Kinetic model of electrochemical nucleation

Abstract

The kinetic model of electrochemical nucleation of micro-and nanoparticles is studied. The functional dependence of probability of the energy of the particle on the relative radius found earlier is used in nucleation in the statistical Heisenberg model. On the basis of the proposed theory, a simple ratio for calculation of probabilities of kinetic processes is obtained for the case of electrochemical nucleation.

Microkinetic model of nucleation and its application in electrochemistry

“…THERMODYNAMIC APPROACH TO THE NUCLEATION PROBLEM Note that, earlier, we obtained a set of results similar to those discussed here, though on the basis of a general formal approach in the framework of the model of statistical nucleation [4,5]. Naturally, the former approach and that proposed here are equivalent, though, methodically, it is interesting to obtain the result on the basis of other general principles, at least with the aim to prove its validity.…”

“…One may surely conclude that the solution of this problem proposed in [1] is evidently interesting and should be analyzed; generalized; and, probably, completed. This paper is devoted, in particular, to these theoretical problems of kinetics of nucleation process, and its main goal is to generalize our earlier results [3][4][5] into a unified system and to find the place of this general theory in the solution of the special problem of electronucleation.…”

“…The specified saddle point defines the probability of the metastable processes. From general considerations of the statistical thermodynamics of quasi-equilibrium processes, the probability of this process is defined as (5) where Q is the thermodynamic activation potential, which involves both the activation energy of an elementary act and the energy expenses related to the change in the state configuration. The latter expenses for a number of processes can even exceed the former, but all the expenses are defined by the value of the free energy of the system F in the vicinity of the saddle point, which, in essence, define the thermodynamic activation potential.…”

“…Then, we write the specified part of the free energy in these variables: (9) where θ ( r ) is the angle between the cylinder axis and the spin vector (the magnetization vector in the theory of micromagnetizm (see [3][4][5][6][7][8][9][10][11][12] for more details)), and r is the radial coordinate. The model kinetic energy T(r) is a classical analogue of the exchange (potential) energy in the Heisenberg model for the two-dimensional space (see [3][4][5][7][8][9][10][11][12][13] for more details). Note, it is not occasional that T(r) coincides in its form with the kinetic energy of the quasiparticle in spherical coordinates.…”

“…In [3][4][5], an instanton model was proposed, which involves, for example, microscopic parameters of the system, such as the energy of interaction of atoms in the nanoparticle. It is expedient to compare the results of these approaches, especially taking into account that an instanton model of disclinations already exists [7][8].…”