Overlap limit

Providing that the interactions between the reactant and the electrode in the electrochemical transition state, and between the two reactants in the homogeneous transition state, are negligible ("weak overlap" limit), the activation barriers for reactions 10 and 11 will be closely related. 

FIG. 7. Simulated (dotted curves) and experimental (solid curves) voltammograms at 100 mV s at a lONEE (0.079 cm geometric area) in 5 pM TMAFc+ and 0.5 mM sodium nitrate. Simulation assumes the total overlap limiting case (i.e., a macroelectrode with area = 0.079 cm ). 

The two primary features of the phenomena are the layer thickness necessary to provide stability and the conditions at which the dispersions flocculate. The first can be quantified by generalizing the potential for terminally anchored chains to interactions between spheres via the Deijaguin approximation, adding the attractive dispersion potential, and then assessing the layer thickness necessary to maintain —fl>mi /fcT < 1 — 2. To illustrate this, consider the small overlap limit of Eq. (122), which transforms into... 

Given that inner-sphere pathways are commonly encountered at metal-solution interfaces, as between reactants in homogeneous solution, a key question concerns the manner and extent to which the reactant-electrode interactions associated with such pathways lead to reactivity enhancements compared with weak-overlap pathways (Sect. 3.5.2). A useful tactic involves the comparison between the kinetics of structurally related reactions that occur via inner- and outer-sphere pathways. This presumes that the outer-sphere route yields kinetics which approximate that for the weak-overlap limit. For this purpose, it is desirable to estimate the work-corrected uni-molecular rate constant for the outer-sphere pathway at a particular electrode potential, k° , from the corresponding work-corrected measured value, kCOTr, using [cf. eqns. (10) and (13)]. 

Variations An additional six-membered transition state example is the cyclic decarboxylation. The overlap limitation for the new carbon-carbon pi bond requires the breaking C-C bond to align coplanar with the carbon p orbital of the carbonyl. 

In dilute solutions, the polymer chains are isolated from one another and only interact during brief encoimters. With increasing polymer concentration, a point is reached where the chains start to overlap, this point C,, is referred to as the eritical concentration of monomers at the overlap limit and can be approximated as = N/Rp, with... 

The summation extends over all the ions present at concentrations c in M multiplied by their stoichiometric coefficients vi (Marcus 2009b). The radius of a hydrated ion, rihydr, may be taken as the sum of the ionic radius and the diameter of a water molecule (see below), so that it is possible to estimate the concentration at which the hydration shells start to overlap d aqueous NaCl and is lower still for solutions of unsymmetrical multivalent electrolytes (1 2, etc.). Below the overlap limit experimental values of (dVildP)T may be used for the estimation of the hydration numbers at finite concentrations from the expression (2.10) for Aicomp given above. 

The monomer concentration at this limit can be estimated, by regarding that for close-packed polymers this concentration must agree with the mean concentration in a single chain. For expanded chains we find for the critical concentration at the overlap limit , c, the expression... 

An especially interesting result is presented in Fig. 3.3. It deals with the same set of data plotted here in a special form. We employ c, the polymer weight fraction at the overlap-limit, and replace Cw by a dimensionless reduced variable x, called the overlap ratio ... 

---