Diffusion nonlimiting

Under conditions where mediator diffusion in phase 2 and ion transport across the ITIES are nonlimiting [conditions (2) and (4)], the steady-state tip current response has been found to be accurately described by the following equations [44,47,48] ... 

The effect on the current-time behavior of varying Kg while keeping the kinetics of the interfacial process high and nonlimiting is shown in Fig. 11, for a typical tip-interface distance log(T) = —0.5. The general trends in Fig. 11 can be explained as follows. At short times, the diffusion field at the UME tip is not of sufficient size to intercept the interface, and there is thus no perturbation of the interfacial equilibrium. In this time regime,... 

As might be expected, similar trends to those identified above are observed as y is varied, while maintaining constant and K high and nonlimiting. The transient and steady-state current responses, shown respectively in Figs. 14 and 15 for = 1 and K = 10, vary between a lower limit which is close to the response for an inert interface when y < 0.01, and an upper limit (when y > 1000) which is characteristic of SECM diffusion-control in phase 1 with no resistance from interfacial kinetics or transport in 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. 

From a plot of the internalisation flux against the metal concentration in the bulk solution, it is possible to obtain a value of the Michaelis-Menten constant, Am and a maximum value of the internalisation flux, /max (equation (35)). Under the assumption that kd kml for a nonlimiting diffusive flux, the apparent stability constant for the adsorption at sensitive sites, As, can be calculated from the inverse of the Michaelis-Menten constant (i.e. A 1 = As = kf /kd). The use of thermodynamic constants from flux measurements can be problematic due to both practical and theoretical (see Chapter 4) limitations, including a bias in the values due to nonequilibrium conditions, difficulties in separating bound from free solute or the use of incorrect model assumptions [187,188],... 

Studies by Strittmatter at Connecticut have provided examples of lateral diffusion-limited, as well as nonlimited, biochemical reactions involving two membrane-bound proteins. 

For nonlimiting diffusion conditions, the disk electrode current density would be ... 

---