Handbook of Solvents - George Wypych - ChemTech - Ventech!

126 Valery Yu. Senichev, Vasiliy V. Tereshatov
tribution to χ 1 stipulated by the difference in free volumes of polymer and solvent. Both
terms of the equation are larger than zero, and as temperature increases the first term decreases
and the second term increases. The expression can be given in a reduced form (with
some additional substitutions): 12
χ1 *
V1
~ 13
13
*
P1
V 1 X 12 V 1
* 13
RT1
P1
V 1 1 24
/
~ / *
~ /
⎛ ⎞
=
⎜ ⎟
⎜ ⎟
− ⎝ ⎠
+
⎡
⎢
⎢
⎢
⎛
⎢
⎜
/ −V
⎣⎢
⎝
~ / 13
3 1
⎞
⎟
⎠
⎤
⎥
⎥
⎥
⎥
⎦⎥
2
τ [4.2.6]
where: ~
* *
V1, P1, T1reduced
molar volume of solvent, pressure and temperature consequently
X12 contact interaction parameter.
These parameters can be calculated if factors of the volumetric expansion, isothermal
compressibility, thermal capacity of a solvent and enthalpy of mixing of solution components
are known.
With temperature decreasing, the first term of the right side of the expression [4.2.6]
increases and the second term decreases. Such behavior implies the presence of the upper
and lower critical temperatures of mixing. Later Flory developed another expression for χ1 that includes the parameter of contact interactions, X12: 13,14
χ
1
⎡
=
V RT ⎣
* *
2
PV ⎛ 1 1 s ⎞ 2 X
⎢
12 ⎜
⎟
~ ⎟ *
⎢
1 ⎝s1
⎠ P1
*
α1T
⎛P
⎞ 2
+ ⎜
2 ⎜ *
⎝P1
⎠
⎟ −
⎧⎪
⎨ τ
⎩⎪
s
s
2
1
X
P
12
*
1
⎫⎪
⎬
⎭⎪
2
⎤
⎥
⎥
⎦
[4.2.7]
where:
s1,s2 ratios of surfaces of molecules to their volumes obtained from structural data.
The large amount of experimental data is then an essential advantage of the Flory’s
theory. 9 Simple expressions exist for parameter X12 in the terms of Xij characteristic parameters
for chemically different segments of molecules of components 1 and 2. Each segment
or chemical group has an assigned value of characteristic length (αi, αj) or surface area as a
fraction of the total surface of molecule: 15
Χ12 = ∑ αi 1 −αi 2 α j 1 −α
j 2 Χij
[4.2.8]
i, j
Bondi’s approach may be used to obtain surface areas of different segments or chemical
groups. 16 To some extent Huggins’ new theory 17-21 is similar to Flory’s theory.
4.2.2 CHEMICAL STRUCTURE
Chemical structure and the polarity determine dissolution of polymers. If the bonds in polymer
and solvent are similar, then the energy of interaction between homogeneous and heterogeneous
molecules is nearly identical which facilitates solubility of polymer. If the
chemical structure of polymer and solvent molecule differ greatly in polarity, then swelling
and dissolution does not happen. It is reflected in an empirical rule that “like dissolves like”.
( , , )( , , )