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 pa rallel hard cylinders of different lengths. We use the Helmholtz free energy truncated at the second virial term. Changing values of q (leng th of a longer cylinder), x (composition) and eta (packing fraction) o f the cylinders, we obtained the transition points at which the nemati c phase becomes unstable for a sinusoidal density perturbation. Phase diagrams on eta vs x plane are drawn for various q's. Depending on q a nd 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 st ructure,each layer of the smetic A contains longer particles and short er particles uniformly. In the other type of the structure, layer of s horter particles and layer of longer particles stack alternatively.