The non-equilibrium charge screening effects in diffusion-driven systems with pattern formation

The effects of non-equilibrium charge screening in mixtures of oppositely charged interacting molecules on surfaces are analyzed in a closed system. The dynamics of charge screening and the strong deviation from the standard Debye-Hückel theory are demonstrated via a new formalism based on computing radial distribution functions suited for analyzing both short-range and long-range spacial ordering effects. At long distances the inhomogeneous molecular distribution is limited by diffusion, whereas at short distances (of the order of several coordination spheres) by a balance of short-range (Lennard-Jones) and long-range (Coulomb) interactions. The non-equilibrium charge screening effects in transient pattern formation are further quantified. It is demonstrated that the use of screened potentials, in the spirit of the Debye-Hückel theory, leads to qualitatively incorrect results.     

A practical integral equation for the structure and thermodynamics of hard sphere Coulomb fluids

A closure for the Ornstein-Zernike equation is presented, applicable for fluids of charged, hard spheres. From an exact, but intractable closure, we derive the radial distribution function of nonlinearized Debye-Hückel theory by subsequent approximations, and use the information to formulate a new closure by an extension of the mean spherical approximation. The radial distribution functions of the new closure, coined Debye-Hückel-extended mean spherical approximation, are in excellent agreement with those resulting from the hyper-netted chain approximation and molecular dynamics simulations, in the regime where the latter are applicable, except for moderately dilute systems at low temperatures where the structure agrees at most qualitatively. The method is numerically more efficient, and more important, convergent in the entire temperature-density plane. We demonstrate that the method is accurate under many conditions for the determination of the structural and thermodynamic properties of homogeneous, symmetric hard-sphere Coulomb systems, and estimate it to be a valuable basis for the formulation of density functional theories for inhomogeneous or highly asymmetric systems.     

Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye-Hückel approximation and Deryagin formulation

We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may dramatically change depending on the interplay between characteristic Debye length, thickness of ion-permeable layers and their respective protolytic features (e.g. location, magnitude and sign of charge density). This formalism extends a recent model by Ohshima which is strictly limited to interaction between soft mono-shell particles within Deryagin and Debye-Hückel approximations under conditions where ionizable sites are completely dissociated.     

Correction of formation constants for ionic strength, from only one or two data points: An examination of the use of the extended Debye-Hückel equation

The results of an extensive examination show the extended Debye-Hückel equation to be efficacious for the use of as few as one or two formation constant values, for a given metal-complex species, for calculation of the value at a lower ionic strength. Approaches to choosing values for the constants in the extended Debye-Hückel equation are described. A statistical analysis shows the chief source of error in the resulting predicted formation constants to be uncertainties in the literature formation-constant values used as data.     

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.     

Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ.     

Electrical double layer interactions for spherical charge regulating colloidal particles

A new way of linearising the Poisson-Boltzmann equation is presented which is capable of producing accurate answers for moderately high surface charge and surface potentials. Unlike the Debye-Hückel approximation, the linearisation is based on the fact that electric potential variation, rather than the magnitude of the potential itself, remains small between two charged plates at close separation. The method can be applied quite generally to any type of surface. The cases of constant surface charge, the constant surfaceppotential and charge regulating systems are considered as examples. The results for constant charge and potentials as high as 5 μC/cm² and 200 mV are within 7% of the exact answers for plate separations of one Debye length or less. In contrast, the Debye-Hückel approximation produces answers that are at least an order of magnitude too large, for the same problems. The application of the method to the problem of calculating the electrostatic forces between charge regulated spherical particles is also addressed in some detail.     

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level.     

A Brownian dynamics study on the self-diffusion of charged tracers in dilute polyelectrolyte solutions

Brownian dynamics simulations with hydrodynamic interactions are conducted to investigate the self-diffusion of charged tracer particles in a dilute solution of charged polymers, which are modeled by bead-spring chains. The Debye-Hückel approximation is used for the electrostatic interactions. The hydrodynamic interactions are implemented by the Ewald summation of the Rotne-Prager tensor. Our simulations find that the difference in short- and long-time diffusivities is very slight in uncharged short-chain solutions. For charged systems, to the contrary, the difference becomes considerable. The short-time diffusivity is found to increase with increasing chain length, while an opposite behavior is obtained for the long-time diffusivity. The former is attributed to the hydrodynamic screening among beads in a same chain due to the bead connectivity. The latter is explained by the memory effect arising from the electrostatic repulsion and chain length. The incorporation of hydrodynamic interactions improves the agreement between the simulation prediction and the experimental result.     

Association constants for the NaSO(4)(-) ion pair in concentrated cesium chloride solutions

Values of the association constant, beta(NaSO(4)(-)), for the weak ion-pair formed by sodium and sulfate ions in aqueous solution have been determined at 25 degrees C by high precision sodium ion-selective electrode potentiometry in solutions of ionic strength ranging from 0.50 to 7.00 M in CsCl media and in 1.00 M Me(4)NCl. The data in CsCl media were fitted to an extended form of the Debye-Hückel equation which yielded log beta(NaSO(4)(-))(0)=0.834+/-0.005 at infinite dilution. Evidence is also presented for the formation of very weak ion-pairs between Cs(+) and SO(4)(2-).     

Determination of the solubility product of Ba(IO(3))(2) by flow injection with amperometric detection

The solubility of Ba(IO(3))(2) has been determined in solutions containing a supporting electrolyte (KCl) to maintain the ionic strength in the 0-0.5 M range. The approach envisaged was based in the amperometric determination of iodine (or triiodide) generated in the reaction involving iodate in equilibrium in the saturated solutions and iodide contained in the solution carrier using a flow injection procedure, the electrode potential being maintained at +0.2 V in a wall-jet cell. The effect of the supporting electrolyte on the solubility of barium iodate was demonstrated and a good approximation of the value for the thermodynamic solubility constant of the precipitate was found by an appropriate correction of the solubility data using mean activity coefficients of barium iodate. The mean activity coefficients were estimated at each ionic strength by using the Debye-Hückel equation and the corrected solubility constant determined at 27 degrees C was found to be 2.7x10(-9) mol(3) l(-3).     

Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length： Functional Theoretical Approach

Introduction The electrostatic potentialΨis the most importantproperty for the electrical double layer( EDL) of acharged particle in an electrolyte solution[1—4]. Thispotential is characterized by the so-called Poisson-Bolt-zmann(PB) equation. The PB equation is a second-or-der nonlinear differential equation with a constant coef-ficient, except a flat-plate model, which cannot besolved analytically by the traditional method. To ourknowledge, apart from the numerical solution to thisequa…     

Rates of ionic reactions with charged nanoparticles in aqueous media

A theory is developed to evaluate the electrostatic correction for the rate of reaction between a small ion and a charged ligand nanoparticle. The particle is assumed to generally consist of an impermeable core and a shell permeable to water and ions. A derivation is proposed for the ion diffusion flux that includes the impact of the equilibrium electrostatic field distribution within and around the shell of the particle. The contribution of the extra- and intraparticulate field is rationalized in terms of a conductive diffusion factor, f(el), that includes the details of the particle geometry (core size and shell thickness), the volume charge density in the shell, and the parameters defining the electrostatic state of the particle core surface. The numerical evaluation of f(el), based on the nonlinear Poisson-Boltzmann equation, is successfully complemented with semianalytical expressions valid under the Debye-Hückel condition in the limits of strong and weak electrostatic screening. The latter limit correctly includes the original result obtained by Debye in his 1942 seminal paper about the effect of electrostatics on the rate of collision between two ions. The significant acceleration and/or retardation possibly experienced by a metal ion diffusing across a soft reactive particle/solution interphase is highlighted by exploring the dependence of f(el) on electrolyte concentration, particle size, particle charge, and particle type (i.e., hard, core/shell, and entirely porous particles).     

The ionization constants of alpha-alanine in NaCl at 25 degrees. Effect of the ionic strength based on three models

In the present work we obtained the experimental pKs of the amino acid alpha-alanine in NaCl at 25 degrees and different ionic strengths. The equilibrium constants have been potentiometrically determined with a commercial glass electrode and the results analysed through three models: two directly based on the Pitzer and Scatchard approaches to the ion specific interaction theory and the other based on a simpler modification of the Debye-Hückel equation. The three models fit the data reasonably well and the extrapolated pK values obtained show a good agreement. The goodness of the ridge regression method cannot be probed in this case.     

Theory of Frequency-Dependent Polarization of General Planar Electrodes with Zeta Potentials of Arbitrary Magnitude in Ionic Media

Electrode polarization effects have long aggravated the efforts of low frequency analysis, particularly those investigations carried out on biological material or in highly conductive media. Beginning from elementary equations of electrostatics and hydrodynamics, a comprehensive model is devised to account for the screening of a general planar electrode by an ionic double layer. The surface geometry of the planar electrode is left unspecified to include any type of micromachined array. Building on the previous work by DeLacey and White (1982, J. Chem. Soc. Faraday Trans. 2 78, 457) using a variational theorem, we extend their numerical results with compact analytic solutions, analogous to the Debye-Hückel potential for dc systems, but applicable now to dynamic ac experiments. The variational approach generates functions that are not restricted by perturbation expansions or numerical convergence, representing optimal approximations to the exact solutions. Copyright 2000 Academic Press.     

DNA translocation through polyelectrolyte‐modified nanopores: An analytical approximation

An analytical model for the electrophoretic speed of DNA translocating through nanopore functionalized with polyelectrolyte (PE) brush is developed for the first time. The electrophoretic speed depends on DNA surface potential, applied electric field, viscosity, and permittivity of solution along with velocity and electrostatic potential at liquid–polyelectrolyte layer (PEL) interface where the interface seemed to behave similar to that of a solid‐state nanopore wall. Under the limit of Debye–Hückel linearization, the electrostatic potential at liquid–PEL interface and at DNA surface have been calculated. Velocity at liquid–PEL interface has been estimated by assuming a linear variation of hydrodynamic frictional force within the PEL. It is observed that velocity and electrostatic potential at liquid–PEL interface strongly depend on PE charge density and softness parameter. Present analytical results show excellent agreement with exact numerical results (i.e., without any approximation) at a higher salt concentration where Debye–Hückel linearization is applicable.     

The Electrical Double-Layer Interaction between a Spherical Particle and a Cylinder

Based on the well-known Debye-Hückel approximation and the Derjaguin's integration method, this paper presents an integral solution for the electrical double-layer (EDL) interaction between a spherical particle and a cylinder. The effects of the relative dimensions of the cylinder to the sphere on the EDL interaction are studied using this numerical solution. The detailed numerical results indicate that, in general, the curvature effect on the EDL interaction cannot be neglected at small separation distances. The widely used sphere-flat plate approximation will considerably overestimate the actual EDL interaction between a spherical particle and a cylinder. The ratio of the radius of the particle to the EDL thickness, tau=kappaa(p), also plays an important role in determining the EDL interaction at small dimensionless separation distances (相似文献   

298.15K下果糖水溶液中卤化钠单个离子活度系数

利用离子选择性电极和甘汞电极分别测定了NaX+果糖+水体系中的单个离子活度系数和离子平均活度系数.结果表明:基于Debye-Hückel扩展方程和Pitzer方程求得的单个离子活度系数彼此一致;由单个离子加合求得的与直接测定的平均离子活度系数也很一致;随果糖含量的增大,单个离子活度系数减小;在相同混合溶剂(果糖+水)和相等电解质浓度条件下,对于不同的NaX,Na+的活度系数大小顺序为NaFNaClNaBr.基于离子间的相互作用对结果进行了讨论.     

A new and simpler approach for the solution of the electrostatic potential differential equation. Enhanced solution for planar, cylindrical and annular geometries

The motivation of the study performed in this project is focused on deriving a more effective, accurate, and mathematically friendly solution for the prediction of the electrostatic potential, commonly used on electrokinetic research and its related applications. In this contribution, based on the Debye-Hückel approximation, a new solution strategy for the differential equations of the electrostatic potential is proposed. In fact, a simple predictor-corrector calculation is developed to achieve more accurate predictions of electrostatic potential profiles. Furthermore, in this study the authors introduce the correction function f(AO) to the inverse Debye length, lambda. The f(AO) function improves the Debye-Hückel approximation and it is a recursive function of the electrical potential. Once the inverse Debye length, lambda, has been corrected by the f(AO) function and introduced in the simplified solution of the Poisson-Boltzmann equation (i.e., the linear approximation, due to Debye and Hückel), the electrostatic potential outcome little differs from the numerical solution of the complete (nonlinear) differential equation. This new approach embraces different geometries of interest, such as planar, cylindrical, and annular, with excellent results in all the cases and for a wide range of electrostatic potential values. This new predicting semi-analytical technique can be a useful tool on electrical field applications such as the separation of a mixture of macromolecules and the removal of contaminants in soil cleaning processes. Illustrative results are presented for the geometries identified above.     

Treatment of charge singularities in implicit solvent models

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 A for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.