Charge Density Parameters Research Articles

Conductivity properties of hyaluronate salts in simple salt-free and sample salt-containing solutions

Electrical conductivities of sodium and calcium hyaluronate were measured in aqueous solution at 25°C. Measurements were also made on sodium hyaluronate in aqueous NaCl in simple salt concentrations of 0.01 and 0.001 mol dm −3. For simple salt-free solutions, the agreement between experimental equivalent conductivity of the polyelectrolyte and the theoretical values according to the Manning theory are satisfactory although relatively insensitive to the value of the linear charge density parameter, for both counterion forms. For sodium hyaluronate in aqueous sodium chloride solutions, the values of the theoretical equivalent conductivities for sodium hyaluronate were calculated for two values of the linear charge parameter, 0.6 and 0.7. Both linear charge parameter values gave reasonable correspondence to the experimental values but, at both concentrations of added sodium chloride, the value of 0.6 for the linear charge parameter of sodium hyaluronate gave closer correspondence. The theoretical dependence of equivalent conductivity on salt concentration is discussed.

The charged dumbbell model for dilute polyelectrolyte solutions in strong flows

A charged dumbbell model is used to investigate the behavior of dilute polyelectrolyte solutions in a general linear two-dimensional flow. The model studied has a nonlinear spring, conformation dependent friction and a Coulombic repulsive force due to an effective electrostatic charge on the two beads. The relative importance of the electrostatic charge is reflected by an effective charge density parameter,E. Equilibrium properties such as end-to-end distance and intrinsic viscosity are strongly dependent onE. In strong flows, which produce a dramatic increase in the dumbbell dimensions (a coil-stretch transition), the onset behavior is influenced byE. IncreasingE causes the onset velocity gradient to shift to much lower values. Large values ofE change the qualitative behavior to that of rigid (or slightly extensible) macromolecules or fibers. Results are presented for a charged dumbbell at equilibrium, in steady flows, and in transient flows.

Direct observation of the transition to counterion condensation

Direct observation of the transition to counterion condensation is demonstrated by measurement of the electrophoretic mobility of 6, 6-ionene, a polyelectrolyte of charge spacing 8.7 Å, under conditions of varying dielectric constant. In this way, the reduced charge density parameter ξ can be varied between 0.82 and 1.85. At precisely ξ=1, we observed a drop in the electrophoretic mobility of greater than a factor of 2. Independent viscosity experiments were used to verify that the polymer does not undergo a major conformational transition under these conditions. The reduction of electrophoretic mobility, presumably the result of the reduction of charge density by counterion condensation, is substantially greater in magnitude than current theories of counterion condensation theory would predict. It is suggested that the physical basis for the departure from theory is the fact that near ξ=1, the spacing of condensed counterions predicted by counterion condensation theory is greater than the Debye screening length.

Counter-ion condensation and system dimensionality.

Condensation of the counter-ions around a highly charged infinitely long cylindrical molecule, such as DNA, can be described in detail in terms of the solutions of the Poisson-Boltzmann (Gouy-Chapman) equation. By using the Alfrey-Berg-Morawetz (1951) solution of this equation one can show that a certain fraction of the counter-ions remain within finite distances of the poly-ion even when the volume of the system is expanded indefinitely; these ions can be appropriately called "condensed". The fraction of the macromolecule's charge represented by these ions is just 1-1/xi, where xi is the linear charge-density parameter of the macromolecule; this is also the value given by Manning's theory. The question arises: Is this property unique to the infinite cylinder? Using the same PB equation, we can consider the infinite charged plane and a large finite charged sphere for comparison. In the case of the plane all of the counter-ions are condensed in the above sense, not just a fraction, for any surface charge density of the plane. These ions form the classical Gouy double layer. On the other hand, none of the counter-ions of the charged sphere are condensed in the above sense, no matter how high the surface charge density. Thus the cylinder is a unique intermediate case in which a fraction of the counter-ions are condensed if the linear charge density is higher than the critical value of unity.

Polyelectrolyte solutions without added salt. Concentration effects and condensation

Concentration effects in salt-free polyelectrolyte solutions are discussed in terms of scaling relations as proposed by Odijk. No explicit use is made however of the condensation approach and all important quantities are expressed in terms of an effective charge density parameter. It is shown that, in the concentration range most accessible to experimental investigation, the exact value of this parameter may have strong bearings on the applicability of the theory and its conclusions. The condensation approach is discussed in terms of the analytical solution of the Poisson-Boltzmann equation for salt-free polyelectrolyte solutions and its validity questioned in the same concentration range. Comparison of the Poisson-Boltzmann solution for the potential at the surface of the charged polyelectrolyte with values derived from filtration data of a weak polyacid shows qualitative agreement but suggests that the effective charge density parameter may be different from its structural value.

The release of monovalent counterions by addition of divalent countemons to aqueous solutions of maleic acid copolymer

Divalent cation binding and the release of monovalent cations accompanying the cation binding were experimentally studied by ion-selective electrode methods in aqueous solutions of copolymer of maleic acid and ethyl vinyl ether. It was found that in the process of Ca2+ addition, all the Ca2+ added was bound to polyions and the initially condensed Na+ was released in proportion to the concentration of the added Ca2+ up to the critical concentration of added Ca2+ at which the condensation of Ca2+ ceases. Values of the structural charge density parameter xi(s), were determined from the end-points of condensation of Ca2+. The process of Na+ release by adding Ca2+ was analyzed on the basis of the counterion condensation theory by using these xi(s) values. In addition, the relationship between the activity coefficient gamma-- of Ca2+ and degree of neutralization alpha in salt-free solutions was obtained from the Manning theory. Agreement between the calculated and experimental values was excellent in both cases.

Joint X-ray and neutron data refinement of structural and charge density parameters

A procedure for joint refinement of X-ray and neutron data is described in which structural, charge density and extinction parameters are adjusted simultaneously in order to arrive at the best least-squares solution with respect to all available diffraction data. This X + N refinement is applied to previously collected low-temperature data on oxalic acid dihydrate, C2H2O4.2H2O, and results are compared with the X-ray-only refinement, and an X-ray refinement with neutron values for the hydrogen structural parameters. The X + N model deformation density shows higher peak heights in the lone-pair regions than the X- ray-only model density and resembles more closely the X-N deformation maps. Though the X + N maps are more strongly model dependent, they contain less noise, provide an analytical description of the deformation density and, unlike the X-N density, can be obtained in principle with a less than complete data set. The estimate of the goodness-of-fit for each of the data sets requires an apportioning of the joint parameters, which in this study is based on the relative magnitude of the least-squares derivatives.

Polyelectrolyte theory. I. Counterion accumulation, site‐binding, and their insensitivity to polyelectrolyte shape in solutions containing finite salt concentrations

AbstractWe have computed the Poisson‐Boltzmann distribution of counterions around polyelectrolytes in solutions containing finite salt concentrations. The polyelectrolytes considered here are highly charged in the sense that ξ > 1, ξ being the linear charge density parameter for cylinders, which is generalized by us to other shapes.Contrary to the situation at zero salt concentration, the counterion distribution is not strongly shape dependent, being similar for cylinders or spheres which have the same superficial charge density and radius of curvature Rc. The distribution resembles that in the neighborhood of a plane with the same charge density.Three regions are distinguished. (1) In the “inner region” which extends up to a distance Rc/2ξ from the surface, the counterion distribution is essentially salt independent. The counterion concentration in the immediate vicinity of the polyelectrolyte surface (CIV) is quite high, typically 1–10M, and proportional to the square of the surface charge density, which is its main determinant. (2) An intermediate region extends out to a distance where the electrostatic potential is equal to κT/e. This distance is comparable to λ for plane and cylinder, and smaller for the sphere. (3) In the outer region, the distribution is hardly influenced by the details of the inner region, on which it cannot, therefore, give much information. Colligative properties are dependent on the distribution in the outer region and are fairly well predicted even by a rudimentary theory.The large value of the CIV implies that site binding must often be significant. It can be computed by applying the mass‐action law to site‐bound counterions in equilibrium with the counterions in the neighborhood, whose concentration is the CIV, the relevant equilibrium constant being that for the binding of counterions to isolated monomer sites. Because the CIV is insensitive to salt concentration, this will also be the case for site binding. With the graphs provided, one can compute the extent of sitebinding within the Poisson‐Boltzmann framework.The “condensation radius,” i.e., the radius encompassing a counterionic charge 1 − ξ−1 around a cylinder, is found to be large. It varies with salt concentration and tends to infinity as the salt is diluted. Neither this radius nor the charge fraction 1 − ξ−1 of condensation theory plays any special role in the counterion distribution.The “finite‐salt” results apply to salt concentrations, typically as low as 1–10 mM. This encompasses, among others, all experiments on biological polyelectrolytes.

Study of the self-diffusion coefficients of cations in the presence of an acidic polysaccharide.

AbstractSelf‐diffusion coefficient measurements have been applied to the study of Na+, Ca++, and Sr++ in the presence of a linear acidic polysaccharide extracted from cartilage, i.e., chondroitin sulfate. A series of experimental determinations was made with and without supporting electrolytes, and an analysis of experiments involving the separation of the electrostatic interaction terms by an extension of Manning's theory produced results showing the preponderant nature of these electrostatic terms. The specificity of each type of ion or the influence of the pH can be considered merely as higher order corrections with respect to the preceding interactions. Counterion concentration ranges and pH ranges were determined, where either the alkaline‐earth counterions become free and hence move with their normal diffusion rate, or these cations are associated with the polyelectrolyte molecule, thus giving a diffusion coefficient similar to that of the macromolecule, or the apparent diffusion coefficients vary between these two extreme diffusion rates as a function of the association equilibria. This variation can be expressed as a function of the linear charge density parameter ξ related to the structure of the polyelectrolyte, the value of which was determined and found in good agreement with published values.

A discussion of the role of dispersion effects on isotopic charge density variations

The role of dispersion correction has been qualitatively studied in isotopic comparison experiments. The correction to elastic electron scattering for electrons of order 100 MeV from three isotopes of Titanium has been estimated using a code due to Rawitscher. The dispersion correction is found to produce variations in the ratio of the cross sections of nearby isotopes of a magnitude sufficient to cast doubt on the magnitude of the variations in charge density parameters.

Charge density and NMR parameters. Aliphatic derivatives

AbstractThe charge distribution in several substituted aliphatic derivatives was determined by a parametric MOLCAO method. The charges were successfully employed to interpret NMR parameters, namely proton and carbon chemical shift and vicinal proton‐proton coupling constants in ethyl derivatives and carbon‐proton coupling constants.The linear correlations found between NMR parameters and charge densities are restricted to substituents of the same row of the periodic system. The decay along the aliphatic chain of the perturbation induced by substituents on proton chemical shift is also reproduced by charge distribution. Some results also seem to indicate that the substituents affect the hybridization of the attached carbon atom.

Electron Population Parameters from Least-Squares Refinement of X-ray Diffraction Data

A least-squares refinement of x-ray diffraction data has been developed in which the parameters are the populations of atomic orbital products describing the molecular electron density distribution. The procedure is applied to alpha-oxalic acid dihydrate and cyanuric acid. Complementary structural information obtained by neutron diffraction has been used. In the absence of complementary information, the method allows simultaneous determination of structural and charge-density parameters. There is an indication of a migration of charge from the ppi to the psigma orbitals in both molecules.

Calculation of Coefficients of Capacitance of Multiconductor Transmission Lines in the Presence of a Dielectric Interface

A method is given for the numerical determination of the coefficients of capacitance for a class of multiconductor transmission-line systems. This class includes systems without ground planes, or with one or two ground planes, with the lines embedded in one or two layers of dielectrics. The conductors can be of any cross section that can be approximated adequately by polygons. The method is a refinement of the subareas method in which the assumption of a "staircase function" surface charge density, that is, constant charge density over each subarea, is replaced by the assumption of a piecewise linear charge density over the conductor surfaces, and the charge density parameters are determined by making a least-squares fit to the potential to the boundary conditions of the problem.

Dielectric Properties of Some Powdered Organic Semiconductors

The use of electrical conductivity measurements to characterize the charge density and/or mobility parameters of a material is discussed. The common practice of using simple, pressed electrodes with dc measurements is felt to be grossly inferior to four-probe techniques. Even this refinement, however, is subject to considerable error for powdered samples. Many workers have used fairly simple ac techniques to eliminate interparticle contact resistances in organic semiconductors; this approach is shown to have been misapplied. It is possible, however, to measure what appears to be a specific conductivity (independent of packing pressure or filling factor) by more elaborate ac analysis. Measurements of the effective parallel resistance and capacitance are given for anthracene (powder and single-crystal), metal-free β-phthalocyanine, and a β-carotene tri-iodide complex for a frequency range of 0.05 cps to 300 Mc/sec.