The nanofluidic capacitor: Differential capacitance in the absence of reservoirs.

Within the framework of the classical, mean-field Poisson-Boltzmann (PB) theory, we carry out direct numerical simulations to determine the differential capacitance of a closed nanochannel of a circular cross section, embedded in a polymeric host with charged walls and sealed at both ends by metal electrodes under an external potential bias. Our approach employs the modified PB equation, which accounts for the finite size of ions and the dependency of the electrolyte's relative permittivity on the local electric field. In view of the absence of reservoirs, the modified PB equation becomes subject to global algebraic constraints, without prior knowledge of a bulk electrolyte concentration.

Asymmetric double-layer charging in a cylindrical nanopore under closed confinement.

This article presents a physical-mathematical treatment and numerical simulations of electric double layer charging in a closed, finite, and cylindrical nanopore of circular cross section, embedded in a polymeric host with charged walls and sealed at both ends by metal electrodes under an external voltage bias. Modified Poisson-Nernst-Planck equations were used to account for finite ion sizes, subject to an electroneutrality condition. The time evolution of the formation and relaxation of the double layers was explored.

Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics.

The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-square displacement grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar substrate. Because the local effective diffusivity is known, we have been able to carry out a direct test of this mechanism for diffusion in inhomogeneous media.