Kinetic pathways of order-disorder and order-order transitions in weakly segregated microstructured systems.

where cs$ rd is the order parameter, e.g., the local magnetization in magnetic systems, or the local density contrast between the two types of monomers in diblock copolymers. t is related to the distance from the order-disorder transition temperature, and the coefficients b, c, u, and y are phenomenological parameters which can be computed from more microscopic models. The last term in Eq. (1) represents the long-range repulsion, which penalizes longwavelength inhomogeneities. The equilibrium properties of systems described by Eq. (1) have been the subject of extensive experimental and theoretical studies [1,2]. In this Letter, we address the phenomenology of the kinetics of the various order-order and order-disorder transitions in weakly segregated, microstructured systems, using a time-dependent Ginzburg-Landau approach. Specifically we study the kinetic pathways of HEX to disordered and HEX to bcc phases after a sudden temperature jump. This study is motivated by the general intrinsic interest in understanding kinetics of phase transitions involving spatially modulated phases, in particular, by recent experiments on diblock copolymers [3–7]. To be concrete, we shall use diblock copolymers as the context; however, we believe the phenomenology is quite general for the class of systems described by the free energy Eq. (1), and will not limit our choice of parameters specifically to those for diblock copolymers [8]. For conserved order parameters, as is appropriate for diblock copolymers, we may write the time-dependent Ginzburg-Landau equation as [9]