Showing papers on "Charge density published in 2006"
TL;DR: In this article, an algorithm for decomposition of electronic charge density into atomic contributions is presented. But instead of explicitly finding and representing the dividing surfaces, which is a challenging task, the algorithm assigns each point on a regular (x,y,z) grid to one of the regions by following a steepest ascent path on the grid.
7,231 citations
TL;DR: In this paper, the effect of the spin-orbit interaction on low-index surfaces of the group V semimetal bismuth has been studied and the main focus is on the geometric and electronic structure.
461 citations
TL;DR: In this paper, surface recombination velocities as low as 10 cm/s have been obtained by treated atomic layer deposition (ALD) of Al 2 O 3 layers on p-type CZ silicon wafers.
441 citations
TL;DR: In this article, the authors discuss high energy hadronic collisions within the theory of the color glass condensate and point out that the initial electric and magnetic fields produced in such collisions are longitudinal, which leads to a novel string like description of the collisions, and a large Chern-Simons charge density made immediately after the collision.
431 citations
TL;DR: The present TrEsp (transition charge from electrostatic potential) method is applied to study strongly coupled pigments in the light-harvesting complexes of green sulfur bacteria, purple bacteria, and higher plants and the "special pairs" of bacterial reaction centers and reaction centers of photosystems I and II.
Abstract: An accurate and numerically efficient method for the calculation of intermolecular Coulomb couplings between charge densities of electronic states and between transition densities of electronic excitations is presented. The coupling of transition densities yields the Forster type excitation energy transfer coupling, and from the charge density coupling, a shift in molecular excitation energies results. Starting from an ab initio calculation of the charge and transition densities, atomic partial charges are determined such as to fit the resulting electrostatic potentials of the different states and the transition. The different intermolecular couplings are then obtained from the Coulomb couplings between the respective atomic partial charges. The excitation energy transfer couplings obtained in the present TrEsp (transition charge from electrostatic potential) method are compared with couplings obtained from the simple point-dipole and extended dipole approximations and with those from the ab initio transition density cube method of Kruger, Scholes, and Fleming. The present method is of the same accuracy as the latter but computationally more efficient. The method is applied to study strongly coupled pigments in the light-harvesting complexes of green sulfur bacteria (FMO), purple bacteria (LH2), and higher plants (LHC-II) and the "special pairs" of bacterial reaction centers and reaction centers of photosystems I and II. For the pigment dimers in the antennae, it is found that the mutual orientation of the pigments is optimized for maximum excitonic coupling. A driving force for this orientation is the Coulomb coupling between ground-state charge densities. In the case of excitonic couplings in the "special pairs", a breakdown of the point-dipole approximation is found for all three reaction centers, but the extended dipole approximation works surprisingly well, if the extent of the transition dipole is chosen larger than assumed previously. For the "special pairs", a large shift in local transition energies is found due to charge density coupling.
351 citations
TL;DR: An exact energy partition method based on a physically sound decomposition of the nondiagonal first-order and diagonal second-order density matrices put forward by Li and Parr is presented and is applicable on quite general wave functions.
Abstract: An exact energy partition method based on a physically sound decomposition of the nondiagonal first-order and diagonal second-order density matrices put forward by Li and Parr (J. Chem. Phys. 1986, 84, 1704) is presented. The method splits the total energy into intra- and interatomic components and is applicable on quite general wave functions. To explore it numerically, the energy components of three test molecules (H2, N2, and LiH) have been computed using four different partitions of the charge density ρ(r) into atomic densities. Several aspects on the chemical bond and the relative importance of different components of the binding energy are analyzed. The merits of different partitions of ρ(r) are also discussed.
261 citations
TL;DR: Friedel oscillations in grapehene are strongly affected by the chirality of electrons in this material and the FO of the charge density around an impurity show a faster decay than in conventional 2D electron systems.
Abstract: We show that Friedel oscillations (FO) in grapehene are strongly affected by the chirality of electrons in this material. In particular, the FO of the charge density around an impurity show a faster (~r-3) decay than in conventional 2D electron systems and do not contribute to a linear temperature-dependent correction to the resistivity. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice lead to a negative linear T dependence of the resistivity.
259 citations
TL;DR: The CD values calculated with MO/DFT are not particularly sensitive to the precise Fe-octahedral geometry, which suggests that a calculated CD is a reasonable approximation in ion adsorption modeling for ill-defined Fe-oxides like HFO and natural Fe oxide materials of soils.
248 citations
TL;DR: This work shows that charge transport at V(oc) can be determined directly from the transient photovoltage rise time using a simple, zero-free-parameter model, and shows the relationship between measured transport rate and measured charge density is consistent with the trap limited transport model.
Abstract: Charge transport rate at open-circuit potential (Voc) is proposed as a new characterization method for dye-sensitized (DS) and other nanostructured solar cells. At Voc, charge density is flat and measurable, which simplifies quantitative comparison of transport and charge density. Transport measured at Voc also allows meaningful comparison of charge transport rates between different treatments, temperatures, and types of cells. However, in typical DS cells, charge transport rates at Voc often cannot be measured by photocurrent transients or modulation techniques due to RC limitations and/or recombination losses. To circumvent this limitation, we show that charge transport at Voc can be determined directly from the transient photovoltage rise time using a simple, zero-free-parameter model. This method is not sensitive to RC limitation or recombination losses. In trap limited devices, such as DS cells, the comparison of transport rates between different devices or conditions is only valid when the Fermi lev...
234 citations
TL;DR: The use of electrostatic charge injection (i.e., the transverse field effect) to induce both very large two-dimensional hole densities and metallic conductivities in poly(3-hexylthiophene) (P3HT) is reported in this paper.
Abstract: The use of electrostatic charge injection (i.e., the transverse field effect) to induce both very large two-dimensional hole densities (∼ 1015 charges cm–2) and metallic conductivities in poly(3-hexylthiophene) (P3HT) is reported. Films of P3HT are electrostatically gated by a solution-deposited polymer-electrolyte gate dielectric in a field-effect-transistor configuration. Exceptionally high hole field-effect mobilities (up to 0.7 cm2 V–1 s–1) are measured concurrently with large hole densities, resulting in an extremely large sheet conductance of 200 μS sq.–1. The large room-temperature conductivity of 1000 S cm–1 together with the very low measured activation energies (0.7–4 meV) suggest that the metal–insulator transition in P3HT is achieved. A maximum in sheet conductance versus charge density is also observed, which may result from near-filling of the valence band or from charge correlations that lower the carrier mobility. Importantly, the large hole densities in P3HT are achieved using capacitive coupling between the polymer-electrolyte gate dielectric and P3HT (i.e., the field effect) and not via chemical or electrochemical doping. Electrostatic control of carrier density up to 1015 charges cm–2 (∼ 1022 charges cm–3) opens opportunities to explore systematically the importance of charge-correlation effects on transport in conjugated polymers without the structural rearrangement associated with chemical or electrochemical doping.
204 citations
TL;DR: The nuclear charge radius of 11Li has been determined for the first time by high-precision laser spectroscopy and a combination of halo neutron correlation and intrinsic core excitation best reproduces the experimental results.
Abstract: The nuclear charge radius of 11Li has been determined for the first time by high-precision laser spectroscopy. On-line measurements at TRIUMF-ISAC yielded a 7Li-11Li isotope shift (IS) of 25 101.23(13) MHz for the Doppler-free [FORMULA: SEE TEXT]transition. IS accuracy for all other bound Li isotopes was also improved. Differences from calculated mass-based IS yield values for change in charge radius along the isotope chain. The charge radius decreases monotonically from 6Li to 9Li, and then increases from 2.217(35) to 2.467(37) fm for 11Li. This is compared to various models, and it is found that a combination of halo neutron correlation and intrinsic core excitation best reproduces the experimental results.
TL;DR: It has been found that the effect of shear rate on the mass fractal dimension depends on polymer charge density, and three cationic polymers were chosen as flocculants to aggregate silica particles.
Abstract: Three cationic polymers with molecular weights and charge densities of 3.0 x 10(5) g/mol and 10%, 1.1 x 10(5) g/mol and 40%, and 1.2 x 10(5) g/mol and 100% were chosen as flocculants to aggregate silica particles (90 nm), under various conditions, including change in polymer dosage, particle concentration, background electrolyte concentration, and shear rate. The size and structure of flocs produced were determined using the static light scattering technique. On the basis of measurements of polymer adsorption and its effect on the zeta potential and floc properties, it has been found that the polymer charge density plays an important role in determining the flocculation mechanism. Polymers with a 10% charge density facilitate bridging, 40% charged polymers bring about either a combination of charge neutralization and bridging or bridging, depending on the polymer dosage, and polymers with the charge density of 100% induce electrostatic patch flocculation mechanism at the optimum polymer dosage and below but bring about bridging mechanism at the polymer dosage approaching the adsorption plateau value. Bridging aggregation can readily be affected by the particle concentration, and an increase in particle concentration results in the formation of larger but looser aggregates, whereas electrostatic patch aggregation is independent of particle concentration. The addition of a background electrolyte aids in bridging aggregation while it is detrimental to electrostatic patch aggregation. It has also been found that the effect of shear rate on the mass fractal dimension depends on polymer charge density.
TL;DR: In this article, the authors investigated how the natural organic matter (NOM) fraction make-up of the raw water influences coagulation performance and showed that simple fractionation, in terms of the hydrophobic/hydrophilic balance of the water, could provide a fast and effective method for improved understanding of coagulations performance.
TL;DR: This model provides a semi-quantitative explanation for the spontaneous self-assembly of several types of metallic and semiconducting charged nanoparticles upon reduction of their surface charge.
Abstract: We present a thermodynamic evaluation of the self-assembly of charged nanometer-sized particles at the water/oil interface. The chemical potentials of the nanoparticles in the bulk (aqueous) phase and at the water/oil interface are calculated taking into account interfacial energies, van der Waals interactions, and electrostatic repulsions. An isotherm of the interfacial particle density as a function of the surface charge density on the particles is obtained and compared with experimental results on gold and CdTe nanoparticles self-assembled at the water/heptane interface. Our model provides a semi-quantitative explanation for the spontaneous self-assembly of several types of metallic and semiconducting charged nanoparticles upon reduction of their surface charge.
TL;DR: In this article, the structural and thermodynamic properties of weak polyelectrolytes end-tethered to surfaces of arbitrary geometry are studied using a molecular theory based on writing down the free energy functional of the system including all the basic interactions and the explicit acid-base equilibrium for the chargeable groups of the polymer.
Abstract: The structural and thermodynamical properties of weak polyelectrolytes end-tethered to surfaces of arbitrary geometry are studied using a molecular theory. The theory is based on writing down the free energy functional of the system including all the basic interactions and the explicit acid-base equilibrium for the chargeable groups of the polymer. The theory explicitly includes the size, shape, conformations, and charge distribution of all the molecular species. The electrostatic interactions include a density-dependent dielectric function, modeled with the Maxwell-Garnett mixing formula, to account for the composition-dependent permittivity. The minimization of the free energy leads to the distribution of all molecular species and their dependence on bulk pH and salt concentration. We apply the theory to polymer chains end-tethered to planar, cylindrical, and spherical surfaces. The radius of the curved surfaces is small to enhance the curvature effect. We find that when the grafting surfaces are uncharged, the approximation of a constant dielectric function works very well for both structural and thermodynamic properties. The structure of weak polyelectrolytes tethered on cylindrical and spherical surfaces is different from that of polymers tethered on planar surfaces due to the available volume as a function of the distance from the surface. Specifically, the degree of dissociation increases with increasing curvature of the surface. This is a manifestation of the coupling between the local density of protons, counterions, and polymer segments. The results can be interpreted in terms of the local Le Chatelier principle for the acid-base equilibrium, with proper account of the three local contributions: counterions, protons, and chargeable groups. We find that one can achieve local changes of pH between one to two units within 1-2 nm. The thickness of the tethered layers as a function of bulk pH shows a large increase when the pH is equal to the bulk pK. However, the variation with salt concentration is different for the different geometries. The largest swelling is found for cylindrical surfaces. The predictions from scaling theories of a maximum in the thickness of the film as a function of salt concentration is found for planar films, but not for curved surfaces. Finally, the interactions between cylinders with tethered polyelectrolytes is very different from the equivalent planar surfaces. These results are important for the interpretation of force measurements with nanoscale AFM tips. The implications of the results for the rational design of responsive tethered polymer layers is discussed together with the limitations of the theoretical approach.
TL;DR: In this paper, a coupled mode space approach to nonequilibrium Green's function (NEGF) simulation is proposed, where the coupling functions arising from coupled mode effects are evaluated in the current and charge density calculations.
Abstract: In this article, we study the coupled mode space approach to nonequilibrium Green’s function (NEGF) simulation. When the lateral confinement of nanoscale devices changes abruptly and the correlation functions arising from coupled mode effects are improperly evaluated in the current and charge density calculations, it becomes difficult to solve nonequilibrium Green’s function equations self-consistently with Poisson’s equation because discrepancies appear in the charge distribution. To avoid this complication, two- and three-dimensional structures with a constant or a slightly varying confinement are often considered in the NEGF coupled mode space approach. We present a rigorous derivation of the method starting from the definition of the Green’s function and its expansion in a coupled mode space, where current and charge density equations fully account for the coupling effects. Excellent agreement with real space calculation demonstrates the strength of the method and its applicability to the simulation o...
TL;DR: Both simulation and experimental results clearly demonstrate that the mean field theory fails not only quantitatively but also qualitatively to describe a C-S-H dispersion under realistic conditions.
Abstract: In this paper, we are concerned with the charging and electrokinetic behavior of colloidal particles exhibiting a high surface charge in the alkaline pH range. For such particles, a theoretical approach has been developed in the framework of the primitive model. The charging and electrokinetic behavior of the particles are determined by the use of a Monte Carlo simulation in a grand canonical ensemble and compared with those obtained through the mean field theory. One of the most common colloidal particles has been chosen to test our theoretical approach. That is calcium silicate hydrate (C-S-H) which is the main component of hydrated cement and is known for being responsible for cement cohesion partly due to its unusually high surface charge density. Various experimental techniques have been used to determine its surface charge and electrokinetic potential. The experimental and simulated results are in excellent agreement over a wide range of electrostatic coupling, from a weakly charged surface in contact with a reservoir containing monovalent ions to a highly charged one in contact with a reservoir with divalent ions. The electrophoretic measurements show a charge reversal of the C-S-H particles at high pH and/or high calcium concentration in excellent agreement with simulation predictions. Finally, both simulation and experimental results clearly demonstrate that the mean field theory fails not only quantitatively but also qualitatively to describe a C-S-H dispersion under realistic conditions.
TL;DR: In this article, the structural and electronic properties of the less known bismuth III-V compounds: BBi, AlBi, GaBi, and InBi were analyzed in terms of valence charge density transfer.
Abstract: We have performed ab initio self-consistent calculations based on the full potential linear augmented plane-wave method with the generalized gradient approximation to investigate the structural and the electronic properties of the less known bismuth III-V compounds: BBi, AlBi, GaBi, and InBi. Ground state parameters are computed and compared with available theoretical and experimental works. The zinc-blende phase is found to be the most stable for BBi, AlBi, and GaBi, while InBi prefers the tetragonal PbO structure. The relativistic contraction of the $6s$ orbital of Bi has strong effect on the band structure of III-Bi compounds, which exhibits some features that differ considerably from those of typical III-V semiconductors. In particular, we found an inverted band gap, which reflects a semimetallic character of these systems. Their bonding nature is analyzed in terms of valence charge density transfer, showing three different natures of the bond. Besides, the calculated valence charge density for BBi shows an anomalous behavior characterized by a charge transfer toward the cation B atom, while the others III-Bi behave as the typical III-V compounds with a small charge transfer to the anion bismuth atom.
TL;DR: High-resolution X-ray diffraction data, in conjunction with DFT(B3LYP) quantum calculations, have been used in a QTAIM analysis of the charge density in the trimethylenemethane (TMM) complex Fe(eta(4)-C[CH(2)](3))(CO)(3).
Abstract: High-resolution X-ray diffraction data, in conjunction with DFT(B3LYP) quantum calculations, have been used in a QTAIM analysis of the charge density in the trimethylenemethane (TMM) complex Fe(η4-C{CH2}3)(CO)3. The agreement between the theoretical and experimental topological properties is excellent. Only one bond path is observed between the TMM ligand and the Fe atom, from the central Cα atom. However, much evidence, including from the delocalization indices and the source function, suggests that there is a strong chemical interaction between the Fe and Cβ atoms, despite the formal lack of chemical bonding according to QTAIM.
TL;DR: In this article, the authors proposed the use of the LTE-diffusion approximation for predicting the properties of electric arcs, which overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero and makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity.
Abstract: This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on De/W, where De is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode.
TL;DR: In this article, the authors derived expressions for the effective charge carrier density in silicon nanowires as a function of Qf, Dit, the nanowire radius, and the dopant density.
Abstract: The electrical properties of Si nanowires covered by a SiO2 shell are influenced by the properties of the Si/SiO2 interface This interface can be characterized by the fixed oxide charge density Qf and the interface trap level density Dit We derive expressions for the effective charge carrier density in silicon nanowires as a function of Qf, Dit, the nanowire radius, and the dopant density It is found that a nanowire is fully depleted when its radius is smaller than a critical radius acrit An analytic expression for acrit is derived
TL;DR: Several methods for characterizing layer charge of smectites were compared in this paper, and four CEC methods were used, based on ion exchange reactions with solutions of barium chloride, ammonium acetate, methylene blue and a chelate complex of Cu(II).
TL;DR: This study uses terminally functionalized alkanethiol self-assembled monolayers (SAMs) to systematically control the surface charge density and suggests the general importance of controlling electrostatic interaction in the formation of stable SPBs.
TL;DR: In this article, the authors reviewed the recent developments of space-charge-limited (SCL) flow or Child-Langmuir (CL) law in the quantum regime and found that the classical concepts of SCL flow such as bipolar flow, transit time, beam-loaded capacitance, emitted charge density, and magnetic insulation are no longer valid in quantum regime.
Abstract: This paper reviews the recent developments of space-charge-limited (SCL) flow or Child-Langmuir (CL) law in the quantum regime. According to the classical CL law for planar diodes, the current density scales as 3∕2’s power of gap voltage and to the inverse squared power of gap spacing. When the electron de Broglie wavelength is comparable or larger than the gap spacing, the classical SCL current density is enhanced by a large factor due to electron tunneling and exchange-correlation effects, and there is a new quantum scaling for the current density, which is proportional to the 1∕2’s power of gap voltage, and to the inverse fourth-power of gap spacing. It is also found that the classical concepts of the SCL flow such as bipolar flow, transit time, beam-loaded capacitance, emitted charge density, and magnetic insulation are no longer valid in quantum regime. In the quantum regime, there exists a minimum transit time of the SCL flows, in contrast to the classical solution. By including the surface properties of the emitting surface, there is a threshold voltage that is required to obtain the quantum CL law. The implications of the Fowler-Nordheim-like field emission in the presence of intense space charge over the nanometer scale is discussed.
Journal Article•
TL;DR: In this paper, the authors used the common intersection point (c.i.p.) of the data obtained at different ionic strengths to locate the p.z.c. only in a asymmetric case when affinities of the anions and cations to associate with oppositely charged surface groups are equal.
Abstract: Mass titration method was developed as a suitable tool for determination of the point of zero charge (p.z.c.) and surface charge density (σ 0 ) of metal oxide colloid particles at different ionic strengths. In the course of mass titration, subsequent portions of a metal oxide powder are added to an aqueous electrolyte solution, and pH of the equilibrated dispersion is measured. The pH of the system changes gradually and approaches a constant value of pH ∞ , which is in the case of a metal oxide free of impurities equal to the point of zero charge pH pzc . Counterion association shifts the pH pzc either to the acidic region (preferential adsorption of cations) or to the basic region (preferential adsorption of anions). Mass titration therefore enables detection of the difference between association affinities of counterions (cations and anions), which is important information about the equilibrium within the electrical interfacial layer. Such an analysis is not possible by the conventional acid-base potentiometric titration of the dispersion, since the location of the p.z.c. is based on the common intersection point (c.i.p.) of the data obtained at different ionic strengths. It is shown that c.i.p. may be used for locating the p.z.c. only in a asymmetric case«, when affinities of the anions and cations to associate with oppositely charged surface groups are equal. Analysis of the mass titration was performed on the basis of experimental data obtained with colloidal titania dispersed in an aqueous sodium chloride solution, and also by numerical simulation based on the Surface Complexation Model and the 2-pK mechanism of surface reactions. Increase in the NaCI concentration shifted the point of zero charge to the basic region, while the isoelectric point was shifted to the acidic region, indicating higher association affinity of chloride ions compared to sodium ions.
TL;DR: In this article, the surface-charge density of a nanowire covered with native oxide is about 2 X 10 12 cm -2 ; the density appears to decrease by a factor of two to four when the native oxide was replaced by a high-quality thermally grown oxide, with further improvement possible.
Abstract: Metal-catalyzed nanowires have previously been proposed as the active elements of field-effect devices, such as metal oxide field effect transistors and sensors. For these applications, the nanowire surface properties must be understood and controlled. Initial measurements of nanowire surface-charge density are presented here. The surface-charge density was obtained by measuring nanowires of different diameters grown between electrodes. The surface-charge density of a nanowire covered with native oxide is about 2 X 10 12 cm -2 ; the density appears to decrease by a factor of two to four when the native oxide is replaced by a high-quality thermally grown oxide, with further improvement possible.
TL;DR: The Brown bond valence approach has been applied to MO/DFT optimized geometries of a series of hydrated complexes of As( III) and As(V) with Fe(III) (hydr)oxide to describe the surface speciation as a function of pH and loading.
TL;DR: The concept of charge distribution in which the ion charge is allowed to be distributed over two electrostatic planes can successfully describe the pH dependent proton binding and the shift in the isoelectric point (IEP) in the presence of variety of monovalent electrolyte ions with a common set of parameters.
TL;DR: In this paper, the size and charge dependence of the C-O stretching frequency, ν(CO), in complexes of CO with gas phase anionic, neutral, and cationic cobalt clusters (ConCO−∕0∕+), anionic and neutral rhodium clusters (RhnCO− ∕ 0∕ +), and Cationic nickel clusters (NinCO+) for n up to 37.
Abstract: We report on the size and charge dependence of the C–O stretching frequency, ν(CO), in complexes of CO with gas phase anionic, neutral, and cationic cobalt clusters (ConCO−∕0∕+), anionic, neutral, and cationic rhodium clusters (RhnCO−∕0∕+), and cationic nickel clusters (NinCO+) for n up to 37. We develop models, based on the established vibrational spectroscopy of organometallic carbonyl compounds, to understand how cluster size and charge relate to ν(CO) in these complexes. The dominating factor is the available electron density for backdonation from the metal to the CO π* orbital. Electrostatic effects play a significant but minor role. For the charged clusters, the size trends are related to the dilution of the charge density at the binding site on the cluster as n increases. At large n, ν(CO) approaches asymptotes that are not the same as found for ν(CO) on the single crystal metal surfaces, reflecting differences between binding sites on medium sized clusters and the more highly coordinated metal surface sites.
TL;DR: The results provide the first quantitative analysis of the effects of membrane charge density on the performance of ultrafiltration membranes.
Abstract: Although several recent studies have demonstrated the importance of electrostatic interactions in ultrafiltration, there have been few quantitative studies of the effects of membrane charge density on protein transport and membrane hydraulic permeability. Data were obtained using a series of charge-modified cellulose membranes, with the surface charge density controlled by varying the extent of addition of a quaternary amine functionality. The membrane charge was evaluated from streaming potential measurements. Protein transmission decreased by a factor of 100 as the membrane ζ potential increased from 0.3 to 6.6 mV. The protein sieving data were in good agreement with a partitioning model accounting for electrostatic effects, while the hydraulic permeability data were consistent with a flow model accounting for the effects of counter-electroosmosis. The results provide the first quantitative analysis of the effects of membrane charge density on the performance of ultrafiltration membranes.