Uniform Charge Density Research Articles

Structure of Polyelectrolyte Solutions at a Charged Surface

The structure of polyelectrolyte solutions at a charged surface is studied using density functional theory and Monte Carlo simulations. The polymer molecules are modeled as freely jointed chains of charged hard spheres, the counterions and co-ions as charged hard spheres, and the surface is a planar, impenetrable hard wall with a uniform surface charge density. The density functional theory treats the ideal gas contribution exactly, uses a weighted density approximation for the hard sphere contribution, and a generalized van der Waals approximation for the electrostatic contribution. At a fixed surface charge density, with increasing concentration of the polyion, the simulations show layering as well as charge inversion phenomena resulting from an interplay between excluded volume and electrostatic interactions. The integrated surface excess is a monotonically decreasing function of polymer concentration at high surface charge densities, but a nonmonotonic function of polymer concentration at lower surfac...

Enzyme/Non-enzyme Discrimination and Prediction of Enzyme Active Site Location Using Charge-based Methods

Calculations of charge interactions complement analysis of a characterised active site, rationalising pH-dependence of activity and transition state stabilisation. Prediction of active site location through large Δp K as or electrostatic strain is relevant for structural genomics. We report a study of ionisable groups in a set of 20 enzymes, finding that false positives obscure predictive potential. In a larger set of 156 enzymes, peaks in solvent-space electrostatic properties are calculated. Both electric field and potential match well to active site location. The best correlation is found with electrostatic potential calculated from uniform charge density over enzyme volume, rather than from assignment of a standard atom-specific charge set. Studying a shell around each molecule, for 77% of enzymes the potential peak is within that 5% of the shell closest to the active site centre, and 86% within 10%. Active site identification by largest cleft, also with projection onto a shell, gives 58% of enzymes for which the centre of the largest cleft lies within 5% of the active site, and 70% within 10%. Dielectric boundary conditions emphasise clefts in the uniform charge density method, which is suited to recognition of binding pockets embedded within larger clefts. The variation of peak potential with distance from active site, and comparison between enzyme and non-enzyme sets, gives an optimal threshold distinguishing enzyme from non-enzyme. We find that 87% of the enzyme set exceeds the threshold as compared to 29% of the non-enzyme set. Enzyme/non-enzyme homologues, “structural genomics” annotated proteins and catalytic/non-catalytic RNAs are studied in this context.

Simulation of Phase Equilibria in Lamellar Surfactant Systems

The coexistence of two lamellar liquid crystalline phases has been investigated by means of Monte Carlo simulations. The surfaces of the negatively charged bilayers formed by the surfactant molecules are modeled as planar infinite walls with a uniform surface charge density. Water is treated as a dielectric continuum, and only electrostatic interactions are considered. The counterions are mono- and divalent point ions, and their ratio is allowed to vary. Monovalent counterions lead to a repulsive osmotic pressure at all separations, while an attractive region exists when the counterions are divalent. In the latter case, one would expect a phase separation to take place, although it is not observed experimentally due to the limited stability of the lamellar phase at high water content. In a system with mixed counterions, however, the osmotic pressure exhibits a van der Waals loop under such conditions that two phases can coexist. A phase diagram is constructed, and the agreement with experimental data is excellent.

Upper critical fieldHc2calculations for the high critical temperature superconductors considering inhomogeneities

We perform calculations to obtain the $H_{c2}$ curve of high temperature superconductors (HTSC). We consider explicitly the fact that the HTSC possess intrinsic inhomogeneities by taking into account a non uniform charge density $\rho(r)$. The transition to a coherent superconducting phase at a critical temperature $T_c$ corresponds to a percolation threshold among different superconducting regions, each one characterized by a given $T_c(\rho(r))$. Within this model we calculate the upper critical field $H_{c2}$ by means of an average linearized Ginzburg-Landau (GL) equation to take into account the distribution of local superconducting temperatures $T_c(\rho(r))$. This approach explains some of the anomalies associated with $H_{c2}$ and why several properties like the Meissner and Nernst effects are detected at temperatures much higher than $T_c$.

Adsorption of charged macromolecules on oppositely charged porous column materials

A family of cationic polyelectrolytes possessing defined chain lengths, narrow chain length distributions, uniform charge density, but substituents of different hydrophilicity at the quaternary ammonium group served as model compounds for adsorption studies. These studies quantitatively revealed that polymer characteristics and electrostatic parameters affect the adsorption behavior on oppositely charged porous column materials. The presence of electrostatic exclusion, in addition to size exclusion, was proved comparing molecular, electrostatic and geometrical parameters. The dominance of electrostatic effects could be concluded evaluating the relation between molecular and electrostatic dimensions. The results provide a contribution how to estimate the threshold for electrostatic exclusion from pores as a function of dimensions and experimental conditions.

Apparent trap-controlled mobility evaluation in insulating polymers through depolarization characteristics derived by space charge measurements

This article illustrates a method for the estimation of apparent trap-controlled mobility of charges (i.e., the mobility of charges trapped at different states due to chemical-physical features) in polymeric insulation, based on the results of space charge measurements. The information provided by the so-called depolarization characteristic, obtained measuring space charge with short-circuited electrodes after a given poling time, is used for this purpose. Two approximate expressions for apparent-trap controlled mobility estimation are compared, the first based on rough assumptions (essentially unipolar injection and uniform charge density within insulation thickness), the second obtained following an approach based on space charge profile conservation under depolarization. These expressions are applied to the results of space charge measurements performed on unaged and aged insulating polymers. The two approaches provide apparent mobility estimates versus depolarization time in substantial agreement, and of the same order of magnitude of apparent mobility data reported in the literature for similar materials. This seems to support the validity of the key idea of the work, i.e., deriving apparent trap-controlled mobility estimates from space charge observations, particularly when such estimates are used to compare different materials or to infer the degradation level of aged insulation for diagnostic purposes.

How electromagnetically sharp is a needle?

The properties of a length of infinitely thin, perfectly conducting straight wire have been discussed extensively in the literature. But there remains a simple static problem, which is the distribution of a charge, q, along the length of the wire. Far from the ends, one may expect a uniform linear charge density, /spl rho//sub l/, and an electric field perpendicular to the axis. The behavior near the tips however is the real problem.

Molecular-Level Theoretical Model for Electrostatic Interactions within Polyelectrolyte Brushes: Applications to Charged Glycosaminoglycans

In this paper, we set forth a general theoretical framework to predict the nanoelectromechanical behavior of polyelectrolyte brushes and then apply it to a model system of negatively charged chondroitin sulfate glycosaminoglycan (CS-GAG) chains. We used a Poisson−Boltzmann (PB) based approach to calculate the electrostatic component of the interaction forces between polyelectrolyte molecules in a brush and to better understand how changes in polyelectrolyte fixed charge distribution affect these forces. The applicability and accuracy of three increasingly refined models were examined via a quantitative comparison with high-resolution force spectroscopy experimental data on a model CS-GAG brush system. In the first model, the polyelectrolyte brush was represented as a uniform, flat constant surface charge density. The second model approximated the polyelectrolyte brush as a uniform volume charge density. The third model represented the time-average space occupied by individual polyelectrolyte macromolecules in the brush as cylindrical rods of uniform volume charge density and finite height. This rod model approximates additional aspects of polymer molecular geometry and nonuniform molecular charge distribution inside the brush. Although the total polyelectrolyte charge was the same in all three models, both the rod and volume charge models, which accounted for the height of the brush, predicted much higher forces than the surface charge model at any given separation distance. The comparison between measured and theoretically predicted forces showed that the rod model gave better agreement with the force data over the widest range of separation distance D and for reasonable best-fit values of the brush height and rod radius. Therefore, in the framework of the PB theory, it appears that molecular-level changes in the charge distribution inside polyelectrolyte brush layers as manifested in the rod model can significantly change the magnitude and the shape of the resulting force profile.

Calculations based on measurements of charge deposited by a streamer on a PTFE surface

Surface charge on an insulator's surface is studied using 3-dimensional finite element modelling. The calculations are based on measurements of surface charge deposited by a streamer on a PTFE surface. The surface electric field strengths associated with uniform surface charge density distributions over a 1 mm/sup 2/ region are calculated for a range of different measured charge densities. The effect of reducing the area of the surface charge whilst keeping the total amount of charge in the region constant is observed. The surface charge is then modelled with a Gaussian distribution of charge and compared to that of a uniform distribution. By assuming a maximum allowable surface electric field strength an estimation of actual charged path diameter is made.

Torque exerted by a moving electric charge on a stationary electric charge distribution

The interaction between a moving electric charge and a stationary electric charge distribution is considered. It is shown that the interaction involves not only an electric attraction or repulsion but also a heretofore unreported electric torque exerted by the moving charge on the stationary charge distribution. The torque is associated with the asymmetry of the electric field of the moving charge and is present even if the stationary charge distribution is highly symmetrical, such as a uniformly charged sphere, for example. As a result of the torque, the stationary charge distribution is set in rotation. The rotating stationary charge distribution creates a magnetic field and an induced electric field that act on the moving charge thus further contributing to the complexity of the interaction. Two types of moving charges are considered: a point charge moving with constant speed along a straight line and a point charge moving with constant speed along a circular orbit. The torques exerted by these charges on stationary charge distributions in the shape of a small circular ring, small disc, and small sphere of uniform charge density are computed and some consequences of these torques are discussed. The possibility of the existence of a similar interaction effect in gravitational systems is also considered.

Coherent transition radiation from spherical electron bunch

Angular distribution of transition radiation (TR) excited by an extended system of charged particles is investigated. A case is considered in which TR is emitted by charges which intersect boundary in series, at equidistant points. Also, TR generated by a spherical bunch with a uniform charge density over the volume is considered. It is shown that at a certain correlation between the wavelength of TR and dimensions of the charge system, the spectral and angular distributions of radiation generated by a single charge and by the extended bunch, are essentially different. At a some possible charge distribution, TR has the properties typical for the Doppler effect, or for the Vavilov–Cherenkov radiation.

Breakdown of fourfold symmetry of Fermi surface and magnetic excitation spectrum

Performing the slave-boson mean-field approximation to the two-dimensional t– J model under the assumption of the uniform charge density, we find two mechanisms that lead to the breaking of fourfold symmetry of the Fermi surface (FS) and the magnetic excitation spectrum. One mechanism originates from the J-term, which has an intrinsic instability toward the formation of a quasi-one-dimensional FS. The other mechanism comes from the inclusion of the small interlayer hopping t ⊥, which can lead to the drastic breaking of fourfold symmetry in the diagonal incommensurate magnetic peaks around (π, π). These findings are discussed with emphasis on possible relevance to La 2− x Sr x CuO 4 systems.

Potential distribution and field intensity for a hyperboloidal probe in a uniform field

The scalar potential and electric field distributions in the gap region of a probe-substrate system are calculated. The probe, modeled as a dielectric medium with the geometry of a one sheeted hyperboloid of revolution, is located above a charged substrate surface which is modeled as a dielectric half space interfaced with a uniform surface charge density. The potential and field distributions are then calculated as functions of the dielectric constant of the medium filling the space between the tip and the surface, and as functions of the hyperboloidal shape parameter. Comparisons are made with the case of a dielectric spheroidal body. The analytical results attained can be used to study other related quantities such as energy density or Coulomb interaction in the neighborhood of the nanometer sized apex region without resorting to numerical methods. This investigation allows for tip shape related field variation in various dielectric media to be studied. Application of this approach to modeling probe tip-sample (probe tip-substrate) interaction in scanning probe microscopy, or to modeling dielectric breakdown processes, are examples of the potential use of the method.

Noncommutative cohomology and electromagnetism on $C_q[SL_2]$ at roots of unity

We compute the noncommutative de Rham cohomology for the finite-dimensional q-deformed coordinate ring $C_q[SL_2]$ at odd roots of unity and with its standard 4-dimensional differential structure. We find that $H^1$ and $H^3$ have three additional modes beyond the generic $q$-case where they are 1-dimensional, while $H^2$ has six additional modes. We solve the spin-0 and Maxwell theory on $C_q[SL_2]$ including a complete picture of the self-dual and anti-self dual solutions and of Lorentz and temporal gauge fixing. The system behaves in fact like a noncompact space with self-propagating modes (i.e., in the absence of sources). We also solve with examples of `electric' and `magnetic' sources including the biinvariant element $\theta\in H^1$ which we find can be viewed as a source in the local (Minkowski) time-direction (i.e. a uniform electric charge density).

Modeling charge transfer and induction in gas–solid fluidized beds

A simple mechanistic model is developed by applying the method of images to distinguish induced and transferred charges, assuming circular bubbles with charged particles around their surfaces. The simulation shows that the trace of induced charge vs. time is insensitive to the thickness of the layer of charged particles at the bubble surface with a uniform charge density distribution. However, charge transfer during a collision of particles surrounding the rising bubble with a probe is a strong function of the particle velocity profile. Experiments in which single bubbles were injected into an acrylic two-dimensional column showed that 321 μm glass beads, fluidized by air, were charged positively. The model with uniform charge on the surface of the bubble gives better predictions of the charge and voltage outputs than when opposite charges are assumed at the front and rear of the bubble as in previous work, but significant improvements are needed to eliminate discrepancies between the predictions and experimental measurements.

M‐component mode of charge transfer to ground in lightning discharges

The M‐component mode of charge transfer to ground is examined using (1) multiple‐station measurements of electric and magnetic fields at distances ranging from 5 to ∼ 500 m from triggered‐lightning channels and (2) measured currents at the channel base. Data have been obtained in 1997, 1999, and 2000 at the International Center for Lightning Research and Testing at Camp Blanding, Florida, for (1) “classical” M‐components that occur during the continuing currents following return strokes and (2) impulsive processes that occur during the initial stage of rocket‐triggered lightning and are similar to the “classical” M components. All lightning events considered here effectively transported negative charge to ground. For one triggered‐lightning event the electric field 45 km from the lightning channel was measured together with the current and close fields. The shapes and magnitudes of the measured close electric and magnetic fields are generally consistent with the guided‐wave mechanism of the lightning M component. Specifically, the M‐component electric field peak exhibits logarithmic distance dependence, ln(kr−1), which is indicative of a line charge density that is zero at ground and increases with height. Such a distribution of charge is distinctly different from the more or less uniform charge density that is characteristic of the dart leaders in triggered lightning, as inferred from close electric field measurements. The M‐component magnetic field peak decreases as the inverse distance (i.e., r−1), which is generally consistent with a uniform current within the lowest kilometer or so of channel. The M‐component electric field at 45 km appeared as a bipolar, microsecond‐scale pulse that started prior to the onset of the M‐component current at the channel base. M‐component‐type processes can produce acoustic signals with peak pressure values of the same order of magnitude as those from the leader/return stroke sequences in triggered lightning.

Electrostatic force density for a scanned probe above a charged surface

The Coulomb interaction of a dielectric probe tip with a uniform field existing above a semi-infinite, homogeneous dielectric substrate is studied. The induced polarization surface charge density and the field distribution at the bounding surface of the dielectric medium with the geometry of half of a two sheeted hyperboloid of revolution located above the dielectric half space interfaced with a uniform surface charge density is calculated. The force density on the hyperboloidal probe medium is calculated as a function of the probe tip shape. The calculation is based on solving Laplace’s equation and employing a newly derived integral expansion for the vanishing dielectric limit of the potential. The involved numerical simulations comprise the evaluation of infinite double integrals involving conical functions.

Chern-Simons theories on the noncommutative plane.

We investigate U(N) Chern-Simons theories on the noncommutative plane. We show that for the theories to be consistent quantum mechanically, the coefficient of the Chern-Simons term should be quantized kappa = n/2pi with an integer n. This is a surprise for the U(1) gauge theory. When uniform background charge density rho(e) is present, the quantization rule changes to kappa+rho(e)straight theta = n/2pi with the noncommutative parameter straight theta. With the exact expression for the angular momentum, we argue in the U(1) theory that charged particles in the symmetric phase carry fractional spin 1/2n and vortices in the broken phase carry half-integer or integer spin -n/2.

Effect of nonzero chain diameter on "DNA" condensation.

We present a simple model to investigate the effect of chain diameter on multivalent-counterion-induced attractions between two charged chains. In our minimal model, the chains are rigid rods of diameter D with a uniform charge density on the surface, and the counterions are point ions. As a function of the separation between two rods, we find a repulsive barrier in the free energy whose height increases with D. We have also explored the effect of counterion valency Z on the interaction. For parameters characteristic of DNA, we find that a minimum valency of Z=3 is required to produce condensation. We also find that the shape of the potential is fairly insensitive to Z for Z>/=3. These results are consistent with experimental observations of DNA condensation.

Ion Distributions in a Cylindrical Capillary as Seen by the Modified Poisson−Boltzmann Theory and Monte Carlo Simulations

The distributions of ions enclosed in a charged cylindrical capillary with impenetrable surfaces are studied by using (i) the Poisson−Boltzmann theory, (ii) the modified Poisson−Boltzmann theory, and (iii) the Monte Carlo method. The ions are treated in the primitive model approximation, while the inner surface of the capillary is taken to have a uniform charge density. The results for the wall-ion distributions are presented for the capillary containing mono- or divalent counterions and size symmetric 1:1 or 2:2 electrolytes. Some calculations for the mean activity coefficients of the added electrolytes are also reported. The Monte Carlo results for the concentration profiles and the electrolyte activities are used to asses the validity of the potential theories. The modified Poisson−Boltzmann theory is found to be in good agreement with the simulation results for both mono- and divalent ions present in the solution. As expected, the regular Poisson−Boltzmann theory provides reasonable descriptions of so...