Poisson–Boltzmann model of space charge layer effects on conductivity in randomly distributed nanoionic composites

Ionic conductivity in nanocomposite electrolytes is examined through the use of a numerical model. A rigorous description of the space charge layer and its impact on conductivity are developed for a composite system consisting of insulating spheres dispersed within an ion conducting material. Model simulations are performed to understand how the effective conductivity, which can exceed the conductivity of the bulk material, depends on the volume fraction, size, configuration, and particle size distribution of the nanoparticles in the bulk material. Several deliberately chosen regular particle configurations are used to establish the lower and upper bounds for conductivity enhancement. A simple cubic array of particles is demonstrated to provide a reasonable estimate for the behavior expected from a random distribution of particles. Finally, conductivity modulation is shown to be significant when the particle radius is comparable to or smaller than the thickness of the space charge layer.

► Presents an improved, physically sound model of conductivity in space charge layers.
► Space charge layer interactions among neighboring particles are treated rigorously.
► Particle configuration can be important for high interface/bulk conductivity ratio.
► Facilitates an analysis of randomly placed, variable-size particle distributions.
► Exact particle distribution insignificant if particles are sufficiently dispersed.