Pseudo-Casimir force in confined nematic polymers

– We investigate the pseudo-Casimir force in a slab of material composed of nematically ordered long polymers. We write the total mesoscopic energy together with the constraint connecting the local density and director fluctuations and evaluate the corresponding fluctuation free energy by standard methods. It leads to a pseudo-Casimir force of a different type than in the case of standard, short molecule nematic. We investigate its separation dependence and its magnitude and explicitly derive the relevant limiting cases. Casimir effect is due to constrained fluctuations in media with long ranged correlations [1]. The physical nature of the medium is not particularly important. Though the standard Casimir effect has been introduced for constrained electromagnetic field fluctuations [2] it has been realized that other systems with long-range correlations exhibit a similar type of fluctuation driven interactions. Most notably critical fluids [3], smectic manifolds [4] and liquid crystals [5], all of them being prime examples of correlated fluids, give rise to a pseudoCasimir effect which comes about through constrained thermal (as opposed to quantum) fluctuations of order parameters. The nature of these order parameters of course depends on the system under study but they all exhibit massless fluctuation spectra that eventually lead to long-ranged fluctuation interactions. Delimiting ourselves to the case of liquid crystals, the pseudo-Casimir effect has been researched in nematic, smectic and columnar uniformly ordered systems [5]. In the case of inhomogeneous or frustrated order as in the case of the hybrid-aligned cell characterized by opposing surface fields or in the Fréedericksz cell where frustration arises from competing bulk and surface fields [6], the interaction induced by director fluctuations is enhanced substantially by frustration, the enhancement being progressively stronger as the system approaches the transition from uniform to distorted structure. There seems to be some experimental evidence that backs up these theoretical predictions [7, 8] but there still lacks a definitive proof of the observability of the pseudo-Casimir interaction. It appears however that in the case of spinodal dewetting of 5CB on a silicon wafer [9] the pseudo-Casimir interaction is essential in giving a consistent interpretation of experimental () To whom correspondence should be addressed. [email protected]