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 V_eff(x), is then defined through the density distribution, ρ{variant}(x), ρ{variant}(x) ∞ e^-βV_eff^x where β = 1/kT. The Langevin dynamics simulation is used to calculate ρ{variant}(x), which in turn gives V_eff(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.