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Langmuir Adsorption Kinetics in Liquid Media: Interface Reaction Model.

ABSTRACT: Adsorption kinetic equation has been derived assuming that the process follows the behavior of a heterogeneous chemical reaction at the solid-liquid interface. This equation is converted into the Langmuir isotherm at equilibrium and describes well the unsteady-state adsorption process. Based on that, a working equation has been developed, which gives adsorption-rate-constant independent of operating parameters including concentration. Also, a kinetic model expressed as a sum of first- and second-order systems available in the literature has been applied (modified with the interface reaction concept) to determine the adsorption rate constant. Both methods gave similar results. Three dimensionless numbers have been developed to determine and distinguish pseudo-first-order and pseudo-second-order kinetics justified from the viewpoint of chemical kinetics. It is shown that curve-fitting with a high correlation coefficient could validate an empirical kinetic model, but the fitted model parameters could not automatically be related to chemical kinetic parameters if the model itself is not grounded on well-defined chemical kinetics. Finally, it is concluded that the currently applied empirical approach could not provide reliable data for comparison among similar systems, while the Langmuir kinetic equation developed based on the concept of heterogeneous reaction would be a good basis for standardization of the method for adsorption system characterization.

SUBMITTER: Islam MA

PROVIDER: S-EPMC8190925 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:For more than a century, monolayer adsorptions in which adsorbate molecules and adsorbing sites behave ideally have been successfully described by Langmuir's adsorption isotherm. For example, the amount of adsorbed material, as a function of concentration of the material which is not adsorbed, obeys Langmuir's equation. In this paper, we argue that this relation is valid only for macroscopic systems. However, when particle numbers of adsorbate molecules and/or adsorbing sites are small, Langmuir's model fails to describe the chemical equilibrium of the system. This is because the kinetics of forming, or the probability of observing, occupied sites arises from two-body interactions, and as such, ought to include cross-correlations between particle numbers of the adsorbate and adsorbing sites. The effect of these correlations, as reflected by deviations in predicting composition when correlations are ignored, increases with decreasing particle numbers and becomes substantial when only few adsorbate molecules, or adsorbing sites, are present in the system. In addition, any change that augments the fraction of occupied sites at equilibrium (e.g., smaller volume, lower temperature, or stronger adsorption energy) further increases the discrepancy between observed properties of small systems and those predicted by Langmuir's theory. In contrast, for large systems, these cross-correlations become negligible, and therefore when expressing properties involving two-body processes, it is possible to consider independently the concentration of each component. By applying statistical mechanics concepts, we derive a general expression of the equilibrium constant for adsorption. It is also demonstrated that in ensembles in which total numbers of particles are fixed, the magnitudes of fluctuations in particle numbers alone can predict the average chemical composition of the system. Moreover, an alternative adsorption equation, predicting the average fraction of occupied sites from the value of the equilibrium constant, is proposed. All derived relations were tested against results obtained by Monte Carlo simulations.

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Langmuir Adsorption Kinetics in Liquid Media: Interface Reaction Model.

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