Interplay between columnar and smectic stability in suspensions of polydisperse colloidal platelets

TL;DR

This study uses density-functional theory to explore how polydispersity in size affects the stability and phase transitions of colloidal platelet suspensions, revealing complex dependencies between smectic and columnar phases.

Contribution

It introduces a detailed model accounting for polydispersity in both length and height, analyzing their effects on phase stability and transitions in colloidal platelet suspensions.

Findings

Smectic phase stabilizes first when length polydispersity exceeds height polydispersity.

Opposite behavior observed when height polydispersity exceeds length polydispersity.

Complex phase behavior includes first-order transitions between nematic, smectic, and columnar phases.

Abstract

The phase behavior of a model suspension of colloidal polydisperse platelets is studied using density-functional theory. Platelets are modelled as parallel rectangular prisms of square section $l$ and height $h$, with length and height distributions given by different polydispersities $\delta_l$ and $\delta_h$. We obtain the phase behavior of the model, including nematic, smectic and columnar phases and its dependence with the two polydispersities $\delta_l$ and $\delta_h$. When $\delta_l>\delta_h$ we observe that the smectic phase stabilises first with respect to the columnar. If $\delta_h>\delta_l$ we observe the opposite behavior. Other more complicated cases occur, e.g. the smectic stabilises from the nematic first but then exists a first-order transition to the columnar phase. Our model assumes plate-rod symmetry, but the regions of stability of smectic and columnar phases are non-symmetric in the $\delta_l-\delta_h$ plane due to the different dimensionality of ordering in the two phases. Microsegregation effects, i.e. different spatial distribution for different sizes within the periodic cell, take place in both phases.