I

Thermodynamic Properties of Fluorinated Alcohols:

Experimental, Molecular Dynamics Simulation and GC-

SAFT-VR Predictions

Gonçalo Miguel Carvalho da Silva

Thesis to obtain a Masters degree in

Chemical Engineering

Supervisors:

Prof. Dr. Eduardo Jorge Morilla Filipe

Prof. Dr. Clare McCabe

Examination Committee

Chairperson: Prof. Dr. Carlos Manuel Faria de Barros Henriques

Supervisor: Prof. Dr. Eduardo Morilla Filipe

Member of the Commitee: Luís Filipe Guerreiro Martins

September 2015

II

III

Acknowledgements

I wish to show my sincere appreciation to those who assisted me on the way to complete this

thesis.

First of all, to my supervisor Prof. Dr. Eduardo Jorge Morilla Filipe for getting me involved

and interested in this research area and also for the wisdom, insights, teachings, comments,

encouragement and dedication; his help was vital to achieve the goals of this thesis.

Furthermore, to Prof. Dr. Clare McCabe and Prof. Dr. Peter Cummings, along with their

respective groups’ researchers, who welcomed me at MUMS in Nashville, and from whom I

learned a lot about modelling, simulation and group work. Also, to Dr. Pedro Morgado, for the

teachings on both experimental and simulation levels, expertise, suggestions, and patience,

from whom I learned an enormous amount and counted on when I had any doubts or problems.

I would also like to thank my nuclear family and close friends who always showed they

believed in my capabilities, for the support and encouraging words along the way.

IV

Resumo

A pressão de vapor de quatro 1H,1H-perfluoroálcoois líquidos (CF3(CF2)n(CH2)OH, n = 1, 2,

3, 4), frequentemente denominados álcoois fluorotelómeros ímpares, foi medida em função da

temperatura entre 278K e 328K. As densidades dos líquidos foram medidas numa gama de

temperatura de 278K a 353K. As entalpias molares de vaporização foram calculadas a partir

dos dados experimentais. Os resultados foram comparados com dados da literatura para outros

perfluoroálcoois assim como com os álcoois hidrogenados equivalentes. Os resultados foram

modelados usando simulações de dinâmica molecular e a equação de estado GC-SAFT-VR.

V

Abstract

The vapour pressure of four liquid 1H,1H-perfluoroalcohols (CF3(CF2)n(CH2)OH, n = 1, 2, 3,

4), often called odd-fluorotelomer alcohols, was measured as a function of temperature

between 278K and 328K. Liquid densities were also measured for a temperature range between

278K and 353K. Molar enthalpies of vaporization were calculated from the experimental data.

The results were compared with data from the literature for other perfluoroalcohols as well as

the equivalent hydrogenated alcohols. The results were modelled using molecular dynamics

simulations and the GC-SAFT-VR equation of state.

VI

Contents

Acknowledgements ............................................................................................................................. III

Resumo ................................................................................................................................................. IV

Abstract ................................................................................................................................................. V

List of Tables ..................................................................................................................................... VII

List of Figures .................................................................................................................................... VII

Nomenclature ................................................................................................................................... VIII

1 - Introduction ..................................................................................................................................... 1

2 - Experimental Techniques ............................................................................................................... 2

2.1 - Purification and Characterization .......................................................................................... 2

2.2 - Vapour Pressure Measurements ............................................................................................. 2

2.3 - Density Measurements ............................................................................................................. 2

3 - Theoretical Introduction and Application ..................................................................................... 3

3.1 - GC-SAFT-VR Theory and Molecular Model ........................................................................ 3

3.2 - Molecular Dynamics Simulations ............................................................................................ 6

4 - Results and Discussion .................................................................................................................... 7

4.1 - Vapour Pressures and Enthalpies of Vaporization ............................................................... 7

4.2 - Liquid Densities and Thermal Expansion Coefficients ....................................................... 12

5 - Conclusions..................................................................................................................................... 17

6 - Bibliography ................................................................................................................................... 18

VII

List of Tables

Table 1 – GC-SAFT-VR parameters ...................................................................................................... 5

Table 2. Experimental vapour pressures for 2:1, 3:1, 4:1 and 5:1 FTOH ............................................... 7

Table 3. Constants for the Antoine equation. .......................................................................................... 8

Table 4. Molar enthalpies of vaporization of 1H,1H-perfluoroalcohols. .............................................. 10

Table 5. Densities for 2:1, 3:1, 4:1 and 5:1 FTOH at atmospheric pressure. ........................................ 12

Table 6. Coefficients for equation 14.................................................................................................... 13

Table 7. Experimental and simulated liquid densities at 298.15 K and thermal expansion coefficients.

.............................................................................................................................................................. 13

List of Figures

Figure 1. Experimental vapour pressures for 2:1 (), 3:1(), 4:1() and 5:1 FTOH(); GC-SAFT-

VR predictions (lines). ............................................................................................................................ 7

Figure 2. Logarithmic representation of the vapour pressures with 1/T for: 2:1 FTOH, this work ()

and Meeks and Goldfarb18 (); 3:1 FTOH, this work (), Meeks and Goldfarb18 (). The lines are

linear (Clausius-Clapeyron) fits to our experimental results. ................................................................. 9

Figure 3. Molar enthalpies of vaporization for the FTOH family as a function of chain length; () this

work; () J. Costa et al.2; () Meeks and Goldfarb18. ........................................................................ 10

Figure 4. Molar enthalpy of vaporization of 2:1 FTOH, 3:1 FTOH, 4:1 FTOH and 5:1 FTOH from

experiment (), simulations () and GC-SAFT-VR predictions (). ................................................. 11

Figure 5. Comparison of the enthalpy of vaporization for fluorotelomer () and hydrogenated

alcohols (). ......................................................................................................................................... 11

Figure 6. Experimental liquid densities for 2:1 (,blue), 3:1(,red), 4:1(,green) and 5:1

FTOH(,purple), GC-SAFT-VR predictions (lines) and Simulation results (X). ................................ 12

Figure 7. Thermal expansion coefficient vs chain length. .................................................................... 14

Figure 8. Average number of hydrogen bonds per molecule vs chain length for: FTOH from this work

() and from [ref] with OPLS-AA (), hydrogenated alcohols with TraPPE21 () and OPLS-UA20

() force fields. .................................................................................................................................... 15

Figure 9. Dihedral distribution function around the C-O bond. ............................................................ 16

VIII

Nomenclature

2:1 FTOH – 1H,1H-perfluoropropan-1-ol

3:1 FTOH – 1H,1H-perfluorobutan-1-ol

4:1 FTOH – 1H,1H-perfluoropentan-1-ol

5:1 FTOH – 1H,1H-perfluoroheptan-1-ol

A – Helmholtz free energyA, B, C -

Antoine equation constants

a1, a2 - first and second order perturbation

terms for the monomeric excess Helmholtz

free energy

AA – All Atom model

AAD – Average Absolute Deviation

c3, c2, c1, c0 – Density fitting constants

CAS - Chemical Abstracts Service registry

number

ddf – dihedral distribution function

Econfig – Configuration Energy

EoS – Equation of State

FTOH - Fluorotelomer Alcohol

g(σ) – Radial distribution function

GC – Group Contribution

HB – Hydrogen Bonding

Hvap – Enthalpy of vaporization

K – Bonding volume between association

sites

kB – Boltzmann constant

mi – Functional group chain length

n – Number of components

N – Number of molecules

𝑛𝑘′ – Number of types of functional groups

in component k

𝑛𝑠′ – Number of sites on a given functional

group

NMR – Nuclear Magnetic Resonance

OPLS - Optimized Potentials for Liquid

Simulations force field

P, p – Pressure

PID - Proportional-integral-derivative

controller

R – Ideal gas constant

SAFT – Statistical Associating Fluid

Theory

SW – Square-Well

T – Temperature

TPT1 – Wertheim’s first-order

perturbation theory

UA – United Atom model

V – Volume

VR – Variable Range

X – Fraction of associated sites not bonded

xk – Mole fraction

y(σ) – Background correlation function

IX

Subscripts

a – Index for association sites

i, j – Index for functional group parameters

k, l – Index for molecular parameters

g – Gas state

l – Liquid state

exp – Experimental data

calc – Calculated data

lit – Data retrieved from literature

Superscripts

ideal – Ideal contribution

mono – monomer-monomer contribution

chain – chain contribution

assoc – association contribution

Greek Symbols

σ – Segment diameter

𝜀𝑖,𝑖𝐻𝐵 – Energy between association sites

𝜀𝑖,𝑖 – Square-well potential depth

λii – Square-well potential range

ρk – Number density

ρ – Mass density

Λ – de Broglie wavelength

νki – Number of each type of functional

group

α – Thermal expansion coefficient

ξij – Cross interaction parameter

γij – Cross interaction parameter

1

1 - Introduction

Highly fluorinated compounds have become important substances, both from the industrial and

fundamental points of view. Fluorinated alcohols in particular, find application in numerous

commercial products from textile protection agents and fire-fighting foams, to detergents,

paints, and as precursors in the production of fluorinated polymers.

Fluorotelomer alcohols are linear highly fluorinated molecules possessing a terminal OH

group, with the general formula, CF3(CF2)n(CH2)mOH (n+1:m FTOH). This molecular

structure results in an enhanced amphiphilic character compared to hydrogenated alcohols, as

fluorinated chains are known to be more hydrophobic than their hydrogenated analogues.

Fluorotelomers can be divided in two major groups: odd FTOH for m=1 and even FTOH for

m=2. In an effort to understand and model these molecules, experimental properties such as

vapour pressure and densities were measured and enthalpies of vaporization calculated.

This work is part of a project in which experimental measurements, molecular simulation

techniques and theoretical calculations, have been simultaneously used to elucidate the

properties of fluorinated substances and their mixtures. Using this approach, diffusion

coefficients have recently been reported of fluorinated alcohols in aqueous solutions1. The

behaviour of mixtures of fluorinated and hydrogenated alcohols has also been described. These

mixtures display a very complex behaviour when compared with mixtures of hydrogenated

alcohols and mixtures of alkanes and perfluoroalkanes. The excess volumes are large and

positive (unlike those of mixtures of hydrogenated alchools) while the excess enthalpies are

large and negative (contrasting with those of mixtures of alkanes and perfluoroalkanes)1. This

peculiar behaviour results from a balance between the weak dispersion forces between the

hydrogenated and fluorinated groups and a preferential hydrogen bond between the

hydrogenated and the fluorinated alcohols.

Following this line of work, we now present new experimental data for the vapour pressures

and liquid densities of four liquid 1H,1H-perfluoroalcohols (CF3(CF2)nCH2OH, n = 1, 2, 3, 4)

as a function of temperature. Molar enthalpies of vaporization were calculated from the

experimental data and the results compared with data from the literature for other

perfluoroalcohols as well as their equivalent hydrogenated alcohols. Vapour pressure

measurements had been previously reported for the longer chain (CF3(CF2)nCH2OH, n=5-9)

even fluorotelomers2, but for the short chain studied in this work, experimental data has not

been reported or is of insufficient accuracy. Molecular dynamics simulations were performed

in order to obtain a molecular level insight into the experimental results. Experimental molar

enthalpies of vaporization and densities were used to validate the force field used in the

molecular dynamics simulations. Additionally, the GC-SAFT-VR equation was used to predict

the experimental results. Excellent agreement has been found between the theoretical

predictions and the experimental results.

2

2 - Experimental Techniques

2.1 - Purification and Characterization

1H,1H-perfluoropropan-1-ol (2:1 FTOH, CAS number:422-05-9), 1H,1H-perfluorobutan-1-ol

(3:1 FTOH, CAS number:375-01-9), 1H,1H-perfluoropentan-1-ol (4:1 FTOH, CAS

number:355-28-2) and 1H,1H-perfluorohexan-1-ol (5:1 FTOH, CAS number:423-46-1) were

purchased from Apollo Scientific Ltd; a 98% purity was indicated for all the alcohols except

perfluoropentanol, for which a 97% purity was claimed. Prior to their use, the compounds

were dried with VWR Prolabo 4A molecular sieves to a maximum water content of 500 ppm

(analysed by Karl-Fischer coulometry) and their purity was confirmed by 1H and 19F NMR

spectroscopy.

2.2 - Vapour Pressure Measurements

The vapour pressure of the fluoroalcohols was measured in the 278 to 328K temperature range,

with the exception of the 3:1 FTOH that was measured from 298 to 328K. The measurements

were made using a static apparatus previously described3, which consists of a spherical glass

cell connected to a vacuum line and to a pressure transducer. The cell is immersed in a

thermostatic water bath controlled by a Hart Scientific 2100 PID temperature controller. The

temperature of the liquid was measured using a calibrated Pt100 temperature sensor connected

to a Keithley 2000 6½ digital multimeter, with an absolute uncertainty of 0.05K. The

temperature stability and uniformity during a measurement is estimated to be better than 0.01

K. The pressure was measured with a Paroscientific Series 1000 quartz absolute pressure

transducer connected to a Paroscientific model 715 display unit. The pressure sensor is capable

of measuring up to 100 psia (0.69MPa), with an accuracy of 0.0001% and has an automatic

temperature compensation system. While measuring, the connecting line between the glass cell

and the pressure transducer was kept at a higher temperature than the bath’s in order to avoid

condensation of the vapour.

The liquids were submitted to freezing in liquid nitrogen, vacuum pumping and melting cycles

to degas them. The samples were further purged to the vacuum line for a few seconds while

agitating the liquid. The procedure was repeated until the vapour pressure was reproducible,

confirming that no volatile species were present. The temperature was then changed and the

pressure recorded after stabilization. Measurements were made in paths of increasing and

decreasing temperature, in order to reduce the possibilities of systematic error.

2.3 - Density Measurements

The liquid densities of the fluoroalcohols were measured in an Anton Paar DMA 5000

vibrating-tube densimeter. The instrument was calibrated with water (distilled, purified with a

Mili-Q 185 plus water purification system, and freshly boiled) and air at 20.000 °C, taking into

account atmospheric pressure. The calibration was checked with water over the whole range of

operating temperatures, and the maximum deviation from literature values was found to be less

than 0.00002 g.cm-3. The density of air was verified at the beginning of each series of

measurements to ensure the cleanliness of the measurement cell.

3

3 - Theoretical Introduction and Application

3.1 - GC-SAFT-VR Theory and Molecular Model

The GC-SAFT-VR equation combines the SAFT-VR4 equation with a group contribution

(GC)5 approach that allows for the description of chains built up from segments of different

size and/or energy of interaction. This approach allows for the location of the functional groups

and association sites within a molecule to be specified, enabling the heterogeneity in molecular

structure to be captured within a SAFT model.

In the approach, molecules are described by tangentially bonded segments in which each type

of segment represents a functional group present in the molecule5, 6. The segments representing

each functional group interact via a square well potential, which can be described by

(1)

where uki,lj represents the interaction between a functional group of type i present in molecule

k with a functional group of type j in molecule l, is the segment diameter, is the depth of

the square well, is the potential range, and r is the distance between the two groups. The

unlike size and energy interactions can be obtained from the Lorentz-Berthelot combining rules

expressed by

(2)

(3)

and the unlike potential range is given by,

(4)

The GC-SAFT-VR equation of state is written in terms of the total Helmholtz free energy,

expressed as a sum of four separate contributions:

𝐴

𝑁𝐾𝐵𝑇=

𝐴𝑖𝑑𝑒𝑎𝑙

𝑁𝐾𝐵𝑇+

𝐴𝑚𝑜𝑛𝑜

𝑁𝐾𝐵𝑇+

𝐴𝑐ℎ𝑎𝑖𝑛

𝑁𝐾𝐵𝑇+

𝐴𝑎𝑠𝑠𝑜𝑐

𝑁𝐾𝐵𝑇 (5)

where N is the total number of molecules in the system, T is the temperature, and kB is the

Boltzmann constant. In equation 5, Aideal is the ideal free energy, Amono is the contribution to

the free energy due to the monomer segments, Achain is the contribution due to the formation of

bonds between monomer segments, and Aassoc is the contribution due to association. Since the

theory has been presented previously5, 7 only a brief overview of the main expressions are

provided below.

The ideal Helmholtz free energy, Aideal, is given by

4

𝐴𝑖𝑑𝑒𝑎𝑙

𝑁𝐾𝐵𝑇= ∑ 𝑥𝑘 ln 𝜌𝑘𝛬𝑘

3 − 1

𝑛

𝑘=1

(6)

where n is the number of compounds, 𝜌𝑘 the molecular number density of component k, 𝑥𝑘 the

mole fraction of component k and 𝛬𝑘 the thermal de Broglie wavelength.

The monomer free energy, Amono, is given by a second order high temperature expansion using

Barker and Henderson perturbation theory for mixtures8

𝐴𝑚𝑜𝑛𝑜

𝑁𝐾𝐵𝑇= ∑ ∑ 𝑥𝑘 𝜈𝑘𝑖𝑚𝑖 𝑎𝑀

𝑛𝑘′

𝑖=1

𝑛

𝑘=1

= ∑ ∑ 𝑥𝑘 𝜈𝑘𝑖𝑚𝑖 (𝑎𝐻𝑆 +𝑎1

𝐾𝐵𝑇

𝑛𝑘′

𝑖=1

𝑛

𝑘=1

+𝑎2

(𝐾𝐵𝑇)2) (7)

where 𝑛𝑘′ is the number of functional groups for component k, 𝜈𝑘𝑖 the number of type i

functional groups existent in component k, 𝑚𝑖 the functional group chain length and 𝑎𝑀 the

excess Helmholtz free energy per monomer segment, which is given by the sum of the hard

sphere free energy,𝑎𝐻𝑆, with the first-order, 𝑎1, and second-order, 𝑎2, perturbation terms

associated with the dispersion interactions given by the square-well potential.

The Helmholtz free energy due to the formation of a hetersegmented square-well (SW) chain

molecule is given by

𝐴𝑐ℎ𝑎𝑖𝑛

𝑁𝐾𝐵𝑇= − ∑ 𝑥𝑘 ∑ ln 𝑦𝑘𝑖,𝑘𝑗

𝑆𝑊 (𝜎𝑘𝑖,𝑘𝑗)

𝑛𝑘′

𝑖𝑗

𝑛

𝑘=1

(8)

where the second sum corresponds to the bonding between monomers within the chain k. The

last term of the equation is related to the radial distribution function, 𝑔𝑘𝑖,𝑘𝑗𝑆𝑊 (𝜎𝑘𝑖,𝑘𝑗) by

𝑦𝑘𝑖,𝑘𝑗𝑆𝑊 (𝜎𝑘𝑖,𝑘𝑗) = exp (−

𝜀𝑘𝑖,𝑘𝑗

𝐾𝐵𝑇) 𝑔𝑘𝑖,𝑘𝑗

𝑆𝑊 (𝜎𝑘𝑖,𝑘𝑗) (9)

where 𝜎𝑘𝑖,𝑘𝑗 and 𝜀𝑘𝑖,𝑘𝑗 are the diameter and well-depth calculated using the Lorentz-Berthelot

combining rules.

Finally, the contribution due to association9, (Aassoc), interactions between sites on different

functional groups that form the molecules of interest is expressed as

𝐴𝑎𝑠𝑠𝑜𝑐

𝑁𝐾𝐵𝑇= ∑ 𝑥𝑘 ∑ 𝜈𝑘𝑖

𝑛𝑘′

𝑖=1

𝑛

𝑘=1

∑ 𝑛𝑖𝑎

𝑛𝑠′

𝑎=1

(ln 𝑋𝑘𝑖𝑎 +1 − 𝑋𝑘𝑖𝑎

2) (10)

where 𝑎 is the association site type, 𝑛𝑠′ is the number of association sites and 𝑋𝑘𝑖𝑎 represents

the non-bonded fractions.

At this point, it is important to note that in the usual homonuclear model of SAFT the

contribution to the free energy due to bonding at separate sites are independent, and as such,

the location of sites on a molecule is arbitrary; the sites are in actuality averaged over the whole

molecule. However, in the GC-SAFT-VR equation, because of the hetero-segmented chain

model used, the location of the association sites can be specified on a given functional group

and hence their position within the model chain defined10.

5

With the Helmholtz free energy defined, thermodynamic properties such as pressure,

temperature, and chemical potential, can then be obtained using standard thermodynamic

relationships.

In this work, the liquids have been modeled using the GC-SAFT-VR equation implementing a

totally predictive approach. The fluoroalcohols, with formula CF3(CF2)nCH2OH, are comprised

of the CF3, CF2, CH2, and terminal OH groups. The parameters, number of spherical segments

forming the chains, the square-well parameters ε, σ, and λ, the association parameters, and the

binary interaction parameters that mediate the strength of the cross interactions were all taken

previous GC-SAFT-VR work5, 9, 11 where the parameters were determined by fitting to

experimental vapor pressure and saturated liquid density data for molecules containing the

groups of interest. Specifically, the alkanes were used to determine CH2 parameters,

perfluoroalkanes and perfluoroalkylalkanes the CF3 and CF2 parameters, and finally the

alcohols were used to determine the parameters for the terminal OH group. Utilizing this

approach, the GC-SAFT-VR theory is used to successfully predict, without any reliance on

experimental data, the thermodynamic properties of the fluoroalcohol molecules. To calculate

properties using the GC-SAFT-VR EoS for a pure compound with 1 type of association

functional group, 6 types of parameters (𝑚𝑖, 𝜎𝑖𝑖, 𝜀𝑖𝑖, 𝜆𝑖𝑖, 𝜀𝑖,𝑖𝐻𝐵, 𝐾𝑖,𝑖

𝐻𝐵) are required and are shown

on table 1. 𝜀𝑖,𝑖𝐻𝐵 and 𝐾𝑖,𝑖

𝐻𝐵𝑎re two of the inputs for the calculation of the associative term of the

Helmholtz free energy, in this case for the hydrogen bonding (HB) associative type.

𝜀𝑖,𝑖𝐻𝐵represents the energy between association sites while 𝐾𝑖,𝑖

𝐻𝐵 represents the volume available

for hydrogen bonding. The number of association sites for the terminal OH groups was set as

3 on account of the 2 non-bonding electron pairs and the electron deficient hydrogen atom.

Table 1 – GC-SAFT-VR parameters

Group 𝑚𝑖 𝜎𝑖𝑖 (Å) 𝜀𝑖𝑖/𝑘𝐵 (𝐾) 𝜆𝑖𝑖 𝜀𝑖,𝑖𝐻𝐵/𝑘𝐵 (𝐾) 𝐾𝑖,𝑖

𝐻𝐵(Å3)

OH (terminal) 0.176 5.299 534.805 1.495 2797 0.16014

CH2 0.333 4.041 237.230 1.667 - -

CF2 0.37 4.345 218.87 1.641 - -

CF3 0.685 4.618 315.56 1.321 - -

The binary interaction parameters that mediate the strength of the cross interactions between

CH2 and CF2 groups (ξij = 1.1 and γij = 0.86) were also taken from McCabe’s previous works.

6

3.2 - Molecular Dynamics Simulations

Molecular dynamics simulations consist of the solving of Newton’s equations of motion

numerically with the aid of a computing machine, in order to calculate thermodynamic

properties or to simply observe the evolution of a given system with time. For an all atom

simulation, the atoms are treated as particles that can interact with each other through bonded

and non-bonded interactions, characterized by potentials. Bonded interactions include the

harmonic bonding, angle bending and torsional potentials while the non-bonded interactions

are given by an electrostatic and dispersion potentials. The last two are usually described by

the Coulombic and Lennard-Jones potentials, respectively.

In this work, molecular dynamics simulations were carried out to obtain molecular-level

information on the behaviour of the studied systems, using an all atom force field based on

OPLS-AA12. For the perfluoroalkyl segments of the molecules, the OPLS-AA parameters from

Watkins and Jorgensen13 were used, while the -CF2CH2OH segment was modelled with the

parameters developed by Duffy for trifluoroethanol14, adjusting the partial charge of the

fluorinated carbon to maintain the neutrality of the molecule. The missing dihedral torsion

parameters, for the fluorinated-hydrogenated junction, were taken from the work of Pádua15.

The simulations were made using the DL_POLY16 Classic software package, in the NPT

ensemble at 1 atm and 298.15 K. Pressure and temperature were kept constant using the Nosé-

Hoover barostat and thermostat, with relaxation times of 2 and 0.5ps, respectively. A total of

20ns were simulated with a 2fs time step for the liquid phases. In the gas phases, for each

compound, 20 independent simulations of a single molecule system, started from different

initial configurations, were performed for 20ns each with 1fs time steps. A cut-off of 14Å was

used for the Lennard-Jones and Coulomb potentials, with analytic tail corrections applied for

the former and the Ewald sum method incorporated to calculate the long range interactions for

the latter.

The system densities were obtained directly from the average values of the box volume of the

NpT simulations, and the enthalpies of vaporization were calculated using equation 11

∆𝐻𝑣𝑎𝑝.𝑐𝑎𝑙𝑐𝑑 = 𝐸𝑐𝑜𝑛𝑓𝑖𝑔,𝑔 − 𝐸𝑐𝑜𝑛𝑓𝑖𝑔,𝑙 + 𝑅𝑇 (11)

where 𝐸𝑐𝑜𝑛𝑓𝑖𝑔,𝑔and 𝐸𝑐𝑜𝑛𝑓𝑖𝑔,𝑙 are the configurational molar energies of the liquid and gas phases

and RT corresponds to the PV-work term for an ideal gas. The work term for the liquid phase

is considered negligible. Gas and liquid phase simulations were performed to obtain the

configurational energies, which are the sum of the contributions of van der Waals, Coulomb,

bonding, angle and dihedral energies.

The average number of hydrogen bonds in the liquid fluorotelomer alcohols was obtained by

integration of the oxygen – hydroxyl hydrogen radial distribution functions (rdf), considering

all intermolecular O-H pairs with a distance lower than 2.67 Ǻ (the first minimum of the rdf)

as hydrogen bonded.1 The analysis of the molecular conformations was performed using the

Travis software17.

7

4 - Results and Discussion

4.1 - Vapour Pressures and Enthalpies of Vaporization

The experimental vapour pressures as a function of temperature of the studied FTOH are

reported in Table 2 and plotted in Figure 1.

Table 2. Experimental vapour pressures for 2:1, 3:1, 4:1 and 5:1 FTOH

2:1 FTOH 3:1 FTOH 4:1 FTOH 5:1 FTOH

T (K) Pvap (kPa) T (K) Pvap (kPa) T (K) Pvap (kPa) T (K) Pvap (kPa)

298.08 6.2055 278.14 0.7213 278.14 0.2236 278.14 0.0688

303.05 8.4158 283.10 1.0470 283.10 0.3363 283.10 0.1098

308.04 11.3058 288.08 1.4954 288.07 0.5020 288.08 0.1712

313.01 14.9656 293.08 2.1173 293.06 0.7329 293.08 0.2615

317.98 19.5864 298.10 2.9653 298.09 1.0700 298.13 0.3944

322.96 25.4116 303.07 4.0862 303.10 1.5312 303.10 0.5819

327.93 32.4857 308.04 5.5515 308.06 2.1523 308.06 0.8405

313.03 7.4728 313.02 2.9794 313.01 1.2052

317.98 9.9047 317.98 4.0707 317.98 1.7082

322.95 13.1446 322.99 5.4963 322.93 2.3494

327.91 17.2579 327.95 7.3149 327.93 3.2499

Figure 1. Experimental vapour pressures for 2:1 (), 3:1(), 4:1() and 5:1 FTOH(); GC-

SAFT-VR predictions (lines).

-4

-3

-2

-1

0

1

2

3

4

2,9E-03 3,1E-03 3,3E-03 3,5E-03 3,7E-03

ln (

P/kP

a)

1/T (K-1)

8

The experimental results were correlated with the Antoine equation

ln(𝑝/𝑘𝑃𝑎) = 𝐴 −𝐵

(𝑇/𝐾) + 𝐶 (12)

where p is the vapour pressure, T is the temperature and A, B and C are Antoine’s adjustable

constants. The obtained constants reproduce the vapour pressure data within the experimental

uncertainty and are presented in Table 3, along with the root mean square deviation (RMSD)

of the fit and the average percent deviation which is defined as:

(13)

where n is the number of experimental points.

Table 3. Constants for the Antoine equation.

The measured vapour pressures for 2:1FTOH and 3:1FTOH are compared with data from the

literature in figure 2. In this work we have measured the vapour pressure of 2:1 FTOH between

298 K and 328 K, complementing the data of Meeks and Goldfarb18 at a lower temperature

range, between 273 K and 298 K. As can be seen, both data sets compare favourably. As for

3:1 FTOH, however, the vapour pressure now reported is much lower than that of Meeks and

Goldfarb18. The relative differences can be as high as 100%, obviously much higher than the

uncertainties of both data sets. It is thus very unlikely that such a discrepancy is due to

experimental error and suggests the existence of a volatile impurity in the sample of Meeks and

Goldfarb18. The temperature dependence is also very different for both data sets and, as will be

shown, that of Meeks and Goldfarb18 is not consistent with those observed for the other

substances in the FTOH family.

Compound A B C RMSD kPa) p/p (%)

2:1 FTOH 15.439 2931.877 -82.748 0.015 0.1

3:1 FTOH 18.821 4808.731 -26.973 0.035 0.2

4:1 FTOH 16.278 3608.616 -75.398 0.004 0.5

5:1 FTOH 25.162 8615.885 31.895 0.042 1.7

9

Figure 2. Logarithmic representation of the vapour pressures with 1/T for: 2:1 FTOH, this work

() and Meeks and Goldfarb18 (); 3:1 FTOH, this work (), Meeks and Goldfarb18 (). The

lines are linear (Clausius-Clapeyron) fits to our experimental results.

The GC-SAFT-VR predictions for the vapour pressure of the fluoroalcohols are compared with

the experimental data in figure 1. As can be seen, the theory is able to reproduce the vapour

pressure in close agreement with the experimental results. It should be emphasized that the

theoretical results are pure predictions, as none of the model parameters was fitted to the

experimental data.

The enthalpies of vaporization of the studied FTOH were estimated from the vapour pressure

data using the Clausius-Clapeyron equation, assuming that the enthalpy of vaporization is

constant in the measured temperature range and that the vapour phase behaves as an ideal gas.

This should be a reasonable approximation since the measured pressures are very low. The

calculated enthalpies of vaporization are reported in table 4 and plotted in figure 3. Also shown

in figure 3 are the enthalpies of vaporization from the literature2, 18 for 1:1 FTOH, 2:1 FTOH,

3:1 FTOH and for longer chain alcohols from 6:1 FTOH to 10:1 FTOH. As can be seen, the

vaporization enthalpy for the FTOH family increases almost linearly with chain length,

displaying an average increment of 4.8 kJ per each additional CF2 group. The vaporization

enthalpy of 2:1 FTOH of Meeks and Goldfarb18 is 4% higher than the value now reported. It

can also be seen that the vaporization enthalpy of 3:1 FTOH deviates from the linear correlation

and is 11% higher than our value. We interpret this deviation as a further confirmation that the

vapour pressure data of Meeks and Goldfarb18 for 3:1 FTOH is inaccurate, probably due to the

presence of a volatile impurity.

-1

0

1

2

3

4

0,003 0,0032 0,0034 0,0036

ln (

p/k

Pa)

1/T (K-1)

10

Table 4. Molar enthalpies of vaporization of 1H,1H-perfluoroalcohols.

Figure 3. Molar enthalpies of vaporization for the FTOH family as a function of chain length;

() this work; () J. Costa et al.2; () Meeks and Goldfarb18.

The enthalpies of vaporization obtained from the simulations and GC-SAFT-VR calculations

are also reported in table 4 and compared with the experimental results in figure 4. As can be

seen, the simulations are able to reproduce the experimentally observed trend, increasing with

molecular weight, but overestimate the vaporization enthalpies by 4 to 10%, which can be

considered quite good. The GC-SAFT-VR approach was also used in a purely predictive

manner to calculate the enthalpies of vaporization using the Clausius-Clapeyron equation with

the vapour pressure results in the 278 K to 328 K temperature range. The GC-SAFT-VR EoS

is also able to reproduce the enthalpies of vaporization with very good agreement, with

deviations of no more than 4%.

40

50

60

70

80

90

2 3 4 5 6 7 8 9 10 11 12

∆𝐻

vap

/ kJ

.mo

l-1

# Carbons

Compound T / K Hvap,exp / kJ mol-1 Hvap,SAFT / kJ

mol-1

Hvap,sim / kJ

mol-1 Hvap,lit / kJ mol-1

1:1 FTOH 285.7 - - - 44.518

2:1 FTOH 313.01 45.1±0.2 46.5 47.1±1.2* 46.9 (284.8K)18

3:1 FTOH 303.04 48.3±0.1 49.6 53.2±1.0* 43.5 (285.6K)18

4:1 FTOH 303.05 53.5±0.2 53.2 59.0±0.8* -

5:1 FTOH 303.05 59.1±0.2 57.0 61.9±0.8* -

6:1 FTOH 298.15 - - - 64.62

7:1 FTOH 298.15 - - - 68.42

8:1 FTOH 298.15 - - - 72.42

9:1 FTOH 298.15 - - - 80.52

10:1 FTOH 298.15 - - - 84.42

*Calculated at 298.15 K.

11

Figure 4. Molar enthalpy of vaporization of 2:1 FTOH, 3:1 FTOH, 4:1 FTOH and 5:1 FTOH

from experiment (), simulations () and GC-SAFT-VR predictions ().

Finally, the enthalpies of vaporization of the fluorinated alcohols are compared with those of

their hydrogenated counterparts in figure 5. As can be seen, for hydrogenated alcohols the

enthalpies of vaporization are higher and also follow a linear trend with approximately the

same slope as the fluorinated ones. The lower vaporization enthalpies observed for the

fluorinated alcohols are consistent with the hypothesis that these compounds display a slightly

lesser degree of hydrogen bonding than their hydrogenated counterparts, which gives the liquid

phase a lower cohesiveness. Moreover, the intramolecular gauche interactions between the

positively charged hydroxyl H and the electronegative fluorine atoms may stabilize these

molecules in the gas phase19, also contributing to a smaller enthalpy of vaporization.

Figure 5. Comparison of the enthalpy of vaporization for fluorotelomer () and hydrogenated

alcohols ().

40

45

50

55

60

65

2 3 4 5 6 7

∆𝐻

vap

/ kJ

.mo

l-1

# Carbons

40

50

60

70

80

90

2 3 4 5 6 7 8 9 10 11 12

𝐻

vap

/ kJ

.mo

l-1

#Carbons

12

4.2 - Liquid Densities and Thermal Expansion Coefficients

The experimental liquid densities for 2:1, 3:1, 4:1 and 5:1 FTOH are collected in table 5 at 5 K

intervals, in the 278 K - 353 K temperature range, and plotted in figure 6.

Table 5. Densities for 2:1, 3:1, 4:1 and 5:1 FTOH at atmospheric pressure.

2:1 FTOH 3:1 FTOH 4:1 FTOH 5:1 FTOH

T (K) (g.cm-3) T (K) (g.cm-3) T (K) (g.cm-3) T (K) (g.cm-3)

278.156 1.542779 278.155 1.633587 278.150 1.689575 278.151 1.746400

283.147 1.533693 283.148 1.624226 283.149 1.680180 283.148 1.737071

288.146 1.524473 288.147 1.614728 288.147 1.670671 288.147 1.727618

293.146 1.515119 293.147 1.605106 293.148 1.661048 293.149 1.718063

298.146 1.505629 298.146 1.595340 298.149 1.651303 298.148 1.708376

303.147 1.495975 303.148 1.585414 303.148 1.641419 303.148 1.698566

308.146 1.486147 308.146 1.575323 308.148 1.631401 308.149 1.688624

313.145 1.476122 313.145 1.565049 313.148 1.621228 313.148 1.678543

318.147 1.465891 318.147 1.554576 318.149 1.610899 318.148 1.668318

323.145 1.455434 323.145 1.543907 323.148 1.600404 323.148 1.657947

328.146 1.444737 328.146 1.533018 328.148 1.589737 328.149 1.647416

333.144 1.433788 333.145 1.521908 333.148 1.578896 333.148 1.636724

338.144 1.422580 338.144 1.510567 338.148 1.567872 338.148 1.625880

343.149 1.411103 343.145 1.498990 343.148 1.556652 343.148 1.614863

348.146 1.399338 348.145 1.487165 348.150 1.545153 348.149 1.603675

353.145 1.387286 353.145 1.475083 353.146 1.533524

Figure 6. Experimental liquid densities for 2:1 (,blue), 3:1(,red), 4:1(,green) and 5:1

FTOH(,purple), GC-SAFT-VR predictions (lines) and Simulation results (X).

1,3

1,4

1,5

1,6

1,7

1,8

270 290 310 330 350

/

g.cm

-3

T (K)

13

Third degree polynomial equations were fitted to the experimental densities in the measured

temperature range. The fitting constants are recorded in table 6.

𝜌(𝑔. 𝑐𝑚−3) = 𝑐3𝑇3 + 𝑐2𝑇2 + 𝑐1𝑇 + 𝑐0 (14)

Table 6. Coefficients for equation 14.

Compound c3 c2 c1 c0

2:1 FTOH -1.913547E-08 -1.825856E-06 -1.787961E-03 1.551769

3:1 FTOH -1.419722E-08 -2.102733E-06 -1.838069E-03 1.642826

4:1 FTOH -1.122842E-08 -1.792072E-06 -1.851884E-03 1.698887

5:1 FTOH -6.976345E-09 -2.023707E-06 -1.835124E-03 1.755626

The liquid densities obtained by molecular dynamics at 298.15 K are compared with the

experimental data in table 7 and in figure 6. The simulations are able to predict the density with

deviations of less than 2% to the experimental results, which are well within the density

deviations obtained in the original OPLS-AA work12. This result, together with the fairly good

estimates obtained for the vaporization enthalpies, validates the molecular model used in the

simulations.

The GC-SAFT-VR predictions for the liquid density of the fluoroalcohols are compared with

the experimental data in figure 6. The theoretical predictions can be considered very good,

specially if it is taken into account that no fitting parameters were introduced in the calculations.

Again it should be realised that a better agreement could be achieved if specific binary

interaction parameters were adjusted for each substance. This however, is not the purpose of

the present work.

Table 7. Experimental and simulated liquid densities at 298.15 K and thermal expansion

coefficients.

Substance exp (g.cm-3) sim (g.cm-3) (K-1).103

2:1 FTOH 1.505624 1.502 1.40

3:1 FTOH 1.595328 1.603 1.35

4:1 FTOH 1.651294 1.679 1.28

5:1 FTOH 1.708357 1.730 1.21(T=313.15K)

14

Finally, in figure 7 the thermal expansion coefficients, , obtained from the temperature

dependence of the experimental liquid densities, are plotted as a function of chain length. This

dependency was fitted with a cubic polynomial function and the expansion coefficient was

obtained from the average of the derivatives at each data point, considering the correspondent

temperature as the mean of the interval. As could be expected, decreases with the increase in

the chain length.

Figure 7. Thermal expansion coefficient vs chain length.

1,20

1,25

1,30

1,35

1,40

1,45

2 3 4 5 6 7

α(K

-1).

10

3

# Carbons

15

4.4 - Molecular Simulations

The average number of hydrogen bonds per fluorotelomer alcohol molecule (nHB) was obtained

from the molecular dynamics trajectories. These results are represented in figure 8, along with

the results for ethanol, butanol and trifluoroethanol from another work of our group20, using

the OPLS-AA forcefield, and simulation results from the literature for methanol and ethanol

using OPLS-UA21 and for ethanol to hexanol using TraPPE22. For the hydrogenated alcohols,

as can be seen, it is not possible to discern a clear tendency for the average number of hydrogen

bonds; however, it is interesting to note that whenever a direct comparison can be made, the

results essentially agree despite the different molecular models used and the slightly different

criteria used for identifying hydrogen bonds. The fluorinated alcohols, however, seem to

present an increasing number of hydrogen bonds as the chain grows, but always remaining

below the values for the alkanols. This lower number of hydrogen bonds in the liquid phase

may contribute to the also lower enthalpies of vaporization observed.

Figure 8. Average number of hydrogen bonds per molecule vs chain length for: FTOH from

this work () and from reference 20 with OPLS-AA (), hydrogenated alcohols with

TraPPE22 () and OPLS-UA21 () force fields.

The conformational equilibrium of the studied fluoroalcohols, specifically the probability

distribution around the rotation of the carbon-oxygen bond, was also obtained from the

simulations for the liquid and the gas phases. This probability distribution, denominated

dihedral distribution function (ddf), is shown in figure 9 in a symmetric representation where

180 degrees corresponds to the fully trans conformation, with the hydroxyl hydrogen pointing

away from the rest of the molecule and 0 degrees is the opposite configuration, with the

hydroxyl hydrogen pointing towards the second carbon atom. It can be seen that the ddf are

similar for all the fluoroalcohols and that in the gas phase it consists of a single peak, centered

around 70 degrees, which corresponds to a gauche conformer; outside this peak, the probability

of finding a given conformer is very low. In the liquid phase, the gauche-like peak shifts to

higher angles, centering now around 90 degrees, and there is now a significant probability of

1,5

1,6

1,7

1,8

1,9

2

0 1 2 3 4 5 6 7

nH

B

# Carbons

FTOH's

OPLS-AA

Trappe

OPLS-UA

16

finding transoid conformers, with dihedral angles close to 180 degrees. This conformational

equilibrium shift is determined by the intermolecular interactions, since the higher dihedral

angles favour the formation of intermolecular hydrogen bonds by H-donation. In the gas phase,

however, the gauche conformations increase the intramolecular electrostatic interactions

between the hydroxil hydrogen and the negatively charged fluorine atoms of the alcohol chain,

lowering the energy of the molecule in the vapour. This kind of interaction does not exist in

the fully hydrogenated alcohols, and certainly contributes to the lower enthalpy of vaporization

observed in the studied fluorinated alcohols.

Figure 9. Dihedral distribution function around the C-O bond.

0 30 60 90 120 150 180

±θ (CCOH)

F3OH_liq

F4OH_liq

F5OH_liq

F6OH_liq

F3OH_gas

F4OH_gas

F5OH_gas

F6OH_gas

17

5 - Conclusions

The vapour pressure of 1H,1H-perfluoroalcohols (CF3(CF2)n(CH2)OH, n = 1, 2, 3, 4) was

measured in the temperature range between 278 K and 328 K. A comparison of the vapour

pressures with previous literature18 results showed good agreement for 2:1 FTOH but a very

significant discrepancy of for 3:1 FTOH, leading to the conclusion that the sample used by

Meeks and Goldfarb18 might have contained volatile impurities. Enthalpies of vaporization

were calculated from the experimental data and a linear dependency with chain length was

observed for the odd fluorotelomer alcohols family, much like the dependency for alkanols and

with roughly the same slope, while comparatively lower in absolute value. An explanation for

these lower enthalpies of vaporization is a lower degree of intermolecular hydrogen bonding

which contributes to a lower aggregation of the liquid molecules.

The results were interpreted with the GC-SAFT-VR5 EoS using a purely predictive approach

and a very good agreement for the vapour pressures and enthalpies of vaporization was

obtained. Liquid density curves were also obtained with this EoS with a good degree of

agreement.

Molecular dynamics simulations were performed using the OPLS-AA12 force field and used to

calculate properties such as enthalpies of vaporization and room temperature densities. The

results showed a satisfactory compliance with the experimental results, particularly for the

liquid densities whose deviations are of the same order as the ones of the original OPLS-AA

work. Further analysis of the simulation results showed that the number of hydrogen bonds

seems to increase with chain length while always remaining lower than that observed for the

hydrogenated counterparts, which may contribute to the lower enthalpy of vaporization

observed for the fluorinated alcohols. The dihedral distribution functions (ddf) were also

obtained around the C-O bond from the simulation data and showed a similar results for all the

fluoroalcohols studied. A comparison between the liquid and gas phase dihedral distribution

functions, however, presented significant differences as a single peak at 70o was obtained for

the gas phase, corresponding to the gauche conformation, while for the liquid phase, the first

peak is at 90o, corresponding to a gauche-like conformation but with a much broader possibility

of conformations available for higher angles. The gauche conformation between the hydroxyl

positive hydrogen and the partially negative fluorines of the gas phase molecules that leads to

an overall lower enthalpy further supports the lower enthalpies of vaporization obtained for the

fluorinated alcohols when compared to the hydrogenated ones.

18

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