Scaling Behavior of Block Copolymers in Spontaneous Growth of Lamellar Domains

The kinetics of microphase-separated lamellar domains is studied in numerical simulations of the cell-dynamical-system model of block copolymers in two dimensions. At early stages the correlation length ξ is found to grow with time as a power law, $\xi \propto t^{1/2}$, and is understood theoretically. The later-stage behavior, where both lamellar period and the correlation length are observed to grow in the same way, as $\xi \sim t^{\phi }$ with $\phi \approx \frac{1}{5}$, suggests that the lamella-forming block copolymers and Rayleigh-Bénard convective systems belong to the same universality class.