Dynamics of phase separation in block copolymer melts

We consider the partial differential equation which describes phase separation in a block copolymer melt. We construct numerically the periodic solution which minimizes the free energy. The lamellar thickness of the final equilibrium pattern is found to scale with the molecular weight as a power law ${\lambda }_L$∼$N^{\theta }$. The exponent θ takes the value (1/2 in the weak-segregation regime and (2/3 in the strong-segregation regime. We propose a scaling theory of the dynamics, from which we obtain θ=2φ, where φ is the scaling exponent in spinodal decomposition, in agreement with a conjecture by Oono and Bahiana [Phys. Rev. Lett. 61, 1109 (1988)]. Lastly, we also study the pattern formed by propagating fronts. The selection of the unique velocity of the front and of the wavelength of the pattern behind the front agrees well with the marginal-stability theory.