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Handbook of Solvents - George Wypych - ChemTech - Ventech!

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246 Valery Yu. Senichev, Vasiliy V. Tereshatov<br />

The detailed comparative evaluation <strong>of</strong> experimental techniques and designs <strong>of</strong> equipment<br />

used for determination <strong>of</strong> enthalpy <strong>of</strong> evaporation can be found in the appropriate<br />

monographs. 7,14 Values <strong>of</strong> solubility parameters <strong>of</strong> solvents are presented in Subchapter 4.1.<br />

5.1.2 METHODS OF EXPERIMENTAL EVALUATION AND CALCULATION OF<br />

SOLUBILITY PARAMETERS OF POLYMERS<br />

It is not possible to determine solubility parameters <strong>of</strong> polymers by direct measurement <strong>of</strong><br />

evaporation enthalpy. For this reason, all methods are indirect. The underlining principles<br />

<strong>of</strong> these methods are based on the theory <strong>of</strong> regular solutions that assumes that the best mutual<br />

dissolution <strong>of</strong> substances is observed at the equal values <strong>of</strong> solubility parameters (see<br />

Chapter 4).<br />

Various properties <strong>of</strong> polymer solutions involving interaction <strong>of</strong> polymer with solvent<br />

are studied in a series <strong>of</strong> solvents having different solubility parameters. A value <strong>of</strong> a solubility<br />

parameter is related to the maximum value <strong>of</strong> an investigated property and is equated<br />

to a solubility parameter <strong>of</strong> polymer.<br />

This subchapter is devoted to the evaluation <strong>of</strong> one-dimensional solubility parameters.<br />

The methods <strong>of</strong> the evaluation <strong>of</strong> components <strong>of</strong> solubility parameters in multi-dimensional<br />

approaches are given in the Subchapter 4.1.<br />

According to Gee, 15 a dependence <strong>of</strong> an equilibrium swelling <strong>of</strong> polymers in solvents<br />

on their solubility parameters is expressed by a curve with a maximum where the abscissa is<br />

equal to the solubility parameter <strong>of</strong> the polymer. For exact evaluation <strong>of</strong> δ, a swelling degree<br />

is represented by an equation resembling the Gaussian function:<br />

where:<br />

Then<br />

2<br />

[ ( ) ]<br />

Q = Q −V δ −δ<br />

[5.1.11]<br />

max exp 1 1 2<br />

Qmax the degree <strong>of</strong> swelling at the maximum on the curve<br />

V1 molar volume <strong>of</strong> solvent<br />

δ1, δ2<br />

solvent and polymer solubility parameters.<br />

1<br />

δ2 = δ1<br />

±<br />

1<br />

⎛<br />

⎜<br />

⎝V<br />

Q<br />

Q<br />

ln max<br />

12 /<br />

⎞<br />

⎟<br />

⎠<br />

[5.1.12]<br />

The dependence [(1/V1)ln(Qmax/Q)] 1/2 =f(δ1 ) is expressed by a direct line intersecting<br />

the abscissa at δ1 = δ2.<br />

This method is used for calculation <strong>of</strong> the parameters <strong>of</strong> many<br />

crosslinked elastomers. 16-19<br />

The Bristow-Watson method is based on the Huggins equation deduced from a refinement<br />

<strong>of</strong> the lattice approach: 20<br />

( V RT)(<br />

)<br />

χ = β+ / δ −δ<br />

[5.1.13]<br />

1 1 2<br />

2<br />

where:<br />

β =(1/z)(1-1/m)<br />

z a coordination number<br />

m the chain length.<br />

β may be rewritten as χS entropy contribution to χ (see Chapter 4).

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