Cluster Formation In Nucleation Theory Research Articles

Classical and generalized Gibbs’ approaches and the work of critical cluster formation in nucleation theory

In the theoretical interpretation of the kinetics of first-order phase transitions, thermodynamic concepts developed long ago by Gibbs are widely employed giving some basic qualitative insights into these processes. However, from a quantitative point of view, the results of such analysis, based on the classical Gibbs approach and involving in addition the capillarity approximation, are often not satisfactory. Some progress can be reached here by the van der Waals and more advanced density functional methods of description of thermodynamically heterogeneous systems having, however, its limitations in application to the interpretation of experimental data as well. Moreover, both mentioned theories--Gibbs' and density functional approaches--lead to partly contradicting each other's results. As shown in preceding papers, by generalizing Gibbs' approach, existing deficiencies and internal contradictions of these two well-established theories can be removed and a new generally applicable tool for the interpretation of phase formation processes can be developed. In the present analysis, a comparative analysis of the basic assumptions and predictions of the classical and the generalized Gibbs approaches is given. It is shown, in particular, that--interpreted in terms of the generalized Gibbs approach--the critical cluster as determined via the classical Gibbs approach corresponds not to a saddle but to a ridge point of the appropriate thermodynamic potential hypersurface. By this reason, the classical Gibbs approach (involving the classical capillarity approximation) overestimates as a rule the work of critical cluster formation in nucleation theory and, in general, considerably.

Crossover model for the work of critical cluster formation in nucleation theory

We propose a relation for the work of critical cluster formation in nucleation theory W for the systems with long-range interparticle interactions. The method of bridge functions is used to combine the system behavior at sufficiently small quenches, adequately predicted by the classical nucleation theory, with nonclassical effects at deep quenches in the vicinity of the thermodynamic spinodal, described within the framework of the field theoretical approach with an appropriate Ginzburg-Landau functional. The crossover between the two types of nucleation behavior takes place in the vicinity of the kinetic spinodal where the lifetime of a metastable state is of the order of the relaxation time to local equilibrium. We argue that the kinetic spinodal corresponds to the minimum of the excess number of molecules in the critical cluster. This conjecture leads to the form of W containing no adjustable parameters. The barrier scaling function Gamma = W/W(cl), where W(cl) is the classical nucleation barrier, depends parametrically on temperature through the dimensionless combination of material properties. The results for argon nucleation are presented.

On different possibilities of a thermodynamically consistent determination of the work of critical cluster formation in nucleation theory

In a recent paper [J. Chem. Phys. 118, 1837 (2003)], Kashchiev claimed to have developed a general thermodynamically consistent formula allowing one to describe correctly the work of critical cluster formation in one-component systems for a variety of cases of formation of gaseous, liquid, and solid phases. It is shown that most of the consequences drawn lack any substantiation.

Kinetics of boiling in binary liquid–gas solutions: Comparison of different approaches

A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluation—Gibbs’ method (employing the capillarity approximation), the van der Waals–Cahn and Hilliard and a newly developed modified Gibbs’ approach—is given in application to phase formation in multicomponent systems. As an example, processes of boiling in binary liquid–gas solutions, in particular, in nitrogen–helium mixtures are investigated. In addition to the work of critical cluster formation, the bulk properties of the critical bubbles, their characteristic sizes and the values of the surface tension are determined in dependence on the initial supersaturation in the system or, equivalently, on the size of the critical clusters. It is shown that latter two mentioned methods (the van der Waals–Cahn and Hilliard and the modified Gibbs’ approach) lead, in the determination of the work of critical cluster formation, to qualitatively and widely even quantitatively equivalent results. As one of the more general consequences from the present analysis, it has been proven that the modified Gibbs’ approach represents a highly effective tool for the determination of the work of formation of clusters or bubbles of critical sizes not only for one-component and quasibinary systems, discussed earlier, but for phase formation in multicomponent systems of, in general, arbitrary numbers of components as well. It is shown that the modified Gibbs’ approach is preferable as compared with Gibbs’ original treatment not only due to its advantages with respect to an appropriate determination of the properties of clusters of critical sizes, but also from general theoretical considerations. In the limit of large sizes of the critical clusters, both approaches—Gibbs’ original treatment and the modified or generalized Gibbs’ approach—lead to equivalent results.

Kinetics of Condensation and Boiling: Comparison of Different Approaches

A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluationGibbs' method (employing the capillari...

Comparison of Different Approaches to the Determination of the Work of Critical Cluster Formation

A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluation—Gibbs' method, the van der Waals-Cahn and Hilliard, and a newly developed modified Gibbs' approach—is given. As a model system for comparison, regular solutions are chosen. In addition to the work of critical cluster formation, the composition of the critical clusters, their characteristic sizes and the values of the surface tension are determined in dependence on the initial supersaturation in the system or, equivalently, on the size of the critical clusters. It is found, in particular, that, for regular solutions, Tolman's equation cannot serve as a first approximation for the description of the curvature dependence of the surface tension even for large cluster sizes and an alternative formula is developed. It is shown that the latter two mentioned methods of determination of the work of critical cluster formation (the van der Waals-Cahn and Hilliard and the modified Gibbs' approach) lead—at least for the model system considered—to qualitatively and partly quantitatively equivalent results. Nevertheless, differences remain which may lead to quantitative deviations when applied to the determination of the steady-state nucleation rates. The possible origin of such deviations is discussed and some further directions of analysis are anticipated.

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The thermodynamics of cluster formation in nucleation theory

We have derived a precise thermodynamic definition of the standard free energy to form a cluster which is used in nucleation theory. The results [Eq. (9)] have a form differing slightly from the form usually used in nucleation theory and show that the Lothe-Pound correction factor is based on a misconception concerning the standard states involved.