Electromotive force and impedance studies of cellulose acetate membranes: Evidence for two binding sites for divalent cations and for an alveolar structure of the skin layer

Sørensen, Torben Smith; Jensen, Jørgen Birger; Malmgren-Hansen, Bjørn

doi:10.1016/0011-9164(91)85164-p

Cited by 16 publications

(16 citation statements)

References 41 publications

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“…2 mV was found in ref 6. Many membranes designed for water desalination of purification seems to act by the principle of ion exclusion by a dense, polymeric layer with a low dielectric constant, and ions of higher valencies are excluded to a much higher degree than monovalent ions, because the free energy of charging of the ions depends quadratically on the ion charge and is inversely proportional to the dielectric permittivity of the medium. 25,26 The present paper suggests that the fixed charge can be used as another mechanism for retention of ions, especially those of higher valencies. In cellulose acetate membranes for reverse osmosis for example, a compromise is made to produce the highest possible salt rejection in the dense skin layer without lowering the water permeability too much; see the articles by Merten, Loeb, and Lonsdale in ref 27.…”

Section: Conclusion and Discussionmentioning

confidence: 96%

Salt Flux and Electromotive Force in Concentration Cells with Asymmetric Ion Exchange Membranes and Ideal 2:1 Electrolytes

Sørensen¹,

Compañ

1996

J. Phys. Chem.

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The previously proposed Nernst-Planck-Donnan description (J. Phys. Chem. 1996, 100, 7623) of the salt flux and the emf in concentration cells with asymmetric ion exchange membranes is generalized to encompass ideal 2:1 electrolytes (doubly charged cation and singly charged anion). Any point in the membrane may be considered to be in Donnan equilibrium with a given external salt concentration. The profile of this salt concentration through the membrane determines the ion concentrations, the local salt flux, the profile of electric field strength, and the immediate value of the emf. The Donnan potential and ion distribution are found as the unique, positive and real root of a third-degree polynomial. In this paper we focus on the stationary state rather than the initial state. For this purpose, the stationary state nonlinear differential equation for the salt concentration profile is solved numerically by the "shooting method". We consider salt concentration profiles, ion concentration profiles, and field strength profiles in three different cases: (1) a very weak cation exchange membrane (VWC), (2) a weak anion exchange membrane (WA), and (3) a strong anion exchange membrane (SA). The membranes are asymmetric with spatial dependence of the Nernst distribution coefficient for the salt, of the fixed charge density, and of the ion diffusion coefficients. We study both directions of stationary flow through the membranes. The emf is a functional of the salt concentration profile and is found by numerical integration. The overall behavior of the VWC is almost Fickian with respect to diffusion of salt in both direction, and there is practically no diffusion asymmetry. However, there may be considerable differences in the stationary state emf values for the two directions of diffusion. The WA is close to Fickian for the diffusion in one direction, but strongly non-Fickian with reversed diffusion flux. There is a large diffusion and emf asymmetry for stationary state diffusion in the two directions for large differences of concentration. The order of magnitude found for the calculated stationary state emf asymmetry corresponds to observed values for various membranes. The SA is strongly non-Fickian, but there is practically no diffusion asymmetry. The SA is almost an ideal anion exchange membrane because of the Donnan exclusion from the membrane of the doubly charged cation. Thus, the emf measured with electrodes reversible to the anion should be zero, and so it is found within numerical uncertainty.

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Section: Conclusion and Discussionmentioning

confidence: 96%

Salt Flux and Electromotive Force in Concentration Cells with Asymmetric Ion Exchange Membranes and Ideal 2:1 Electrolytes

Sørensen¹,

Compañ

1996

J. Phys. Chem.

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“…Electrolyte sorption and nonuniform charge distribution in the membrane may be responsible for the deviations to the Donnan equilibrium, and a correction of the membrane electrolyte activity coefficients can be made to take these effects into account . In fact, an important assumption often used is to consider the ions activity coefficients independent of the ionic concentration and equal to unity on the grounds that the membranes are swollen in water. ,− For hydrophilic membranes the ratio of the activity coefficients, γ A γ C /γ ± 2 , can be made equal to unity . The errors due to these approaches are incorporated in the determination of the membrane charge density .…”

Section: Theorymentioning

confidence: 99%

“…The errors due to these approaches are incorporated in the determination of the membrane charge density . The correction of the activity coefficients only appears to be important for concentrations higher than 0.5 M …”

Section: Theorymentioning

confidence: 99%

Mass Transfer Modeling for Salt Transport in Amphoteric Nanofiltration Membranes

and¹,

Pinho²

1998

Ind. Eng. Chem. Res.

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The mass transfer in the tangential turbulent flow inside a nanofiltration tubular membrane is described by a modified eddy diffusivity model, which accounts for the effect of high permeation fluxes on the mass transfer rates through a permeation Reynolds number. The correlation achieved for the polarization modulus in this situation is C = exp(0.162Re p 0.93 Re -0.29 Sc 2/3). The ionic transport in the membrane active layer is described through the extended Nernst−Planck equations and the Donnan equilibrium at the membrane-solution interfaces. The active layer of the nanofiltration membrane is made of an amphoteric polymer containing quaternary amine and sulfonic acid groups. In the experiments of permeation of sodium chloride solutions, the Reynolds number ranges from 9.6 × 103 to 1.1 × 105, the pressure from 10 to 25 bar, and the feed concentration from 1.8 to 193 mol/m3. A good agreement is observed between the experimental and the calculated permeation fluxes and the salt rejections. The membrane effective charge depends on the feed concentration upon the relationship ln C M (mol/m3) = 4.14 + 0.527 ln C S f (mol/m3).

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“…At lower external concentrations, enhancing moreover electrostatic exclusion, becomes smaller. In the regions x Ͻ Ϫ2r i and x Ͼ l s ϩ 2r i , the W i ( x) profile including ion shielding is described by the Onsager-Samaras theory (14), which can be applied to the present system (15). For these parts of the profile, we find for c ϭ 0.1 M and ϭ 0.10 Å Ϫ1 indeed deviations from the predictions for W i ( x) according to Neumcke and Läuger.…”

Section: Influence Of Ion Shielding On the Image Force Potential W I (X)mentioning

confidence: 74%

Theoretical and Experimental Study of the Voltage–Current Characteristic of an Asymmetric Cellulose Acetate Membrane

Hijnen

Smit

1999

Journal of Colloid and Interface Science

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Electromotive force and impedance studies of cellulose acetate membranes: Evidence for two binding sites for divalent cations and for an alveolar structure of the skin layer

Cited by 16 publications

References 41 publications

Salt Flux and Electromotive Force in Concentration Cells with Asymmetric Ion Exchange Membranes and Ideal 2:1 Electrolytes

Salt Flux and Electromotive Force in Concentration Cells with Asymmetric Ion Exchange Membranes and Ideal 2:1 Electrolytes

Mass Transfer Modeling for Salt Transport in Amphoteric Nanofiltration Membranes

Theoretical and Experimental Study of the Voltage–Current Characteristic of an Asymmetric Cellulose Acetate Membrane

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