Dynamics of nanoparticle self-assembly by liquid crystal sorting

We 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, using nonlinear dynamical equations that couple nanoparticle concentration and liquid crystal order parameter. We contrast the 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 an initial linear regime where the ordering of the nematic phase proceeds exponentially with time and, after a lag period, a second regime where the onset of nonlinear dynamics leads to nanoparticle segregation to locally isotropic regions 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. Our modeling approach can be extended from instantaneous quenches to cases where the cooling rate is finite and to other systems where a locally conserved concentration is coupled to a orientation field.