Simulation of self-assembly and lyotropic liquid crystal phases in model discotic solutions

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Abstract
A prototype model of amphiphilic discotic binary solutions is proposed, and its statistical mechanics investigated by Monte Carlo computer simulation procedures. Data are presented from a large number of simulations, over 50 separate systems in all, carried out at a single relatively low pressure but covering almost the entire temperature-composition range of phase space beyond the melting line, including successful simulations of equilibrated cluster distributions throughout the isotropic solution phase. These data are in agreement with the well known theory of linear aggregation, but a major surprise is found in that the associated equilibrium constant possesses a strong concentration dependence at low temperature. The global aggregation behaviour is described in detail and discussed in the context of the standard state that is usually invoked when applying linear aggregation theory to experimental systems. It is concluded that as the temperature decreases the ideal behaviour of these cluster distribution data shows more and more influence from the nearby infinite polydispersity limit. At sufficiently high surfactant concentration our model discotic solutions melt first into partially ordered states of aligned aggregates (columns of discs) surrounded by liquid solvent. Both a nematic phase and a hexagonally ordered columnar phase are observed. Simulation procedures are used to investigate the phase behaviour and especially the microscopic structure of these lyotropic liquid crystal systems. The thermodynamic behaviour of our prototype molecular model shows a qualitative resemblance to experimental results obtained from aqueous solutions of the discotic amphiphile known as TP6EO2M.