Tailored porous electrode resistance for controlling electrolyte depletion and improving charging response in electrochemical systems (original) (raw)
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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.
Comparing Macroscale and Microscale Simulations of Porous Battery Electrodes
Journal of The Electrochemical Society
This describes a vertically-integrated exploration of NMC electrode rate limitations, combining experiments with corresponding macroscale (macro-homogeneous) and microscale models. Parameters common to both models were obtained from experiments or based on published results. Positive electrode tortuosity was the sole fitting parameter used in the macroscale model, while the microscale model used no fitting parameters, instead relying on microstructural domains generated from X-ray microtomography of pristine electrode material held under compression while immersed in electrolyte solution (additionally providing novel observations of electrode wetting). Macroscale simulations showed that the capacity decrease observed at higher rates resulted primarily from solution-phase diffusion resistance. This ability to provide such qualitative insights at low computational costs is a strength of macroscale models, made possible by neglecting electrode spatial details. To explore the consequences of such simplification, the corresponding, computationally-expensive microscale model was constructed. This was found to have limitations preventing quantitatively accurate predictions, for reasons that are discussed in the hope of guiding future work. Nevertheless, the microscale simulation results complement those of the macroscale model by providing a reality-check based on microstructural information; in particular, this novel comparison of the two approaches suggests a reexamination of salt diffusivity measurements.
Russian Journal of Electrochemistry, 2012
We present porous electrode theory for the general situation of electrolytes containing mixtures of mobile ions of arbitrary valencies and diffusion coefficients (mobilities). We focus on electrodes composed of primary particles that are porous themselves. The predominantly bimodal distribution of pores consists of the interparticle or macroporosity outside the particles through which the ions are transported (transport pathways), and the intraparticle or micropores inside the particles, where electrostatic double layers (EDLs) are formed. Both types of pores are filled with electrolyte (solvent plus ions). For the micropores we make use of a novel modified-Donnan (mD) approach valid for strongly overlapped double layers. The mD-model extends the standard Donnan approach in two ways: 1. by including a Stern layer in between the electrical charge and the ions in the micropores, and 2. by including a chemical attraction energy for the ion to go from the macropores into the micropores. This is the first paper where the mD-model is used to model ion transport and electrochemical reactions in a porous electrode. Furthermore we investigate the influence of the charge transfer kinetics on the chemical charge in the electrode, i.e., a contribution to the electrode charge of an origin different from that stemming from the Faradaic reaction itself, e.g. originating from carboxylic acid surface groups as exist in activated carbon electrodes. We show that the chemical charge depends on the current via a shift in local pH, i.e. "current-induced charge regulation." We present results of an example calculation where a divalent cation is reduced to a monovalent ion which electro-diffuses out of the electrode.
Journal of The Electrochemical Society, 2002
This work presents a mathematical model for charge/discharge of electrochemical capacitors that explicitly accounts for particlepacking effects in a composite electrochemical capacitor consisting of hydrous RuO 2 nanoparticles dispersed within porous activated carbon. The model is also used to investigate the effect of nonuniform distributions of salt in the electrolyte phase of the electrode in the context of dilute solution theory. We use the model to compare the performance of capacitors with electrodes made from different activated carbons and to investigate the effects of varying carbon content and discharge current density. Even at low discharge current density, concentration polarization in the electrodes results in underutilization of the electrodes' charge-storage capability, and thus decreased performance. Among various types of activated carbons, those with large micropore surface areas and low meso-and macropore surface areas are preferred because they give high double-layer capacitance and favor efficient packing of RuO 2 nanoparticles, thus maximizing faradaic pseudocapacitance. Increasing the electrode carbon content decreases the delivered charge and energy density, but the reductions are not severe at moderate carbon content and high discharge current. This suggests the possibility of optimizing the carbon content to minimize cost while achieving acceptable discharge performance.
Probing Kinetics of Water-in-Salt Aqueous Batteries with Thick Porous Electrodes
ACS Central Science, 2021
Aqueous electrochemical systems suffer from a low energy density due to a small voltage window of water (1.23 V). Using thicker electrodes to increase the energy density and highly concentrated "water-in-salt" (WIS) electrolytes to extend the voltage range can be a promising solution. However, thicker electrodes produce longer diffusion pathways across the electrode. The highly concentrated salts in WIS electrolytes alter the physicochemical properties which determine the transport behaviors of electrolytes. Understanding how these factors interplay to drive complex transport phenomena in WIS batteries with thick electrodes via deterministic analysis on the rate-limiting factors and kinetics is critical to enhance the rate-performance in these batteries. In this work, a multimodal approachRaman tomography, operando X-ray diffraction refinement, and synchrotron X-ray 3D spectroscopic imagingwas used to investigate the chemical heterogeneity in LiV 3 O 8 −LiMn 2 O 4 WIS batteries with thick porous electrodes cycled under different rates. The multimodal results indicate that the ionic diffusion in the electrolyte is the primary rate-limiting factor. This study highlights the importance of fundamentally understanding the electrochemically coupled transport phenomena in determining the rate-limiting factor of thick porous WIS batteries, thus leading to a design strategy for 3D morphology of thick electrodes for high-rate-performance aqueous batteries.
Time-dependent ion selectivity in capacitive charging of porous electrodes
2012
In a combined experimental and theoretical study we show that capacitive charging of porous electrodes in multicomponent electrolytes may lead to the phenomenon of time-dependent ion selectivity of the electrical double layers (EDLs) in the electrodes. This effect is found in experiments on capacitive deionization of water containing NaCl/CaCl 2 mixtures, when the concentration of Na + ions in the water is 5 times higher than the Ca 2+-ion concentration. In this experiment, after applying a voltage difference between two porous carbon electrodes, first the majority monovalent Na + cations are preferentially adsorbed in the EDLs, and later they are gradually replaced by the minority, divalent Ca 2+ cations. In a process where this ion adsorption step is followed by washing the electrode with freshwater under open-circuit conditions, and subsequent release of the ions while the cell is shortcircuited, a product stream is obtained which is significantly enriched in divalent ions. Repeating this process three times by taking the product concentrations of one run as the feed concentrations for the next, a final increase in the Ca 2+ /Na +-ratio of a factor of 300 is achieved. The phenomenon of timedependent ion selectivity of EDLs cannot be explained by linear response theory. Therefore, a nonlinear time-dependent analysis of capacitive charging is performed for both porous and flat electrodes. Both models attribute time-dependent ion selectivity to the interplay of the transport resistance for the ions in the aqueous solution outside the EDL, and the voltage-dependent ion adsorption capacity of the EDLs. Exact analytical expressions are presented for the excess ion adsorption in planar EDLs (Gouy-Chapman theory) for mixtures containing both monovalent and divalent cations.
Journal of The Electrochemical Society
We study the linear stability of transient electrodeposition in a charged random porous medium, whose pore surface charges can be of any sign, flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem for the dispersion relation that is solved numerically, which agrees well with the analytical approximation obtained from a boundary layer analysis valid at high wavenumbers. Under galvanostatic conditions in which an overlimiting current is applied, in the classical case of zero surface charges, the electric field at the cathode diverges at Sand's time due to electrolyte depletion. The same phenomenon happens for positive charges but earlier than Sand's time. However, negative charges allow the system to sustain an overlimiting current via surface conduction past Sand's time, keeping the electric field bounded. Therefore, at Sand's time, negative charges greatly reduce surface instabilities and suppress dendritic growth, while zero and positive charges magnify them. We compare theoretical predictions for overall surface stabilization with published experimental data for copper electrodeposition in cellulose nitrate membranes and demonstrate good agreement between theory and experiment. We also apply the stability analysis to how crystal grain size varies with duty cycle during pulse electroplating.