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Showing papers on "Charge density published in 1972"


Journal ArticleDOI
TL;DR: In this article, it is shown that it is possible to partition a molecular system in such a way that the same virial relationship between the average kinetic and potential energies observed for a total molecular system is found to hold for individual fragments.
Abstract: Arguments and numerical examples are presented which suggest that the distribution of electronic charge in a molecular system can be related to the total virial of all the forces exerted on each element of the charge density. Further numerical evidence is given indicating that it is possible to partition a molecular system in such a way that the same virial relationship between the average kinetic and potential energies observed for a total molecular system is found to hold for the individual fragments. This partitioning scheme is based on an observable property of the charge distribution. The proposals presented here provide a basis for the understanding and prediction of molecular charge distributions and their properties.

461 citations


Journal ArticleDOI
TL;DR: In this paper, the status of the electron structure of superheavy atoms with nuclear charge Z > Zc is described, where Zc≈170 is the critical value of the nuclear charge, at which the energy of the ground state of the 1S 1/2 electron reaches the limit of the lower continuum of the solutions of the Dirac equation.
Abstract: We describe the status of the problem of the electron structure of superheavy atoms with nuclear charge Z > Zc ; here Zc≈170 is the critical value of the nuclear charge, at which the energy of the ground state of the 1S1/2 electron reaches the limit of the lower continuum of the solutions of the Dirac equation (∊ = - mec2) . We discuss the dependence of Zc on the nuclear radius R and on the character of the distribution of the electric charge inside the nucleus, and also the form of the wave functions at Z close to Zc . Owing to the Coulomb barrier , the state of the electron remains localized at Z > Zc , in spite of the fact that its energy approaches the continuum. An analysis of the polarization of the vacuum in a strong Coulomb field shows that a bare nucleus with supercritical charge Z > Zc produces spontaneously two positrons and, in addition a charge density with a total of two units of negative charge in the vacuum. The distribution of this density is localized in a region of dimension r ~ ħ/mec at the nucleus. The possibility of experimentally observing the effect of quasistatic production of positrons in the collision of two bare uranium nuclei (i.e., without electrons) is discussed. A brief review is presented of work on the motion of levels with increasing depth of the potential well in other relativistic equations (Kelin-Gordon, Proca, etc.).

318 citations


Journal ArticleDOI
TL;DR: In this article, the electron conductivity mobility on weakly inverted Si surfaces covered with thermally grown oxide is reported at temperatures from 30 to 300 °K as a function of the surface oxide charge density.

245 citations


Journal ArticleDOI
TL;DR: In this article, the excess charge density distribution near gaps and steps in microstrip transmission lines is calculated by the solution of singular integral equations, and the results are believed to be accurate to within a few percent.
Abstract: The excess charge density distribution near gaps and steps in microstrip transmission lines is calculated by the solution of singular integral equations. Data are presented for gaps in microstrips of width-to-substrate-thickness ratios of 0.5, 1.0, and 2.0 and relative dielectric constants ranging from 1.0 to 15.0. For steps in a microstrip line results are given for width-to-thickness ratio of unity, relative dielectric constants of 1.0 and 9.6, while the change of width-to-height ratio is from 0.1 to 10.0. The excess charges are calculated explicitly in relatively short computing times, and the results are believed to be accurate to within a few percent.

184 citations


Journal ArticleDOI
TL;DR: In this article, the dielectric behavior of electro-fluids which show the Winslow effect, one of the electro-viscous effect, was studied experimentally, and it was shown that water film adsorbed to the particles directly affects the surface charge density of electric double layers.
Abstract: Dielectric behaviour of electro-fluids which show the Winslow effect, one of the electro-viscous effect, is studied experimentally. From the experimental results that water film adsorbed to the particles directly affects the surface charge density of electric double layers and makes dielectric constant of electro-fluids increase, the model of electric double layers proposed by Schwarz is able to be applied to the Winslow effect. Using Krieger-Maron's method about non-Newtonian flow, electro-fluids under an electric field are found to be approximated by the Bingham body with the yielding shear stress proportional to the square of electric field strength. Besides, electro-fluids show the negative thixotropy that the viscosity increases with time under an electric field.

131 citations


Journal ArticleDOI
TL;DR: In this article, a comprehensive account of the electrical double-layer interaction forces between spheres with the condition of either constant surface potential or constant surface charge density is given, and simple formulas involving quadratures are derived for the plate interaction free energy at both constant potential and constant charge, and the difference formula of Frens is generalized.

105 citations


Journal ArticleDOI
TL;DR: In this article, the interaction energy of a static point charge with a metal surface was calculated by treating the metal surface in the jellium approximation with the positive ions replaced by a uniform background and the electrons characterized parametrically by their total charge density.
Abstract: We have calculated the interaction energy of a static point charge with a metal surface. The metal surface is treated in the jellium approximation with the positive ions replaced by a uniform background and the electrons characterized parametrically by their total charge density. The energy of the system is written as a functional of the total electron density, including that induced by the point charge external to the metal. The distribution of this induced charge is varied to minimize the energy and thus calculate the image potential. We find that we can write the image potential for $Dg2$ \AA{} as $\ensuremath{-}\frac{{Q}^{2}}{4(D\ensuremath{-}d)}$, where $Q$ is the size of the point charge, $D$ the distance of the point charge from that jellium discontinuity, and $d$ an origin shift which is a function of the electron density at the metal surface. For smaller distances the potential no longer scales as ${Q}^{2}$ and saturation sets in.

104 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derived and approximately evaluated a theoretical relation between the variance of the surface potential and the autocovariance function of the interface charge distribution for the case of a single-dimensional charge sheet model of the MOS device.
Abstract: Small‐signal conductance peaks in metal‐oxide‐semiconductor (MOS) devices have been found experimentally to be much wider than predicted by the surface‐state continuum model of Lehovec. This increased width has been attributed by Nicollian and Goetzberger to surface potential fluctuations generated by inhomogeneities in the interface charge density. However, no theoretical estimate of the amount of additional width to be expected from such inhomogeneities nor of the dependence of this additional width upon device parameters has been presented. In this paper these theoretical estimates are provided for the case when the surface potential departs slightly from its value as estimated in the usual one‐dimensional charge sheet model of the MOS device. To do this we derive and approximately evaluate a theoretical relation between the variance of the surface potential and the autocovariance function of the interface charge distribution. For a random interface charge distribution we obtain a logarithmic dependence of the variance upon the sum of the oxide, space‐charge, and surface‐state capacitances. In the limiting case in which only long‐wavelength charge fluctuations contribute to the variance of the surface potential, this logarithmic dependence is replaced by the dependence appropriate to a quasiuniform model. The results indicate that the magnitude and bias dependence of the effect of a random distribution is in fair agreement with experiment, but that more data are needed at various oxide thicknesses on samples of low or uniform surface‐state density with known flat‐band shifts before it can be concluded that surface potential fluctuations are indeed responsible for the anomalous width of the conductance peaks. Should this prove to be true, the dependence of the conductance‐peak width upon device parameters would serve to identify both the presence and the nature of interface charge inhomogeneities.

89 citations


Journal ArticleDOI
TL;DR: A system of flux equations consistent with non-equilibrium thermodynamics is developed and the minimum assumptions and idealizations needed to obtain well-defined results are identified and methods of computation have been developed which permit the observable behaviour of the system to be predicted in terms of the ascertainable concentration of the bulk solutions.
Abstract: When a steady electric current is passed through a porous membrane which separates two electrolyte solutions at different concentrations the system can, in a suitable experimental configuration, enter a state of stable oscillations of the trans-membrane pressure and potential. This system, sometimes called the Teorell membrane oscillator, also displays unusual stationary state behaviour when the pressure difference across the membrane is held constant. These phenomena arise because the pressure-driven flow of volume through the membrane is virtually independent of the concentration of the solution in its pores, whereas the electro-osmotic flow decreases as the concentration increases. If the pressure-driven and electro-osmotic flows are opposed and pressure is applied to the concentrated solution then at low currents pressure drives the concentrated solution into the pores and at high currents electro-osmosis drags the dilute solution into the pores. At some intermediate current the transition from concentrated to dilute solution in the pores occurs and is accompanied by a sudden increase in the membrane resistance and potential difference. These observations have been made on various membranes of ill-defined structure, it is shown here that they can be reproduced with Nuclepore filters which have readily characterized uniform circular and parallel pores. This observation has facilitated the development and testing of a quantitative theory of the phenomenon. The theory developed here follows the lines laid down by Kobatake & Fujita (1964) and by Mikulecky & Caplan (1966). The membrane pores are treated as independent capillaries lined by an electrical double layer with a diffuse counter charge in the pore solution. A system of flux equations consistent with non-equilibrium thermodynamics is developed and the minimum assumptions and idealizations needed to obtain well-defined results are identified. Flow in the pores is treated via the Navier-Stokes equation and equations for the membrane fluxes and forces are obtained in terms of the membrane properties and external parameters under the control of an experimenter. Two cases are considered. In the first the surface charge density on the pore walls is independent of the solution concentration and in the second the surface charge density is proportional to the cube root of the concentration. The second case applies to Nuclepore membranes because the surface charge on poly-carbonate is probably due mainly to adsorption of anions from solution. In the first case the electro-osmotic flow is inversely proportional to the one-half power of the concentration and in the second case to the one-sixth power. In order to convert the barycentric local flux equations to equations describing the macroscopic phenomena account must be taken of the radial variation of parameters over a pore cross-section and to their variation along the pore from one membrane boundary to the other. Radial variation is dealt with first by transferring from the barycentric to the membrane-fixed frame. The flux equations are then averaged over the pore cross-section and finally integrated across the membrane under the assumption of a steady state. This procedure has the advantage of producing manageable flux equations, with no adjustable parameters, which can therefore be given an unequivocal test. It has the disadvantage that no information is obtained concerning the precise mechanisms of the sudden transitions between the high and low resistance states. The flux equations predict the observed types of transitions in fluxes and forces and give a correct general picture of the expected behaviour of the system. In order to devise a quantitative test it is necessary to bear in mind that it is not technically possible to stir bulk solutions very vigorously against the surfaces of a thin porous membrane without exaggerating pore end effects or even pulsing solutions right through the pores. This difficulty has been dealt with by superimposing upon the membrane flux equations, transport equations across Nernst hypothetical diffusion layers at the membrane/solution boundaries. Methods of computation have been developed which permit the observable behaviour of the system to be predicted in terms of the ascertainable concentration of the bulk solutions. It is interesting to note that, whereas the low power of the concentration dependence of electro-osmosis in Nuclepore membranes, as compared with constant charge membranes, lowers the scale of the expected force-flux transitions, the presence of stagnant solution layers at the membrane faces increases the scale of these transitions. The quantitative test of this theory has been based on the comparison of observed and predicted current-voltage curves. A membrane cell has been devised in which the solutions are stirred by paddles and pump circulation to give stable and characterizable stirring conditions. An electric current can be passed through the cell but the products from the electrodes are excluded by ion-exchange membranes. The membrane potential can be measured, and controlled with a potentiostat, via probe holes close to the membrane faces. The pressure difference across the membrane can be maintained at a desired level or allowed to fluctuate in attached vertical tubes. The pore characteristics of the membranes have been measured optically and by studying hydrodynamic and electro-osmotic flows through them. Teorell-type oscillations and steady-state dynatron-type current-voltage curves have been recorded in membranes of 0.5, 0.8, 1.0 and 2.0 $\mu $m pore diameter at various currents and pressure differentials in the presence of solutions of NaCl at several concentrations, MgCl$\_{2}$ and Na$\_{2}$SO$_{4}$. Transitions were observed in current-voltage curves at high enough pressures. The curves showed hysteresis-like loops. They were characterized by the values of the upper or \`flip' current and lower or \`flop' current on the boundaries of the hysteresis loop and by the difference in the cell resistance between the low current and high current states. Theoretical values were calculated for the flip and flop currents and the resistance changes under the conditions studied experimentally and a direct comparison made. Within the limits of the assumptions of ideal solutions and of simple diffuse double-layer theory it was found that agreement was satisfactory on all important matters. In particular, factors that decreased the hydrodynamic permeability or increased the electro-osmotic permeability were correctly found to make the system less sensitive to changes of pressure. This was borne out by the response of the membrane system to changes in the membrane pore size and surface charge, to varying the valence type of the electrolyte and to varying the concentrations of the bulk solutions. Proceeding from this evidence in favour of the correctness of the theory with regard to current-voltage characteristics, it has been possible to make various predictions regarding the behaviour of the volume and ion fluxes through the membrane in the transition region. It has not yet been possible to measure these fluxes and so to test the predictions which emphasize the importance of the volume flux in controlling the nonlinearity of the system.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the amplitudes and phases of beams of electrons diffracted from thin (≤ 100 nm) crystals of W4Nb26O77 are calculated using 11-beam 00l electron microscope lattice images and the effects of instrument aberrations are considered.
Abstract: The calculation of amplitudes and phases of beams of electrons diffracted from thin (≤ 100 nm) crystals of W4Nb26O77 is described. These diffraction data are used to compute 11-beam 00l electron microscope lattice images and the effects of instrument aberrations are considered. Several approximations are compared with a more exact 435-beam, two-dimensional computation, and with experimental diffraction data and lattice images. Finally, the projected charge density approximation to image contrast is evaluated.

69 citations


Journal ArticleDOI
TL;DR: In this paper, a new approach is presented to the calculation of the charge density induced around a charged point particle in the electron gas; this approach includes contributions beyond those considered in linear-response theory.
Abstract: A new approach is presented to the calculation of the charge density induced around a charged point particle in the electron gas; this approach includes contributions beyond those considered in linear-response theory. The method can be used to treat impurities with infinite as well as finite mass. Results from calculations with various charges, positive and negative, are presented. In particular, results for the electron density distribution around a positron are presented. The positron-annihilation rates obtained are compared with results of other authors and with experiments.


Journal ArticleDOI
TL;DR: In this paper, the relationship between several physical properties and electron population parameters is given, and the physical properties that follow from electron population analysis can serve as criteria in judging the reliability of x-ray diffraction data for charge density information.
Abstract: It is assumed that the one‐electron density function for a molecular crystal can be determined from x‐ray diffraction data with the use of generalized x‐ray scattering factors. The relationship between several physical properties and electron population parameters are given. These include molecular dipole moments and atomic electric field gradients, which can be compared to results from other experiments. The physical properties that follow from electron population analysis can serve as criteria in judging the reliability of x‐ray diffraction data for charge density information.

Journal ArticleDOI
TL;DR: In this paper, it is shown that the discharge current is given by the product of charge density at, and velocity of, the zero-field plane, and the resulting expression includes the displacement current.
Abstract: When a previously charged dielectric is short circuited, discharge currents result due to the movement of charge carriers in the field of the space charge. It is shown for plane‐parallel geometry that the discharge current is given by the product of charge density at, and velocity of, the zero‐field plane. The resulting expression includes the displacement current. It can also be applied to the case where the dielectric is exposed to a beam of penetrating radiation; it then allows one to evaluate the effect of space charge on the external current.

Journal ArticleDOI
TL;DR: In this article, the effect of the distributed nuclear charge on the magnetic-dipole hyperfine-structure (hfs) interaction between the nucleus and the atomic electron is calculated.
Abstract: A diffuse nuclear charge distribution, with approximately the trapezoidal Hofstadter shape, is used to calculate the effect of the distributed nuclear charge on the magnetic-dipole hyperfine-structure (hfs) interaction between the nucleus and the atomic electron. For a surface or a uniform charge distribution model this effect is known as the Breit-Rosenthal-Crawford-Schawlow correction to the point-charge interaction. The hfs interactions calculated with the diffuse and with the uniform charge distributions differ by over 4% for medium to heavy nuclei. The results, combined with our previously calculated values for the Bohr-Weisskopf correction (the effect on the hfs due to the nonpunctual distribution of nuclear magnetization), allow a more realistic determination of the total hfs anomalies, caused by the extended nuclear electric and magnetic structures, and therefore also of ${|\ensuremath{\psi}(0)|}^{2}$, the probability of the electron wave function at the origin.

Journal ArticleDOI
TL;DR: In this paper, the electric fields of a sheet of charged dielectric positioned between two parallel metal electrodes are calculated assuming the presence of gaps between dielectrics and both electrodes.
Abstract: The electric fields of a sheet of charged dielectric positioned between two parallel metal electrodes are calculated assuming the presence of gaps between dielectric and both electrodes. The charge distribution within the dielectric is assumed to consist of a quasipermanent space charge and a quasipermanent dipole polarization, both being arbitrary functions of the coordinate normal to the electrodes and slowly varying functions of the other coordinates. The plane of zero field in the dielectric and the forces on the electrodes and on the dielectric are also calculated.

Journal ArticleDOI
TL;DR: In this article, a fit to the experimental data with a Fermi-like charge distribution yields satisfactory agreement with the results of the recent Stanford measurements, which is described model-independent by two functions, the mean radius function and the moment function.

Journal ArticleDOI
TL;DR: In this paper, the effects on spectrally resolved response caused by variations in applied electrical field, wavelength sweep rate, and optical belaching are reported, and the experiments were made on metal-oxide-semiconductor capacitors.

Journal ArticleDOI
TL;DR: In this article, the authors measured the free energy of exchange at 25°C for the high-freeness chabazite-type zeolite, K-G1, and involving the cation pairs: K+⇌ Na+, Na+ ⇌ Li, Na+ↆ Cs+, Na+,↌ Ca2+, Na + ↌ Sr2+, and Na+ ∆ Ba2+.
Abstract: Ion-exchange isotherms have been measured at 25°C for the high framework charge chabazite-type zeolite, K-G1, and involving the cation pairs: K+⇌ Na+, Na+⇌ Li+, Na+⇌ Cs+, Na+⇌ Ca2+, Na+⇌ Sr2+, and Na+⇌ Ba2+. The results have been compared with those for an isostructural natural chabazite of lower charge density. The values of the thermodynamic equilibrium constants show that the larger ion is preferred by the zeolite of lower charge density. In terms of a solid state reaction involving exchange of ions between both zeolites, the standard free energy of exchange is negative if the larger ion goes from G1 to chabazite. All these results can be explained in terms of dielectric theory if the local dielectric constant in solution is greater than that in either zeolite, and if this constant is greater in a given cationic form of the zeolite of high charge density than in the corresponding form of the zeolite of lower charge density. The correctness of these assumptions for the zeolites was supported by measurements of the refractive indices. The exchanges involving caesium are incomplete in both G1 and the natural chabazite. The different limiting values for these two exchangers have been discussed in terms of steric, electrostatic and hydration effects. The pattern of exchange behaviour observed is consistent with that reported previously for the isostructural zeolites X and Y.

Journal ArticleDOI
TL;DR: In this article, the x-ray structure amplitudes for the 27 lowest-angle Bragg reflections of beryllium metal have been measured on an absolute scale and compared with those predicted both by the free atom Hartree-Foch wave functions and by a free electron orthogonalized plane wave model.
Abstract: The x-ray structure amplitudes for the 27 lowest-angle Bragg reflections of beryllium metal have been measured on an absolute scale. These can be used to deduce the charge density. The measured structure amplitudes are compared with those predicted both by the free atom Hartree-Foch wave functions and by a free electron orthogonalized plane wave model. For both models the predicted value for the lowest angle reflection is close to that observed, but the structure amplitudes of subsequent reflections given by the models are significantly greater than those observed. To account for these discrepancies a model of beryllium involving 2p-like tight binding functions is proposed.

Journal ArticleDOI
TL;DR: In this article, a selfconsistent numerical calculation of the displaced charge density n'(r) around a completely screened ionic potential V0 in a metal has been carried out for the Hartree-Fock-Slater equations.
Abstract: A selfconsistent calculation of the displaced charge density n'(r) around a completely screened ionic potential V0 in a metal has been carried out for the Hartree-Fock-Slater equations. V/sub /0 is the sum of the true ionic core potential Vion and the potential of a given (auxiliary) screening charge density nu (r). The resulting selfconsistent potential V'(r) is used to calculate the rigid neutral atom density n(r) which allows an approximate calculation of the metal selfconsistent potential. The main part of this work deals with the selfconsistent numerical calculation of the density n'(r) displaced by V0. The following approximations are made. The Kohn and Sham one-body formulation of the many-body problem is used. The wave equation is solved numerically inside a sphere of large but finite radius. The Coulomb potential due to the outer displaced charge is approximately calculated from the Friedel asymptotic formula. The continuous integration over the Fermi sea energy levels is replaced by a discrete summation. Selfconsistency is achieved by the use of a modified iterative process, using the linearized Thomas-Fermi equation in order to deal with the long range character of the Coulomb interaction. The method has been applied to metallic lithium and sodium, and results are given for n(r), on-the-Fermi-shell scattering matrix and nonstructural band structure properties.

Journal ArticleDOI
TL;DR: In this article, an electromagnetic analysis of a black-box type yields a general model-independent surface plasmon dispersion relation, which confirms and extends the validity of Harris and Griffin's formula 2 in terms of the charge density fluctuation and its dipole moment, but it shows furthermore that there is an extra term due to surface current fluctuations.

Journal ArticleDOI
TL;DR: In this article, a family of simple charge distributions was proposed and a phase shift analysis was performed, and the charge distribution parameters were displayed as a function of mass number for the modified Gaussian fit which was preferred.

Journal ArticleDOI
TL;DR: In this article, the formation of charged defects in ionic crystals is accompanied by surface defects: kinks, which contribute to a Debye-Huckel charge distribution at the surface.
Abstract: The formation of charged defects in ionic crystals is shown to be accompanied by the formation of surface defects: kinks. The resultant defect pairs contribute to a Debye‐Huckel charge distribution at the surface. Surface charge, surface structure, and crystal defect equilibria are found to be interrelated and to influence sublimation rates. The theory is applied to the case of sublimation of II‐VI compounds and compared with experiments.

Journal ArticleDOI
TL;DR: In this article, the quadrupole effects in nuclear magnetic resonance were used to determine the electric field gradients at nearest and in some cases next nearest host Cu nuclei to various impurities in dilute Cu alloy single crystals.
Abstract: For Pt. I see abstr. A1732 of 1972. The electric field gradients at nearest and in some cases next nearest host Cu nuclei to various impurities in dilute Cu alloy single crystals have been determined by the quadrupole effects in nuclear magnetic resonance. The impurities are In, Sn, Sb and Ge. The field gradients at nearest neighbour sites are far from rotational symmetric around the direction towards the impurity and in the case of CuGe it does not even have the main component in that direction. These results question the validity of the theoretical models assuming spherical symmetry for the charge density around the impurity, at least in host metals like copper.

Journal ArticleDOI
TL;DR: In this paper, an analytical solution to the cloud charge screening-layer model of Brown et al. is obtained for planar, cylindrical, and spherical cloud geometries, and the maximum (saturation) space charge is found to be (4/e2) (e0E0/λ0), where e = 2.718, e0 is the permittivity of air, and λ 0 is the mean free path of ions in an uncharged cloud.
Abstract: Analytical solutions to the cloud charge screening-layer model of Brown et al. are obtained for planar, cylindrical, and spherical cloud geometries. Two specifications of the negative ion concentration n− at the surface of a positively charged cloud, representing upper and lower approximations to the actual supply of ions, are employed: (1) n− = n0 = constant, and (2) n− decays with time t approximately as (1 + αt)−1, where α is constant. The latter form for n− comes from a model that allows for space charge divergence outside the cloud but ignores ionization and recombination. In mksa units the maximum (saturation) space charge is found to be (4/e2) (e0E0/λ0), where e = 2.718 …, e0 is the permittivity of air, E0 is the initial cloud electric field, and λ0 is the mean free path of ions in an uncharged cloud (typically, λ0 = 10 meters). The surface electric field when the cloud particles first become saturated is E0/e2, and the final depth of the saturated layer is λ0/4. If the relaxation time of the surface electric field for the first case is τ (typically 40 sec), then the relaxation time for the second case is 1.94 τ. The screening-layer formation time (i.e., the time required for the surface screening-layer charge density to be within e−1 of its saturation value) is 0.49 τ in the first case and 0.67 τ in the second. Brown et al. obtained numerical solutions for the field and screening charge density as a function of time and depth for the special case of a flat layer cloud with n− = n0 at the surface. The agreement between their results and ours for these same conditions is excellent.

Journal ArticleDOI
TL;DR: In this paper, the potentiometric titration curves of carboxymethylcellulose and poly(D-glutamic acid) in the helical region are compared with the theoretical curves calculated assuming that the polyions are rods and have smeared charges on their surfaces.
Abstract: The potentiometric titration curves of carboxymethylcellulose, which has a relatively stiff backbone, and also of poly(D-glutamic acid) in the helical region are compared with the theoretical curves calculated assuming that the polyions are rods and have smeared charges on their surfaces. For carboxymethylcellulose good agreement is observed when its charge density is high, whereas as the charge density decreases the calculated curves deviate from the observed ones. The main reason for the disagreement at low charge densities may be attributed to the flexibility of the polymer backbone. For helical poly(D-glutamic acid) satisfactory agreement between calculated and observed curves is found if a radius thicker than the realistic radius is employed. The reason for the excessively large radius may be attributed to the inapplicability of the smeared charge model.



Journal ArticleDOI
TL;DR: In this article, the electrostatictheory for a dielectric spherical or spheroidal cavity, with arbitrary charge distribution within it, is presented, and the results are used to calculate the adsorption potential for a species with specified dipole and quadrupole moments.
Abstract: The electrostatictheory for a dielectric spherical or spheroidal cavity, with arbitrary charge distribution within it, is presented. The cavity is located in a dielectric medium which is separated from another uniform dielectric medium by a planar interface. The use of a cavity avoids the singularities in the image potential for point charges as they approach the interface. It is shown that the adsorption potential is directly related to the resolvent of a matrix whose elements depend on the position and the dimensions of the cavity. The results are used to calculate the adsorption potential for a species with specified dipole and quadrupole moments. The adsorption potential thus calculated is used to analyze the difference between the surface tension of zwitterionic solutions and the pure solvent. We discuss how the diffuseness of the interface diminishes the calculated increase in the surface tension. The calculated changes, arising from electrostatic forces, in the surface tension of aqueous solutions of small amino acids belonging to an homologous series, compare favorably with those derived from the experimental measurements.