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A. R. Mackenzie - One of the best experts on this subject based on the ideXlab platform.
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are the solid liquid Kelvin Equation and the theory of interfacial tension components commensurate
Journal of Physical Chemistry B, 1997Co-Authors: A. R. MackenzieAbstract:The theory of interfacial tensions, ITC theory, developed over the last half-century from contact angle and wetting studies, has proven to be reliable in many fields of physical and biophysical chemistry. However, interfacial tensions for curved solid surfaces in liquids, estimated in various ways from the Kelvin Equation (itself, of course, a very successful theory), give very different results from those estimated by ITC theory. That is, a clear distinction must be made between the Kelvin Equation parameter (KEP) of classical freezing theory and the contact angle parameter (CAP) of ITC theory. The difference between KEPs and CAPs is to some degree caused by the incorrect application of addition rules, Antonow's rule, for example, but a more profound discrepancy remains even when correct addition rules are used. One source of a discrepancy in measures of solid−vapor surface tension has been known since Gibbs, but has often not been acted upon, and does not appear to have been routinely quantified. Discre...
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ARE THE (SOLID-LIQUID) Kelvin Equation AND THE THEORY OF INTERFACIAL TENSION COMPONENTS COMMENSURATE ?
The Journal of Physical Chemistry B, 1997Co-Authors: A. R. MackenzieAbstract:The theory of interfacial tensions, ITC theory, developed over the last half-century from contact angle and wetting studies, has proven to be reliable in many fields of physical and biophysical chemistry. However, interfacial tensions for curved solid surfaces in liquids, estimated in various ways from the Kelvin Equation (itself, of course, a very successful theory), give very different results from those estimated by ITC theory. That is, a clear distinction must be made between the Kelvin Equation parameter (KEP) of classical freezing theory and the contact angle parameter (CAP) of ITC theory. The difference between KEPs and CAPs is to some degree caused by the incorrect application of addition rules, Antonow's rule, for example, but a more profound discrepancy remains even when correct addition rules are used. One source of a discrepancy in measures of solid−vapor surface tension has been known since Gibbs, but has often not been acted upon, and does not appear to have been routinely quantified. Discre...
H. Arstila - One of the best experts on this subject based on the ideXlab platform.
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Comment on ''Generalized Kelvin Equation and the water content of a cloud''
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 1996Co-Authors: Timo Vesala, H. ArstilaAbstract:Kuz @Phys. Rev. E. 51, 5136 ~1995!# presents the novel Kelvin Equation, which would reduce to ordinary forms if some assumptions were made regarding the ratio of the number of molecules in the gas to that in the liquid phase. We feel that the definition used for the Gibbs free energy as a starting point of calculations is not a proper one and, in addition, it is not correctly treated. We present practical situations contradicting the conclusion concerning the liquid-water content in clouds. Some minor inaccuracies are also highlighted. @S1063-651X~96!03911-6#
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comment on generalized Kelvin Equation and the water content of a cloud
Physical Review E, 1996Co-Authors: Timo Vesala, H. ArstilaAbstract:Kuz [Phys. Rev. E. 51, 5136 (1995)] presents the novel Kelvin Equation, which would reduce to ordinary forms if some assumptions were made regarding the ratio of the number of molecules in the gas to that in the liquid phase. We feel that the definition used for the Gibbs free energy as a starting point of calculations is not a proper one and, in addition, it is not correctly treated. We present practical situations contradicting the conclusion concerning the liquid-water content in clouds. Some minor inaccuracies are also highlighted. \textcopyright{} 1996 The American Physical Society.
Kenneth S. W. Sing - One of the best experts on this subject based on the ideXlab platform.
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Historical aspects of capillarity and capillary condensation
Microporous and Mesoporous Materials, 2012Co-Authors: Kenneth S. W. Sing, Ruth WilliamsAbstract:Abstract The basic Equation of capillarity is generally associated with the names of Thomas Young and Pierre Simon Laplace. Careful perusal of the early literature has revealed some unexpected historical aspects. For example, Young’s 1805 essay on the ‘cohesion of fluids’ was purely descriptive, but it did provide a basis for the ‘classical’ treatment of capillarity and wetting. In contrast, Laplace’s 1806 work involved a more ‘modern’ energetic approach to capillary attraction, but avoided any direct reference to surface tension. The related capillary condensation Equation is now universally known as the Kelvin Equation. However, this exponential relationship was not the form of the original Equation proposed in 1871 by William Thomson (later Lord Kelvin). Zsigmondy (1911) [11] applied Thomson’s original linear Equation in his seminal study of silica gels. Although the Kelvin Equation is still widely used for mesopore size analysis, its limitations began to be recognised in the 1930s.
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surface area and porosity
Handbook of Heterogeneous Catalysis, 2008Co-Authors: Alexander V Neimark, Kenneth S. W. Sing, Matthias ThommesAbstract:The sections in this article are Introduction Physisorption of Gases Determination of Surface Area The BET Method The Standard Isotherm Concept Assessment of Porosity Capillary Condensation and the Kelvin Equation Adsorption Hysteresis Microporosity Micropore Analysis: Dubinin's Theory of Micropore Filling Micropore Analysis: Empirical Methods Other Methods for Micropore Pore Size Analysis Application of Density Functional Theory Adsorption at the Liquid–Solid Interface Adsorption from Solution Heat of Immersion Mercury Porosimetry General Conclusions Keywords: physisorption; pore size; mercury porosimetry; heat of immersion
Robert Mcgraw - One of the best experts on this subject based on the ideXlab platform.
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Thermodynamics, gas-liquid nucleation, and size-dependent surface tension
Europhysics Letters (EPL), 1996Co-Authors: Ari Laaksonen, Robert McgrawAbstract:Phenomenological nucleation theories are considered from the viewpoint of Gibbs' surface thermodynamics. We point out, in defining the critical nucleus, that it is important to make a distinction between the number of molecules enclosed by the surface of tension and the excess number of molecules over the uniform vapor phase. We show that the Kelvin Equation should be employed in determining the size of the critical nucleus even if the nucleus free energy contains a size-dependent surface energy term. Furthermore, we make use of the fact that the classical form of Kelvin Equation (containing the surface tension of a flat interface) predicts the equimolar radius of the critical nucleus well down to nuclei of about 40 molecules, and derive a new Equation for the size-dependent surface tension that differs from the Tolman relation. Density functional calculations support the new formula.
Nobuya Shinozaki - One of the best experts on this subject based on the ideXlab platform.
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Modified classical homogeneous nucleation theory and a new minimum in free energy change. 1. A new minimum and Kelvin Equation
Fluid Phase Equilibria, 2007Co-Authors: Kyoko Wasai, G Kaptay, Kusuhiro Mukai, Nobuya ShinozakiAbstract:Abstract The main concern of classical homogeneous nucleation theory has been a thermodynamic description of initial stage of nucleation from embryo to nucleus with a little larger size over the critical one, thus, the change of parent phase in the system has been assumed to be negligible because of the largeness in volume and mass comparing that of nuclei. As a result, the nucleation curve (free energy change versus nucleus size) passes through well-known single maximum point corresponding to the critical size of the nucleus. In the present study, thermodynamics of the classical homogeneous nucleation was re-visited and developed a modified Equation for multi-component solution and gas system with multi-component nuclei by taking into account the change of the free energy of parent phase. Using this Equation, the calculation of nucleation curve beyond the size of critical nucleus became possible. A calculation of A–B binary solution system revealed a new minimum point in the nucleation curve, in addition to the maximum point. This minimum point indicates the theoretical possibility to stabilize a large amount of nano-nuclei in equilibrium with the supersaturated parent phase. In addition, Kelvin Equation was proved at the extremum on the nucleation curve. Many scientists have misunderstood that Kelvin Equation corresponds to the maximum state because they have unnoticed the presence of the minimum and its stability. At the minimum state, the nuclei should be more stable than those at the maximum state. Thus, Kelvin Equation should correspond to the minimum state rather than the maximum state.
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Modified classical homogeneous nucleation theory and a new minimum in free energy change
Fluid Phase Equilibria, 2007Co-Authors: Kyoko Wasai, G Kaptay, Kusuhiro Mukai, Nobuya ShinozakiAbstract:The main concern of classical homogeneous nucleation theory has been a thermodynamic description of initial stage of nucleation from embryo to nucleus with a little larger size over the critical one, thus, the change of parent phase in the system has been assumed to be negligible because of the largeness in volume and mass comparing that of nuclei. As a result, the nucleation curve (free energy change versus nucleus size) passes through well-known single maximum point corresponding to the critical size of the nucleus. In the present study, thermodynamics of the classical homogeneous nucleation was re-visited and developed a modified Equation for multi-component solution and gas system with multi-component nuclei by taking into account the change of the free energy of parent phase. Using this Equation, the calculation of nucleation curve beyond the size of critical nucleus became possible. A calculation of A–B binary solution system revealed a new minimum point in the nucleation curve, in addition to the maximum point. This minimum point indicates the theoretical possibility to stabilize a large amount of nano-nuclei in equilibrium with the supersaturated parent phase. In addition, Kelvin Equation was proved at the extremum on the nucleation curve. Many scientists have misunderstood that Kelvin Equation corresponds to the maximum state because they have unnoticed the presence of the minimum and its stability. At the minimum state, the nuclei should be more stable than those at the maximum state. Thus, Kelvin Equation should correspond to the minimum state rather than the maximum state
