Limiting-current measurement diffusion coefficients

The diffusion coefficient of an electroactive species can be obtained from a limiting-current measurement at an RDE and a transient measurement (e.g., a potential step measurement) at the same electrode (at o = 0) under identical conditions. It is not necessary to know the electrode area, n, or C. Explain how this is accomplished and discuss the possible errors in this procedure. 

Table 1. The photovoltaic and EIS parameters of the DSSCs based on bi-ionic liquids with various side chain lengths and anions. The ionic diffusion coefficients were calculated from the limiting currents measured by a 10 pm radius Pt ultramicroelectrode (Lee et al, 2009b).

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 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. 

Using Levich s equation we can determine the diffusion coefficients for the reactant species by measuring the limiting current densities at known angular velocities. 

Calculate the lower limit and the upper limit for the sweep rate in a cyclic voltammetry. The double-layer capacitance is 50 pF/cm2 and the diffusion coefficient is 10-5 cm2/s. The measurable current density is 100 pA/cm2 and the sweep range is 10 V. (Kim)... 

The measurement of a molecular diffusion coefficient D by electrochemical techniques is generally done with a rotating disk electrode in the limiting diffusion current condition and application of the Levich s equation [8]. 

The measurement of limiting currents is probably the simplest and most widely applicable method for measuring the diffusion coefficients of redox species. In agreement with Cottrell s equation, the value of D, can be obtained from the plot of... 

While experiments involving solution-phase reactants have provided deep insights into the dynamics of heterogeneous electron transfer, the magnitude of the diffusion-controlled currents over short timescales ultimately limits the maximum rate constant that can be measured. For diffusive species, the thickness of the diffusion layer, S, is defined as S = (nDt)1/2, where D is the solution-phase diffusion coefficient and t is the polarization time. Therefore, the depletion layer thickness is proportional to the square root of the polarization time. One can estimate that the diffusion layer thickness is approximately 50 A if the diffusion coefficient is 1 x 10-5 cm2 s-1 and the polarization time is 10 ns. Given a typical bulk concentration of the electroactive species of 1 mM, this analysis reveals that only 10 000 molecules or so would be oxidized or reduced at a 1 pm radius microdisk under these conditions The average current for this experiment is only 170 nA, which is too small to be detected with high temporal resolution. 

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