Lateral and normal forces between patterned substrates induced by nematic fluctuations

Abstract

We consider a nematic liquid crystal confined by two parallel flat substrates whose anchoring conditions vary periodically in one lateral direction. Within the Gaussian approximation, we study the effective forces between the patterned substrates induced by the thermal fluctuations of the nematic director. The shear force oscillates as function of the lateral shift between the patterns on the lower and the upper substrates. We compare the strength of this fluctuation-induced lateral force with the lateral van der Waals force arising from chemically structured adsorbed monolayers. The fluctuation-induced force in normal direction is either repulsive or attractive, depending on the model parameters.

Pseudo-Casimir interactions across nematic films with disordered anchoring axis

“…, and can be evaluated straightforwardly by using the standard path-integral methods [9][10][11][12][13]29] giving…”

“…The coupling between the latter and the fluctuating fields is modelled within the RapiniPapoular surface interaction phenomenology [26]. In the case of annealed disorder, we obtain an effective free energy for the fluctuating director field which takes a standard pseudo-Casimir form [9][10][11][12][13][14] but with a renormalized anchoring energy, while in the case of quenched disorder, we find that the disorder in the homeotropic easy direction leads to a distinct additive term besides the pseudo-Casimir contribution in the total interaction free energy. This is very similar to the general state of affairs in the context of Coulomb fluids under imposed external disorder in the monopolar charge distribution on bound-ing surfaces [19].…”

Fluctuation-induced interactions in nematics with disordered anchoring energy

“…Now since the fields appear in quadratic forms in the effective Hamiltonian, we can perform the functional integrals over n i in Eq. (9) using the standard methods [11][12][13][14][15][16][17], which gives…”

“…Among these the liquid crystalline (LC) order [5][6][7] could serve as the prime example and interactions engendered by thermal fluctuations of the LC order parameter(s) in confined geometries with surface anchoring have been studied extensively in this context [8,9]. Surface anchoring conditions were found to be important not only in determining the equilibrium phase behavior of confined LC films, a fundamental problem in LC physics, but also in determining the effective pseudo-Casimir or fluctuation-induced interaction mediated between the bounding surfaces [10][11][12][13][14][15][16][17][18]. Their effect is strongest in uniformly ordered confined LC films, close to an ordering transition, that correspond most closely to long-range correlated media and are exemplified by LC dispersions in porous glasses, aerogels and polymer networks where they represent a direct analogue of the thermal electromagnetic Casimir interaction with which they share many of the fundamental characteristics.…”

Imprinting substrate structures onto a nematic liquid crystal

“…15 Haddadan and Dietrich studied lateral and normal forces in a liquid crystal confined between plane parallel substrates decorated with periodically varying regions of different anchoring conditions. 16 Atherton and Sambles investigated the director field in a nematic liquid crystal in a twisted nematic cell set up with micropatterned substrates. 17 They could show that the director field is very sensitive to small changes in the elastic constants characterizing the liquid crystal.…”