Electrostatic interaction between an ion-penetrable sphere and an ion-impenetrable sphere

The exact expression for the electrostatic interaction between an ionpenetrable sphere and an ion-impenetrable rigid sphere is derived on the basis of the linearized Poisson-Boltzmann equation without recourse to Derjaguin's approximation.     

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.     

Electrostatic interaction between a cylinder and a planar surface

 An exact analytical expression for the potential energy of the electrostatic interaction between a plate-like particle 1 and a cylindrical particle 2 of radius a ₂ immersed in an electrolyte solution of Debye–Hückel parameter κ is derived on the basis of the linearized Poisson–Boltzmann equation without recourse to Derjaguin's approximation. Both particles may have either constant surface potential or constant surface charge density. In the limit of κa ₂→0, in particular, the interaction between a plate with zero surface charge density and a cylinder having constant surface charge density becomes identical to the usual image interaction between a line charge (a charged rod of infinitesimal thickness) and an uncharged plate. Received: 22 September 1998  Accepted in revised form: 27 January 1999     

Electroosmotic velocity in an array of parallel soft cylinders in a salt-free medium

A theory of electroosmosis in an array of parallel soft cylinders (i.e. polyelectrolyte-coated cylinders) in a salt-free medium is presented. It is shown that there is a certain critical value of the particle charge and that if the particle charge is greater than the critical value, then the electroosmotic velocity becomes constant independent of the particle charge due to the counterion condensation effects, as in the case of other electrokinetic phenomena in salt-free media.     

Electrostatic interaction of ion-penetrable membranes. Effects of ionic solubility

An analytic, approximate expression for the electrostatic interaction between two membranes immersed in an electrolyte solution is derived on the basis of a simple membrane model. This model assumes that the membrane has a surface layer in which charged groups are uniformly distributed and that electrolyte ions can penetrate into the surface layer. The partition coefficients of cations and anions between the solution and the surface layer, which are related to their solubilities in the surface layer, may be different from unity.The electrostatic interaction depends on the ionic partition coefficients between the solution and the surface layer, and the relative permittivity of the surface layer, as well as on the membrane-fixed charges, the electrolyte concentration in the solution, and the surface layer thickness. It is shown, in particular, that even where the charge layer has no fixed charges, the electrostatic interaction force can be produced if the solubilities of cations and anions are different in the surface layer.     

Electrostatic interaction between two parallel cylinders

Explicit exact analytic expressions are obtained for the electric potential distribution and for the electrostatic interaction energy for the system of two parallel dissimilar cylinders in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation.     

Potential distribution around a charged spherical colloidal particle in a medium containing its counterions and a small amount of added salts

A theory is developed for the potential distribution around a charged spherical colloidal particle carrying ionized groups on the particle surface in a medium containing its counterions (i.e., counterions produced from dissociation of the particle surface groups) and a small amount of added salts on the basis of the theory of Imai and Oosawa. Numerical solutions to the Poisson–Boltzmann equation for the potential distribution are obtained for the case of dilute (but not infinitely dilute) particle suspensions of volume fraction 1 for a1 (where is the Debye–Hückel parameter and a is the particle radius). Here we have taken into account the effects of (i) counterions from the particle surface groups, and (ii) the finite particle volume fraction. These effects, which are usually neglected in the conventional Poisson–Boltzmann equation, are found to be important. It is found that, as in the case of completely salt-free media, there is a certain critical value of the particle charge (which is the same as that for the completely salt-free case). When the particle charge is lower than the critical value, the potential is given by a Coulomb potential. If the particle charge is higher than the critical value, then counterions are accumulated in the vicinity of the particle surface (counterion condensation) and the potential becomes less dependent on the particle charge. The above behaviors can be observed even for the case where the electrolyte concentration is higher than the concentration of counterions from the particle surface groups, if the conditions 1 and a1are both satisfied.     

Electrostatic interaction between a charge-regulated particle and a solid surface in electrolyte solution: effect of cationic electrolytes

The effect of cations on the electrostatic interaction between a negative charge-regulated particle and a solid surface of constant negative potential in electrolyte solution is analyzed. Here, we assume that the rate of approach of a particle to a solid surface is faster than that of the dissociation of the ionogenic groups on the surface of particle. In other words, the effect of the time-dependent dissociation of ionogenic groups on the surface of a particle is taken into account. The result of the present study reveals that, although the solid surface is negatively charged, the presence of cations in the suspension medium has a negative effect on the rate of adhesion. The qualitative behaviors in the variation of the interaction force between a particle and a solid surface as a function of separation distance between them predicted by a kinetic model and the corresponding equilibrium model and constant charge density model are entirely different. The rate of approach of a particle to a solid surface is on the order (constant charge density model)>(kinetic model)>(equilibrium model).     

Electrokinetic flow in an elliptic microchannel covered by ion-penetrable membrane

The electrokinetic flow of an electrolyte solution in an elliptical microchannel covered by an ion-penetrable, charged membrane layer is examined theoretically. The present analysis extends previous results in that a two-dimensional problem is considered, and the system under consideration simulates the flow of a fluid, for example, in a microchannel of biological nature such as vein. The electroosmostic volumetric flow rate, the total electric current, the streaming potential, and the electroviscous effect of the system under consideration are evaluated. We show that, for a constant hydraulic diameter, the variations of these quantities as a function of the aspect ratio of a 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. For a constant cross-sectional area, the electroosmostic volumetric flow rate, the total electric current, and the streaming potential increase monotonically with the increase in the aspect ratio, but the reverse is true for the electroviscous effect.     

Electrokinetic flow and electric conduction of salt-free solutions in a capillary

The electrokinetic flow and accompanied electric conduction of a salt-free solution in the axial direction of a charged circular capillary are analyzed. No assumptions are made about the surface charge density (or surface potential) and electrokinetic radius of the capillary, which are interrelated. The Poisson–Boltzmann equation and modified Navier–Stokes equation are solved for the electrostatic potential distribution and fluid velocity profile, respectively. Closed-form formulas for the electroosmotic mobility and electric conductivity in the capillary are derived in terms of the surface charge density. The relative surface potential, electroosmotic mobility, and electric conductivity are monotonic increasing functions of the surface charge density and electrokinetic radius. However, the rises of the relative surface potential and electroosmotic mobility with an increase in the surface charge density are suppressed substantially when it is high due to the effect of counterion condensation. The analytical prediction that the electroosmotic mobility grows with increases in the surface charge density and electrokinetic radius agrees with the experimental results for salt-free solutions in circular microchannels in the literature.     

Electrostatic interaction effect for human DNA separation with functionalized mesoporous silicas

This work describes the development of highly efficient human DNA separation with functionalized mesoporous silica (FMS) materials. To demonstrate the electrostatic interaction effect between the target DNA molecules and FMS, three aminofunctionality types comprised of a mono-, a di-, and a tri-amine functional group were introduced on the inner surfaces of mesoporous silica particles. Systematic characterization of the synthesized materials was achieved by solid-state ²⁹Si and ¹³C-NMR techniques, BET, FT-IR, and XPS. The DNA separation efficiency was explored via the function of the amino-group number, the amount used, and the added NaCl concentration. The DNA adsorption yields were high in terms of the use of triaminofunctionalized FMS at the 10 ng/L level, and the DNA desorption efficiency showed the optimum level at over 3.0 M NaCl concentration. The use of FMS in a DNA separation process provides numerous advantages over the conventional silica-based process.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Approaches to separation interfaces: Electrostatic interaction and local structures of ions at zwitterionic interface

The interaction and separation of ions with zwitterionic layers are reviewed principally based on a series of the author's work. An electrostatic model has allowed us to discuss the chromatographic retention of ions on the zwitterionic stationary phase, and has revealed the ionic interaction occurring at the zwitterionic interface. Similar consideration is applicable to the ionic partition into zwitterionic micelles having the spherical dimension. In the electrostatic models, ion association and solvation changes of ions have been assumed to explain the selectivity in ion recognition. Both assumptions are applicable to polarizable large ions, whereas the former cannot account for the results obtained for small and well-hydrated ions (Cl⁻ and Br⁻). A special X-ray absorption finestructure (XAFS) measurement, which allows selective access to ions interacting with surface monolayers, has been developed, and applied to ions attracted by a zwitterionic monolayer. The X-ray absorption spectra suggest that Zn²⁺ attracted by the zwitterionic monolayer is still hydrated. In contrast, the direct interaction of Br⁻ has been confirmed, indicating that the electrostatic model involving either ion association or the solvation change of an ion does not properly explain the observed phenomena but both effects should be taken into consideration.     

Calculation of electrostatic interaction forces between ellipsoidal particles

An analytical expression is presented for describing the electrostatic interaction forces between various shaped particles having mutual orientations. The expression is derived by applying the surface integration method, which is a generalization of the Derjaguin summation procedure. Based on previous theoretical considerations it is possible to calculate the electrostatic interaction force between regularly shaped bodies (both convex or concave in the vicinity of their contact point) by multiplying the interaction energy derived for paralled plates with the corresponding geometric factor. The forces acting between two equal shaped ellipsoids are described and discussed, considering three different limiting orientations, the parallel, the perpendicular, and the contact of the edges' orientation.     

Interaction between an ion-penetrable particle and a solid particle. 1. Electrical double-layer interaction

Expressions are derived for the force and potential energy of the electrical double layer interaction between two parallel plates of different nature, i. e., an ion-penetrable plate and an ion-impenetrable plate. The latter may have either constant surface potential or constant surface charge density. It is shown that when the ion-impenetrable plate has a constant surface potential, the interaction force may, under certain conditions, become attractive even if the surface potentials of the two plates at infinite separation are of the same sign. In contrast, when the ion-impenetrable plate has a constant surface charge density, the interaction force may, under certain conditions, become repulsive even if the two plates at infinite separation are of opposite sign. This means that an ion-penetrable plate shows a dual behavior. That is, under certain conditions, it behaves like a solid plate with constant surface potential or surface charge density, depending on whether it interacts with a solid plate having a constant surface potential or a constant surface charge density.     

Resolution enhancement in hydrophobic interaction chromatography via electrostatic interactions

In this work, a new type of hydrophobic stationary phase that provide electrostatic interactions with analytes was developed by bonding β-phenylethylamine as a functional ligand to silica. This stationary phase can separate proteins with similar hydrophobicity that traditional hydrophobic resins cannot. Hen egg white was separated to examine the selectivity. The results show that the introduced electrostatic interactions are an important factor for the resolution enhancement and the new resin could have important applications in separation and purification of biological macromolecules.     

Impact of Electrostatic Interaction on Non-radiative Recombination Energy Losses in Organic Solar Cells Based on Asymmetric Acceptors

Reducing non-radiative recombination energy loss (ΔE₃) is one key to boosting the efficiency of organic solar cells. Although the recent studies have indicated that the Y-series asymmetric acceptors-based devices featured relatively low ΔE₃, the understanding of the energy loss mechanism derived from molecular structure change is still lagging behind. Herein, two asymmetric acceptors named BTP-Cl and BTP-2Cl with different terminals were synthesized to make a clear comparative study with the symmetric acceptor BTP-0Cl. Our results suggest that asymmetric acceptors exhibit a larger difference of electrostatic potential (ESP) in terminals and semi-molecular dipole moment, which contributes to form a stronger π–π interaction. Besides, the experimental and theoretical studies reveal that a lower ESP-induced intermolecular interaction can reduce the distribution of PM6 near the interface to enhance the built-in potential and decrease the charge transfer state ratio for asymmetric acceptors. Therefore, the devices achieve a higher exciton dissociation efficiency and lower ΔE₃. This work establishes a structure-performance relationship and provides a new perspective to understand the state-of-the-art asymmetric acceptors.     

Electrostatic effects in enzyme catalysis: a quantum mechanics/molecular mechanics study of the nucleophilic substitution reaction in haloalkane dehalogenase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations have been carried out to study the cleavage of the carbon–chlorine bond in 1,2-dichloroethane catalysed by haloalkane dehalogenase from Xanthobacter Autotrophicus GJ10. The process has been compared with an adequate counterpart in aqueous solution, the nucleophilic attack of acetate anion on 1,2-dichloroethane. Within the limitations of the model, mainly due to the use of a semiempirical Hamiltonian, our results reproduce the magnitude and characteristics of the catalytic effect. Comparisons of the enzymatic and in solution potentials of mean force reveal that, irrespective of the reference state, the enzyme shows a larger affinity for the transition state. The origin of this increased affinity is found in the differences in the electrostatic pattern created by the environment in aqueous solution and in the enzyme.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Electrostatic self-assembly of quaternized 2,(3)-tetra(oxo-pyridine) phthalocyaninato chloroindium(III) with a series of tetrasulfonated phthalocyanines

The self-assembly of oppositely charged phthalocyanines, fabricated using quaternized 2,(3)-tetra(oxo-pyridine) phthalocyaninato chloroindium (III) (QInPyPc) as the positively charge molecule and a series of tetrasulfonate phthalocyanine (MTSPc), M = 2H, Mn, Fe, Co and Ni as negatively charged molecules are reported. The self-assembly results in the formation of heteroaggregates. The metallated sulfonated phthalocyanines form nanorod and nanoleaf shaped structures as evidenced by transmission electron microscopy (TEM). The UV–Vis spectra showed blue shifted Q bands, suggesting that these structures were in a face-to-face arrangement. The Raman spectra of the heteroaggregates showed shifting compared to the spectra of the precursors.     

纳米雄黄与脂质体仿生膜的相互作用研究

本工作以卵磷脂与胆固醇组成的磷脂小单层脂质体（small unilamelarvesicles,suv）作为仿生膜的简单模型,采用表面等离子共振技术（SPR）、荧光偏振、拉曼（Raman）光谱、核磁共振（NMR）及原子力显微镜（AFM）研究纳米雄黄与SUV仿生膜的相互作用,证实了磷脂是纳米雄黄作用的关键靶分子．随纳米雄黄结合,SUV仿生膜的相对粘度聃值增大,膜的流动性减小．Raman光谱数据计算表明,作用后膜的纵向有序性参数s。。及横向有序性参数Slat值增大,说明纳米雄黄的结合使磷脂膜的脂酰基链全反式构型比例上升,膜的流动性减小．由Raman光谱和引PNMR结果推测,磷脂极性头部是纳米雄黄与磷脂的主要结合位点。AFM实时观测,纳米雄黄通过在膜表面打“孔”或“洞”的方式,损坏磷脂膜．