Transport and kinetics in electrocatalytic thin film biosensors: bounded diffusion with non-Michaelis-Menten reaction ki
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ORIGINAL PAPER
Transport and kinetics in electrocatalytic thin film biosensors: bounded diffusion with non-Michaelis-Menten reaction kinetics Michael E. G. Lyons 1 Received: 17 February 2020 / Revised: 24 March 2020 / Accepted: 24 March 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we describe the problem of describing the transport and catalytic kinetics at immobilized enzymes in an electronically conductive polymer thin film where substrate inhibition is important. Here, the enzyme kinetics are not well described by the Michaelis-Menten equation. We describe a mathematical procedure based on the recently developed Akbari-Ganji method (AGM) which facilitates a full analytical solution of the boundary value problem which is valid for all values of substrate concentration. Closed form expressions for both the substrate concentration in the film and the steady-state amperometric current response are presented. Limiting kinetic cases are identified and are expressed pictorially in parameter space using a kinetic case diagram. Keywords Amperometric polymer sensor modelling . Non-Michaelis-Menten kinetics . Transport and kinetics in polymer modified electrodes . Reaction diffusion equations
Introduction The problem of quantitatively describing the transport and kinetics of reactants within bounded thin polymeric films (also known as chemically modified electrodes) is very challenging and has been the subject of considerable attention over the last 40 years. The seminal papers of Andrieux, Saveant and their co-workers [1–3] and by Albery and Hillman [4] are noteworthy. In these reactions within electroactive polymers were examined: The Fick steady-state diffusion equations were coupled with bimolecular rate expressions and approximate analytical solutions for the steady-state current response derived. This early work has been reviewed by Lyons [5]. The early work on heterogeneous mediated electrocatalysis by electroactive polymer films and homogeneous molecular catalysis has been recently extended by Costentin and coworkers in a series of comprehensive papers [6,7]. Leddy and co-workers [8] have further extended the original This paper is dedicated to Professor Dr Fritz Scholz on the occasion of his 65th birthday. * Michael E. G. Lyons [email protected] 1
School of Chemistry and AMBER National Centre, Trinity College Dublin, University of Dublin, Dublin 2, Ireland
Andrieux-Saveant analysis. The analysis of reactant transport and kinetics within bounded electroactive thin films deposited either on macro size or micro electrode supports has also been applied to the important area of amperometric electrochemical biosensing where the steady-state or transient current response is derived via solving the Fick diffusion equation for substrate within the film [9–11]. Using this approach, the analytical solution to a well formulated reaction/diffusion problem (where the Fick diffusion equation is coupled to a chemical reaction term) is developed describing how the concentration of sub
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