CORRELATION BETWEEN THE COMBINATORY ENTROPY OF POLYMER AND IDEAL LIQUID SOLUTIONS

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 DELTAS(M,1) obtained in this work is given by: DELTAS(M,1)/k = - lnphi1 - phi2(1 - r-1) + alphaphi1phi2 + ln{[phi1 + (phi2/r)]/[phi1 + (phi2/r) + alphaphi1phi2]} + alphaphi2(2)ln{(r-1 + alphaphi1)/[phi1 + (phi2/r) + alphaphi1phi2]} where phi(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 alpha is a parameter characterizing the flexibility of polymer chain such that alpha = 0 for flexible polymers and alpha = (1 - r-1)/phi1 for rigid-rod polymers. The chemical potential of solvent in the polymer solution is given by: mu1 - mu1(0) = RT[ - DELTAS(M,1)/k + chi1(0)(1 + alpha)phi2(2)] where chi1(0) is the polymer-solvent interaction parameter in the Flory-Huggins theory.