Nanoscale Electrokinetic Analysis for Permselective Nanofluidic Systems

Abstract

Due to advances in nano-fabrication technologies, the electrokinetics to analyze the nanofluidic system has drawn significant attention. Although the microfluidic system could be described well by the conventional electrokinetics which was governed by the Poisson-Boltzmann equation, the continuity equation, and Stokes equations, the nanofluidic system could not be analyzed by the same theory. In nanofluidic system, followings arise as dominant phenomena: (1) the overlap of the electric double layer (EDL), (2) the transport mechanisms through the EDL, and (3) the transition to nonequilibrium state. Therefore, a set of equations such as the Poisson equation, the Nernst-Planck equations, the Stokes equations, and the continuity equations should be solved by coupled manner in order to consider arisen phenomena in nanofluidic system. Nevertheless, additional constraints should be required to analyze the nanofluidic system under nonlinear nanoscale regime so that theoretical modeling has been focused on finding additional constraints. In this work, two theoretical models with additional constraints are proposed to describe nanofluidic systems: (1) modified metal-oxide-electrolyte model with fringing field effect and counter-ion condensation and (2) modified ion concentration polarization with field-induced mobility jump. First, theoretical model with fringing field effect and counter-ion condensation as additional constraints was derived to describe the electrokinetic phenomena inside the ionic field effect transistor (IFET). IFET is a device which enables active modulation of ions and molecules transportation through nanofluidic channels. Conventional models for ionic field effect transistor were well-matched with fully gated IFET of which gate electrode completely covers the full length of the nanochannel. However, in case of partially gated IFET, conventional models had non-negligible errors to describe the current-voltage relation of the partially gated IFET so that the modified model adapted Poisson-Nernst-Planck-Stokes (PNPS) formulations with additional nonlinear constraints of a fringing field effect and a counter-ion condensation which had not been considered as major factors. Using the model, theoretical and experimental results were well matched. The investigated mechanisms of the partially gated IFET provide effective means to control the motion of both negatively and positively charged molecules which is important in biomolecule transport through nanochannels, medical diagnosis system and point-of-care system, etc. Second, theoretical model with hypothetical mobility jump was derived to describe the ICP layer in depletion side. Typical nanofluidic system has a permselectivity: ions of the same charge as the nanochannel surface (coions) exhibit a lower permeability, while ions of the opposite charge (counter-ions) have a higher permeability through the nanochannel. Due to this unique property, ion concentration around the permselective nanofluidic system could be polarized under external driving fields, which is known as ion concentration polarization (ICP) phenomenon. By previous experimental study, concentration profile inside the ICP layer in depletion side has stepwise distribution which could not be described by conventional model for ICP. Therefore, we adopted area-averaging 1D formulation of Poisson-Nernst-Planck-Stokes equations with field-induced mobility jump as an additional nonlinear constraint which is caused by dehydration of ionic species. As a result, our model could produce the stepwise concentration profile inside the ICP layer and could explain the different profile depending on cation species. Furthermore, our model could be verified by experiments of direct concentration measurement using mass spectroscopy. Consequently, stepwise concentration profile inside ICP layer is induced by field-induced mobility jump and this phenomenon provide effective mechanism to separate ionic species in liquid phase.