Simple charge transfer

Although charge transfer is not a primary subject of this chapter, we begin this section with it since it is the simplest of the ion—molecule reactions and accordingly the one for which most rigorous theoretical treatments are possible. 

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Single-Stack Acceptor. Simple charge-transfer salts formed from the planar acceptor TCNQ have a stacked arrangement with the TCNQ units facing each other (intermolecular distances of ca 0.3 nm (- 3). Complex salts of TCNQ such as TEA(TCNQ)2 consist of stacks of parallel TCNQ molecules, with cation sites between the stacks (17). The interatomic distance between TCNQ units is not always uniform in these salts, and formation of TCNQ dimers (as in TEA(TCNQ)2) and trimers (as in Cs2(TCNQ)Q can lead to complex crystal stmctures for the chainlike salts. 

Hence, reactions which proceed via complex formation or stripping reactions involving transfer of a relatively massive moiety either are not observed or are registered at grossly distorted intensities. An additional complication is that elastic or nonreactive scattering collisions may allow a primary ion to be detected as a secondary ion. Simple charge transfer... 

The choice of a particular type of gas discharge for quantitative studies of ion-molecule reactions is essential if useful information is to be obtained from ion abundance measurements. Generally, two types of systems have been used to study ion-molecule reactions. The pulsed afterglow technique has been used successfully by Fite et al. (3) and Sayers et al. (1) to obtain information on several exothermic reactions including simple charge transfer processes important in upper atmosphere chemistry. The use of a continuous d.c. discharge was initiated in our laboratories and has been successful in both exothermic and endothermic ion-molecule reactions which occur widely within these systems. 

A discussion of the charge transfer reaction on the polymer-modified electrode should consider not only the interaction of the mediator with the electrode and a solution species (as with chemically modified electrodes), but also the transport processes across the film. Let us assume that a solution species S reacts with the mediator Red/Ox couple as depicted in Fig. 5.32. Besides the simple charge transfer reaction with the mediator at the interface film/solution, we have also to include diffusion of species S in the polymer film (the diffusion coefficient DSp, which is usually much lower than in solution), and also charge propagation via immobilized redox centres in the film. This can formally be described by a diffusion coefficient Dp which is dependent on the concentration of the redox sites and their mutual distance (cf. Eq. (2.6.33). 

Kinetic Scheme. Generally, metal ions in a solution for electroless metal deposition have to be complexed with a ligand. Complexing is necessary to prevent formation of metal hydroxide, such as Cu(OH)2, in electroless copper deposition. One of the fundamental problems in electrochemical deposition of metals from complexed ions is the presence of electroactive (charged) species. The electroactive species may be complexed or noncomplexed metal ion. In the first case, the kinetic scheme for the process of metal deposition is one of simple charge transfer. In the second case the kinetic scheme is that of charge transfer preceded by dissociation of the complex. The mechanism of the second case involves a sequence of at least two basic elementary steps ... 

In a general way, the measured current 1° when a constant or time variable potential perturbation is applied to a simple charge transfer reaction at an electrode of a given geometry G can be defined from the equivalence between the gradient at the electrode surface and the difference between bulk (c 0) and surface (Cq) concentrations divided by the diffusion layer thickness, SG, of the concentration profile of electroactive species O or R [62],... 

Fig. 3.26 Variation of the normalized current of a CE mechanism versus / calculated from Eqs. (3.194b) under limiting current conditions and (3.195b). The values of K = 1 //sfeq are on the curves. E — Ef1 = —0.3, T= 298.15 K. Dashed lines correspond to the behavior of a simple charge transfer without chemical complications (E mechanism see Eq. (2.36))...

When the condition k +k2)< D/r is fulfilled, the enhancement of the diffusion transport freezes the chemical reaction, so the response is that corresponding to a simple charge transfer process and therefore does not contain any information about the chemical kinetics. So, Eq. (3.260) under these conditions becomes... 

The ratios given in Eq. (4.66) are only dependent on the electrode shape and size but not on parameters related to the electrode reaction, like the number of transferred electrons, the initial concentration of oxidized species, or the diffusion coefficient D. For fixed time and size, the values of f or Qf2 are characteristic for a simple charge transfer (see Fig. 4.4 for the plot of Qf2 calculated at time (ti + T2) for planar, spherical, and disc electrodes) and, as a consequence, deviations from this value are indicative of the presence of lateral processes (chemical instabilities, adsorption, non-idealities, etc.) [4, 32]. Additionally, for nonplanar electrodes, these values allow to the estimation of the electrode radius when simple electrode processes are considered. 

Note that the expressions for the surface concentrations of species B and C given by Eq. (4.201) are similar to those corresponding to species O and R of a simple charge transfer (see Eqs. (4.25) and (4.26)), (although in the case of a catalytic mechanism K refers to the inverse of the chemical equilibrium constant of species B and C). 

In the following sections, the behavior of soluble solution species giving rise to simple charge transfer reactions (electronic and ionic) is analyzed. The case corresponding to more complex reaction mechanisms is the subject of Chap. 6. 

Note that the expression of the current given by Eq. (6.15) is formally identical to that corresponding to a simple charge transfer process (Eq. (5.18)) by simply... 

In both cases, it is clear that the response can be expressed as the sum of the solution for planar electrodes given by Eq. (6.33) and a contribution related to the electrode size (the second addend in the right-hand side of Eqs. (6.40) and (6.41)). When the electrode radius decreases, the current evolves from the transient peakshaped response to a sigmoidal stationary one in the same way as observed for a simple charge transfer process (see Sects. 5.2.3.2 and 5.2.3.3). For small values of the electrode radius, the planar term in (6.40) and (6.41) becomes negligible and the current simplifies to... 

Equation (6.42) clearly shows that the CV stationary responses of disc and spherical electrodes hold the same equivalence relationship as that observed for a simple charge transfer process ... 

For jDj k + 2) > 10<7G, the kinetics of the chemical step is masked (the catalytic process behaves as a simple charge transfer process), and a micro-geometrical steady state is reached ... 

The different assumptions needed to make a statement of this problem will be presented in the following section. Then the general solution corresponding to the application of a sequence of potential pulses to attached molecules giving rise to simple charge transfer processes and particular solution corresponding to Multipulse Chronoamperometry and Chronocoulometry and Staircase Voltammetry will be deduced. Cyclic Voltammetry has a special status and will be discussed separately. Finally, some effects that cause deviation from the ideal behavior and more complex reaction schemes like multielectronic processes and chemical reactions in the solution coupled to the surface redox conversion will be discussed. 

When a sequence of p consecutive potential pulses of the same length t is applied, the analytical expression of the surface excess of species O is, in line with the above discussion, identical to that given for a simple charge transfer reaction in Eq. (6.127) by changing k p for k p with ... 

The effects of the catalytic reaction on the CV curve are related to the value of dimensionless parameter A in whose expressions appear variables related to the chemical reaction and also to the geometry of the diffusion field. For small values of A, the surface concentration of species C is scarcely affected by the catalysis for any value of the electrode radius, such that r)7,> —> c c and the current becomes identical to that corresponding to a pseudo-first-order catalytic mechanism (see Eq. (6.203)). In contrast, for high values of A and f —> 1 (cathodic limit), the rate-determining step of the process is the mass transport. In this case, the catalytic limiting current coincides with that obtained for a simple charge transfer process. 

Concerning the half-peak width (W1/2), as can be deduced from Fig. 7.36, its value is independent of the electrode radius and the catalytic rate constants. The dependence ofWul on the square wave amplitude is identical to that obtained for a simple charge transfer given by Eq. (7.32) (see also Fig. 7.8), i.e., it increases with Sw from W1/2 = 90mV for Esw < lOmV to Wy2 = 2 Sw for sw > lOOmV. 

Appendix A. Dimensionless Parameter Method Solution for the Application of a Constant Potential to a Simple Charge Transfer Process at Spherical Electrodes When the Diffusion Coefficients of Both Species are Different... 

The simple charge transfer from K to C60 observed in the fee K3C60 is not always the case in potassium fullerides. Similar comparison between the LDA band structure of the bcc K6C60 fulleride and that of the hypothetical bcc pristine solid... 

The experimental impedance is always obtained as if it were the result of a resistance and capacitance in series. We have already seen in (11.20) and (11.21) the relation between an RC series combination and the Rct + zw combination. It can be shown for the full Randles equivalent circuit for this simple charge transfer reaction, see Fig. 11.4, on separating the in-phase and out-of-phase components of the impedance, that... 

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