Coupling between meniscus and smectic-A films: circular and catenoid profiles, induced stress, and dislocation dynamics

In this paper we discuss the formation and shape of the meniscus between a free-standing film of a smectic-A phase and a wall (in practice the frame that supports the film). The wall may be flat or circular, and the system with or without a reservoir of particles. The formation of the meniscus is always an irreversible thermodynamic process, since it involves the creation of dislocations in the bulk (therefore it involves friction). The four basic shapes of meniscus discussed are the following: exponential, algebraic (x(3/2)), circular, and catenoid. Three principal regions of the whole meniscus must be distinguished: close to the wall with a high density of dislocations, away from the wall with medium density of dislocations, and far from the wall (i.e., close to the film) with a low density of dislocations (vicinal regime). The region with medium density of dislocations is observable using a microscope, and is determined by the competition between surface tension, energy of dislocations, and pressure difference set by the mass of the meniscus or by the reservoir. Its profile is circular as observed in recent experiments [J.-C. Geminard, R. Holyst, and P. Oswald, Phys. Rev. Lett. 78, 1924 (1997)]. By contrast, the vicinal regime with low density of dislocations is never observable with an optical microscope. In the regime with a high density of dislocations, the reasons why the dislocations tend to gather by forming giant dislocations and rows of focal conics are discussed. Finally, we discuss the stability of a smectic film with respect to the formation of a dislocation loop. We show experimentally that the critical radius of the loop is proportional to the curvature radius of the meniscus in its circular part, in agreement with the theory. In addition, we show that the mobility of edge dislocations measured in thick films is in agreement with that found in bulk samples from a creep experiment. This result confirms again our model of the meniscus.