Kinetics of microphase segregation in one-dimensional symmetric diblock copolymer systems

An analytical one-dimensional model of the microphase separation in symmetr ic diblock copolymers is developed. Three stages of the process of the micr ophase segregation of a quenched diblock copolymer system into a lamella st ructure are predicted. The first stage involves a fast increase of the ampl itude of the quasi-periodical lamella structure (with the average wave vect or q(0)) up to a nearly equilibrium value; the second stage is a slow phase diffusion process which is characterized by increasing coherency of the la mella structure; the third stage is the slow process of the lamella swellin g, which is driven by the thermally activated process of the spontaneous de letion of excessive lamellas, the lamella size increasing from the initial value 2 pi /q(0) to the equilibrium 2 pi /q(eq) > 2 pi /q(0) during the pro cess. The last two stages are described with the specially introduced coars e-grained "amplitude-phase" approximation. It is shown that the relaxation of the gradient of the phase of the lamellar structure is the slowest relax ation process and, thus, can be used as an effective order parameter of the lamellar structure at the later stages of the microphase segregation.