Electrostatics of B-DNA in NaCl and CaCl2 solutions: ion size, interionic correlation, and solvent dielectric saturation effects

The epsilon-modified Poisson-Boltzmann (-MPB) equations ( J. Phys. Chem. B, 2007, 111, 5264) have been solved on a three-dimensional grid for an all-atom geometry model of B-DNA. The approach is based on the implicit solvent model including finite sizes of hydrated ions and a dielectric approximation of the ion hydration shell. Results were obtained for the detailed geometry model of B-DNA in dilute and moderately concentrated solutions of NaCl and CaCl(2). All -MPB parameters of ions and dielectric medium were extracted from published results of all-atom molecular dynamics simulations. The study allows evaluations of the ion size, interionic correlation, and the solvent dielectric saturation effects on the ion distributions around DNA. It unambiguously suggests that the difference between the -MPB and Poisson-Boltzmann distributions of ions is low for Na(+) counterions. Such a difference in the case of divalent counterions Ca(2+) is dramatic: the dielectric saturation of the ion hydration shell leads to point-like adsorption of Ca(2+) on the phosphate groups of DNA. The -MPB equations were also applied to calculate the energy of interaction between two B-DNA molecules. Results agree with previously published simulations and experimental data. Some aspects of ion specificity of polyelectrolyte properties are discussed.     

Flow of Multicomponent Electrolyte Solutions through Narrow Pores of Nanofiltration Membranes

The slow flow of a multicomponent electrolyte solution in a narrow pore of a nanofiltration membrane is considered. The well-known semiempirical method of subdivision of electrical potential into quasi-equilibrium and streaming parts and the definition of streaming concentrations and pressure are discussed. The usefulness of this tool for solving the electrohydrodynamic equations is shown and justified: the use of a small parameter enables a system of electrohydrodynamic partial differential equations to be reduced to a system of ordinary differential equations for streaming functions. Boundary conditions for streaming functions at both the capillary inlet and outlet are derived. The proposed model is developed for the flow of a multicomponent electrolyte solution with an arbitrary number of ions. This is coupled with (i) the introduction of specific interactions between all ions and the pore wall and (ii) the inclusion of the dissociation of water in both conservation and transport equations. Effective distribution coefficients of ions are introduced that are functions of both the specific interaction potentials and the surface potential of the nanofiltration membrane material. The axial dependency of surface potential is expressed by the use of a charge regulation model from which the discontinuity in electric potential and ion pore concentrations at the pore inlet and outlet can be described.A relation between the frequently used capillary and homogeneous models of nanofiltration membranes is developed. An example of application of the homogeneous model for interpretation of experimental data on nanofiltration separation of electrolyte solutions is presented, which shows a reasonable predictive ability for the homogeneous model.     

Dielectric saturation of the ion hydration shell and interaction between two double helices of DNA in mono- and multivalent electrolyte solutions: foundations of the epsilon-modified Poisson-Boltzmann theory

Potentials of mean force between single Na+, Ca2+, and Mg2+ cations and a highly charged spherical macroion in SPC/E water have been determined using molecular dynamics simulations. Results are compared to the electrostatic energy calculations for the primitive polarization model (PPM) of hydrated cations describing the ion hydration shell as a dielectric sphere of low permittivity (Gavryushov, S.; Linse, P. J. Phys. Chem. B 2003, 107, 7135). Parameters of the ion dielectric sphere and radius of the macroion/water dielectric boundary were extracted by means of this comparison to approximate the short-range repulsion of ions near the interface. To explore the counterion distributions around a simplified model of DNA, the obtained PPM parameters for Na+ and Ca2+ have been substituted into the modified Poisson-Boltzmann (MPB) equations derived for the PPM and named the epsilon-MPB (epsilon-MPB) theory. epsilon-MPB results for DNA suggest that such polarization effects are important in the case of 2:1 electrolyte and highly charged macromolecules. The three-dimensional implementation of the epsilon-MPB theory was also applied to calculation of the energies of interaction between two parallel macromolecules of DNA in solutions of NaCl and CaCl2. Being compared to results of MPB calculations without the ion polarization effects, it suggests that the ion hydration shell polarization and inhomogeneous solvent permittivity might be essential factors in the experimentally known hydration forces acting between charged macromolecules and bilayers at separations of less than 20 A between their surfaces.     

Effect of gate length and dielectric thickness on ion and fluid transport in a fluidic nanochannel

We have simulated the effect of gate length and dielectric thickness on ion and fluid transport in a fluidic nanochannel with negative surface charge on its walls. A short gate is unable to induce significant cation enrichment in the nanochannel and ion current is controlled mostly by cation depletion at positive gate potentials. The cation enrichment increases with increasing gate length and/or decreasing dielectric thickness due to higher changes induced in the surface charge density and zeta-potential. Thus, long gates and thin dielectric layers are more effective in controlling ion current. The model without Navier-Stokes equations is unable to correctly predict phenomena such as cation enrichment, increase in channel conductivity, and decreasing electric field. Body force and induced fluid velocity decrease slowly and then rapidly with gate potentials. The effectiveness of ion current control by a gate reduces with increasing surface charge density due to reduced fractional change in zeta-potential.     

Dielectric analysis of sheep erythrocyte ghost. Examination of applicability of dielectric mixture equations

The purpose of this study is to confirm the applicability of dielectric mixture equations in dielectric analysis of biological cell suspensions. Two dielectric mixture equations, the Pauly-Schwan (P-S) equation and the Hanai-Asami-Koizumi (H-A-K) equation were tested using sheep erythrocyte ghosts whose internal solution is identical with the external solution. Dielectric measurements were carried out for the ghost suspensions over a frequency range 10 kHz to 100 MHz; a single dielectric relaxation was found between 100 kHz and 10 MHz. From the dielectric relaxation, the conductivity and permittivity of the ghost interior and the capacitance of the cell membrane were calculated following the P-S and H-A-K equations. When the H-A-K equation was employed (and as expected from the property of the ghosts), the estimated internal conductivity was in good agreement with the external conductivity at volume fractions up to about 0.7. With the P-S equation, on the other hand, the same results as above were obtained but only at low volume fractions below about 0.3. In addition, the H-A-K equation provided a better simulation for the observed relaxation curves than did the P-S equation, especially at high volume fractions. It is, therefore, concluded that the H-A-K equation is applicable to a wider range of volume fraction than is the P-S equation.     

Dielectric permittivity in a dense layer of the hydration shell of an ion in a strong-electrolyte solution

Based on the experimental data on the dielectric dispersion and the static dielectric permittivity of solutions of strong electrolytes, the effective value of the latter in the dense layer of the hydration shell of an ion has been calculated. The calculations have been carried out in terms of the three-layer model of the hydration complex. The calculations have shown that for the solutions of strong electrolytes the value of the static dielectric permittivity (dielectric constant) in the dense layer of the hydration shell of an ion proves to be close to 2 and is almost independent of the concentration and temperature.     

Dielectric properties and surface morphology of swift heavy ion beam irradiated polycarbonate films

Swift heavy ion beam irradiation induces modification in the dielectric properties and surface morphologies of polycarbonate (PC) films. The PC films were irradiated by 55 MeV energy of C⁵⁺ beam at various ions fluences ranging from 1 × 10¹¹ to 1 × 10¹³ ions cm^?2. The dielectric properties (i.e., dielectric constant, dielectric loss, and AC conductivity) and surface morphologies of pristine and SHI beam irradiated PC films were investigated by dielectric measurements, atomic force microscopy (AFM), and optical microscopy. The dielectric measurements show that the dielectric constant, dielectric loss, and AC conductivity increase with ion fluences and temperature, however, the dielectric constant and AC conductivity decrease while dielectric loss increases with frequency. AFM shows the increase in average roughness values with ion fluences. The change of color in PC films has been observed from colorless to yellowish and then dark brown with increases of ion fluence by using optical microscopy.     

The importance of excluded solvent volume effects in computing hydration free energies

Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.     

Microwave dielectric permittivity and relaxation of aqueous potassium trimethylacetate solutions

The MW dielectric properties of aqueous potassium trimethylacetate (pivalate) solutions have been measured at six frequencies (10–25 GHz) at 288, 298, and 308 K. The static dielectric constants and dielectric relaxation times and activation parameters have been calculated. Trimethylacetate ion leads to the decrease in the mobility of water molecules and strengthening of their hydrogen bonds. These changes of water are similar to those in solutions of other carboxylates with a large number of nonpolar groups. The hydrophobic hydration of the trimethylacetate ion is maximal in this series.     

Solid- and liquid-state studies of a wide range of chemicals by isothermal and scanning dielectric thermal analysis

We have observed unique variations in AC electrical conductivity of solids when studied with respect to temperature, time, and frequency. A wide range of solids were examined for this study e.g., organics, polymers, carbohydrates, active pharmacy ingredients (APIs), and amino acids. The observed dielectric analysis conductivity for this great number of organic materials follows an Arrhenius plot of log polar ionic conductivity which is linearly related to reciprocal temperature and the correlation of coefficient is 0.992–0.999. These experimental observations support the polaron hopping conduction model. Experimental results clearly show novel dielectric behavior of a linear increase in a log ionic conductivity versus temperature in the pre-melt/solid-state transition regions. We have differentiated the solids which show the conductivity variations in pre-melt from those which do not. Isothermal dielectric analysis was used to study the cause of this variation in solids which yielded the measure of behavior, i.e., the polarization time property. We have also studied the effect of various experimental factors (e.g., moisture and purity) on the results. Correlating dielectric with calorimetric analyses gave us a better understanding of solid-state properties. Calorimetric analysis was used to assure that the observed variations in the solid-state properties are not due to moisture or impurities present in the sample. The ASTM E698 “purity method” was employed to verify the purity of the chemicals. Activation energies were calculated based on Arrhenius behavior to better interpret the solid-state properties. As the different chemicals were heat–cool cycled they were more amorphous, as evidenced by the decreasing activation energy for charge transfer with an increasing amorphous content.     

The effect of stoichiometry on chain segment and ion mobility in partially polymerized epoxy systems

The temperature dependence of steady-shear viscosity and ionic conductivity were measured for a series of unreacted mixtures and partially cured, ungelled samples of diglycidyl ether of bisphenol-A (DGEBA) and an amine cross-linking agent, diamino diphenyl sulfone (DDS). Six stoichiometric ratios of epoxide groups to amine hydrogens were examined. Free volume expressions were used to model the temperature dependence of the conductivity and viscosity for the unreacted DGEBA-DDS mixtures. In addition, these expressions were combined to successfully correlate changes in viscosity and conductivity during the DGEBA-DDS polymerization prior to gelation. It also was demonstrated that the change in weight average molecular weight during polymerization could be interpreted from the dielectric data. Through studying variations in the stoichiometry, it was possible to examine the effects of changes in chemical structure and ion concentration on the fitted parameters in the free volume models. The inherent ion transport factor (ζ₀) was found to be inversely proportional to the concentration of ions in the test samples. The fractional free volume for segmental motion (B) was found to increase with an increase in the glass transition temperature and to be a function of the rigidity of the polymer. ©1995 John Wiley & Sons, Inc.     

Microwave dielectric permittivity and relaxation for aqueous potassium trifluoroacetate solutions

The results of microwave dielectric measurements in aqueous potassium trifluoroacetate solutions at seven frequencies (ranging within 7.5–25 GHz) at 288, 298, and 308 K are presented. Static dielectric constants, dielectric relaxation times and activation parameters are calculated. The H-bond network in potassium trifluoroacetate solutions is shown to experience molecular-kinetic stabilization and an increase in connectivity and structuring, which are similar to those experienced by water in potassium acetate solutions. These changes are associated with the hydrophobic hydration of trifluoroacetate ion, which was first determined by microwave dielectric spectroscopy and arises from the effect of the low-polarity CF₃ group of trifluoroacetate ion.     

Polarizability and complex conductivity of dilute suspensions of spherical colloidal particles with uncharged (neutral) polymer coatings

The polarizability of polymer-coated colloidal particles, as measured via dielectric relaxation spectroscopy, reflects on the degree to which convection, diffusion, and electromigration deform the equilibrium double layer. With a polymer coating, convection and electro-osmosis are resisted by hydrodynamic drag on the polymer segments. The electro-osmotic flow near the underlying bare surface is therefore diminished. Characteristics of the particles and the adsorbed polymer can, in principle, be inferred by measuring the frequency-dependent polarizability. In this work, "exact" numerical solutions of the electrokinetic equations are used to examine how adsorbed polymer changes the particle polarizability and, hence, the conductivity and dielectric constant increments of dilute suspensions. For neutral polymer coatings, the conductivity and dielectric constant increments are found to be very similar to those of the underlying bare particles, so the response depends mostly on the underlying bare particles. These observations suggest that dielectric spectroscopy is best used to determine the underlying surface charge, with characteristics of the coating inferred from the electrophoretic or dynamic mobility, together with the hydrodynamic radius obtained from sedimentation or dynamic light scattering. Addressed briefly are the effects of added counterions and nonspecific adsorption. The electrokinetic model explored in this work can be used to guide experiments (frequency and ionic strength, for example) to either minimize or maximize the sensitivity of the complex conductivity to the coating thickness or permeability.     

Many-body effects on structure and dynamics of aqueous ionic solutions

We performed several molecular dynamic studies of metal cations in aqueous solution. The alkali metal ion Li(+) and the first-row transition metal ion Mn(2+) have been chosen as model systems. Two different three-body corrections are proposed to mimic the crucial many-body effects of electrolyte solutions. The correction function, which includes attractive features of the three-body potential, performs considerably better than the purely repulsive interaction function. Structural and dynamic results show that this simple enhancement is able to satisfactorily reproduce experimental and higher-level results for the first hydration shell.     

Remarks on triple ion formation. Interpretation of conductance data

It is shown that it is possible to fit conductance data in solvents of low dielectric constant without the additional assumption of triple ion formation. With the aid of two new conductance equations, which incoporate in different ways a mass action law for ion pairing but not for ion triplets, we can account for the conductivity data for the systems LiBr in octanol and NaI in butanol. One of the equations incorporates the mean spherical approximation.     

Quantitative insights into electrostatics and structure of polymer brushes from microslit electrokinetic experiments and advanced modelling of interfacial electrohydrodynamics

The development of theories for the electrohydrodynamics at soft surfaces enabled major progress in the quantitative interpretation of streaming current and surface conductivity data collected for polymer brushes. In this paper, we review the basics of the methodology and discuss illustrative examples of practical interest. In particular, we demonstrate how the combination of self-consistent field and soft surface electrokinetic theories using Poisson–Boltzmann (PB) formulations allow the evaluation of the segment density distribution within poly(ethylene oxide) brushes beyond the resolution limits of neutron reflectivity. The application of the methodology for the analysis of the charge, structure, and pairing with chaotropic anions is illustrated for strong cationic poly(2-(methacryloyloxy)ethyltrimethylammonium chloride) brushes. Finally, we report refinements of the PB theory that account for ion hydration, ion pairing, and dielectric decrement in brushes and we present an example of glycosaminoglycan brushes where those effects are significant.     

Effect of varying counterions on the sensitivity of electrohydrodynamic and fast atom bombardment mass spectrometry

The abundance of ion pairs (CA⁺) relative to that of doubly charged ions (C²⁺) in electrohydrodynamic (EH) mass spectra of a series of anions with a common dication in glycerol was found to increase in the order acetate < nitrite < chloride < bromide ≈ nitrate < iodide < perchlorate. Correlation with enthalpies of hydration for the anions suggests that this trend reflects the solution chemistry of ion association. These spectra also reveal that solvation rather than interactions with the extracting field is more important in determining the overall EH mass spectrometric sensitivity to doubly charged ions. Therefore, the use of anions that promote more extensive ion pairing enhances the overall sensitivity to multiply charged ions that otherwise interact strongly with the solvent, but reduces sensitivity to singly charged ions. These observations hold in fast atom bombardment mass spectrometry, surviving the invasive effects of the primary beam.     

Dielectric properties of aqueous zwitterionic liposome suspensions

The dielectric spectra of aqueous suspensions of unilamellar liposomial vesicles built up by zwitterionic phospholipids (dipalmitoylphosphatidyl-choline, DPPC) were measured over the frequency range extending from 1 kHz to 10 MHz, where the interfacial polarization effects, due to the highly heterogeneous properties of the system, prevail. The dielectric parameters, i.e., the permittivity epsilon'(omega) and the electrical conductivity sigma(omega), have been analyzed in terms of dielectric models based on the effective medium approximation theory, considering the contribution associated with the bulk ion diffusion on both sides of the aqueous interfaces. The zwitterionic character of the lipidic bilayer has been modeled by introducing an "apparent" surface charge density at both the inner and outer aqueous interface, which causes a tangential ion diffusion similar to the one occurring in charged colloidal particle suspensions. A good agreement with the experimental results has been found for all the liposomes investigated, with size ranging from 100 to 1000 nm in diameter, and the most relevant parameters have briefly discussed in the light of the effective medium approximation theory.