Cell impedance control

Jung, K.-N., and Pyun, S.-I. 2006b. The cell-impedance-controlled lithium transport through LiMn2O4 film electrode with fractal surface by analyses of ac-impedance spectra, potentiostatic current transient and linear sweep voltammograms. Electrochimica Acta 51, 4649 658. 

In this respect, this chapter details the fundamentals and most important advances in the research activities on lithium intercalation into and deintercalation from transition metals oxides and carbonaceous materials, especially from thermodynamic and kinetic points of view, including methodological overviews. The thermodynamics of lithium intercalation/deintercalation is first introduced with respect to a lattice gas model with various approximations, after which the kinetics of lithium intercalation/deintercalation are described in terms of a cell-impedance-controlled model. Finally, some experimental methods which have been widely used to explore the thermodynamics and kinetics of lithium intercalation/deintercalation are briefly overviewed. 

Recently, it was reported by Pyun et al. thatthe CTs of transition metal oxides such as Lii 8CoO2 [14,77-79], l i,, AiO. [11,12], Li, sMii.O [17,80,81], Lij + 8[Ti5/3Lii/3]O4 [11, 28], V2O5 [11, 55] and carbonaceous materials [18, 82-84] hardly exhibit a typical trend of diffusion-controlled lithium transport - that is, Cottrell behavior. Rather, it was found that the current-potential relationship would hold Ohm s law during the CT experiments, and it was suggested that lithium transport at the interface of electrode and electrolyte was mainly limited by internal cell resistance, and not by lithium diffusion in the bulk electrode. This concept is referred to as cell-impedance-controlled lithium transport. 

The above argument, along with the evidences presented in Sections 5.3.2.1-5.3.2.2, indicates that other transport mechanisms than diffusion-controlled lithium transport may dominate during the CT experiments. Furthermore, the Ohmic relationship between Jiiu and A indicates that internal cell resistance plays a critical role in lithium intercalation/deintercalation. If this is the case, it is reasonable to suggest that the interfacial flux of lithium ion is determined by the difference between the applied potential E pp and the actual instantaneous electrode potential (t), divided by the internal cell resistance Keen- Consequently, lithium ions barely undergo any real potentiostatic constraint at the electrode/electrolyte interface. This condition is designated as cell-impedance-controlled lithium transport. 

For the sake of clarity of the above argument regarding cell-impedance-controlled lithium transport, it is very useful to determine experimentally the internal cell resistance as a function of the electrode potential, using EIS, and to compare this with the cell resistance as determined with the CT technique. Pyun et al. showed that internal cell resistances estimated via the Eni versus A plot at various lithium contents approximated satisfactorily values determined experimentally with EIS — the sum of the resistances from the electrolyte and conducting substrate, the resistance associated with the particle-to-particle contact among the oxide particles, and the resistance related to the absorption reaction of adsorbed lithium ion into the... 

Calculation Procedure of Cell-Impedance-Controlled Current Transients... 

Extension of Cell-Impedance-Controlled Lithium Transport Concept to the Disordered Carbon Electrode... 

Now, we can consider the kinetics of lithium intercalation/deintercalation of amorphous carbon electrodes having different lithium intercalation sites, as compared to graphite electrode in terms of cell-impedance-controlled lithium transport. 

Figure 5.14 (a) Logarithmic cathodic current transients of the Lii 5NiO2 electrode, theoretically determined by means of numerical analysis based upon the cell-impedance-controlled lithium intercalation (b) /(t) versus In t plots reproduced from panel (a). (Reproduced with permission from (a) Ref. [12] (b) Ref. [96].)... 

From the numerical solution to the modified McNabb-Foster equation, the anodic CTs determined at the potential jumps of 0.3, 0.2, and 0.05 V (versus Li/Li+) to various lithium extraction potentials Fext are illustrated in Figure 5.19a-c. The anodic CTs theoretically calculated based upon the modified McNabb-Foster equation, along with the cell-impedance-controlled constraint in Figure 5.19a-c, almost coincide with experimental CTs (see Figure 5.18a-c). This strongly indicates that the appearance of an inflexion point in the CT is due to the lithium deintercalation from two different kinds of sites with clearly distinguishable activation energies. 

Figure 5.21a presents, on a logarithmic scale, the anodic CTs calculated on a theoretical basis, with and without considering the interaction between lithium ions in the Lii 8Mn2O4 electrode under the cell-impedance-controlled constraint with the conversion factor/= 0.2 at the potential step across the disorder-order and backward transition points. In the case when no interaction is assumed, the theoretical CT does not display any transition time, but rather shows a monotonic increase of its slope from an almost flat value to one of infinity. 

Li/Li+ ). All CTs calculated theoretically and accounting for the interaction under the cell-impedance-controlled constraint coincided well in shape with the experimentally measured CTs. 

Recently, the analysis of the anomalous current response is beginning to enter a new phase with the help of the concept based upon a cell-impedance controlled constraint, which has been systematically studied by Pyun et... 

They have extended the kinetic study of lithium intercalation to such transition metal oxides as Lii.gNi02," " " Lii.8Mn204," " Li +s[Ti5/3Li,/3]04," 205, and carbonaceous materials. In these works, they have reported that the theoretical CTs, based upon the cell-impedance control concept, matched quantitatively those experimentally measured all the anomalous features of the experimental transients were readily interpreted in the cell-impedance controlled transients with such simplified parameters as electrochemical active area, dimensionality of the diffusion path, cell impedance, etc. 

III. In Section IV, the physical aspects of the CTs are discussed in terms of total cell resistance. Finally, Section V is devoted to the theoretical consideration of the cell-impedance controlled lithium transport, and to the comparison of experimental curves with theoretical ones. 

For the sake of clarity of the above argument about the cell-impedance controlled lithium transport, it is very useful to determine experimentally the internal cell resistance as a function of the electrode... 

V. THEORETICAL DESCRIPTION OF CELL-IMPEDANCE CONTROLLED LITHIUM TRANSPORT... 

The governing equation for the cell-impedance controlled lithium transport is Fiek s diffusion equation. The initial condition (I.C.) and the boundary conditions (B.C.) are given as... 

Probably one of the most serious objections to the above theoretical model for the cell-impedance controlled lithium transport is the use of the conventional Pick s diffusion equation even during the phase transition, because lithium diffusion inside the electrode should be influenced by the phase boundary between two different phases. However, the contribution of the phase boundary to lithium transport is complicated and not well known. For instance, one can neither know precisely the distribution nor the shape of the growing/shrinking phase during the phase transition. 

So far as lithium intercalation/deintercalation into/from transition metal oxides and graphite proceeds under the cell-impedance controlled constraint Eq. (8), it is unlikely that the disturbance of lithium diffusion inside the electrode due to the presence of the phase boundary and the phase boundary movement causes any significant change in the CTs. It is likely predicted from Eq. (8) that unlike the case of the diffusion controlled phase transformation, the flux of lithium at the electrode/electrolyte interface under the cell-impedance controlled constraint is hardly dependent on the location of the phase boundary within the electrode. 

However, in the case of cell-impedance controlled lithium... 

The intersection of cathodic and anodic CTs from U1.BC0O2 (Figure 4) and Lii+8[Ti5/3Li /3]04 (Figure 5) is also clearly observed in the cell-impedance controlled CTs of Figures. 15 and 16, respectively. 

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