On the analytical solution presented in “Theoretical analysis of homogeneous catalysis of electrochemical reactions: steady-state current–potential”

This note examines the mathematical derivation presented by Rani et al. for the steady-state analysis of a nonlinear reaction–diffusion model arising in homogeneous electrocatalysis. The principal contribution of the original paper is the derivation of closed-form expressions for the concentration profiles and the associated current–potential response. Since all subsequent analytical results of Rani et al. depend upon these expressions, it is important that the underlying boundary-value problem be solved rigorously. Herein, I show that the derivation of Rani et al. does not establish that the proposed trial functions satisfy the governing nonlinear differential equations throughout the spatial domain. In particular, the derivation reduces the differential equations to algebraic relations at the electrode surface, but does not demonstrate that the governing equations are satisfied on the semi-infinite interval. I further identify inconsistencies in the published analytical formulae and discuss the extent to which the accompanying numerical computations provide an independent validation of the proposed solution. These observations suggest that the analytical results require further mathematical justification before they may be regarded as established solutions of the nonlinear model.