameter (Г) and specific
78
heat ratio (γ) reported in Table 4.5 are temperature sensitive and
provide significant information regarding intermolecular interaction.
4.3 DISCUSSION
4.3.1 Excess Parameters
Deviation in ultrasonic velocity (Δu) for all the three systems
as a function of mole fraction of DMA at 293.15, 303.15 and 313.15
K are shown in Fig. 4.1. Examination of curves reveal that the
values of Δu are positive for all the three systems and varies in a
manner; 1-propanol < methanol < water. Moore & Fort [20] and
many other workers [21-24] suggest that positive values of Δu are an
indication of presence of strong intermolecular interaction between
the unlike liquid molecules. Positive values of Δu for DMA + 1-
propanol, DMA + methanol and DMA + water indicate that the
formation of hydrogen bonds between oxygen atom of >C=O group
of DMA and hydrogen atom of -OH of alcohols and water
molecules. Proton accepting ability of DMA attributes to the
formation of hydrogen bonds with alcohols and water. This
contribution is found to be most significant for DMA + water as
compared to DMA + methanol system and is least significant for
DMA + 1-propanol system. The higher positive values of Δu
amongst all three systems show that DMA is more interactive with
water than methanol or 1-propanol.
Similarly, deviation in ultrasonic velocity (Δu), excess
acoustic impedance (ZE) is positive for all the systems (Fig. 4.2)
over entire range of composition at all the three temperatures which
supports the presence of strong intermolecular interaction between
unlike molecules. The strength of interaction varies according to the
79
hydrocarbon chain length of alcohols. The increase in hydrocarbon
chain length of the alcohol diminishes its polarity and therefore,
interaction due to hydrogen bonding vary in the manner; 1-propanol
< methanol < water.
The intermolecular free length (Lf) is one of the important
acoustical parameter, which is used to study the nature and strength
of molecular interaction. As can be seen in Fig. 4.3, the values of
excess intermolecular free length (LfE) are negative for all the
mixtures at all three temperatures. The negative values of LfE
indicate that the sound wave needs to cover a large distance. These
negative values also support the formation of hydrogen bonds
between unlike molecules.
4.3.2 Thermo-acoustical Parameters
Figs. 4.4 and 4.5 represent the variation of density (ρ) and
isentropic compressibility (Ks) with mole fraction of DMA for all
three systems at 293.15, 303.15 and 313.15 K. Density increases as
the concentration of DMA increases and isentropic compressibility
has an inverse relationship with the density, it decreases as the
concentration of DMA increases. In case of DMA + Methanol, Figs.
4.4b and 4.5b show sudden changes of ρ and Ks at lower
concentration of DMA. This non-linear behavior of density and
isentropic compressibility reflects the strong hydrogen bonding
between oxygen atom of >C=O in DMA and -OH hydrogen atom of
methanol. For the mixture DMA + Water (Fig. 4.4c), density
increases and reaches a maximum and then decreases. Similar
behavior is also shown in Ks (Fig. 4.5c). The occurrence of maxima
in ρ and minima in Ks at 0.0999 and 0.1998 mole fractions
respectively at all three temperatures, shows that the complexation
80
become maximum at these concentrations and decreases with further
increase of concentration of DMA. This may be interpreted in
terms of the formation of strong hydrogen bonding resulting into
complex formation. In case of DMA + 1-propanol, density (Fig.
4.4a) and isentropic compressibility (Fig. 4.5a) show almost linear
behavior with concentration of DMA. This explains that hydrogen
bond formed between 1-propanol and DMA molecule is weak in
strength as compared to hydrogen bond form between DMA and
methanol/water.
Effective Debye temperature (ϴD) and specific heat ratio (γ)
decreases with increase in temperature for all the three mixtures. It is
also observed that these parameters are affected by changing the
mole fraction of DMA. ϴD and γ vary non-linearly with composition
and temperature in the order of 1-propanol < methanol < water.
4.3.3 Semi-empirical Relations
Table 4.6 shows the values of APD of ultrasonic velocity
predicted by various relations and theories. For estimation of
ultrasonic velocity theoretically, Nomoto’s relation is best suited for
DMA + 1-propanol and DMA + methanol mixtures and CFT is best
for DMA + water system. However, Vandeal’s relation shows very
high APD values for all three binary mixtures.
From the literature values (Table 4.7) of Critical temperature,
Characteristic volume, Accentric factor, Critical pressure, Unique
constant and Critical volume of pure liquids, in order to see the
accuracy in density measurements, theoretical values of density
were calculated both from HBT and modified Rackett models. Root
mean square deviations in experimental values of density from
81
theoretical values are reported in Table 4.8. Rackett density model is
best suited for these binary mixtures
4.4 CONCLUSION
Deviation in ultrasonic velocity (Δu), excess acoustic
impedance (ZE) and excess intermolecular free length (LfE),
calculated from experimentally measured density and ultrasonic
velocity at three temperatures and atmospheric pressure are
correlated with Curve Expert 1.3 linear regression polynomial
equation. Estimated values of various thermo-acoustic parameters
(Ks, ϴD and γ) and excess parameters suggested the occurrence of
complexations through hetero-molecular H-bonding between DMA
and 1-propanol, methanol and water in these binary mixtures. The
effect of temperature on the strength and extent of interaction among
the component molecules of liquid mixtures seems to be significant.
Comparison of experimental and estimated values of ultrasonic
velocity in terms of average percentage deviation exhibits the
suitability of semi-empirical relations and theories. Root mean
square deviations obtained from the HBT and modified Rackett
models for prediction of density show the excellent agreement
between experimental and theoretical values. It is also concluded
that proton donating ability of alcohol and proton accepting ability
of amide linearly vary with alkyl chain length.
82
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure4.1. Deviation in ultrasonic velocity (Δu) vs. mole fraction of DMA (x1) for binary mixtures of (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water at varying temperatures.
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Δu (m
. sec
-1)
0
20
40
60
80
100
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Δu (m
. s.-1
)
0
50
100
150
200
250
300
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Δu (m
. s.-1
)
83
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure4.2. Excess acoustic impedance (ZE) vs. mole fraction of DMA (x1) for binary mixtures, (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water at varying temperatures.
0.00
0.05
0.10
0.15
0.20
0.25
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ZE ×
10-5
(kg.
m.-2
s.-1
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ZE ×
10-5
(kg.
m.-2
s.-1
)
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ZE ×
10-5
(kg.
m.-2
s-1 )
84
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure4.3. Excess intermolecular free length (LfE) vs. mole
fraction of DMA (x1) for binary mixtures, (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water at varying temperatures.
-0.025
-0.020
-0.015
-0.010
-0.005
0.0000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
L fE (A
0 )
-0.080-0.070-0.060-0.050-0.040-0.030-0.020-0.0100.000
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
L fE
(A
0 )
-0.080-0.070-0.060-0.050-0.040-0.030-0.020-0.0100.000
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
L fE (A
0 )
85
(a) DMA + 1-Propanol
(b) DMA + Methanol
(c) DMA + Water
Figure4.4 Density (ρ) vs. mole fraction of DMA (x1) for binary mixtures, (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water at varying temperatures
0.760.780.800.820.840.860.880.900.920.940.96
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
ρ (m
. sec
-1)
0.750.770.790.810.830.850.870.890.910.930.95
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
ρ (m
. sec
-1)
0.910.920.930.940.950.960.970.980.991.001.01
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
ρ (m
. sec
-1)
86
(a) DMA + 1-propanol
(b) DMA + Methanol
(c) DMA + Water
Figure4.5 Isentropic compressibility (Ks) vs. mole fraction of DMA (x1) for binary mixtures, (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water at varying temperatures
4E-10
5E-10
6E-10
7E-10
8E-10
9E-10
1E-09
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
Ks (
N-1
m2 )
4E-105E-106E-107E-108E-109E-101E-09
1.1E-091.2E-09
0 0.2 0.4 0.6 0.8 1
293.15 K 303.15 K313.15 K
x1
Ks (
N-1
m2 )
3E-10
3.5E-10
4E-10
4.5E-10
5E-10
5.5E-10
6E-10
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
Ks (
N-1
m2 )
87
(a) DMA + 1-Propanol
(b) DMA + Methanol
(c) DMA + Water
Figure4.6 Effective Debye’s temperature (ϴD) vs. mole fraction of DMA (x1) for binary mixtures, (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water at varying temperatures.
24
25
26
27
28
29
30
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
ϴD (
K)
26
27
28
29
30
31
32
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
ϴD (
K )
20
25
30
35
40
45
50
55
0 0.2 0.4 0.6 0.8 1
293.15 K303.15 K313.15 K
x1
ϴD (
K )
88
(a) DMA + 1-Propanol
(b) DMA + Methanol
(c) DMA + Water
Figure4.7 Specific heat ratio (γ) vs. mole fraction of DMA (x1) for binary mixtures, (a) DMA + 1-propanol, (b) DMA + Methanol and (c) DMA + Water at varying temperatures
1.36
1.38
1.40
1.42
1.44
1.46
1.48
0 0.2 0.4 0.6 0.8 1
292.15 K303.15 K313.15 K
x1
γ
1.341.361.381.401.421.441.461.481.50
0 0.2 0.4 0.6 0.8 1
292.15 K303.15 K313.15 K
x1
γ
1.321.331.341.351.361.371.381.391.401.41
0 0.2 0.4 0.6 0.8 1
292.15 K303.15 K313.15 K
x1
γ
89
Table 4.1 Ultrasonic velocity (u) of pure liquids at temperatures, 293.15, 303.15, 313.15 K and their literature values
Ultrasonic velocity u (m.s-1)
Component Temp.(K) Expt. Lit.
DMA 293.15 1472.0 -
303.15 1432.0 1432.0[15]
313.15 1402.0 -
1-Propanol 293.15 1229.3 1224[25]
303.15 1193.1 1184.9[15]
1193.4[26]
1193.0[27]
1188.8[28]
1194.4[29]
1189[25]
313.15 1156..0 1154.7[28]
1155[25]
Methanol 293.15 1116.0 1116.0[16,18]
303.15 1082.2 1084.0[18]
1103.0[27]
1093.2[29]
1084[16]
313.15 1053.1 1050.0[18,16]
Water 293.15 1483.0 1482.336[30,31]
303.15 1518.0 1509.0[31,32]
313.15 1529.0 1530.0[31,32]
90
Table 4.2 Experimental values of density (ρm) and ultrasonic velocity (um) for the systems DMA + 1-propanol, DMA + methanol and DMA + water at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of DMA 293.15 K 303.15 K 313.15 K
x1 ρm
(gm.cm.-3) um
(m.s.-1) ρm
(gm.cm.-3) um
(m.s.-1) ρm
(gm.cm.-3) um
(m.s.-1) DMA + 1-Propanol
0.0000 0.0999 0.1998 0.2998 0.3998 0.4999 0.5998 0.7998 0.8997 1.0000
0.8038 0.8224 0.8385 0.8535 0.8675 0.8807 0.8937 0.9184 0.9297 0.9398
1229.3 1260.7 1289.9 1318.5 1343.2 1366.7 1388.6 1430.8 1451.3 1472.0
0.7957 0.8143 0.8303 0.8451 0.8590 0.8722 0.8853 0.9100 0.9212 0.9315
1193.1 1226.7 1257.2 1284.0 1307.9 1330.7 1352.1 1393.2 1413.2 1432.0
0.7874 0.8063 0.8223 0.8369 0.8507 0.8637 0.8766 0.9011 0.9126 0.9234
1156.0 1192.5 1224.6 1252.8 1276.9 1299.3 1320.8 1362.9 1383.4 1402.0
DMA + Methanol 0.0000 0.0999 0.2000 0.3999 0.4984 0.5998 0.6993 0.8026 0.8982 1.0000
0.7915 0.8277 0.8552 0.8916 0.9041 0.9147 0.9234 0.9307 0.9364 0.9398
1116.0 1207.7 1274.6 1356.3 1386.3 1409.6 1429.3 1448.8 1463.2 1472.0
0.7820 0.8181 0.8451 0.8819 0.8947 0.9054 0.9144 0.9219 0.9277 0.9315
1082.2 1164.8 1234.4 1316.0 1343.9 1368.0 1386.9 1406.4 1418.6 1432.0
0.7727 0.8092 0.8355 0.8724 0.8856 0.8962 0.9054 0.9131 0.9193 0.9234
1053.1 1127.4 1199.3 1280.0 1305.0 1325.4 1345.2 1363.0 1378.4 1402.0
DMA + Water 0.0000 0.0999 0.1998 0.2999 0.3998 0.5000 0.6975 0.7949 0.9000 1.0000
0.9982 1.0000 0.9994 0.9961 0.9865 0.9739 0.9597 0.9533 0.9464 0.9398
1483.0 1768.5 1741.1 1722.8 1664.9 1639.0 1550.1 1523.8 1498.5 1472.0
0.9956 0.9932 0.9924 0.9866 0.9771 0.9686 0.9511 0.9438 0.9374 0.9315
1518.0 1718.6 1702.8 1690.5 1639.7 1601.3 1521.9 1481.1 1459.0 1432.0
0.9922 0.9866 0.9851 0.9776 0.968
0.9598 0.942
0.9352 0.9284 0.9234
1529.0 1689.7 1676.0 1658.9 1600.9 1555.2 1481.2 1448.9 1417.3 1402.0
91
Table 4.3 Deviation in ultrasonic velocity (Δu), excess acoustic impedance (ZE) and intermolecular free length (Lf
E) for binary mixture of DMA + 1-propanol at 293.15, 303.15 and 313.15 K 293.15K 303.15K 313.15K
x1 Δu (m.s.-1)
ZE
(kg.m-2s-1) Lf
E
(A0) Δu
(m.s.-1) ZE
(kg.m-2s-1) Lf
E
(A0) Δu
(m.s.-1) ZE
(kg.m-2s-1) Lf
E
(A0) DMA + 1-Propanol
0.0000 0.0999 0.1998 0.2998 0.3998 0.4999 0.5998 0.7998 0.8997 1.0000
0.00 7.14
12.16 16.37 16.88 16.08 13.69 7.38 3.63 0.00
0.0000 0.0919 0.1454 0.1867 0.1910 0.1795 0.1576 0.0979 0.0552 0.0000
0.0000 -0.0074 -0.0120 -0.0151 -0.0157 -0.0151 -0.0134 -0.0079 -0.0042 0.0000
0.00 9.70
16.42 19.28 19.32 18.14 15.74 9.06 5.16 0.00
0.0000 0.1111 0.1771 0.2047 0.2042 0.1902 0.1704 0.1092 0.0650 0.0000
0.0000 -0.0092 -0.0149 -0.0175 -0.0179 -0.0170 -0.0151 -0.0091 -0.0050 0.0000
0.00 11.96 19.45 23.04 22.58 20.32 17.23 10.13 6.07 0.00
0.0000 0.1291 0.1996 0.2299 0.2238 0.1982 0.1702 0.1044 0.0644 0.0000
0.0000 -0.0114 -0.0179 -0.0209 -0.0211 -0.0195 -0.0171 -0.0102 -0.0057 0.0000
DMA + Methanol 0.0000 0.0999 0.2000 0.3999 0.4984 0.5998 0.6993 0.8026 0.8982 1.0000
0.00 56.10 87.37 97.97 92.86 80.07 64.38 47.07 27.44 0.00
0.0000 0.6631 1.0669 1.2601 1.2080 1.0610 0.8683 0.6373 0.3766 0.0000
0.0000 -0.0410 -0.0603 -0.0642 -0.0592 -0.0504 -0.0400 -0.0283 -0.0159 0.0000
0.00 47.64 82.22 93.90 87.31 75.98 60.07 43.48 22.21 0.00
0.0000 0.5791 0.9937 1.1929 1.1303 0.9982 0.8089 0.5893 0.3177 0.0000
0.0000 -0.0402 -0.0627 -0.0677 -0.0619 -0.0530 -0.0417 -0.0293 -0.0154 0.0000
0.00 39.44 76.42 87.35 77.99 63.01 48.10 29.86 11.91
0.00
0.0000 0.5052 0.9211 1.1062 1.0229 0.8565 0.6793 0.4487 0.2151 0.0000
0.0000 -0.0388 -0.0645 -0.0697 -0.0626 -0.0517 -0.0402 -0.0264 -0.0129 0.0000
DMA + Water 0.0000 0.0999 0.1998 0.2999 0.3998 0.5000 0.6975 0.7949 0.9000 1.0000
0.00 286.60 260.31 243.10 186.35 161.50 74.76 49.50 25.44 0.00
0.0000 2.9785 2.9010 2.6482 2.0090 1.6436 0.7491 0.4933 0.2514 0.0000
0.0000 -0.0693 -0.0652 -0.0625 -0.0500 -0.0430 -0.0213 -0.0144 -0.0076 0.0000
0.00 209.16 202.02 198.32 156.07 126.33 63.85 31.47 18.40 0.00
0.0000 2.1329 2.1403 2.0976 1.6175 1.2844 0.5988 0.2758 0.1602 0.0000
0.0000 -0.0522 -0.0526 -0.0528 -0.0433 -0.0362 -0.0193 -0.0098 -0.0059 0.0000
0.00 173.40 172.37 167.95 122.69 89.70 40.76 20.85
2.63 0.00
0.0000 1.7222 1.7840 1.7135 1.2156 0.8684 0.3337 0.1478 -0.0100 0.0000
0.0000 -0.0445 -0.0465 -0.0466 -0.0359 -0.0277 -0.0133 -0.0071 -0.0009 0.0000
92
Table 4.4 Coefficients ia of Curve Expert 1.3 linear regression polynomial equation for excess parameters and their standard deviation for the systems DMA + 1-propanol, DMA + Methanol and DMA + water at three temperatures Functions a1 a2 a3 a4 a5 σ(YE)
DMA + 1-Propanol T=293.15 K Δu (m.sec-1) -0.1554 86.7147 -116.0834 1.8411 27.7995 0.4392 ZE (Kg.m-2s-1) -0.0012 1.1543 -2.2857 1.6891 -0.5552 0.0044 Lf
E (A0) 0.00003 -0.0895 0.1589 -0.0931 0.0236 0.0002 T=303.15 K Δu (m.sec-1) -0.1799 129.2783 -277.6603 221.5275 -72.8690 0.3009 ZE (Kg.m-2s-1) -0.0011 1.4772 -3.5939 3.5249 -1.4065 0.0019 Lf
E (A0) 0.00004 -0.1166 0.2499 -0.2064 0.0731 0.00008 T=313.15 K Δu (m.sec-1) -0.2844 163.7629 -386.0706 344.2287 -121.4353 0.5059 ZE (Kg.m-2s-1) -0.0018 1.7512 -4.4974 4.4702 -1.7207 0.0036 Lf
E (A0) 0.00004 -0.1457 0.3329 -0.2929 0.1056 0.00009 DMA + Methanol
T=293.15 K Δu (m.sec-1) 0.0206 719.4808 -1722.0712 1596.4119 -593.8128 0.8357 ZE (Kg.m-2s-1) -0.0026 8.4645 -18.7969 16.3298 -5.9918 0.0089 Lf
E (A0) -0.0004 -0.5184 1.3325 -1.3021 0.4888 0.0008 T=303.15 K Δu (m.sec-1) -0.7762 639.0182 -1391.6110 1116.7376 -363.5353 1.8402 ZE (Kg.m-2s-1) 0.0079 7.5549 -15.4656 11.7512 -3.8324 0.0169 Lf
E (A0) -0.00002 -0.5213 1.2781 -1.1766 0.4201 0.0007 T=313.15 K Δu (m.sec-1) -1.6176 560.9438 -1059.4882 536.8676 -36.6780 3.1794 ZE (Kg.m-2s-1) -0.0130 6.7499 -12.4255 6.6326 -0.9426 0.0248 Lf
E (A0) 0.0004 -0.5212 1.2144 -1.0068 0.3133 0.0012 DMA + Water
T=293.15 K Δu (m.sec-1) 21.8986 3044.8484 -11094.579 13804.9984 -5786.9105 36.0507 ZE (Kg.m-2s-1) 0.1963 33.4995 -122.1126 151.5864 -63.2677 0.3212 Lf
E (A0) -0.0049 -0.7438 2.6412 -3.2391 1.3488 0.0081 T=303.15 K Δu (m.sec-1) 13.8508 2290.4042 -8014.7883 9629.9490 -3925.4604 23.0465 ZE (Kg.m-2s-1) 0.1267 24.1115 -83.9868 99.9696 -40.2773 0.2125 Lf
E (A0) -0.0033 -0.5731 1.9308 -2.2627 0.9096 0.0054 T=313.15 K Δu (m.sec-1) 10.1288 1994.9188 -7123.6009 8604.9702 -3493.1798 17.4459 ZE (Kg.m-2s-1) 0.0887 20.5102 -73.1977 87.7487 -35.2135 0.1553 Lf
E (A0) -0.0024 -0.5116 1.7424 -2.0321 0.8054 0.0042
93
Table 4.5 The calculated values of isentropic compressibility (Ks), effective Debye temperature (θD) and specific heat ratio (γ) for the systems DMA + 1-propanol, DMA + methanol and DMA + water at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of DMA
293.15K 303.15K 313.15K x1 Ks (N-1m-2) ϴD(K) γ Ks (N-1m-2) ϴD(K) γ Ks (N-1m-2) ϴD(K) γ
DMA + 1-Propanol 0.0000 0.0999 0.1998 0.2998 0.3998 0.4999 0.5998 0.7998 0.8997 1.0000
8.2322E-10 7.6504E-10 7.1669E-10 6.7401E-10 6.3890E-10 6.0787E-10 5.8033E-10 5.3188E-10 5.1068E-10 4.9108E-10
26.6805 27.0722 27.4079 27.7239 27.9612 28.1719 28.3536 28.6940 28.8531 29.0131
1.4728 1.4616 1.4522 1.4436 1.4358 1.4286 1.4216 1.4088 1.4030 1.3980
8.8289E-10 8.1615E-10 7.6195E-10 7.1773E-10 6.8052E-10 6.4752E-10 6.1784E-10 5.6613E-10 5.4355E-10 5.2352E-10
25.6661 26.1102 26.4786 26.7631 26.9882 27.1893 27.3698 27.6992 27.8532 27.9825
1.4559 1.4447 1.4354 1.4269 1.4192 1.4120 1.4050 1.3922 1.3865 1.3814
9.5036E-10 8.7208E-10 8.1093E-10 7.6133E-10 7.2092E-10 6.8583E-10 6.5394E-10 5.9746E-10 5.7256E-10 5.5095E-10
24.6534 25.1675 25.5721 25.8904 26.1246 26.3225 26.5072 26.8650 27.0357 27.1681
1.4400 1.4287 1.4194 1.4111 1.4034 1.3963 1.3894 1.3767 1.3709 1.3656
DMA + Methanol 0.0000 0.0999 0.2000 0.3999 0.4984 0.5998 0.6993 0.8026 0.8982 1.0000
1.0144E-09 8.2840E-10 7.1979E-10 6.0968E-10 5.7554E-10 5.5021E-10 5.3009E-10 5.1189E-10 4.9881E-10 4.9108E-10
29.7903 30.81902 31.25296 31.05302 30.81841 30.47545 30.13026 29.80244 29.46761 29.01313
1.4803 1.4584 1.4426 1.4227 1.4161 1.4107 1.4062 1.4025 1.3997 1.3980
1.0919E-09 9.0093E-10 7.7657E-10 6.5474E-10 6.1889E-10 5.9018E-10 5.6857E-10 5.4838E-10 5.3564E-10 5.2352E-10
28.6246 29.4557 29.9924 29.8603 29.6106 29.3153 28.9801 28.6795 28.3220 27.9825
1.4643 1.4425 1.4269 1.4068 1.4001 1.3946 1.3899 1.3862 1.3833 1.3814
1.1669E-09 9.7222E-10 8.3210E-10 6.9962E-10 6.6304E-10 6.3519E-10 6.1036E-10 5.8951E-10 5.7252E-10 5.5095E-10
27.6077 28.2623 28.8839 28.7909 28.5074 28.1586 27.8691 27.5582 27.2884 27.1681
1.4491 1.4270 1.4119 1.3917 1.3847 1.3792 1.3746 1.3707 1.3676 1.3656
DMA + Water 0.0000 0.0999 0.1998 0.2999 0.3998 0.5000 0.6975 0.7949 0.9000 1.0000
4.5551E-10 3.1974E-10 3.3007E-10 3.3824E-10 3.6568E-10 3.8223E-10 4.3366E-10 4.5179E-10 4.7053E-10 4.9108E-10
49.95081 53.48041 48.52616 44.94306 41.05389 38.46875 33.60128 31.94423 30.39845 29.01313
1.3702 1.3693 1.3696 1.3711 1.3756 1.3815 1.3883 1.3914 1.3947 1.3980
4.3589E-10 3.4090E-10 3.4751E-10 3.5466E-10 3.8066E-10 4.0262E-10 4.5396E-10 4.8300E-10 5.0115E-10 5.2352E-10
50.7467 51.5431 47.0675 43.7174 40.0792 37.2844 32.7057 30.7775 29.3389 27.9825
1.3511 1.3522 1.3525 1.3552 1.3595 1.3635 1.3718 1.3753 1.3785 1.3814
4.3111E-10 3.5501E-10 3.6139E-10 3.7172E-10 4.0308E-10 4.3077E-10 4.8388E-10 5.0935E-10 5.3620E-10 5.5095E-10
50.7360 50.2736 45.9507 42.5378 38.8013 35.9063 31.5613 29.8552 28.2590 27.1681
1.3332 1.3358 1.3364 1.3398 1.3443 1.3481 1.3565 1.3598 1.3631 1.3656
94
Table 4.6 Average percentage deviation (APD) of various theoretical mixing rules and theory used for evaluation of ultrasonic velocity (um) at varying temperatures Temperature Nomoto Vandeal Junjie CFT FST
DMA + 1-propanol 293.15 K 0.2920 0.3730 1.4073 0.5195 0.7120 303.15 K 0.4613 3.4300 1.5994 0.6994 -1.1245 313.15 K 0.6169 3.7167 1.8479 8.7498 -2.9339
DMA + Methanol 293.15 K 1.4095 15.0327 3.3642 3.4008 2.0367 303.15 K 1.2076 14.9392 3.2206 3.2584 0.1853 313.15 K 0.6651 14.6489 2.7778 2.8024 -1.9924
DMA + Water 293.15 K 7.7528 21.1827 7.7760 5.8192 9.5936 303.15 K 7.2443 19.1958 7.3438 4.3209 7.3986 313.15 K 6.6258 17.8053 6.7998 3.1629 5.1687
Table 4.7
Critical temperature, Characteristics volume, Accentric factor, Critical pressure, Unique constant and Critical volume of pure liquids DMA 1-Propanol Methanol Water
Tc(K) 618 536.8 512.6 647.37 V*(L/mol) 0.1830 0.2305 0.1198 0.0436
ωSRK 0.4292 0.6249 0.5536 0.3852 Pc(bar) 54.7 51.7 80.9 221.2
ZRA 0.2965 0.2541 0.2334 0.2338 Vc×106(m3/mol) 253 219 118 57.1
Table 4.8
Root Mean Square deviations in density using HBT and Rackett Models for binary mixtures DMA + 1-propanol, DMA + Methanol and DMA + Water at varying temperatures Root Mean Square deviation (in density)
HBT Rackett Temperature (K) DMA + 1-Propanol
293.15 0.07776 0.01042 303.15 0.07892 0.01038 313.15 0.07462 0.01036
DMA + Methanol 293.15 0.09985 0.01043 303.15 0.09824 0.01015 313.15 0.09650 0.00983
DMA + Water 293.15 0.16097 0.01950 303.15 0.15851 0.01872 313.15 0.15611 0.01807
95
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CHAPTER 5 Studies on Molecular Association in Binary
Liquid Mixtures of Poly(propylene glycol)monobutyl ether340 (PPGMBE 340) with Toluene, Benzene and Benzyl alcohol
form Density, Viscosity and Refractive Index Data at 293.15, 303.15 and 313.15 K
5.1 Introduction 5.2 Chemicals 5.3 Results 5.4 Discussion 5.4.1 Excess Parameters 5.4.2 Thermophysical Parameters 5.5 Conclusion
References
98
5.1 INTRODUCTION
Poly (propylene glycol) monobutyl ether 340 (PPGMBE340)
is a unique synthetic polymer, among other polyalkylene glycols
having the structure,
PPGMBE340 is inexpensive, biodegradable, insoluble in
water [1], and is widely used as lubricant for automobile engine in
cold climates [2, 3]. This fluid shows the expected low carbon and
low sludge, as well as cleans engine parts and satisfactory cranking
at low temperature down to -60oF. PPGMBE340 does not readily
crystallize. Instead, it becomes too thick to flow at a temperature
known as pour point. The pour point for this polymer is very low
(-56oC). Even at temperatures below its pour point, it does not
crystallize but forms glass like solid. It is also used as fire-resistant
fluid, brake fluid, compressor lubricant, textile lubricant,
metalworking fluid, refrigeration lubricant, two-cycle engine
lubricant, crankcase lubricant etc.
PPGMBE340 is also used as hydraulic fluid, metal working
fluid, heat transfer fluid, solder assist fluid, plasticizer and foam
control agent. The pendent methyl group on each repeat unit in
poly(propylene oxide) led to a lower cohesive energy density and
surface tension that reduces the intermolecular interaction between
99
polymer segments, resulting in a higher solubility of poly(propylene
oxide) verses poly(ethylene oxide) [4].
The solubility of a PPGMBE340 is determined by its
structure. It is a polar molecule and according to solubility rules it
should dissolve in polar solvents. The solubility derived from the
presence of propylene oxide group in its molecule is responsible for
its water insolubility and solubility in nonpolar solvents to some
level [5].
In a dilute solution, the properties of polymer are
characterized by the interaction between the solvent and the
polymer. In a good solvent, the polymer appears swollen and
occupies a large volume. When a polymer is added to given solvent,
attraction as well as dispersion forces becomes active between its
segments, according to their polarity, chemical characteristics and
solubility parameters. If the polymer-solvent interactions are higher
than its intramolecular attraction forces, the chain segment of the
polymer start to entrap solvent molecules, increasing the volume of
the polymer matrix and loosening out their coiled shape.
A rigorous literature survey reveals that molecular interaction
studies on binary liquid mixtures in PPGMBE340 are almost lacking
[4]. Seeing the importance of PPGMBE340, in the present study, it
is proposed to initiate with the molecular interaction studies on
binary mixtures of PPGMBE340 with non-polar aromatic
hydrocarbons namely benzene, toluene and a polar aromatic liquid
benzyl alcohol at three temperatures 293.15, 303.15 and 313.15 K
over the entire range of composition. Density, viscosity and
refractive index of these mixtures were experimentally measured at
several mole fractions of PPGMBE340 and thermodynamic
100
properties namely excess molar volume VmE, deviation in viscosity
∆η and deviation in molar refraction ∆Rm were calculated and fitted
to Curve Expert 1.3 linear regression polynomial equation. The
results have been discussed in terms of molecular association
occurring between the components.
Using various semi empirical mixing rules proposed by
Lorentz-Lorenz (L-L), Gladstone-Dale (G-D), Wiener (W), Heller
(H), Arago-Biot (A-B), Newton (N), Eykman (E) and Oster (O),
refractive index was also theoretically calculated. A comparative
study has been made between the experimental and theoretical
values of refractive index at all the three temperatures and results
have been discussed in terms of average percentage deviation
(APD).
5.2 CHEMICALS
Poly(propylene glycol)monobutyl ether 340 (grade analytical
standard) was supplied by Sigma-Aldrich Pvt. Ltd. Toluene (mass
fraction ≥ 0.995) was supplied by Ranbaxy Laboratories Ltd,
benzene (mass fraction ≥ 0.995) and benzyl alcohol (mass fraction ≥
0.990) were supplied by Qualigens Fine Chemicals, India. All these
solvents were stored under moisture free conditions to avoid the
alterations of their specifications. The measured density, viscosity
and refractive index of pure liquids along with their literature values
are given in table 5.1 and are in good agreement.
5.3 RESULTS
The values of density, viscosity and refractive index measured
for PPGMBE340 + toluene, PPGMBE340 + benzene and
101
PPGMBE340 + benzyl alcohol mixtures over the entire range of
compositions at three temperatures, 293.15, 303.15 and 313.15 K are
given in Table 5.2. The calculated excess parameters like excess
molar volume (VmE), deviation in viscosity (Δη) and deviation in
molar refraction (ΔRm) are given in Table 5.3. Table 5.4 displays the
values of the Curve Expert 1.3 linear regression polynomial
coefficient, ia evaluated by Curve Expert 1.3 software along with
their standard deviations. The Table 5.5 shows optical dielectric
constant (ε), polarizability (α) and interaction parameter (d) of the
systems PPGMBE340 + toluene, PPGMBE340 + benzene and
PPGMBE340 + benzyl alcohol. APD of theoretically estimated
values of refractive index are listed in Table 5.6.
5.4 DISCUSSION
5.4.1 Excess Parameters
Non-ideal liquid mixtures show considerable deviation from
the linearity in their physical parameters with respect to
concentration and these have been interpreted in terms of the
presence of weak or strong interactions. The excess properties
provide valuable information about microscopic and macroscopic
behavior of liquid mixtures [6, 7], and can be used to test and
improve thermodynamic models for calculating and predicting the
fluid phase equilibria. These excess properties are fundamentally
important in understanding the intermolecular interactions and
nature of molecular agitation in dissimilar molecules. These
functions give an idea about the extent to which a liquid mixture
deviates from ideality [8, 9].
102
The variation of VmE values with x1 at three temperatures are
shown graphically in Fig. 5.1. The VmE values are negative for all the
three mixtures over whole composition range at all the temperatures.
The extent of negative deviation in VmE on mole fraction follows the
sequence: toluene < benzene < benzyl alcohol. Negative values of
VmE are an indication for presence of specific intermolecular
interaction in these systems.
VmE values are found to be more negative for PPGMBE340 +
benzene system in comparison to PPGMBE340 + toluene system
(Fig. 5.1) probably due to the strong non-polar interaction between
benzene and non-polar chain of PPGMBE340, whereas the
interaction of toluene with polymer is less due to the +I effect of
–CH3 group of toluene. The higher negative values of VmE (Fig.
5.1c), in the case of PPGMBE340 + benzyl alcohol amongst all three
systems, show that PPGMBE340 is more interactive with benzyl
alcohol molecules than benzene or toluene molecules because of H-
bond formation between –OH group of both polymer and benzyl
alcohol molecules viz.
CH2
O HH O
H O
CH2
H
O
CH3
CH3
n
OOH3C
CH3
n
Hydrogen bonding between the molecules of benzyl alcohol and PPGMBE340
Polymer size and structure also play an important role to
understand the interaction in solution. The structural contributions are
mostly negative and arise from several effects, especially from
103
interstitial accommodation and changes in the free volume. The actual
value of excess parameters would depend on the relative strength of
these effects. The experimental values of VmE suggest that H-bonding
and interstitial accommodation both are leading to the negative values
while increase in negative values with temperature suggest that
structural effect is more prominent than chemical effect in these
solutions due to the fitting of smaller molecules of benzene, toluene and
benzyl alcohol into the voids created by bigger molecules of
PPGMBE340 and the large difference in molar volumes of components
(molar volumes of PPGMBE340, toluene, benzene and benzyl
alcohol are 354.43, 106.29, 88.87 and 103.36 cm3mol-1 respectively at
293.15K. The actual value of excess parameters would depend on the
relative strength of these effects.
Hansen [10] proposed that the cohesive energy has three
components, corresponding to the three types of interactions;
E = ED + EP + EH
Dividing the cohesive energy by the molar volume gives the
square of the Hildebrand solubility parameter as the sum of the
squares of the Hansen dispersion (D), polar (P) and hydrogen
bonding (H) components;
E/Vm = ED/Vm + EP/ Vm + EH/ Vm
δ2 = δ2D + δ2
P + δ2H
where δ, δD, δP and δH are total Hildebrand solubility parameter,
Hansen dispersive solubility parameter, Hansen polar solubility
parameter and Hansen hydrogen bonding solubility parameter
respectively.
104
Solubility parameters for toluene, benzene and benzyl alcohol
are shown below,
Component δ δD δP δH
Toluene 18.2 18.0 1.4 2.0
Benzene 18.6 18.4 0.0 2.0
Benzyl alcohol 23.8 18.4 6.3 13.7
Viscosity is also an important bulk property that provides a
measure of the internal friction of a fluid and is closely related to the
self-association of molecules in liquids. The viscosity deviations Δη
are negative for the systems PPGMBE340 + toluene and
PPGMBE340 + benzene, over the entire composition range at all the
three temperatures and increase with rise in temperature as can be
seen from Figs. 5.2(a) and 5.2(b). From the above discussion total
Hildebrand solubility parameter (δ) of toluene and benzene are
highly dependent upon Hansen dispersive solubility parameter (δD)
indicating that the interaction between polymer and benzene /
toluene is because of dispersive forces. Dispersive forces are weak
intermolecular forces which give negative deviation in PPGMBE340
+ toluene and PPGMBE340 + benzene. Figs. 5.2(a) and 5.2(b) show
that, Δη values are more negative in PPGMBE340 + toluene than
PPGMBE340 + benzene mixture, which implies that benzene is
comparatively more interactive with PPGMBE340 than toluene.
Negative deviation in Δη values may also be on account of the
difference in the molecular size of the component molecules. Similar
conclusions have also been reported by other workers [11, 12].
Furthermore, the Δη values become less negative and tend towards
zero with rise in temperature indicating that the system approaches
105
ideal behavior at higher temperatures meaning thereby the thermal
energy enhances the molecular order in the mixture.
The viscosity deviation, Δη, is positive for the system
PPGMBE340 + benzyl alcohol, over the entire composition range at
all three temperatures and decrease with increase in temperature as
can be seen from Fig. 5.2(c). The positive values of Δη indicate the
presence of strong intermolecular interaction between the
components of the mixture. From above solubility parameter table,
the Hansen hydrogen bonding solubility parameter (δH) of benzyl
alcohol is sufficiently high. Hansen hydrogen bonding solubility
parameter (δH) and presence of –OH group on both polymer and
benzyl alcohol shows that moderate hydrogen bonding occurs
between PPGMBE340 and benzyl alcohol molecule. The increase in
temperature decreases the strength of H-bonding between unlike
molecules. Consequently the values of Δη become less positive as
the temperature is raised in PPGMBE340 + benzyl alcohol mixture.
Refractometry is one of the earliest techniques used to study
polymer dissolution [13]. The basic of this technique is that during
the dissolution process, the polymer concentration increases
continuously in the solvent and this concentration can be measured
by the refractive index. Molar refraction deviation (∆Rm) is found to
be negative for all the three mixtures (Fig. 5.4). The observed
negative values of ∆Rm support that specific interactions occur
between unlike molecules in mixture. The effect of temperature is
not prominent in molar refraction deviation study.
106
5.4.2 Thermophysical Parameters
Optical properties of liquids and liquid mixtures have been
widely studied to obtain information on their physical, chemical and
molecular behavior. Maxwell’s theory for electromagnetic materials
[14-17] gives the following relation between optical dielectric
constant and refractive index assuming that for non-magnetic
materials permeability approximately approaches unity.
𝜀 = 𝑛𝐷2
The permittivity ε, of nonpolar solvents can be explained by
considering, both, the properties of the isolated molecules and the
effects of the molecular interactions. At different densities, the
variations of permittivity with temperature are calculated from
theories taking account of pair interactions only. The classical
calculations of the average field at a molecule due to identical
polarized neighbors in a structure of cubic symmetry lead to the
Clausius-Mossotti equation [18,19], which gives polarisability as,
𝛼 = 3
4𝜋𝜌 �𝜀 − 1𝜀 + 2�
where ρ is the density and α is the total polarisability of the isolated
molecule, assumed to be independent of interactions with neighbors.
The interaction parameter d, in Gruenberg and Nissan
equation [20] is a measure of the strength of interaction between the
mixing components. The magnitude and sign of interaction
parameter are said to indicate the particular type of interaction
present in the solution. Large and positive d values indicate strong
specific interactions; small positive values indicate weak specific
interaction and large negative values indicate no specific interaction.
ln 𝜂𝑚 = 𝑥1ln 𝜂1 + 𝑥2ln𝜂2 + 𝑥1𝑥2𝑑
107
Table 5.5 reveals that optical dielectric constant (ε) for the
systems PPGMBE340 + toluene, PPGMBE340 + benzene and
PPGMBE340 + benzyl alcohol varies non-linearly with mole
fraction of PPGMBE340 (Fig. 5.4). It indicates that benzyl alcohol
is more interactive with PPGMBE340 than benzene and toluene.
Polarizability (α) of the mixture as given in Table 5.5 shows that the
polarizability of studied mixture decreases monotonously with mole
fraction of PPGMBE340. There is negligible change in
polarizability with temperature that may be due to small permanent
electric dipole moments of the components and their mixtures, as
orientation of molecular dipoles is slightly disturbed by temperature.
The values of interaction parameter (d) in all the three
systems under investigation are positive. These large and positive
values of interaction parameter indicate specific interaction to be
present in the solutions under study.
Table 5.6 shows the results of estimation of refractive index in
terms of average percentage deviation (APD) for all the three
mixtures. It may be seen from Table 5.6 that all the mixing rules are
best suited for estimation of refractive index in these mixtures.
5.5 CONCLUSION
Significant specific intermolecular interactions are
observed in all the three systems. From observed experimental data
and calculated excess parameters, it is found that the interaction is
strongest in the system PPGMBE340 + benzyl alcohol. The
difference in molar volumes of the components is much large hence
the structural effect is prominent in these mixtures. Derived
parameters (ε, α and d) also support that intermolecular interactions
108
are present between solvents and polymer. The effect of temperature
on the strength and extent of interaction among the component
molecules of liquid mixtures seems to be significant. Comparison of
experimental and estimated values of refractive index in terms of
average percentage deviation exhibits the suitability of semi-
empirical relations.
109
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure5.1 Excess molar volume (Vm
E) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.000.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
x1
V mE(c
m3 m
ol-1
)
-0.50
-0.40
-0.30
-0.20
-0.10
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
V mE(c
m3 m
ol-1
)
-1.60
-1.40
-1.20
-1.00
-0.80
-0.60
-0.40
-0.20
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
V mE(c
m3 m
ol-1
)
110
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure5.2 Deviation in viscosity (Δη) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
-5.00
-4.00
-3.00
-2.00
-1.00
0.000.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
x1
Δη (c
p)
-4.00
-3.50
-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Δη (c
p)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Δη (c
p)
111
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure5.3 Molar refraction deviation (∆Rm) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
-20.00
-15.00
-10.00
-5.00
0.000.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
x1
ΔRm
-25.00
-20.00
-15.00
-10.00
-5.00
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ΔRm
-20.00
-15.00
-10.00
-5.00
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ΔRm
112
Fig. 4(a)
Fig. 4(b)
Fig. 4(c)
Figure5.4 Optical dielectric constant (ε) against mole fraction of PPGMBE340 (x1): ■, toluene ▲, benzene; ◆, benzyl alcohol. (a) 293.15K, (b) 303.15K and (c) 313.15K
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
0.0 0.2 0.4 0.6 0.8 1.0
TolueneBenzeneBenzyl alcohol
x1
ε
293.15K
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
0.0 0.2 0.4 0.6 0.8 1.0
TolueneBenzeneBenzyl alcohol
x1
ε
303.15K
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
0.0 0.2 0.4 0.6 0.8 1.0
TolueneBenzeneBenzyl alcohol
313.15K
x1
ε
113
Table 5.1 Density (ρ), Viscosity (η) and Refractive index (n) of Pure Liquids at Temperatures, (293.15, 303.15, 313.15) K with their Literature Data Density ρ
(gm.cm-3) Viscosity η
(cp) Refractive index n
Component Temp.(K) Expt. Lit. Expt. Lit. Expt. Lit.
PPGMBE340 293.15 0.9593 - 21.1855 - 1.437 1.44[21]
303.15 0.9515 - 14.2792 - 1.433 -
313.15 0.9438 - 9.7252 9.6[21] 1.429 -
Toluene 293.15 0.8668 - 0.6120 - 1.498 -
303.15 0.8574 0.85754[22]
0.8578[23]
0.5459 0.526[23] 1.492 1.4907[24]
313.15 0.8484 0.84815[22] 0.5146 0.4662[24] 1.486 1.4837[24]
Benzene 293.15 0.8789 - 0.6440 - 1.501 -
303.15 0.8682 0.86828[22]
0.8682[25]
0.5626 0.5632[25] 1.494 1.4942[25]
313.15 0.8581 0.85797[22] 0.5012 0.4991[24] 1.487 1.4886[24]
Benzyl alcohol 293.15 1.0462 - 6.3490 - 1.539 -
303.15 1.0384 1.0365[25]
1.0371[26]
4.5161 4.5042[25]
4.5250[26]
1.536 1.5188[25]
1.5352[26]
313.15 1.0313 - 3.4252 - 1.533 -
114
Table 5.2 Experimental Values of Density (ρm), Viscosity (ηm), Refractive Index (nm) for the systems, PPGMBE340 + Toluene, PPGMBE340 + Benzene and PPGMBE340 + Benzyl alcohol at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of PPGMBE340
x1 ρm (g.cm-3)
ηm (cp)
nm ρm (g.cm-3)
ηm (cp)
nm ρm (g.cm-3)
ηm (cp)
nm
293.15K 303.15K 313.15K PPGMBE340 + Toluene
0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
0.8668 0.8924 0.9099 0.9318 0.9391 0.9495 0.9533 0.9593
0.5912 1.2590 1.9671 4.5747 6.3857
11.1892 14.2769 21.1855
1.497 1.481 1.470 1.457 1.452 1.445 1.442 1.437
0.8574 0.8836 0.9014 0.9236 0.9310 0.9416 0.9455 0.9515
0.5229 1.2157 1.6177 3.6469 4.8809 8.0306
10.0847 14.2792
1.491 1.476 1.465 1.452 1.447 1.441 1.438 1.433
0.8484 0.8751 0.8931 0.9156 0.9231 0.9339 0.9378 0.9438
0.4656 1.1567 1.3998 2.9292 3.9171 6.0125 7.3323 9.7252
1.484 1.470 1.460 1.447 1.442 1.437 1.434 1.429
PPGMBE340 + Benzene
0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
0.8789 0.9044 0.9204 0.9389 0.9446 0.9524 0.9551 0.9593
0.6440 1.3311 2.3659 5.3998 7.4116
12.2148 15.0933 21.1855
1.501 1.481 1.468 1.454 1.449 1.443 1.441 1.437
0.8682 0.8947 0.9113 0.9304 0.9363 0.9443 0.9472 0.9515
0.5626 1.1159 1.8915 4.1370 5.6441 8.6993
10.4602 14.2792
1.494 1.475 1.463 1.449 1.445 1.439 1.436 1.433
0.8581 0.8854 0.9023 0.9222 0.9282 0.9365 0.9394 0.9438
0.5012 0.9838 1.6090 3.3878 4.3712 6.9243 7.6927 9.7252
1.487 1.469 1.457 1.444 1.440 1.435 1.432 1.429
PPGMBE340 + Benzyl alcohol
0.0000 0.0999 0.2919 0.4983 0.5994 0.6990 0.8901 1.0000
1.0462 1.0284 1.0027 0.9854 0.9769 0.9732 0.9636 0.9593
6.3409 9.8835
15.2119 18.4084 19.1286 20.0505 20.8891 21.1855
1.539 1.516 1.483 1.464 1.448 1.451 1.442 1.437
1.0384 1.0206 0.9951 0.9775 0.9689 0.9650 0.9552 0.9515
4.5161 7.1884
10.6429 12.7436 13.1168 13.9241 14.0952 14.2792
1.536 1.511 1.479 1.459 1.452 1.447 1.438 1.433
1.0313 1.0131 0.988
0.9699 0.9613 0.9571 0.9478 0.9438
3.4252 5.3218 7.7353 9.0482 9.2941 9.7559
10.0073 9.7252
1.533 1.506 1.474 1.455 1.456 1.443 1.434 1.429
115
Table 5.3 Excess Molar Volume (Vm
E), Viscosity Deviation (∆η) and Molar Refraction Deviation (∆Rm) for the systems, PPGMBE340 + Toluene, PPGMBE340 + Benzene and PPGMBE340 + Benzyl alcohol at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of PPGMBE340
x1 VmE
(cm3mol-1) Δη (cp)
ΔRm VmE
(cm3mol-1) Δη (cp)
ΔRm VmE
(cm3mol-1) Δη (cp)
ΔRm
293.15K 303.15K 313.15K PPGMBE340 + Toluene
0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
0.0000 -0.0874 -0.1821 -0.2883 -0.2832 -0.2169 -0.1504 0.0000
0.0000 -1.3916 -2.7409 -4.2275 -4.4985 -3.8180 -2.7794 0.0000
0.0000 -10.5103 -15.7223 -17.8084 -16.5437 -11.3610 -7.9605 0.0000
0.0000 -0.1219 -0.2269 -0.3279 -0.3170 -0.2530 -0.1948 0.0000
0.0000 -0.6828 -1.6551 -2.3606 -2.5174 -2.1217 -1.4364 0.0000
0.0000 -10.4578 -15.6883 -17.8248 -16.5889 -11.3202 -7.9388 0.0000
0.0000 -0.1541 -0.2610 -0.3692 -0.3585 -0.3097 -0.2331 0.0000
0.0000 -0.2349 -0.9168 -1.2282 -1.1765 -0.9348 -0.5364 0.0000
0.0000 -10.4359 -15.6263 -17.8299 -16.6288 -11.2799 -7.9125 0.0000
PPGMBE340 + Benzene
0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
0.0000 -0.1061 -0.2174 -0.3367 -0.3364 -0.2705 -0.1738 0.0000
0.0000 -1.3650 -2.3782 -3.4464 -3.4970 -2.7857 -1.9777 0.0000
0.0000 -13.8282 -20.0485 -21.9028 -20.1362 -13.6620 -9.4133 0.0000
0.0000 -0.1323 -0.2595 -0.3772 -0.3750 -0.2789 -0.2057 0.0000
0.0000 -0.8170 -1.4089 -1.9026 -1.7727 -1.4498 -1.0716 0.0000
0.0000 -13.7788 -19.9641 -21.8868 -20.0421 -13.6037 -9.5402 0.0000
0.0000 -0.1525 -0.2618 -0.4315 -0.4139 -0.3319 -0.2286 0.0000
0.0000 -0.4389 -0.7333 -0.7965 -0.7392 -0.0236 -0.1849 0.0000
0.0000 -13.7359 -19.9519 -21.8830 -20.0701 -13.5600 -9.5098 0.0000
PPGMBE340 + Benzyl alcohol
0.0000 0.0999 0.2919 0.4983 0.5994 0.6990 0.8901 1.0000
0.0000 -0.7687 -1.3026 -1.4781 -0.8907 -1.2047 -0.4340 0.0000
0.0000 2.0596 4.5378 4.6704 3.8891 3.3332 1.3351 0.0000
0.0000 -10.4872 -17.7203 -16.4930 -15.2704 -11.3485 -4.3904 0.0000
0.0000 -0.7821 -1.3613 -1.4809 -0.8546 -1.1100 -0.2351 0.0000
0.0000 1.6970 3.2769 3.3626 2.7482 2.5836 0.8889 0.0000
0.0000 -10.5885 -17.7515 -16.6124 -14.2164 -11.3196 -4.3351 0.0000
0.0000 -0.7662 -1.4503 -1.5003 -0.8728 -1.0523 -0.3380 0.0000
0.0000 1.2672 2.4712 2.4837 2.0924 1.9270 0.9745 0.0000
0.0000 -10.6912 -17.8919 -16.6281 -13.1665 -11.3057 -4.3608 0.0000
116
Table 5.4 Coefficients ia of Curve Expert 1.3 linear regression polynomial equation for Excess Parameters and their Standard Deviation for the Systems PPGMBE340 + Toluene, PPGMBE340 + Benzene and PPGMBE340 + Benzene alcohol at three temperatures Functions a1 a2 a3 a4 a5 σ(YE)
PPGMBE340 + Toluene T=293.15 K Vm
E(cm3.mol-1) 0.0022 0.9602 -0.2044 2.6627 -1.5009 0.0067 ηE(cp) 0.0095 -15.0971 4.6043 19.6398 -9.1517 0.0619 ∆Rm -0.0784 -130.6644 311.3614 -280.9301 100.3344 0.2086 T=303.15 K Vm
E(cm3.mol-1) 0.0027 -1.4956 1.8748 -0.3799 -0.0029 0.0083 ηE(cp) 0.0299 -8.5609 1.3117 14.9836 -7.7592 0.1225 ∆Rm -0.0757 -129.8190 306.5289 -272.8679 96.2541 0.2009 T=313.15 K Vm
E(cm3.mol-1) 0.0007 -1.8443 3.0471 -2.1229 0.9196 0.0076 ηE(cp) 0.0452 -4.2814 -1.6378 14.2784 -8.4044 0.1339 ∆Rm -0.0819 -128.9217 301.8472 -265.3111 92.4866 0.2141
PPGMBE340 + Benzene T=293.15 K Vm
E(cm3.mol-1) 0.0015 -1.1403 -0.1765 2.9830 -1.6671 0.0090 ηE(cp) -0.0045 -15.0938 15.4829 3.1895 -3.5707 0.0249 ∆Rm
-0.1492 -172.4886 436.0236 -417.1125 153.7709 0.3936 T=303.15 K Vm
E(cm3.mol-1) 0.0031 -1.5712 1.1797 1.3747 -0.9874 0.0082 ηE(cp) 0.0109 -10.2669 18.3727 -12.7059 4.5878 0.0489 ∆Rm -0.1372 -172.3802 437.5350 -421.5178 156.5344 0.3448 T=313.15 K Vm
E(cm3.mol-1) -0.0009 -1.5224 0.3587 2.7632 -1.5986 0.0134 ηE(cp) 0.0155 -5.9102 11.4574 -3.6242 -1.9567 0.1532 ∆Rm -0.1334 -171.8478 434.4071 -416.0924 153.6989 0.3371
PPGMBE340 + Benzene alcohol T=293.15 K Vm
E(cm3.mol-1) -0.0056 -9.5379 22.7942 -22.5227 9.2882 0.2284 ηE(cp) -0.0524 26.4539 -43.2401 18.8465 -1.9805 0.1538 ∆Rm -0.1898 -124.3702 276.5099 -226.1148 74.2906 0.6238 T=303.15 K Vm
E(cm3.mol-1) -0.0116 -9.1527 18.3793 -12.2965 3.1084 0.2325 ηE(cp) 0.0039 20.5235 -38.8121 25.7250 -7.4693 0.1673 ∆Rm -0.1438 -128.5535 297.4733 -255.4266 86.7509 0.3165 T=313.15 K Vm
E(cm3.mol-1) 0.0140 -10.1499 22.3052 -17.6329 5.4636 0.2022 ηE(cp) -0.0267 17.1574 -39.9463 38.8862 -16.0539 0.0909 ∆Rm -0.0717 -134.3170 326.2352 -296.9372 105.1592 0.5113
117
Table 5.5 Optical dielectric constant (ε), polarizabilities (α) and interaction parameter (d) for the systems , PPGMBE340 + Toluene, PPGMBE340 + Benzene and PPGMBE340 + Benzyl alcohol at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of PPGMBE340
293.15K 303.15K 313.15K x1 ε α(cm3g-1) d ε α(cm3g-1) d ε α(cm3g-1) d
PPGMBE340 + Toluene 0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
2.2410 2.1934 2.1609 2.1229 2.1083 2.0880 2.0794 2.0650
0.0806 0.0762 0.0732 0.0698 0.0686 0.0669 0.0663 0.0652
- 4.4225 3.0432 2.5829 2.3637 2.0729 2.0143
-
2.2231 2.1786 2.1462 2.1083 2.0938 2.0765 2.0678 2.0535
0.0807 0.0762 0.0733 0.0698 0.0686 0.0670 0.0663 0.0652
- 5.6997 2.9278 2.6015 2.3231 1.9838 1.9670
-
2.2023 2.1609 2.1316 2.0938 2.0794 2.0650 2.0564 2.0420
0.0806 0.0762 0.0733 0.0697 0.0685 0.0670 0.0663 0.0652
- 6.7343 3.0839 2.6172 2.4433 2.0517 2.0394
-
PPGMBE340 +Benzene 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
2.2530 2.1934 2.1550 2.1141 2.0996 2.0823 2.0765 2.0650
0.0801 0.0752 0.0721 0.0689 0.0678 0.0665 0.0660 0.0652
- 4.1934 3.7803 3.0498 2.7899 2.3816 2.2516
-
2.2320 2.1756 2.1404 2.0996 2.0880 2.0707 2.0621 2.0535
0.0801 0.0752 0.0722 0.0689 0.0679 0.0665 0.0659 0.0652
- 4.0233 3.5494 2.9343 2.7591 2.2724 2.1010
-
2.2112 2.1580 2.1229 2.0851 2.0736 2.0592 2.0506 2.0420
0.0801 0.0751 0.0721 0.0688 0.0678 0.0666 0.0660 0.0652
- 4.2056 3.5957 3.0302 2.7358 2.6289 2.2446
-
PPGMBE340 + Benzyl alcohol 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
2.3685 2.2983 2.1993 2.1433 2.0967 2.1054 2.0794 2.0650
0.0715 0.0702 0.0680 0.0669 0.0655 0.0661 0.0656 0.0652
- 3.5958 2.5300 1.8588 1.5870 1.4640 1.2112
-
2.3593 2.2831 2.1874 2.1287 2.1083 2.0938 2.0678 2.0535
0.0717 0.0701 0.0681 0.0668 0.0665 0.0661 0.0656 0.0652
- 3.8903 2.5217 1.8551 1.5667 1.5272 1.1607
-
2.3501 2.2680 2.1727 2.1170 2.1199 2.0823 2.0564 2.0420
0.0719 0.0701 0.0679 0.0668 0.0675 0.0662 0.0656 0.0652
- 3.7411 2.4675 1.8056 1.5521 1.5079 1.4647
-
118
Table 5.6 Average percentage deviation (APD) of various theoretical mixing rules used for evaluation of refractive index (n) at varying temperatures Temp. (K)
Lorentz- Lorenz
Gladstone-Dale
Wiener’s relation
Heller’s relation
Arago- Biot
Newton Eykman’s relation
Oster’s relation
PPGMBE340 + Toluene 293.15 K 0.0108 0.0253 0.0293 0.0369 0.0253 0.0144 0.0004 -0.0025 303.15 K 0.0039 0.0239 0.0277 0.0348 0.0239 0.0136 -0.0001 -0.0074 313.15 K -0.0111 0.0143 0.0178 0.0245 0.0143 0.0046 -0.0012 -0.0204
PPGMBE340 + Benzene 293.15 K -0.0451 -0.0244 -0.0201 -0.0124 -0.0244 -0.0359 -0.0041 -0.0582 303.15 K -0.0484 -0.0225 -0.0186 -0.0115 -0.0224 -0.0331 -0.0043 -0.0590 313.15 K -0.0589 -0.0287 -0.0251 -0.0187 -0.0287 -0.0383 -0.0050 -0.0674
PPGMBE340 + Benzyl alcohol 293.15 K -0.0142 0.0931 0.1033 0.1222 0.0931 0.0666 -0.0018 -0.0323 303.15 K 0.0299 0.1321 0.1426 0.1620 0.1321 0.1049 0.0016 0.0099 313.15 K 0.0687 0.1712 0.1819 0.2018 0.1712 0.1433 0.0047 0.0476
119
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26. A. Ali and M. Tariq, J. Mol. Liq., 128 (2006) 50.
CHAPTER 6 Thermoacoustical Studies in Binary Liquid
Mixtures of Poly(propylene glycol)monobutyl ether340 (PPGMBE340) with Toluene,
Benzene and Benzyl alcohol at Three Temperatures
6.1 Introduction 6.2 Results 6.3 Discussion 6.4 Conclusion
References
121
6.1 INTRODUCTION
Ultrasonic technique is a powerful and effective tool for
investigation of properties of polymer solutions and behavior of
polymer chains under the influence of ultrasonic field [1].
Poly (propylene glycol) monobutyl ether 340 (PPGMBE340)
is most useful as lubricant and fire resistant fluid [2, 3]. It is a unique
synthetic polymer among other polyalkylene glycols due to its
biodegradability, insolubility in water and low cost [4].
Previous Chapter 5, deals with the molecular interaction
studies in binary solutions of PPGMBE340 with benzene, toluene
and benzyl alcohol using density, viscosity and refractive index
measurements. In the present chapter, it is proposed to apply a more
sensitive ultrasonic velocity technique for those binary solutions, in
order to confirm our findings arrived at earlier in Chapter 5.
From the experimental data of density and ultrasonic velocity,
deviation in ultrasonic velocity (Δu), deviation in isentropic
compressibility (ΔKsE), excess acoustic impedance (ZE), excess
intermolecular free length (LfE) and excess molar enthalpy (Hm
E)
were calculated for binary systems PPGMBE340 + toluene,
PPGMBE340 + benzene and PPGMBE340 + benzyl alcohol over
the whole composition range at temperatures 293.15, 303.15 and
313.13K and the results have been fitted to Curve Expert 1.3 linear
regression polynomial equation.
122
6.2 RESULTS
The values of density and ultrasonic velocity measured
experimentally for PPGMBE340 + toluene, PPGMBE340 + benzene
and PPGMBE340 + benzyl alcohol solutions over the entire range of
composition at three temperatures, 293.15, 303.15 and 313.15 K are
given in Table 6.1. The calculated excess parameters like deviation
in ultrasonic velocity (Δu), deviation in isentropic compressibility
(ΔKsE), excess acoustic impedance (ZE), excess intermolecular free
length (LfE) and excess molar enthalpy (Hm
E) are presented in Tables
6.2 - 6.4. Table 6.5 displays the values of the Curve Expert 1.3 linear
regression polynomial coefficient, ia evaluated form Curve Expert
1.3 software along with standard deviations.
6.3 DISCUSSION
Fig. 6.1a shows that Δu values are negative for PPGMBE340
+ toluene at all the three temperatures where as in the case of
PPGMBE340 + benzene system (Fig. 6.1b); values of Δu are found
to be negative at temperature 293.15K, which turns to be positive
at 303.15 and 313.15K. In system PPGMBE340 + benzyl alcohol
(Fig. 6.1c) the values of Δu is positive at all the three temperatures.
The negative values of Δu show that a weak intermolecular
interaction occurs between unlike molecules and positive values of
Δu show specific intermolecular interaction between unlike
molecules in mixtures, as interpreted earlier by Fort and Moore [5].
It can be observed from Fig. 6.2 that the deviation in
isentropic compressibility, ΔKs is positive over the whole range of
composition for PPGMBE340 + toluene. However, ΔKs values are
123
negative for the mixtures PPGMBE340 + benzene and PPGMBE340
+ benzyl alcohol, that may be due to decrease in volume on mixing
of liquids of different molecular size, as have also been reported by
Fort and Moore in past [5]. The observed negative values of ΔKs in
case of PPGMBE340 + benzyl alcohol can also be explained on the
basis of complex formation through hydrogen bonding between
unlike molecules. Similar results have been found by Singh et al [6]
for the binary mixtures of 2-butoxyethanol with PEG200 and
PEG400. However, in PPGMBE340 + toluene, an expansion in free
volume is expected to occur, making this mixture more compressible
than the ideal mixture, which ultimately culminates into the positive
values of ΔKs.
The variation of excess acoustic impedance against mole frac-
tion is given in Fig. 6.3. The values are found to be positive for all
the three systems under investigation. The positive values of ZE vary
according to toluene < benzene < benzyl alcohol at all the
temperatures and suggest the presence of specific interaction in all
these systems, which is more prominent in PPGMBE340 + benzyl
alcohol. The maximum value at around x=0.5 for ZE indicates the
enhancement of bond strength at this concentration. This kind of
variations suggest that significant interactions are operative in these
mixtures, already reported by Ali et al. [7] for the binary systems of
benzyl alcohol and benzene.
Due to intermolecular interactions, geometry of the molecule
is deformed, which affects the compressibility and thus a change in
ultrasonic velocity. The ultrasonic velocity in a mixture is mainly
influenced by the free length between the surfaces of the molecules
of the mixture. The inverse dependence of intermolecular free length
124
on ultrasonic velocity has been evolved from the model of sound
propagation proposed by Eyring and Kincaid [8]. Excess
intermolecular free length (LfE) is found to be negative for all three
binary mixtures (Fig. 6.4). The negative contribution of LfE indicates
the presence of strong interaction between unlike molecules. The
extent of negative variation in LfE follows the sequence: toluene <
benzene < benzyl alcohol. Similar results have been found by
Yasmin et al [9] for the binary mixtures of PEG200 with
ethanolamine / m-cresol/ aniline.
The excess molar enthalpy HmE versus mole fraction curve
(Fig. 6.5a) shows the zig-zag shape for PPGMBE340 + toluene
mixture and negative for PPGMBE340 + benzene / benzyl alcohol
mixtures (Fig. 6.5b and 6.5c). The values of HmE for PPGMBE340 +
toluene are positive at 293.15K and negative at 303.15K and
313.15K. The negative values of HmE indicate the presence of strong
intermolecular interaction between unlike molecules. However, the
positive values of HmE in case of PPGMBE340 + toluene mixture at
293.15K, suggest the weak intermolecular interaction between
unlike molecules. Yasmin et al [10] have also reported the similar
positive and negative behavior of HmE for pentanol with poly
(ethylene glycol) diacrylate / poly (ethylene glycol) dimethacrylate
solutions.
Effect of temperature on molecular interaction is significant in
all three systems. In the binary mixtures, PPGMBE340 + toluene
and PPGMBE340 + benzene the interaction between unlike
molecules increases with increase in temperature. In case of
PPGMBE340 + benzyl alcohol, reverse results are observed i.e. with
increase in temperature, intermolecular interaction decreases
125
between unlike molecules, perhaps due to the difficulty of hydrogen
bond formation between PPGMBE340 and benzyl alcohol.
6.4 CONCLUSION
On the basis of deviation in ultrasonic velocity (Δu), deviation
in isentropic compressibility (ΔKsE), excess acoustic impedance (ZE),
excess intermolecular free length (LfE) and excess molar enthalpy
(HmE), it was concluded that specific intermolecular interaction was
present in all the three systems which is more prominent in
PPGMBE340 + benzyl alcohol system probably due to hetero-
molecular hydrogen bond formation. These results confirmed the
findings reported in Chapter 5.
126
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure6.1 Deviation in ultrasonic velocity (Δu) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
-18.00-16.00-14.00-12.00-10.00
-8.00-6.00-4.00-2.000.00
0.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
x1
Δu (m
. sec
-1)
-5.00
-3.00
-1.00
1.00
3.00
5.00
7.00
9.00
11.00
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Δu (m
. sec
-1)
0.0010.0020.0030.0040.0050.0060.0070.0080.0090.00
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Δu (m
. sec
-1)
127
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure6.2 Deviation in isentropic compressibility (ΔKs
E) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
0.00
0.02
0.04
0.06
0.08
0.10
0.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
x1
ΔKsE
× 1
010 (N
-1 m
2 )
-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.010.00
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ΔKsE
× 1
010 (N
-1 m
2 )
-1.40
-1.20
-1.00
-0.80
-0.60
-0.40
-0.20
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ΔKsE
× 1
010 (N
-1 m
2 )
128
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure6.3 Excess acoustic impedance (ZE) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
x1
ZE ×
10-5
(kg.
m-2
s-1)
0.000.050.100.150.200.250.300.350.400.45
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ZE ×
10-5
(kg.
m-2
s-1)
0.000.040.080.120.160.200.240.280.320.360.400.440.48
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
ZE ×
10-5
(kg.
m-2
s-1)
129
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure6.4 Excess intermolecular free length (Lf
E) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
-0.007
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
00.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
x1
L fE (A
0 )
-0.014
-0.012
-0.010
-0.008
-0.006
-0.004
-0.002
0.0000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
L fE
(A0 )
-0.030
-0.025
-0.020
-0.015
-0.010
-0.005
0.0000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
L fE (A
0 )
130
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure6.5 Excess molar enthalpy (Hm
E) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
0.0 0.2 0.4 0.6 0.8 1.0293.15K303.15K313.15K
x1
Hm
E (K
J. m
ol-1
)
-12.00
-10.00
-8.00
-6.00
-4.00
-2.00
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Hm
E (K
J. m
ol-1
)
-25.00
-20.00
-15.00
-10.00
-5.00
0.000 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
x1
Hm
E (K
J. m
ol-1
)
131
Table 6.1 Experimental values of density (ρm) and ultrasonic velocity (um) for the systems PPGMBE340 + toluene, PPGMBE340 + benzene and PPGMBE340 + benzyl alcohol at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of PPGMBE340 293.15K 303.15K 313.15K
X1 ρm(gm.cm-3) um(m.s-1) ρm(gm.cm-3) um(m.s-1) ρm(gm.cm-3) um(m.s-1) PPGMBE340 + Toluene
0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
0.8668 0.8924 0.9099 0.9318 0.9391 0.9495 0.9533 0.9593
1332.9 1319.4 1313.6 1311.7 1311.3 1312.8 1313.1 1313.6
0.8574 0.8836 0.9014 0.9236 0.9310 0.9416 0.9455 0.9515
1288.0 1278.6 1274.4 1273.6 1275.4 1277.6 1278.6 1279.2
0.8484 0.8751 0.8931 0.9156 0.9231 0.9339 0.9378 0.9438
1244.0 1238.8 1236.6 1239.1 1241.4 1245.8 1247.4 1250.2
PPGMBE340 + Benzene 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
0.8789 0.9044 0.9204 0.9389 0.9446 0.9524 0.9551 0.9593
1325.7 1322.1 1320.7 1319.2 1318.7 1316.8 1315.9 1313.6
0.8682 0.8947 0.9113 0.9304 0.9363 0.9443 0.9472 0.9515
1281.0 1281.5 1281.8 1282.8 1283.7 1285.0 1284.6 1279.2
0.8581 0.8854 0.9023 0.9222 0.9282 0.9365 0.9394 0.9438
1232.0 1235.3 1238.4 1245.2 1248.3 1253.9 1255.6 1250.2
PPGMBE340 + Benzyl alcohol 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
1.0462 1.0284 1.0027 0.9854 0.9769 0.9732 0.9636 0.9593
1548.8 1545.2 1538.7 1509.7 1481.7 1445.7 1365.7 1313.6
1.0384 1.0206 0.9951 0.9775 0.9689 0.9650 0.9552 0.9515
1514.6 1509.6 1499.2 1472.8 1444.5 1409.6 1327.9 1279.2
1.0313 1.0131 0.9880 0.9699 0.9613 0.9571 0.9478 0.9438
1479.2 1473.8 1461.9 1436.9 1409.0 1374.2 1296.2 1250.2
132
Table 6.2 Deviation in ultrasonic velocity (Δu), deviation in isentropic compressibility (ΔKs
E), excess acoustic impedance (ZE), excess intermolecular free length (Lf
E) and excess molar enthalpy (HmE) for the system PPGMBE340 +
Toluene at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of PPGMBE340
x1 Δu (m.s-1)
ΔKsE×1010
(N-1m2) ZE×10-5
(kg.m-2s-1) Lf
E
(A0) Hm
E
(KJ.mol-1) 293.15K
0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
0.00 -11.57 -15.44 -13.51 -11.95 -6.59 -4.37 0.00
0.0000 0.0658 0.0811 0.0554 0.0472 0.0183 0.0110 0.0000
0.0000 11.5970 18.9417 25.1091 23.7157 17.8008 12.6499 0.0000
0.0000 -0.0004 -0.0013 -0.0029 -0.0029 -0.0025 -0.0018 0.0000
0.0000 -0.3773 2.2749 1.8975 1.7797 0.7770 -0.2713 0.0000
303.15K 0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
0.00 -8.52
-11.84 -10.89 -8.20 -4.24 -2.36 0.00
0.0000 0.0565 0.0765 0.0630 0.0403 0.0146 0.0043 0.0000
0.0000 14.1570 21.8587 26.9814 26.6750 19.6776 14.3794 0.0000
0.0000 -0.0017 -0.0029 -0.0042 -0.0046 -0.0037 -0.0029 0.0000
0.0000 -4.1066 0.4233 -1.7701 -1.4078 -1.2192 -1.9513 0.0000
313.15K 0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
0.00 -5.82 -8.64 -7.37 -5.70 -2.54 -1.56 0.00
0.0000 0.0562 0.0863 0.0737 0.0572 0.0249 0.0154 0.0000
0.0000 16.2114 24.1045 29.4606 28.2871 20.8726 14.8411 0.0000
0.0000 -0.0031 -0.0046 -0.0062 -0.0062 -0.0048 -0.0035 0.0000
0.0000 -6.1999 -1.3052 -3.8799 -4.7331 -3.7454 -3.8315 0.0000
133
Table 6.3 Deviation in ultrasonic velocity (Δu), deviation in isentropic compressibility (ΔKs
E), excess acoustic impedance (ZE), excess intermolecular free length (Lf
E) and excess molar enthalpy (HmE) for the system PPGMBE340 +
Benzene at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of PPGMBE340
x1 Δu (m.s-1)
ΔKsE×1010
(N-1m2) ZE×10-5
(kg.m-2s-1) Lf
E
(A0) Hm
E
(KJ.mol-1) 293.15K
0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
0.00 -2.39 -2.58 -1.67 -0.95 -0.44 -0.12 0.00
0.0000 -0.0154 -0.0292 -0.0396 -0.0402 -0.0280 -0.0202 0.0000
0.0000 21.0611 31.4568 35.5141 33.0254 22.5819 15.7039 0.0000
0.0000 -0.0040 -0.0061 -0.0070 -0.0066 -0.0045 -0.0032 0.0000
0.0000 -0.7564 -2.1879 -4.0856 -4.5961 -4.1559 -3.5795 0.0000
303.15K 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
0.00 0.68 1.16 2.52 3.60 5.26 5.04 0.00
0.0000 -0.0302 -0.0429 -0.0545 -0.0611 -0.0675 -0.0602 0.0000
0.0000 23.9049 34.9832 39.4286 37.2983 27.8806 20.6447 0.0000
0.0000 -0.0058 -0.0084 -0.0095 -0.0092 -0.0073 -0.0056 0.0000
0.0000 -1.5618 -3.1092 -5.7458 -6.9803 -4.9587 -3.5724 0.0000
313.15K 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
0.00 1.50 2.77 5.93 7.21 9.18 9.05 0.00
0.0000 -0.0009 -0.0031 -0.0316 -0.0455 -0.0751 -0.0798 0.0000
0.0000 24.3095 35.7263 42.1264 40.1499 31.3015 24.1606 0.0000
0.0000 -0.0068 -0.0100 -0.0121 -0.0118 -0.0097 -0.0078 0.0000
0.0000 -2.8873 -4.9560 -8.7326 -8.7955
-10.0881 -5.8485 0.0000
134
Table 6.4 Deviation in ultrasonic velocity (Δu), deviation in isentropic compressibility (ΔKs
E), excess acoustic impedance (ZE), excess intermolecular free length (Lf
E) and excess molar enthalpy (HmE) for the system PPGMBE340 +
Benzyl alcohol at 293.15, 303.15 and 313.15 K with respect to the mole fraction x1 of PPGMBE340
x1 Δu (m.s-1)
ΔKsE×1010
(N-1m2) ZE×10-5
(kg.m-2s-1) Lf
E
(A0) Hm
E
(KJ.mol-1) 293.15K
0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
0.00 19.90 58.55 78.10 73.89 61.30 26.25 0.00
0.0000 -0.4790 -0.9768 -1.1218 -1.0431 -0.8954 -0.4056 0.0000
0.0000 0.0472 0.2765 0.4680 0.4305 0.3839 0.1626 0.0000
0.0000 -0.0047 -0.0154 -0.0227 -0.0222 -0.0199 -0.0094 0.0000
0.0000 -13.6558 -23.2556 -19.9673 -15.7062 -12.6760 -4.6456 0.0000
303.15K 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
0.00 18.52 53.31 75.50 71.01 59.54 22.83 0.00
0.0000 -0.5117 -1.0298 -1.2015 -1.1135 -0.9591 -0.4082 0.0000
0.0000 0.0346 0.2289 0.4410 0.3998 0.3607 0.1217 0.0000
0.0000 -0.0048 -0.0152 -0.0238 -0.0231 -0.0209 -0.0089 0.0000
0.0000 -13.0759 -20.0616 -17.1709 -13.3014 -11.7882 -3.8540 0.0000
313.15K 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
0.00 17.48 49.55 71.81 67.07 55.07 20.83 0.00
0.0000 -0.5343 -1.0704 -1.2525 -1.1562 -0.9843 -0.4176 0.0000
0.0000 0.0213 0.1973 0.4034 0.3612 0.3129 0.1062 0.0000
0.0000 -0.0047 -0.0151 -0.0241 -0.0233 -0.0206 -0.0087 0.0000
0.0000 -11.1491 -17.4379 -14.7609 -11.8197 -10.4153 -5.1285 0.0000
135
Table 6.5 Coefficients ia of Curve Expert 1.3 linear regression polynomial equation for Excess Parameters and their Standard Deviation for the Systems PPGMBE340 + Toluene, PPGMBE340 + Benzene and PPGMBE340 + Benzene alcohol at three temperatures Functions a1 a2 a3 a4 a5 σ(YE)
PPGMBE340 + Toluene T=293.15 K Δu (m.sec-1) -0.1877 -150.3927 459.8539 -505.7983 196.8501 0.6105 ΔKs
E(N-1m2) 0.0015 0.8753 -3.0180 3.5752 -1.4344 0.0052 ZE (kg.m-2s-1) -0.0009 138.0528 -238.5854 134.1676 -33.6332 0.2990 Lf
E (A0) 0.00003 -0.0026 -0.0319 0.0644 -0.0299 0.0001 Hm
E (KJ.mol-1) -0.2656 6.9412 17.3406 -65.7780 41.7646 0.7952 T=303.15 K Δu (m.sec-1) -0.0309 -114.6050 341.1333 -355.0293 128.5498 0.2295 ΔKs
E(N-1m2) 0.0001 0.7860 -2.5056 2.6942 -0.9748 0.0021 ZE (kg.m-2s-1) 0.1389 168.4664 -345.9397 276.9734 -99.6708 0.4086 Lf
E (A0) -0.00001 -0.0184 0.0206 -0.0039 0.0018 0.0001 Hm
E (KJ.mol-1) -0.6821 -18.4678 88.3447 -142.6803 73.5091 1.9775 T=313.15 K Δu (m.sec-1) 0.0504 -82.9871 250.8909 -263.4743 95.5166 0.1508 ΔKs
E(N-1m2) -0.0008 0.8162 -2.4336 2.5135 -0.8952 0.0023 ZE (kg.m-2s-1) 0.2188 191.8650 -415.9588 351.1588 -127.3383 0.5473 Lf
E (A0) -0.00006 -0.0341 0.0612 -0.0418 0.0148 0.0002 Hm
E (KJ.mol-1) -0.9238 -33.6969 125.6657 -187.7129 96.7398 2.4492 PPGMBE340 + Benzene
T=293.15 K Δu (m.sec-1) -0.0739 -31.4247 117.6865 -147.3870 61.2228 0.2097 ΔKs
E(N-1m2) 0.0002 -0.1841 0.1886 0.0849 -0.0897 0.0009 ZE (kg.m-2s-1) 0.1645 261.8316 -624.6971 562.4014 -199.7483 0.4431 Lf
E (A0) -0.00002 -0.0497 0.1145 -0.0991 0.0344 0.00007 Hm
E (KJ.mol-1) 0.0654 -8.5992 -17.9297 39.4807 -13.0406 0.1910 T=303.15 K Δu (m.sec-1) 0.0138 8.2375 -25.2909 75.1551 -58.1236 0.0602 ΔKs
E(N-1m2) -0.0005 -0.3836 1.1488 -1.7183 0.9538 0.0015 ZE (kg.m-2s-1) 0.2321 299.3786 -760.9376 775.1016 -313.8444 0.6153 Lf
E (A0) -0.00007 -0.0727 0.1904 -0.2068 0.0892 0.0002 Hm
E (KJ.mol-1) -0.0629 -9.0393 -55.3565 125.2708 -60.8114 0.3465 T=313.15 K Δu (m.sec-1) -0.0354 18.6111 -37.6518 100.0384 -80.9308 0.2416 ΔKs
E(N-1m2) 0.0002 -0.0029 0.0176 -0.7851 0.7699 0.0029 ZE (kg.m-2s-1) 0.2127 302.3125 -751.1457 773.8983 -325.3132 0.5286 Lf
E (A0) -0.00006 -0.0844 0.2109 -0.2287 0.1022 0.0002 Hm
E (KJ.mol-1) -0.1227 -25.1171 -4.3831 38.9662 -9.2197 1.0769 PPGMBE340 + Benzene alcohol
T=293.15 K Δu (m.sec-1) -0.2008 185.1481 282.8081 -906.1000 438.7872 1.2079 ΔKs
E(N-1m2) -0.0043 -5.4169 8.0724 -4.0575 1.4077 0.0103 ZE (kg.m-2s-1) -0.0022 0.0518 5.7958 -10.5297 4.6916 0.0168 Lf
E (A0) 0.00004 -0.0393 -0.1124 0.2541 -0.1024 0.0003 Hm
E (KJ.mol-1) 0.0353 -178.4503 444.7083 -401.8447 135.5788 0.3764
136
Functions a1 a2 a3 a4 a5 σ(YE) T=303.15 K Δu (m.sec-1) 0.4144 136.2929 454.1619 -1133.8776 542.9892 1.2504 ΔKs
E(N-1m2) -0.0090 -5.5390 7.4048 -2.3948 0.5434 0.0205 ZE (kg.m-2s-1) 0.0037 -0.4157 7.5248 -13.0011 5.8877 0.0195 Lf
E (A0) -0.0002 -0.0286 -0.1733 0.3484 -0.1463 0.0005 Hm
E (KJ.mol-1) -0.2023 -164.0633 437.9201 -433.9588 160.56224 0.8716 T=313.15 K Δu (m.sec-1) 0.5636 117.5941 487.1627 -1170.0623 564.7739 1.7662 ΔKs
E(N-1m2) -0.0101 -5.7384 7.4760 -1.9563 0.2337 0.0227 ZE (kg.m-2s-1) 0.0034 -0.5557 7.6859 -13.1515 6.0194 0.0199 Lf
E (A0) -0.0002 -0.0244 -0.1983 0.3917 -0.1688 0.0006 Hm
E (KJ.mol-1) 0.0018 -150.1839 431.6447 -475.3238 193.8789 0.3429
137
REFERENCES
1. I. Perpechko, Acoustical Methods of Investigating Polymers,
Mir Publishers, Moscow, 65, (1975). 1
2. B. Rubin and E. M. Glass, SAE Q. Trans., 4 (1950) 287. 2
3. J. M. Russ, Lubri. Eng., 151 (1946). 3
4. Union Carbide Corp., UCON Fluids and Lubricants, booklet
P5-2616 (1996). 4
5. R. J. Fort and W. R. Moore Trans. Faraday Soc., 61 (1965)
2102.
6. K. P. Singh, H. Agarwal, V. K. Shukla, M. Yasmin, M. Gupta
and J. P. Shukla, J. Pure App. Ultrason., 31 (2009) 124.
7. A. Ali and M. Tariq, J. Mol. Liq., 128 (2006) 50.
8. J. F. Kincaid and H. Eyring, J. Phys. Chem., 41 (1937) 249.
9. M. Yasmin and M. Gupta, Thermochimica Acta, 518 (2011)
89.
10. M. Yasmin and M. Gupta, Int. J. Thermodyn, 15(2) (2012)
111.
CHAPTER 7 Theoretical Calculations of Some
Thermophysical Parameters for Binary Liquid Mixtures of PPGMBE340 with Toluene,
Benzene and Benzyl alcohol
7.1 Introduction 7.2 Calculation of Surface Tension and Other Thermophysical Parameters 7.3 Results 7.4 Discussion 7.5 Conclusion
References
138
7.1 INTRODUCTION
The present chapter is theoretical and deals with the
calculations of surface tension and various other thermophysical
properties like relaxation time (τ), molecular association (MA), van
der Waal’s constant (b), relaxation strength (r), molecular radius
(rm), geometrical volume (B), molar surface area (Y) and collision
factor (S) for the binary mixtures of the polymer PPGMBE340 with
toluene, benzene and benzyl alcohol at temperatures 293.15, 303.15
and 313.15K from experimentally determined values of density,
viscosity, refractive index and ultrasonic velocity of their mixtures
reported in Chapters 5 and 6. These parameters are quite sensitive
towards the interactions between the component molecules of the
mixture. The dependence of these parameters on the composition of
the mixture reveals the nature and extent of interaction between
component molecules [1, 2].
7.2 CALCULATION OF SURFACE TENSION AND OTHER
THERMOPHYSICAL PARAMETERS
The surface tension of solutions has been calculated using the
well-known Auerbach relation [3]
𝑢𝑚 = �𝜎𝑚
6.3 × 10−4𝜌𝑚�2/3
𝜎𝑚 = 𝑢𝑚3/26.3 × 10−4𝜌𝑚 (7.1)
Relaxation time (τ) [4] and molecular association (MA) are
calculated using equations (7.2) and (7.3) viz.
139
𝜏 = 4𝜂3𝑢2𝜌
(7.2)
𝑀𝐴 = 𝑢𝑚∑ 𝑥𝑖𝑢𝑖
2 −12𝑖=1
(7.3)
The non-linearity parameter ( AB ) has been defined [5] in
terms of specific heat ratio as:
K2K2AB '' += γ (7.4)
where K and ''K are the isobaric acoustical parameter and isochoric
acoustical parameter and are given by:
( )
+
+
+=T
TT
Kα
αα 13
411
21
and ( )1C
''
V~T2T2121K
αα+
−=
where C1 is Moelwyn-Hughes parameter and is given by:
3T4
T1
313
dPlndT
Tlndlnd
TlndlndC
TPV1
αα
αβ
ααα++=
+
=
=
where α and 𝑉� are the thermal expansion coefficient and reduced
volume.
van der Waal’s constant (b), relaxation strength (r), molecular
radius (rm), geometrical volume (B), molar surface area (Y) and
collision factor (S) are calculated [6,7] using the following relations:
van der Waal’s constant:
𝑏 = 4 𝑉𝑚(𝑛𝑚2 −1)(𝑛𝑚2 +2)
(7.5)
Relaxation strength:
𝑟 = 1 − � 𝑢𝑢∞�2 (7.6)
Molecular radius:
140
𝑟𝑚 = � 3𝑏16𝜋𝑁𝐴
�13� (7.7)
Geometrical volume:
𝐵 = �43� 𝜋𝑟3𝑁𝐴 (7.8)
Molar surface area:
𝑌 = (36𝜋𝑁𝐴𝐵2)1 3� (7.9)
Collision factor:
𝑆 = 𝑢𝑚𝑉𝑢∞𝐵
(7.10)
where NA, Vm and 𝑢∞ denote Avagadro number (NA= 6.023 × 1023),
molar volume of mixture and 𝑢∞ is taken 1600 m/sec.
7.3 RESULTS
The theoretically calculated values of surface tension (σ),
relaxation time (τ), molecular association (MA) and non-linearity
parameter (B/A) are presented in Tables 7.1, 7.2 and 7.3 for
PPGMBE340 + toluene, + benzene and + benzyl alcohol
respectively over entire range of mole fractions at 293.15, 303.15
and 313.15K. Other thermophysical parameters viz. van der Waal’s
constant (b), relaxation strength (r), molecular radius (rm),
geometrical volume (B), molar surface area (Y) and collision factor
(S) are similarly reported in Tables 7.4, 7.5 and 7.6.
7.4 DISCUSSION
The surface tension of a liquid mixture is not a simple
function of the surface tension of pure components, since in a
mixture the composition of the surface is not the same as that of the
bulk. In a typical situation, the bulk composition is known but not
141
the surface composition. Figs. 7.1(a), (b) and (c) show variation of
surface tension of solution against mole fraction of PPGMBE340 for
all the three systems. The surface tension of the PPGMBE340 +
toluene and PPGMBE340 + benzene systems at 293.15K increases
almost linearly with increase in concentration of PPGMBE340. As
the temperature is raised the nonlinearity is observed in
PPGMBE340 + toluene and PPGMBE340 + benzene systems,
which suggest that specific intermolecular interaction occurs
between unlike molecules at 303.15 and 313.15K. PPGMBE340 +
benzyl alcohol system shows a reverse trend i.e. the surface tension
of the mixture decreases with increase in concentration of polymer.
From Fig. 7.1(c), it is clear that the non-linear variation in the
PPGMBE340 + benzyl alcohol system is larger than the other two
systems at all the three temperatures indicating stronger
intermolecular interaction in this system.
The variation of relaxation time (τ) with the mole fraction of
PPGMBE340 can be seen from Fig. 7.2. The values of τ increase
non-linearly with increasing mole fraction of PPGMBE340 for all
three systems. The non-linearity shows that the specific interactions
are present between polymer and toluene, benzene and benzyl
alcohol molecules.
Molecular association is an attractive interaction between
two molecules that results in a stable association in which the
molecules are close to each other resulting in the formation of
a molecular complex, which is a loose association of two or more
molecules. The non-linear variation of molecular association with
142
mole fraction of PPGMBE340 interprets presence of specific
interaction between polymer and other liquids, Fig. 7.3.
The variation of non-linear parameter (B/A) against mole
fraction of polymer shows non-linear behavior (Fig. 7.4). In case of
PPGMBE340 with toluene and benzene, Figs. 7.4(a) and 7.4(b), the
values of B/A decrease at lower concentrations and further increase
with increase in concentration indicating a specific interaction which
occurs between polymer and toluene / benzene molecules at all three
temperatures. For the system PPGMBE340 + benzyl alcohol, Fig.
7.4(c), the higher non-linearity as compared to PPGMBE340 +
benzene / toluene systems suggest that PPGMBE340 is highly
interactive with benzyl alcohol rather than benzene and toluene.
It can be seen from the Tables 7.4, 7.5 and 7.6 that most of the
parameters show the non-linear variation with the mole fraction
which again supports the presence of significant molecular
interaction existing between component molecules.
7.5 CONCLUSION
Theoretically estimated values of various thermophysical
parameters suggest the occurrence of complexations through
heteromolecular interaction between PPGMBE340 and toluene,
benzene and benzyl alcohol. Various thermophysical and non-linear
parameters offer a convenient means for elucidating liquid state
properties related to the sound propagation data.
143
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure7.1 Surface tension (σ) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol.
24.525.025.526.026.527.027.528.028.529.0
0.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
X1
σ (N
/m)
24.525.025.526.026.527.027.528.028.529.0
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
σ (N
/m)
26.0
28.0
30.0
32.0
34.0
36.0
38.0
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
σ (N
/m)
144
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure7.2. Relaxation time (τ) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol
02468
1012141618
0.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
τ×10
11 (s
ec)
X1
02468
1012141618
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
τ×10
11 (s
ec)
02468
1012141618
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
τ×10
11 (s
ec)
145
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure7.3 Molecular association (MA) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol
0.00074
0.00075
0.00076
0.00077
0.00078
0.00079
0.00080
0.00081
0.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
X1
MA
0.00075
0.00076
0.00077
0.00078
0.00079
0.00080
0.00081
0.00082
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
MA
0.00063
0.00068
0.00073
0.00078
0.00083
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
MA
146
(a) PPGMBE340 + Toluene
(b) PPGMBE340 + Benzene
(c) PPGMBE340 + Benzyl alcohol
Figure7.4 Non-linearity parameter (B/A) against mole fraction of PPGMBE340 (x1): ■, 293.15 K; ▲, 303.15 K; ◆, 313.15 K. (a) PPGMBE340 + Toluene, (b) PPGMBE340 + Benzene and (c) PPGMBE340 + Benzyl alcohol
11.90
11.95
12.00
12.05
12.10
12.15
12.20
12.25
0.0 0.2 0.4 0.6 0.8 1.0
293.15K303.15K313.15K
X1
B/A
11.90
11.95
12.00
12.05
12.10
12.15
12.20
12.25
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
B/A
11.90
12.00
12.10
12.20
12.30
12.40
12.50
12.60
0 0.2 0.4 0.6 0.8 1
293.15K303.15K313.15K
X1
B/A
147
Table 7.1 The calculated values of surface tension (σ), non-linearity parameter (B/A), relaxation time (τ) and molecular association (MA) along with the mole fraction for binary mixture, PPGMBE340 + Toluene at 293.15, 303.15 and 313.15K
X1 σ(N/m) τ×1011(sec) MA B/A 293.15K
0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
26.4978 26.6912 26.9354 27.4171 27.6263 27.9907 28.1412 28.4010
0.5119 1.0806 1.6705 3.8046 5.2727 9.1169
11.5810 17.0646
0.000750 0.000745 0.000744 0.000747 0.000749 0.000754 0.000756 0.000761
12.1754 12.1599 12.1544 12.1639 12.1716 12.1900 12.1980 12.2116
303.15K 0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
25.6701 25.9422 26.2338 26.7732 27.0166 27.4147 27.5817 27.8598
0.4902 1.1221 1.4734 3.2457 4.2973 6.9668 8.6990 12.228
0.000776 0.000772 0.000770 0.000772 0.000774 0.000778 0.000779 0.000782
12.0644 12.0490 12.0437 12.0524 12.0631 12.0800 12.0879 12.1016
313.15K 0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
24.8425 25.2112 25.5667 26.2008 26.4747 26.9308 27.1183 27.4393
0.4728 1.1484 1.3666 2.7782 3.6714 5.5309 6.6997 8.7902
0.000804 0.000800 0.000797 0.000798 0.000798 0.000799 0.000800 0.000800
11.9613 11.9455 11.9406 11.9501 11.9597 11.9769 11.9855 12.0025
148
Table 7.2 The calculated values of surface tension (σ), non-linearity parameter (B/A), relaxation time (τ) and molecular association (MA) along with the mole fraction for binary mixture, PPGMBE340 + Benzene at 293.15, 303.15 and 313.15K
X1 σ(N/m) τ×1011(sec) MA B/A 293.15K
0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
26.6307 26.8169 27.0660 27.5317 27.7299 28.0495 28.1826 28.4010
0.5559 1.1227 1.9649 4.4063 6.0160 9.8620
12.1683 17.0646
0.000754 0.000754 0.000754 0.000756 0.000757 0.000759 0.000760 0.000761
12.1762 12.1737 12.1728 12.1801 12.1866 12.1971 12.2039 12.2116
303.15K 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
25.7675 26.0507 26.3573 26.8983 27.1264 27.4981 27.6468 27.8598
0.5265 1.0126 1.6844 3.6028 4.8774 7.4389 8.9228
12.2280
0.000781 0.000781 0.000782 0.000783 0.000783 0.000785 0.000785 0.000782
12.0638 12.0616 12.0605 12.0701 12.0782 12.0945 12.1000 12.1016
313.15K 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
24.7739 25.1853 25.5862 26.2715 26.5510 27.0086 27.1935 27.4393
0.5131 0.9708 1.5503 3.1590 4.0296 6.2702 6.9257 8.7902
0.000812 0.000811 0.000811 0.000811 0.000810 0.000809 0.000808 0.000800
11.9558 11.9493 11.9507 11.9610 11.9723 11.9924 12.0018 12.0025
149
Table 7.3 The calculated values of surface tension (σ), non-linearity parameter (B/A), relaxation time (τ) and molecular association (MA) along with the mole fraction for binary mixture, PPGMBE340 + Benzyl alcohol at 293.15, 303.15 and 313.15K
X1 σ(N/m) τ×1011(sec) MA B/A 293.15K
0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
37.9975 35.8706 33.3663 31.6440 30.9136 30.2548 29.0589 28.4010
3.3689 5.3668 8.5436
10.9285 11.8919 13.1433 15.4972 17.0646
0.000646 0.000663 0.000699 0.000732 0.000743 0.000750 0.000759 0.000761
12.4830 12.4251 12.4513 12.4480 12.4556 12.3820 12.2877 12.2116
303.15K 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
37.5030 35.3644 32.8301 31.1176 30.3791 29.7203 28.4973 27.8598
2.5278 4.1209 6.3447 8.0136 8.6507 9.6825
11.1579 12.2280
0.000660 0.000677 0.000713 0.000749 0.000760 0.000768 0.000777 0.000782
12.3596 12.3062 12.3229 12.3294 12.3359 12.2708 12.1780 12.1016
313.15K 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
36.9430 34.8309 32.3275 30.6437 29.9127 29.2547 28.0608 27.4393
2.0239 3.2245 4.8846 6.0245 6.4933 7.1970 8.3791 8.7902
0.000676 0.000693 0.000729 0.000766 0.000777 0.000785 0.000794 0.000800
12.2422 12.1958 12.2000 12.2133 12.2179 12.1594 12.0674 12.0025
150
Table 7.4 The calculated values of van der Waal’s constant (b), relaxation strength (r), molecular radius (rm), geometrical volume (B), molar surface area (Y) and collision factor (S) for PPGMBE340 + Toluene at 293.15, 303.15 and 313.15K
X1 b(cm3/mol) r rm(nm) B×105 Y×10-4 S 293.15K
0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
124.4214 149.1493 173.7819 223.2583 248.2214 297.8428 322.299
371.4191
0.3060 0.3199 0.3260 0.3279 0.3283 0.3268 0.3265 0.3260
0.2311 0.2455 0.2583 0.2808 0.2909 0.3091 0.3173 0.3327
3.1105 3.7287 4.3446 5.5815 6.2055 7.4461 8.0575 9.2855
40.3867 45.5746 50.4636 59.6366 64.0031 72.2714 76.1753 83.7307
2.8469 2.8977 2.9426 3.0102 3.0380 3.0829 3.1017 3.1337
303.15K 0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
124.4946 149.2948 173.8161 223.1099 247.9814 297.9965 322.4001 371.4763
0.3520 0.3614 0.3656 0.3664 0.3646 0.3624 0.3614 0.3608
0.2311 0.2455 0.2583 0.2807 0.2908 0.3091 0.3174 0.3327
3.1124 3.7324 4.3454 5.5778 6.1995 7.4499 8.0600 9.2869
40.4025 45.6042 50.4702 59.6103 63.9619 72.2963 76.1913 83.7393
2.7795 2.8333 2.8812 2.9506 2.9834 3.0238 3.0442 3.0762
313.15K 0.0000 0.1000 0.1999 0.3987 0.4998 0.7000 0.7995 1.0000
124.2859 149.1149 173.8062 222.9023 247.6746 298.0822 322.4609 371.4865
0.3955 0.4005 0.4027 0.4003 0.3980 0.3937 0.3922 0.3895
0.2310 0.2454 0.2583 0.2806 0.2907 0.3092 0.3174 0.3327
3.1072 3.7279 4.3452 5.5726 6.1919 7.4521 8.0615 9.2872
40.3574 45.5676 50.4683 59.5733 63.9091 72.3101 76.2008 83.7408
2.7176 2.7751 2.8219 2.8985 2.9324 2.9720 2.9937 3.0309
151
Table 7.5 The calculated values of van der Waal’s constant (b), relaxation strength (r), molecular radius (rm), geometrical volume (B), molar surface area (Y) and collision factor (S) for PPGMBE340 + Benzene at 293.15, 303.15 and 313.15K
X1 b(cm3/mol) r rm(nm) B×105 Y×10-4 S 293.15K
0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
104.7329 131.2442 157.5153 210.7618 237.3575 290.7702 318.0062 371.4191
0.3135 0.3172 0.3187 0.3202 0.3207 0.3227 0.3236 0.3260
0.2182 0.2352 0.2499 0.2754 0.2866 0.3066 0.3159 0.3327
2.6183 3.2811 3.9379 5.2690 5.9339 7.2693 7.9502 9.2855
36.0050 41.8499 47.2632 57.3900 62.1217 71.1227 75.4974 83.7307
2.8124 2.9036 2.9694 3.0447 3.0728 3.1044 3.1145 3.1337
303.15K 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
104.7661 131.2505 157.6256 210.6596 237.6116 290.9622 317.4939 371.4763
0.3590 0.3585 0.3582 0.3572 0.3563 0.3550 0.3554 0.3608
0.2182 0.2352 0.2500 0.2754 0.2867 0.3067 0.3157 0.3327
2.6192 3.2813 3.9406 5.2665 5.9403 7.2741 7.9374 9.2869
36.0127 41.8513 47.2853 57.3715 62.1661 71.1540 75.4163 83.7393
2.7501 2.8448 2.9087 2.9891 3.0145 3.0534 3.0707 3.0762
313.15K 0.0000 0.0999 0.1996 0.3993 0.4997 0.6989 0.7997 1.0000
104.7203 131.1913 157.4181 210.4795 237.3449 291.0576 317.5691 371.4865
0.4071 0.4039 0.4009 0.3943 0.3913 0.3858 0.3842 0.3895
0.2182 0.2352 0.2499 0.2753 0.2866 0.3067 0.3158 0.3327
2.6180 3.2798 3.9355 5.2620 5.9336 7.2764 7.9392 9.2872
36.0022 41.8387 47.2438 57.3388 62.1195 71.1696 75.4282 83.7408
2.6773 2.7723 2.8420 2.9298 2.9603 3.0033 3.0256 3.0309
152
Table 7.6 The calculated values of van der Waal’s constant (b), relaxation strength (r), molecular radius (rm), geometrical volume (B), molar surface area (Y) and collision factor (S) for PPGMBE340 + Benzyl alcohol at 293.15, 303.15 and 313.15K
X1 b(cm3/mol) r rm(nm) B×105 Y×10-4 S 293.15K
0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
129.5235 154.2553 200.3112 250.5412 270.8866 299.0362 345.4498 371.4191
0.0630 0.0673 0.0752 0.1097 0.1424 0.1836 0.2714 0.3260
0.2342 0.2482 0.2708 0.2918 0.2995 0.3095
0.32475 0.3327
3.2381 3.8564 5.0078 6.2635 6.7722 7.4759 8.6363 9.2855
41.4834 46.6089 55.4769 64.4013 67.8422 72.4643 79.7808 83.7307
3.089999 3.197398 3.367332 3.419463 3.459278 3.355783 3.225967 3.133743
303.15K 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
129.8911 154.1650 200.4125 250.2201 275.2328 299.2597 345.7447 371.4763
0.1039 0.1098 0.1220 0.1527 0.1849 0.2238 0.3112 0.3608
0.2344 0.2482 0.2709 0.2917 0.3011 0.3096 0.3248 0.3327
3.2473 3.8541 5.0103 6.2555 6.8808 7.4815 8.6436 9.2869
41.5618 46.5907 55.4956 64.3462 68.5659 72.5004 79.8262 83.7393
3.035850 3.149449 3.304276 3.367161 3.346580 3.297327 3.161563 3.076220
313.15K 0.0000 0.0999 0.2919 0.4983 0.5995 0.6990 0.8901 1.0000
130.1744 154.0229 200.0481 250.2831 279.5288 299.3864 345.6717 371.4865
0.1453 0.1515 0.1652 0.1935 0.2245 0.2623 0.3437 0.3894
0.2346 0.2481 0.2707 0.2917 0.3026 0.3096 0.3248 0.3327
3.2544 3.8506 5.0012 6.2571 6.9882 7.4847 8.6418 9.2872
41.6222 46.5620 55.4283 64.3570 69.2775 72.5209 79.8149 83.7408
2.978809 3.100381 3.251130 3.309994 3.239577 3.239681 3.110841 3.030927
153
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