CELL-DYNAMICS MODEL OF DROPLET FORMATION IN POLYMER-DISPERSED LIQUID-CRYSTALS

We present a model for the dynamics of formation and morphology of pol ymer-dispersed liquid crystals (PDLCs). This incorporates, in a simpli fied manner, all the key physical ingredients of the actual fabricatio n process, via., polymerization and gelation, phase separation, and gr owth and stabilization of a spatially inhomogeneous structure. We mode l phase separation of the initial pre-PDLC mixture into monomer- and l iquid-crystal (LC)-rich phases by the cell dynamics systems (CDS) meth od of Oono and Purl [Phys. Rev. Lett. 58, 836 (1987); Phys. Rev. A 38, 434 (1988); 38, 1542 (1988)]. Gelation at the expense of monomers is described by an auxiliary held (the phase held), which also obeys a CD S equation for the conserved-order-parameter cease. Growth is assumed to occur at the gel surface. Finally, structure stabilization is achie ved by the inclusion of a nonlocal term that mimics the effect of the long-range interaction responsible for gel cohesion. We have performed detailed numerical calculations on a two-dimensional system for an in itial composition of 30% LC plus 70% monomer. A pattern of LC-rich dro plets is found to develop that is stable as t --> infinity, where t is time. Moreover, the droplet size distribution exhibits a very sharp p eak, in agreement with observations on real PDLCs.