Entropy and the Tolman Parameter in Nucleation Theory

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.

Effects of DOM on the Migration of Cr (VI) in Soils

Dissolved organic matter is an important and active component in both terrestrial and aquatic ecosystem. It has become a hotspot in environment science, with active functional groups such as carboxyl, hydroxyl, amino that can influence adsorption and migration of heavy metal contaminants in soil system. Through soil column leaching experiment the article demonstrates that Cr (VI) is dominated by physical adsorption in soils. By using DOM eluent and distilled water to leach at different temperatures in soil, this article shows that release ability of Cr increases with temperature rising, while its deposition capacity increases with temperature decreasing in Water Level Fluctuating Zone. Combined with Gibbs theory, Cr (VI) may take complexation reaction with DOM in soil medium. Thus, new substances appear under the proof of XRD graph.

Modeling Nucleation of Hydrogen Induced Cracking in Steels during Sour Service

A model, which can be used to illustrate the process of nucleation of hydrogen induced cracking (HIC) in steels during sour service, was developed with the aid of Gibbs theory. A set of criteria for crack nucleation were then derived from the model. Metallurgical parameters influencing the criteria and thusly the susceptibility of the material to HIC, which are measurable and controllable in industrial processing, were also advanced in the present article.