Finite difference techniques overview

Molecular dynamics [MD] is a well-established technique for simulating the structure and properties of materials in the solid, liquid, and gas phases and will only be briefly overviewed here [1]. In these simulations, N atoms are placed in a simulation cell with an initial set of positions and interact via an interatomic potential 7[r]. The force on each particle is determined by its interaction with all other atoms to within an interaction cutoff specified by 7[r]. For a given set of initial particle positions, velocities, and a specification of the position- or time-dependent forces acting on the particles, MD simulations solve the classical Newton s equations of motions numerically via finite-difference methods to calculate the time evolution of the particle trajectories. 

Current and potential distributions are affected by the geometry of the system and by mass transfer, both of which have been discussed. They are also affected by the electrode kinetics, which will tend to make the current distribution uniform, if it is not so already. Finally, in solutions with a finite resistance, there is an ohmic potential drop (the iR drop) which we minimise by addition of an excess of inert electrolyte. The electrolyte also concentrates the potential difference between the electrode and the solution in the Helmholtz layer, which is important for electrode kinetic studies. Nevertheless, it is not always possible to increase the solution conductivity sufficiently, for example in corrosion studies. It is therefore useful to know how much electrolyte is necessary to be excess and how the double layer affects the electrode kinetics. Additionally, in non-steady-state techniques, the instantaneous current can be large, causing the iR term to be significant. An excellent overview of the problem may be found in Newman s monograph [87]. 

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