Lithium transport

Therefore, the temperature dependence of the conductivity of complexes (LiX)o, igy/MEEP (X=CF3C00, SCN, SO3CF3, BF4) were also compared. The highest conductivity was obtained with BF4, and the activation energies for ion transport were found to be similar, suggesting that the mechanism for ion motion is independent on the salt. The lithium transport number, which varies from 0.3 to 0.6, depending on the complexed salt, does not change with concentration. 

Okpaku, S., Frazer, A. Mendels, J. (2005). A pilot study of racial differences in erythrocyte lithium transport. Am.. Psychiatry, 137, 120-1. 

Duan, Y., Halley, J.W., Curtiss, L., Redfem, P. Mechanisms of lithium transport in amorphous polyethylene oxide. J. Chem. Phys. 2005, 122, 054702-1-8. 

Hitzemann R, Mark C, Hirschowitz J, et al RBC lithium transport in the psychoses. Biol Psychiatry 25 296-304, 1989... 

Mota de Freitas DE, Espanol MT, Dorus E Lithium transport in red blood cells of bipolar patients, in Lithium and the Blood. Edited by Gallicchio VS. Farmington, CT, Karger, 1991, pp 96-120... 

Dorus E, Pandey GN, Shaughnessy R, et al. Lithium transport across red blood cell membrane a cell membrane abnormality in manic-depressive illness. Science 1979 205 932-934. 

Greger R. Possible sitesof lithium transport in the nephron. Kidney Int. 1990 37 (suppi 28) S26-S30. 

Imai M, lsozaklT,Yasoshima K, Yoshitomi K. Permeability characteristics and probability of lithium transport in the thin limbs of Henle s loop. Kidney Int 1990 37 (suppi 28) S31-S35. 

The most extensive studies for lithium transport across cell membranes have used erythrocytes because they are readily obtained and occur as individual cells freely floating in a suspending plasma medium. However, lithium uptake in these cells may not reflect uptake into other tissues due to their atypical morphology and metabolism. 

Lithium uptake experiments in erythrocytes may have value in the prediction of those patients who are most likely to respond to treatment (114-117). Other studies have used squid axon, hepatocytes, 3T3 fibroblast cell cultures, and liposomes to investigate lithium transport across the plasma membrane (77, 118). 

Five pathways for lithium transport in erythrocytes have been described (119) ... 

Leak is a downhill lithium transport system inhibited by dipyridamole (and partly by phloretin). Sodium and potassium may share this pathway (119). 

Go, J.-Y., and Pyun, S.-L 2004. A study on lithium transport through fi-actal l.p.sCoOj film electrode by analysis of current transient based upon fractal theory. Electrochimica Acta 49, 2551-2562. 

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. 

However, various types of anomalous behavior of lithium transport have been... 

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. 

Diffusion-controlled lithium transport involves the following the system is so kinetically facile that the equilibrium concentration of lithium is quickly reached at the interface between the electrode and electrolyte at a moment of potential stepping for CT experiments. The instantaneous depletion and accumulation in the lithium concentration at the interface caused by the chemical diffusion away from and to the interface (and to and away from the bulk electrode) is completely compensated by the supply and release away from and into the electrolyte, respectively. This condition is referred to as real potentiostatic constraint at the interface between the electrode and the electrolyte. 

If the electrode material is assumed to be homogeneous, then the concentration gradient of lithium through the electrode is the only factor that drives lithium transport. Hence, lithium will enter/leave the planar electrode only at the electrode/ electrolyte interface, and cannot penetrate into the back of the electrode. Under such an impermeable (impenetrable) constraint, the electric current (I) can be expressed by Equation (5.18) during the initial stage of diffusion, and by Equation (5.19) during the later stage [45] ... 

Serious efforts have been made to explain the atypical lithium transport behavior using modified diffusion control models. In these models the boundary conditions -that is, "real potentiostatic constraint at the electrode/electrolyte interface and impermeable constraint at the back of the electrode - remain valid, while lithium transport is strongly influenced by, for example (i) the geometry of the electrode surface [53-55] (ii) growth of a new phase in the electrode [56-63] and (iii) the electric field through the electrode [48, 56]. 

Bearing in mind that a current plateau implies a constant driving force for lithium intercalation, it is unlikely that the phase transformation from a to P is governed by diffusion-controlled lithium transport, where the rate of the phase boundary movement (i.e., the current) decreases significantly with time [60-63]. 

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. 

Recently, Pyun et al. applied a kinetic Monte Carlo (KMC) method to explore the effect of phase transition due to strong interaction between lithium ions in transition metal oxides with the cubic-spinel structure on lithium transport [17, 28, 103]. The group used the same model for the cubic-spinel structure as described in Section 5.2.3, based on the lattice gas theory. For KMC simulation in a canonical ensemble (CE) where all the microstates have equal V, T, and N, the transition state theory is employed in conjunction with spin-exchange dynamics [104, 105]. 

The potentiostatic current transient (PCT) technique has been known as the most popular method to understand lithium transport through an intercalation electrode, based on the assumption that lithium diffusion in the electrode is the rate-determining process of lithium intercalation/deintercalation [45]. By solving Eick s second equation for planar geometry with I.C. in Equation (5.28), impermeable B.C. in Equation (5.29), and potentiostatic B.C. 

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