Theoretical study of the dynamics of the nematic-smectic A phase transition

We consider the dynamics of the nematic-smectic A phase transition in a system of parallel hard cylinders. We derive a time evolution equation of the density distribution from a free energy functional truncated at the 2nd virial approximation. When the packing fraction is changed, the stable density distribution is transformed from uniform density (nematic phase) to periodic density wave (smectic A phase). We show that the growth of the smectic A structure involves two kinds of dynamical processes. One is the growth of the amplitude of the density wave, and the other is the growth of the coherent length of the periodic structure. We also investigate the equilibrium density distribution as a function of the packing fraction.