Article
pubs.acs.org/JPCB
Vapor Pressure of Perfluoroalkylalkanes: The Role of the Dipole
Pedro Morgado,† Gaurav Das,‡ Clare McCabe,‡,§ and Eduardo J. M. Filipe*,†
†
Centro de Química Estrutural, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Department of Chemical and Biomolecular Engineering and §Department of Chemistry, Vanderbilt University, Nashville, Tennessee
37235, United States
‡
ABSTRACT: The vapor pressure of four liquid perfluoroalkylalkanes
(CF3(CF2)n(CH2)mCH3; n = 3, m = 4,5,7; n = 5, m = 5) was measured as a function of
temperature between 278 and 328 K. Molar enthalpies of vaporization were calculated from
the experimental data, and the results were compared with data from the literature for the
corresponding alkanes and perfluoroalkanes. The heterosegmented statistical associating
fluid theory was used to interpret the results at the molecular level both with and without
the explicit inclusion of the dipolar nature of the molecules. Additionally, ab initio
calculations were performed for all perfluoroalkylalkanes studied to determine the dipole
moment to be used in the theoretical calculations. We demonstrate that the inclusion of a
dipolar 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, which
decrease the vapor pressure, and the relatively weak dispersive interactions between the hydrogenated and fluorinated segments.
1. INTRODUCTION
Perfluoroalkylalkanes (PFAAs) are diblock compounds formed
by hydrogenated and fluorinated hydrocarbon segments that
are covalently bonded together to form a single molecule. They
display a wide range of interesting properties, from surfactant
activity toward alkane−perfluoroalkane liquid−liquid interfaces
to the ability to self-organize, forming liquid crystals, micelles,
and nanostructured monolayers, etc.1−5 At the origin of these
properties lies the yet unexplained “antipathy” between the
fluorinated and hydrogenated segments. Allied to their
chemical inertness and biocompatibility, PFAAs have become
useful in a range of applications from components of artificial
blood substitutes to fluids in eye surgery and liquid ventilation.
Being the simplest molecules exhibiting such complex behavior,
PFAAs have garnered strong interest from the scientific
community.
Despite the practical and fundamental interest in PFAAs,
there is a surprising gap in the knowledge of their
thermophysical properties and chiefly of their vapor pressures.
In fact, the only data that can be found in the literature is for
the 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 the
above-mentioned biomedical applications, the design of
industrial separation processes such as distillation, and even
the assessment of the environmental impact of these
compounds, requires such data. Furthermore, the knowledge
of the vapor pressure (and/or the related vaporization
enthalpy) is crucial for the development and testing of
molecular model (or force field) parameters to be used in
computer simulations of PFAAs or molecular-based theoretical
calculations.
This work is part of a systematic study of the thermophysical
properties of PFAAs with different relative hydrogenated and
© 2014 American Chemical Society
fluorinated segment lengths. In previous work we reported
densities as a function of temperature and pressure,8,9 and
viscosities as a function of temperature10 for perfluorobutylpentane (F4H5), perfluorobutylhexane (F4H6), perfluorobutyloctane (F4H8), perfluorohexylhexane (F6H6), and perfluorohexyloctane (F6H8). The density results were interpreted in
terms of the volumes of the constituent hydrogenated and
perfluorinated segments corrected for the corresponding excess
volumes and the volume contribution of the CH2−CF2
junction. Using the same strategy, the viscosity data was
interpreted from the contributions to the viscosity due to the
CF3, CF2, CH2 ,and CH3 groups, and the differences found
between calculated and experimental viscosities were rationalized in terms of the contribution of the CH2−CF2 bond and the
deviations from ideality seen in mixtures of n-alkanes and
perfluoroalkanes.
As for mixtures involving PFAAs, partial molal volumes for
the same series of PFAAs (F4H5, F4H6, F4H8, F6H6, F6H8)
plus perfluorodecyloctane (F10H8) and perfluorooctyloctadecane (F8H18) were measured in n-octane at 25 °C.11,12 It was
found that whereas for perfluoroalkanes the partial molar
volumes at infinite dilution in n-octane are 13% higher than the
corresponding pure molar volumes, for PFAAs this increment is
only about 5%. Again, the results were rationalized in terms of
the partial molar volumes at infinite dilution of the
corresponding hydrogenated and perfluorinated segments and
the contribution from the CH2−CF2 link. It was found that the
contribution to the volume of the diblock junction is
independent of chain length of the hydrogenated segment
but decreases with the chain length of the fluorinated segment.
Received: October 31, 2014
Revised: December 18, 2014
Published: December 19, 2014
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DOI: 10.1021/jp5109448
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The Journal of Physical Chemistry B
Article
measurements, both the pressure sensor and the connecting
line are maintained above the sample temperature to avoid
condensation of the vapor. The glass part of the apparatus that
is exposed to the sample vapor during measurement is
maintained immersed in the thermostatic bath.
All liquids were degassed by submitting them to cycles of
freezing in liquid nitrogen, vacuum pumping, and melting. This
was followed by directly pumping the samples for a few seconds
while agitating the liquid. The procedure was repeated until the
measured vapor pressure was reproducible, ensuring 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.
Additionally, these systems were studied with the heterosegmented statistical associating fluid theory (hetero-SAFTVR) equation of state, which describes the molecules as diblock
heteronuclear chains within the SAFT-VR framework.13,14 The
model parameters for the alkyl and perfluoroalkyl segments and
the binary interaction parameters between the segments were
obtained by fitting to the phase behavior of pure alkanes,
perfluoroalkanes, and their mixtures.15−17 Through this simple
approach, the densities and partial molal volumes of PFAAs
were predicted and the results found to be in close agreement
with the experimental results without fitting to experimental
data 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. The
data was correlated with appropriate equations, and the
corresponding enthalpies of vaporization were estimated. The
hetero-SAFT-VR approach has again been used to predict the
vapor pressures and densities of the PFAAs studied. While in
previous studies the contribution of the dipole moment to the
physical properties of PFAAs was not considered, here this
contribution was explicitly taken into account for the first time.
It should be emphasized that the combined presence of
hydrogenated and fluorinated segments, which are essentially
nonpolar, gives rise to a charge distribution corresponding to a
considerable dipole that in the case of CH3CF3 (F1H1) is 2.32
D.18 This electrical moment leads to additional cohesion in the
liquid phase, which should be especially important in the
rationalization of a property such as the vapor pressure. As it
will be shown, the inclusion of a dipolar term brings the heteroSAFT-VR predictions to much closer agreement with the
experimental vapor pressures, demonstrating the importance of
the dipole contribution to the interaction between PFAA
molecules. Finally, the present results also reveal the potential
importance of including a dipolar term in the modeling of other
physical properties of PFAAs (e.g., surface tension and
viscosity) and perhaps more importantly when describing the
interaction of PFAAs with other dipolar molecules, water in
particular.
3. THEORY
In previous work, PFAA molecules were modeled as diblock
chains of tangentially bonded hard spherical heterogeneous
segments that interact through square-well (SW) interactions.
Here, to explicitly capture polar interactions, the monomer
segments interact through both dispersive SW and dipolar
interactions, as illustrated in Figure 1.
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 the
CF2−CH2 junction contain embedded dipoles.
As can be seen from Figure 1, in the proposed dipolar model
for PFAAs the two fluorinated segments at the CF2−CH2
juncture are considered to have an electric dipole oriented
parallel to the axis joining the segments, with the dipole
moment divided equally between the two segments. This
model was chosen based on electron density maps determined
for PFAA molecules that provide molecular level insight into
the electrostatics of the PFAA molecules.19 The dipolar nature
of the molecule is described by the combination of the SAFTVR+D equation with the hetero-SAFT-VR framework.13,20
SAFT-VR+D is based on a version of SAFT-VR that was
developed to model dipolar fluids by explicitly accounting for
dipolar interactions and their effect on the thermodynamics and
structure of a fluid. This is achieved through the use of the
generalized mean spherical approximation (GMSA) to describe
a monomer fluid of nondipolar and dipolar square-well
segments enabling the study of pure fluids and mixtures of
dipolar associating fluids of arbitrary size and dipole moment.21−23
The potential model for the intermolecular interactions is
given by
2. EXPERIMENTAL SECTION
Perfluorobutylpentane (F4H5), perfluorobutylhexane (F4H6),
perfluorobutyloctane (F4H8), and perfluorohexylhexane
(F6H6) were ultrapurified chemicals obtained from Fluoron
GMBH, with a claimed purity of 100%. 19F and 1H NMR
spectra of these compounds were obtained, and only very small
unexpected 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 spherical
glass cell connected to a pressure sensor and a vacuum line.
During the measurements, the sample cell was immersed in a
water thermostatic bath equipped with a Hart Scientific 2100
digital PID temperature controller. The temperature stability
and uniformity during a measurement is estimated to be better
than 0.01 K. The temperature of the liquid sample was
measured 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 were
made with a Paroscientific Series 1000 quartz absolute pressure
transducer connected to a Paroscientific Model 715 display
unit. The pressure sensor used has a range of 100 psia (0.69
MPa), accuracy better than 0.01% of the full scale, a resolution
of 0.0001%, and automatic temperature compensation. During
u(r ) = uSW (r ) + u dipole(r )
(1)
where the SW potential is given by
⎧+∞ if r < σij
⎪
⎪
Uij(r ) = ⎨ −εij if σij ≤ r < λijσij
⎪
⎪ 0 if r ≥ λijσij
⎩
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Article
and εij and λij are the attractive SW depth and range parameters,
respectively, and σij is the hard sphere diameter. For the
calculation of the inter- and intramolecular cross interactions
between segments, a modified set of Lorentz−Berthelot
combining rules24 has been used
σij =
aSW = (a HS + βa1 + β 2a 2)
where a is the free energy due to hard sphere monomeric
interactions; a1 and a2 are the SW attractive first- and secondorder perturbation terms, respectively; and β = (1/kbT). For a
detailed description of the isotropic SW term, the reader is
directed to the original papers.15,16,25
The anisotropic dipolar contribution is obtained from the
solution of the Ornstein−Zernike equation for dipolar hard
spheres of arbitrary size using the mean spherical approximation (MSA) closure.26 For the symmetric case when all of
the segments have the same diameter and dipole moment, the
solution agrees with that proposed by Wertheim.27 The
Helmholtz free energy of a mixture of dipolar segments is
given as
σii + σjj
(3)
2
εij = ξij εiiεjj
λij = γij
(4)
λiiσii + λjjσjj
2σij
(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
μi μj
udipole(rω1ω2) = − 3 Dij(n1n 2riĵ )
rij
(6)
a
(7)
In eqs 6 and 7, r̂iĵ is the unit vector in the direction of rij and ni
is a unit vector parallel to the dipole moment of segment i.
In the SAFT theoretical framework, the Helmholtz free
energy is given as
A
Aideal
Amono
Achain
Aassoc
=
+
+
+
Nk bT
Nk bT
Nk bT
Nk bT
Nk bT
yij =
(8)
kij =
n polar n polar
∑∑
xps, ixps, j yij
i=1 j=1
∫0
β
kij(β′) dβ′
(12)
4πβρps, i1/2 μi μj ρps, j1/2
(13)
9
3
10
∫0
∞
112
hiĵ (r )
r
dr
(14)
where ĥij112(r) is the expansion coefficient of the total
correlation function. A more detailed description of the dipole
term can be found in the original papers.21,23,26,27
The Helmholtz free energy contribution due to the chain
formation is given by21,25
Achain
SW
SW
= (1 − mCH) ln gCH
(σCH) + (m′CF − mCF) ln gCF
(σCF)
Nk bT
DSW
SW
+ (1 − m′CF ) ln gCF
(σCF) − ln gCF
(σ
)
− CH CF − CH
(9)
DSW
(15)
SW
where g (r) and g (r) correspond to the radial distribution
function (RDF) at the contact value for the dipolar square-well
and square-well monomer fluid, respectively. mCH, mCF, m′CF
represent the number of CH segments, CF segments, and
dipolar CF segments, respectively. We note that in this work
the linearized version of the exponential (LEXP)28 approximation has been used to determine the RDF of the dipolar
square well fluid.
where ρ = N/V is the molecular number density and Λ the
thermal de Broglie wavelength which incorporates the kinetic
(translational, rotational, and vibrational) contributions to the
partition function of the molecule.
Following the SAFT-VR+D approach, the contribution to
the Helmholtz free energy due to monomeric interaction
between segments is given by
Amono
Amono
=m
= maSW + m′adipole
Nk bT
Nsk bT
3
=−
β
where ρps,i and μi are the segment density and dipole moment
of the ith polar segment, respectively. The scaling parameter kij
is given by
where N is the total number of molecules, kb the Boltzmann
constant, 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 the
nonassociating nature of the PFAA molecules, the free energy
contribution due to association (Aassoc) is not included in this
work. We briefly consider each of the remaining terms in turn.
The ideal Helmholtz free energy is given by
Aideal
= ln(ρ Λ3) − 1
Nk bT
dipole
where npolar represents the number of polar segments in the
system; xps,i is the segment fraction of the ith polar segment, yij
the strength of the dipolar effects, and kij the scaling parameter.
The so-called strength of the dipolar effect yij is given by
where
Dij(n1n 2riĵ ) = [3(n1·riĵ )(n 2 ·riĵ ) − n1·n 2]
(11)
HS
4. AB INITIO CALCULATIONS
Dipole moments for each of the PFAA molecules studied were
obtained from ab initio calculations. Previously, Jorgensen et
al.29 performed structural optimization (HF/6-31G*) and
single-point energy (LMP2/cc-pVTZ(-f)) calculations for
several perfluoroalkanes. The torsional energy profiles for the
linear CCCC dihedral was found to exhibit an energy minima
around 170°. Subsequently, Pádua30 investigated the torsional
energy profile of several diblock PFAAs and found the energy
minima to be around 180° for the CF−CF−CH−CH dihedral
in F2H2.
(10)
where Ns represents the total number of segments in the
mixture, obtained by multiplying the number of molecules (N)
with the total number of segments per molecule (m). The
excess Helmholtz free energy per monomer (amono) has two
kinds of contributions: isotropic square-well (aSW) and
anisotropic dipolar (adipole). m′ is the number of segments
with dipolar interactions.
The isotropic contribution to the monomer free energy is
given by
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with the largest fluorinated segment has the highest vapor
pressure. This is to be expected because all perfluoroalkanes
longer than perfluoropropane are more volatile than the
corresponding alkane with the same chain length.
The Antoine equation was used to correlate the experimental
data
In this work, the geometry of the PFAAs has been optimized
using Gaussian 09 and the same level of theory (HF/6-31G(d))
as used in the work of Pádua27 and the dipole moments of the
structures then calculated. As an example, an optimized
conformation of one of the compounds studied, F4H5, is
shown in Figure 2. From this figure, we can note that the linear
ln(p /kPa) = A −
B
(T /K) + C
(16)
where p is the vapor pressure and T is the temperature; A, B,
and C are adjustable constants. The obtained constants
correlate the vapor pressure data within the experimental
uncertainty and are presented in Table 3, along with the rootmean-square deviation (RMSD) of the fit and the average
percent deviation, which is defined as
Δp /p % =
(all trans) conformation of the hydrogenated side of the chain
and the helical conformation of the fluorinated side, as well as
the 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 molecules
studied are reported in Table 1. As can be seen from the table,
Table 1. Theoretically Obtained Values of Dipole Moments
for Various FnHn Compounds Using HF/6-31G(d) Level of
Theory
theory (D) (HF/6-31G(d))
experimental dipole moment (D)
2.2634
2.6155
2.8162
2.8656
2.9001
2.9526
2.9887
2.32
−
−
−
−
−
−
∑
pexp − pcal
pexp
(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 the
enthalpy of vaporization is constant in the measured temperature range and that the vapor phase behaves as an ideal gas,
which should be a reasonable approximation because the
measured pressures are very low. The reported enthalpies of
vaporization should thus be regarded as mean values in the
measured temperature range.
The vaporization enthalpies for the studied PFAAs are
plotted in Figure 4, along with literature values for some nalkanes33 and perfluoroalkanes34,35 as a function of chain
length. The data for the n-alkanes correspond to literature
values reported at 298.15 K, and the values for perfluoroalkanes
were estimated by the original authors with the same method as
in this work, using vapor pressure data in approximately the
same temperature range. It can be seen that the ΔHvap of F4H5
is very close to that of perfluorononane and slightly lower than
that of n-nonane. Unfortunately, direct comparison of the
ΔHvap of perfluoroalkanes longer than perfluorononane is not
possible because no data is available for these compounds as
they are solids at room temperature. However, a linear
extrapolation of the existing data for the perfluoroalkanes
(dashed line in Figure 4) seems to indicate that the increment
in ΔHvap with chain length for perfluoroalkanes is slightly lower
than that for alkanes. The vaporization enthalpies of F4H6,
F4H8, and F6H6 seem to be lower than that of the
corresponding alkanes, but quite close to the line extrapolated
for the perfluoroalkanes. This might suggest that the cohesive
forces in liquid PFAAs are closer to perfluoroalkanes than to
alkanes.
The relative volatility of alkanes and perfluoroalkanes
changes as chain length increases. The lightest alkanes
methane, ethane, and propaneare more volatile than
perfluoromethane, perfluoroethane, and perfluoropropane.
However, from butane onward, the perfluoroalkanes become
more volatile than the alkanes.
It is also known that mixtures of alkanes and perfluoroalkanes
show large positive deviations from Raoult’s law, displaying
vapor pressures that can be considerably higher than either
pure compounds.36,37 PFAAs which are, in a way, “chemical
mixtures” of alkanes and perfluoroalkanes, could thus be
Figure 2. Optimized structure of F4H5. Fluorine atoms are shown in
blue, carbon atoms in black, and hydrogen atoms in gray. Side view of
F4H5 diblock chain (top); axial view of chain from fluorinated side
(bottom left); axial view of chain from hydrogenated side (bottom
right).
F1H1
F4H2
F4H5
F4H6
F4H8
F6H6
F6H8
100
n
the calculations for CH3CF3 (F1H1) predict a dipole moment
that is in good agreement with the reported experimental
value,18 thus providing confidence in the estimated values for
the other PFAAs. The obtained values for the dipole moments
slightly increase with the length of both the fluorinated and the
hydrogenated segments, suggesting that longer chains induce a
larger asymmetry in the electronic distribution at the
hydrogenated−fluorinated junction.
5. RESULTS AND DISCUSSION
The experimental unsmoothed vapor pressures of the PFAAs
studied, as a function of temperature, are presented in Table 2
and plotted in Figure 3. As expected, the volatility decreases
with the length of the carbon chain. When two PFAAs (F4H8
and F6H6) molecules have the same total chain length, the one
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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
280.57
282.89
285.53
288.02
290.50
293.00
295.46
297.90
300.42
302.93
305.39
307.90
310.36
312.87
315.32
317.86
320.28
322.77
325.25
327.78
0.303
0.364
0.428
0.515
0.607
0.718
0.840
0.993
1.158
1.349
1.564
1.806
2.087
2.393
2.762
3.132
3.605
4.065
4.614
5.216
5.894
278.12
280.59
283.08
285.56
288.05
290.51
292.98
295.48
297.95
300.45
302.92
305.39
307.90
310.36
312.87
315.32
317.85
320.29
322.78
325.27
327.90
0.109
0.126
0.154
0.184
0.213
0.259
0.310
0.365
0.430
0.506
0.592
0.694
0.832
0.943
1.118
1.265
1.497
1.677
1.925
2.206
2.539
297.98
300.50
302.99
305.46
307.96
310.54
312.94
315.51
317.99
320.49
322.91
325.48
327.97
0.057
0.070
0.084
0.100
0.121
0.148
0.170
0.208
0.241
0.286
0.330
0.395
0.457
288.06
290.54
293.03
295.52
297.99
300.47
302.96
305.45
307.92
310.45
312.91
315.41
317.97
320.42
322.95
325.39
327.93
0.033
0.041
0.050
0.062
0.070
0.086
0.101
0.123
0.143
0.179
0.203
0.245
0.286
0.339
0.394
0.461
0.539
Figure 4. Enthalpies of vaporization of alkanes, perfluoroalkanes, and
the studied PFAAs. Symbols: (⧫) alkanes, (■) PFAAs, and (▲) PFAs.
Figure 3. Experimental vapor pressure of the studied PFAAs. Symbols:
(⧫) F4H5, (■) F4H6, (●) F6H6, and (▲) F4H8. The lines represent
the Antoine equation correlations.
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 and
perfluoroalkanes with the same chain length. The alkane and
perfluoroalkane data was taken from the literature,6,20 except
for perfluorodecane and perfluorododecane which are SAFTVR predictions using parameters extrapolated from molecular
weight-based correlations, as described in more detail below.
This comparison highlights several points. First, the vapor
pressure of F1H1 is much lower than that of ethane and
perfluoroethane. Second, the vapor pressure of F4H2 is
practically identical to that of hexane, and both are considerably
less volatile than perfluorohexane. Third, F4H5 is significantly
more volatile than nonane (its vapor pressure is very similar to
that of perfluorononane, in spite of the hydrogenated segment
being longer than the fluorinated), and the vapor pressure of
F4H6 is already slightly higher than that of perfluorododecane
(and both are much more volatile than decane). Finally, the
vapor pressures of F4H8 and F6H6 are considerably higher
than that of dodecane; for these longer compounds, the
comparison with the corresponding perfluoroalkane is difficult,
Table 3. Constants for the Antoine Equation
Antoine constants
molecule
A
B
C
RMSD (kPa)
Δp/p (%)
F4H5
F4H6
F4H8
F6H6
13.821
13.958
15.875
19.006
3019.67
3269.972
4499.913
6299.936
−77.088
−76.913
−57.785
−6.893
0.005
0.009
0.002
0.002
0.3
1.4
0.7
1.2
Table 4. Clausius−Clapeyron Estimates of the Enthalpy of
Vaporization of the Studied Compounds
FnHm
F4H5
F4H6
F4H8
F6H6
ΔHvap (kJ mol−1)
45.3
48.5
56.4
54.7
±
±
±
±
0.1
0.2
0.3
0.3
expected to be more volatile than both alkanes and
perfluoroalkanes.
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Figure 5. Vapor pressures of PFAAs, alkanes, and perfluoroalkanes.
as the melting point of perfluorododecane is 350 K, already
above the temperature range covered in this work. Nevertheless, extrapolations of the vapor pressure curve of
perfluorododecane, as predicted by the SAFT-VR equation,
and of the vapor pressures of the two perfluoroalkylalkanes
seem to indicate that both F4H8 and F6H6 are more volatile
than 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 as
a consequence, vapor pressure decreases. As the length of the
segments increases, the contribution of the dipole to the overall
interaction decreases and the weak unlike dispersive
interactions between the hydrogenated and fluorinated segments become increasingly more important. This would explain
the gradual increase in the volatility of PFAAs relative to both
alkanes and perfluoroalkanes.
The vapor−liquid equilibrium of the PFAAs studied was also
modeled using both a nondipolar and a dipolar version of the
hetero-SAFT-VR approach, as previously described. As in
earlier work,8,9,11,12 the modeling was focused on obtaining a
molecular level understanding of the studied compounds rather
than on reproducing the observed experimental results. With
this in mind, a fully predictive approach was adopted and no
parameters were fitted to experimental data for the studied
PFAA molecules. For the alkyl segments, the correlations for
the model parameters developed by McCabe et al.15 as a
function of molecular weight were used rather than specific
parameters for each “alkane”. Following the same method,
correlations have been derived for the model parameters of
perfluoroalkanes using data from the literature11,16,17,38 and are
given by
mλ = 0.01129M w + 0.2724
mσ 3 = 0.6793M w + 24.8656
(19)
m(ε /k) = 2.0202M w + 118.3754
(20)
where Mw represents molecular weight of the perfluoroalkanes.
This strategy provides a more coherent set of parameters than
using those fitted to each substance individually, which in the
case 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 the
dipolar interactions.21 For a clean comparison between the two
approaches, and to enable the effect of the dipole to be clearly
seen, the dipole moment taken from ab initio calculations was
used and the square-well model parameters were not refitted.
The full set of molecular parameters used for the calculations is
presented 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 and
perfluoroalkanes (ξij = 0.840 and γij = 1.0451).17 As a first
approximation, it might be expected that these cross interaction
Table 5. SAFT-VR Parameters for the Segments of the
Molecules Studied
H1
H2
H5
H6
H8
F1
F4
F6
(18)
1628
Mw (g mol−1)
λ
ε/k (K)
σ (Å)
m
15.035
29.061
71.142
85.168
113.222
69.006
219.028
319.043
1.49895
1.53006
1.56947
1.57598
1.58506
1.22324
1.39362
1.42965
175.578
198.623
227.826
232.648
239.376
299.907
284.743
281.537
3.651
3.756
3.882
3.902
3.929
4.370
4.451
4.467
0.665
0.998
1.998
2.332
2.998
0.685
1.795
2.535
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Figure 6. Comparison of experimental data and hetero-SAFT-VR predictions for the vapor pressures of F1H1, F4H2, F4H5, F4H6, F4H8, and
F6H6. 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 as
short dashed lines.
reproduce the experimental vapor pressure of the studied
PFAAs. Because the nondipolar hetero-SAFT-VR calculations
do not consider the dipolar nature of the molecules, the theory
does not provide sufficient cohesive energy between the
molecules to correctly reproduce the PFAA vapor pressures.
With the explicit inclusion of dipolar interactions in the
theoretical model, we would therefore expect to increase the
cohesiveness of the liquid and thus decrease the calculated
vapor pressures.
The SAFT-VR predictions for the vapor pressure of the
studied PFAAs, which include the contribution of the dipolar
term, 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 still
considerably higher than the experimental values, the
importance of the dipole to the vapor−liquid equilibria of
these 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
parameters would be suitable for describing the interactions
between chemically bonded alkyl and perfluoroalkyl segments
in PFAAs; therefore, this cross interaction parameter has been
used. However, given the small size of the segments in F1H1,
binary interaction parameters taken from the work of McCabe
et al.,16 in which mixtures of CH4 and short perfluoroalkanes
were studied, were used for this compound. The nondipolar
hetero-SAFT-VR predictions using these parameters are
compared 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 PFAAs
studied. It can be argued, however, that the forced coexistence
between the alkyl and perfluoroalkyl segments within the same
molecule 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 in
Figure 6, this does lower the predicted vapor pressures;
however, even this “limit” hypothesis seems to be insufficient to
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Article
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 same
cross interaction parameters plus the dipole term as short dashed lines.
A comparison of the PFAA experimental data with literature
vapor pressures for alkanes and perfluoroalkanes clearly shows
the influence of the coexisting hydrogenated and fluorinated
segments on the vapor−liquid behavior of the PFAAs studied.
For short-chain PFAAs, the dipolar interactions are prevalent
and decrease their vapor pressure. As the length of the
segments increases, the relative weight of dispersive interactions
increases, unveiling the influence of the weak hydrogenated−
fluorinated interactions and the fluorous amphipathic nature of
the PFAA molecules.
The results were interpreted using the hetero-SAFT-VR
approach in a purely predictive way, both with and without the
inclusion of the dipolar interactions. The theoretical calculations without the dipolar contribution predict values for the
vapor pressure that are systematically higher than the
experimental data, showing that the model used is underestimating the molecular interactions in the liquid. Because the
same model accurately predicts the vapor pressures of alkanes,
perfluoroalkanes, and their mixtures, this suggests that the
unaccounted for dipolar interactions play a significant role in
the cohesiveness of PFAA molecules in the liquid state. It is
shown that inclusion of the dipolar term leads to significantly
lower predictions for the vapor pressure that are in better
agreement with the experimental data. Quantitative agreement
between theoretical predictions and experimental results can be
obtained if an effective dipole moment for the liquid phase is
used or if binary interaction parameters are adjusted to the
experimental data.
property for isolated molecules in the gas phase. It is known,
however, that in the liquid phase the effective dipole moments
tend to be larger than those determined from the gas phase. In
the case of liquid CH3CF3, the dipole moment obtained from
relative permittivity measurements varies from 2.530 to 3.293 D
depending on the theory used,39 which corresponds to an
increase of 12−45% relatively to the gas-phase value. We have
found that increasing the dipole moments by 18−20% would
be enough to obtain theoretical estimations of the vapor
pressure in agreement with the experimental values.
An alternative way of improving the agreement between
theory and experiment would be to modify the binary
interaction parameters. As mentioned before, the parameters
fitted to results of mixtures of alkanes and perfluoroalkanes
should probably not be fully transferrable for the calculation of
the VLE of PFAAs. We have found that increasing the ξ
parameter from 0.84 to 0.92−0.93 (depending on the
compound) is sufficient to bring the theoretical calculations
in quantitative agreement with the experimental results, using
the gas-phase dipole moments.
Finally, in Figure 7, the hetero-SAFT-VR predictions of the
saturated liquid density, with and without the dipole term, are
compared with the experimental data previously reported.8,9
Again, it is seen that inclusion of the dipole term results in a
considerable improvement of the theoretical predictions.
5. CONCLUSIONS
The vapor pressure of four liquid perfluoroalkylalkanes
(CF3(CF2)n(CH2)mCH3; n = 3, m = 4,5,7; n = 5, m = 5) was
measured as a function of temperature between 278 and 328 K
and the molar enthalpies of vaporization calculated from the
experimental data.
■
AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
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J. Phys. Chem. B 2015, 119, 1623−1632
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Article
■
ACKNOWLEDGMENTS
P.M. acknowledges funding from Fundaçaõ para a Ciência e
Tecnologia, in the form of Grant SFRH/BPD/81748/2011.
E.J.M.F. and P.M. acknowledge support from Fundaçaõ para a
Ciência e a Tecnologia through Grant Pest-OE/QUI/UI0100/
2013. C.M. and G.D. acknowledge support from the National
Science Foundation through Grant CBET-1067642.
■
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