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, 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) ∼ r-5 as expected from the quadrupolar nature of the interaction, while the long-range potential is dominated by an exponential function U (r) ∼ d/r exp (-2πr/d), where d is the cell thickness. These two regimes are interchanged at r/d 0.8. This behavior of U (r) is in a good semiquantitative agreement with the experimental finding.