Free volume analysis of the viscosity of concentrated polymer solutions

Abstract

The fractional free volume f of a polymer solution as a function of temperature T and polymer volume fraction ф p is expressed as f(T, ф p ) = f 0 p (T)ф p + f s (T, ф p )(1 − ф p ) , and s, the fractional free volume of the solvent, in the entangled region is determined from viscosity data on some typical polymer + solvent systems by using the established empirical relation η( viscosity)∼ζ p ф 3.5 p M 3.5 w . Here, ζ p is the friction coefficient of a polymer jumping unit and related to f by ζ p ∼ exp( 1 f ) . For all the systems examined, which include both rubbery and glassy polymers, f s is virtually independent of ф p in entangled solutions, but, except for one system, it is much smaller than f 0 s, the solvent fractional free volume in the pure state. This finding shows that the additivity in the fractional free volume, i.e., the relation f = f 0 p ф p + f 0 s (1 − ф p ) does not hold in general. The concentration dependence of η of entangled polymer solutions is essentially governed by f 0 p and f∗ s , the latter being f s at the limit ф p → 1 .