Lattice Boltzmann study of hydrodynamic effects in lamellar ordering process of two-dimensional quenched block copolymers

Abstract

By incorporating self-consistent field theory with lattice Boltzmann method, a model for polymer melts is proposed. Compared with models based on Ginzburg-Landau free energy, our model does not employ phenomenological free energies to describe systems and can consider the chain topological details of polymers. We use this model to study the effects of hydrodynamic interactions on the dynamics of microphase separation for block copolymers. In the early stage of phase separation, an exponential growth predicted by Cahn-Hilliard treatment is found. Simulation results also show that the effect of hydrodynamic interactions can be neglected in the early stage. For the late stage of phase separation, it is easy to see the effects of hydrodynamic interactions on the ordering process of lamellae phase. From the analysis of structure factor curves, we find that the growth of domains is faster if hydrodynamic interactions are introduced. Furthermore, the scaling of the pattern dynamics is investigated for the late stage at zero thermal noise. By studying the behavior of scaling exponents of the structure factor and the nematic order-parameter correlation function C(nn), we can see that the effects of hydrodynamic interactions lead to bigger growth exponent for both functions.