Dynamics of Nanoparticle Self-Assembly by Liquid Crystal Sorting in Two Dimensions

Abstract

We study nonlinear dynamical equations for coupled conserved and non-conserved fields describing nanoparticle concentration and liquid crystal order parameter, respectively, and solve them numerically over bidimensional domains. These equations model the rapid segregation of nanoparticles away from nematic domains, which has been observed experimentally in a suspension of gold nanoparticles in 5CB below the isotropic-nematic transition temperature. We contrast the different behaviors obtained when the LC order parameter is treated as a scalar or a tensor, as well as the different rates of evolution observed with each of these. We find, after an instantaneous quench lowering the temperature below the transition one, an initial linear regime where the ordering of the nematic phase proceeds exponentially with time. Only after a lag period the nanoparticle material couples effectively to the LC order parameter and segregates to regions that are less orientationally ordered (extended domain walls for a scalar order parameter, but point disclinations for a tensor one). The lag period is followed by the onset of nonlinear dynamics and saturation of the order parameter. The choice of a scalar or tensor LC order parameter does not change this sequence but results in a clear overshooting of the nonlinear saturation level for the tensor order parameter case. These results are found to be insensitive to weak anchoring due to coupling of gradients of the conserved and non-conserved variables, for the nanoparticle concentrations and anchoring parameters studied. Our modeling approach can be extended in a straightforward manner to cases where the cooling rate is finite and to other systems where a locally conserved concentration is coupled to a orientation field, such as active Langmuir monolayers, and possibly to other examples of nonlinear dynamics in ecological or excitable media problems.