Homogeneous Nucleation—Kelvins Equation

Let us consider the thermodynamics of processes of the homogeneous nucleation of a new phase with the formation of fluid drops from the over saturated vapor as an example. While the chemical potential of the equihb rium substance vapor over spherical particles of its condensed phase is given by the Kelvin Thomson equation (5.2), only those drops that have the critical size r.. 

We find that the Kelvin equation for the critical cluster size depends on the ratio of the product of the partial pressures of NH3 and HCl to the equilibrium constant Kp. The product pNH,f>HCi must exceed Kp for a critical cluster to exist. Physically this condition merely means that the product of the gas-phase partial pressures must exceed the equilibrium partial pressure product at that temperature for a solid phase to exist. It is equivalent to the condition that 5 > 1 for a critical cluster to exist for homogeneous-homomolecular nucleation. 

Warneck, P. (2000) Chemistry of the natural atmosphere. Academic Press, New York, 969 pp Warneck, P. (2003) In-cloud chemistry opens pathway to the formation of oxalic acid in the marine atmosphere. Atmospheric Environment 37, 2423-2427 Wasai, K., G. Kaptay, K. Mukai and N. Shinozaki (2007) Modified classical homogeneous nucleation theory and a new minimum in free energy change 1. A new minimum and Kelvin equation. Fluid Phase Equilibria 254, 67-74 Waterman, L. S. (1983) Comments on The Montsouris series of carbon dioxide concentration measurements, 1877-1910 by Stanhill . Climate Change 5, 413-415... 

Homogeneous nucleation of solid particles in solution is generally analyzed in terms of the classical theories developed for vapor-to-liquid and vapor-to-solid transformations which are described in detail by Christian (47). We shall briefly outline the main features of the classical theories for vapor-to-liquid transformation and then examine how they are applied to nucleation of solid particles from solution. In a supersaturated vapor consisting of atoms (or molecules), random thermal fluctuations give rise to local fluctuations in density and free energy of the system. Density fluctuations produce clusters of atoms referred to as embryos, which can grow by addition of atoms from the vapor phase. A range of embryo sizes will be present in the vapor with vapor pressures assumed to obey the Kelvin equation ... 

Again, the primary phase particles of the required substance modifica tion (material precursors) are usually very small. When seeds of the synthe sized phase are used, these primary particles are identical in size to the seeds. In the homogeneous liquid solutions or gas mixtures, the size ofpri mary particles is determined by the nucleation processes. The small size of the primary phase particles can influence considerably the chemical poten tial of the phase to be formed. For example, in the case of spherical parti cles, the chemical potential is determined by equation (1.5). Hence, the equilibrium partial pressure, p, of the saturated vapor or concentration, c of the saturated solution of the substance—for example, of the synthe sized one component phase—is determined by the Kelvin Thomson equation... 

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