Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface

Water ordering near a charged membrane surface is important for many biological processes such as binding of ligands to a membrane or transport of ions across it. In this work, the mean-field Poisson-Boltzmann theory for point-like ions, describing an electrolyte solution in contact with a planar charged surface, is modified by including the orientational ordering of water. Water molecules are considered as Langevin dipoles, while the number density of water is assumed to be constant everywhere in the electrolyte solution. It is shown that the dielectric permittivity of an electrolyte close to a charged surface is decreased due to the increased orientational ordering of water dipoles. The dielectric permittivity close to the charged surface is additionally decreased due to the finite size of ions and dipoles.     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

Allometric scaling and morphological variation in sinking rate of phytoplankton

Since the first decades of the last century, several hypotheses have been proposed on the role of phytoplankton morphology in maintaining a favorable position in the water column. Here, by an extensive review of literature on sinking rate and cell volume, we firstly attempted to explore the dependency of sinking rate on morphological traits using the allometric scaling approach. We found that sinking rate tends to increase with increasing cell volume showing the allometric scaling exponent of 0.43, which is significantly different than the Stokes’ law exponent of 0.66. The violation of the 2/3 power rule clearly indicates that cell shape changes as size increases. Both size and shape affect how phytoplankton sinking drives nutrient acquisition and losses to sinking. Interestingly, from an evolutionary perspective, simple and complex cylindrical shapes can get much larger than spherical and spheroidal shapes and sink at similar rates, but simple and complex cylindrical shapes cannot get small enough to sink slower than small spherical and spheroidal shapes. Cell shape complexity is a morphological attribute resulting from the combination of two or more simple geometric shapes. While the effect of size on sinking rate is well documented, this study deepens the knowledge on how cell shape or geometry affect sinking rates that still needs further consideration.     

Nonlinear heavy-ion-acoustic waves in an adiabatic collisionless Bi-ion plasma

The basic properties of heavy-ion-acoustic (HIA) waves have been investigated in a collisionless plasma system which is supposed to be composed of nonthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions. The Kortewg-de Vries and Burgers equations are derived in nonplanar (cylindrical and spherical) geometry by employing the standard reductive perturbation method for studying the basic features (viz. amplitude, phase speed, etc.) of HIA solitary and shock waves, which are associated with either positive or negative potential. It is found that the effects of nonplanar geometry, adiabaticity of positively charged inertial heavy ions, the presence of nonthermal (Cairns distributed) electrons, and number densities of the plasma components significantly modify the basic features of nonplanar HIA waves. It has been observed that the properties of solitary and shock waves associated with HIA waves in a nonplanar geometry differ from those in a planar geometry. The implications of our results may be helpful in understanding the electrostatic perturbations in various laboratory and astrophysical plasma environments.     

Interaction of planar double layers in the modified Gouy-Chapman approximation

The force between two charged planar surfaces containing an electrolyte solution is calculated. The calculation is done for a 1-1 electrolyte with size-asymmetric ions using a Modified Gouy-Chapman theory. It is shown that at least part of the explanation for the sharp rise in the force between charged surfaces at small separations seen in experimental data may be related to finite-sized ion effects in the double layer. An interesting effect of size-asymmetric ions is the prediction of a force between uncharged surfaces.     

Properties of cylindrical and spherical heavy ion-acoustic solitary and shock structures in a multispecies plasma with superthermal electrons

A theoretical investigation on heavy ion-acoustic (HIA) solitary and shock structures has been accomplished in an unmagnetized multispecies plasma consisting of inertialess kappa-distributed superthermal electrons, Boltzmann light ions, and adiabatic positively charged inertial heavy ions. Using the reductive perturbation technique, the nonplanar (cylindrical and spherical) Kortewg–de Vries (KdV) and Burgers equations have been derived. The solitary and shock wave solutions of the KdV and Burgers equations, respectively, have been numerically analyzed. The effects of superthermality of electrons, adiabaticity of heavy ions, and nonplanar geometry, which noticeably modify the basic features (viz. polarity, amplitude, phase speed, etc.) of small but finite amplitude HIA solitary and shock structures, have been carefully investigated. The HIA solitary and shock structures in nonplanar geometry have been found to distinctly differ from those in planar geometry. Novel features of our present attempt may contribute to the physics of nonlinear electrostatic perturbation in astrophysical and laboratory plasmas.     

Stability of the low-temperature states of high-pressure microwave discharges

Symmetric (planar, cylindrical, and spherical) models of microwave discharges in air are considered assuming that the deposited energy is removed via heat conduction. The characteristic features of spherical discharges are analyzed in detail, and the conditions for discharge stability are examined. It is shown that discharges in the low-temperature (unstable) state can be stabilized by varying the power of a feedback-controlled microwave source.     

Effect of cation and anion of an electrolyte on apparent molar volume, isentropic compressibility and refractive index of glycine in aqueous solutions

Experiments at 298.15 K have been performed to measure the density, velocity of sound and refractive index in three water+glycine+electrolyte systems. The electrolytes studied were KCl, KNO3 and NaNO3. The values of apparent molar volume and isentropic compressibility of glycine in aqueous electrolyte solutions were calculated from the measured data. The results obtained in this study and those reported previously for water+glycine+NaCl system have been comparatively studied. The results show that the nature of both the cation and the anion of an electrolyte influence the behaviour of glycine in aqueous solutions. For all four electrolytes studied, the comparison shows a positive volume transfer for glycine from an electrolyte solution to a more concentrated solution of the same electrolyte. The results also show a negative apparent isentropic compressibility for glycine in the presence of the electrolytes studied. These effects indicate that the volume of a glycine molecule is larger in solutions with higher electrolyte concentration and the water molecules around the glycine molecules are less compressible than the water molecules in the bulk solution. These effects were attributed to the doubly charged behaviour of glycine and to the formation of physically bonded ion-pairs between the charged groups of glycine and the cation and the anion of the electrolyte.     

Critical polyelectrolyte adsorption under confinement: planar slit, cylindrical pore, and spherical cavity

We explore the properties of adsorption of flexible polyelectrolyte chains in confined spaces between the oppositely charged surfaces in three basic geometries. A method of approximate uniformly valid solutions for the Green function equation for the eigenfunctions of polymer density distributions is developed to rationalize the critical adsorption conditions. The same approach was implemented in our recent study for the "inverse" problem of polyelectrolyte adsorption onto a planar surface, and on the outer surface of rod-like and spherical obstacles. For the three adsorption geometries investigated, the theory yields simple scaling relations for the minimal surface charge density that triggers the chain adsorption, as a function of the Debye screening length and surface curvature. The encapsulation of polyelectrolytes is governed by interplay of the electrostatic attraction energy toward the adsorbing surface and entropic repulsion of the chain squeezed into a thin slit or small cavities. Under the conditions of surface-mediated confinement, substantially larger polymer linear charge densities are required to adsorb a polyelectrolyte inside a charged spherical cavity, relative to a cylindrical pore and to a planar slit (at the same interfacial surface charge density). Possible biological implications are discussed briefly in the end.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

Ion concentration and charge adjacent to electrically charged cell membrane

Equations describing ion concentration profiles and electric charge in electrolyte solutions adjacent to an electrically charged cell membrane model in the electrochemical equilibrium state are developed and completely solved. The membrane system model consists of an infinitely large planar sheet of finite thickness separating two electrolyte solutions. Electric charges in the membrane model consist of planes of charge parallel to the surfaces of the planar sheet. The charge in solution adjacent to each surface of the membrane is due to differences in the total anion and cation concentrations in each solution.Expressions of concentration and charge are functions of the quantity and location of charge in the membrane, the various permittivities and thickness of the membrane, and the ionic compositions, permittivities, and temperature of the electrolyte solutions.The validity and relation of the model to real membranes are discussed.     

Monte Carlo simulation of the double layer at an electrode including the effect of a dielectric boundary

Monte Carlo values of the density profiles and related properties of the double layer formed by an electrolyte near a charged electrode are reported for the cases where the electrode has a dielectric coefficient greater, equal, and smaller than that of the electrolyte that causes a surface polarization that can be represented by electrostatic images. As expected, compared to the case where there is no dielectric boundary the ions near the electrode are attracted or repelled by the electrode if the dielectric coefficient is greater or smaller, respectively, than that of the electrolyte. This effect is most pronounced near the electrode and is stronger for 2:2 electrolytes than for 1:1 electrolytes. For both monovalent and divalent ions the effect of the dielectric boundary is stronger at low concentrations.     

Ionomigration of Neutral Phases in Ionic Conductors

Without sensing any physical force, a neutral object in an ion conducting solid can move in a uniform electrochemical field by coupling a global ion wind with localized counterion diffusion at the interface. This happens to pores and gas bubbles at 840 °C in a fast O^2? conductor, yttria‐stabilized zirconia (YSZ), despite having cations that are essentially frozen with lattice diffusivities 10¹² times slower than the O^2? diffusivity. Through‐thickness migration and massive electro‐sintering in thin YSZ ceramics are observed at voltages similar to those in YSZ fuel cells and electrolysis cells. This effect should apply to any electrochemically‐loaded multiphase ionic conducting solid, with or without an electric field, and can lead to electrolyte sintering, phase accumulation and electrode debonding, resulting in unexpected benefit or damage in electrochemical devices. As the velocity obeys a pseudo Stokes‐Einstein equation, inversely proportional to the object size, an especially enhanced size effect is expected in nanocomposites.     

Numerical Modelling of Electroosmotic Driven Flow in Nanoporous Media by Lattice Boltzmann Method

The lattice Boltzmann method was employed to simulate electroosmotic driven flow and Debye layer screening in conducting electrolyte around a porous structure with average size of 40 nm. The charge screening around the nanopores was investigated by solving the vector-superpositioned potential equilibrium distribution function and adding electro-kinetic force term to the evolution equation. In this intermediate case of moderate Debye length, the electrophoresis problem becomes complicated. The motion of the particles distorts the screening cloud, which becomes asymmetric, resulting in very complex interactions between the electrolyte, the screening cloud and the particle; but the Electroosmotic Flow (EOF) behaviour was still considered based on the Helmoholtz-Smoluchowski model with adaptation to fit nanoporous flow in the porous structure. In the present approach, the flow in the nanopores is directly modelled; the detailed flow information can be obtained by simplifying the repeated macrostructure. Due to the symmetry of the domain, the size of computational domain can be largely reduced by less repeated spherical nanoparticles. Each pore of the medium contains several lattice nodes on the simplified curved edges and potential gradients are produced by adjusting the zeta potential value. The velocity results for pressure-driven and EOF flows agree well with the analytical solutions and recent experimental results. In particular, the interface between solid particles and fluids, the influences of porosity, solid particle diameter, yield stress and electric parameters in EOF were investigated. The anti-adhesion effect of electroosmotic pumping effect was evaluated, and the pulsed DC was applied in order to enhance the performance of the electroosmotic pumping. The results demonstrate that the present lattice Boltzmann model is capable of modelling flow through nanoporous media at certain restrictions while some results deviate from the predictions based on the macroscopic theories.     

The δ-function counterion condensate around a line charge derived from the Fuoss,Katchalsky, and Lifson polyelectrolyte theory

It has recently been proven that the counterion condensate around an isolated line charge in an electrolyte, as characterized by nonlinear Poisson-Boltzmann theory, is an encapsulating δ-function. Here the identical result is shown to hold in the framework of the polyelectrolyte theory of Fuoss, Katchalsky, and Lifson. The proof fully exploits analytic solutions to the differential equation which are not available for the nonlinear, cylindrical Poisson-Boltzmann equation.     

Monte Carlo calculations of ion distributions surrounding the oligonucleotide d(ATATATATAT)2 in the B, A, and wrinkled D conformations.

We calculated the uni-univalent ion distributions around the oligonucleotide d(AT)5.d(AT)5 in the A, B and wrinkled D conformation using the Metropolis Monte Carlo method. All atoms were included in the oligonucleotide model with partial charges and hard sphere radii assigned to each atom. The univalent counter- and coions were modeled as hard spheres with radius 0.3 nm. The solvent was assigned a dielectric constant of 80, corresponding to a temperature of 298K. The counterion distribution surrounding each of the conformers and the distribution surrounding an impenetrable cylinder, were calculated for four salt concentrations. We found significant counterion density in the major groove of the A DNA while fewer counterions occupied the grooves of B DNA. In the wrinkled D DNA, where groove occupancy is sterically hindered, the ion distributions were identical to the distributions surrounding the impenetrable, cylindrical model. This suggests that excluded volume effects significantly influence the details of the ion distributions near the oligomer, while the detailed charge distributions of the oligomer affects the ion distributions only minimally. Although substantial variation in counterion density was observed near the oligomers of differing conformations, the total number of counterions located within a cylinder surrounding the oligomer bounded radially by 2.4 nm was independent of the conformation of the oligomer. Therefore, for this model system, the local univalent counterion distributions are extremely sensitive to the geometry of the oligonucleotide whereas the extent of neutralization of the oligoanion is insensitive to the conformation of the oligomer.     

Membrane nanotubes in the electric field as a model for measurement of mechanical parameters of the lipid bilayer

Pulling a membrane cylindrical tubule from a planar bilayer lipid membrane held under a high lateral tension produces a nanotube (NT) with an internal radius of several nanometers. When NT is pulled in an electrolyte solution, its interior is conductive and the internal radius is calculated from the hyperbolic fitting of the NT conductance-length relationship. Depending on the membrane lipid composition, the internal radius of NT varies from 2 to 20 nm, the higher the cholesterol and lysolipid content, the wider the tubes. The application of an electrical field across the NT membrane allows variation of effective lateral tension according to the Lippman effect. The NT radii were measured at different values of voltage applied along NT, and the membrane bending modulus was recalculated upon the supposition that the shape of NT deviates from cylindrical only slightly. The calculated values of the phospholipid membrane stiffness obtained in this work correspond to previously published data.     

Dielectric behavior of polyelectrolytes. IV. Electric polarizability of rigid biopolymers in electric fields

The equilibrium Kerr effect of a system of mobile charges constrained to the surface of biomacromolecules is calculated. Cylindrical and spherical geometries are considered. For the cylinder we determine the anisotropy of electric polarizability as a function of length, temperature, and number of charged species in the low-field regime, and the fraction of the maximum induced dipole in the field direction for higher electric fields. The results are compared to experimental data for DNA oligomers taken from the literature. With spherical geometry we calculate the fractional induced dipole moment as a function of electric field strength and from this deduce the orientation function. The field dependence of the orientation function is compared to experimental data in the literature for bovine disk membrane vesicles.     

Interaction Between Equally Charged Membrane Surfaces Mediated by Positively and Negatively Charged Macro-Ions

In biological systems, charged membrane surfaces are surrounded by charged molecules such as electrolyte ions and proteins. Our recent experiments in the systems of giant phospholipid vesicles indicated that some of the blood plasma proteins (macro-ions) may promote adhesion between equally charged membrane surfaces. In this work, theory was put forward to describe an IgG antibody-mediated attractive interaction between negatively charged membrane surfaces which was observed in experiments on giant phospholipid vesicles with cardiolipin-containing membranes. The attractive interactions between negatively charged membrane surfaces in the presence of negatively and positively charged spherical macro-ions are explained using functional density theory and Monte Carlo simulations. Both, the rigorous solution of the variational problem within the functional density theory and the Monte Carlo simulations show that spatial and orientational ordering of macro-ions may give rise to an attractive interaction between negatively charged membrane surfaces. It is also shown that the distinctive spatial distribution of the charge within the macro-ions (proteins) is essential in this process.