Yu. G. Chirkov

Theory of porous electrodes: Calculation of overall cathode characteristics for the case where the polarization curve has segments with different slopes

It is demonstrated how one should carry on with calculations of overall currents and other parameters that characterize active layers of porous electrodes in the case where polarization curves for the catalyst display two or more segments with different slopes and exchange currents. A calculation of overall currents presumes that the active layer of an electrode has an optimum thickness, over which the current reaches a maximum. The entire range of values of the cathode potential is considered, specifically, the high potentials (from a steady-state potential up to the point where there is observed an inflection in the polarization curve), the intermediate potentials (near the front surface and near the rear surface of the active layer there are realized segments of the polarization curve with different slopes), and the low potentials (throughout the entire thickness of the active layer there is observed a second segment of the polarization curve). To give an example, calculations of overall characteristics of a cathode with Nafion and platinum are performed.

Computer modeling of positive electrode operation in lithium-ion battery: Model of equal-sized grains, percolation calculations

A computer simulation of the structure of the cathode active material in a lithium-ion battery is performed. The model of equal-sized grains of three types (active grains, grains of electrolyte, and carbon black grains) is studied. Acceptable bulk concentration of active grains g is estimated. It is in the range of zero to 0.3. Dependence of the key parameters of the electrode active material on its composition is determined: specific conductivity of electrolyte and specific surface area on which the electrochemical process occurs. It is shown that the average number of electrochemically active faces of active grains cannot be 100%, as usually assumed in the studies of diffusion processes occurring in an individual active grain. In the range of 0.0 ≤ g ≤ 0.3, the average number of active faces is in the approximate range of 2 ≤ ñ ≤ 3. The final choice of the optimum composition of components for the active material of a lithium-ion battery cathode (and, primarily, choice of the value for parameter g) requires performing an additional complex of computer simulations.

Active layer of the cathode of a fuel cell with a solid polymer electrolyte: The effect of the Nafion concentration on the overall characteristics

A computer-aided simulation of the structure of the active layer of the cathode of a fuel cell with a solid polymer electrolyte (Nafion) is performed under the assumption about equidimensionalness of dimensions of grains of the substrate (with platinum crystallites in them) and grains (agglomerates of molecules) of Nafion. It is analyzed how the Nafion concentration affects principal parameters, which include the specific surface area, in the vicinity of which electrochemical process goes on; the effective ionic electroconductivity, and the effective diffusion coefficient of a gas. It is demonstrated how one can determine the Nafion concentration at which the overall current takes on a maximum value. Dependences of the optimum value of the overall current and the thickness of the active layer and the weight of platinum, which correspond to it, on the Nafion concentration are calculated. It is demonstrated that there in principle cannot exist one individual optimum concentration of Nafion, which is suitable for all techniques used for the preparation of the active layer. The mutual relationship between values of the effective diffusion coefficient of a gas and the effective ionic electroconductivity of Nafion determines the value of the optimum of the Nafion concentration.

Gas-generating porous electrodes: Chlorine generation in DSA at low and intermediate overpotentials

Parameters of gas-generating porous electrodes (GPE) in the range of low overpotentials, where all the pores are filled with electrolyte and the gas generation and transport occur in an internal diffusion mode, are calculated and analyzed. A criterion for estimating critical overpotential values, upon achieving which first gas pores start appearing in GPE, is found. Theoretical critical overpotentials of chlorine generation in DSA satisfactorily agree with experiment. About 20% of porous space takes part in the chlorine generation in DSA of “standard” thickness (5 μm), provided there are no limitations on chlorine transport outside the electrode. The appearance of the “low-polarizability” part in the anodic branch of polarization curve for DSA is caused by the appearance, in GPE, of a system of gas pores connected with each other and the front electrode surface. This assumption is partially confirmed by theoretical estimation.

Active layer of fuel cell electrode with polymer electrolyte: Nature of proton and oxygen supply channels

The nature of proton and oxygen supply channels in the active layer of a cathode of fuel cell with polymer electrolyte is discussed. There are three types of electron, proton, and oxygen carriers in the active layer: agglomerates of carbon particles with supported platinum (support grains), agglomerates of Nafion molecules (Nafion grains), and void grains. In computer simulation of the active layer structure, the three types of grains were assumed equal-sized, cube-shaped and arranged into a cubic node lattice (in the terms of the percolation theory). Impossibility of forming on the basis solely the above three grain types of three percolation clusters (“electron”, “proton”, and “gas”) that could supply all that is required for the electrochemical process is proved. But in this, the following question arises: how can satisfactory operation of the cathode with polymer electrolyte be provided? The required supply of protons and oxygen can be provided only if the support grains can feature not only electronic conductivity, but can also participate in transport of both protons and oxygen. As a result, the transport of protons and oxygen is carried out via special combined percolation clusters that must include apart from the support grains either Nafion grains (combined “proton” cluster) or void grains (combined “gas” cluster). The paper describes the technique of calculation of effective specific conductivity of a combined “proton” cluster. The effective specific diffusion coefficient of a combined “gas” cluster can also be calculated in a similar way.

Calculation of optimum thickness of active layer of oxygen and air cathodes of fuel cell with Nafion and platinum

It is shown that, for the electrodes of fuel cells with solid polymer electrolyte, the dependence of overall current on the active layer thickness contains an extremum. There is an optimum thickness of active layer, at which the overall current reaches its maximum possible value. The nature of this dependence is explained. The character of the distribution of electrochemical process intensity over the depth of active layer of cathode with solid polymer electrolyte is analyzed. The optimum thicknesses of active layers of oxygen and air cathodes of fuel cells with Nafion and platinum and the corresponding overall currents and contents of catalyst in the active layer are calculated. In the calculations, the temperature of fuel cell, the pressure in the cathode gas chamber, and the cathodic potential were varied. The optimization of active layer thickness of cathode with solid polymer electrolyte can reduce the platinum consumption, i.e. its amount per 1 kW of power produced in a membrane-electrode assembly.

Fractals and Percolation in the Theory of Porous Electrodes

A computer-aided simulation of the structure of a porous electrode is performed using flat lattices of sites (they are capable of conducting electrons and are randomly distributed in the electrode) as an example. To adequately describe properties of a porous electrode, information about the degree of dispersion of the particles that make up the electrode (“fractal dimensionality”) must be complemented by that on their clusterization (presence of “percolation clusters”). These factors impart two properties to a porous electrode, specifically, a developed surface, on which an electrochemical process may proceed, and the possibility of a continuous supply of electrons to this surface. A percolation cluster may be dismembered to a “trunk” (it provides for the electron transport) and a “crown” (aggregate of particles that make a major contribution to the electrochemical process). The dismembering was performed via computer flow diagrams proposed by the authors. A computer-aided analysis of characteristics of a porous electrode points to the existence of an optimum structure in which the electrochemical activity is capable of reaching a maximum.

Computer simulation of active layers in the electric double layer supercapacitor: Optimization of active layer charging modes and structure, calculation of overall characteristics

The structure and functioning modes of active layers in an electric double layer capacitor (EDLC) with an aqueous electrolyte are simulated by means of a computer. A model of active layers prepared from activated carbon materials is proposed, percolation estimates are performed and effective ionic conductivities are calculated. The polarization of active layers includes a sequence of two charging processes: first, galvanostatic and then potentiostatic. The proposed program of calculations involves mutual matching and optimization of seven parameters characterizing the active layer and conditions of charging processes. According to calculations, galvanostatic polarization of wide pores in the EDLC biporous active layer up to the limiting potential followed by potentiostatic polarization of fine pores allows the capacity Csp = 246 F/g and the energy Wsp = 107 kJ/kg to be obtained in fractions of second.

Computer simulation of negative electrode operation in lithium—ion battery: Galvanostatic discharg active intercalating agent grains, role of diffusion limitations

Computer simulation of the negative electrode (anode) operation in a lithium-ion battery under galvanostatic discharge mode is performed. The amount of active intercalating agent grains that may take part in the electrochemical process is calculated. Special attention was paid to evaluation of diffusion limitations arising under recovery of lithium atoms from an intercalating agent grains related to the low value of the diffusion coefficient of lithium atoms D. It is shown that the common model of a spherical intercalating agent grain, when its whole outer surface participates in an electrochemical process, contradicts the model of equally-sized cubic grains studied in this work. It is found that the average amount of electrochemically active faces of active intercalating agent grains varies in the range of 1.91 to 3.55. A new model of the structure and depletion of an intercalating agent grain is suggested. The process of full depletion of intercalating agent grains may be implemented in the case when they either have rather small dimensions L, more specifically, if the L/D ratio is low, or if the anode discharge current density I is sufficiently low. The optimum working anode parameters are calculated under the condition of reaching full depletion of intercalating agent grains: active layer depth, discharge time, specific electric capacitance and final anode potential at the active layer/inter-electrode space interface.

Computer modeling of negative electrode operation in lithium-ion battery: Model of equal-sized grains, galvanostatic discharge mode, calculation of characteristic parameters

A computer simulation of the negative electrode (anode) operation in a lithium-ion battery is performed. A complete research program is carried out in accordance with the recommendations of the theory of porous electrodes: the “model of equal-sized grains of two types” was studied, percolation properties of the anode active layer were researched, values of effective coefficients were calculated for charge transfer and mass transport, a complete system of equations describing operation of the anode is presented. Two specific cases of galvanostatic mode of anode discharge are considered in detail: an “ideal” anode and anode with nanosize particles. Working anode parameters are calculated: optimum bulk concentration of graphite in the active layer, active layer thickness, time of complete anode discharge, its specific electric capacitance and final potential on the active/layer interelectrode space interface. Advisability of working with anodes with nanosize grains and electrolyte with enhanced specific conductivity is shown.