Experimental measurements of ionic conductivity in water are analysed in order to obtain insight into the pressure dependence of limiting ionic conductivity of individual ions (λ0) for ions of differing sizes. Conductivities of individual ions, λ0 do not exhibit the same trend as a function of pressure for all ions. Our analysis suggests that the effect of pressure on ionic conductivity depends on the temperature. At low temperatures, the effect of pressure on relatively small ions such as Li+ exhibit an increase in conductivity with pressure. Intermediate sized ions exhibit an increase in conductivity with increase in pressure initially and then at still higher pressures, a decrease in ionic conductivity is observed. Although there are data at low temperatures for ions of large radius, the effect of increased pressure is expected to lower conductivity with increase in pressure over the whole range. At higher temperatures, the dependence of conductivity on pressure changes and these changes are discussed. Divalent ions such as SO2−4 exhibit different trends as a function of pressure at different temperatures. Both the divalent ions (Ca2+ and SO2−4 ) for which experimental data exists, exhibit an increase with pressure at lower temperatures. At slightly higher temperatures, a maximum in conductivity is seen as a function of pressure over the same range of pressure.

Many disordered systems can be modelled by percolation. Applications of this standard model range from amorphous and porous media to composites, branched polymers, gels and complex ionic conductors. In this brief review we give a short introduction to percolation theory and describe applications in materials science. We start with the structural properties of percolation clusters and their substructures. Then we turn to their dynamical properties and discuss the way the laws of diffusion and conduction are modified on these structures. Finally, we review applications of the percolation concept for transport in various kinds of heterogeneous ionic conductors.

A simulation study of the static and dynamic critical behavior of a symmetric binary Lennard-Jones mixture is briefly reviewed. Using a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near the critical temperature of liquid-liquid unmixing, the correlation length and “susceptibility” related to the critical concentration fluctuations are estimated, as well as the self- and interdiffusion coefficients. While the self-diffusion coefficient does not show a detectable critical anomaly, the interdiffusion coefficient is found to vanish when one approaches the critical temperature at fixed critical concentration. It is shown that in the corresponding Onsager coefficient both a divergent singular part and a nonsingular background term need to be taken into account. With appropriate finite-size scaling analysis (the particle numbers studied for the dynamics lie only in the range from N = 400 to 6400), the critical behavior of the interdiffusion coefficient is found to be compatible both with the theoretically predicted behavior and with corresponding experimental evidence.

We investigate random walk of a particle constrained on cells, where cells behave as a lattice gas on a two dimensional square lattice. By Monte Carlo simulation, we obtain the mean first passage time of the particle as a function of the density and temperature of the lattice gas. We find that the transportation of the particle becomes anomalously slow in a certain range of parameters because of the cross over in dynamics between the low and high density regimes; for low densities the dynamics of cells plays the essential role, and for high densities, the dynamics of the particle plays the dominant role.

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