Microphase separation in block copolymers

We introduce a microscopic model for the phase separation in block copolymers and carry out Monte Carlo simulations in two dimensions. We find that the equilibrium structure function satisfies a scaling relation with $D_{\mathrm{eq}}$, the thickness of the microdomains. We also find that $D_{\mathrm{eq}\mathrm{\sim }{N}^{\theta }}$, where N is the chain length and θ=(1/2 in the weak-segregation limit, in agreement with calculations in a cell-dynamics model. This suggests that the microscopic and the continuum models of block copolymers are in the same universality class.