Diffusion galvanostatic method

Since the charge is injected in a very short time (< 1 Jts), measurement often can be completed before diffusion limitation hn ij become significant. In this respect the charge-injection (coulostatfc) ii method is similar to the double-pulse galvanostatic method, except lh< f one has more freedom in the choice of the parameters of the pulse, sinot there is no need to match it to the second pulse. 

The galvanostatic intermittent titration technique (GITT) has been first proposed by Weppner and Huggins in 1977 [22], This method is of particular interest for the measurement of ion transport properties in solid intercalation electrodes, used in lithium-ion batteries, for instance [18]. The determination of the diffusion constants relies on Fick s law. The GITT method records the transient potential response of a system to a perturbation signal a current step (/s) is applied for a set time xs, and the change of the potential (E) versus time (0 is recorded (Figure 1.11) [18,22],... 

The potentiostatic method is less ambiguous than the galvanostatic one. Its application, however, requires more sophisticated instrumentation. The rise time of the potentiostat should be fast enough to ensure rapid step change of the potential. Errors may arise from slow rise times as well as from current integration. With porous electrodes, all sites may not be under the same potential diffusion of reactant into or out of the pores may be slow compared with the potential change, which can lead to incorrect estimates of surface coverage and utilization. 

For the study of diffusion phenomena in solids it is also possible to work with potential pulses (potentiostatic pulses) or with constant current pulses (galvanostatic pulses). Examples described in the following paragraphs are based on the coulometric titration method described in Chapter 3. Weppner and Huggins reviewed these methods.In a continuous series of pulses the concentration of lithium in a sheet of aluminum is increased. The diffusion in each pulse is followed by either potential or current measurements. 

Chronopotentiometry—A variation of the galvanostatic charging method has been suggested by Laitinen, when mass transfer is the only process involved. The total transition time due to adsorbed and solution phases is determined and the diffusion contribution is extrapolated out. This method has not been used and would not seem to offer any advantages over the charging method where diffusion control is not involved. 

Two other factors should be considered in comparing results obtained by different methods surface diffusion of the metal atoms in the upd layer and their diffusion into the substrate, sometimes referred to as surface alloy formation [161]. Steady state of these processes is generally not achieved when deposition is conducted at high current density. A study of the influence of the current density on the EQCM response could help to understand the role of these processes in the early stages of deposition. In any event, it seems to be preferable to use galvanostatic conditions in these experiments rather than cyclic voltammetry. 

Another approach to TG/SC experiments does not rely on the mediator feedback [56]. The reactant galvanostatically electrogenerated at the tip diffuses to the substrate and undergoes the reaction of interest at its surface. The substrate current is recorded as a function of either time or the tip/ substrate separation distance (approach cnrves). The theory for transient responses, steady-state TG/SC approach curves, and polarization cnrves (i.e., 4 vs. E ) was generated solving the diffnsion problem numerically (an explicit finite difference method was used). The substrate process was treated as a first-order irreversible reaction, and the effects of its rate constant and the experimental parameters were illnstrated by families of the dimensionless working curves (Figure 5.11). 

Hin presented a combined continuum and KMC method for simulating the kinetics of Li intercalation and structural changes, as well as the morphological evolution of the Li-rich/Li-poor phase boundary in Li FeP04 electrode particles. The KMC model was coupled with a finite difference continuum model to treat the Li-ion diffusion flux within the electrolyte. Also, the local particle adsorption was coupled to concentration fields by Butler-Volmer kinetics. The KMC-simulated galvanostatic discharge process was performed at room temperature, and a comparison of the computational and experimental results is shown in Figure 3. 

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