Toward the Physical Basis of Complex Systems: Dielectric Analysis of Porous Silicon Nanochannels in the Electrical Double Layer Length Range

Abstract

Dielectric analysis (DEA) shows changes in the properties of
a materials as a response to the application on it of a time dependent electric field. Dielectric measurements are extremely sensitive to small changes in materials properties, that molecular relaxation, dipole changes, local motions that involve the reorientation of dipoles, and so can be observed by DEA. Electrical double layer (EDL), consists in a shielding layer that is naturally created within the liquid near a charged surface. The thickness of the EDL is given by the characteristic Debye length what grows less with the ionic strength defined by half summ products of concentration with square of charge for all solvent
ions (co-ions, counterions, charged molecules). The typical length scale for the Debye length is on the order of 1 nm, depending on the ionic contents in the solvent; thus, the EDL becomes significant for nano-capillaries that nanochannels. The electrokinetic e®ects in the nanochannels depend essentialy on the distribution of charged species in EDL, described by the Poisson-Boltzmann equation those solutions require the solvent dielectric permittivity. In this work we propose a model for solvent low-frequency permittivity and a DEA profile taking into account both the porous silicon electrode and aqueous solvent properties in the Debye length range.