Heterogeneous rate constant, upper limit

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

The rates of most IT processes are too fast to be accurately measured at either macroscopic- or micrometer-sized interfaces. In contrast, the mass-transfer coefficient for a 10 nm radius pipette is >10 cm/s (assuming D= 10" cm%), and the corresponding upper limit for the determinable heterogeneous rate constant is -50 cm/s. The first IT kinetics studied at the nanopipette-supported ITIES was that of potassium transfer from the aqueous filling solution to DCE facilitated by dibenzo-18-crown-6 (DB18C6) ... 

Figure 7. Feedback transients simulated for various rate constants of an irreversible heterogeneous process at the substrate. The upper and lower dashed curves correspond to the limits Kb s 00 and Kbs — 0, respectively. The solid curves (from top to bottom) log Kb s = 3.0, 1.5, 1.0, 0.5,0, —0.5, and—1.0. RG— 10. Taken with permission from Ref. [60]. Copyright 1992, American Chemical Society.

Reactions 53. 54, and 58 are not well established, and the rate constants given in Table AI are somewhat speculative. For example. Reaction 53 is presumably a termolecular gas phase reaction of NO, NO2, and H2O (62), but the possibility of a heterogeneous mechanism cannot be entirely eliminated. The photo-dissociation rate for Reaction 58 (63, 64) is probably an upper limit, based on available experimental data. In any case, with the rate constants given in Table AI, exclusion of... 

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