Schmelzer Jürn W P, Abyzov Alexander S, Baidakov Vladimir G
Institute of Physics, University of Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany.
National Science Center Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine.
Entropy (Basel). 2019 Jul 9;21(7):670. doi: 10.3390/e21070670.
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.
成核理论的热力学方面通常是根据吉布斯界面现象理论及其推广来考虑的。利用吉布斯理论，可以针对环境相的任何亚稳态唯一地确定控制成核的临界团簇的体相参数。通常，在这种处理中，它们与新形成的宏观相的性质非常相似。因此，解决成核速率理论预测准确性及成核过程相关特征问题的主要工具是引入表面张力的尺寸或曲率依赖性的方法。在描述结晶过程时，这个量经常通过结晶过程中的熵（或焓）变化来表示，即通过熔化或结晶的潜热来表示。毛细现象与熵变化之间的这种关联最初是由斯特凡在考虑凝结和蒸发时提出的。在晶体成核中的应用中，它被称为斯卡普斯基 - 特恩布尔关系。由于上述原因，这个关系更准确地应称为斯特凡 - 斯卡普斯基 - 特恩布尔规则，最近我们中的一些人将其扩展到不仅描述平面界面处相平衡的表面张力，还描述临界团簇的表面张力及其尺寸或曲率依赖性。这种依赖性通常由托尔曼导出的一个关系式表示。正如我们所表明的，托尔曼方程不仅可以用于描述由压力变化引起的单组分系统中的凝结和沸腾（吉布斯和托尔曼对此进行了分析），而且一般也可用于由温度变化引起的相形成。除了这个特定应用外，只要环境相的组成保持不变，并且压力或温度的变化不会导致临界团簇的组成变化，它就可以用于多组分系统。后一个要求是经典成核理论的基本假设之一。因此，自然也将其用于确定表面张力的尺寸依赖性。我们基于斯特凡 - 斯卡普斯基 - 特恩布尔规则的方法允许确定表面张力对压力和温度的依赖性，或者确定托尔曼方程中的托尔曼参数。在本文中，我们扩展了这种方法，并将其与描述表面张力尺寸依赖性的其他方法以及在可能使用托尔曼方程的情况下确定托尔曼参数的其他方法进行比较。将这些想法应用于凝结和沸腾，我们推导出了一个表面张力曲率依赖性的关系式，该关系式涵盖了从双节线曲线到旋节线曲线的整个亚稳态初始状态范围。
