Porosity and tortuosity of layer-by-layer assemblies of spherical particles

We have used the extended random sequential adsorption model of hard spheres to mimic the layer by layer self-assembling process of monodisperse colloidal particles at a solid-liquid interface. We have studied five multilayers of similar thickness, each created at a different single-layer surface coverage. Our results suggest that the single-layer coverage has a significant effect on the film transport properties. The local values of multilayer porosity and tortuosity exhibit decaying oscillatory variations in the distance range dependent on the surface coverage. The mean multilayer porosity and tortuosity describe equations linear with respect to the surface coverage. The mean tortuosity and porosity of multilayers created with our model are also connected by a linear equation valid for any single-layer coverage and any number of layers. We have also determined the normalized equivalent thickness of stagnant solution layer as a function of the multilayer coverage and number of layers. This parameter grows asymptotically with the number of layers and can be approximated with good accuracy by the ratio of the squared mean tortuosity to the mean porosity of a multilayer.