ABSTRACT
The assembly of nematic colloids relies on long-range elastic interactions that can be manipulated through external stimuli. Confinement and the presence of a hydrodynamic field alter the defect structures and the energetic interactions between the particles. In this work, the assembly landscape of nanoparticles embedded in a nematic liquid crystal confined in a nanochannel under a pressure-driven flow is determined. The dynamics of the liquid crystal tensor alignment field is determined through a Poisson-Bracket framework, namely the Stark-Lubensky equations, coupled with the zero-Reynolds momentum equations and the liquid crystal Landau-de Gennes free energy functional. A second order semi-implicit time integration and a three-dimensional Galerkin finite element method are used to resolve flow and nematic fields under several conditions. In general, the zero Reynolds flow displaces the defects around the particles in the upstream direction and renders the surface anchoring ineffective when the flow strength dominates over the nematic elasticity. More importantly, the potential of mean force for particle assembly is non-monotonic independent of surface anchoring. Our results show that the confinement length scale determines the repulsion/attraction transition between colloids, while the flow strength modifies the static defect structure surrounding the particles and determines the magnitude of the energetic barrier for successful assembly. In the attractive regime, the particles move at different rates through the nematic until one particle eventually catches up with the other. This process occurs against or along the direction of flow depending on the flow strength. Ultimately, these results provide a template for engineering and controlling the transport and assembly of nanoparticles under far-from equilibrium conditions in anisotropic media.
ABSTRACT
Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.
ABSTRACT
In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor's invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi's notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic-nematic transition, and we identify the uniaxial-biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4'-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.
