Adsorption–desorption phenomenon and the kinetic equation at interfaces in liquid crystalline systems

Abstract

The adsorption–desorption phenomenon in a sample having the shape of a slab is investigated by using a particular form for the kinetic equation at the limiting surfaces. A closed solution for the time evolution of the ion density in a nematic liquid crystal sample submitted to an external field is obtained in the limit in which the effective field coincides with the external field. In this framework it is shown that the intrinsic time connected with the presence of the electric field is proportional to the drift time. The constant of proportionality is of the order of the ratio between the thermal agitation energy and the electrostatic energy. In a similar manner, the time evolution of the bulk and surface densities, in the case of neutral particles, is also determined in a closed form by means of a simple expression. A microscopic model giving rise to a kinetic equation, similar to the one used in the analysis, is presented. We propose a statistical interpretation of the adsorption–desorption phenomenon in the framework of Maxwell–Boltzmann statistics, in which the relationship between the phenomenological parameters, entering into the kinetic equation at the boundary surfaces, with the microscopic model is derived. The analysis is suitable for the description of the adsorption phenomena of neutral particles (dyes) as well as charged particles (ions) in nematic liquid crystals.