Theory of Ion and Water Transport in Electron-Conducting Membrane Pores with 
<i>p</i>
H-Dependent Chemical Charge

Zhang, Li; Biesheuvel, P.M.; Ryzhkov, Ilya I.

doi:10.1103/physrevapplied.12.014039

Cited by 19 publications

(30 citation statements)

References 47 publications

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“…It may depend on the concentration of ions, pH of the solution, potential inside the pore, etc. [37]. The chemical charge in this work is assumed to be constant (such a situation can be observed, for example, at a fixed pH of the medium).…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Let us now consider the diffuse layer, in which the electric potential, ion concentration, and pressure depend on the distance along the pore and are independent of the radial coordinate. In this case, one can use the one-dimensional uniform potential model [32,37], which is a simplification of the two-dimensional space charge model based on the Navier-Stokes, Nernst-Planck, and Poisson equations [31]. We introduce the ion flux density (mol/m 2 s) and the volume flow density (velocity) of the solution (m 3 /m 2 s = m/s) in the direction normal to the pore cross section.…”

Section: Mathematical Model Equationsmentioning

confidence: 99%

“…and are the dimensionless potentials corresponding to and and is the total volume charge density. The latter is equal in magnitude and opposite in sign to the ionic charge density due to the electroneutrality condition (6) The equations of the homogeneous potential model have the form [37] (7)…”

Section: Mathematical Model Equationsmentioning

confidence: 99%

“…However, calculations based on this model [36] showed that the range of surface potential values, within which the membrane selectivity changes from cation to anion, is an order of magnitude lower than in the experiment [16,17]. A one-dimensional model of ion transfer through a nanopore was proposed in [37] with elec-tronic and chemical charges simultaneously present on the surface (the latter is associated with the dissociation of surface groups and depends on the pH of the medium).…”

Section: Introductionmentioning

confidence: 99%

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Modelling of Conductive Nanoporous Membranes with Switchable Ionic Selectivity

Ryzhkov

Vyatkin

Mikhlina

2020

Membr. Membr. Technol.

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An interesting area of modern membrane science is the development of "smart" membranes, which can affect the transport properties of selected components via external tuning. When the target components are ions, such a tuning can be realized with the help of electric field created by the conductive pore surface. We have proposed in this work a mathematical model of ions transport in a cylindrical nanopore with the electronic charge at the conductive surface and the chemical charge, which is separated from the surface by the Stern layer. The model is based on one-dimensional equations for potential, ion concentrations, and pressure in the diffuse layer. It is applied for describing the membrane potential at zero current, which characterizes the type and strength of ionic selectivity. It is shown that the change of surface potential in the direction from negative to positive results in the continuous change of pore selectivity from cation to anion. The decrease in the Stern layer capacitance and increase in the pore radius lead to the decrease in ionic selectivity. The presence of positive (negative) chemical charge causes the shift of potential value, at which the selectivity is switched, in the direction of negative (positive) values. At this value of potential, the membrane becomes non-selective, the diffusive flux of ions reaches maximum, and the osmotic flow ceases. The suggested model provides a qualitative and quantitative description of experimental results on switchable selectivity of tracketched membranes modified by the gold coating.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Mathematical Model Equationsmentioning

confidence: 99%

Section: Mathematical Model Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling of Conductive Nanoporous Membranes with Switchable Ionic Selectivity

Ryzhkov

Vyatkin

Mikhlina

2020

Membr. Membr. Technol.

Self Cite

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“…However, the increase in pore radius decreases the effective volume charge (4), thus the pore size effects can still be described by the presented uniform potential (UP) model. Comparison between values of membrane potential between uniform potential (1D) and space charge (2D) models [11,49] shows good agreement, even when the pore radius exceeds the Debye length.…”

Section: Mathematical Modelmentioning

confidence: 84%

Glass/Au Composite Membranes with Gold Nanoparticles Synthesized inside Pores for Selective Ion Transport

Лебедев¹,

Novomlinsky²,

Kochemirovsky³

et al. 2020

Materials

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4Grebenshchikov Institute of Silicate Chemistry (ISCh) RAS, 2 Adm. Makarova emb., St Petersburg 199155, Russia; anfimova-i@mail.ru (I.A.); antr2@yandex.ru (T.A.) Abstract: Nanocomposite membranes have been actively developed in the last decade. The involvement of nanostructures can improve the permeability, selectivity, and anti-fouling properties of a membrane for improved filtration processes. In this work, we propose a novel type of ion-selective Glass/Au composite membrane based on porous glass (PG), which combines the advantages of porous media and promising selective properties. The latter are achieved by depositing gold nanoparticles into the membrane pores by the laser-induced liquid phase chemical deposition technique. Inside the pores, gold nanoparticles with an average diameter 25 nm were formed, which was confirmed by optical and microscopic studies. To study the transport and selective properties of the PG/Au composite membrane, the potentiometric method was applied. The uniform potential model was used to determine the surface charge from the experimental data. It was found that the formation of gold nanoparticles inside membrane pores leads to an increase in the surface charge from −2.75 mC/m 2 to −5.42 mC/m 2 . The methods proposed in this work allow the creation of a whole family of composite materials based on porous glasses. In this case, conceptually, the synthesis of these materials will differ only in the selection of initial precursors.Nanocomposite membranes have been actively developed in the last decade [17]. The involvement of nanostructures can improve the permeability, selectivity, and anti-fouling properties of a membrane for improved filtration processes. One of the most promising approaches to producing such composite materials is the formation of nanoparticles inside the porous structure of a membrane. As with nanotechnology in general [18], there are two main methods [17] for the formation of nanoparticles inside the membranous pores: "top down"-bulk modification through blending (called mixed-matrix membranes) and "bottom up"-surface modification. In the fabrication of bulk-modified nanocomposite membranes, the nanoparticles are dispersed in a homogeneous polymeric precursor solution before the final formation process [19]. However, this method is difficult to use, for example, in the synthesis of inorganic solid membranes. The surface modification technique is the most convenient method in this case [11]. The surface modification technique deals with deposition of nanoparticles onto a membrane.Silicate (high silica) porous glasses (PGs) are channel-type nanostructures [20] with thermal, chemical and microbiological stability, in combination with controlled surface structural characteristics [21][22][23]. Special attention is worth paying to the PG application for the separation of liquid mixtures by reverse osmosis. This method has found application in water desalination, sanitary household water cleaning, water regeneration from vital function products in space, radioactive ...

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Unidimensional Approximation of the Diffuse Electrical Layer in the Inner Volume of Solid Electrolyte Grains in the Absence of Background Ions

Tarabanko

Тaran

2020

ChemPhysChem

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In this paper we continue working on our theory of electrical double layers resulting exclusively from dissociation of a solid electrolyte, which we previously proposed as a medium for catalytic interaction between solid cellulose and solid acid catalysts of hydrolysis. Two theoretical unidimensional models of the inner grain volume are considered: an infinitely long cylindrical pore, and a gel electrolyte near a grain outer surface. Despite the model simplicity, the predictions for the cylindrical pore case are in semi‐quantitative agreement with literature data on electroosmotic experiments, adequately explaining high proton selectivity of sulfonic membranes, and decline of such selectivity at high background acid concentration. The gel model predicts less concentrated diffuse layer in comparison to electrolytes with impenetrable skeleton (e. g., sulfonated carbons). This suggests limited suitability of gel electrolytes as catalysts if a substrate cannot diffuse into the gel bulk and the reaction is thereby spatially limited to the near‐surface region, for example if a substrate is solid like aforementioned cellulose.

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Theory of Ion and Water Transport in Electron-Conducting Membrane Pores with p H-Dependent Chemical Charge

Cited by 19 publications

References 47 publications

Modelling of Conductive Nanoporous Membranes with Switchable Ionic Selectivity

Modelling of Conductive Nanoporous Membranes with Switchable Ionic Selectivity

Glass/Au Composite Membranes with Gold Nanoparticles Synthesized inside Pores for Selective Ion Transport

Unidimensional Approximation of the Diffuse Electrical Layer in the Inner Volume of Solid Electrolyte Grains in the Absence of Background Ions

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