Influence of the Electric Field on Edge Dislocations in Smectics

Robert Holyst; Patrick Oswald

doi:doi:10.1051/jp2:1995197

Numéro		J. Phys. II France Volume 5, Numéro 10, October 1995


Page(s)		1525 - 1532
DOI		https://doi.org/10.1051/jp2:1995197

DOI: 10.1051/jp2:1995197
J. Phys. II France 5 (1995) 1525-1532

Influence of the Electric Field on Edge Dislocations in Smectics

Robert Holyst^{1, 2} and Patrick Oswald²

¹ Institute of Physical Chemistry of the Polish Academy of Sciences and College of Sciences, Dept III, Kasprzaka 44/52, 01224 Warsaw, Poland
² Ecole Normale Superieure de Lyon, Laboratoire de Physique, 46 Allée d'Italie, 69364 Lyon Cedex 07, France

(Received 11 May 1995, received in final form 29 June 1995, accepted 6 July 1995)

Abstract
The electric field applied perpendicularly to smectic layers breaks the rotational symmetry of the system. Consequently, the elastic energy associated with distortions induced by an edge dislocation diverges logarithmically with the size of the system. In freely suspended smectic films the dislocations in the absence of the electric field are located exactly in the middle of the film. The electric field, E, above a certain critical value, $E_{\rm c}$ , can shift them towards the surface. This critical field (in Gauss cgs units) is given by the following approximate formula $E_{\rm c}=\sqrt{4\pi B (a\gamma/\sqrt{KB} -b)/(\epsilon_{\rm a}(N-2))}$ . Here, B and K are smectic elastic constants, $\gamma$ is the surface tension, N is the number of smectic layers and $\epsilon_{\rm a}$ is the dielectric anisotropy. The constant $b=0.85\pm 0.07$ and $a=1.45\pm 0.01$ . Additionally, we assumed that $\sqrt{K/B}=d$ , where d is the smectic period. This formula is valid for $\gamma/\sqrt{KB}>2$ and N>12. For smaller values of the surface tension and large N the linear relation between $E_{\rm c}^2$ and $\gamma/\sqrt{KB}$ breaks down, since eventually for $\gamma/\sqrt{KB}\rightarrow 1$ and $N\rightarrow\infty$ , $E_{\rm c}^2(N-2)$ approaches 0. The equilibrium location of a dislocation in the smectic film, $h_{\rm eq}$ , equals NdG(x), where $x=E^2/E_{\rm c}^2$ and G(x) is a function independent of the film thickness (for N>12) and of the value of the surface tension.