Calculation of combinatory entropy in complex polymer solutions based on the Flory–Huggins theory

Abstract

The combinatory entropy for two types of complex polymer solutions has been calculated based on the Flory–Huggins theory. The combinatory entropy for polymer solution with polymer chains consisting of two kind of parts, rod and flexible parts is given by: ΔS f–r /R= ΔS F–H /R+{1+β−(1−r −1)Φ 2} ln {1−Φ 2(1−r −1)/(β+1)}−(r −1+β)Φ 2 ln {1−(1−r −1)/(β+1)} where Δ S F–H/ R=− Φ 1 ln Φ 1−( Φ 2/ r) ln Φ 2 corresponds to the F–H theory, Φ i is the volume fraction of component ( i), r is the number of segment per polymer, β= a/ c where a is the number of segments in the flexible part and c is the number of segments in the rod part, m is the number of repeated units in a chain and the unit consists of a flexible part and a rod part and m( a+ c)= r−1. The combinatory entropy in the polymer solution where some solvent molecules interact with polymer segments strongly as `solvation' is given by: ΔS solv /R=−(1/r) ln Φ 2−{(1+ϵ) −1−Φ 2} ln {1−Φ 2(1+ϵ)} where ϵ is defined by ϵ= r s/ r and r s is the number of solvents solvated per polymer. Correlation between Δ S f–r in this work and those obtained by Guggenheim, Miller, Huggins and Kurata has been discussed and found that these are essentially the same. The partial molar entropy of solvent Δ S 1/ R in polymer solution calculated in this work agreed with those obtained based on the experimental data in solution of polyisobutylene in n-pentane where Δ S 1/ R is negative over low polymer concentration.