Pseudo-Casimir interactions and surface anchoring duality in bookshelf geometry of smectic-A liquid crystals

Abstract

We analyze the transverse intersubstrate pseudo-Casimir force, arising as a result of thermal fluctuations of the liquid crystalline layers of a smectic-A film confined between two planar substrates in a bookshelf geometry, in which the equidistant smectic layers are placed perpendicular to the bounding surfaces. We discuss the variation of the interaction force as a function of the intersubstrate separation in the presence of surface anchoring to the substrates, showing that the force induced by confined fluctuations is attractive and depends on the penetration length as well as the layer spacing. The strongest effect occurs for tightly confined fluctuations, in which the surface anchoring energy is set to infinity, where the force per area scales linearly with the thermal energy and inversely with the fourth power of the intersubstrate separation. By reducing the strength of the surface anchoring energy, the force first becomes weaker in magnitude but then increases in magnitude as the surface anchoring strength is further reduced down to zero, in which case the force tends to that obtained in the limit of strong anchoring.

References in corpus (8)

• The `Friction' of Vacuum, and other Fluctuation-Induced Forces
• Lateral and normal forces between patterned substrates induced by nematic fluctuations
• Casimir Effect in Fluids above the Isotropic-Lamellar Transition
• Liquid crystal cells with "dirty" substrates
• Path integrals for stiff polymers applied to membrane physics
• Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate
• Pseudo-Casimir force in confined nematic polymers
• Pseudo-Casimir stresses and elasticity of a confined elastomer film

Cited by in corpus (4)

• Qualitative chirality effects on the Casimir-Lifshitz torque with liquid crystals
• Path integrals for higher derivative actions
• Continuum theory of electrostatic-elastic coupling interactions in colloidal crystals
• Surface alignment disorder and pseudo-Casimir forces in smectic-A liquid crystalline films