On the determination of the kinetic pre-factor in classical nucleation theory

A critical overview on some basic assumptions of the classical nucleation theory (CNT) in application to segregation and crystal nucleation and growth processes in glass-forming liquids is given. It is shown how the classical theory can be generalized in order to overcome at part serious contradictions between theoretical predictions and experimental data. These generalizations refer both to the method of determination of the work of formation of clusters of sub-, super- and critical sizes and to the way of determination of the coefficients of attachment and the kinetic pre-factor in the expression for the steady-state nucleation rate being essential ingredients of the theoretical description of the processes under consideration. Reviewing briefly recent developments in the methods of determination of the work of critical cluster formation and the understanding of the scenario of phase formation processes, particular attention is devoted here to the analysis of the main kinetic assumptions and related topics in application to phase formation in multi-component glass-forming liquids (determination of the effective diffusion coefficient governing nucleation and growth, estimation of the size of the structural units entering the expression for the steady-state nucleation rate, validity of the Stokes–Einstein relation, etc.). In application to crystal nucleation in multi-component solutions it can be shown that one fairly ambiguous concept, the problem of determination of the size of a structural unit determining the melt-crystal transformation can be widely removed from the description.