Multiscale models of colloidal dispersion of particles in nematic liquid crystals

Abstract

We use homogenization theory to develop a multiscale model of colloidal dispersion of particles in nematic liquid crystals under weak-anchoring conditions. We validate the model by comparing it with simulations by using the Landau-de Gennes free energy and show that the agreement is excellent. We then use the multiscale model to study the effect that particle anisotropy has on the liquid crystal: spherically symmetric particles always reduce the effective elastic constant. Asymmetric particles introduce an effective alignment field that can increase the Fredericks threshold and decrease the switch-off time.

Fast algorithms for liquid crystal modelling

“…theory 30 rather than a multiple scale expansion as in the DFQTA approximation, but both asymptotic methods rely on the existence of the manifold to yield non-stiff dynamical equations for the reorientation of the liquid crystals. The detailed calculations for the derivation of the approximate director equations are available in Bennett et al 29 Here, as in the previous sections, we summarize the methods and list the main results. In section 4.1 we outline the system studied, in section 4.2 we present and interpret the model, referring for the full details to Bennett et al 29 In section 4.3 we present an example applications of the approximate macroscopic equations.…”

“…The detailed calculations for the derivation of the approximate director equations are available in Bennett et al 29 Here, as in the previous sections, we summarize the methods and list the main results. In section 4.1 we outline the system studied, in section 4.2 we present and interpret the model, referring for the full details to Bennett et al 29 In section 4.3 we present an example applications of the approximate macroscopic equations.…”

“…The situation is more interesting if we consider anisotropic particles: for these q is nonzero and both q and the polarization p depend on the orientation of the particles. Careful choice of particle geometry 29 can decrease both the switch on and off times and either increase or decrease the Frederiks threshold with respect to a pure liquid crystal.…”

“…7 Rather than solving the Euler-Lagrange equations for the alignment of the nematic in the complete domain pictured in figure 3 we have derived a set of computationally efficient equations for the macroscopic description of this system. 29 In this case approximate equations are obtained using homogenization 0000000 0000000 0000000 0000000 0000000 0000000 1111111 1111111 1111111 1111111 1111111 1111111 Figure 3. Domains used in defining scale separation taken from Bennett et al 29 The macroscopic domain consists of an open region D containing nematic liquid crystal, with external boundary ∂D, constructed from unit cells Ω with outer boundaries B and metallic inclusions of volume Ωnp and boundary Γi, with i an index that runs over the total number of inclusions.…”

“…29 In this case approximate equations are obtained using homogenization 0000000 0000000 0000000 0000000 0000000 0000000 1111111 1111111 1111111 1111111 1111111 1111111 Figure 3. Domains used in defining scale separation taken from Bennett et al 29 The macroscopic domain consists of an open region D containing nematic liquid crystal, with external boundary ∂D, constructed from unit cells Ω with outer boundaries B and metallic inclusions of volume Ωnp and boundary Γi, with i an index that runs over the total number of inclusions. We seek a description of the nematic in the limit as Ly tends to zero with Lx fixed.…”