Showing papers on "Charge density published in 1970"

Theory of Metal Surfaces: Charge Density and Surface Energy

Abstract: The first part of this paper deals with the jellium model of a metal surface. The theory of the inhomogeneous electron gas, with local exchange and correlation energies, is used. Self-consistent electron density distributions are obtained. The surface energy is found to be negative for high densities (${\mathcal{r}}_{s}\ensuremath{\le}2.5$). In the second part, two corrections to the surface energy are calculated which arise when the positive background model is replaced by a pseudopotential model of the ions. One correction is a cleavage energy of a classical neutralized lattice, the other an interaction energy of the pseudopotentials with the electrons. Both of these corrections are essential at higher densities (${\mathcal{r}}_{s}\ensuremath{\le}4$). The resulting surface energy is in semiquantitative agreement with surface-tension measurements for eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al), typical errors being about 25%. For Pb there is a serious disagreement.

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

Abstract: 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.

Counterion fluctuation and dielectric dispersion in linear polyelectrolytes

Abstract: The thermal fluctuation in the concentration of counterions bound to a rodlike polyion was analyzed by expanding the fluctuation in a Fourier series along the rod. The amplitude and the relaxation time of fluctuations of various wave lengths were obtained as functions of the charge density and the length of the polyion. From these results the real and imaginary parts of the dielectric constant of the polyelectrolyte solution were derived as the sum of contributions of fluctuations of different modes. The dielectric dispersion curve or the Cole-Cole plot obtained was found to be in good agreement with experimental data.

Surface Charge and the Conductance of Phospholipid Membranes

Abstract: Bilayer membranes, formed from various phospholipids, were studied to assess the influence of the charge of the polar head groups on the membrane conductance mediated by neutral „carriers” of cations and anions. The surface charge of an amphoteric lipid, phosphatidyl ethanolamine, was altered by varying the pH, and the surface charge of several lipids was screened by increasing the ionic strength of the solution with impermeant monovalent and divalent electrolytes. The surface charge should be a key parameter in defining the membrane conductance for a variety of permeation mechanisms; conductance measurements in the presence of carriers may be used to estimate the potential difference, due to surface charge, between the interior of the bilayer and the bulk aqueous phase. The large changes in conductance observed upon varying the surface charge density and the ionic strength agree with those predicted by the Gouy-Chapman theory for an aqueous diffuse double layer. Explicit expressions for the dependence of the membrane conductance on the concentrations of the carrier, the permeant ion, the surface charge density, and the ionic strength are presented.

Linear and Nonlinear Attenuation of Acoustic Surface Waves in a Piezoelectric Coated with a Semiconducting Film

Abstract: The interaction of acoustic surface waves in a piezoelectric with carrier waves in a semiconducting film on the surface is considered. Particular attention is paid to the limitation of the small signal theory due to nonlinear effects. It is found that large signal effects, which occur at moderate acoustic power levels, are important when the maximum rf charge density exceeds the available background charge density. Measurements of acoustic attenuation and acoustoelectric current in a CdS film on the surface of Y‐cut quartz are reported. A fair agreement between theory and experiment is found.

Superconductors containing impurities with crystal-field split energy levels

Abstract: We investigate theoretically the problem of a superconducting matrix containing paramagnetic rare earth impurities with crystal-field split energy levels. There are two competing mechanisms which change the superconducting transition temperatureTc. One is inelastic charge scattering of conduction electrons from the aspherical part of the 4f charge distribution, which leads to an increase inTc similar to that of optical phonons. The other and often predominant mechanism comes from the exchange interaction, which depressesTc and can be very effective even among non-magnetic levels via off-diagonal matrix elements. Crystalline fields serve to alter the effectiveness of the two kinds of scattering depending upon the symmetry character of the low-lying levels, and in favorable cases one may study separately the effects of the two types of scattering by adding different impurities to a given host. We find that crystal-field levels at energies quite high compared tokB·Tc can still have an important effect onTc. It is shown that the crystalline-field splitting should be directly observable as structure in the tunneling characteristics.

Theory of Charge Transfer in Aromatic Donor-Acceptor Crystals

Abstract: A narrow‐band, localized model is developed for charge transfer (CT) interactions in 1:1 stacks of planar, π‐electron donors (D) and acceptors (A). The inequivalence of D and A sites and the Madelung constant for the ionic lattice are treated phenomenologically. The electronic states, for arbitrary CT in the aromatic D–A stacks, are found self‐consistently by an equation‐of‐motion method. The ground‐state charge density and the band structures correspond to primarily neutral, ···DADA···, diamagnetic or to primarily ionic, ···D+A−D+A−···, paramagnetic one‐dimensional semiconductors. The activation energies for CT and for semiconduction, together with the CT stabilization, are found self‐consistently. In ionic lattices, CT is shown to provide an activation energy for paramagnetism of the proper magnitude. When the sites are equivalent, the theory reduces to a half‐filled Hubbard model, and the self‐consistent solutions are in good agreement with exact results.

Surface state related noise in MOS transistors

Abstract: The theory of surface state effects on 1 ƒ noise in p−n junctions is extended to explain low-frequency excess noise in MOS transistors. Experimental results are critically compared to theory. The results show that low-frequency excess noise in MOS transistors is due to the fluctuation of charge density in the conduction channel caused by the surface potential fluctuation. The fluctuation of the surface potential is introduced by the random charge occupancy of surface states. The low-frequency excess noise in MOS transistors is found to be proportional to the surface state density and the square of the transconductance of the device, and inversely proportional to the gate area and the square of the unit area gate-insulator capacitance. It is also shown that the surface state density when the surface is strongly inverted can be obtained from noise measurements. Finally it is shown that by proper heat treatment it is possible to reduce the low-frequency excess noise of MOS transistors.

The potential due to a charged metallic strip on a semiconductor surface

Abstract: We solve numerically the problem of finding the potential and electric field around a negatively charged metallic contact on the surface of an n-type semiconductor. The semiconductor, which has permittivity ∊ 1 , fills the half-space y 0 is vacuum with permittivity ∊ 0 . In suitable dimensionless coordinates the potential ϕ satisfies Laplace's equation in y > 0 and the equation ▽2ϕ = eϕ − 1 in y 0 0 | » 1 and η = ∊ 0 /∊ 1 > « 1. We examine in considerable detail the limiting case η = 0, first for the less practical situation where |ϕ 0 | « 1 and then for |ϕ 0 | » 1. In case the |ϕ 0 | « 1 we show that our numerical solution agrees well with the exact analytical solution of a linearized version of the problem. For |ϕ 0 | » 1, we give plots of the equipotential curves, curves of equal charge density, and curves of constant electric field amplitude. These results also yield expressions for the capacitance of both a strip and a circular electrode. The modifications of these results when η > 0 are also given in some detail. Finally, we discuss the numerical calculations at some length.

The Formation of Cluster Ions in Laboratory Sources and in the Ionosphere

Abstract: Publisher Summary This chapter discusses about those cluster ions that may be formed in the ionosphere and the corresponding laboratory observations. The existence of cluster ions in the ionosphere and under a variety of laboratory conditions is indisputable. There remains, however, a considerable disparity among laboratory observations regarding the mass spectral distributions of these ions. Ionospheric observations may similarly be at fault, although the sparsity of experiments and experimental groups in this area does not permit a rigorous conclusion at this time. The preponderance of laboratory results and some cursory theoretical calculations suggest that there is a special stability for the cluster ion consisting of a singly charged arrangement of four water molecules and a hydrogen atom. At this time there are no conclusive experimental or theoretical results to suggest any definitive structure or charge distribution for these ions. A considerable amount of work has been stimulated by these early observations and publications in this field have been burgeoning at a rapidly increasing rate.

Charge and Potential Distributions in Shielded Striplines

Abstract: A new method is presented for calculating the charge and potential distribution in shielded microstrip lines with stratified dielectric fillings. The boundary value problem associated with this structure is formulated in a rigorous manner and the solution is constructed by an extension of the function-theoretic technique. Several advantages of this method are pointed out. The most important of these is its numerical efficiency. Numerical results are presented for charge and potential distributions for several choices of design parameters. The characteristic impedance and the guide wavelength are obtained from the knowledge of the charge distribution. Comparisons are made with the published data and the agreement is found to be very satisfactory.

The decomposition of a triply-charged metastable positive ion of biphenyl

Abstract: The transition, [C12H10]+3[C11H7]+2 + [CH3]+, has been detected both in the ion kinetic energy spectrum and in the mass spectrum of biphenyl. The width of a resulting ‘metastable peak’ has been measured by setting the magnetic field to accept [C11H7]+2 ions and scanning the high voltage at fixed electric sector voltage. The kinetic energy released in the decomposition, calculated from the peak width, amounted to 4.5 eV. With the assumption that this energy release is due entirely to charge separation, the charge distribution in [C12H10]+3 is discussed. The derivation of the equations used to calculate the energy released is given in the Appendix.

Determination of the Charge Distribution of Methane by a Method of Density Constraints

Abstract: The molecular charge distribution of methane is expressed in terms of an orthonormal set of molecular orbitals which are determined solely by imposing a set of constraints on the derived one-electron charge density, the constraints being that the charge density reproduce the experimental expectation values of a set of one-electron operators. The molecular orbitals are expanded in terms of an SCF set of atomic orbitals on carbon and a single 1s STO on each hydrogen. The derived charge distribution is found to be equal to the SCF Hartree-Fock distribution in its prediction of one-electron expectation values. The energy, as determined by the associated wave function, is −40.156 a.u. This energy value is comparable to that obtained in a SCF LCAO MO calculation with a similar basis set and is 0.048 a.u. above the best calculated value of the Hartree-Fock limit.

Evaluation of the KKR method for the dilute alloy problem

Abstract: A method of calculation for the problem of a single substitutional impurity in an infinite lattice is presented. Beeby's generalization of the Korringa-Kohn-Rostoker method of band-structure theory is put into a form suitable for numerical calculation of the charge density on the impurity site, and a preliminary calculation for Cu-Ni is performed. The calculated charge density exhibits the expected 'd resonance' and is in reasonable agreement with experimental data.

Impurity screening near a metal surface

Abstract: The linear response of a metal to an embedded charge impurity near the surface is treated within the random phase approximation. The surface is assumed to be perfectly reflecting, which allows the boundary value problem to be solved by symmetric continuation of the metal. The resulting integral equation for the symmetrized charge density is solved numerically in momentum space. When quantum-mechanical interference effects are neglected (quasi-classical limit) an analytic solution is obtained. Graphs are presented for the potential and the normal field at the surface in the quantum-mechanical and quasi-classical case. These graphs display the Friedel oscillations as a function of the radial co-ordinate on the surface and of the distance of the impurity from the surface. In the quasi-classical case, asymptotic expressions which describe these oscillations are obtained. The results for the Fermi-Thomas approximation are also given for comparison. In every case the impurity charge is completely screened, in the sense that the average of the normal field at the surface is zero.

Dust devil properties

Abstract: Measurements of electric moment are reported for seventeen New Mexico dust devils. Estimates of charge and charge density were made for eight of these; charge densities appear generally to be of the order of 106 elementary charges cm−3. Ground speeds ranged from 5–11 m sec−1.

On the capacity of the circular disc condenser at small separation

Abstract: A pair of identical circular discs, held at equal and opposite potentials, forms a condenser whose capacity C depends on the ratio e of separation against diameter. The determination of an asymptotic expansion for C when e is small poses an axisymmetric boundary-value problem for harmonic functions that has engaged the attention of numerous investigators over a long span of time. It is a simple matter to construct a Fredholm integral equation of the first kind for the charge density ± σ on the discs, in terms of which the potential field and the capacity are implicitly determined, but the equation is unsuitable if e ≪ 1. Integral equations of the second kind and of the dual variety have also been proposed as a means of securing a more manageable formulation of the boundary-value problem. An elementary approximation follows from the hypothesis that the charge density is almost the same as though the discs were of infinite extent, except for a region close to the edges, and leads to the result C ∼ l/8e as e → 0. Kirchhoff considerably improved on this crude estimate by suggesting a plausible edge correction which yields two further terms for C, of orders log ∈ and a constant, respectively, and his results have been rigorously established by the more refined analysis of Hutson. In the present work an integral equation of the first kind for the distribution of potential off the discs is derived and utilized to obtain an approximation for C when e is small, reproducing the result of Kirchhoff and Hutson. Furthermore, an estimate of the error provides explicit details regarding the next term in the asymptotic expansion of C, which is of the order e(log e)2.

The cylindrical antenna as a probe for studying the electrical properties of media

Abstract: When a base-driven cylindrical monopole (or center-driven dipole) is immersed in an arbitrary medium, the electric and magnetic fields on its surface depend not only on its length and radius but also on the effective conductivity and permittivity of the medium. These fields can be explored and measured with small probes designed to travel along the cylindrical surface of the antenna. The interpretation of the observations depends on the availability of a general theory that correctly describes the distributions of current and charge on the conductor. The results of a new theory that is valid for electrically thin monopoles up to 5\lambda/8 (dipoles up to 5\lambda/4) in length over all practical ranges of conductivity and permittivity of the ambient medium, including those characteristics of under- and overdense cold plasmas, are described together with their experimental verification.

Correlation of the Surface Charge Characteristics of Polymers with Their Antithrombogenic Characteristics

Abstract: A knowledge of the structure of the double layer is essential in the investigation of reactions at an inierface between two dissimilar media. This aspect is briefly presented in respect to charge separation and potential distribution in the interfacial region. The types of reactions that can occur at solid-solution interfaces (electron transfer, electrosorption, and electro-phoretic deposition) are discussed. The electrokinetic methods for determination of surface charge characteristics of insulator materials in electrodes are reviewed. Thrombosis on the blood vessel wall and on prosthetic materials is an interfacial chemical reaction. The evidence for an electrochemical mechanism of thrombosis on conducting materials is outlined. Under normal conditions, the blood vessel wall is negatively charged. Injury or atherosclerosis makes it less negatively or even positively charged. With decrease of pH, there is an increase in the surface charge density of the blood vessel wall with an isoelectric poin...