Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem

Abstract

The question of constructing models for the evolution of clusters that differ in shape based on the Boltzmann’s H-theorem is investigated. The first, simplest kinetic equations are proposed and their properties are studied: the conditions for fulfilling the H-theorem (the conditions for detailed and semidetailed balance). These equations are to generalize the classical coagulation–fragmentation type equations for cases when not only mass but also particle shape is taken into account. To construct correct (physically grounded) kinetic models, the fulfillment of the condition of detailed balance is shown to be necessary to monitor, since it is proved that for accepted frequency functions, the condition of detailed balance is fulfilled and the H-theorem is valid. It is shown that for particular and very important cases, the H-theorem holds: the fulfillment of the Arrhenius law and the additivity of the activation energy for interacting particles are found to be essential. In addition, based on the connection of the principle of detailed balance with the Boltzmann equation for the probability of state, the expressions for the reaction rate coefficients are obtained.