Phase segregation in gradient copolymer melts

Local segregation in melts of copolymers with composition gradients along their backbones is analyzed. The transition to a lamellar periodic structure as the effective degree of incompatibility χN increases is studied for symmetric copolymers with various composition gradients. A numerical self-consistent mean-field (SCMF) technique is used to characterize the ordered lamellar state in the weak and strong segregation regimes, and the random phase approximation (RPA) is used to calculate the scattering function analytically and find the location of the critical order-disorder transition for each melt. The critical point increases from (χN)_c = 10.495 for block copolymers to (χN)_c = 29.25 for a fully tapered linear gradient copolymer. For broad composition gradients the equilibrium lamellar repeat length is shorter for a given value of χN, and the unit cell composition profile is more sinusoidal. The dependence of the equilibrium repeat distance on χN is nearly universal when renormalized by the critical point of each copolymer.