A. E. Antipov

Electroreduction of bromate anion on inactive RDE under steady-state conditions: Numerical study of ion transport processes and comproportionation reaction

The study is devoted to analyzing the electroreduction of bromate anion BrO 3- on catalytically inactive (e.g., carbon) electrodes by numerical methods. This process is realized due to the combination of the reversible mediator pair Br2/Br- and the process of comproportionation (reaction of bromate and bromide anions) in solution phase. These reactions increase the concentration of bromine and bromide near the electrode surface; hence, this process is autocatalytic (EC″ mechanism). Within the framework of this study, a numerical algorithm which allows the system of diffusion-kinetic equations to be solved for this system is proposed for one-dimensional transport and the process under steady-state conditions. The results are compared with the conclusions of the approximate analytical theory published in Electrochim. Acta, 2015, vol. 173, p. 779, which allows inferring that both approaches are correct. The deviation between the latter is observed only in the cases of violation of approximations lying in the basis of the corresponding analytical relationships. Thus, the predictions of the analytical theory of practical interest can be considered as reliably confirmed by numerical calculations, particularly, the prediction on the nonmonotonous dependence of the maximum current on the diffusion layer thickness (or the RDE rotation rate) including the anomalous region of this dependence in which the current increases with the increase in the diffusion layer thickness.

Communication: Drift velocity of Brownian particle in a periodically tapered tube induced by a time-periodic force with zero mean: Dependence on the force period

We study the drift of a Brownian particle in a periodically tapered tube, induced by a longitudinal time-periodic force of amplitude ∣F∣ that alternates in sign every half-period. The focus is on the velocity dependence on the force period, which is usually considered not tractable analytically. For large ∣F∣ we derive an analytical solution that gives the velocity as a function of the amplitude and the period of the force as well as the geometric parameters of the tube. The solution shows how the velocity decreases from its maximum value to zero as the force period decreases from infinity (adiabatic regime) to zero. Our analytical results are in excellent agreement with those obtained from 3D Brownian dynamics simulations.

Electroreduction of bromate anion in acidic solutions at the inactive rotating disc electrode under steady-state conditions: Numerical modeling of the process with bromate anions being in excess compared to protons

The process of electroreduction of bromate anion BrO3 in acidic solutions at catalytically inactive electrodes when bromate anions are in excess compared to protons has been studied by numerical integration of transport equations. Under these conditions, the maximum possible current is limited by the limiting diffusion current of protons (rather than bromate), since both ions are consumed in the comproportionation reaction. It has been demonstrated that the curve of maximum current versus diffusion layer thickness has an anomalous segment where the current increases with an increase of the latter.

Directed transport of a Brownian particle in a periodically tapered tube

The problem of the motion of a Brownian particle in a periodically tapered tube induced by a time-periodic longitudinal force with zero mean is considered. Under the action of this force, the particle is shown to drift in a direction opposite to the constant load force applied to it. Analytical solutions for the drift velocity, the stopping force (the load causing the effect to disappear), and the efficiency of converting the energy introduced by perturbations into directed motion have been obtained at a large amplitude of the driving force, when the effect being discussed is maximal. In the range of its applicability extending from zero to asymptotically large force switching frequencies (proportional to the amplitude of the driving force), these solutions are in good agreement with the results of Brownian dynamics simulations.

Mediator reduction of bromate anion at rotating disk electrode under steady-state conditions for high current densities

Theoretical study of the bromate anion reduction under steady-state conditions is performed for rotating disk electrode. Transport of the components in solution is described within the framework of the Nernst stagnant layer model. Numerical calculations carried out recently for the same system confirmed the validity of our previous approximate analytical approaches for the weak current and thin kinetic layer regimes for small and moderate values of the principal parameters of the system: ratio of the diffusion and kinetic layer thicknesses, xdk = zd/zk, for the whole range of possible currents. At the same time, these numerical results showed a pronounced change of the calculated concentration distributions, compared to the predictions of the thin kinetic layer model, for very large values of the xdk parameter. A new theoretical analysis performed in this study provides approximate analytical expressions for the concentration distributions under conditions of very strong current exceeding the bromate diffusion-limited one. These expressions demonstrate that the passing of such currents results in a cardinal change of the kinetic layer structure, compared to that for weaker currents. The comproportionation reaction takes place mainly inside a layer near the electrode surface for moderate current densities while for strong currents a BrO3−-free layer is formed near the surface, so that the reaction is localized within a narrow “reaction zone” displaced from the electrode surface.

Bromate anion reduction: novel autocatalytic (EC″) mechanism of electrochemical processes. Its implication for redox flow batteries of high energy and power densities

Abstract Recent theoretical studies of the bromate electroreduction from strongly acidic solution have been overviewed in view of very high redox-charge and energy densities of this process making it attractive for electric energy sources. Keeping in mind non-electroactivity of the bromate ion the possibility to ensure its rapid transformation via a redox-mediator cycle (EC′ mechanism) is analyzed. Alternative route via the bromine/bromide redox couple and the comproportionation reaction inside the solution phase is considered within the framework of several theoretical approaches based on the conventional Nernst layer model, or on its recently proposed advanced version (Generalized Nernst layer model), on the convective diffusion transport equations. This analysis has revealed that this process corresponds to a novel (EC″) electrochemical mechanism since the transformation of the principal oxidant (bromate) is carried out via autocatalytic redox cycle where the bromate consumption leads to progressive accumulation of the bromine/bromide redox couple catalyzing the process. As a result, even a tracer amount of its component, bromine, in the bulk solution leads under certain conditions to extremely high current densities which may even overcome the diffusion-limited one for bromate, i.e. be well over 1 A/cm2 for concentrated bromate solutions. This analysis allows one to expect that the hydrogen–bromate flow battery may generate very high values of both the current density and specific electric power, over 1 A/cm2 and 1 W/cm2.

Asymmetry of the shape of surroundings as a mechanism for generating directed motion

A mechanism for generating a directed motion of a Brownian particle in an asymmetric channel under the action of a varying force field is considered. The setup implementing such a mechanism resembles typical Brownian motors using asymmetry of the energy potential (ratchet effect). It is shown that under certain conditions, the asymmetry of the shape may ensure the maximal level of rectification for a large intensity of the external field drawing the system from equilibrium. The main question formulated here is the dependence of the rectifying ability of such a mechanism on the external action parameters and, above all, on the form of the time dependence. The results obtained here for a sine signal and an aperiodic train of pulses are compared with the previous results obtained by the authors for bipolar rectangular pulses. General estimates obtained for pulses of an arbitrary shape determine its influence on the velocity of directed motion. Analysis of the proposed mechanism is based of the combination of analytic calculations for a strong external field with simulation by the method of Brownian dynamics for arbitrary parameters.

Generalization of the Nernst layer model to take into account the difference in diffusivity between the components of the system in bromate reduction in steady-state one-dimensional mode: Current limiting by proton transport

The reduction of nonelectroactive bromate anion BrO3- from acidic solutions while limiting the maximum current by diffusion transport of protons was studied by methods of numerical integration of transport equations. The calculation was performed based on a generalization of the Nernst steady diffusion layer model, in which the choice of the layer thickness for each component of the system is made using the Levich formula and takes into account the difference in diffusivity between the components. This difference in layer thickness was shown to have a significant effect on the main characteristics of the system, such as the maximum possible discharge current, and also the concentration profiles of the components.

Biased diffusion in tubes of alternating diameter: Numerical study over a wide range of biasing force

This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficients--mobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determine the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small.

Biased diffusion in tubes of alternating diameter: Analytical treatment in the case of strong bias

This paper is devoted to the effective transport coefficients of a particle in a tube of alternating diameter. Analytical expressions are derived for the effective mobility and diffusivity under strong bias conditions, i.e., in the limiting case where the external biasing force tends to infinity. The expressions give the transport coefficients as functions of the geometric parameters of the tube and the external force. They show that the effective diffusivity is a linear function of the square of the external force, whereas the effective mobility is independent of the force. The problem of finding effective transport coefficients in a tube of alternating diameter is too complex to be analyzed by conventional methods. Therefore, the expressions are derived in the framework of an intuition-based approach and validated by Brownian dynamics simulations. The obtained results extend a short list of available analytical expressions for the effective transport coefficients.