Impedance-Controlled Transport

The presence of water is critical for operation but in current PEMFCs proper water management is a delicate issue and poor control can greatly reduce the efficiency of the device. An excess of water can flood the catalyst and porous transport layers impeding the transport of reactants and eventually drowning the fuel cell. At low water content, the polymer electrolyte membrane can become a poor conductor and the reactivity at the electrodes is affected. Local hot spots arising due to the inefficient operation result in early degradation of the cell. ... 

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. 

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... 

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

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. 

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... 

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. 

The above results of Figures 20 and 21 indicate clearly that both the instantaneous electrode potential, E, and the internal cell resistance Rceii play major roles in the flux of lithium at the electrode/electrolyte interface in the cell-impedance controlled lithium transport model, characterized by the B.C. of Eq. (8). 

The present chapter summarized first briefly the conventional and modified dijfusion controlled lithium transport models for explaining the CTs of intercalation compoimds. Second, this article presented the anomalous features of the experimental CTs for various transitional metal oxides and graphite, and then discussed the physical origin of the experimental CTs in terms of internal cell resistance. Finally, this article gave the theoretical CTs under the assumption that internal cell resistance plays a major role in lithium intercalation/deintercalation, to compare those with experimental CTs. On the basis of the cell-impedance controlled lithium transport concept, one can analyze quantitatively the CTs for transition metal oxides and graphite, and readily understand the anomalous features which one can hardly interprete under the dijfusion control concept. 

The atypical features in the linear sweep/cyclic voltammograms include the asymmetry in shape between anodic and cathodic current peaks, and the abnormal dependence of peak current on potential scan rate. The cell-impedance controlled lithium transport concept is expected to provide a reasonable explanation of these atypical voltammetric responses, and give us a new insight into the lithium transport behavior during potential scanning. 

This Chapter discusses lithium transport through transition metal oxides and carbonaceous material (graphite) during CT experiments. The structure of this review is as follows in Section II, the conventional and modified dijfusion control models for explaining the CTs are briefly summarized. Typical experimental CTs from transition metal oxides and carbonaceous material (graphite) are presented and then several anomalous behaviors in these curves are pointed out in Section 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. 

Moreover, the calculated current increases rather than deaeases with time to ca. 200, 600, and 800 s at the potential jumps of 3.65 to 4.00, 3.60 to 4.00, and 3.55 to 4.00 V vs. Li/Lr, respectively. This current increase in the cell-impedance controlled anodic CTs of Lii. gNi02 is due to the fact that the reduction in the potential difference (Eapp-E) is much exceeded by the fall in internal cell resistance Rcdt during lithium deintercalation, to enhance the driving force for lithium transport. This is readily predieted in the Rcdi vs. E plot of Figure 12. 

As a prelude to the discussion of reactions at micellar interfaces and in the interstices of micelles we should examine what is special about the nature of reactions at liquid-liquid interfaces. Adsorption of substances at interfaces can lead to an ordering of molecules that is not encountered in bulk solution. The topic has been reviewed by Menger [3,4] who has illustrated the possibilities of reactions at interfaces by investigation of the reaction of the water-insoluble ester p-nitrophenyl laurate in heptane with imidazole in an adjacent aqueous phase. Because of the insolubility of the ester in water any reaction between the species must occur at the interface. Migration of the reactants to the interface was partially rate-determining small amounts of laurate ion which adsorb at the interface retarded the interfacial hydrolysis of the ester. The adsorbed laurate ion probably impedes the transport of one or more of the reactants to the interface, suggesting a means of control of reactions not available in normal bulk reactions. 

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