The structure factor of a wormlike chain and the random-phase-approximation solution for the spinodal line of a diblock copolymer melt

Abstract

An efficient and convenient numerical approach to calculate the structure factor of a wormlike chain model is proposed by directly dealing with a formal solution of the Green's function. A precise numerical representation of the structure factor of the wormlike chain model is then obtained, for arbitrary chain rigidity. On one hand, in the flexible limit, the numerical results recover the well-known Debye function of the structure factor of a Gaussian chain and furthermore predict the correct large-k behavior that a Gaussian model fails to capture; on the other hand, in the rigid limit, the numerical results recover the well-known Neugebauer function of the structure factor of a rigid rod. Based on the calculated structure factor, the random phase approximation is employed to study the physical properties of the order–disorder transition for asymmetric wormlike diblock copolymers; particularly, the spinodal line of the disordered phase is calculated. For the case of symmetric diblock copolymer microphase separation, the present calculation reproduces the phase boundary previously determined by self-consistent field theories and yields the entire picture crossing over from the flexible-chain limit to the rigid-chain limit.