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Multiscale Perturbation Methods for Dynamic/Programmable Catalysis
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DOI：10.1021/acs.iecr.5c03023.png)
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Abstract
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Within the search for more efficient catalytic processes, dynamic or programmable catalysis has been explored as a means to increase overall reaction rates by periodically oscillating the binding energies of catalysts. This strategy offers the potential to overcome limitations associated with the Sabatier principle by promoting different elementary reaction steps at different points in time. Modeling such systems has relied on numerical techniques, which can be computationally expensive and have inherent errors. Here, we employ perturbation methods to develop a framework for dynamic catalysis that allows analytical derivation of closed-form expressions for surface coverage fraction averages and limit cycles. We derive a method using multiple-scales expansion to decompose the response of a dynamic catalytic system into slow (averaged) and fast (oscillatory) components. The proposed approach is applied to two reaction schemes previously analyzed in the literature. Our results show favorable agreement with predictions obtained via numerical simulations, employing a boundary value problem (BVP) approach, when the underlying assumptions of perturbation methods are met, namely, high-frequency forcing and small-to-moderate forcing amplitudes. We show the application of the techniques to linear systems relevant to dynamic catalysis and comment on the applicability for nonlinear systems. Overall, this work adds to the increasing development of methods for simulating and, ultimately, improving dynamic catalytic processes.
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