Phase Diagram of the Nematic-Smectic A Transition of the Binary Mixture of Parallel Hard Cylinders of Different Lengths

We study the nematic-smetic A phase transition of binary mixture of parallel hard cylinders of different lengths. We use the Helmholtz free energy truncated at the second virial term. Changing values of q (length of a longer cylinder), x (composition) and η (packing fraction) of the cylinders, we obtained the transition points at which the nematic phase becomes unstable for a sinusoidal density perturbation. Phase diagrams on η vs x plane are drawn for various q 's. Depending on q and x , the stable region of the smetic A is suppressed or enlarged, and two types of structures of the smetic A appear. In one type of the structure,each layer of the smetic A contains longer particles and shorter particles uniformly. In the other type of the structure, layer of shorter particles and layer of longer particles stack alternatively.