50th Anniversary Perspective: Phase Behavior of Polymer Solutions and Blends

Abstract

We summarize our knowledge of the phase behavior of polymer solutions and blends using a unified approach. We begin with a derivation of the Flory–Huggins expression for the Gibbs free energy of mixing two chemically dissimilar polymers. The Gibbs free energy of mixing of polymer solutions is obtained as a special case. These expressions are used to interpret observed phase behavior of polymer solutions and blends. Temperature- and pressure-dependent phase diagrams are used to determine the Flory–Huggins interaction parameter, χ. We also discuss an alternative approach for measuring χ due to de Gennes, who showed that neutron scattering from concentration fluctuations in one-phase systems was a sensitive function of χ. In most cases, the agreement between experimental data and the standard Flory–Huggins–de Gennes approach is qualitative. We conclude by summarizing advanced theories that have been proposed to address the limitations of the standard approach. In spite of considerable effort, there is no consensus on the reasons for departure between the standard theories and experiments.

Alkyl side chain length dependent compatibility of poly(4‐n‐alkylstyrene)s and 1,4‐rich polyisoprene blends

“…Temperature dependence of χ is generally described as χ = A + B / T . From the plots of χ c s evaluated here and the 1/ T c s given by phase diagrams as shown in Supporting Information Figure S13, A and B values were estimated to be −0.036 and 24, respectively.…”

“…Substituting the values for N A and N B in Table 1 into Temperature dependence of v is generally described as v 5 A 1 B/T. 1 From the plots of v c s evaluated here and the 1/ T c s given by phase diagrams as shown in Supporting Information Figure S13, A and B values were estimated to be 20.036 and 24, respectively. This result is naturally pointing the UCST type phase diagram of B > 0.…”

“…There are, however, several polymer pairs showing miscible phase behavior. For this reason, many researchers are attracted by polymer blends, and there are many extensive reports, both theoretical and experimental approaches.…”

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We investigated the compatibility of blends of 1,4rich polyisoprene (1, and poly(4-n-alkylstyrene)s with six kinds of n-alkyl side groups, that is, methyl, ethyl, propyl, butyl, hexyl, and octyl focusing on carbon number of alkyl groups. Poly(4-methylstyrene)/1,4-PI blend was turned out to be immiscible at all temperature range adopted in this work and poly(4-ethylstyrene)/1,4-PI blend revealed UCST type phase behavior, while the others were found to be compatible.

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Polymer crystallization at liquid‐liquid interface

“…The change in free energy per segment, ΔG m , when mixing gaussian polymer chains on an incompressible lattice was estimated 70 years ago independently by Flory and Huggins and is given by where k b is the Boltzmann's constant, T is the temperature, ϕ A is the volume fraction of polymer A, and N A and N b are the degree of polymerization of polymers A and B, respectively. The term χ is known as the Flory‐Huggins interaction parameter and its sign and magnitude is determined by the choice of monomeric units composing polymers A and B. Derivations using Equation can be utilized to construct theoretical phase diagrams in either χ N vs composition or temperature vs composition parameter space.…”