Microphase segregation in molten randomly grafted copolymers

We study microphase ordering of molten randomly grafted copolymers (RGCs) by using a mean field theory and the replica method to calculate the quenched average. Our results illustrate that in the weak segregation limit (WSI), the optimal wave vector $q*$ of the lamellar phase formed by molten RGCs, has a temperature dependence different from either linear random copolymers (LRCs) or diblock copolymers (DCPs): when close, but below the microphase separation transition (MST) temperature, $q*$ increases sharply with decreasing temperature; then $q*$ gradually acquires an asymptotic value determined by the length of the branch and the average distance between branch points on the backbone. Our results are compared with recent experiments, and the effects of chain architecture on the microphase separation characteristics of RGCs are delineated. Our results suggest a new method for controlling the microphase spacing by exploiting quenched disorder.