Effective potentials from Langevin dynamic simulations of framework solid electrolytes

Ionic motion in framework solid electrolytes constitutes a special sort of classical many-body problem. In such electrolytes, the conductivity is due to the motion of interacting mobile ions modulated by the presence of an essentially immobile framework sublattice. Here, a one-dimensional model of interacting particles, governed by Langevin's equations of motion in a sinusoidal potential, is used to calculate particle distribution functions and effective potentials. The effective potential Veff(x), is then defined through the density distribution, ϱ(x), ϱ(x) ∞ e−βVeffx where β = 1/kT. The Langevin dynamics simulation is used to calculate ϱ(x), which in turn gives Veff(x). The dc conductivity and the other distribution functions can be used to investigate commensurability effects, pinning effects, and screening effects. Comparisons can then be made between correct numerical many-body results and various analytical approximations.