Charge Density Parameters Research Articles

Systematics of nuclear central densities

The nuclear central density is calculated from the nuclear charge-density parameters measured by elastic electron scattering and muonic atom spectroscopy. The nucleon number and asymmetry dependences of the obtained nuclear central density are discussed based on the macroscopic description of nuclei. It is shown that the nuclear central density decreases slowly as the nucleon number or the nuclear asymmetry increases. The proton number and neutron number dependences of the nuclear central density show some structure that seems like the shell effect, since density peaks are formed around the proton and neutron magic numbers. The data fit to the nuclear half density radii measured by muonic atom spectroscopy yields the nuclear radius constant ${r}_{0}=1.141 \mathrm{fm}$, and the data fit to the calculated nuclear central densities gives an estimation for the nuclear matter incompressibility ${K}_{0}$ in the range around 220--250 MeV.

Landau model of polarisation switching in layered ferroelectric structures

A Landau model is used to describe the time response of the polarisation switching in a thin film capacitor structure. The presence of non-switching layers near the electrodes is modelled by including two internal charged interfaces, with a 180o domain structure in the normal switching ferroelectric region. The Landau free energy of the total system is used to derive the Landau relaxation equations for the charge density and domain fraction parameters describing the system. We investigate the frequency dependence of the hysteresis, and the time dependence of the polarisation response to switching inputs.

Conductance and Counterion Activity of Ionene Solutions

The conductance and counterion activity of aliphatic ionenes with counterions of F - , Cl - , Br - , I - , and NO 3 - in both the absence and presence of salts were measured and compared with Manning's equations for both cases. Samples used were 3,3-, 4,5-, 6,6-, and 6,9-ionenes, where the numbers are those of methylene groups between the quaternized nitrogen atoms. The activity coefficients of counterions for ionenes in the absence of salts were lower than the theoretical values, and experimentally determined values of the charge density parameters, higher than the theoretical ones, could explain the departure between the experimental and the theoretical values at least semiquantitatively. The conductance of ionenes in the presence of salts deviated from the additivity rules, dependent on charge density of the ionenes as well as the counterions used. It also deviated from the theoretical prediction in which the interaction between small ions was taken into account. On the other hand, the additivity holds approximately for the counterion activity irrespective ofthe species ofionenes and counterions, in marked contrast to the case of conductivity. The viscosity of the ionene solution exhibited a strong dependence on the salts added. The effect of salts on the viscosity was more prominent in the samples with higher charge density parameter, corresponding to larger conformational change in the polyion. These results may give useful information on the conformation of ionenes in solution as well as the mechanism of the electrical conductivity of polyelectrolytes.

Effects of the charge density and counterion species on the conductance of ionene solutions

The conductance, pH and counterion activity of aliphatic x,y-ionenes were measured to clarify the interaction between ionenes and counterions. The conductometric and potentiometric titrations of basic form ionenes showed that the ionenes are typical strong bases. The conductances of salt form ionenes both in the absence and presence of salts were compared with Manning's equations for both cases. The equivalent conductances for ionenes were lower than the theoretical values. The experimentally determined values of the charge density parameters, higher than the theoretical values, could explain the departure between the experimental and the theoretical values at least semi-quantitatively. The conductance of ionenes in the presence of salts also deviated from the theoretical values, and revealed a marked departure from the additivity rules, dependent on charge density of the ionene as well as the counterions used. On the other hand, the additivity holds approximately for the activity of counterions irrespective of the species of ionenes and counterions. These results may give some information on the conformation of ionenes in solution as well as the mechanism of the electrical conductivity of polyelectrolytes.

Interaction of sodium and calcium ions with poly(alkylene phosphate)—a synthetic analogue of natural teichoic acids

The competitive binding of sodium and calcium ions to poly(alkylene phosphate)s, which can be considered as synthetic models of bacterial teichoic acids, and to poly(styrenesulfonate)s was studied experimentally by potentiometry with ion-selective electrodes. The fractions of apparently free counterions, ffi, were determined and compared with theoretical predictions obtained from the Poisson–Boltzmann theory applied to the cylindrical cell model of polyelectrolyte solutions containing a mixture of counterions differing in charge. For the studied systems, the dependence of ffNa and ffCa on the composition of the counterion mixture and on a charge density parameter of the polyion was found to be fairly well described by theory. For poly(alkylene phosphate)s the calculated values of ffi noticeably exceeded the measured fractions of apparently free ions. Much better agreement between theory and experiment was obtained if the effective value of the charge density parameter was used.

Transferability of multipole charge-density parameters: application to very high resolution oligopeptide and protein structures.

Crystallography at sub-atomic resolution permits the observation and measurement of the non-spherical character of the electron density (parameterized as multipoles) and of the atomic charges. This fine description of the electron density can be extended to structures of lower resolution by applying the notion of transferability of the charge and multipole parameters. A database of such parameters has been built from charge-density analysis of several peptide crystals. The aim of this study is to assess for which X-ray structures the application of transferability is physically meaningful. The charge-density multipole parameters have been transferred and the X-ray structure of a 310 helix octapeptide Ac-Aib2-L-Lys(Bz)-Aib2-L-Lys(Bz)-Aib2-NHMe refined subsequently, for which diffraction data have been collected to a resolution of 0.82 A at a cryogenic temperature of 100 K. The multipoles transfer resulted in a significant improvement of the crystallographic residual factors wR and wR free. The accumulation of electrons in the covalent bonds and oxygen lone pairs is clearly visible in the deformation electron-density maps at its expected value. The refinement of the charges for nine different atom types led to an additional improvement of the R factor and the refined charges are in good agreement with those of the AMBER molecular modelling dictionary. The use of scattering factors calculated from average results of charge-density work gives a negligible shift of the atomic coordinates in the octapeptide but induces a significant change in the temperature factors (DeltaB approximately 0.4 A2). Under the spherical atom approximation, the temperature factors are biased as they partly model the deformation electron density. The transfer of the multipoles thus improves the physical meaning of the thermal-displacement parameters. The contribution to the diffraction of the different components of the electron density has also been analyzed. This analysis indicates that the electron-density peaks are well defined in the dynamic deformation maps when the thermal motion of the atoms is moderate (B typically lower than 4 A2). In this case, a non-truncated Fourier synthesis of the deformation density requires that the diffraction data are available to a resolution better than 0.9 A.

Osmotic coefficients of vinylic polyelectrolyte solutions without added salt

The osmotic pressures of –polyelectrolyte solutions without added salt was measured in the concentration ranges 0.001–0.02 and 0.2–1.9 mol kg-1. Our results show that the osmotic coefficients φp were strongly dependent on the chemical structures of polyelectrolyte through the polyion radius and the interaction between the ionic moiety and counterions. The osmotic pressures in polyelectrolyte solutions without added salt, calculated on the basis of the counterion contribution, are in agreement with the experimental results. We conclude that the counterion contribution is dominant in the osmotic pressures and thus, the polymer contribution is negligible in the examined concentration range 0.2–1.9 mol kg-1. The P–B approach gave a fair prediction of the absolute values of the osmotic pressures with λ=4.5, where λ is the charge density parameter, except for NaPA. In other words, the concentration dependence of the φp values can be explained in terms of the counterion contribution.

Heteroxylans from maize bran in aqueous solution. Part II: Studies of polyelectrolyte behaviour

Potentiometric and viscosimetric behaviours of four samples of heteroxylans, extracted from corn bran at different temperatures with varying type and concentration of alkali were studied in dilute solutions. All four samples behave as typical polyelectrolytes with a low charge density parameter (λ = 0.15). They could be described by the Lifson and Katchalsky model pK 0≈3.15), indicating a rather homogeneous repartition of the charges along the macromolecules. Their intrinsic viscosities varied linearly with the reciprocal of the square root of the ionic strength. Their flexibility parameters, B (≈0.024), were similar to those of semi-flexible macromolecules, and their intrinsic viscosities extrapolated to infinite ionic strength were between 144 and 177ml/g. Their conformational dimensions depended on the type of counter-ion in solution (dimensions minimal with divalent cations and decreasing with size of monovalent alkali metal ions), of the temperature and the pH of the solution. The radius of gyration for unchanged heteroxylans was estimated from intrinsic viscosities extrapolated to infinite ionic strength ( R 2 g∞ 1/2 = 21−25 nm).

The influence of an acid treatment on the surface charge density of silica gel

The influence of an acid treatment on the pore structure as well as on the surface charge density of porous silica was investigated. It is shown that this treatment causes only small changes of the pore structure. Positive values of the surface charge density at pH>4 are interpreted in terms of surface impurities consisting of Na+ ions resulting from the synthesis of the gel from sodium silicate solution. This effect is strongly influenced by the acid treatment. The surface charge density parameters were evaluated on the basis of the triple-layer model for the electrical double layer. Here two different mechanisms of counterion attachment in the inner Helmholtz plane are discussed.

Influence of polyelectrolyte adsorption on the electro‐optical behavior of aerosil particles

AbstractThe adsorption of polyelectrolyte, sodiumcarboxymethyl‐cellulose (Na‐CMC) on Aerosil (SiO2) particles is studied by means of electric light scattering and electrophoresis. The electro‐optical effect α increases with the rise of polyelectrolyte concentration. Simultaneously the increase of particles' electrophoretic mobility reveals the adsorption of polyion on identically charged particles. The similarity of the frequency dependence of the electrooptic effect at different polyelectrolyte concentrations is an indication that the particles' induced dipole moment is mainly determined by polyelectrolyte' counterions behaviour.Two relaxations of the electro‐optical effect are observed at frequencies ranging from 500 Hz to 100 kHz the first relaxation is about 1 kHz, the second one ‐ in the 10 kHz region. The increase of charge density parameter ζ doesn't influence the first relaxation, but the second one becomes wider and more noticeable. According to Manning predictions the rising of ζ(ζ>1) results in the increase of the fraction of diffuse counterions. So their contribution to the induced dipole moment is more clearly demonstrated in the frequency dependence. Most probably the first relaxation of α is connected with the “bound” counterions whereas the second is due to the diffuse counterions. In the case of polyelectrolyte adsorption on the particles of the same charge sign an analogy with Manning consideration for free polyelectrolytes in solution could be drawn.

Determination of surface charge density parameters of silicon nitride

Abstract The surface charge density of silicon nitride was determined by potentiometric pH titration at two different concentrations of the background electrolyte NaCl. Surface charge density parameters were evaluated under application of the surface ionization model with a diffuse electrical double layer. The determined intrinsic acid constant, p K a i = 7.51, is not substantially different from published values for silanol groups of pure silica. The best agreement between the recalculated σ vs. pH plots and the experimental data was found with an intrinsic constant for the protonation of basic groups, log( K b i ) = 7.89.

Some phenomena of counterion condensation on dextran sulphate

The counterion condensation of mono- and divalent cations on the polyanion dextran sulphate (DS) was studied by conductometry and dye spectroscopy. The measurements were analysed using the limiting law for the conductance of polyelectrolytes and the two-variable theory of G. S. Manning. There are significant deviations between the experimental results and the predictions of the theories. Conductivity measurements show only at high temperatures and low polyion concentrations according to Manning's limiting law. The condensation of Ca 2+-ions, measured by dye spectroscopy, is affected by the species of monovalent counterion and the bulk solvent permittivity. We used Manning's formulae to adjust the apparent permittivity of the condensation volume of the polyelectrolyte and the charge-density parameter. The apparent permittivity ranges from 80 (ε r of pure water) to over 200. Counterion condensation only takes place if the permittivity is lower than 160. According to theory the critical charge-density parameter is 1, experimentally it is found that ξ c is 1.4.

Electrolyte transport through nanofiltration membranes by the space-charge model and the comparison with Teorell-Meyer-Sievers model

The space-charge (SC) model was applied to predict salt rejection with charged capillaries in reverse osmosis as a model system of nanofiltration membranes. Straightforward numerical calculation was carried out using parameters of feed concentration, pore radius and surface charge density. The rejection dependency on Peclet number by the SC model has been compared with that obtained by the Teorell-Meyer-Sievers (TMS) model which does not take into account the radial distributions of electric potential and ion concentration. The two models show good agreement for capillaries having smaller radius and lower surface charge density. Membrane parameters, reflection coefficient σ and solute permeability coefficient ω have been numerically calculated using the SC model as a function of two dimensionless parameters: the ratio of pore radius to Debye length r p λ d and the dimensionless potential gradient in the pore surfaces q 0, and the comparison of σ and ω calculated by the SC model with those by the Smit method and by the TMS model has been carried out. It is shown that the TMS model shows good agreement with the SC model in the calculation of the membrane parameters when q 0 is less than 1.0, while σ and ω by the Smit method show excellent agreement with those by the SC model when rejection is larger than 0.5.

Transferability of Norm-Conserving Pseudopotentials: Si, Al and Alkali Metal Elements Embedded in a Jellium

Transferability of the first-principle pseudopotentials is tested for a pseudoatom embedded in a jellium. The Hamann's pseudopotential (Phys. Rev. B 40 (1989) 2980) and its separable form are analyzed in this transferability test. Elements examined in this paper are classified into two; the first class is elements in which even pseudopotential without core-correction can assure sufficient transferability, e.g. Al, Si; the second one is elements in which only psedopotential with core-correction can assure sufficient transferability, e.g. alkali metal elements. The neutral sphere radius is the most important parameter for the transferability which is sensibly dependent upon the charge density parameter r s of the jellium. Once the neutral sphere radius is smaller than the core radius of the pseudopotential, sufficient transferability cannot revive even with the core-correction in a pseudoatom-in-jellium model.

Theoretical estimation of capillary zone electrophoresis behaviour of metal complexes using multivariate regression analysis

The migration of lanthanide metal ions complexed with aminopolycarboxylic reagents (ethylenediaminetetraacetic acid and chemically similar analogues containing varying degrees of basicity and size) in capillary zone electrophoresis was investigated. Electrophoretic mobilities were measured for a series of complexes in borate buffer electrolytes of variable pH and buffer concentration (62 different compositions). A migration model was developed to relate the electrophoretic mobility with charge density parameters of a metal complex (the net charge, the stability constant and ligand structural increments) and electrophoretic system variables such as the electrolyte pH. The predictive ability of the derived regression equation was evaluated in terms of its statistical significance. The good agreement observed between the calculated electrophoretic mobilities and experimental values demonstrates the applicability of the multivariate regression approach to the prediction of migration behaviour in capillary electrophoresis on the basis of small-number measurements. The results confirm also that the separation mechanism for metal complexes is based on the differential electrophoretic migration governed by differences in charge-to-size parameters.

Studies of Polyelectrolyte Solutions V. Effects of Counterion Binding by Polyions of Varying Charge Density and Constant Degree of Polymerization

The effect of the charge density on the behaviour of polyelectrolytes in contact with counterions was studied by activity measurements, Donnan dialysis, dye-spectrophotometry, and potentiometric titration. The polyelectrolytes investigated were poly(acrylic acid), i.e., PAA, and acrylic acid/acrylamide copolymers, i.e., PAM-y, where y is the degree of hydrolysis. This gave charge density parameters, ξ, which range from 0.12 to 2.88. Activity coefficients were determined for Na+ and K+ ions at T=25°C. The results were compared with those predicted from the theories of Manning and of Iwasa. Above the critical value, ξc=1, agreement with theory is satisfactory, but for ξ 20%), but within this error no counterion binding is observed. The binding of the divalent counterion Mg2+ was examined by a dye spectrophotometric method, where Na+ or K+ ions were added in excess. The results were analyzed within Manning’s two-variable theory. For ξ>1, the binding isotherms are in reasonable agreement with theory. For ξ<1, the Manning theory tends to under-estimate the degree of Mg2+ binding, θMg. Interestingly, θMg is not zero at ξ=0.28, suggesting that for divalent ions counterion binding occurs above ξc=0.5 as well as below. Potentiometric titration shows that there is some polyion folding for PAM-y. The degree of folding increases with decreasing y. This leads to increase of the effective polyion charge, so that ξ should be replaced by ξeff. It is observed that there is a small binding specificity for Na+ over K+ at large ξ. This vanishes when ξ becomes small. The reason is not clear yet. It may be due to increase in the content of helical segments of PAM-y as y decreases.

DNA double helices with positive electric dichroism and permanent dipole moments: Non-symmetric charge distributions and “frozen” configurations

The stationary electric dichroism of DNA restriction fragments with chain lengths of 399, 587 and 859 base pairs (bp) is shown to be positive at low electric field strengths in the range up to about 1 kV/cm; the dichroism is changed to values with the usual negative sign at higher electric field strengths. A positive dichroism at low field strengths has been observed in buffers with Na +-cations of various ionic strengths from 1 to 11 m M. Experiments with reversal of the electric field vector indicate that the alignment is induced by a permanent electric moment at low field strengths; when the field strength is increased, the contribution from an induced dipole moment increases and becomes dominant at high field strengths. Thus, the permanent dipole mechanism is prevailing in the range with positive values of the dichroism found at low electric fields, whereas the induced dipole mechanism is dominant in the range with negative values of the stationary dichroism found at high electric fields. In contrast to these results obtained in buffers containing only monovalent ions, the electric dichroism is negative in the whole accessible range of electric field strengths, when the buffer contained 100 μ M Mg 2+. The stationary values of the dichroism are negative under all tested conditions of buffer concentrations and electric field strengths for DNA double helices with 95, 179, 256, 4361 and 48502 bp. The positive dichroism found in the intermediate range of chain lengths is reduced and finally changed to the standard negative dichroism by UV irradiation. Positive values of the linear dichroism are predicted by Monte Carlo simulations for ensembles of wormlike chains with the charge density and optical parameters of DNA double helices, when the polarizability along the chain axis is negligible and when the internal mobility is frozen. The positive dichroism is due to the fact that virtually all DNA fragments are bent by thermal agitation; most of these bent DNA's are asymmetric and, thus, are associated with permanent dipole moments; the majority of dipole vectors in a given range of chain lengths is perpendicular to the end-to-end vector and, thus, leads to positive values of the linear dichroism at low degrees of bending. The model predicts a chain length dependence consistent with the experimental one due to a superposition of chain length dependences of the dipole moment and of the dichroism. The change from positive to negative values of the linear dichroism at increasing field strengths suggests some increase of the polarizability with the field strength, but may also be partly due to field induced stretching. The absence of the special effect in the presence of Mg 2+ indicates a particularly high compensation of the phosphate charges by this ion. The time constants of electrooptical rise curves observed in the range with the positive stationary dichroism are rather close to those of the decay curves. It is shown by Brownian dynamics simulations that this result is consistent with the existence of a permanent dipole moment. The deviation from the standard expected for permanent dipoles is due to the fact that in the present case the dipole vectors are mainly perpendicular to the long axis of the molecules. The decrease of the positive dichroism by UV irradiation is consistent with the interpretation of the data by a frozen ensemble of configurations and indicates that photoproducts introduce flexible joints into the DNA chains.

Measurement and interpretation of counterion distributions around cylindrical micelles

Radial distributions of heavy monovalent counterions around cylindrical micelles are measured directly using a small angle x-ray scattering. For the purpose of the analysis, the shape and size of the micelles are determined separately by a small angle neutron scattering. The micelles we used are formed by a comb-shaped copolymer poly(1-octadecene-co-maleic anhydride), abbreviated as PODMA in aqueous solutions neutralized by cesium hydro-oxides. The results are used to critically test the validity of solutions of non-linear Poisson-Boltzmann (PB) equation in the cell model to predict the radial distributions of monovalent counterions. The accuracy of the solutions of the non-lineaar PB equation for different magnitudes of linear charge density parameter is checked against Monte Carlo simulations. For comparison, we also show results of a similar experiment and analysis done for the counterion distributions around persistent length DNA in solution

Electrostatic Properties of Molecules from the X-Ray Charge Density. Application to Deuterated Benzene, 1-Alanine and d,l-Histidine

It has been shown (Z. Su and P. Coppens, Acta Cryst. A 48, 188 (1992)) that the electrostatic potential, the electric field, and the electric field gradient (EFG) can be expressed in closed forms in terms of the positions and the charge-density parameters of individual atoms, whose aspherical density is described by a pseudoatom model (e.g., N. Hansen and P. Coppens, Acta Cryst. A 34, 909 (1978)). A F o r t r a n program Molprop91 based on this method has been written (Z. Su, State Univ. of New York at Buffalo 1991). The method has been applied to the title compounds. Low-temperature X-ray diffraction data of fully deuterated benzene (G. A. Jeffrey, J. R. Ruble, Y. Yeon, and C. Lemann, private communication, 1991), /-alanine (R. Destro, R. E. Marsh, and R. Bianchi, J. Phys. Chem. 92, 966 (1988) and d,/-histidine (N. Li, Ph.D. thesis, State University of New York at Buffalo 1989) were analyzed using the least-squares deformation density refinement program Lsmol90 (a modified version of M o l l y ) . Molprop91 was subsequently used to calculate the electrostatic-potential maps in selected sections, and at the nuclear positions. For the latter, the EFGs were also evaluated. The electrostatic potentials were used to fit net atomic charges and estimate the molecular energies. Errors in the derived quantities are given.

High frequency dielectric dispersion of polyelectrolyte solutions and its relation to counterion condensation

The dielectric properties of polyelectrolyte solutions are studied in terms of counterion condensation by measurements of the dielectric response of pH buffered Na polyacrylate solutions. pH values are selected to allow variation of the charge density parameter ξ in the range between 0.5–2.8, that is, across ξ=1, the theoretical critical level for counterion condensation. The dielectric increment of the high frequency dispersion, Δε2, is found to have nonzero values only above the counterion condensation threshold and is therefore linked to the occurrence of counterion condensation. Above the condensation threshold Δε2 (≊6) and its corresponding polarizability α∥2 (≊6×10−16 cm3) are found to be approximately constant with increasing ξ. This result is predicted by Manning’s polarizability model for condensed counterions which results in a good fit to the experimental data when the average length of the polyion segments parallel to the external field, Ls, is set to 284 Å. This value of Ls is also shown to be in relatively close agreement with the value calculated for the length of a rigid subunit in Mandel’s polyion model, obtained using the relaxation time of the high frequency dispersion. The length Ls, which is larger than the persistence length, is estimated to be of the order of magnitude of the correlation length between segments.