Second-order irreversible dimerization

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). 

The TG/SC theory was developed for several mechanisms E/ 2i (ET followed by second-order irreversible dimerization of the product) (21), (22), and more compli-... 

Second-order irreversible chemical reaction following a reversible electron transfer dimerization. It is quite common in chemical reactions that newly formed radicals couple to each other. This also often happens in the electrochemical generation of radicals according to a dimerization process that can be written as ... 

In an EC2j process, the initial ET step is followed by a second-order irreversible homogeneous reaction. For example, the feedback mode of SECM was employed to study the reductive hydrodimerization of the dimethyl fumarate (DF) radical anion [22]. The experiments were carried out in solutions containing either 5.15 or 11.5 mM DF and 0.1 M tetrabutylammonium tetrafluoroborate in A,A,-dimethyl form amide (DMF). The increase in the feedback current with increasing concentration of DF indicated that the homogeneous step involved in this process is not a first-order reaction. The analysis of the data based on the EC2 theory yielded the fc2 values of 180M-1 s-1 and 160M-1 s-1 for two different concentrations. Another second order reaction studied by the TG/SC mode was oxidative dimerization of 4-nitrophenolate (ArO-) in acetonitrile [23]. In this experiment, the tip was placed at a fixed distance from the substrate. The d value was determined from the positive feedback current of benzoquinone, which did not interfere with the reaction of interest. The dimerization rate constant of (1.2 0.3) x 108 M x s-1 was obtained for different concentrations of ArO-. 

In the EC2i process, an initial electron transfer step is followed by a second-order irreversible chemical reaction (typically a dimerization process, as considered in the practical examples in Sec. III.B). The use of SECM to characterize the kinetics of the second-order chemical reactions is based on the same principles as for the EQ case, discussed in Sec. II, with a generator electrode employed to electrogenerate the species of interest [B, see Eq. (1)], which is collected at a second electrode. The second-order process involving the consumption of B to form electroinactive products occurs in the gap between the two electrodes ... 

Example 4.12 used N stirred tanks in series to achieve a 1000-fold reduction in the concentration of a reactant that decomposes by first-order kinetics. Show how much worse the CSTRs would be if the 1000-fold reduction had to be achieved by dimerization i.e., by a second order of the single reactant type. The reaction is irreversible and density is constant. 

Diagnostic criteria to identify an irreversible dimerization reaction following a reversible electron transfer. In the presence of a chemical reaction following an electron transfer, the dependence of the cyclic voltammetric parameters from the concentration of the redox active species are sufficient by themselves to reveal preliminarily a second-order complication (a ten-fold change in concentration from = 2 10-4 mol dm-3 to 2 10-3 mol dm-3 represents a typical path). 

The theoretical study of other electrode processes as a reduction followed by a dimerization of the reduced form or a second-order catalytic mechanism (when the concentration of species Z in scheme (3.IXa, 3.IXb) is not too high) requires the direct use of numerical procedures to obtain their voltammetric responses, although approximate solutions for a second-order catalytic mechanism have been given [83-85]. An approximate analytical expression for the normalized limiting current of this last mechanism with an irreversible chemical reaction is obtained in reference [86] for spherical microelectrodes, and is given by... 

The simplest case of parallel second-order steps is that of formation of two different dimers of a reactant A, corresponding to the network 5.23 and rate equations 5.24 (see next page). At all times, both products are formed in the same ratio rP rQ = kAP kAQ, so that the decay of A is an ordinary second-order reaction with rate coefficient k = kAP + kAQ. Likewise, the product formations are ordinary second-order reactions. (One could think of the initial amount of A as divided into two portions in the ratio kAV kAQ that react independently of one another and at the same rate, one to P and the other to Q.) All equations and plots for irreversible second-order reactions thus are valid (see Section 3.3.1). 

The deactivation path includes reversible second-order generation of dormant species, followed by their irreversible deactivation. A high amount of the cocatalyst is needed to prevent the formation of inactive zirconocene dimers thus for modeling purposes, the deactivation constant had a following dependence on concentration of MAO... 

Reoxidation of the cosubstrate at an appropriate electrode surface will lead to the generation of a current that is proportional to the concentration of the substrate, hence the coenzyme can be used as a kind of mediator. The formal potential of the NADH/NAD couple is - 560 mV vs. SCE (KCl-saturated calomel electrode) at pH 7, but for the oxidation of reduced nicotinamide adenine dinucleotide (NADH) at unmodified platinum electrodes potentials >750 mV vs. SCE have to be applied [142] and on carbon electrodes potentials of 550-700 mV vs. SCE [143]. Under these conditions the oxidation proceeds via radical intermediates facilitating dimerization of the coenzyme and forming side-products. In the anodic oxidation of NADH the initial step is an irreversible heterogeneous electron transfer. The resulting cation radical NADH + looses a proton in a first-order reaction to form the neutral radical NAD, which may participate in a second electron transfer (ECE mechanism) or may react with NADH (disproportionation) to yield NAD [144]. The irreversibility of the first electron transfer seems to be the reason for the high overpotential required in comparison with the enzymatically determined oxidation potential. 

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