Surface conductivity in electrokinetic systems with porous and charged interfaces: Analytical approximations and numerical results

Abstract

We derive an approximate analytical representation of the conductivity for a 1D system with porous and charged layers grafted onto parallel plates. Our theory improves on prior work by developing approximate analytical expressions applicable over an arbitrary range of potentials, both large and small as compared to the thermal voltage (RTF). Further, we describe these results in a framework of simplifying nondimensional parameters, indicating the relative dominance of various physicochemical processes. We demonstrate the efficacy of our approximate expression with comparisons to numerical representations of the exact analytical conductivity. Finally, we utilize this conductivity expression, in concert with other components of the electrokinetic coupling matrix, to describe the streaming potential and electroviscous effect in systems with porous and charged layers.

Electrokinetic Measurements of Thin Nafion Films

“…The parameter ϕ̂ in the conductivity scale is a measure of the mobility of the current-carrying ions (see the Supporting Information for a brief description). We discuss this parameter at length elsewhere …”

“…We discuss this parameter at length elsewhere. 14 Our model for the conductivity accounts for conduction in the bulk (driven by the electrophoretic motion of ions) along with Ohmic and electroosmotic excess conductivities within the Nafion film:…”

“…This result depends only upon the parameters α, γ, ρ f *, and the ionic potentials ϕ i * which may be calculated 14 from values in the literature for a variety of electrolytes, including ions within Nafion film. 41 We apply eq 10 to our conduction data, and perform a regression analysis to determine the values of λ 0 and ρ f , which are the only free parameters.…”

“…Electrokinetic techniques are often used to measure physical and chemical properties of porous and charged layers . Typically, streaming current, streaming potential, and conductivity measurements are coupled with physical measurements of the porous layer and a numerical − or approximate analytical ,− models of the transport in the layer. Zimmermann et al performed a combined analysis to study protein adsorption within a planar electrokinetic cell designed to extract information from streaming current/potential and conductivity measurements.…”

“…We first describe our electrokinetic cell in detail, and outline the program of measurements, which we perform to characterize the physical and chemical properties of the thin Nafion films. Then, we present results from our streaming potential and conductivity measurements that we interpret using a model , to predict the charge density and resistive properties of the Nafion film. We then compare these results with available data from other electrokinetic studies on Nafion (performed in different configurations), and propose an explanation for our observed data.…”