Diffusion coefficient limited current

Proving the existence of a kinetic current is the best possible under polarographic conditions when the studied kinetic current is lower than about 20% of the theoretical diffusion-controlled limiting current. Such currents are independent of mercury pressure, i.e., height of mercury column. Furthermore, such currents have much higher temperature coefficient (5-10% K-1) than diffusion currents (1.8% K-1). 

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

The plot of normalized steady-state current vs. tip-interface distance, shown in Fig. 12, demonstrates that as the tip-interface distance decreases the steady-state current becomes more sensitive to the value of Kg. Under the defined conditions the shape of the approach curve is highly dependent on the concentration in the second phase, for Kg values over a very wide range, with a lower limit less than 0.1 and upper limit greater than 50. This suggests that SECMIT can be used to determine the concentration of a target solute in a phase, without the UME entering that phase, provided that the diffusion coefficients of the solute in the two phases are known. 

The effect of increasing y is to increase the diffusion coefficient of the solute in phase 2 compared to that in phase 1. For a given value of this means that when a SECMIT measurement is made, the higher the value of y the less significant are depletion effects in phase 2 and the concentrations at the target interface are maintained closer to the initial bulk values. Consequently, as y increases, the chronoamperometric and steady-state currents increase from a lower limit, characteristic of an inert interface, to an upper limit corresponding to rapid interfacial solute transfer, with no depletion of phase 2. 

Under conditions of nonlimiting interfacial kinetics the normalized steady-state current is governed primarily by the value of K y, which is the relative permeability of the solute in phase 2 compared to phase 1, rather than the actual value of or y. In contrast, the current time characteristics are found to be highly dependent on the individual K. and y values. Figure 16 illustrates the chronoamperometric behavior for K = 10, log(L) = —0.8 and for a fixed value of Kf.y = 2. It can be seen clearly from this plot that whereas the current-time behavior is sensitive to the value of Kg and y, in all cases the curves tend to be the same steady-state current in the long-time limit. This difference between the steady-state and chronoamperometric characteristics could, in principle, be exploited in determining the concentration and diffusion coefficient of a solute in a phase that is not in direct contact with the UME probe. 

For comparable diffusion coefficients of the target solute in the two phases and nonlimiting transfer kinetics, systems characterized by different should be resolvable on the basis of transient and steady-state current responses to a value of up to 50 at practical tip-interface separations. If the diffusion coefficient in phase 2 becomes lower than that in phase 1, diffusion in phase 2 will be partly limiting at even higher values of K. On the other hand, as the value of y increases or interfacial kinetics become increasingly limiting, lower values of suffice for the constant-composition assumption for phase 2 to be valid. 

If all the constants in the expression for the limiting diffusion current are known, including the diffusion coefficient, then the number of electrons consumed in the reaction can be found from the limiting current data. However, this condition is often not fulfilled, or the limiting diffusion... 

X10 cm /s. This is over 1,000 X smaller than the Hiffusion coefficient for this osmium complex diffusing freely in the acetonitrile solvent (obtained from the limiting current at the naked Pt electrode), and the observed PD corresponds to a very low permeability of the polymer film to luch bulky permeants. 

Let us consider the case when the diffusion coefficient is small, or, more precisely, when the barrier height A is much larger than kT. As it turns out, one can obtain an analytic expression for the mean escape time in this limiting case, since then the probability current G over the barrier top near xmax is very small, so the probability density W(x,t) almost does not vary in time, representing quasi-stationary distribution. For this quasi-stationary state the small probability current G must be approximately independent of coordinate x and can be presented in the form... 

De Jong, H. G. and van Leeuwen, H. P. (1987). Voltammetry of metal-complex systems with different diffusion-coefficients of the species involved. 2. Behaviour of the limiting current and its dependence on association/dissociation kinetics and lability, J. Electroanal. Chem., 234, 17-29. 

Occasionally, we want to know the value of a diffusion coefficient D. The Cottrell equation (equation (6.3)) is one simple means of obtaining D, i.e. by plotting fiimu) against and obtaining a value for the gradient. (/ im( ) here means the limiting current as a function of time.)... 

The limiting current at a wall-jet electrode is a function of the radius of the circular electrode, r, the rate of flow of solution, V/, the diameter a of the jet supplying the solution of analyte, the diffusion coefficient D of the analyte and the bulk concentration of analyte, Camiyte- hm also depends, in a complicated way, on the distance between the electrode and the nozzle, which we will denote here as k. 

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