Handbook of Solvents - George Wypych - ChemTech - Ventech!

6.2 Equilibrium swelling in binary solvents 321
where:
χ13 and χ 23 parameters of interaction of components 1 and 2 with polymer, correspondingly
χ12 parameter of interaction of components 1and 2 of liquid mixture
In the equation obtained from the fundamental work by Scott, 5 mixed solvent is represented
as “a uniform liquid” with the variable thermodynamic parameters depending on
composition.
If the χ123 value is considered as a criterion of existence of a maximum of equilibrium
swelling of polymer in the mixed solvent, a maximum of Q should correspond to the minimum
of χ123. For practical use of Eq. [6.2.2] it is necessary to know parameters χ13, χ23, and
χ12. The values χ13 and χ23 can be determined by the Flory-Rehner equation, with data on
swelling of a crosslinked elastomer in individual solvents 1 and 2. The evaluation of the χ12 value can be carried out with use of results of the experimental evaluation of vapor pressure,
viscosity and other characteristics of a binary mixture. 6,7
To raise the forecasting efficiency of prediction force of such criterion as χ123 minimum,
the amount of performance parameters determined experimentally must be reduced.
For this purpose, the following expression for the quality criterion of the mixed solvent (the
analogy with expression of the Flory-Huggins parameter for individual solvent-polymer
system) is used:
s V12
2
χ123 = χ123 + ( δ3 − δ12)
V12 = V1x1+ V2x 2
[6.2.2]
RT
where:
V12 molar volume of the liquid mixture
V1,V2 molar volumes of components 1 and 2
x1,x2 molar fractions of components 1 and 2 in the solvent
R universal gas constant
T temperature, K.
s
χ123 constant, equal to 0.34
s s
The values of entropy components of parameters χ13 and χ 23 (essential for quality prediction)
8 were taken into account. Using the real values of entropy components of interac-
s s
tion parameters χ13 and χ 23,
we have:
s V1
2
χ13 = χ13 − ( δ3 − δ1)
[6.2.3]
RT
s V2
2
χ23 = χ23 − ( δ3 − δ2)
[6.2.4]
RT
quality criterion of mixed solvent is represented by: 3
( )
12
χ123 = χ13 ϕ1+ χ23 ϕ2+ δ −δ
RT
s s V
3 12
2
[6.2.5]
The values of parameters χ13 and χ23 were calculated from the Flory-Rehner equation,
s s
using data on swelling of crosslinked polymer in individual solvents, the values χ13, χ 23,
and χ123 were estimated from Eqs. [6.2.3-6.2.5). Then equilibrium swelling of elastomer in
SL was calculated from the equation similar to Flory-Rehner equation, considering the mix-