As implied in Section B.4.a, the special conditions necessary for steady state catalytic voltammograms in linear sweep or cyclic voltammetry are

Caled.

Caled.

Figure 11.15 Cyclic voltammogram (background subtracted) of 1 mM Co(II)tetraphenyl-porphyrin in 0.1 M TBABr at 25°C showing the results of fitting the data using the DIGI-SIM package.

Program |
-E°', V vs. SCE |
a |
k"' cm s"1 |
106D0(avg) cm2 s'2 |

CVFIT" |
0.763 |
0.32 |
0.088 |
4.6 |

DIGISIM" |
0.763 |
0.28 |
0.090 |
4.6 |

CVFIT* |
0.763 |
0.43 |
0.059 |
5.0 |

DIGISIM6 |
0.763 |
0.44 |
0.060 |
5.0 |

not always experimentally attainable. Also, reaction mechanisms for electrochemical catalysis are often more complex than the simple catalytic pathway in Box 11.2.

A method combining nonlinear regression analysis with models computed by digital simulation has been developed for estimating rate constants and analyzing mechanistic nuances for two-electron electrochemical catalysis [21], The method analyzed forward scans of voltammograms only and includes a linear background term. We illustrate the use of this method by discussing its results for the two-electron catalytic reduction of aryl halides (ArX). The detailed reaction pathway is shown in Box 11.3.

The catalyst P accepts an electron from the electrode in Box 11.3 to begin the reaction. The rate-determining step of the reaction may be either eq. (11.7) or eq. (11.8). Subsequently, several fast reactions (eqs. (11.9) and (11.10), which do not influence the shape of the current-potential curve, give the final hydrocarbon product.

P + e |
^ Q (at electrode), E°' |
(11.6) |

ArX + Q |
^ ArX- + P k2 |
(11.7) |

ArX- |
-» Ar + X~ |
(11.8) |

Ar + Q |
P + Ar |
(11.9) |

At" + (H+) |
-* ArH |
(11.10) |

Box 11.3 Detailed pathway for electrochemical catalytic reduction of aryl halides

Box 11.3 Detailed pathway for electrochemical catalytic reduction of aryl halides

A general model based on digital simulation of voltammograms following Box 11.3 was developed to compute the current-potential curves [21]. For analysis of data, the model was considered to represent three separate cases

(i) eq. (11.7) as the rate-determining step (rds) (KE or kinetic electron transfer case), (ii) eq. (11.8) as rds (KC or kinetic chemical case), and (iii) mixed kinetic control of both reactions (11.7) and (11.8) (KG or kinetic general case).

Data for the catalytic reduction of 4-chloro- and 4-bromobiphenyl (4-CB and 4-BB) using phenanthridine as a catalyst were analyzed using a regression program employing the Marquardt-Levenberg algorithm. The data were evaluated with the models in the following order: (i) KC model,

(ii) KE model, and (iii) KG model. This was done because, when data representing one of the limiting KE or KC cases were fit onto the KG model, serious parameter correlation between rate constants resulted. This occurs because in each limiting case the data contain little information about the rate constant of the step that is not rate determining.

Deviation plots and other criteria of goodness of fit showed that the KE model fit the data best for 4-CB and 4-BB under the experimental conditions used [21]. An example is given in Figure 11.16. Values of k\ were

Figure 11.16 Catalytic voltammogram at a Hg-drop electrode for 0.87 mM phenanthridine and 2 mM 4-BB in 0.1 M tetrabutylammonium bromide in DMF. The solid line shows the best fit by regression-simulation onto the KE model and circles are experimental data. The dotted line is voltammogram computed for phenanthridine alone. (Reproduced with permission from [21], copyright by the American Chemical Society.)

Figure 11.16 Catalytic voltammogram at a Hg-drop electrode for 0.87 mM phenanthridine and 2 mM 4-BB in 0.1 M tetrabutylammonium bromide in DMF. The solid line shows the best fit by regression-simulation onto the KE model and circles are experimental data. The dotted line is voltammogram computed for phenanthridine alone. (Reproduced with permission from [21], copyright by the American Chemical Society.)

(1.42 ± 0.12) X 103M 's 1 for the reaction of phenanthridine anion radical (Q) with 4-CB and (5.1 ± 1.8) X 104 AfV for reaction with 4-BB. Both of these values were of similar magnitude but much of better precision than rate constants found under pseudo-first-order conditions.

The inclusion of second-order kinetics in the model allows estimation of much larger rate constants than possible under pseudo-first-order conditions. This is because nearly equal concentrations of reactants can be employed, thus minimizing the rates of very fast reactions compared to pseudofirst-order conditions and making them more accessible to voltammetric measurement. Use of second-order conditions also minimizes contributions to the current from the direct reduction of the reactant. These considerations increase the possible upper limit of k\ from simulation-regression to 108 ATV1. The largest rate constant known by the authors to be measured by this method was for the reaction of the Co(I) form of vitamin B,2 with

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