Entropic segregation in smectic phases of hard-body mixtures

Using an extension of the Parsons-Lee density-functional theory, we have calculated the phase behaviour of mixtures of hard bodies, focusing on the formation of smectic phases. The interactions are represented by hard spherocylinders, and the mixtures have two components of lengths L-1, L-2 and widths D-1, D-2, respectively, with D-1 = D-2. The special case where one of the components is a hard sphere (L-1 = 0, L-2 not equal 0) is also studied. Particular emphasis is put on the interplay between smectic-phase formation and smectic-smectic segregation. In general, smectic-smectic segregation is seen to occur in a wide range of compositions and pressures, except when the length ratio q equivalent to L-1/L-2 is relatively close to unity, i.e. particles have similar lengths; in this case segregation appears only at high pressure. Finally, in the case where q is very different from unity and the composition is such that there is a small fraction of long molecules, even when the mixture is macroscopically homogeneous, there appears a microsegregated phase where the minority component is expelled to the interstitial regions between the smectic layers.