Meniscus and Dislocations in Free-Standing Films of Smectic-ALiquid Crystals

Abstract

A flat, freely suspended film of smectic-A liquid crystal supports a pressure difference, Dp, across its two free surfaces. The size of its meniscus is about 10 mm, 2 orders of magnitude smaller than the capillary length, and its profile is predicted to be circular, in accordance with our measurement. The measurement of its radius of curvature gives Dp. We nucleate ex nihilo an elementary edge dislocation loop, and from its critical radius and growth dynamics (governed by Dp), we find the line tension ͑ϳ8 3 10 27 dyn͒ and the mobility of an elementary edge dislocation ͑ϳ4 3 10 27 cm 2 s͞g͒. [S0031-9007(97)02572-6]

Faceting and stability of smectic A droplets on a solid substrate

“…A straightforward calculation, similar to that already used to calculate the profile of a meniscus surrounding a free-standing film [11,24], yields:…”

“…Note that a similar situation exists in a free-standing smectic film surrounded by a straight meniscus. In that case, σ = ∆P in the film, whereas σ = 0 in the meniscus [11,24].…”

Collapse dynamics of smectic-A bubbles

“…This formula shows also that the thinner the film, the smaller the critical radius of nucleation. For N = 500, this formula gives r c ≈ 0.25 µm by taking E d /b ≈ 2 dyn/cm [1,7,22] and ∆P r (max) ≈ 0.2. It can be easily checked that the associated energy barrier is still much larger than k B T , so that homogeneous nucleation is forbidden.…”

“…where E d is the dislocation energy, proportional to b [1,7]. This formula comes from the competition between the line tension which tends to collapse the island and the pressure force which tends to grow it.…”

“…The thinning takes place by nucleation and growth of pores (which are usually loops of elementary edge dislocations) which slowly grow until they reach the meniscus surrounding the film. Note that one can also thin a film by one layer at lower temperature than T AN or a e-mail: francois.caillier@ens-lyon.fr b e-mail: Patrick.Oswald@ens-lyon.fr T AI by artificially nucleating a pore with the aid of a thin heating wire placed under the film [7,8]. In all cases, the thinning is accompanied by dissipative processes which are mainly localized close to the core of the dislocation (characterized by its mobility m) and at the entrance of the meniscus in which the film material empties [1,9].…”