Determining Electron Transfer Kinetics at Porous Electrodes (original) (raw)
Related papers
Charge transfer kinetics at the solid–solid interface in porous electrodes
Nature Communications, 2014
Interfacial charge transfer is widely assumed to obey Butler-Volmer kinetics. For certain liquid-solid interfaces, Marcus-Hush-Chidsey theory is more accurate and predictive, but it has not been applied to porous electrodes. Here we report a simple method to extract the charge transfer rates in carbon-coated LiFePO 4 porous electrodes from chronoamperometry experiments, obtaining curved Tafel plots that contradict the Butler-Volmer equation but fit the Marcus-Hush-Chidsey prediction over a range of temperatures. The fitted reorganization energy matches the Born solvation energy for electron transfer from carbon to the iron redox site. The kinetics are thus limited by electron transfer at the solid-solid (carbon-Li x FePO 4) interface, rather than by ion transfer at the liquid-solid interface, as previously assumed. The proposed experimental method generalizes Chidsey's method for phase-transforming particles and porous electrodes, and the results show the need to incorporate the Marcus kinetics in modeling batteries and other electrochemical systems.
1 Diffuse charge and Faradaic reactions in porous electrodes
2016
Porous electrodes are widely used in electrochemical systems instead of flat electrodes to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer formed in between; (ii) the charge transfer rate is generally equated to the salt transfer rate, not only at the nanoscale of the matrix/pore interface, but also at the macroscopic scale of transport through the electrode pores. In this work, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the ...
Diffuse charge and Faradaic reactions in porous electrodes
Physical Review E, 2011
Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore dimensions, e.g., for high-porosity metallic foams (macropores >50 nm) and (ii) a modified Donnan model for strongly overlapping DLs, e.g., for porous activated carbon particles (micropores <2 nm). Our theory is valid for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to allow us to derive analytical approximations for the steady-state and early transients. We also present numerical solutions to validate the analysis and to illustrate the evolution of ion densities, pore potential, surface charge, and reaction rates in response to an applied voltage.
Sensors and Actuators B: Chemical, 2008
Cyclic voltammetry is recorded of the oxidation of ferrocyanide on a glassy carbon electrode modified with multiple layers of single-walled carbon nanotubes. The current response is interpreted in terms of semi-infinite planar diffusion towards the macro-electrode surface and in terms of oxidation of the electroactive species trapped in pockets in between the nanotubes. A thin layer model is used to illustrate the effects of diffusion within a porous layer. It is found that a semi-infinite planar diffusion model alone is not appropriate for interpreting the kinetics of the electron transfer at this electrode surface. In particular, caution should be exercised in respect of comparing voltammetric peak-to-peak potential separations between naked electrodes and nanotube-modified electrodes for the inference of electrocatalysis via electron transfer via the nanotubes.
Journal of Electroanalytical Chemistry, 2015
We survey recently-reported, analytical solutions for the study of simple and complicated charge transfer reactions by means of any voltammetric technique with electrodes of very different geometries under conditions where the mass transfer takes place only by diffusion, that is, in fully-supported media where migration can be neglected. Under transient conditions, expressions are reported for one-electron and multi-electron reversible transfers, electrode reactions coupled to homogeneous chemical equilibria and the first-order catalytic mechanisms with electrodes of any geometry. The steady-state voltammetric response of the above systems will also be considered at submicro-and nanoelectrodes of very different shapes and arrays. Also, a universal approach to the steady-state voltammetry of sluggish electron transfer processes is presented. Finally, solutions for ion transfer processes across (sub)micrometric liquid|liquid interfaces is discussed.
Solute transport and reaction in porous electrodes at high Schmidt numbers
Journal of Fluid Mechanics
We present lattice Boltzmann pore-scale numerical simulations of solute transport and reaction in porous electrodes at a high Schmidt number, Sc = 10 2. The three-dimensional geometry of real materials is reconstructed via X-ray computed tomography. We apply a volume-averaging upscaling procedure to characterise the microstructural terms contributing to the homogenised description of the macroscopic advection-reaction-dispersion equation. We firstly focus our analysis on its asymptotic solution, while varying the rate of reaction. The results confirm the presence of two working states of the electrodes: a reaction-limited regime, governed by advective transport, and a mass-transfer-limited regime, where dispersive mechanisms play a pivotal role. For all materials, these regimes depend on a single parameter, the product of the Damköhler number and a microstructural aspect ratio. The macroscopic dispersion is determined by the spatial correlation between solute concentration and flow velocity at the pore scale. This mechanism sustains reaction in the mass-transfer-limited regime due to the spatial rearrangement of the solute transport from low-velocity to high-velocity pores. We then compare the results of pre-asymptotic transport with a macroscopic model based on effective dispersion parameters. Interestingly, the model correctly represents the transport at short characteristic times. At longer times, high reaction rates mitigate the mechanisms of heterogeneous solute transport. In the mass-transfer-limited regime, the significant yet homogeneous dispersion can thus be modelled via an effective dispersion. Finally, we formulate guidelines for the design of porous electrodes based on the microstructural aspect ratio.
One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes
Colloids and Interfaces
Energy storage in porous capacitor materials, capacitive deionization (CDI) for water desalination, capacitive energy generation, geophysical applications, and removal of heavy ions from wastewater streams are some examples of processes where understanding of ionic transport processes in charged porous media is very important. In this work, one-and two-equation models are derived to simulate ionic transport processes in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two-step volume averaging technique is used to derive the averaged transport equations for multi-ionic systems without any further assumptions, such as thin electrical double layers or Donnan equilibrium. A comparison between both models is presented. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. A theoretical analysis shows that the value of interphase pseudo-transport coefficients determines which model to use.
Linear sweep voltammetry in flooded porous electrodes at low sweep rates
Journal of Electroanalytical Chemistry, 1998
A theoretical analysis of linear sweep voltammetry (LSV) in flooded-porous electrodes is treated for reversible (Nernstian) and first-order irreversible reactions. At low sweep rates, the ohmic potential drop within the electrode is negligible and concentration gradients are predominantly in the axial direction. The solution to the reversible case is mathematically simple, but the results are presented to understand the influence external mass-transfer resistance has on the voltammogram. For irreversible kinetics, a Green's function technique is used to obtain an analytical solution to the diffusion equation. An analytical solution for the current as a function of the electrode dimensions, sweep rate and reaction kinetic parameters allows one to predict the voltammogram over a wide range of conditions. The analytical solution is used to develop correlations that enable the kinetic parameters (i.e. exchange current density per unit volume and the transfer coefficient) to be easily extracted from experimental data.
Theory of Electrochemical Electron Transfer
Introduction to Marcus Theory of Electron Transfer Reactions, 2020
INTRODUCTION References CHAPTER 2 ELECTRON TRANSFER REACTIONS: CLASSIFICATION AND EXAMPLES 2.1 Introduction 2.2 Outer and Inner Sphere ET Reactions 2.3 Adiabatic and Nonadiabatic ET Reactions References CHAPTER 3 HISTORICAL BACKGROUND 3.1 Introduction 3.2 Classical Theory of Electron Transfer 3.3 Quantum Me.chanical Treatment of Electron Transfer 3.4 Other Developments References CHAPTER 4 THE ROLE OF SOLVENT DYNAMICS IN ELECTRON TRANSFER 4.