Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.4 Measurement of solvent activity 213
c 3c is the total number of external degrees of freedom per molecule
When c = 1, Equation [4.4.100] reduces to the common Soave-Redlich-Kwong (SRK)
equation of state. 378 Temperature functions and combining/mixing rules for parameters
a,b,c are not discussed here because quite different approximations may be used. Problems,
how to fit these parameters to experimental PVT-data for polymers, have been discussed by
several authors. 375-380
Orbey and Sandler 380 applied the Peng-Robinson equation of state as modified
by Stryjek and Vera 381 (PRSV):
PV
RT
()
V
aT
= −
V − b RT V bV b
2 2 ( + 2 − )
[4.4.101]
to calculate solvent activities in polymer solutions using Wong-Sandler mixing rules 382 that
combine the equation of state with excess energy models (EOS/GE-mixing rules). They
have shown that a two-parameter version can correlate the solvent partial pressure of various
polymer solutions with good accuracy over a range of temperatures and pressures with
temperature-independent parameters. Harrismiadis et al. 379 worked out some similarities
between activity coefficients derived from van der Waals like equations-of-state and Equations
(4.4.92 and 93), i.e., the Elbro-fv model. Zhong and Masuoka 383 combined SRK equation
of state with EOS/GE-mixing rules and the UNIFAC model to calculate Henry’s
constants of solvents and gases in polymers. Additionally, they developed new mixing rules
for van der Waals-type two-parameter equations of state (PRSV and SRK) which are particularly
suitable for highly asymmetric systems, i.e., also polymer solutions, and demonstrated
that only one adjustable temperature-independent parameter is necessary for
calculations within a wide range of temperatures. 384 In a following paper, 385 some further
modifications and improvements could be found. Orbey et al. 386 successfully proposed
some empirical relations for PRSV-equation-of-state parameters with polymer molar mass
and specific volume to avoid any special parameter fitting for polymers and introduced a
NRTL-like local-composition term into the excess energy part of the mixing rules for taking
into account of strong interactions, for example, in water + poly(propylene glycol)s. They
found infinite-dilution activity coefficient data, i.e., Henry’s constants, to be most suitable
for fitting the necessary model parameter. 386
Orbey et al. 387 summarized three basic conclusions for the application of cubic equations
of state to polymer solutions:
(i) These models developed for conventional mixtures can be extended to quantitatively
describe VLE of polymer solutions if carefully selected parameters are used for the
pure polymer. On the other hand, pure-component parameters of many solvents are already
available and VLE between them is well represented by these cubic equations of state.
(ii) EOS/GE-mixing rules represent an accurate way of describing phase equilibria.
Activity coefficient expressions are more successful when they are used in this format than
directly in the conventional gamma-phi approach.
(iii) It is not justifiable to use multi-parameter models, but it is better to limit the number
of parameters to the number of physically meaningful boundary conditions and calculate
them according to the relations dictated by these boundary conditions.