Curvature dependence of the surface tension and crystal nucleation in liquids

2018 ◽  
Vol 10 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Jürn W. P. Schmelzer ◽  
Alexander S. Abyzov ◽  
Eduardo B. Ferreira ◽  
Vladimir M. Fokin
Keyword(s):  
Surface Tension ◽  
Crystal Nucleation ◽  
Curvature Dependence

scholarly journals Entropy and the Tolman Parameter in Nucleation Theory

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 670 ◽  
Author(s):  
Jürn W. P. Schmelzer ◽  
Alexander S. Abyzov ◽  
Vladimir G. Baidakov
Keyword(s):  
Surface Tension ◽  
Size Dependence ◽  
Nucleation Theory ◽  
Crystal Nucleation ◽  
Alternative Methods ◽  
Classical Nucleation Theory ◽  
Component Systems ◽  
Bulk Parameters ◽  
Curvature Dependence ◽  
Gibbs 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.

scholarly journals Modeling of a sessile droplet with the curvature dependence of surface tension

2018 ◽  
Vol 42 (6) ◽  
pp. 699-705 ◽  
Author(s):  
Sergo REKHVIASHVILI ◽  
Aslan SOKUROV
Keyword(s):  
Surface Tension ◽  
Sessile Droplet ◽  
Curvature Dependence

Curvature dependence of the surface tension of liquid and vapor nuclei

1999 ◽  
Vol 59 (1) ◽  
pp. 469-475 ◽  
Author(s):  
V. G. Baidakov ◽  
G. Sh. Boltachev
Keyword(s):  
Surface Tension ◽  
Curvature Dependence

The cavity models and the curvature dependence of the surface tension. Spherical cavities in anisotropic solvents

1993 ◽  
Vol 22 (6) ◽  
pp. 507-517 ◽  
Author(s):  
Raquel M. C. Gon�alves ◽  
Ana M. N. Sim�es ◽  
Joaquim J. Moura-Ramos
Keyword(s):  
Surface Tension ◽  
Spherical Cavities ◽  
Curvature Dependence

Curvature Dependence and Tolman Length of Surface Tension of Nano-Droplet of Attractive Hard Sphere Liquid

2015 ◽  
Vol 12 (12) ◽  
pp. 5654-5658
Author(s):  
Xiao-Song Wang ◽  
Zhi-Bo Yang ◽  
Aijun Hu ◽  
Long Zhou ◽  
Bao-Zhan Lv
Keyword(s):  
Surface Tension ◽  
Hard Sphere ◽  
Hard Sphere Liquid ◽  
Tolman Length ◽  
Curvature Dependence

Positron Annihilation Parameters in Connection to Surface Phenomenon of Liquids

2012 ◽  
Vol 733 ◽  
pp. 121-126
Author(s):  
Bichitra Nandi Ganguly
Keyword(s):  
Surface Tension ◽  
Positron Annihilation ◽  
Theoretical Basis ◽  
Liquid Drop ◽  
Minute Volume ◽  
Surface Phenomenon ◽  
The Past ◽  
Bulk Surface ◽  
Positronium Annihilation ◽  
Curvature Dependence

Surface tension is an important property of liquid, the bulk surface tension concept changes considerably when minute volume of a given liquid (drop let radius<10nm) is considered. Although an extensive thermodynamical treatment and theoretical basis have been considered in the past on the curvature dependence of surface tension, yet its experimental evaluation is deemed necessary and it has been shown hither to that positronium annihilation parameters serve faithfully to this purpose. However, the drastic lowering of surface tension with the dispersion of surfactant in the liquid phase display a different phenomenon altogether and has been dealt separately by positron annihilation results.

scholarly journals Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1098 ◽  
Author(s):  
Jürn W. P. Schmelzer ◽  
Timur V. Tropin ◽  
Vladimir M. Fokin ◽  
Alexander S. Abyzov ◽  
Edgar D. Zanotto
Keyword(s):  
Surface Tension ◽  
Structural Relaxation ◽  
Driving Force ◽  
Cluster Formation ◽  
Supercooled Liquid ◽  
Crystal Nucleation ◽  
Metastable Equilibrium ◽  
Theoretical Treatment ◽  
Relaxation Processes ◽  
Thermodynamic Driving Force

In the application of classical nucleation theory (CNT) and all other theoretical models of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after the supercooled liquid or the glass have completed structural relaxation processes towards the metastable equilibrium state. Only employing such an assumption, the thermodynamic driving force of crystallization and the surface tension can be determined in the way it is commonly performed. The present paper is devoted to the theoretical treatment of a different situation, when nucleation proceeds concomitantly with structural relaxation. To treat the nucleation kinetics theoretically for such cases, we need adequate expressions for the thermodynamic driving force and the surface tension accounting for the contributions caused by the deviation of the supercooled liquid from metastable equilibrium. In the present paper, such relations are derived. They are expressed via deviations of structural order parameters from their equilibrium values. Relaxation processes result in changes of the structural order parameters with time. As a consequence, the thermodynamic driving force and surface tension, and basic characteristics of crystal nucleation, such as the work of critical cluster formation and the steady-state nucleation rate, also become time-dependent. We show that this scenario may be realized in the vicinity and below the glass transition temperature, and it may occur only if diffusion (controlling nucleation) and viscosity (controlling the alpha-relaxation process) in the liquid decouple. Analytical estimates are illustrated and confirmed by numerical computations for a model system. The theory is successfully applied to the interpretation of experimental data. Several further consequences of this newly developed theoretical treatment are discussed in detail. In line with our previous investigations, we reconfirm that only when the characteristic times of structural relaxation are of similar order of magnitude or longer than the characteristic times of crystal nucleation, elastic stresses evolving in nucleation may significantly affect this process. Advancing the methods of theoretical analysis of elastic stress effects on nucleation, for the first time expressions are derived for the dependence of the surface tension of critical crystallites on elastic stresses. As the result, a comprehensive theoretical description of crystal nucleation accounting appropriately for the effects of deviations of the liquid from the metastable states and of relaxation on crystal nucleation of glass-forming liquids, including the effect of simultaneous stress evolution and stress relaxation on nucleation, is now available. As one of its applications, this theoretical treatment provides a new tool for the explanation of the low-temperature anomaly in nucleation in silicate and polymer glasses (the so-called “breakdown” of CNT at temperatures below the temperature of the maximum steady-state nucleation rate). We show that this anomaly results from much more complex features of crystal nucleation in glasses caused by deviations from metastable equilibrium (resulting in changes of the thermodynamic driving force, the surface tension, and the work of critical cluster formation, in the necessity to account of structural relaxation and stress effects) than assumed so far. If these effects are properly accounted for, then CNT appropriately describes both the initial, the intermediate, and the final states of crystal nucleation.

Curvature Dependence of the Surface Tension and the Theory of Solubility

1970 ◽  
Vol 53 (7) ◽  
pp. 2608-2614 ◽  
Author(s):  
Dong Sik Choi ◽  
Mu Shik Jhon ◽  
Henry Eyring
Keyword(s):  
Surface Tension ◽  
Curvature Dependence
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