# Prof. Giampaolo D'Alessandro: Multiscale models of nematics with inclusions

**Multiscale models of nematics with inclusions**

__Prof. Giampaolo D'Alessandro__: University of Southampton, England

Suspension of nanoparticles in liquid crystals have been modelled on a range of scales, from molecular simulations to macroscopic models. The former are computationally expensive and only a few particles can be modelled. The second rely on macroscopic parameters whose values are not determined self-consistently.

In this talk I will show how to use homogenisation theory to derive macroscopic models of colloidal suspensions in the limit of weak anchoring between particles and liquid crystals. These models contain no free parameters: the coefficients of the macroscopic equations are fixed by the microscopic interaction between particles and liquid crystals and by the geometry of the problem.

In the case of fixed particles, the macroscopic equations for the director alignment contain three key differences with respect to those for a pure liquid crystal: (i) the elastic constants are in general smaller, (ii) there is a forcing term proportional to the anisotropy of the particles and, (iii) the dielectric susceptibility of the system is altered due to the fringe fields created by the particles.

In the case of rotating particles, the macroscopic equations describe the particle-nematic interaction in terms of (i) their elastic coupling through surface anchoring, (ii) the screening effect of the particle on the nematic distortions and (iii) the coupling of the particles with the applied electric field. Depending on the strength of the particle-liquid crystal interaction the system may display one or two time scales and non-trivial threshold behaviour.

Kindly invited!