Correlation between the combinatory entropy of polymer and ideal liquid solutions

Abstract

A semiempirical equation of combinatory entropy in binary solutions of semiflexible or rod-like polymers in solvent has been derived, based on a correlation between the combinatory entropy in polymer solution derived by Flory, Huggins, Miller and Guggenheim and an ideal simple liquid solution. The expression for the partial entropy of mixing of solvent ΔS M,1 obtained in this work is given by: ΔS M,1/k= −ln ø 1 − ø 2(1−r −1)+αø 1ø 2+ln{[ø 1+(ø 2/r)]/[ø 1+(ø/r)+αø 1ø 2]}+αø 2 2ln{(r −1+αø 1)/[ø+(ø 2/r)+αø 1ø 2]} where ø i is the volume fraction of polymer ( i = 2) and solvent (1), r is the number of segments per polymer, k is the Boltzmann constant and α is a parameter characterizing the flexibility of polymer chain such that α = 0 for flexible polymers and α = (1 − r −1)/ ø 1 for rigid-rod polymers. The chemical potential of solvent in the polymer solution is given by: μ 1−μ 0 1= RT[−ΔS M,1/k+X 0 1(1+α)ø 2 2] where X 0 1 is the polymer-solvent interaction parameter in the Flory-Huggins theory.