Surfing the order parameter: Nanoparticle transport at a moving nematic-isotropic phase boundary

Upon cooling a thermotropic liquid crystal through the nematic-isotropic phase transition, nematic domains are nucleated and grow. If colloidal nanoparticles are initially uniformly distributed in the isotropic phase, they are found to be experimentally transported by the moving phase boundary. Here we create a simple model for this transport process by coupling a scalar Allen-Cahn equation describing the phase transition to a Fokker-Planck equation describing the particle distribution. The resulting equations provide a surprising new analogy between this nonequilibrium "surfing" process and chemotaxis of bacteria. By solving the equations numerically, we find a number of regimes of behavior. Prospects for connecting results with experiments and using this model to understand the assembly of higher order structures will also be presented.