Ion-penetrable Charged Membrane Research Articles

Effect of Ionic Size on the Deposition of Charge-Regulated Particles to a Charged Surface

The deposition of charge-regulated particles to a rigid, planar charged surface is modeled theoretically, taking the effects of the excluded area arising from deposited particles and finite ionic sizes into account. Here, a particle comprises a rigid core and an ion-penetrable charged membrane layer, which represents a general type of particle. If the membrane layer has a negligible thickness, the particle simulates a regular inorganic particle, and if the membrane layer has a finite thickness, it simulates biocolloids such as cells. The results of numerical simulation reveal that the rate of particle deposition is faster under the following conditions: (1) lower potential of the planar surface, (2) thicker membrane, (3) higher counterion valance, (4) lower fixed charge density, (5) smaller counterions, (6) larger co-ions, (7) larger functional group, and (8) lower pH. Neglecting the sizes of ionic species may lead to an appreciable deviation in both the electrical repulsive force between particle and surface and the rate of deposition. Typical deviation for the former is approximately 20%, and that for the latter is approximately -75%.

Effects of sizes of charged species on the flocculation of biocolloids: Absorption of cations in membrane layer

The rate of flocculation of suspended biocolloidal particles each covered with an ion-penetrable charged membrane immersed in an electrolyte solution is investigated theoretically. We take into account the effects of sizes of charged species, including cations, anions, and functional groups in the membrane layer, where the absorption of cations by the functional groups leads to the variations in fixed charge density of the membrane phase of a biocolloid. The simulated results reveal that the sizes of cations, anions, and fixed groups have negative effect on the rate of biocolloidal flocculation for an originally negatively charged membrane (ONCM), and the classical point-charge model overestimates this rate. The discrepancy between an ONCM and an originally uncharged membrane (OUCM) for the time required for flocculation increases with the number of functional groups involved in the absorption or chelation of mobile cations. The rate of flocculation produced by an OUCM is faster than that by an ONCM under the same conditions. For an ONCM, the stronger the effect of the cationic absorption by the functional groups, the faster the rate of flocculation, and the reverse is true for an OUCM. Comparing with an OUCM, the effects of membrane thickness, concentration of functional groups, ionic strength of the bulk liquid and relative permittivity of the solution on the variations of flocculation time ratio are more considerable for an ONCM. A thicker membrane, a lower concentration of functional groups, a higher ionic strength of the bulk liquid and a larger relative permittivity of the solution cause a faster rate of flocculation.

Effect of Ionic Sizes on the Electrokinetic Flow in a Planar Slit Covered by an Ion-Penetrable Charged Membrane

The electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane in an a:b electrolyte solution, taking the effect of the sizes of charged species into account, is analyzed theoretically. The electrokinetic properties such as volumetric flow rate, total electric current, and streaming potential of the system under consideration are evaluated. The influences of the key parameters, which include the frictional coefficient of the membrane layer, membrane thickness, ionic strength, valence of counterions, fixed charge concentration, and sizes of cations and anions, are discussed. We demonstrate the importance of the steric ionic effects by showing that a substantial difference between the classic point-charge model and the present model.

Interactions between a Particle Covered by an Ion-Penetrable Charged Membrane and a Charged Surface: A Modified Gouy−Chapman Theory

The interaction between a colloidal particle and a surface plays an important role in various interfacial phenomena in both industrial and biological processes. Previous efforts are mainly based upon a point-charge model where the effect of the sizes of all the charged species is neglected. Here, we consider the case where a particle is covered by an ion-penetrable charged membrane, which mimics a biological entity, by taking this effect into account. We show that the sizes of the charged species are in the estimation of the electrical interaction force between particle and surface; the general trend of the result obtained is consistent with the experimental observations reported in the literature. The effects of the following key factors on the energy barrier for the particle−surface interaction are examined: the surface potential, the fixed charge density and the thickness of membrane layer, and the sizes of charged species.

Electrokinetic Flow of an Electrolyte Solution in a Rectangular Microchannel Covered by an Ion-Penetrable Charged Membrane

The electrokinetic flow of an electrolyte solution in a rectangular microchannel is investigated theoretically. The present analysis extends previous results in that a two-dimensional problem is considered and the wall of the microchannel is covered by an ion-penetrable charged membrane layer; the latter simulates a biological system. The electroosmotic flow rate and total electric current, the electroviscous effect, and the streaming potential of the system under consideration are evaluated. We show that the variations of these quantities as a function of the aspect ratio of the microchannel may have a local minimum or a local maximum at a medium level of ionic strength, which depends on the thickness of the membrane layer. Some phenomena, which are predicted by the corresponding bare-wall model, may not be observed in the present case. For example, the variation of the electroviscous effect as a function of the electrokinetic radius may not have a local maximum.

Electrical interaction between two cylinders with an ion-penetrable charged membrane in an oil/water interface

The electrical interaction between two long, parallel cylinders each is covered by an ion-penetrable charged membrane immersed in an oil/water interface is investigated. The effects of contact angle, radius of cylinder, and membrane thickness on the electrical interaction force are examined. The results of numerical simulation reveal that the following conditions lead to a greater electrical interaction force: (i) a larger contact angle, i.e. a larger fraction of a cylinder in the oil phase; (ii) a larger cylinder radius; and (iii) a thinner membrane. For a fixed ionic strength, the electrical interaction force is insensible to the type of electrolytes in the water phase, in general. However, if two cylinders are close enough, then the higher the valence of counterions the greater the electrical interaction force.

Electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane.

The electrokinetic flow of an electrolyte solution in a planar slit covered by an ion-penetrable charged membrane layer is analyzed theoretically. An approximate analytical expression for the spatial variation in the electrical potential is derived, and the electroosmotic velocity, the total electric current, and the streaming potential of the system under consideration are evaluated. The effects of epsilon' (relative permittivity of liquid phase/relative permittivity of membrane layer), eta' (viscosity of liquid phase/viscosity of membrane layer) and the valence of anions (coions) on the volumetric flow rate and total current are examined. We show that the effect of the valence of cations (counterions) on the volumetric flow rate is less significant than that of epsilon' and that of eta'. However, the effect of epsilon' on the total current is less significant than that of the valence of cations and that of eta'. The variation of total current as a function of ionic strength is found to have a local minimum, regardless of whether a pressure gradient is applied or not. The absolute streaming potential has a local maximum as the concentration of fixed charge varies, which was not found in previous studies.

Electrical Interactions between Two Ion-Penetrable Charged Membranes: Effect of Sizes of Charged Species

A diffuse double-layer model for evaluation of the electrical interactions between two particles each covered by an ion-penetrable charged membrane in an electrolyte solution is proposed by taking the sizes of charged species into account. We show that the ionic sizes have a significant effect on the electrical interaction force between two particles. For constant fixed charge density, the corresponding point charge model will underestimate the interaction force, and the reverse is true for constant membrane potential. The deviation due to the assumption of point charges is more serious for constant fixed charge density than that for constant membrane potential. It is found that the smaller the counterions, the greater the interaction force, and the reverse is true for co-ions.

Double-Layer Properties of an Ion-Penetrable Charged Membrane: Effect of Sizes of Charged Species

In this paper we have proposed a double-layer model, which takes the sizes of the charged species into account, for an ion-penetrable charged membrane immersed in an electrolyte solution. Analytical expressions for the electrical potential distribution, the potential drop across the membrane, and the net penetration charge into the membrane are derived for the case in which the linearized Gouy-Chapman model is employed. We will show that, if charged species have different sizes, the behavior of a positively charged membrane is unsymmetrical to that of a negatively charged membrane. Also, the larger the counterions, the greater the potential drop across a membrane and the smaller the net penetration charge into a membrane; the reverse is true for co-ions.

Modified Göuy–Chapman theory for an ion-penetrable charged membrane

The classic Göuy–Chapman theory is modified to describe the electrical potential distribution in an ion-penetrable charged membrane by taking the sizes of the charged species into account. We show that for a negatively charged membrane, if the density of fixed charge is low, a reverse in electrical potential may occur if cations are smaller than both anions and fixed groups. Also, only one plane of zero charge (PZC) exists. If a membrane is positively charged, there may exist zero to two PZC, depending upon the fixed charge density and the relative magnitudes of anions and fixed groups. Under a critical condition determined mainly by the sizes of the charged species, a unique PZC exists in the inner plane of fixed charge. The present model is capable of explaining why microorganisms can adjust the degree of dissociation of the ionogenic groups in their cell membranes to absorb nutritive ingredients and to shun toxic species by fluctuations in the extent to which specific ions penetrate the membranes.

Electrical interaction between two spherical particles covered by an ion-penetrable charged membrane

The electrical interaction between two spherical particles, each comprises a rigid uncharged core and an ion-penetrable (porous) charged membrane, in an electrolyte solution is examined. The Poisson equation governing the spatial variation of electrical potential is solved by the Green's function approach, and the interaction energy of the system under consideration evaluated. Several approximate analytical expressions for the interaction energy are derived. We show that if the membrane is thick, and/or the electrical double layer is either very thin or very thick, a particle can be treated as a porous one, and the linear superposition approach often adopted in the literature becomes appropriate.

The Stability Ratio for a Dispersion of Particles Covered by an Ion-Penetrable Charged Membrane

The electrostatic interaction between two particles covered by an ion-penetrable charged membrane suspended in ana:belectrolyte solution is estimated. A perturbation method is employed to solve the governing nonlinear Poisson–Boltzmann equation. The approximate analytical expression derived for potential distribution yields a sufficiently accurate estimate. Both the stability ratio and the critical coagulation concentration of the counterions of the system under consideration are derived. The results of a numerical simulation reveal that the stability ratio decreases with an increase in the size of a particle and increases with the total amount of fixed charges in the membrane phase. For a constant total amount of fixed charges and particle size, the stability ratio increases with a decrease in the thickness of the membrane. We show that monodispersed particles are more stable than polydispersed particles.

The Electrostatic Interaction Force between a Charge-Regulated Particle and a Rigid Surface

The electrostatic interaction force between a charge-regulated particle covered by an ion-penetrable charged membrane and a rigid charged surface immersed in a mixed (a:b) + (c:b) electrolyte solution is analyzed. The membrane contains both acidic and basic functional groups, and a general form for each is assumed which allows multiple proton transfer among functional groups. The rigid surface is negatively charged, and the net charges carried by the particle is also negative. We show that if the separation distance between the particle and the surface is greater than a critical value, the multivalent cations present in the liquid phase have the effect of reducing the repulsion force between the particle and the surface. The reverse is true if the separation distance is smaller than the critical value. For a constant total number of functional groups in the membrane phase, if the membrane is sufficiently thin, the variation of repulsion force as a function of separation distance exhibits a maximum.

Electrostatic interactions between particles with an ion-penetrable charged membrane

The electrostatic interactions between spherical particles suspended in an electrolyte solution is analyzed. The surfaces of these particles are coated with an ion-penetrable membrane, which bears nonuniformly distributed fixed charges. We consider two classes of fixed charge distributions; these distributions all yield the same amount of total fixed charges in the membrane phase. The exact solution to the governing Poisson–Boltzmann equation is derived for the case the potential of the system under consideration is low. Based on this solution, the stability ratio and the critical coagulation concentration of a dispersed system are estimated.

Electrophoretic Mobility of a Particle Coated with a Charged Membrane: Effects of Fixed Charge and Dielectric Constant Distributions

The electrophoretic mobility of a particle coated with an ionpenetrable charged membrane in a uniform electric field is investigated. In particular, the effects of the distribution of fixed charges and that of the dielectric constant in the membrane phase on the electrophoretic mobility are investigated. The results of numerical simulation reveal that these effects can be significant. In particular, for a constant total amount of fixed charges, assuming a homogeneous fixed charge distribution may lead to an appreciable deviation.

Solution to the Poisson–Boltzmann equation for particles covered by an ion-penetrable charged membrane

The Poisson-Boltzmann equation governing the distribution of electrical potential of a planar, cylindrical or spherical particle covered by a charged, ion-penetrable membrane immersed in an a : b electrolyte solution has been analysed. Approximate analytical expressions for the distribution of electrical potential as well as its derivative have been derived. The former is readily applicable for the evaluation of the total free energy of the system under consideration. We have shown that in the limiting case, the present result reduces to that for a rigid, charged-surface model.

Approximate Analytical Expressions for the Properties of a Double Layer with Asymmetric Electrolytes: Ion-Penetrable Charged Membranes

The Poisson equation describing the electrostatic potential distribution for a planar geometry with asymmetric electrolytes in the liquid phase is analyzed. In particular, an ion-penetrable charged membrane is considered. Typical examples in practice include biological cells and some artificial membranes. An approximate analytical solution to the nonlinear Poisson equation is derived, and explicit expressions for the properties of the double layer including surface excess of co-ions, Helmholtz free energy, and entropy are presented. The results of numerical simulation reveal that the present approximate results provide reasonably accurate estimations for both the electrostatic potential distribution and the relevant thermodynamic properties of the system under consideration.

Effect of Dielectric Constant on the Electrostatic Interactions between Two Ion-Penetrable Charged Membranes

The electrostatic interactions between two ion-penetrable charged membranes are investigated theoretically. In particular, the effect of the difference in the dielectric constant of bulk solution and that of membrane on potential distribution and electrostatic force are discussed. We conclude that the difference between these two dielectric constants has a significant effect on both the potential distribution and the electrostatic force; assuming that these dielectric constants are equal, as in the previous studies, may lead to a significant deviation from the exact result.

Electrostatic Interactions between Two Ion-Penetrable Charged Membranes

The electrostatic interactions between two ion-penetrable charged membranes are investigated theoretically. Here, the effect of Donnan potential on the electrostatic repulsion between two membranes, and the potential and pH distributions across a membrane are investigated. The present analysis extends those of H. Ohshima and T. Kondo ( J. Theor. Biol. 124, 191 (1987) and J. Theor. Biol. 128, 187 (1987)) in that the fixed charges are distributed nonuniformly across a surface layer of the membrane. We show that the distribution of the fixed charges in the surface layers of two ion-penetrable membranes has a significant effect on their electrostatic interactions. Thus, assuming that the fixed charges are homogeneously distributed in the surface of a membrane may lead to a serious deviation.

Additivity of unperturbed potentials from two interacting ion-penetrable charged membranes

Additivity of unperturbed potentials from two interacting ion-penetrable charged membranes