Front propagation in a diblock copolymer melt

Abstract

The dynamics of front propagation in a diblock copolymer melt are described. Systems in which stable ordered phases invade unstable and metastable disordered phases are considered. Employing a model equation deduced by Oono and Shiwa [Mod. Phys. Lett. B 1, 49 (1987)] from a cell-dynamical scheme, these systems are studied in the weak-segregation limit. In this limit, a bifurcation parameter whose magnitude quantifies the distance from the spinodal naturally arises. Exploiting the smallness of this parameter, stationary solutions to the equation of motion are perturbatively constructed for the cases of lamellar, triangular (often referred to as IhexagonalR), and bcc ordered structures. Generalizing this technique, equations of motion describing the invasion processes are derived, and from these, traveling-wave solutions are found numerically. Propagation velocities and front-envelope profiles are determined, and a number of qualitative features of the various invasion processes are described. Experimental observability of the invasion processes and experimental identification of the phenomenological parameters appearing in the equation of motion are discussed. Using existing experimental data, estimates are made of the propagation velocity which would be observed in a particular physical system and the range of temperatures, in degrees Centigrade, over which our perturbative calculation is applicable. It is found that this range includes temperatures well into the mean-field regime.