Dislocation loops in finite systems.

Abstract

The distortions induced by dislocation loops are studied in finite systems. The influence of finite size, D, of the system, surface tension, and surface-bending elastic constant on the nematic-smectic (NA) phase transition is discussed. In thin freely suspended smectic liquid-crystal films the nematic-smectic transition temperature, ${\mathit{T}}_{\mathrm{NA}}$(D), is proportional to 1/ \ensuremath{\surd}D , providing the transition is initiated by the unbinding of the dislocation loops. The smectic phase is stabilized in films, i.e., ${\mathit{T}}_{\mathrm{NA}}$(D)g${\mathit{T}}_{\mathrm{NA}}$(\ensuremath{\infty}). The loop-unbinding mechanism for the NA transition is completely suppressed in films sandwiched between solid boundaries, because the distortion energy in this case is proportional to the area of the loop, while the loop configurational entropy is proportional to its length. For temperatures T\ensuremath{\ge}${\mathit{T}}_{\mathrm{NA}}$(\ensuremath{\infty}) the equilibrium size of the loop, ${\mathit{R}}_{\mathrm{eq}}$, is proportional to the distance between solid boundaries, D. It could grow to infinity only for D\ensuremath{\rightarrow}\ensuremath{\infty} and T\ensuremath{\ge}${\mathit{T}}_{\mathrm{NA}}$(\ensuremath{\infty}).