Vapor Pressure of Perfluoroalkylalkanes: The Role of the DipolePedro Morgado,† Gaurav Das,‡ Clare McCabe,‡,§ and Eduardo J. M. Filipe*,†

†Centro de Química Estrutural, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal‡Department of Chemical and Biomolecular Engineering and §Department of Chemistry, Vanderbilt University, Nashville, Tennessee37235, United States

ABSTRACT: The vapor pressure of four l iquid perfluoroalkyla lkanes(CF3(CF2)n(CH2)mCH3; n = 3, m = 4,5,7; n = 5, m = 5) was measured as a function oftemperature between 278 and 328 K. Molar enthalpies of vaporization were calculated fromthe experimental data, and the results were compared with data from the literature for thecorresponding alkanes and perfluoroalkanes. The heterosegmented statistical associatingfluid theory was used to interpret the results at the molecular level both with and withoutthe explicit inclusion of the dipolar nature of the molecules. Additionally, ab initiocalculations were performed for all perfluoroalkylalkanes studied to determine the dipolemoment to be used in the theoretical calculations. We demonstrate that the inclusion of adipolar term is essential for describing the vapor−liquid equilibria of perfluoroalkylalkanes.It is also shown that vapor−liquid equilibria in these compounds result from a subtle balance between dipolar interactions, whichdecrease the vapor pressure, and the relatively weak dispersive interactions between the hydrogenated and fluorinated segments.

1. INTRODUCTION

Perfluoroalkylalkanes (PFAAs) are diblock compounds formedby hydrogenated and fluorinated hydrocarbon segments thatare covalently bonded together to form a single molecule. Theydisplay a wide range of interesting properties, from surfactantactivity toward alkane−perfluoroalkane liquid−liquid interfacesto the ability to self-organize, forming liquid crystals, micelles,and nanostructured monolayers, etc.1−5 At the origin of theseproperties lies the yet unexplained “antipathy” between thefluorinated and hydrogenated segments. Allied to theirchemical inertness and biocompatibility, PFAAs have becomeuseful in a range of applications from components of artificialblood substitutes to fluids in eye surgery and liquid ventilation.Being the simplest molecules exhibiting such complex behavior,PFAAs have garnered strong interest from the scientificcommunity.Despite the practical and fundamental interest in PFAAs,

there is a surprising gap in the knowledge of theirthermophysical properties and chiefly of their vapor pressures.In fact, the only data that can be found in the literature is forthe vapor pressure curve of 1,1,1-trifluoroethane (CH3CF3)

6

and a vapor pressure correlation for perfluorobutylethane(F4H2).7 Besides being an essential property to some of theabove-mentioned biomedical applications, the design ofindustrial separation processes such as distillation, and eventhe assessment of the environmental impact of thesecompounds, requires such data. Furthermore, the knowledgeof the vapor pressure (and/or the related vaporizationenthalpy) is crucial for the development and testing ofmolecular model (or force field) parameters to be used incomputer simulations of PFAAs or molecular-based theoreticalcalculations.This work is part of a systematic study of the thermophysical

properties of PFAAs with different relative hydrogenated and

fluorinated segment lengths. In previous work we reporteddensities as a function of temperature and pressure,8,9 andviscosities as a function of temperature10 for perfluorobutyl-pentane (F4H5), perfluorobutylhexane (F4H6), perfluorobu-tyloctane (F4H8), perfluorohexylhexane (F6H6), and perfluor-ohexyloctane (F6H8). The density results were interpreted interms of the volumes of the constituent hydrogenated andperfluorinated segments corrected for the corresponding excessvolumes and the volume contribution of the CH2−CF2junction. Using the same strategy, the viscosity data wasinterpreted from the contributions to the viscosity due to theCF3, CF2, CH2 ,and CH3 groups, and the differences foundbetween calculated and experimental viscosities were rational-ized in terms of the contribution of the CH2−CF2 bond and thedeviations from ideality seen in mixtures of n-alkanes andperfluoroalkanes.As for mixtures involving PFAAs, partial molal volumes for

the same series of PFAAs (F4H5, F4H6, F4H8, F6H6, F6H8)plus perfluorodecyloctane (F10H8) and perfluorooctyloctade-cane (F8H18) were measured in n-octane at 25 °C.11,12 It wasfound that whereas for perfluoroalkanes the partial molarvolumes at infinite dilution in n-octane are 13% higher than thecorresponding pure molar volumes, for PFAAs this increment isonly about 5%. Again, the results were rationalized in terms ofthe partial molar volumes at infinite dilution of thecorresponding hydrogenated and perfluorinated segments andthe contribution from the CH2−CF2 link. It was found that thecontribution to the volume of the diblock junction isindependent of chain length of the hydrogenated segmentbut decreases with the chain length of the fluorinated segment.

Received: October 31, 2014Revised: December 18, 2014Published: December 19, 2014

Article

pubs.acs.org/JPCB

© 2014 American Chemical Society 1623 DOI: 10.1021/jp5109448J. Phys. Chem. B 2015, 119, 1623−1632

Additionally, these systems were studied with the hetero-segmented statistical associating fluid theory (hetero-SAFT-VR) equation of state, which describes the molecules as diblockheteronuclear chains within the SAFT-VR framework.13,14 Themodel parameters for the alkyl and perfluoroalkyl segments andthe binary interaction parameters between the segments wereobtained by fitting to the phase behavior of pure alkanes,perfluoroalkanes, and their mixtures.15−17 Through this simpleapproach, the densities and partial molal volumes of PFAAswere predicted and the results found to be in close agreementwith the experimental results without fitting to experimentaldata for the systems being studied.In this work, the vapor pressure of four liquid PFAAs was

measured as a function of temperature from 278 to 328 K. Thedata was correlated with appropriate equations, and thecorresponding enthalpies of vaporization were estimated. Thehetero-SAFT-VR approach has again been used to predict thevapor pressures and densities of the PFAAs studied. While inprevious studies the contribution of the dipole moment to thephysical properties of PFAAs was not considered, here thiscontribution was explicitly taken into account for the first time.It should be emphasized that the combined presence ofhydrogenated and fluorinated segments, which are essentiallynonpolar, gives rise to a charge distribution corresponding to aconsiderable dipole that in the case of CH3CF3 (F1H1) is 2.32D.18 This electrical moment leads to additional cohesion in theliquid phase, which should be especially important in therationalization of a property such as the vapor pressure. As itwill be shown, the inclusion of a dipolar term brings the hetero-SAFT-VR predictions to much closer agreement with theexperimental vapor pressures, demonstrating the importance ofthe dipole contribution to the interaction between PFAAmolecules. Finally, the present results also reveal the potentialimportance of including a dipolar term in the modeling of otherphysical properties of PFAAs (e.g., surface tension andviscosity) and perhaps more importantly when describing theinteraction of PFAAs with other dipolar molecules, water inparticular.

2. EXPERIMENTAL SECTIONPerfluorobutylpentane (F4H5), perfluorobutylhexane (F4H6),perfluorobutyloctane (F4H8), and perfluorohexylhexane(F6H6) were ultrapurified chemicals obtained from FluoronGMBH, with a claimed purity of 100%. 19F and 1H NMRspectra of these compounds were obtained, and only very smallunexpected peaks were found which, when integrated,corresponded to much less than 1% of the main peaks.The vapor pressures were measured using the static method,

in an apparatus that essentially consists of a 20 cm3 sphericalglass cell connected to a pressure sensor and a vacuum line.During the measurements, the sample cell was immersed in awater thermostatic bath equipped with a Hart Scientific 2100digital PID temperature controller. The temperature stabilityand uniformity during a measurement is estimated to be betterthan 0.01 K. The temperature of the liquid sample wasmeasured with a calibrated platinum (Pt100) thermometer,connected to a Keithley 2000 6-1/2-digit digital multimeter,with a total uncertainty of 0.05 K. Pressure measurements weremade with a Paroscientific Series 1000 quartz absolute pressuretransducer connected to a Paroscientific Model 715 displayunit. The pressure sensor used has a range of 100 psia (0.69MPa), accuracy better than 0.01% of the full scale, a resolutionof 0.0001%, and automatic temperature compensation. During

measurements, both the pressure sensor and the connectingline are maintained above the sample temperature to avoidcondensation of the vapor. The glass part of the apparatus thatis exposed to the sample vapor during measurement ismaintained immersed in the thermostatic bath.All liquids were degassed by submitting them to cycles of

freezing in liquid nitrogen, vacuum pumping, and melting. Thiswas followed by directly pumping the samples for a few secondswhile agitating the liquid. The procedure was repeated until themeasured vapor pressure was reproducible, ensuring that novolatile species were present. The temperature was thenchanged and the pressure recorded after stabilization. Measure-ments were made in paths of increasing and decreasingtemperature in order to reduce the possibilities of systematicerror.

3. THEORYIn previous work, PFAA molecules were modeled as diblockchains of tangentially bonded hard spherical heterogeneoussegments that interact through square-well (SW) interactions.Here, to explicitly capture polar interactions, the monomersegments interact through both dispersive SW and dipolarinteractions, as illustrated in Figure 1.

As can be seen from Figure 1, in the proposed dipolar modelfor PFAAs the two fluorinated segments at the CF2−CH2juncture are considered to have an electric dipole orientedparallel to the axis joining the segments, with the dipolemoment divided equally between the two segments. Thismodel was chosen based on electron density maps determinedfor PFAA molecules that provide molecular level insight intothe electrostatics of the PFAA molecules.19 The dipolar natureof the molecule is described by the combination of the SAFT-VR+D equation with the hetero-SAFT-VR framework.13,20

SAFT-VR+D is based on a version of SAFT-VR that wasdeveloped to model dipolar fluids by explicitly accounting fordipolar interactions and their effect on the thermodynamics andstructure of a fluid. This is achieved through the use of thegeneralized mean spherical approximation (GMSA) to describea monomer fluid of nondipolar and dipolar square-wellsegments enabling the study of pure fluids and mixtures ofdipolar associating fluids of arbitrary size and dipole mo-ment.21−23

The potential model for the intermolecular interactions isgiven by

= +u r u r u r( ) ( ) ( )SW dipole(1)

where the SW potential is given by

σ

ε σ λ σ

λ σ

=

+∞ <

− ≤ <

≥

⎧⎨⎪⎪

⎩⎪⎪

U r

r

r

r

( )

if

if

0 ifij

ij

ij ij ij ij

ij ij (2)

Figure 1. Schematic representation of a PFAA molecule. Silver spheres(left) represent fluorinated segments and golden spheres (right)represent hydrogenated segments. Two fluorinated segments at theCF2−CH2 junction contain embedded dipoles.

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and εij and λij are the attractive SW depth and range parameters,respectively, and σij is the hard sphere diameter. For thecalculation of the inter- and intramolecular cross interactionsbetween segments, a modified set of Lorentz−Berthelotcombining rules24 has been used

σσ σ

=+2ij

ii jj

(3)

ε ξ ε ε=ij ij ii jj (4)

λ γλ σ λ σ

σ=

+2ij ij

ii ii jj jj

ij (5)

where ξij and γij are the unlike cross-interaction parameters.The dipole−dipole potential is a long-range anisotropic

interaction that is expressed as

ω ωμ μ

= − ur

Dr n n r( ) ( )i j

ijij 1 2 ij

dipole1 2 3

(6)

where

= · · − ·D n n r n r n r n n( ) [3( )( ) ]ij 1 2 ij 1 ij 2 ij 1 2 (7)

In eqs 6 and 7, r ij is the unit vector in the direction of rij and niis a unit vector parallel to the dipole moment of segment i.In the SAFT theoretical framework, the Helmholtz free

energy is given as

= + + +ANk T

ANk T

ANk T

ANk T

ANk Tb

ideal

b

mono

b

chain

b

assoc

b (8)

where N is the total number of molecules, kb the Boltzmannconstant, and T the temperature; Aideal, Amono, Achain, and Aassoc

are the free energy contributions due to the ideal, monomer,chain, and association interactions, respectively. Because of thenonassociating nature of the PFAA molecules, the free energycontribution due to association (Aassoc) is not included in thiswork. We briefly consider each of the remaining terms in turn.The ideal Helmholtz free energy is given by

ρ= Λ −ANk T

ln( ) 1ideal

b

3

(9)

where ρ = N/V is the molecular number density and Λ thethermal de Broglie wavelength which incorporates the kinetic(translational, rotational, and vibrational) contributions to thepartition function of the molecule.Following the SAFT-VR+D approach, the contribution to

the Helmholtz free energy due to monomeric interactionbetween segments is given by

= = + ′ANk T

mAN k T

ma m amono

b

mono

s b

SW dipole

(10)

where Ns represents the total number of segments in themixture, obtained by multiplying the number of molecules (N)with the total number of segments per molecule (m). Theexcess Helmholtz free energy per monomer (amono) has twokinds of contributions: isotropic square-well (aSW) andanisotropic dipolar (adipole). m′ is the number of segmentswith dipolar interactions.The isotropic contribution to the monomer free energy is

given by

β β= + +a a a a( )SW HS1

22 (11)

where aHS is the free energy due to hard sphere monomericinteractions; a1 and a2 are the SW attractive first- and second-order perturbation terms, respectively; and β = (1/kbT). For adetailed description of the isotropic SW term, the reader isdirected to the original papers.15,16,25

The anisotropic dipolar contribution is obtained from thesolution of the Ornstein−Zernike equation for dipolar hardspheres of arbitrary size using the mean spherical approx-imation (MSA) closure.26 For the symmetric case when all ofthe segments have the same diameter and dipole moment, thesolution agrees with that proposed by Wertheim.27 TheHelmholtz free energy of a mixture of dipolar segments isgiven as

∫∑ ∑β

β β= − ′ ′β

= =

a x x y k3

( ) di

n

j

n

i j ij ijdipole

1 1ps, ps,

0

polar polar

(12)

where npolar represents the number of polar segments in thesystem; xps,i is the segment fraction of the ith polar segment, yijthe strength of the dipolar effects, and kij the scaling parameter.The so-called strength of the dipolar effect yij is given by

πβρ μ μ ρ=y

4

9iji i j jps,1/2

ps,1/2

(13)

where ρps,i and μi are the segment density and dipole momentof the ith polar segment, respectively. The scaling parameter kijis given by

∫=∞

kh r

rr

310

( )dij

ij

0

112

(14)

where h ij112(r) is the expansion coefficient of the totalcorrelation function. A more detailed description of the dipoleterm can be found in the original papers.21,23,26,27

The Helmholtz free energy contribution due to the chainformation is given by21,25

σ σ

σ σ

= − + ′ −

+ − ′ − − −

ANk T

m g m m g

m g g

(1 ) ln ( ) ( ) ln ( )

(1 ) ln ( ) ln ( )

chain

bCH CH

SWCH CF CF CF

SWCF

CF CFDSW

CF CF CHSW

CF CH (15)

where gDSW(r) and gSW(r) correspond to the radial distributionfunction (RDF) at the contact value for the dipolar square-welland square-well monomer fluid, respectively. mCH, mCF, mCF′represent the number of CH segments, CF segments, anddipolar CF segments, respectively. We note that in this workthe linearized version of the exponential (LEXP)28 approx-imation has been used to determine the RDF of the dipolarsquare well fluid.

4. AB INITIO CALCULATIONSDipole moments for each of the PFAA molecules studied wereobtained from ab initio calculations. Previously, Jorgensen etal.29 performed structural optimization (HF/6-31G*) andsingle-point energy (LMP2/cc-pVTZ(-f)) calculations forseveral perfluoroalkanes. The torsional energy profiles for thelinear CCCC dihedral was found to exhibit an energy minimaaround 170°. Subsequently, Padua30 investigated the torsionalenergy profile of several diblock PFAAs and found the energyminima to be around 180° for the CF−CF−CH−CH dihedralin F2H2.

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In this work, the geometry of the PFAAs has been optimizedusing Gaussian 09 and the same level of theory (HF/6-31G(d))as used in the work of Padua27 and the dipole moments of thestructures then calculated. As an example, an optimizedconformation of one of the compounds studied, F4H5, isshown in Figure 2. From this figure, we can note that the linear

(all trans) conformation of the hydrogenated side of the chainand the helical conformation of the fluorinated side, as well asthe CF−CF−CH−CH and CF−CF−CF−CF dihedrals obtained,are in good agreement with earlier work.31,32

The calculated dipole moments of the PFAA moleculesstudied are reported in Table 1. As can be seen from the table,

the calculations for CH3CF3 (F1H1) predict a dipole momentthat is in good agreement with the reported experimentalvalue,18 thus providing confidence in the estimated values forthe other PFAAs. The obtained values for the dipole momentsslightly increase with the length of both the fluorinated and thehydrogenated segments, suggesting that longer chains induce alarger asymmetry in the electronic distribution at thehydrogenated−fluorinated junction.

5. RESULTS AND DISCUSSIONThe experimental unsmoothed vapor pressures of the PFAAsstudied, as a function of temperature, are presented in Table 2and plotted in Figure 3. As expected, the volatility decreaseswith the length of the carbon chain. When two PFAAs (F4H8and F6H6) molecules have the same total chain length, the one

with the largest fluorinated segment has the highest vaporpressure. This is to be expected because all perfluoroalkaneslonger than perfluoropropane are more volatile than thecorresponding alkane with the same chain length.The Antoine equation was used to correlate the experimental

data

= −+

p AB

T Cln( /kPa)

( /K) (16)

where p is the vapor pressure and T is the temperature; A, B,and C are adjustable constants. The obtained constantscorrelate the vapor pressure data within the experimentaluncertainty and are presented in Table 3, along with the root-mean-square deviation (RMSD) of the fit and the averagepercent deviation, which is defined as

∑Δ =−

p pn

p p

p/ %

100 exp cal

exp (17)

where n is the number of experimental points.The enthalpies of vaporization of the studied PFAAs were

estimated from the vapor pressure data, using the Clausius−Clapeyron equation (Table 4). This method assumes that theenthalpy of vaporization is constant in the measured temper-ature range and that the vapor phase behaves as an ideal gas,which should be a reasonable approximation because themeasured pressures are very low. The reported enthalpies ofvaporization should thus be regarded as mean values in themeasured temperature range.The vaporization enthalpies for the studied PFAAs are

plotted in Figure 4, along with literature values for some n-alkanes33 and perfluoroalkanes34,35 as a function of chainlength. The data for the n-alkanes correspond to literaturevalues reported at 298.15 K, and the values for perfluoroalkaneswere estimated by the original authors with the same method asin this work, using vapor pressure data in approximately thesame temperature range. It can be seen that the ΔHvap of F4H5is very close to that of perfluorononane and slightly lower thanthat of n-nonane. Unfortunately, direct comparison of theΔHvap of perfluoroalkanes longer than perfluorononane is notpossible because no data is available for these compounds asthey are solids at room temperature. However, a linearextrapolation of the existing data for the perfluoroalkanes(dashed line in Figure 4) seems to indicate that the incrementin ΔHvap with chain length for perfluoroalkanes is slightly lowerthan that for alkanes. The vaporization enthalpies of F4H6,F4H8, and F6H6 seem to be lower than that of thecorresponding alkanes, but quite close to the line extrapolatedfor the perfluoroalkanes. This might suggest that the cohesiveforces in liquid PFAAs are closer to perfluoroalkanes than toalkanes.The relative volatility of alkanes and perfluoroalkanes

changes as chain length increases. The lightest alkanesmethane, ethane, and propaneare more volatile thanperfluoromethane, perfluoroethane, and perfluoropropane.However, from butane onward, the perfluoroalkanes becomemore volatile than the alkanes.It is also known that mixtures of alkanes and perfluoroalkanes

show large positive deviations from Raoult’s law, displayingvapor pressures that can be considerably higher than eitherpure compounds.36,37 PFAAs which are, in a way, “chemicalmixtures” of alkanes and perfluoroalkanes, could thus be

Figure 2. Optimized structure of F4H5. Fluorine atoms are shown inblue, carbon atoms in black, and hydrogen atoms in gray. Side view ofF4H5 diblock chain (top); axial view of chain from fluorinated side(bottom left); axial view of chain from hydrogenated side (bottomright).

Table 1. Theoretically Obtained Values of Dipole Momentsfor Various FnHn Compounds Using HF/6-31G(d) Level ofTheory

theory (D) (HF/6-31G(d)) experimental dipole moment (D)

F1H1 2.2634 2.32F4H2 2.6155 −F4H5 2.8162 −F4H6 2.8656 −F4H8 2.9001 −F6H6 2.9526 −F6H8 2.9887 −

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expected to be more volatile than both alkanes andperfluoroalkanes.

In Figure 5, the vapor pressures of all PFAAs studied,including those of F1H1 and F4H2 taken from the literature,are compared to the corresponding values for the alkanes andperfluoroalkanes with the same chain length. The alkane andperfluoroalkane data was taken from the literature,6,20 exceptfor perfluorodecane and perfluorododecane which are SAFT-VR predictions using parameters extrapolated from molecularweight-based correlations, as described in more detail below.This comparison highlights several points. First, the vaporpressure of F1H1 is much lower than that of ethane andperfluoroethane. Second, the vapor pressure of F4H2 ispractically identical to that of hexane, and both are considerablyless volatile than perfluorohexane. Third, F4H5 is significantlymore volatile than nonane (its vapor pressure is very similar tothat of perfluorononane, in spite of the hydrogenated segmentbeing longer than the fluorinated), and the vapor pressure ofF4H6 is already slightly higher than that of perfluorododecane(and both are much more volatile than decane). Finally, thevapor pressures of F4H8 and F6H6 are considerably higherthan that of dodecane; for these longer compounds, thecomparison with the corresponding perfluoroalkane is difficult,

Table 2. Experimental Vapor Pressure of the Studied Compounds

F4H5 F4H6 F4H8 F6H6

T (K) p (kPa) T (K) p (kPa) T (K) p (kPa) T (K) p (kPa)

278.02 0.303 278.12 0.109 297.98 0.057 288.06 0.033280.57 0.364 280.59 0.126 300.50 0.070 290.54 0.041282.89 0.428 283.08 0.154 302.99 0.084 293.03 0.050285.53 0.515 285.56 0.184 305.46 0.100 295.52 0.062288.02 0.607 288.05 0.213 307.96 0.121 297.99 0.070290.50 0.718 290.51 0.259 310.54 0.148 300.47 0.086293.00 0.840 292.98 0.310 312.94 0.170 302.96 0.101295.46 0.993 295.48 0.365 315.51 0.208 305.45 0.123297.90 1.158 297.95 0.430 317.99 0.241 307.92 0.143300.42 1.349 300.45 0.506 320.49 0.286 310.45 0.179302.93 1.564 302.92 0.592 322.91 0.330 312.91 0.203305.39 1.806 305.39 0.694 325.48 0.395 315.41 0.245307.90 2.087 307.90 0.832 327.97 0.457 317.97 0.286310.36 2.393 310.36 0.943 320.42 0.339312.87 2.762 312.87 1.118 322.95 0.394315.32 3.132 315.32 1.265 325.39 0.461317.86 3.605 317.85 1.497 327.93 0.539320.28 4.065 320.29 1.677322.77 4.614 322.78 1.925325.25 5.216 325.27 2.206327.78 5.894 327.90 2.539

Figure 3. Experimental vapor pressure of the studied PFAAs. Symbols:(⧫) F4H5, (■) F4H6, (●) F6H6, and (▲) F4H8. The lines representthe Antoine equation correlations.

Table 3. Constants for the Antoine Equation

Antoine constants

molecule A B C RMSD (kPa) Δp/p (%)

F4H5 13.821 3019.67 −77.088 0.005 0.3F4H6 13.958 3269.972 −76.913 0.009 1.4F4H8 15.875 4499.913 −57.785 0.002 0.7F6H6 19.006 6299.936 −6.893 0.002 1.2

Table 4. Clausius−Clapeyron Estimates of the Enthalpy ofVaporization of the Studied Compounds

FnHm ΔHvap (kJ mol−1)

F4H5 45.3 ± 0.1F4H6 48.5 ± 0.2F4H8 56.4 ± 0.3F6H6 54.7 ± 0.3

Figure 4. Enthalpies of vaporization of alkanes, perfluoroalkanes, andthe studied PFAAs. Symbols: (⧫) alkanes, (■) PFAAs, and (▲) PFAs.

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as the melting point of perfluorododecane is 350 K, alreadyabove the temperature range covered in this work. Never-theless, extrapolations of the vapor pressure curve ofperfluorododecane, as predicted by the SAFT-VR equation,and of the vapor pressures of the two perfluoroalkylalkanesseem to indicate that both F4H8 and F6H6 are more volatilethan this perfluoroalkane.These observations can be rationalized as follows. In the case

of PFAAs with small alkyl and perfluoroalkyl segments,interactions in the liquid are dominated by the dipole and asa consequence, vapor pressure decreases. As the length of thesegments increases, the contribution of the dipole to the overallinteraction decreases and the weak unlike dispersiveinteractions between the hydrogenated and fluorinated seg-ments become increasingly more important. This would explainthe gradual increase in the volatility of PFAAs relative to bothalkanes and perfluoroalkanes.The vapor−liquid equilibrium of the PFAAs studied was also

modeled using both a nondipolar and a dipolar version of thehetero-SAFT-VR approach, as previously described. As inearlier work,8,9,11,12 the modeling was focused on obtaining amolecular level understanding of the studied compounds ratherthan on reproducing the observed experimental results. Withthis in mind, a fully predictive approach was adopted and noparameters were fitted to experimental data for the studiedPFAA molecules. For the alkyl segments, the correlations forthe model parameters developed by McCabe et al.15 as afunction of molecular weight were used rather than specificparameters for each “alkane”. Following the same method,correlations have been derived for the model parameters ofperfluoroalkanes using data from the literature11,16,17,38 and aregiven by

λ = +m M0.01129 0.2724w (18)

σ = +m M0.6793 24.86563w (19)

ε = +m k M( / ) 2.0202 118.3754w (20)

where Mw represents molecular weight of the perfluoroalkanes.This strategy provides a more coherent set of parameters thanusing those fitted to each substance individually, which in thecase of vapor pressure calculations is particularly important.The effect of the molecular dipole was also considered by

including an explicit term into the theoretical approach for thedipolar interactions.21 For a clean comparison between the twoapproaches, and to enable the effect of the dipole to be clearlyseen, the dipole moment taken from ab initio calculations wasused and the square-well model parameters were not refitted.The full set of molecular parameters used for the calculations ispresented in Table 5.In previous work we reported optimized binary interaction

parameters that quantitatively describe vapour−liquid equilibria(VLE) and volumetric data of mixtures of alkanes andperfluoroalkanes (ξij = 0.840 and γij = 1.0451).17 As a firstapproximation, it might be expected that these cross interaction

Figure 5. Vapor pressures of PFAAs, alkanes, and perfluoroalkanes.

Table 5. SAFT-VR Parameters for the Segments of theMolecules Studied

Mw (g mol−1) λ ε/k (K) σ (Å) m

H1 15.035 1.49895 175.578 3.651 0.665H2 29.061 1.53006 198.623 3.756 0.998H5 71.142 1.56947 227.826 3.882 1.998H6 85.168 1.57598 232.648 3.902 2.332H8 113.222 1.58506 239.376 3.929 2.998F1 69.006 1.22324 299.907 4.370 0.685F4 219.028 1.39362 284.743 4.451 1.795F6 319.043 1.42965 281.537 4.467 2.535

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parameters would be suitable for describing the interactionsbetween chemically bonded alkyl and perfluoroalkyl segmentsin PFAAs; therefore, this cross interaction parameter has beenused. However, given the small size of the segments in F1H1,binary interaction parameters taken from the work of McCabeet al.,16 in which mixtures of CH4 and short perfluoroalkaneswere studied, were used for this compound. The nondipolarhetero-SAFT-VR predictions using these parameters arecompared with the experimental results in Figure 6.As can be seen, using these binary interaction parameters, the

theory over predicts the vapor pressures of all the PFAAsstudied. It can be argued, however, that the forced coexistencebetween the alkyl and perfluoroalkyl segments within the samemolecule leads to cross interactions that are less “unfavorable”than those found in “real” alkane and perfluoroalkane mixtures,thus corresponding to higher binary interaction parameters.The limiting situation would correspond to using the Lorentz−Berthelot combining rules (ξij = 1 and γij = 1). As can be seen inFigure 6, this does lower the predicted vapor pressures;however, even this “limit” hypothesis seems to be insufficient to

reproduce the experimental vapor pressure of the studiedPFAAs. Because the nondipolar hetero-SAFT-VR calculationsdo not consider the dipolar nature of the molecules, the theorydoes not provide sufficient cohesive energy between themolecules to correctly reproduce the PFAA vapor pressures.With the explicit inclusion of dipolar interactions in thetheoretical model, we would therefore expect to increase thecohesiveness of the liquid and thus decrease the calculatedvapor pressures.The SAFT-VR predictions for the vapor pressure of the

studied PFAAs, which include the contribution of the dipolarterm, are also plotted in Figure 6 (orange lines).As can be seen, the contribution of the dipole has a large

effect, lowering the vapor pressure of all PFAAs studied by ca.50%. Although the predicted vapor pressures are stillconsiderably higher than the experimental values, theimportance of the dipole to the vapor−liquid equilibria ofthese substances is clearly demonstrated.It should also be kept in mind that the values of the dipole

moments used in the calculations refer to estimations of this

Figure 6. Comparison of experimental data and hetero-SAFT-VR predictions for the vapor pressures of F1H1, F4H2, F4H5, F4H6, F4H8, andF6H6. Experimental results are shown as symbols, and the theoretical predictions with cross interaction parameters from refs 16 and 17 as solid lines,with Lorentz−Berthelot cross interactions as long dashed lines, and with cross interaction parameters from refs 16 and 17 plus the dipole term asshort dashed lines.

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property for isolated molecules in the gas phase. It is known,however, that in the liquid phase the effective dipole momentstend to be larger than those determined from the gas phase. Inthe case of liquid CH3CF3, the dipole moment obtained fromrelative permittivity measurements varies from 2.530 to 3.293 Ddepending on the theory used,39 which corresponds to anincrease of 12−45% relatively to the gas-phase value. We havefound that increasing the dipole moments by 18−20% wouldbe enough to obtain theoretical estimations of the vaporpressure in agreement with the experimental values.An alternative way of improving the agreement between

theory and experiment would be to modify the binaryinteraction parameters. As mentioned before, the parametersfitted to results of mixtures of alkanes and perfluoroalkanesshould probably not be fully transferrable for the calculation ofthe VLE of PFAAs. We have found that increasing the ξparameter from 0.84 to 0.92−0.93 (depending on thecompound) is sufficient to bring the theoretical calculationsin quantitative agreement with the experimental results, usingthe gas-phase dipole moments.Finally, in Figure 7, the hetero-SAFT-VR predictions of the

saturated liquid density, with and without the dipole term, arecompared with the experimental data previously reported.8,9

Again, it is seen that inclusion of the dipole term results in aconsiderable improvement of the theoretical predictions.

5. CONCLUSIONSThe vapor pressure of four liquid perfluoroalkylalkanes(CF3(CF2)n(CH2)mCH3; n = 3, m = 4,5,7; n = 5, m = 5) wasmeasured as a function of temperature between 278 and 328 Kand the molar enthalpies of vaporization calculated from theexperimental data.

A comparison of the PFAA experimental data with literaturevapor pressures for alkanes and perfluoroalkanes clearly showsthe influence of the coexisting hydrogenated and fluorinatedsegments on the vapor−liquid behavior of the PFAAs studied.For short-chain PFAAs, the dipolar interactions are prevalentand decrease their vapor pressure. As the length of thesegments increases, the relative weight of dispersive interactionsincreases, unveiling the influence of the weak hydrogenated−fluorinated interactions and the fluorous amphipathic nature ofthe PFAA molecules.The results were interpreted using the hetero-SAFT-VR

approach in a purely predictive way, both with and without theinclusion of the dipolar interactions. The theoretical calcu-lations without the dipolar contribution predict values for thevapor pressure that are systematically higher than theexperimental data, showing that the model used is under-estimating the molecular interactions in the liquid. Because thesame model accurately predicts the vapor pressures of alkanes,perfluoroalkanes, and their mixtures, this suggests that theunaccounted for dipolar interactions play a significant role inthe cohesiveness of PFAA molecules in the liquid state. It isshown that inclusion of the dipolar term leads to significantlylower predictions for the vapor pressure that are in betteragreement with the experimental data. Quantitative agreementbetween theoretical predictions and experimental results can beobtained if an effective dipole moment for the liquid phase isused or if binary interaction parameters are adjusted to theexperimental data.

■ AUTHOR INFORMATIONNotesThe authors declare no competing financial interest.

Figure 7. Comparison of experimental data and hetero-SAFT-VR predictions for the liquid densities of F4H5, F4H6, F4H8, and F6H6.Experimental results are shown as symbols, the theoretical predictions using the cross interaction parameters from ref 17 as solid lines, and the samecross interaction parameters plus the dipole term as short dashed lines.

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■ ACKNOWLEDGMENTS

P.M. acknowledges funding from Fundacao para a Ciencia eTecnologia, in the form of Grant SFRH/BPD/81748/2011.E.J.M.F. and P.M. acknowledge support from Fundacao para aCiencia e a Tecnologia through Grant Pest-OE/QUI/UI0100/2013. C.M. and G.D. acknowledge support from the NationalScience Foundation through Grant CBET-1067642.

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