scholarly journals Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results

2019 ◽  
Author(s):  
Jürn W.P. Schmelzer
Keyword(s):  
Surface Tension ◽  
Liquid Phase ◽  
Thermodynamic Description ◽  
Heterogeneous Systems ◽  
Chem Phys ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Starting Point ◽  
Component Systems ◽  
Nucleation Theorem

Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs' approach in the thermodynamic description of heterogeneous systems and assuming that the basic assumptions of classical nucleation theory commonly employed in application to crystallization hold, a general form of the nucleation theorem can be formulated valid not only for one-component but generally for multi-component systems. This result is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, recently developed by us expressions for the curvature dependence of the surface tension, respectively, the dependence of the surface tension on pressure and/or temperature are employed. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)] holds also for multi-component systems as far as mentioned above assumptions are fulfilled. In the application of classical nucleation theory to crystallization processes it is assumed as one of its basic ingredients that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. This assumption is, however, in general, it is not true. This limitation of the theoretical description can be overcome by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem as derived based on classical nucleation theory holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.

scholarly journals Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1147 ◽  
Author(s):  
Jürn W. P. Schmelzer
Keyword(s):  
Liquid Phase ◽  
Basic Assumption ◽  
Thermodynamic Description ◽  
Heterogeneous Systems ◽  
Nucleation Theory ◽  
Crystal Nucleation ◽  
Classical Nucleation Theory ◽  
Starting Point ◽  
Component Systems ◽  
Nucleation Theorem

Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs’ approach in the thermodynamic description of heterogeneous systems, a general form of the nucleation theorem can be formulated that is valid not only for one-component but generally for multi-component systems. In this analysis, one basic assumption of classical nucleation theory is utilized. In addition, commonly employed in application to crystallization, it is supposed that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)], also relying widely on the standard classical approach in the description of crystal nucleation, holds for multi-component systems as well. The general form of the nucleation theorem derived by us is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, expressions recently developed by us for the curvature dependence of the surface tension, respectively, its dependence on pressure and/or temperature are employed. The basic assumption of classical nucleation theory mentioned above is, however, in general, not true. The bulk and surface properties of the critical crystal clusters may differ considerably from the properties of the evolving macroscopic phases. Such effects can be incorporated into the theoretical description by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem, as derived based on classical nucleation theory, holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.

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 Pore condensation and freezing is responsible for ice formation below water saturation for porous particles

2019 ◽  
Vol 116 (17) ◽  
pp. 8184-8189 ◽  
Author(s):  
Robert O. David ◽  
Claudia Marcolli ◽  
Jonas Fahrni ◽  
Yuqing Qiu ◽  
Yamila A. Perez Sirkin ◽  
...  
Keyword(s):  
Liquid Phase ◽  
Radiative Forcing ◽  
Water Saturation ◽  
Ice Nucleation ◽  
Nucleation Theory ◽  
Ice Formation ◽  
Classical Nucleation Theory ◽  
Radiative Balance ◽  
Porous Particles ◽  
Pore Condensation

Ice nucleation in the atmosphere influences cloud properties, altering precipitation and the radiative balance, ultimately regulating Earth’s climate. An accepted ice nucleation pathway, known as deposition nucleation, assumes a direct transition of water from the vapor to the ice phase, without an intermediate liquid phase. However, studies have shown that nucleation occurs through a liquid phase in porous particles with narrow cracks or surface imperfections where the condensation of liquid below water saturation can occur, questioning the validity of deposition nucleation. We show that deposition nucleation cannot explain the strongly enhanced ice nucleation efficiency of porous compared with nonporous particles at temperatures below −40 °C and the absence of ice nucleation below water saturation at −35 °C. Using classical nucleation theory (CNT) and molecular dynamics simulations (MDS), we show that a network of closely spaced pores is necessary to overcome the barrier for macroscopic ice-crystal growth from narrow cylindrical pores. In the absence of pores, CNT predicts that the nucleation barrier is insurmountable, consistent with the absence of ice formation in MDS. Our results confirm that pore condensation and freezing (PCF), i.e., a mechanism of ice formation that proceeds via liquid water condensation in pores, is a dominant pathway for atmospheric ice nucleation below water saturation. We conclude that the ice nucleation activity of particles in the cirrus regime is determined by the porosity and wettability of pores. PCF represents a mechanism by which porous particles like dust could impact cloud radiative forcing and, thus, the climate via ice cloud formation.

scholarly journals Intrusion and extrusion of water in hydrophobic nanopores

2017 ◽  
Vol 114 (48) ◽  
pp. E10266-E10273 ◽  
Author(s):  
Antonio Tinti ◽  
Alberto Giacomello ◽  
Yaroslav Grosu ◽  
Carlo Massimo Casciola
Keyword(s):  
Heterogeneous Systems ◽  
Nanoporous Materials ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Collective Variables ◽  
Microscopic Mechanism ◽  
Energy Applications ◽  
Nanoconfined Water ◽  
Reduced Dimensions ◽  
Molecular Springs

Heterogeneous systems composed of hydrophobic nanoporous materials and water are capable, depending on their characteristics, of efficiently dissipating (dampers) or storing (“molecular springs”) energy. However, it is difficult to predict their properties based on macroscopic theories—classical capillarity for intrusion and classical nucleation theory (CNT) for extrusion—because of the peculiar behavior of water in extreme confinement. Here we use advanced molecular dynamics techniques to shed light on these nonclassical effects, which are often difficult to investigate directly via experiments, owing to the reduced dimensions of the pores. The string method in collective variables is used to simulate, without artifacts, the microscopic mechanism of water intrusion and extrusion in the pores, which are thermally activated, rare events. Simulations reveal three important nonclassical effects: the nucleation free-energy barriers are reduced eightfold compared with CNT, the intrusion pressure is increased due to nanoscale confinement, and the intrusion/extrusion hysteresis is practically suppressed for pores with diameters below 1.2 nm. The frequency and size dependence of hysteresis exposed by the present simulations explains several experimental results on nanoporous materials. Understanding physical phenomena peculiar to nanoconfined water paves the way for a better design of nanoporous materials for energy applications; for instance, by decreasing the size of the nanopores alone, it is possible to change their behavior from dampers to molecular springs.

scholarly journals Dynamic Surface Tension Enhances the Stability of Nanobubbles in Xylem Sap

2021 ◽  
Vol 12 ◽  
Author(s):  
Stephen Ingram ◽  
Yann Salmon ◽  
Anna Lintunen ◽  
Teemu Hölttä ◽  
Timo Vesala ◽  
...  
Keyword(s):  
Surface Tension ◽  
Surface Composition ◽  
Xylem Sap ◽  
Dynamic Surface Tension ◽  
External Pressure ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Dynamic Surface ◽  
Biologically Relevant ◽  
Dynamics Simulations

Air seeded nanobubbles have recently been observed within tree sap under negative pressure. They are stabilized by an as yet unidentified process, although some embolize their vessels in extreme circumstances. Current literature suggests that a varying surface tension helps bubbles survive, but few direct measurements of this quantity have been made. Here, we present calculations of dynamic surface tension for two biologically relevant lipids using molecular dynamics simulations. We find that glycolipid monolayers resist expansion proportionally to the rate of expansion. Their surface tension increases with the tension applied, in a similar way to the viscosity of a non-Newtonian fluid. In contrast, a prototypical phospholipid was equally resistant to all applied tensions, suggesting that the fate of a given nanobubble is dependent on its surface composition. By incorporating our results into a Classical Nucleation Theory (CNT) framework, we predict nanobubble stability with respect to embolism. We find that the metastable radius of glycolipid coated nanobubbles is approximately 35 nm, and that embolism is in this case unlikely when the external pressure is less negative than –1.5 MPa.

scholarly journals Eliminating the Pre-exponential Factor in Classical Nucleation Theory

2019 ◽  
pp. 1-6
Author(s):  
John H. Jennings
Keyword(s):  
Molecular Weight ◽  
Surface Tension ◽  
Nucleation Rate ◽  
Homogeneous Nucleation ◽  
Polymer Concentration ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Low Molecular Weight ◽  
Exponential Factor ◽  
New Equation

Blander and Katz give a formula in classical nucleation theory, J = A exp K, for homogeneous nucleation (liquid-->gas). Jennings proved that dlnA/dK = 1/6K for all pure liquids by combining two theories, taking the limit as polymer concentration-->0. This gives lnA = (1/12)ln(K2) + C, where C is the integration constant. The conjecture is that C is a constant for fluids of low molecular weight.  We used data for 7 sample solvents, and solved for C. The surface tension drops out in C, which makes C more accurate, as the surface tension is difficult to get at 0.89Tc, the limit of superheat. Tc = critical point in Kelvin. All quantities are evaluated at the limit of superheat, which is approximately 0.89Tc for solvents. C = 74.77 ± 0.33 for the 7 solvents (not all alkanes). This eliminates the prefactor A, streamlining J: ln J = (1/12)ln(K2) + 74.77 + K is the exact new equation.  A computer can more easily be used to calculate J, the nucleation rate.

scholarly journals Scaling Theory of a Polymer Ejecting from a Cavity into a Semi-Space

Polymers ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3014
Author(s):  
Pai-Yi Hsiao
Keyword(s):  
Volume Fraction ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Stage Model ◽  
Nucleation Time ◽  
Ejection Time ◽  
Scaling Properties ◽  
Initial Volume Fraction ◽  
Starting Point ◽  
Dynamics Simulations

A two-stage model is developed in order to understand the scaling behaviors of single polymers ejecting from a spherical cavity through a nanopore. The dynamics of ejection is derived by balancing the free energy change with the energy dissipation during a process. The ejection velocity is found to vary with the number of monomers in the cavity, m, as mz1/(Nx1D3z1) at the confined stage, and it turns to be m−z2 at the non-confined stage, where N is the chain length and D the cavity diameter. The exponents are shown to be z1=(3ν−1)−1, z2=2ν and x1=1/3, with ν being the Flory exponent. The profile of the velocity is carefully verified by performing Langevin dynamics simulations. The simulations further reveal that, at the starting point, the decreasing of m can be stalled for a good moment. It suggests the existence of a pre-stage that can be explained by using the concept of a classical nucleation theory. By trimming the pre-stage, the ejection time are properly studied by varying N, D, and ϕ0 (the initial volume fraction). The scaling properties of the nucleation time are also analyzed. The results fully support the predictions of the theory. The physical pictures are given for various ejection conditions that cover the entire parameter space.

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