SECM of More Complicated Chemical Systems

A homogeneous chemical reaction occurring in the gap between the tip and substrate electrodes causes a change in iT, therefore its rate can be determined from SECM measurements. If both heterogeneous processes at the tip and substrate electrodes are rapid (at extreme potentials of both working electrodes) and the chemical reaction (rate constant, kc) is irreversible, the SECM response is a function of a single kinetic parameter K = const X kc/D, and its value can be extracted from IT vs. L dependencies. 

SECM theory has been developed for lour mechanisms with homogeneous chemical reactions coupled with electron transfer, i.e., a first-order irreversible reaction (ErQ mechanism) (5), a second-order irreversible dimerization (ErC2i mechanism) (36), ECE and DISP1 reactions (38). [The solution obtained for a EqCr mechanism in terms of multidimensional integral equations (2) has not been utilized in any calculations.] While for ErC, and ErC2i mechanisms analytical approximations are available (39), only numerical solutions have been reported for more complicated ECE and DISP1 reactions (38). 

Three approaches to kinetic analysis were proposed (1) steady-state measurements in a feedback mode, (2) generation/collection experiments, and (3) analysis of the chronoamperometric SECM response. Unlike the feedback mode, the generation/collection measurements included simultaneous analysis of both IT-L and Is-L curves or the use of the collection efficiency parameter (IS/IT when the tip is a generator and the substrate is a collector). The chronoamperometric measurements were found to be less reliable (5), so only steady-state theory will be discussed here. 

First-Order Following Reaction For the ErCi mechanism 

It was solved numerically using the alternating-direction implicit (ADI) finite difference method (5). The steady-state results were obtained as a long time limit and presented in the form of two-parameter families of working curves (5). These represent steady-state tip current or collection efficiency as functions of K = akc/D and L. 

---