Effects of diffusion-controlled association in kinetic model of crystal nucleation in external orienting field

Abstract

Translational and rotational diffusion equation of orientable single elements in external orienting potential field is used to discuss effective rate of association and dissociation during cluster growth. First and second harmonic terms of orientation-dependent potential energy of single elements are taken into consideration. Tolerance angle accounting for orientational limitations for association is introduced.

Effective rate of association of single elements is derived with first-order correction for the effects of orienting potential. Net rate of cluster growth depends on orientation in the field, and it is controlled by longrange diffusion (rotational and translational) of single elements. Influence of diffusion is higher, the narrower the tolerance angle and the faster the association.

At slow association, long-range diffusion does not influence the process, the growth of a cluster is controlled by thermodynamic, orientation-dependent potential of the species involved in the process.

Effective rate constants of association and dissociation, as well as effective concentration of single elements are derived as functions of orientation angle in the field.

The Fokker-Planck equation is proposed for the distribution of cluster size in external orienting potential, with the effects of finite translational and rotational diffusion of single elements, for the case of non-polar clusters.