Handbook of Solvents - George Wypych - ChemTech - Ventech!

154 Christian Wohlfarth
where:
a,b,c,d empirical fitting parameters for the χ-function
β00 , β01, β10 , β11
empirical fitting parameters for the g-function
T absolute temperature
P pressure
All these fitting parameters may be concentration dependent and may be included into
Equations [4.4.15 or 4.4.16]. Details are omitted here. More theoretical approaches will be
discussed shortly in Subchapter 4.4.4.
The χ-function can be divided into an enthalpic and an entropic parts:
∂χ
∂χ
χ = χ + χ χ =− χ
∂
∂
⎛ ⎞
⎜ ⎟ =
⎝ ⎠
⎛ T ⎞
H S with H T and S ⎜ ⎟
T
⎝ T ⎠
p,
ϕ P,
ϕ
[4.4.18]
where:
χH enthalpic part
χS entropic part
An extension of all these equations given above to multi-component mixtures is possible.
Reviews of continuous thermodynamics which take into account the polydisperse character
of polymers by distribution functions can be found elsewhere. 52-54
4.4.3 EXPERIMENTAL METHODS, EQUIPMENT AND DATA REDUCTION
4.4.3.1 Vapor-liquid equilibrium (VLE) measurements
Investigations on vapor-liquid equilibrium of polymer solutions are the most important
source for obtaining solvent activities in polymer solutions. Therefore, emphasis is laid to
the experimental methods which use this equilibrium. These methods are:
(i) absolute vapor pressure measurement,
(ii) differential vapor pressure measurement,
(iii) isopiestic sorption/desorption methods, i.e. gravimetric sorption,
piezoelectric sorption, or isothermal distillation,
(iv) inverse gas-liquid chromatography (IGC) at infinite dilution,
IGC at finite concentrations, and head-space gas-chromatography
(HSGC),
(v) ebulliometry and
(vi) the non-equilibrium steady-state method vapor-pressure
osmometry (VPO).
The measurement of vapor pressures for polymer solutions is generally more difficult
and more time-consuming than that of low-molecular mixtures. The main difficulties can be
summarized as follows: Polymer solutions exhibit strong negative deviations from Raoult’s
law. These are mainly due to the large entropic contributions caused by the difference between
the molar volumes of solvents and polymers, as was explained by the classical
Flory-Huggins theory 46,47 about 60 years ago, Equation [4.4.12]. However, because of this
large difference in molar mass, vapor pressures of dilute solutions do not differ markedly
from the vapor pressure of the pure solvent at the same temperature, even at polymer concentrations
of 10-20 wt%. This requires special techniques to measure very small differences
in solvent activities. Concentrated polymer solutions are characterized by rapidly
increasing viscosities with increasing polymer concentration. This leads to a strong increase
in time required to obtain real thermodynamic equilibrium caused by a slow solvent diffu-