Prediction of microstructures for polydisperse block copolymers, using continuous thermodynamics

Abstract

AbstractA generalization of an earlier theory (Leary–Henderson–Williams) developed for microphase separation in monodisperse block copolymers is made for copolymers having moderate degrees of polydispersity and illustrated for the Schultz molecular weight distribution (MWD). First, an explicit study is made of molecular weight (M) effects for monodisperse poly (styrene–butadiene) diblock (SB) and triblock (SBS) copolymers. For a fixed temperature, it is shown how the critical molecular weight (Mc)—above which the copolymer is phase‐separated at equilibrium —varies with molecular composition (ϕS, volume fraction of S component) for both molecular architectures. Also predicted are the microstructural parameters ΔT(M) and f(M)—interphase thickness and volume fraction, respectively—and the high‐M limiting functions ΔT ∝︁ Mα2, f ∝︁ Mα3, D ∝︁ Mα4 (D is domain repeat distance) and Ts ∝︁ Mα5 (Ts is separation temperature). Then, for polydisperse systems in the range 1 ≲ p ≲ 3 ( where \[ P = \bar M_w /\bar M_n \] ) corresponding predictions at constant \[ \bar M_n \] are made after identifying the mixture free‐energy‐minimum state with a weight average of the free energy minima of each fraction of the MWD. Calculations are made specifically for ϕS = 0.50 and Ts = 298 K. It is shown that, even when \[ \bar M_n < M_c \] , polydispersity can induce microphase separation if p is sufficiently large. Good success is obtained in comparisons of D predictions with data on blends of two polydisperse diblock samples.