Birk-Perone

The Birk-Perone system, a flash photolysis experiment with subsequent second-order decay, is a little more interesting because it can, with an unsuitable simulation method, lead to negative concentration values. The simultaneous reactions are... 

There is an example program described in Appendix C, BPROS, applying Rosenbrock to the Birk-Perone system, in which we have both time-dependence and nonlinear equations. It is described in Chap. 2, pages 22-22. Equation (2.73), with boundary conditions, when semidiscretised using equal intervals in space, leads to the DAE system... 

E.3.9 A Nonlinear System Programs for the Birk/Perone Reaction... 

A solution for this system was first attempted by Birk and Perone [121], who however oversimplified their assumptions. This was pointed out later [146] and the more rigorous solution (current only) was found to be... 

To show how this is done both in the linearised and the nonlinear form, a simple example is chosen, having the advantage of being a single-species mechanism. It is that described by Birk and Perone [121]. The electroactive substance A is formed at a uniform (bulk) concentration in a cell by a flash of light. It begins immediately to decay in a second-order her, while being electrolysed in a Cottrell-like experiment. This system will be called BP here. The equations are... 

The number 2 seems to be controversial but seems logical because every time two molecules of A react, both are removed from solution. Birk and Perone presented a solution for the current, but this was incorrect and was later corrected and augmented by solutions for various electrode geometries [146], So a solution exists that can be used to test a simulation. 

Birk JR, Perone SP (1968) Electrochemical studies of rapid photolytic processes. A theoretical and experimental evaluation of potentiostatic analysis in flash photolysed solutions. Anal Chem 40 496-500... 

One of the problems mentioned in Chap. 8 is that of second-order homogeneous chemical reactions, which give rise to nonlinear terms in the transport equations. One such system is the Birk and Perone reaction [10, 11], in which a light flash produces an electroactive substance in solution, which decays with a second-order reaction while it is electrolysed. If CN is used to simulate this, the term in Cj can be linearised to a good, second-order approximation. If one does not choose or is prevented from linearisation, a Newton approach, as described in that chapter, must... 

---