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We discuss theoretically, using density-functional theory, the phasestability of nematic and smectic ordering in a suspension of platelets of thesame thickness but with a high polydispersity in diameter, and study theinfluence of polydispersity on this stability. The platelets are assumed tointeract like hard objects, but additional soft attractive and repulsiveinteractions, meant to represent the effect of depletion interactions are alsoconsidered. The aspect (diameter to thickness) ratio is taken to be very high,in order to model solutions of mineral platelets recently exploredexperimentally. In this regime a high degree of orientational ordering occurs;therefore the model platelets can be taken as completely parallel and areamenable to analysis via a fundamental-measure theory. Our focus is on thenematic vs. smectic phase interplay, since a high degree of polydispersity indiameter suppresses the formation of the columnar phase. When interactions arepurely hard, the theory predicts a continuous nematic-to-smectic transition,regardless of the degree of diameter polydispersity. However, polydispersityenhances the stability of the smectic phase against the nematic phase.Predictions for the case where an additional soft interaction is added areobtained using mean-field perturbation theory. In the case of the one-componentfluid, the transition remains continuous for repulsive forces, and the smecticphase becomes more stable as the range of the interaction is decreased. Theopposite behaviour with respect to the range is observed for attractive forces,and in fact the transition becomes of first order below a tricritical point.Also, for attractive interactions, nematic demixing appears, with an associatedcritical point. When platelet polydispersity is introduced the tricriticaltemperature shifts to very high values.

Effect of polydispersity and soft interactions on the nematic vs. smectic phase stability in platelet suspensions