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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.

The formation of the liquid, crystalline and glassy states in binary mixtures of aqueous suspensions of charged polystyrene spheres of different sizes is investigated using molecular dynamics simulations. It is shown that on merely mixing the particles, crystalline (a substitutional body-centered cubic) and glassy states are readily formed for a 1:1 mixture at appropriate values of the density. These results are in agreement with recent experimental studies. The ease of formation of the crystal and the glassy phases is rationalised by an analysis of the local potential energy profiles calculated using the Hessian (dynamical matrix). It is suggested that the eigenvalues of such a Hessian can be used to define a preferred length scale in any glassy system.

The disorder-order transition observed in aqueous suspension of charged macroions is investigated with use of both simulations and a simple theoretical model. Molecular-dynamics (MD) simulations were performed by assuming that the interaction between the charge stabilized particles interact via a modified Debye-H\"uckel potential. The parameters of the potential were chosen to mimic the experimental study of Lindsay and Chaikin. Simulation results predict that the liquid freezes into a bcc phase in accord with the experimental findings. For comparison, the phase diagram with use of the self-consistent phonon theory (SCP) is presented. It is shown that the predictions of the SCP theory in the weak screening limit are in disagreement with both the MD results and the experiments. Possible reasons for this failure are pointed out. Finally, similar calculations have been carried out for the Yukawa potential. It is found that for the parameters considered here, this is an unphysical model for the suspensions of polystyrene spheres. No evidence for reentrant transitions is found in either of these models. This is in agreement with the predictions of the self-consistent phonon theory.

The pair correlation function and the velocity autocorrelation function of screened-Coulomb colloidal liquids, interacting via the Derjaguin-Landau-Verweg-Overbeek potential, are calculated using molecular dynamics. Examination of the structure reveals liquidlike behavior even at the lowest density which corresponds to a volume fraction less than ${10}^{\ensuremath{-}4}$. The calculated radial distribution functions are in excellent agreement with experiment. The velocity autocorrelation function exhibits distinct oscillations at all densities, which indicates that the motion of a single particle is very strongly coupled to the collective modes of the screened-Coulomb colloidal liquid.