Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes

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 in the electrode 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 ions 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 found 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.     

Relaxation of the electrical double layer after an electron transfer approached by Brownian dynamics simulation

In this paper, the dynamical properties of the electrochemical double layer following an electron transfer are investigated by using Brownian dynamics simulations. This work is motivated by recent developments in ultrafast cyclic voltammetry which allow nanosecond time scales to be reached. A simple model of an electrochemical cell is developed by considering a 1:1 supporting electrolyte between two parallel walls carrying opposite surface charges, representing the electrodes; the solution also contains two neutral solutes representing the electroactive species. Equilibrium Brownian dynamics simulations of this system are performed. To mimic electron transfer processes at the electrode, the charge of the electroactive species are suddenly changed, and the subsequent relaxation of the surrounding ionic atmosphere are followed, using nonequilibrium Brownian dynamics. The electrostatic potential created in the center of the electroactive species by other ions is found to have an exponential decay which allows the evaluation of a characteristic relaxation time. The influence of the surface charge and of the electrolyte concentration on this time is discussed, for several conditions that mirror the ones of classical electrochemical experiments. The computed relaxation time of the double layer in aqueous solutions is found in the range 0.1 to 0.4 ns for electrolyte concentrations between 0.1 and 1 mol L(-1) and surface charges between 0.032 and 0.128 C m(-2).     

Determining the Diffusion Coefficient of Lithium Insertion Cathodes from GITT measurements: Theoretical Analysis for low Temperatures**

Accurate knowledge of transport properties of Li-insertion materials in application-relevant temperature ranges is of crucial importance for the targeted optimization of Li-ion batteries (LIBs). Galvanostatic intermittent titration technique (GITT) is a widely applied method to determine Li-ion diffusion coefficients of electrode materials. The well-known calculation formulas based on Weppner's and Huggins’ approach, imply a square-root time dependence of the potential during a GITT pulse. Charging the electrochemical double layer capacitance at the beginning of a GITT pulse usually takes less than one second. However, at lower temperatures down to −40 °C, the double layer charging time strongly increases due to an increase of the charge transfer resistance. The charging time can become comparable with the pulse duration, impeding the conventional GITT diffusion analysis. We propose a model to describe the potential change during a galvanostatic current pulse, which includes an initial, relatively long-lasting double layer charging, and analyze the accuracy of the lithium diffusion coefficient, derived by using the Weppner-Huggins method within a suitably chosen time interval of the pulse. Effects leading to an inaccurate determination of the diffusion coefficient are discussed and suggestions to improve GITT analyses at low temperature are derived.     

Impedance spectroscopy studies of changes in the properties of lithium-sulfur cells in the course of cycling

Changes in the properties of lithium-sulfur cells during cycling were studied by impedance spectroscopy. The electric conductivity of the electrolyte changed during the charging and discharging of the lithium-sulfur cells as a result of the dissolution of lithium polysulfides formed in electrochemical reactions. The maximum resistance of the electrolyte and the surface layers on the sulfur and lithium electrodes was achieved in the region of the transition between the low- and high-voltage areas on the charge and discharge curves of the cells. This region corresponded to the highest concentration of lithium polysulfides in the electrolyte. For nearly charged or discharged lithium-sulfur cells, the impedance spectra contained linear segments which could be attributed to diffusion limitations at low frequencies. An analysis of the results of impedance studies suggested that the electrochemical processes in lithium-sulfur cells were controlled by diffusion in the surface layer on the sulfur electrode at high degrees of charge or discharge and by the transport properties of the electrolytic system at moderate degrees of charging.     

聚苯胺/活性碳复合型超电容器的电化学特性

电化学电容器作为一种新型储能器件具有广泛的应用.采用(NH₄)₂S₂O₈化学氧化聚合苯胺法制备了聚苯胺电极材料，采用化学物理二次催化活化法制备了高比表面积活性碳材料.并用循环伏安、恒流充放电以及交流阻抗等方法对上述电极材料的电化学特性进行了研究.实验结果表明,所制备的聚苯胺电极材料具有高于420 F•g^－1的法拉第赝电容和良好的电化学特性，所制备的活性碳电极材料则具有160 F•g^－1的双电层电容量.分别采用聚苯胺作为正极，活性碳作为负极，38％硫酸作为电解液制备了复合型电化学电容器.复合型电容器工作电压达到1.4 V, 电容器单体比电容达到57 F•g^－1，最大比能量和最大真实比功率分别达到15.5 W•h•kg^－1和2.4 W•g^－1, 峰值比功率达到20.4 W•g^－1,电容器循环工作寿命超过500次. 与活性碳双电层电容器相比，复合型电容器还具有较低的自放电率.     

锂离子电池多孔电极理论的回顾与新思考

本文总结了Newman多孔电极理论的基本内容,提出若干改进思路. 提出基于离子-空穴耦合传输机制描述浓电解质中的离子输运过程,在此基础上引入离子-电子耦合转移反应的思想处理电极材料中的离子传输问题,并通过计算嵌锂材料的离子扩散系数验证其合理性. 总结了描述多孔电极多尺度结构的相关理论和技术,表明均质化方法和基于结构重建的介观模拟方法均能给出比较合理的有效输运参数,从而提高多孔电极理论模拟结果的准确性.     

The role of electrode impedance and electrode geometry in the design of microelectrode systems

Microelectromechanical systems (MEMS) employing spatially and/or temporally nonuniform electric fields have been extensively employed to control the motion of suspended particles or fluid flow. Design and control of microelectromechanical processes require accurate calculations of the electric field distribution under varying electrolyte conditions. Polarization of electrodes under the application of an oscillating voltage difference produces dynamic electrical double layers. The capacitive nature of the double layers significantly inhibits the penetration of the electric field through the double layer and into the surrounding bulk electrolyte at low frequencies. This paper quantitatively discusses the effect of electrode impedance on the electric field distribution as a function of field frequency, electrolyte composition, and electrode zeta potential in microelectrode systems. The design principles for the electrode geometry and configuration are also discussed in terms of their effects on the electric field magnitude and nonuniformity.     

Changes in zeta potential caused by a dc electric current for thin double layers

An asymptotic solution was obtained to describe one-dimensional, steady-state transport of a symmetric binary electrolyte normal to two large parallel electrodes, in the limit in which the Debye length is infinitesimal compared to the distance separating the two electrodes. Despite the nonzero ion flux, Boltzmann's equation continues to describe the relationship between either ion concentration and the electrostatic potential inside the diffuse part of the double layer, while local electroneutrality applies outside, even for current densities approaching the limiting value. In the absence of ion adsorption or dissociation reactions at the electrodes, the magnitude of any charge or zeta potential arising on the electrodes at zero current is determined by the equilibrium constant for the redox reactions which would exchange ionic charge carriers for electric charge carriers at the electrode surface. Nonzero current causes the ionic strength of the bulk to vary with position. This perturbs the Debye length of the diffuse cloud on either electrode: it is the local ionic strength just outside the cloud which determines the Debye length for that cloud. Nonzero current also changes the zeta potential. The dimensionless rate of change dζ/dJ was as large as 30.     

Numerical Simulation of Electrochemical Systems by Coupling Analytical Calculation of the Diffuse Double Layer and Finite Element Description of Solution Bulk

Numerical modelling of electrochemical systems covers length scales from the nanometers up to the macroscopic scale. With finite element methods, the mesh must be extremely fine to describe the diffuse double layer, thus increasing the needed computational resources. We propose a method to describe the diffuse double layer by analytical equations, expressed as boundary conditions for the partial differential equations describing the solution bulk. We apply the method to a one-dimensional system, i. e. to a cell with plane parallel electrodes, in the presence of a redox couple and a supporting electrolyte. We provide evidence of the precision of the method.     

Highly conductive nanostructured C-TiO2 electrodes with enhanced electrochemical stability and double layer charge storage capacitance

The present work reports the structural and electrochemical properties of carbon-modified nanostructured TiO(2) electrodes (C-TiO(2)) prepared by anodizing titanium in a fluoride-based electrolyte followed by thermal annealing in an atmosphere of methane and hydrogen in the presence of Fe precursors. The C-TiO(2) nanostructured electrodes are highly conductive and contain more than 1 × 10(10) /cm(2) of nanowires or nanotubes to enhance their double layer charge capacitance and electrochemical stability. Electrogenerated chemiluminescence (ECL) study shows that a C-TiO(2) electrode can replace noble metal electrodes for ultrasensitive ECL detection. Dynamic potential control experiments of redox reactions show that the C-TiO(2) electrode has a broad potential window for a redox reaction. Double layer charging capacitance of the C-TiO(2) electrode is found to be 3 orders of magnitude higher than an ideal planar electrode because of its high surface area and efficient charge collection capability from the nanowire structured surface. The effect of anodization voltage, surface treatment with Fe precursors for carbon modification, the barrier layer between the Ti substrate, and anodized layer on the double layer charging capacitance is studied. Ferrocene carboxylic acid binds covalently to the anodized Ti surface forming a self-assembled monolayer, serving as an ideal precursor layer to yield C-TiO(2) electrodes with better double layer charging performance than the other precursors.     

Dynamic diffuse double-layer model for the electrochemistry of nanometer-sized electrodes

A dynamic diffuse double-layer model is developed for describing the electrode/electrolyte interface bearing a redox reaction. It overcomes the dilemma of the traditional voltammetric theories based on the depletion layer and Frumkin's model for double-layer effects in predicating the voltammetric behavior of nanometer-sized electrodes. Starting from the Nernst-Planck equation, a dynamic interfacial concentration distribution is derived, which has a similar form to the Boltzmann distribution equation but contains the influence of current density. Incorporation of the dynamic concentration distribution into the Poisson and Butler-Volmer equations, respectively, produces a dynamic potential distribution equation containing the influence of current and a voltammetric equation containing the double-layer effects. Computation based on these two equations gives both the interfacial structure (potential and concentration profiles) and voltammetric behavior. The results show that the electrochemical interface at electrodes of nanometer scales is more like an electric-double-layer, whereas the interface at electrodes larger than 100 nm can be treated as a concentration depletion layer. The double-layer nature of the electrode/electrolyte interface of nanometer scale causes the voltammetric responses to vary with electrode size, reactant charge, the value of formal redox potential, and the dielectric properties of the compact double-layer. These voltammetric features are novel in comparison to the traditional voltammetric theory based on the transport of redox molecules in the depletion layer.     

The role of supporting electrolyte in heterogeneous electron transfer

The effects of supporting electrolyte on the kinetics of the elementary step of electron transfer are considered as unavoidable interplay of interfacial phenomena and ionic equilibria in solution. For the former, the problems to separate contributions of electrostatic electrode-reactant interactions and specific adsorption are addressed, and various aspects of the traditional Frumkin correction (“psi-prime effect”) are discussed. The construction of corrected Tafel plots is shown to be a procedure containing the internal contradiction resulting in an uncertainty. This uncertainty can be eliminated by combining the principles of traditional analysis of the “double layer” effects with physical theory instead of phenomenological approaches. Specific manifestations of parallel electron transfer to an ensemble of reacting species are presented in the context of “mean reactant charge in solution bulk.” The approach to account for non-spherical shape and inhomogeneous charge distribution in reacting species is considered in terms of “molecular psi-prime effect.” Finally, some comments are given on analogy of “double layer” effects at metal/solution interface and interfacial phenomena specific for more complex and highly relevant electrochemical systems.     

Supercapattery: Merit merge of capacitive and Nernstian charge storage mechanisms

Supercapattery is the generic name for hybrids of supercapacitor and rechargeable battery. Batteries store charge via Faradaic processes, involving reversible transfer of localised or zone-delocalised valence electrons. The former is governed by the Nernst equation. The latter leads to pseudocapacitance (or Faradaic capacitance) which may be differentiated from electric double layer capacitance with spectroscopic assistance such as electron spin resonance. Because capacitive storage is the basis of supercapacitors, the combination of capacitive and Nernstian mechanisms has dominated supercapattery research since 2018, covering nanostructured and compounded metal oxides and sulphides, water-in-salt and redox active electrolytes and bipolar stacks of multicells. The technical achievements so far, such as specific energy of 270 Wh/kg in aqueous electrolyte, and charging–discharging for more than 5000 cycles, benchmark a challenging but promising future of supercapattery.     

Analysis of diffuse-layer effects on time-dependent interfacial kinetics

We investigate the subtle effects of the diffuse charged layer on interfacial kinetics by solving the governing equations for ion transport (Nernst–Planck) with realistic boundary conditions representing reaction kinetics (Butler–Volmer) and compact-layer capacitance (Stern) in the asymptotic limit =λ_D/L→0, where λ_D is the Debye screening length and L is the distance between the working and counter electrodes. Using the methods of singular perturbation theory, we derive the leading-order steady-state response to a nonzero applied current in the case of the oxidation of a neutral species into cations, without any supporting electrolyte. In certain parameter regimes, the theory predicts a reaction-limited current smaller than the classical diffusion-limited current; this over potential effect is not due to ohmic drop effects in the bulk of the cell but rather to antagonist processes involved in the surface charge transfer and diffuse layer charging respectively. We demonstrate that the charging of diffuse charge, since it is intimately coupled to the surface reaction and cannot be considered independently, plays a fundamental role in nonequilibrium surface reactions when the transport of one of the reacting species is coupled to the total interfacial response of the compact and diffuse layers.     

Electrochemistry,ion adsorption and dynamics in the double layer: a study of NaCl(aq) on graphite

Graphite and related sp² carbons are ubiquitous electrode materials with particular promise for use in e.g., energy storage and desalination devices, but very little is known about the properties of the carbon–electrolyte double layer at technologically relevant concentrations. Here, the (electrified) graphite–NaCl(aq) interface was examined using constant chemical potential molecular dynamics (CμMD) simulations; this approach avoids ion depletion (due to surface adsorption) and maintains a constant concentration, electroneutral bulk solution beyond the surface. Specific Na⁺ adsorption at the graphite basal surface causes charging of the interface in the absence of an applied potential. At moderate bulk concentrations, this leads to accumulation of counter-ions in a diffuse layer to balance the effective surface charge, consistent with established models of the electrical double layer. Beyond ∼0.6 M, however, a combination of over-screening and ion crowding in the double layer results in alternating compact layers of charge density perpendicular to the interface. The transition to this regime is marked by an increasing double layer size and anomalous negative shifts to the potential of zero charge with incremental changes to the bulk concentration. Our observations are supported by changes to the position of the differential capacitance minimum measured by electrochemical impedance spectroscopy, and are explained in terms of the screening behaviour and asymmetric ion adsorption. Furthermore, a striking level of agreement between the differential capacitance from solution evaluated in simulations and measured in experiments allows us to critically assess electrochemical capacitance measurements which have previously been considered to report simply on the density of states of the graphite material at the potential of zero charge. Our work shows that the solution side of the double layer provides the more dominant contribution to the overall measured capacitance. Finally, ion crowding at the highest concentrations (beyond ∼5 M) leads to the formation of liquid-like NaCl clusters confined to highly non-ideal regions of the double layer, where ion diffusion is up to five times slower than in the bulk. The implications of changes to the speciation of ions on reactive events in the double layer are discussed.

CμMD reveals multi-layer electrolyte screening in the double layer beyond 0.6 M, which affects ion activities, speciation and mobility; asymmetric charge screening explains concentration dependent changes to electrochemical properties.     

Relation between the charge efficiency of activated carbon fiber and its desalination performance

Four types of activated carbon fibers (ACFs) with different specific surface areas (SSA) were used as electrode materials for water desalination using capacitive deionization (CDI). The carbon fibers were characterized by scanning electron microscopy and N(2) adsorption at 77 K, and the CDI process was investigated by studying the salt adsorption, charge transfer, and also the charge efficiency of the electric double layers that are formed within the micropores inside the carbon electrodes. It is found that the physical adsorption capacity of NaCl by the ACFs increases with increasing Brunauer-Emmett-Teller (BET) surface area of the fibers. However, the two ACF materials with the highest BET surface area have the lowest electrosorptive capability. Experiments indicate that the charge efficiency of the double layers is a key property of the ACF-based electrodes because the ACF material which has the maximum charge efficiency also shows the highest salt adsorption capacity for CDI.     

Unlocking Charge Transfer Limitations for Extreme Fast Charging of Li-Ion Batteries

Extreme fast charging (XFC) of high-energy Li-ion batteries is a key enabler of electrified transportation. While previous studies mainly focused on improving Li ion mass transport in electrodes and electrolytes, the limitations of charge transfer across electrode–electrolyte interfaces remain underexplored. Herein we unravel how charge transfer kinetics dictates the fast rechargeability of Li-ion cells. Li ion transfer across the cathode–electrolyte interface is found to be rate-limiting during XFC, but the charge transfer energy barrier at both the cathode and anode have to be reduced simultaneously to prevent Li plating, which is achieved through electrolyte engineering. By unlocking charge transfer limitations, 184 Wh kg⁻¹ pouch cells demonstrate stable XFC (10-min charge to 80 %) which is otherwise unachievable, and the lifetime of 245 Wh kg⁻¹ 21700 cells is quintupled during fast charging (25-min charge to 80 %).     

Voltammetry at a de Levie brush electrode as a model for electrochemical supercapacitor behaviour

Electrochemical supercapacitors provide electrical energy storage systems complementary to batteries. Based on the double layer capacitance of high area porous electrode materials, e.g. carbon powders, felts, foams, aerogels or on the redox pseudocapacitance of oxide or polymer films, specific capacitances of the order of 50100 F g⁻¹ are realizable. However, the porous nature of the electrode structures introduces a distribution of resistive and capacitative elements giving rise to electrical behaviour like that of a transmission line, as treated by de Levie, with a resulting complex power spectrum depending on charging or discharging rates. The present paper examines the cyclic voltammetry behaviour of de Levie type wire brush electrodes as models for porous electrodes, in comparison with that of single wire electrodes of the same metal. Comparisons are also made with constant current charging behaviour and with the electrochemical behaviour of specially made, 3 V, non aqueous solution, double layer capacitor modules, examined under similar conditions in relation to the current response profiles of a 5 RC element hardware model circuit. These approaches enable the effects of the distribution of R and C elements on charge acceptance and delivery at various rates to be quantitatively evaluated for various resistivities of the conducting electrolyte in pores.     

Range of Validity of a Simplified Model for Diffuse Charge Dynamics

The modelling of electrochemical processes often requires the solution of the Poisson‐Nernst‐Planck (PNP) equations. In complex geometries, such as porous electrodes, that is challenging due to the presence of disparate length scales, ranging from the Debye screening length (～nm) to the device length scale (～cm). To overcome this difficulty, one often assumes that the electric double layer (EDL) is at quasi‐equilibrium to construct a simplified model that accounts for ion diffusion in the electro‐neutral bulk of the electrolyte while replacing the EDLs with appropriate boundary conditions. Various researchers have demonstrated that such an approach is valid in the asymptotic limit of a thin EDL and moderate electrode potentials. In this note, we explore the range of validity of this approximation by considering a one‐dimensional electrolytic cell with blocking electrodes subjected to a step change and time‐periodic alternations in the electrodes’ potentials by calculating the errors associated with the approximate approach as functions of the EDL thickness and electric field frequency and intensity. Additionally, we delineate numerical instabilities associated with the numerical solutions of the bulk equations with the nonlinear boundary condition peculiar to this problem.     

Time-dependent ion selectivity in capacitive charging of porous electrodes

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 five times 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 short-circuited, 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 time-dependent 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 between 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.