Lattice Boltzmann method for multiscale self-consistent field theory simulations of block copolymers

A new Lattice Boltzmann (LB) approach is introduced to solve for the block copolymer propagator in polymer field theory. This method bridges two desired properties from different numerical techniques, namely: (i) it is robust and stable as the pseudo-spectral method and (ii) it is flexible and allows for grid refinement and arbitrary boundary conditions. While the LB method is not as accurate as the pseudo-spectral method, full self-consistent field theoretic simulations of block copolymers on graphoepitaxial templates yield essentially indistinguishable results from pseudo-spectral calculations. Furthermore, we were able to achieve speedups of ∼100× compared to single CPU core implementations by utilizing graphics processing units. We expect this method to be very useful in multi-scale studies where small length scale details have to be resolved, such as in strongly segregating block copolymer blends or nanoparticle-polymer interfaces.