Correlation between the combinatory entropy of polymer and ideal liquid solutions: 2. Ternary polymer-polymer-solvent and binary polymer-polymer systems

Abstract

A semiempirical equation of combinatory entropy in ternary solutions containing two semiflexible polymers and flexible and semiflexible polymers in solvent has been derived, based on a previous equation for a binary polymer solution. The partial entropy of mixing for solvent, ΔS M,0, in the ternary system polymer (1)-polymer (2)-solvent (0) is expressed by: ΔS M,0 k =lnф 0+a−1+ln[ a (a+b) ]+b+k 1ф 2 1ln{ [r −1 1+k 1+k 1−ф)] (a+b) }+k 2ф 2 2ln{ [r −1 2+k 2(1− 2)] (a+b) } where a = ф 0 + ( ф 1 r 1 ) + ( ф 2 r 2 ) , b = k 1ф 1(1 − ф 1) + k 2ф 2(1 − ф 2), ф i is the volume fraction of component i, and k i is a constant characterizing the flexibility of polymer, for example k i = 0 for a flexible polymer and k i > 0 for a semiflexible polymer. Values of partial entropy of mixing for polymers, ΔS M, i , are evaluated in the ternary solution of two polymers with different flexibilities in solvent. The combinatory entropy in a binary polymer-polymer system is also discussed.