The exclusion-diffusion potential in charged porous membranes

Westermann-Clark, G.B.; Christoforou, Cleopatra

doi:10.1016/0022-0728(86)90001-x

Cited by 48 publications

(64 citation statements)

References 13 publications

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“…At very low electrolyte concentrations, there is a conductance saturation that occurs because the co-ion concentration is zero (total co-ion exclusion) while the counter-ion concentration is equal to the (constant) fixed charge concentration inside the nanopore (electroneutrality condition). This saturation is observed experimentally in membranes and nanopores in the low concentration limit (Westermann-Clark and Christoforou 1986;Stein et al 2004). At moderate electrolyte concentrations, the conductance increase with c s , in agreement with the experimental observations, due to the increase of c þ h i þ c À h i with c s .…”

Section: Electrical Conductancesupporting

confidence: 84%

“…Some approaches consider the linearized P-B equation for point ions (Schoch et al 2008;Jorne 2006, Aguilella-Arzo et al 2006. In those cases where the exact, nonlinear P-B equation is employed, ion size effects are usually ignored (Westermann-Clark and Christoforou 1986;Cervera et al 2006;Aguilella-Arzo et al 2006;Vlassiouk and Siwy 2007) despite the fact that the electrolyte solution is confined to the reduced free space available within the nanopore. Studies of the nanopore selectivity using a generalized P-B equation that incorporates explicitly the size of the ions (Bontha and Pintauro 1994;Basu and Sharma 1997;Cervera et al 2003) are lacking.…”

Section: Introductionmentioning

confidence: 99%

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Incorporating ionic size in the transport equations for charged nanopores

Cervera

Ramı́rez

Manzanares

et al. 2009

Microfluid Nanofluid

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Nanopores with fixed charges show ionic selectivity because of the high surface potential and the small pore radius. In this limit, the size of the ions could no longer be ignored because they occupy a significant fraction of the pore and, in addition, they would reach unrealistic concentrations at the surface if treated as point charges. However, most models of selectivity assume point ions and ignore this fact. Although this approach shows the essential qualitative trends of the problem, it is not strictly valid for high surface potentials and low nanopore radii, which is just the case where a high ionic selectivity should be expected. We consider the effect of ion size on the electrical double layer within a charged cylindrical nanopore using an extended Poisson-Boltzmann equation, paying special attention to (non-equilibrium) transport properties such as the streaming potential, the counter-ion transport number, and the electrical conductance. The first two quantities are related to the nanopore selectivity while the third one characterizes the conductive properties. We discuss the nanopore characteristics in terms of the ratio between the electrolyte and fixed charge concentrations and the ratio between the ionic and nanopore radii showing the experimental range where the point ion model can still be useful. Even for relatively small inorganic ions at intermediate concentrations, ion size effects could be significant for a quantitative estimation of the nanopore selectivity in the case of high surface charge densities.

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Section: Electrical Conductancesupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Incorporating ionic size in the transport equations for charged nanopores

Cervera

Ramı́rez

Manzanares

et al. 2009

Microfluid Nanofluid

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“…Given the concentration profiles of counter-ions and co-ions the integral in Equation (23) can be evaluated numerically. Equation (23) can be simplified by using the Meyer-Sievers assumptions (see Reference [18] for details), i.e. assuming that the ionic concentrations (c i ) k in a charged pore are related to the bulk concentration…”

Section: Mass Transport Through a Charged Slit Openingmentioning

confidence: 99%

Investigation of nanoscale electrohydrodynamic transport phenomena in charged porous materials

Pivonka

Smith

2005

Int. J. Numer. Meth. Engng

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SUMMARYDepending on the permeability of porous materials, different mass transport mechanisms have to be distinguished. Whereas mass transport through porous media characterized by low permeabilities is governed by diffusion, mass transport through highly permeable materials is governed by advection. Additionally a large number of porous materials are characterized by the presence of surface charge which affects the permeability of the porous medium. Depending on the ion transport mechanism various phenomena such as co-ion exclusion, development of diffusion-exclusion potentials, and streaming potentials may be encountered. Whereas these various phenomena are commonly described by means of different transport models, a unified description of these phenomena can be made within the framework of electrohydrodynamics.In this paper the fundamental equations describing nanoscale multi-ion transport are given. These equations comprise the generalized Nernst-Planck equation, Gauss' theorem of electrostatics, and the Navier-Stokes equation. Various phenomena such as the development of exclusion potentials, diffusionexclusion potentials, and streaming potentials are investigated by means of finite element analyses. Furthermore, the influence of the surface charge on permeability and ion transport are studied in detail for transient and steady-state problems. The nanoscale findings provide insight into events observed at larger scales in charged porous materials.

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“…This approach remains poor because experimental data are needed to evaluate the phenomenological coefficients and no understanding of the underlying processes is accomplished. More elaborate models include the influence of the microstructure (i.e., the topology of the interconnected pore space and matrix pore interface) to membrane potential and electrical conductivity (11,12). However, these models usually oversimplify the microstructure by considering the pores to be formed by capillaries or parallel plates.…”

Section: Introductionmentioning

confidence: 99%