Confinement effect on the interaction between colloidal particles in a nematic liquid crystal: An analytical study

Motivated by a recent experimental study on the interaction between colloidal particles in a confined nematic liquid crystal [M. Vilfan, N. Osterman, M. Copic, M. Ravnik, S. Zumer, J. Kotar, D. Babic, and I. Poberaj, Phys. Rev. Lett. 101, 237801 (2008)], we discuss in an analytical manner how the interaction potential U between spherical colloidal particles in a confined nematic cell behaves as a function of the interparticle distance r. We show that the short-range potential follows a power law U(r)similar to r(-5) as expected from the quadrupolar nature of the interaction, while the long-range potential is dominated by an exponential function U(r)similar to root d/r exp(-2 pi r/d), where d is the cell thickness. These two regimes are interchanged at r/d similar or equal to 0.8. This behavior of U(r) is in a good semiquantitative agreement with the experimental finding.