Electroanalytical Methods Utilizing Small Signal Current or Potential Excitations for the Characterization of Porous Electrodes Comprising Insertion Materials

Abstract

Three common methods to characterize and diagnose battery behavior are electrochemical impedance spectroscopy (EIS), the potentiostatic intermittent titration technique (PITT), and the galvanostatic intermittent titration technique (GITT). All three methods rely on small signal excitation in order to linearize the system behavior and simplify analysis. Analytic solutions are derived that can be used in conjunction with EIS, PITT, and GITT experiments to identify governing resistances, and extract parameters and properties that characterize half-cell behavior using a lithium reference electrode. The solutions include the effects of intercalate diffusion, charge-transfer kinetics, and ohmic losses in the electrolyte and solid phase of the porous electrode. A simple modification also includes the effect of electrolyte diffusion, once it has reached a quasi-steady state. Comparisons are given to numerical solutions, including transient electrolyte diffusion, which show the accuracy of the derived formulas. These comparisons also indicate that electrolyte diffusion takes about 30 seconds from the start of a PITT or GITT experiment to reach quasi-steady state.The rate at which lithium diffuses into and out of solid phase intercalate materials is a primary limiting factor for lithium batteries operating at high rates of charge and discharge. Texts are available that review methods to characterize irreversible processes in electrochemical systems. 1-5 Specific to lithium ion battery systems, 6-17 the most common methods for determining the solid phase diffusion coefficient of lithium within the host material are (i) analysis of lowfrequency data from electrochemical impedance spectroscopy (EIS) measurements, 18-23 (ii) the potentiostatic intermittent titration technique (PITT), 24-36 and (iii) and the galvanostatic intermittent titration technique (GITT). [37][38][39][40][41][42] The analysis of data is aided by the use of analytic solutions; for the analytic solutions referenced, voltage losses in the electrolyte phase or ohmic losses in the solid phase of the porous electrode are ignored. The successful application of these analytic tools thus requires electrodes that are specially designed to make the above-mentioned losses negligible, and a set of inequalities that determines when such conditions hold has been given. 43 In contrast, optimized electrode design must balance voltage losses against power and capacity needs, and this is consistent with the observation that commercial electrodes used in traction batteries are not dominated by losses from solid-phase diffusion in comparison to other types of transport loss. It is the purpose of this work to generalize the analytic solutions mentioned above so that they can be applied to more general types of electrodes, such as those used in traction applications today, without the above-mentioned restrictions.The conventional governing equations for charge transport in lithium electrodes 4,7,8,10,17 will be employed in this work, and we shall not further question potential...

Similarities and Differences between Potential-Step and Impedance Methods for Determining Diffusion Coefficients of Lithium in Active Electrode Materials

“…The impedance spectrum and PITT response of a graphite half-cell with lithium counter and reference electrodes, which we shall consider in this work, have been analyzed in some detail. 1 A characteristic set of material values, taken from the literature, were used for simulations, and numerical calculations of impedance were then done and shown in Figure 1 of Reference 1. The Nyquist plot of impedance, taken from Reference 1 and based on the values shown in Table I, is shown in Figure 1 of this paper as the green curve.…”

“…Below this range, the double-layer is in quasi-steady state, and it is only the charge-transfer resistance, combined with ohmic resistance in the solid and electrolyte phases, that is observed. [1][2][3][4][5] Salt diffusion impacts impedance in the intermediate range. Below this range, the salt diffusion is also in quasi-steady state, and its contribution to impedance appears as a multiplicative factor on the ohmic resistance in the electrolyte.…”

“…Below this range, the salt diffusion is also in quasi-steady state, and its contribution to impedance appears as a multiplicative factor on the ohmic resistance in the electrolyte. 1 In the lowest range, intercalate diffusion of lithium in graphite is occurring. Note that there is some overlap in the ranges in which salt and lithium intercalate diffusion are occurring.…”

Guidelines for the Analysis of Data from the Potentiostatic Intermittent Titration Technique on Battery Electrodes

“…These two processes are described in P2D models by two parameters, namely the reaction-rate constant k 0 and the solid chemical diffusion coefficient D S . Numerous experimental methods were developed to determine them, e.g., potentiostatic intermittent titration technique (PITT), [6][7][8][9][10] galvanostatic intermittent titration technique (GITT), [11][12][13] cyclic voltammetry (CV), 14 and electrochemical impedance spectroscopy (EIS). 15,16 Depending on the method, a wide range of solid diffusion coefficients is reported in the literature for a similar AM.…”

“…Later on, Baker et al proposed an analytic expression that accounts for porous-electrode effect providing that salt diffusion is in a quasi-steady state. 12 Hence, it restricts the analysis of PITT current decays at times longer than 20-30 s, which may compromise on the accuracy of fitted parameters. In summary, all reported expressions neglect the influence of particle size distribution (PaSD); Equations 1 to 5 neglect porous-electrode effects and Equations 1 to 3 additionally assume an infinite reaction rate for Li insertion/deinsertion.…”