Self-assembly of lamellar microphases in linear gradient copolymer melts

We investigate lamellar microphases in linear gradient copolymer melts by a combination of techniques, including numerical solutions of self-consistent field equations, scaling theory, and analysis of the strong-segregation limit. In particular, we construct a Flory theory to predict the scaling of the equilibrium lamellar width L_eq as a function of comonomer incompatibility measured by πN. The Flory theory balances chain stretching with increased monomer repulsive interactions resulting from conformational fluctuations about a state of uniformly stretched chains, that obtains in the strong-segregation limit. We find L_eq/R_g ∼ (πN)^1/6, which agrees well with numerical results. Remarkably, this is the same result as for symmetric diblock copolymers, although for quite different physical reasons.