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Thermodynamic aspects of the theory of nucleation are commonly considered employing Gibbs’ theory of interfacial phenomena and its generalizations. Utilizing Gibbs’ theory, the bulk parameters of the critical clusters governing nucleation can be uniquely determined for any metastable state of the ambient phase. As a rule, they turn out in such treatment to be widely similar to the properties of the newly-evolving macroscopic phases. Consequently, the major tool to resolve problems concerning the accuracy of theoretical predictions of nucleation rates and related characteristics of the nucleation process consists of an approach with the introduction of the size or curvature dependence of the surface tension. In the description of crystallization, this quantity has been expressed frequently via changes of entropy (or enthalpy) in crystallization, i.e., via the latent heat of melting or crystallization. Such a correlation between the capillarity phenomena and entropy changes was originally advanced by Stefan considering condensation and evaporation. It is known in the application to crystal nucleation as the Skapski–Turnbull relation. This relation, by mentioned reasons more correctly denoted as the Stefan–Skapski–Turnbull rule, was expanded by some of us quite recently to the description of the surface tension not only for phase equilibrium at planar interfaces, but to the description of the surface tension of critical clusters and its size or curvature dependence. This dependence is frequently expressed by a relation derived by Tolman. As shown by us, the Tolman equation can be employed for the description of the surface tension not only for condensation and boiling in one-component systems caused by variations of pressure (analyzed by Gibbs and Tolman), but generally also for phase formation caused by variations of temperature. Beyond this particular application, it can be utilized for multi-component systems provided the composition of the ambient phase is kept constant and variations of either pressure or temperature do not result in variations of the composition of the critical clusters. The latter requirement is one of the basic assumptions of classical nucleation theory. For this reason, it is only natural to use it also for the specification of the size dependence of the surface tension. Our method, relying on the Stefan–Skapski–Turnbull rule, allows one to determine the dependence of the surface tension on pressure and temperature or, alternatively, the Tolman parameter in his equation. In the present paper, we expand this approach and compare it with alternative methods of the description of the size-dependence of the surface tension and, as far as it is possible to use the Tolman equation, of the specification of the Tolman parameter. Applying these ideas to condensation and boiling, we derive a relation for the curvature dependence of the surface tension covering the whole range of metastable initial states from the binodal curve to the spinodal curve.

We collect and critically analyze extensive literature data, including our own, on three important kinetic processes--viscous flow, crystal nucleation, and growth--in lithium disilicate (Li(2)O·2SiO(2)) over a wide temperature range, from above T(m) to 0.98T(g) where T(g) ≈ 727 K is the calorimetric glass transition temperature and T(m) = 1307 K, which is the melting point. We found that crystal growth mediated by screw dislocations is the most likely growth mechanism in this system. We then calculated the diffusion coefficients controlling crystal growth, D(eff)(U), and completed the analyses by looking at the ionic diffusion coefficients of Li(+1), O(2-), and Si(4+) estimated from experiments and molecular dynamic simulations. These values were then employed to estimate the effective volume diffusion coefficients, D(eff)(V), resulting from their combination within a hypothetical Li(2)Si(2)O(5) "molecule". The similarity of the temperature dependencies of 1/η, where η is shear viscosity, and D(eff)(V) corroborates the validity of the Stokes-Einstein/Eyring equation (SEE) at high temperatures around T(m). Using the equality of D(eff)(V) and D(eff)(η), we estimated the jump distance λ ~ 2.70 Å from the SEE equation and showed that the values of D(eff)(U) have the same temperature dependence but exceed D(eff)(η) by about eightfold. The difference between D(eff)(η) and D(eff)(U) indicates that the former determines the process of mass transport in the bulk whereas the latter relates to the mobility of the structural units on the crystal/liquid interface. We then employed the values of η(T) reduced by eightfold to calculate the growth rates U(T). The resultant U(T) curve is consistent with experimental data until the temperature decreases to a decoupling temperature T(d)(U) ≈ 1.1-1.2T(g), when D(eff)(η) begins decrease with decreasing temperature faster than D(eff)(U). A similar decoupling occurs between D(eff)(η) and D(eff)(τ) (estimated from nucleation time-lags) but at a lower temperatureT(d)(τ) ≈ T(g). For T > T(g) the values of D(eff)(τ) exceed D(eff)(η) only by twofold. The different behaviors of D(eff)(τ)(T) and D(eff)(U)(T) are likely caused by differences in the mechanisms of critical nuclei formation. Therefore, we have shown that at low undercoolings, viscosity data can be employed for quantitative analyses of crystal growth rates, but in the deeply supercooled liquid state, mass transport for crystal nucleation and growth are not controlled by viscosity. The origin of decoupling is assigned to spatially dynamic heterogeneity in glass-forming melts.

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General equations for the dependence of the thermodynamic driving force and the specific interfacial energy melt‐crystal of critical clusters on temperature and pressure are derived. Analytical estimates of these and related thermodynamic quantities are advanced directly applicable in the analysis of experimental data of crystal nucleation. Similar to the well‐known notation of a Kauzmann temperature, the concept of a Kauzmann pressure is introduced. It is shown that the thermodynamic driving force of crystal nucleation has maxima not only at the Kauzmann temperature but also at the Kauzmann pressure. Estimates of the magnitude of the thermodynamic driving force of crystallization at these states are given and some consequences are discussed.

A first attempt to probe the size distribution of homogeneously formed nuclei in polymers was realized employing Tammann's two-stage crystal nuclei development method and fast scanning calorimetry. A transfer heating rate of 500 000 K·s −1 prevents nuclei growth on heating in poly(ε-caprolactone) (PCL). Data collected in a wide range of crystallization temperatures allow, in combination with a theoretical model based on classical nucleation theory, for an estimate of the nuclei size distribution and the growth rate. The employed temperature profile was adapted from Tammann's two-stage crystal nuclei development method implying formation of nuclei at large undercooling (low temperatures) and following their isothermal growth at higher temperatures. Fast scanning calorimetry allowed us to reach the deep supercooling of the melt at 100 000 K·s −1 avoiding homogeneous nuclei formation and heterogeneous nuclei growth. Then crystal nuclei were allowed to form isothermally at the temperature corresponding to the maximum of the steady-state nucleation rate for homogeneous nucleation (210 K for PCL, T g = 209 K), where both the effect of heterogeneous nucleation and the growth rate are low. The presence of these crystal nuclei and its effect on crystallization were probed by heating the sample to higher temperatures and observation of the overall crystallization process, determining the crystallization half-time. The transfer heating rates up to 500 000 K·s −1 were applied in order to minimize growth on heating. A theoretical explanation of the observations was developed. The study focuses on early stages of nucleation and growth and is therefore widely independent of specific features of polymer crystallization.