Size dependent surface charge properties of silica nano-channels: double layer overlap and inlet/outlet effects

Transport inside nano-channels and tubes is highly dependent on their surface charge properties. While previous studies assume that the charge density of a surface is a material property and independent of confinement size, this study properly characterized the surface charge of a nanochannel as a function of channel height and length under various solution conditions. By calculating the local surface charge based on local ionic concentrations, the surface charge of a nano-channel was studied by considering the effects of both overlapping electrical double layers (EDLs) and inlet/outlet regions. First, the surface charge of silica decreased with the increase in EDL overlap, which is characterized by the ratio of EDL thickness to channel height. Second, the local surface charge showed variation at the inlet/outlet regions where the channel's electrokinetics was in development. We defined a general entrance length as a function of EDL thickness for the electrokinetically developing part of different cases, after which the surface charge reached its equilibrium value and remained constant. Based on such length scales, we extended the existing theory to include nano-effects. A phenomenological model was developed, which can predict the average nano-channel surface charge as a function of EDL thickness, pH, channel length and channel height.