n - PATh :.: Process and Product Applied Thermodynamics research ...

Modeling
From the optimised parameters of the linear perfluoroalkanes from C1 to C9, a
simple relationship of the molecular parameters with the carbon number, CN, was
obtained:
m = 0.3580 + 0.679 CN (III.31)
mσ 3 = 35.49 + 42.38 CN (III.32)
mε/kB B = 96.60 + 91.64 CN (III.33)
Units of σ and ε/kB are Å and K, respectively. Parameters from these relationships
deviate from the fitted parameters with an absolute averaged deviation (AAD) lower than
1%. One of the advantages of molecular theories compared to macroscopic models is that
the former need fewer meaningful parameters. To provide additional evidence of this,
optimised size and energy parameters are plotted in Figure III.2 with respect the carbon
number CN for the linear perfluoroalkane chain. Because the model is homonuclear and
the effect of the extreme CF3 groups weakens as the chain length increases, the LJ
parameters should tend to an asymptotic value, as seen in Figure III.2. Furthermore,
molecular simulation united-atom model (Cui et al., 1998; Hariharan and Harris, 1996) in
which the LJ potential for the nonbonded interactions is used (without Coulombic
interactions), employ optimised values for the size parameter in the range σCF2 = σCF3 =
4.65 ± 0.05 Å. These simulations give quantitative predictions for equilibrium properties of
chains from n-perfluoropentane to n-perfluorohexadecane. The corresponding value from
our model (equivalent to a chain of infinite number of carbons), straightforwardly
calculated from Equations III.31-III.33, is 4.63 Å. The similarity among the parameters of
different theories acts in favour of the physical meaning of them.
Figures III.3-III.7 present equilibrium liquid densities and vapour pressures for the
gases, linear perfluoroalkanes and cyclic and substituted fluoroalkanes under study. Results
obtained with the soft-SAFT EoS were compared with the ones given by the original form
of the Peng-Robinson EoS (Peng and Robinson, 1976). Full lines represent the soft-SAFT
correlation using the parameters given in Table III.1 while dashed lines represent the
results given by the Peng-Robinson EoS. Since no critical data were found for
perfluorodecalin nor substituted fluoroalkanes, only the correlation from the soft-SAFT
EoS is presented in these cases.
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