Size of a crystal nucleus in the isothermal crystallization of supercooled liquid

We present an alternative to classical nucleation theory (CNT). We introduce a size-dependent surface energy into the total Gibbs free-energy of formation of a crystal (ΔG). We consider the free-energy in the core part of the total volume of crystal and the free-energy in the surface-layer part of it, separately, for the evaluation of ΔG. As a result, we present an explicit model to evaluate a characteristic size of an initial nucleus that differs from the critical nucleus of CNT, but whose temperature dependence agrees well with that reported for the temperature dependency initial fold length of isotactic polystyrene and polyethylene in the literature. Our model has fitted the experimental data in the literature with only one adjustable parameter that is defined as nucleation constant. The nucleation constant is the Gibbs free-energy difference between the crystal and supercooled liquid phases for the volume of initial nucleus. We also present an expression to approximate the evolution of free-energy in the surface-layer part of crystal during the crystal growth.