Method of Cellular Automata for Simulation of Physico-Chemical Processes on Nanocatalyst

• Дата: 2021
• Автори: Гранкін, Денис, Гранкін, Михайло, Гранкін, Віктор
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Кам'янець-Подільський національний університет імені Івана Огієнка 2021
• Онлайн доступ: http://mcm-math.kpnu.edu.ua/article/view/251138
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

The paper considers a new approach to describe dynamic physicochemical processes on a nanocatalyst. The growing difficulties in describing the catalysis of a heterogeneous chemical reaction by nanocatalysts are due to the fact that the described phenomena are nonlinear, dissipative, in some cases accompanied by self-oscillating and stochastic flow and cannot be described by traditional mathematical models, such as systems of differential equations. To solve the problem considered in the publication, it is proposed to use, as an alternative to differential equations for continuous mathematics, discrete models, which are extensions of the classical von Neumann's cellular automaton. In this case, the cellular automaton is considered as a discrete expression of the space-time function and performs the same task as the differential equations in partial derivatives. A stepwise reaction mechanism has been developed that takes into account the recombination of atoms, the formation of vibrationally excited molecules, their diffusion and relaxation, and a cellular automaton model of a heterogeneous chemical reaction on a nanocatalyst with a system of spatially distributed nanoclusters on the surface. The results of CA-modeling are presented and it is shown that the asynchronous cellular automaton developed in the presented work allows modeling a chemical reaction, including recombination of atoms, on the surface of a nanocatalyst with spatially distributed nanoclusters on the surface. The constructed CA-model describes the kinetics of the process in real physical time and uses physical cross sections and interaction constants.