Eur. Phys. J. E 7, 117-122 (2002)
DOI: 10.1140/epje/i200101162
Colloidal dipolar interactions in 2D smectic-C films
P. Patrício, M. Tasinkevych and M.M. Telo da GamaDepartamento de Física da Faculdade de Ciências and Centro de Física Teórica e Computacional, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa Codex, Portugal patricio@cii.fc.ul.pt
(Received 26 October 2001 and Received in final form 14 December 2001 )
Abstract
We use a two-dimensional (2D) elastic free energy to calculate the
effective interaction between two circular disks immersed in smectic-C films.
For strong homeotropic anchoring, the distortion of
the director field caused by the disks generates
topological defects that induce an effective interaction between the
disks. We use finite elements, with adaptive meshing, to minimize the 2D
elastic free energy. The method is shown to be accurate and efficient for
inhomogeneities on the length scales set by the disks and the defects,
that differ by up to 3 orders of magnitude.
We compute the effective interaction between two disk-defect pairs
in a simple (linear) configuration.
For large disk separations,
D, the elastic free energy scales as
, confirming the dipolar character of the long-range effective
interaction. For small
D the energy exhibits a pronounced minimum. The
lowest energy corresponds to a symmetrical configuration of the
disk-defect pairs, with the inner defect at the mid-point between the
disks. The disks are separated by a distance that is twice the distance
of the outer defect from the nearest disk. The latter is identical to the
equilibrium distance of a defect nucleated by an isolated disk.
61.30.Jf - Defects in liquid crystals.
82.70.Dd - Colloids.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002
