Showing papers on "Charge density published in 2002"
TL;DR: An efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three‐dimensional lattice and a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies.
Abstract: This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three-dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 571 3 can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono- and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.
682 citations
TL;DR: In this article, quantum mechanically determined electrostatic potentials for isosurfaces of electron density of a variety of CHNO explosive molecules are analyzed to identify features that are indicative of sensitivities.
Abstract: Quantum mechanically determined electrostatic potentials for isosurfaces of electron density of a variety of CHNO explosive molecules are analyzed to identify features that are indicative of sensit...
491 citations
TL;DR: Analysis shows that all the three approaches are able to capture the important electrostatic interactions between ions and the charge distribution of the channel that govern ion permeation and selectivity in OmpF, which suggests that a treatment on the basis of a rigid protein and continuum dielectric solvent is valid in the case of Ompf.
372 citations
TL;DR: For the first time it was possible to show plasma protein adsorption patterns on a range of nanoparticles with variation of only one parameter, i.e. the charge, while size and surface hydrophobicity remain practically unchanged.
279 citations
TL;DR: In this article, the authors derived the ratio between mobility and diffusion parameters for a Gaussian-like density of states for a wide range of organic materials (polymers or small molecules) and showed that there is an inherent dependence of the transport in trap-free disordered organic materials on the charge density.
Abstract: The ratio between mobility and diffusion parameters is derived for a Gaussian-like density of states. This steady-state analysis is expected to be applicable to a wide range of organic materials (polymers or small molecules) as it relies on the existence of quasiequilibrium only. Our analysis shows that there is an inherent dependence of the transport in trap-free disordered organic materials on the charge density. The implications for the contact phenomena and exciton generation rate in light emitting diodes as well as channel width in field-effect transistors is discussed.
253 citations
TL;DR: In this paper, the influence of the charge density along a polyelectrolyte chain on the buildup of multilayer films formed by the sequential adsorption of alternating layers of polyanions and polycations was examined.
Abstract: We examine the influence of the charge density along a polyelectrolyte chain on the buildup of multilayer films formed by the sequential adsorption of alternating layers of polyanions and polycations (the layer-by-layer technique). Model random copolymers of diallyldimethylammonium chloride (DADMAC) and N-methyl-N-vinylacetamide (NMVA) having matched molecular weights and varying percentages (24−100%) of the cationic DADMAC component are alternated with polyanionic polystyrene sulfonate (PSS). Multilayer buildup is monitored by UV−vis and FTIR spectroscopies, and with a quartz crystal microbalance (QCM) and is correlated with structural information obtained using atomic force microscopy. When films are deposited from polyelectrolyte solutions containing added salt, a critical charge density limit (between 75% and 53%), below which no significant layer growth is possible, becomes apparent. Below the critical charge density, addition of the polyanion leads to almost complete removal of the previously deposi...
243 citations
TL;DR: In this article, it was shown that the volume flux of fluid through a straight microfluidic channel of arbitrary cross-sectional geometry and distribution of wall charge is a linear function of the applied pressure drop and electric potential drop across it, the coefficients of which may be calculated explicitly in terms of the geometry and charge distribution on the wall.
Abstract: Electro-osmotic flow is a convenient mechanism for transporting fluid in microfluidic devices. The flow is generated through the application of an external electric field that acts on the free charges that exist in a thin Debye layer at the channel walls. The charge on the wall is due to the particular chemistry of the solid–fluid interface and can vary along the channel either by design or because of various unavoidable inhomogeneities of the wall material or because of contamination of the wall by chemicals contained in the fluid stream. The channel cross-section could also vary in shape and area. The effect of such variability on the flow through microfluidic channels is of interest in the design of devices that use electro-osmotic flow. The problem of electro-osmotic flow in a straight microfluidic channel of arbitrary cross-sectional geometry and distribution of wall charge is solved in the lubrication approximation, which is justified when the characteristic length scales for axial variation of the wall charge and cross-section are both large compared to a characteristic width of the channel. It is thereby shown that the volume flux of fluid through such a microchannel is a linear function of the applied pressure drop and electric potential drop across it, the coefficients of which may be calculated explicitly in terms of the geometry and charge distribution on the wall. These coefficients characterize the ‘fluidic resistance’ of each segment of a microfluidic network in analogy to the electrical ‘resistance’ in a microelectronic circuit. A consequence of the axial variation in channel properties is the appearance of an induced pressure gradient and an associated secondary flow that leads to increased Taylor dispersion limiting the resolution of electrophoretic separations. The lubrication theory presented here offers a simple way of calculating the distortion of the flow profile in general geometries and could be useful in studies of dispersion induced by inhomogeneities in microfluidic channels.
177 citations
TL;DR: In this paper, the influence of the charge density of polyelectrolytes on the growth of poly electrolyte multilayers via layer-by-layer self-assembly from pure aqueous solutions was studied.
Abstract: The influence of the charge density of polyelectrolytes on the growth of polyelectrolyte multilayers via layer-by-layer self-assembly from pure aqueous solutions was studied. Multilayers were built from strong polyanions, namely poly(styrenesulfonate) and an exfoliated synthetic hectorite, and cationic copolymers of diallyldimethylammonium chloride (DADMAC) with N-methyl-N-vinylformamide (NMVF) for which the composition and thus the charge density was varied systematically. The analysis of the system {cationic copolymer/poly(styrenesulfonate)} reveals that a critical linear charge density lambda(c) of 0.036 elementary charge/Angstrom of contour length is necessary to obtain stable multilayer growth in pure water. Above lambda(c) the increment of thickness/deposition cycle varies with the linear charge density of the cationic copolymers, in good agreement with current theories of polyelectrolyte solutions. As linear charge density increases, the system passes successively through a charge-dependent "Debye-Huckel" regime and then through a charge-independent "strong-screening" regime where counterion condensation dominates the behavior. Analogous results were obtained for the variation of the basal spacing of internally structured hybrid multilayers {cationic copolymer/hectorite}. However, by contrast with the first system, no critical linear charge density was found for the hybrid system. This is explained by additional, nonelectrostatic interactions between the clay platelets and the formamide fragment.
175 citations
TL;DR: In this article, the effects of image charges in spherical geometry and their implication for charged colloidal systems are investigated analytically and exactly a single microion interacting with a dielectric sphere and discuss the similarities and discrepancies with the case of a planar interface.
Abstract: The effects of image charges (i.e., induced surface charges of polarization) in spherical geometry and their implication for charged colloidal systems are investigated. We study analytically and exactly a single microion interacting with a dielectric sphere and discuss the similarities and discrepancies with the case of a planar interface. By means of extensive Monte Carlo simulations, we study within the framework of the primitive model the effects of image charges on the structure of the electrical double layer. Salt-free environment as well as salty solutions are considered. A remarkable finding of this study is that the position of the maximum in the counterion density (appearing at moderately surface charge density) remains quasi-identical, regardless of the counterion valence and the salt content, to that obtained within the single-counterion system.
153 citations
TL;DR: A detailed topological analysis of theoretical charge densities for two benchmark carbene systems, viz., 1,2-dimethylpyrazol-3-ylidene 1a and 2a, and their corresponding stable chromium pentacarbonyl complexes 1 and 2, highlights the advantages of charge-density-based criteria to analyze such complex electronic situations.
Abstract: Combined experimental and theoretical charge-density studies on free and metal-coordinated N-heterocyclic carbenes have been performed to investigate the extent of electron delocalization in these remarkable species. Tracing the orientation of the major axis of the bond ellipticity (the least negative curvature in the electron density distribution) along the complete bond paths distinguishes unambiguously between fully delocalized systems and those with interrupted cyclic electron delocalization. Evaluation of charge-density-based properties such as atomic quadrupole moments serves as a direct and quantitative measure of the extent of π-electron delocalization and reveals consistency between theory and experiment. A detailed topological analysis of theoretical charge densities for two benchmark carbene systems, viz., 1,2-dimethylpyrazol-3-ylidene 1a and 1,3-dimethylimidazol-2-ylidene 2a, and their corresponding stable chromium pentacarbonyl complexes 1 and 2, highlights the advantages of charge-density-ba...
151 citations
TL;DR: In this article, an improved charge control model for lattice mismatched AlGaN/GaN HEMTs is proposed, valid over the entire operating region, and the model for estimation of two-dimensional electron gas (2-DEG) sheet carrier concentration accounts for the strongly dominant spontaneous and piezoelectric polarization at the Al GaN/GAN heterointerface.
Abstract: The present paper proposes an improved charge control model of lattice-mismatched AlGaN/GaN HEMTs, valid over the entire operating region. The model for estimation of two-dimensional electron gas (2-DEG) sheet carrier concentration accounts for the strongly dominant spontaneous and piezoelectric polarization at the AlGaN/GaN heterointerface. The dependence of 2-DEG sheet carrier concentration on the aluminum composition and AlGaN layer thickness has been investigated in detail. Current–voltage characteristics developed from the 2-DEG model include the effect of field dependent mobility, velocity saturation and parasitic source/drain resistances. Close proximity with experimental data confirms the validity of the proposed model.
TL;DR: In this article, the effect of polyelectrolyte charge density on the surface cation exchange at the mica basal plane from low ionic strength solutions was analyzed using the XPS (ESCA) method.
Abstract: The XPS (ESCA) method was employed to quantitatively determine polyelectrolyte adsorption on the mica basal plane from low ionic strength solutions. Particular emphasis was given to the effect of the polyelectrolyte charge density. By combining the results obtained from XPS and surface force measurements it was possible to analyze the cation exchange at the surface that occurs as a result of polyelectrolyte adsorption. AFM-imaging was used to obtain information on the structure of the adsorbed layer when the polyelectrolyte coverage was low. Further, the desorption of preadsorbed polyelectrolyte layers by addition of inorganic salt and by addition of an anionic surfactant was investigated by XPS and some complementary surface force measurements. The results demonstrate that the lower the polyelectrolyte charge density is, the easier it is to remove the polyelectrolyte from the surface. The surfactant, which by itself does not adsorb to the mica surface, is more efficient in this respect than the inorganic salt. This observation can be rationalized by considering that the surfactant and polyelectrolyte form complexes with each other. Thus, the surfactant brings negative charges into the adsorbed layer that reduces the affinity to the surface. However, high-charge-density polyelectrolytes are removed to a very limited degree even when the surfactant concentration is above the critical micellar concentration, which is explainable by the poor solubility of the polyelectrolyte-surfactant complexes formed.
TL;DR: In this article, various thermodynamic elements of the density functional theory of electronic structure are reviewed and clarified, and detailed argumentation is given for the particular "del dot del" definition of the local kinetic energy density and local temperature.
Abstract: Various thermodynamic elements of the density functional theory of electronic structure are reviewed and clarified. Detailed argumentation is given for the particular “del dot del” definition of the local kinetic energy density and local temperature. The temperature measures the “nighness” of an electron pair, thus playing a key role in quantitative (exchange and kinetic energy functionals) and qualitative (electron localization functions) tools based on the electron pair density. Two different derivations are given of the Gaussian model for the phase-space distribution function, from which one obtains an approximation to the entropy of the charge distribution. The full thermodynamic description is briefly discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002
TL;DR: In this article, the elastic modulus of a series of strong polyelectrolyte hydrogels based on acrylamide and 2-acrylamido-2-methylpropane sulfonic acid sodium salt (AMPS) was investigated.
TL;DR: In this article, a polyaniline (PANI) synthesized by a potentiostatic method at 4°C in 1 M HNO3 with the polymerization charge density equal to/less than 0.45 C cm−2 was demonstrated to exhibit ideally capacitive characteristics (i.e. high reversibility and high power property) with a high specific capacitance of 210 F g−1 for the application of electrochemical supercapacitors in NaNO3.
TL;DR: Experiments using Ca-exchanged SWy-1, variation of the ionic strength by addition of salt, and the use of different size fractions of the clays confirm the finding that the main factor ruling the adsorption behavior of the probe is the size of the clay particles.
TL;DR: In this article, the adsorption of ammonia on the Au(111) surface at coverages of 1/4 and 1/9 of a monolayer using density-functional theory employing the pseudopotential method, periodic imaging, a plane-wave basis set, and the PW91 density functional.
Abstract: We have modeled the adsorption of ammonia on the Au(111) surface at coverages of 1/4 and 1/9 of a monolayer using density-functional theory employing the pseudopotential method, periodic imaging, a plane-wave basis set, and the PW91 density functional. The geometries of the adsorbate and the surface are fully optimized. The adsorption is found to be highly favored on top of a surface atom. Adsorption energies of 26 and 32 kJ mol−1 are obtained for the 1/4 and 1/9 of a monolayer coverage, respectively, extrapolating to 34 kJ mol−1 at zero coverage; the experimental estimate is 32–42 kJ mol−1. Small changes in the work function are predicted and interpreted as arising from a surface layer whose effective dipole moment is 2.15 D, 0.77 D larger than the calculated value of isolated ammonia. Examination of the calculated charge density and the local electric field strengths indicate that the change in dipole moment is due to polarization effects and that ammonia to gold charge transfer is minimal, at most 0.01...
TL;DR: The density matrix renormalization (DMRG) group method for ladders works much more efficiently with open boundary conditions and one consequence of these boundary conditions is ground-state charge density oscillations that often appear to be nearly constant in magnitude or to decay only slightly away from the boundaries.
Abstract: The density matrix renormalization (DMRG) group method for ladders works much more efficiently with open boundary conditions. One consequence of these boundary conditions is ground-state charge density oscillations that often appear to be nearly constant in magnitude or to decay only slightly away from the boundaries. We analyze these using bosonization techniques, relating their detailed form to the correlation exponent and distinguishing boundary induced generalized Friedel oscillations from true charge density waves. We also discuss a different approach to extracting the correlation exponent from the finite size spectrum which uses exclusively open boundary conditions and can therefore take advantage of data for much larger system sizes. A general discussion of the Friedel oscillation wave vectors is given, and a convenient Fourier transform technique is used to determine it. DMRG results are analyzed on Hubbard and $t\ensuremath{-}J$ chains and 2 leg $t\ensuremath{-}J$ ladders. We present evidence for the existence of a long-ranged charge density wave state in the $t\ensuremath{-}J$ ladder at a filling of $n=0.75$ and near $J/t\ensuremath{\approx}0.25.$
TL;DR: The Localized-Orbital Locator (LOL) as discussed by the authors is based on the noninteracting kinetic energy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity.
Abstract: We examine and compare two previously introduced functions of the one-particle density matrix that are suitable to represent its off-diagonal structure in a condensed form and that have illustrative connections to the nature of the chemical bond. One of them, the Localized-Orbital Locator (LOL) [J. Molec. Struct. (THEOCHEM) 527, 51 (2000)], is based only on the noninteracting kinetic-energy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity. Alternatively, LOL focuses on regions that are dominated by single localized orbitals. The other one, the Parity Function P [J. Chem. Phys. 105, 11134 (1996)], is a section through the Wigner phase-space function at zero momentum, and contains information about the phase of the interference of atomiclike orbital contributions from bound centers. In this paper, we discuss the way in which these functions condense information in the density matrix, and illustrate on a variety of examples of unusual chemical bonds how they can help to understand the nature of “covalence.”
TL;DR: In this paper, the structural and electronic properties of bulk and both oxidized and reduced SnO2(1 1 0) surfaces as well as the adsorption process of O2 on the reduced surface have been investigated by periodic DFT calculations at B3LYP level.
TL;DR: In this paper, the authors used time-of-flight and energy analysis techniques to measure the charge, specific charge and stopping potential of primary and satellite droplets generated by electrosprays of tributyl phosphate solutions.
Abstract: We use time-of-flight and energy analysis techniques to measure in a vacuum the charge, specific charge and stopping potential of primary and satellite droplets generated by electrosprays of tributyl phosphate solutions. This information, of interest in itself, is subsequently analysed to obtain the following relevant parameters of the jet emanating from the Taylor cone: the velocity of the fluid at the breakup point, the voltage difference between the liquid cone and jet breakup location, and the most probable wavelength for varicose breakup. A large fraction of the electrospray needle voltage is used to accelerate the jet. Indeed, for the solutions of lowest electrical conductivities studied here, the voltage difference between electrospray needle and jet breakup location becomes approximately 90% of the needle voltage. In addition, the pressure of the jet fluid at the breakup point is negligible compared to its specific kinetic energy. The specific charge distribution function of the main droplets produced in the varicose breakup is remarkably narrow. Hence, the limiting and commonly accepted case of varicose breakup at constant electric potential is not consistent with this experimental observation. On the other hand, a scenario in which the electric charge is bound to the jet surface seems to be a good approximation to simulate the effect of charge on capillary breakup. It is also found that the effect of viscosity on the formation of droplets is paramount in electrosprays of moderate and high electrical conductivity. We expect that these measurements will guide the analytical modelling of cone-jets.
TL;DR: In this paper, a thermodynamic model for the adsorption of charged colloidal particles to air−water and oil−water interfaces from water-based suspensions is presented, where the effects of electrolyte concentration, surface charge density of both the particles and the air-water (oil−water) interface, particle contact angle, and particle volume fraction are studied in detail.
Abstract: In this paper we present a thermodynamic model for the adsorption of charged colloidal particles to air−water and oil−water interfaces from water-based suspensions and derive the equations for the respective particle adsorption isotherms. The effects of electrolyte concentration, surface charge density of both the particles and the air−water (oil−water) interface, particle contact angle, and particle volume fraction are studied in detail. The model is based on a detailed account of the interfacial free energy of particles and electric double layer formation, as well as collective effects related to the free energy of mixing of the particles with the liquid phases (water and oil) and surface charge displacement. The effect of particle size on the adsorption at the air−water and the oil−water interfaces is discussed. An analytical expression for the distribution coefficient of particles between oil and water has been derived and discussed in terms of the effects of electrolyte, contact angle, surface charge...
Abstract: Direct measurements of a long-range force between charged solid surfaces in a nonpolar liquid are presented for the first time. Measurements were made between mica surfaces in solutions of the anionic surfactant sodium di-2-ethylhexylsulfosuccinate (AOT) at millimolar concentrations in n-decane using a surface force apparatus which has been modified to improve its sensitivity for detecting a weak and long-range force. Modifications include a magnetic drive system, the use of a weak cantilever spring with the apparatus mounted in a vertical configuration, and a detailed consideration of the interference optics to allow accurate measurements of surface separations up to several micrometers. The results show a repulsion that is well fitted by theoretical curves based on a model in which only counterions enter the calculation, in other words, in the absence of a reservoir of ions in the solvent. Fitting the theory to the data allows an estimate of the mica surface charge density of ∼1 mC/m2. A mechanism for s...
01 Jan 2002
TL;DR: In this paper, a model considering the compensation of piezoelectric effect and the dislocation theory of fault was developed to investigate theoretically the generation of co-seismic electric signals.
Abstract: A model considering the compensation of piezoelectric effect and the dislocation theory of fault is developed to investigate theoretically the generation of co-seismic electric signals. Charges are assumed to be induced by the stress changes associated with earthquakes. The stressinduced charges are quantified by the charge density as a function of the polarization, which can be calculated using a piezoelectric model and an analytical solution of seismic stress. The theoretical charge distribution around the Nojima fault, which moved at the 1995 Kobe earthquake (M=7.2), was obtained. The co-seismic electric field consistent with that observed at the Kobe earthquake was estimated as the field due to the charges, which compensated the piezoelectric charges.
TL;DR: It is demonstrated, quantitatively, that the charge overcompensation observed on the isotherm plateau can be attributed to the denser positive charge on the adsorbing polycation and that the ultimate coverage obtained corresponds to the advertisersorption of one oligomer onto each original negative silica charge.
TL;DR: In this article, the effect of charge density on the course of polyelectrolyte complex (PEC) formation and the response of the PECs to subsequent addition of salt was investigated.
Abstract: Cationic copolymers of diallyldimethylammonium chloride (DADMAC) and N-methyl-N-vinylacetamide (NMVA) were synthesized by radical polymerization in a broad range of composition. Since the cyclocopolymerization of DADMAC and NMVA proceeded as nearly ideal reaction, linear copolymers of different charge densities but approximately equal molecular weights and acceptable polydispersities could be obtained. These polycations were used in combination with a sodium poly(styrene sulfonate) to study the effect of charge density on the course of polyelectrolyte complex (PEC) formation and the response of the PECs to subsequent addition of salt. Static light scattering was employed for the characterization of the complex structures. PEC formation followed in deionized water for all copolymers the same scheme, but yielding higher swollen particles with decreasing charge density of the polycations. In the cases of stronger mismatching of the charge densities of the components the presence of NaCl during complex formation led to highly swollen complexes on a very low level of aggregation. Subsequent addition of NaCl resulted for these polyelectrolyte combinations at first in disintegration into very small subunits before flocculation occurred.
TL;DR: Negative hyperconjugation is shown to arise from delocalization of the lone pair or the Li-C bonding electrons over the alkyl fragment, with depletion of the metal-directed charge concentration at Calpha, and characteristic ellipticity profiles for the bonds involved inhyperconjugativedelocalization are shown.
Abstract: In this paper we present the results of density functional theory (DFT) calculations on the ethyl ligand and some related organic moieties; we then proceed to consider a range of alkyllithium complexes studied by DFT calculations and high-resolution X-ray and neutron diffraction. Topological analysis of the charge density is used to follow changes in the electronic structure of the organic fragment. The charge concentrations (CCs) in the valence shell at the alpha and beta atoms reveal faithfully the delocalization of the lone pair at the Calpha atom or of the Li-C bonding electrons. Negative hyperconjugation is thus shown to arise from delocalization of the lone pair or the Li-C bonding electrons over the alkyl fragment, with depletion of the metal-directed charge concentration at Calpha, and characteristic ellipticity profiles for the bonds involved in hyperconjugative delocalization. In the case of so-called lithium agostic complexes, we show that close Li.H contacts are a consequence of this delocalization and further secondary interactions, with Li.H-C agostic interactions, playing only a minor role. The ellipticity profiles and the magnitude of the CCs at Calpha provide a quantitative measure of the extent of delocalization, and show excellent agreement between experiment and theory.
TL;DR: The use of surface voltage and surface photovoltage measurements has broadened from initial application of minority carrier diffusion length measurements to a wide variety of semiconductor characterization, including surface voltage, surface barrier height, flatband voltage, oxide thickness, oxide charge density, interface trap density, mobile chargedensity, oxide integrity, generation lifetime, recombination lifetime and doping density.
Abstract: Surface voltage and surface photovoltage measurements have become important semiconductor characterization techniques, largely because of their contactless nature and the availability of commercial equipment. The use of these contactless measurement techniques has broadened from initial application of minority carrier diffusion length measurements to a wide variety of semiconductor characterization, including surface voltage, surface barrier height, flatband voltage, oxide thickness, oxide charge density, interface trap density, mobile charge density, oxide integrity, generation lifetime, recombination lifetime and doping density. It is likely that this range of applications will broaden further. As with all characterization techniques, there are limitations but they are frequently compensated by the contactless nature of the measurement thereby simplifying test structure fabrication.
TL;DR: It is demonstrated that in anomalous x-ray scattering at the oxygen K edge of the cuprates, the contribution of carriers to the scattering amplitude is selectively magnified 82 times, permitting direct structural analysis of the superconducting ground state.
Abstract: An unresolved issue concerning cuprate superconductors is whether the distribution of carriers in the CuO2 plane is uniform or inhomogeneous. Because the carriers comprise a small fraction of the total charge density and may be rapidly fluctuating, modulations are difficult to detect directly. We demonstrate that in anomalous x-ray scattering at the oxygen K edge of the cuprates, the contribution of carriers to the scattering amplitude is selectively magnified 82 times. This enhances diffraction from the doped holes by more than 10(3), permitting direct structural analysis of the superconducting ground state. Scattering from thin films of La2CuO4+delta (superconducting transition temperature = 39 K) at temperature = 50 +/- 5 kelvin on the reciprocal space intervals (0,0,0.21) --> (0,0,1.21) and (0,0,0.6) --> (0.3,0,0.6) shows a rounding of the carrier density near the substrate suggestive of a depletion zone or similar effect. The structure factor for off-specular scattering was less than 3 x 10(-7) electrons, suggesting an absence of in-plane hole ordering in this material.