B 16 Baidakov, V. G. Comparison of Different Approaches to the Determination of the Work of Critical Cluster Formation / V. G. Baidakov, G. Sh. Boltachev, J. W. P. Schmelzer // Journal of Colloid and Interface Sience. - 2000. - Vol. 231, № 2. - С. 312-321 Рубрики: ФИЗИКА Кл.слова (ненормированные): CRITICAL CLUSTER -- GIBBS' METHOD -- NUCLEATION RATES Аннотация: 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 |
S 34 Schmelzer, J. W. P. Kinetics of boiling in binary liquid–gas solutions: Comparison of different approaches / J. W. P. Schmelzer, V. G. Baidakov, G. Sh. Boltachev // Journal of Chemical Physics. - 2003. - Vol.119, №12. - С. 6166-6183 Рубрики: ФИЗИКА Кл.слова (ненормированные): CRITICAL CLUSTER -- GIBBS' METHOD -- VAN-DER-WAALS Аннотация: 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 |
S 34 Schmelzer, J. W. P. Kinetics of Condensation and Boiling: Comparison of Different Approaches / J. W. P. Schmelzer, V. G. Baidakov // Journal of Physical Chemistry B. - 2001. - Vol.105, №47. - С. 11595-11604 Рубрики: ФИЗИКА Кл.слова (ненормированные): CRITICAL CLUSTER -- GIBBS' METHOD -- VAN-DER-WAALS METHOD -- HILLIARD METHOD Аннотация: 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 capillarity approximation), the van der Waals−Cahn and Hilliard method, and a newly developed modified Gibbs approachis given. As a particular application, the processes of condensation and boiling in one-component fluids are analyzed. As a model system for comparison, van der Waals fluids are chosen. In addition to the work of critical cluster formation, the bulk properties of the critical clusters (drops or 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 of determination of the work of critical cluster formation (the van der Waals−Cahn & Hilliard and the modified Gibbs approach) leadat least for the model system consideredto 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 and further basic characteristics of nucleation-growth processes. The possible origin of such deviations is discussed, and some further directions of analysis are anticipated |
B 16 Baidakov, V. G. Comparison of Different Approaches to the Determination of the Work of Critical Cluster Formation / V. G. Baidakov, G. Sh. Boltachev, J. W. P. Schmelzer // Journal of Colloid and Interface Sience. - 2000. - Vol. 231, № 2. - С. 312-321 Рубрики: ФИЗИКА Кл.слова (ненормированные): CRITICAL CLUSTER -- GIBBS' METHOD -- NUCLEATION RATES Аннотация: 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 |
S 34 Schmelzer, J. W. P. Kinetics of boiling in binary liquid–gas solutions: Comparison of different approaches / J. W. P. Schmelzer, V. G. Baidakov, G. Sh. Boltachev // Journal of Chemical Physics. - 2003. - Vol.119, №12. - С. 6166-6183 Рубрики: ФИЗИКА Кл.слова (ненормированные): CRITICAL CLUSTER -- GIBBS' METHOD -- VAN-DER-WAALS Аннотация: 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 |
S 34 Schmelzer, J. W. P. Kinetics of Condensation and Boiling: Comparison of Different Approaches / J. W. P. Schmelzer, V. G. Baidakov // Journal of Physical Chemistry B. - 2001. - Vol.105, №47. - С. 11595-11604 Рубрики: ФИЗИКА Кл.слова (ненормированные): CRITICAL CLUSTER -- GIBBS' METHOD -- VAN-DER-WAALS METHOD -- HILLIARD METHOD Аннотация: 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 capillarity approximation), the van der Waals−Cahn and Hilliard method, and a newly developed modified Gibbs approachis given. As a particular application, the processes of condensation and boiling in one-component fluids are analyzed. As a model system for comparison, van der Waals fluids are chosen. In addition to the work of critical cluster formation, the bulk properties of the critical clusters (drops or 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 of determination of the work of critical cluster formation (the van der Waals−Cahn & Hilliard and the modified Gibbs approach) leadat least for the model system consideredto 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 and further basic characteristics of nucleation-growth processes. The possible origin of such deviations is discussed, and some further directions of analysis are anticipated |