On the electrical double layer theory. I. A numerical method for solving a generalized Poisson—Boltzmann equation

Gur, Y.; Ravina, Israela; Babchin, A.J.

doi:10.1016/0021-9797(78)90368-5

Cited by 41 publications

(19 citation statements)

References 5 publications

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“…The introduction of relationships accounting for the final volume of the ions and the polarization of the solvent would be more exact [51, 67,68]. The net result would be somewhat smaller values for C,.…”

Section: Discussionmentioning

confidence: 99%

Effect of pH and Monovalent Cations on the Ionization State of Phosphatidylglycerol in Monolayers

Lakhdar-Ghazal

Tichadou

Tocanne

1983

European Journal of Biochemistry

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Ionization of the acidic phospholipid phosphatidylglycerol has been studied by measuring the surface potential of monomolecular films of the lipid as a function of the aqueous subphase pH and the concentration of monovalent cations (Li, Na, Cs). It is shown that theexperimental data can be interpreted by means of the Gouy-Chapman theory in its simplest formulation, provided an adsorption of cations at the membrane surface is accounted for. This allows us to predict the ionization state of the lipid for given ionic conditions in the subphase. Above pH 4, for subphase ion concentration higher than 10 mM, or for ion concentrations above 0.1 mM at pH 5.6, phosphatidylglycerol is fully deprotonated. Within the limits of our theoretical approach, association constants of the cations to the lipid lie around 0.1-0.6 M-I.With the exception of phosphatidylcholine and phosphatidylethanolamine which are zwitterions over a large pH range (3 -8) [l], phospholipids in biomembranes are acidic substances bearing a net negative charge when they are ionized. Ionization or protonation of these acidic lipids as well as their interactions with cations can have considerable consequences on both membrane structure and functions.From a structural point of view, changes in the pH or the ionic strength of the aqueous phase have been shown to trigger phase transition of acidic phospholipids [2-111. The bivalent cations Mg2+ and Ca2+ can bring about phase separation within mixtures of zwitterionic and acidic phospholipids [12-191. Cations can also modify the dynamic properties of lipids, i.e. their lateral diffusion rate [20], as well as being able to promote morphological changes [21]. As an example, cardiolipin, which normally exists in a lamellar phase in the presence of sodium, adopts the hexagonal H,, phase in the presence of calcium [22, 231. Dipalmitoylglycerophosphoglycerol, which normally stays in a lamellar phase in the presence of sodium, has been shown to exist in an interdigitated phase in the presence of the organic cations choline and acetylcholine [24].From a functional point of view, phospholipids can modulate the activity of membrane enzymes by monitoring, at the membrane surface, a concentration of protons, cations and of any charged metabolites which is quite different from that existing in the bulk [25]. Charges at the membrane surface also contribute to the establishment of transmembrane potentials which are involved in energy-linked transmembrane transport processes [26] and which are postulated to monitor the orientation [27 -291 and the activity of certain membrane proteins [28 -341.For all these reasons, it is of great importance to have a full understanding of the ionization process of acidic phospholipids in membrane systems. This would allow a correct prediction of their ionization state and of the surface potential they generate, for given ionic conditions in the aqueous phase. As a first approach, ionization of phosphatidylglycerol was studied in monolayers by measuring changes in film surface pressure again...

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Section: Discussionmentioning

confidence: 99%

Effect of pH and Monovalent Cations on the Ionization State of Phosphatidylglycerol in Monolayers

Lakhdar-Ghazal

Tichadou

Tocanne

1983

European Journal of Biochemistry

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“…The first exponential term describes electrostatic forces acting on the ions. The second term accounts for additional forces due to the existence of gradients in the dielectric constant, which Gur et al (1978b) approximated with a Born hydration model. The hydration term can also be viewed as an activity coefficient for ionic species in the pore, as described by Hodgson (1970) in his analysis of reverse-osmosis cellulose acetate membranes.…”

Section: Nj = R T~~mentioning

confidence: 99%

“…Because of the symmetric nature of the electric field about the pore centerline, to is equal to the free-solution solvent dielectric constant. The total potential of each ion is modified to include the standard electrostatic forces and forces due to ionic hydration (Gur et al, 1978b). Variations in the dielectric constant of pore solvent affect the hydration properties of the electrolyte.…”

Section: Nj = R T~~mentioning

confidence: 99%

Development of a space‐charge transport model for ion‐exchange membranes

et al. 1990

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A two-dimensional, electrokinetic transport model that incorporates ionic hydration, orientation of solvent molecules by an applied electric field, and solvent dipole-dipole interactions is developed. The model is used to simulate equilibrium and transport experiments for perfluorosulfonic acid membranes containing aqueous alkali metal sulfate solutions. The membrane is modeled as an array of cylindrical pores. Solution of the mathematical model requires that the membrane porosity, water partition coefficient, coion partition coefficient, water diffusion coefficients, and coion and counterion diffusion coefficients be known. Membrane coion and counterion diffusion coefficients were determined from free solution equivalent conductance data. All other parameters were determined experimentally for a Nafion (of E. I. du Pont de Nemours Inc.) cation-exchange membrane and five 0.1 M alkali metal sulfate solutions. Experimental radiotracer data for coion absorption as well as for coion and water transport are compared with theoretical predictions to test the accuracy of the model.

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“…It should be noted thatEquation5 is a special solution [40] of the Poisson-Boltzmann equation, which generally describes the charge density of a double layer [41]. Please note that Equation 4 should be simultaneously solved with the continuity equation of Equation 3.…”

Section: Electric Field-affected Flowsmentioning

confidence: 99%