PHASE-TRANSITIONS IN RANDOM COPOLYMERS

Ideal random AB copolymers with degree of polymerization N are mixture s of N + 1 types of chains with different compositions (fractions f(i) of A monomers). Conditions for single phase and multiphase equilibria are studied using Flory-Huggins free energy of mixing with chi repres enting the A-B interaction parameter. The spinodal for one phase insta bility is given by chi(s) = [2f(1 - f)]-1 for all N, where f is the av erage A fraction in the system. The transition from one to two phases is continuous at chi = chi(s) when f = 0. 5 and discontinuous at chi < chi(s) when f not-equal 0.5. Three, four, and more phases become stab le at larger values of chi. Our numerical solution suggests that the s tability range for multiple phases approaches DELTA(chi) almost-equal- to 0.15 at large (but finite) N. Macroscopically and microscopically p hase separated states are investigated with the Landau approach of Fre drickson, Milner and Leibler. The Landau method gives reasonable but i nexact results for two macroscopic phases when the random copolymer ha s compositional symmetry (f = 0. 5). A disordered mesophase is expecte d to be the most stable state at least over a range DELTA(chi) almost- equal-to 0. 15 above the critical point when N much greater than 1. Th e Landau approach with a single order parameter cannot be used for dis continuous transitions in random copolymers (f not-equal 0.5).