Handbook of Solvents - George Wypych - ChemTech - Ventech!

6.2 Equilibrium swelling in binary solvents 325
At the same values of Q v difference between coordinates on the abscissa axes of points
of the curves 1-1�, 2-2� (Figures 6.2.5-6.2.8) are equal ε (Figure 6.2.9).
As expected, 10 preferential sorption was observed, with the essential distinction of
molar volumes V 1 and V 2 of components of the mixed solvent (hexane-DBP, DOS-DEP).
For swelling of the crosslinked elastomer SCN-26 in the mixture of components, having
similar molar volumes V 1 and V 2 (e.g., amyl acetate-dimethyl phthalate) the preferential
sorption of components of SL is practically absent. Influence of V 1 and V 2 and the influence
of double interaction parameters on the sorption of binary liquids by crosslinked elastomers
was examined by the method of mathematical experiment. Therewith the set of equations
describing swelling of crosslinked elastomers in binary mixture, similar to the equations obtained
by Bristow 6 from the Flory-Rehner theory 11 and from the work of Schulz and Flory, 12
were used:
2
( 1 l) ( 1 l)
2
2
lnϕ + − ϕ + χ ϕ = lnυ
+ − υ + υ + χ υ + χ υ +
1 2 12 2
1 2 3 12 2
⎛ 13 2
+ ( χ12 + χ13 − lχ23) υ2υ3+ ( νe V3) V1⎜υ3−
υ
⎝ f
/
/
1
1 2
1
( 1 ) 1 12 1 2 ( 1 )
lnϕ + − l ϕ + l χ ϕ = lnυ
+ − l υ + υ + l
2
− − − −1
1 3
⎡ 13 / 2 ⎤
χ υ + lχ υ + χ12 + lχ23 − χ13 υ1υ3+ ν V3V2υ3− υ3
⎣
⎢ f ⎦
⎥
2
2
⎣ 12 1 23 3 ( ) ⎦ ( e / )
3
⎞
⎟
⎠
12 3
[6.2.6]
[6.2.7]
where:
l =V1/V2 f functionality of a network
The analysis of calculations from Eqs. [6.2.6] and [6.2.7] has shown that if V1 χ13. The greater is χ12 value at V1 ≠ V2 the more likely preferential sorption takes place with all
other parameters being equal. The same applies to the diluted polymer solutions.
To improve calculations of the preferential sorption in the diluted solutions of polymers,
the correction of Flory’s theory is given in works 9,13-15 by introduction of the parameter
of three-component interaction, χT, into the expression for free energy of mixing, and
substitution of χT by qT. 14 This approach is an essential advancement in the analysis of a
sorption of two-component liquids by polymer. On the other hand, the increase in the number
of experimental parameters complicates the task of prediction of the preferential sorption.
In swelling crosslinked elastomers, the preferential sorption corresponds to the maximum
QV value and compositions in a swollen polymer and a liquid phase practically coincide
(Figures 6.2.5-6.2.8). This observation can be successfully used for an approximate
evaluation of the preferential sorption.
Assuming that ϕ1 = φ1and
ϕ2 = φ2
at extremum of the total sorption (φ3 = φ3
min ), AUL 5
e
can be used to calculate the effective value of χ12 from the expression for χ123: 16
χ
e
12
m
χ13
χ 23V1 χ123V1
= + − [6.2.8]
m m
m m m
ϕ ϕ V V ϕ ϕ
2
1 2
12 1 2