On Oscillations and Noise in Multicomponent Adsorption: The Nature of Multiple Stationary States

Abstract

Starting from the fact that monocomponent adsorption, whether modeled by Lagergren or nonlinear Riccati equation, does not sustain oscillations, we speculate about the nature of multiple steady state states in multicomponent adsorption with second-order kinetics and about the possibility that multicomponent adsorption might exhibit oscillating behavior, in order to provide a tool for better discerning possible oscillations from inevitable fluctuations in experimental results or a tool for a better control of adsorption process far from equilibrium. We perform an analysis of stability of binary adsorption with second-order kinetics in multiple ways. We address perturbations around the steady state analytically, first in a classical way, then by introducing Langevin forces and analyzing the reaction flux and cross-correlations, then by applying the stochastic chemical master equation approach, and finally, numerically, by using stochastic simulation algorithms. Our results show that stationary states in this model are stable nodes. Hence, experimental results with purported oscillations in response should be addressed from the point of view of fluctuations and noise analysis.

Monolayer Gas Adsorption on Graphene-Based Materials: Surface Density of Adsorption Sites and Adsorption Capacity

“…If the conditions are met that the equation set can be retarded to the set of linear differential equations, for instance if the depletion of the number of molecules in the gas phase due to the adsorption is negligible, then there is a solution in a closed form, as documented in [44]. The process is stable, without oscillations [45]. Whether obtained numerically or analytically, the solutions to rate equations represent the transient response and prove that the monolayer adsorption belongs to the natural processes with exponential relaxation towards the steady state.…”