Cell dynamics model of droplet formation in polymer-dispersed liquid crystals
Phys. Rev. E , Volume 53 p. 1805- 1815
We present a model for the dynamics of formation and morphology of polymer-dispersed liquid crystals (PDLCs). This incorporates, in a simplified manner, all the key physical ingredients of the actual fabrication process, viz., polymerization and gelation, phase separation, and growth and stabilization of a spatially inhomogeneous structure. We model phase separation of the initial pre-PDLC mixture into monomer- and liquid-crystal (LC)-rich phases by the cell dynamics systems (CDS) method of Oono and Puri [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 field (the phase field), which also obeys a CDS equation for the conserved-order-parameter case. Growth is assumed to occur at the gel surface. Finally, structure stabilization is achieved 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 initial composition of 30% LC plus 70% monomer. A pattern of LC-rich droplets is found to develop that is stable as t Æ , where t is time. Moreover, the droplet size distribution exhibits a very sharp peak, in agreement with observations on real PDLCs.