Electrochemical simulations—a few questions

To predict the electrochemical response when the problem has no known or simple analytical solution, e.g. cyclic voltammetry, microelectrodes, coupled chemical reactions, etc. 

Typically, an electrochemical simulation models the transport of the reactant from the bulk to the electrode surface, the transfer of electrons at the electrode/solution interface and the transport of the product away from the electrode. Depending on the complexity of the electrochemical process, the simulation may account for the rate of electron transfer kinetics, the possibility and rate of preceding or following chemical reactions, the possibility and rate of adsorption processes and even combinations of different forms of mass transport (planar or spherical diffnsion, convection and migration). In other words, the simulation performs a series of actions which mimic the sequence of events thought to occur in the electrode reaction. 

Traditionally, a simulation is constructed as follows (1) the real world problem is analysed and cast in terms of mathematical expressions (e.g. the differential equations for mass transport and the initial and boundary conditions for what happens at the electrode surface and in the bulk) (2) the expressions are then rewritten in dimensionless form (3) the continuous variables (typically, concentration, space and time) are discretised (4) the differential equations and boundary conditions are disaetised (5) an algorithm is chosen and a program written in Fortran, Pascal, Basic or C (6) the simulation is tested with conditions yielding a known solution (7) finally, the simulation is applied to the conditions of interest. 

Physical approaches not reqniring the numerical solution of the differential equations have also been developed. For example, an atomistic model considers the cell as a domain filled with a popnlation of particles and diffusion is simulated by the random walk of the particles within the domain (53, 54). The current is computed by counting the number of particles that reach the electrode per unit time. Convection and migration can even be included. Another model, the box method nsed in the early days of electrochemical simulation (55), divides the solntion in thin slabs (boxes wherein the concentration is assumed to be uniform) and calculates the movement of species between slabs nsing Fick s first law of diffusion. Althongh more intuitive, these approaches are in fact eqnivalent to solving the transport eqnation. 

---