Modeling the surface charge evolution of spherical nanoparticles by considering dielectric discontinuity effects at the solid/electrolyte solution interface

It is well known that the electrostatic repulsions between charges on neighboring sites decrease the effective charge at the surface of a charged nanoparticle (NP). However, the situation is more complex close to a dielectric discontinuity, since charged sites are interacting not only with their neighbors but also with their own image charges and the image charges of all neighbors. Titrating site positions, solution ionic concentration, dielectric discontinuity effects, and surface charge variations with pH are investigated here using a grand canonical Monte Carlo method. A Tanford and Kirkwood approach is used to calculate the interaction potentials between the discrete charged sites. Homogeneous, heterogeneous, and patch site distributions are considered to reproduce the various titrating site distributions at the solid/solution interface of spherical NPs. By considering Coulomb, salt, and image charges effects, results show that for different ionic concentrations, modifications of the dielectric constant of NPs having homogeneous and heterogeneous site distributions have little effect on their charging process. Thus, the reaction field, due to the presence of image charges, fully counterbalances the Coulomb interactions. This is not the case for patch distributions, where Coulomb interactions are not completely counterbalanced by the reaction field. Application of the present model to pyrogenic silica is also performed and comparison is made with published experimental data of titration curves at various ionic concentrations.     

Modifying the charge state distribution of proteins in electrospray ionization mass spectrometry by chemical derivatization

Electrospray ionization (ESI) of denatured proteins produces a broad distribution of multiply-charged ions leading to multiple peaks in the mass spectrum. We investigated changes in the positive-mode ESI charge state distribution produced by several chemical modifications of denatured proteins. Capping carboxylic acid groups with neutral functional groups yields little change in charge state distribution compared with unmodified proteins. The results indicate that carboxyl groups do not play a significant role in the positive charging of denatured proteins in ESI. The modification of proteins with additional basic sites or fixed positive charges generates substantially higher charge states, providing evidence that the number of ionizable sites, rather than molecular size and shape, determines ESI charging for denatured proteins. Fixed charge modification also significantly reduces the number of protons acquired by a protein, in that the charge state envelope is not increased by the full number of fixed charges appended. This result demonstrates that Coulombic repulsion between positive charges plays a significant role in determining charge state distribution by affecting the gas-phase basicity of ionizable sites. Addition of fixed-charge moieties to a protein is a useful approach for shifting protein charge state distributions to higher charge states, and with further work, it may help limit the distribution of protein ions to fewer charge states.     

Interfacial phenomena in polymer films and generation of maxwell displacement current

Interfacial electrostatic phenomena in ultrathin polyimide films have been examined, and the space charge distribution and electronic density of states have been determined. The presence of excess negative charges at the film-metal interface of nanometer thickness has been revealed and the alignment of the surface Fermi level of polymer films and Fermi level of metals have been elucidated. Taking into account the interfacial space charge, a step structure observed in the I-V characteristic of metal-polyimide-rhodamine-polyimide-metal junction, very similar to Coulomb staircase, is well explained. Furthermore, the electrical breakdown mechanism of a nanometer-thick polyimide film is found quite different from that of micrometer-thick films, owing to the presence of this interfacial nanometric space charge. Finally, for a profound understanding of the behaviour of surface monolayer, the Maxwell displacement current measurement coupled with optical second harmonic generation measurement has been employed.     

Continuum Field Charging of Dielectric Spheroids

Classical continuum theory for field charging is applied in an analysis of the ionic charging of spheroidal dielectrics. Assuming that the particle orientation is fixed during the charging process, the saturation charge and charging rate are determined as functions of the orientation and aspect ratio of spheroids. For spheroids of small dielectric constants the saturation charge becomes the largest when the electric field is directed perpendicular to the major axis of the spheroid. For an ensemble of randomly oriented spheroids the average saturation charge can be approximated as the arithmetic average of the saturation charges for the spheroid with the electric field directed along the three principal axes of the spheroid. In addition, the ensemble average of the dimensionless charging rate of randomly oriented spheroids of moderate axial ratio approximates the dimensionless charging rate of a sphere. Copyright 2000 Academic Press.     

Self-consistent treatment of the local dielectric permittivity and electrostatic potential in solution for polarizable macromolecular force fields

A self-consistent method is presented for the calculation of the local dielectric permittivity and electrostatic potential generated by a solute of arbitrary shape and charge distribution in a polar and polarizable liquid. The structure and dynamics behavior of the liquid at the solute∕liquid interface determine the spatial variations of the density and the dielectric response. Emphasis here is on the treatment of the interface. The method is an extension of conventional methods used in continuum protein electrostatics, and can be used to estimate changes in the static dielectric response of the liquid as it adapts to charge redistribution within the solute. This is most relevant in the context of polarizable force fields, during electron structure optimization in quantum chemical calculations, or upon charge transfer. The method is computationally efficient and well suited for code parallelization, and can be used for on-the-fly calculations of the local permittivity in dynamics simulations of systems with large and heterogeneous charge distributions, such as proteins, nucleic acids, and polyelectrolytes. Numerical calculation of the system free energy is discussed for the general case of a liquid with field-dependent dielectric response.     

The charging of a liquid dielectric upon its flow past a flat-plate

The charging of a liquid dielectric upon its flow past a flat-plate is considered. Analytical expressions for the density distribution of electric charge and charging current are derived. The dependences of the current and charge density distribution on the system parameters are investigated. The effect of the electric field that emerges owing to charge separation on the charging process is taken into account. Consideration of the electric field is shown to lead to lower values of the electric charge density and charging current. As the Debye number decreases, the charge density also decreases. The charging current increases with an increase in the Debye number.     

Dielectric relaxation in an enzyme active site: molecular dynamics simulations interpreted with a macroscopic continuum model.

Dielectric relaxation plays an important role in many chemical processes in proteins, including acid-base titration, ligand binding, and charge transfer reactions. Its complexity makes experimental characterization difficult, and so, theoretical approaches are valuable. The comparison of molecular dynamics free energy simulations with simpler models such as a dielectric continuum model is especially useful for obtaining qualitative insights. We have analyzed a charge insertion process that models deprotonation or mutation of an important side chain in the active site of the enzyme aspartyl-tRNA synthetase. Complexes with the substrate aspartate and the analogue asparagine were studied. The resulting dielectric relaxation was found to involve both ligand and side chain rearrangements in the active site and to account for a large part of the overall charging free energy. With the continuum model, charge insertion is performed along a two-step pathway: insertion into a static environment, followed by relaxation of the environment. These correspond to different physical processes and require different protein dielectric constants. A low value of approximately 1 is needed for the static step, consistent with the parametrization of the molecular mechanics charge set used. A value of 3-6 (depending on the exact insertion site and the nature of the ligand) is needed to describe the dielectric relaxation step. This moderate value indicates that, for this system, the local protein polarizability in the active site is within at most a factor of 2 of that expected at nonspecific positions in a protein interior.     

Further studies on the origins of asymmetric charge partitioning in protein homodimers

Dissociation of gas-phase protonated protein dimers into their constituent monomers can result in either symmetric or asymmetric charge partitioning. Dissociation of alpha-lactalbumin homodimers with 15+ charges results in a symmetric, but broad, distribution of protein monomers with charge states centered around 8+/7+. In contrast, dissociation of the 15+ heterodimer consisting of one molecule in the oxidized form and one in the reduced form results in highly asymmetric charge partitioning in which the reduced species carries away predominantly 11+ charges, and the oxidized molecule carries away 4+ charges. This result cannot be adequately explained by differential charging occurring either in solution or in the electrospray process, but appears to be best explained by the reduced species unfolding upon activation in the gas phase with subsequent separation and proton transfer to the unfolding species in the dissociation complex to minimize Coulomb repulsion. For dimers of cytochrome c formed directly from solution, the 17+ charge state undergoes symmetric charge partitioning whereas dissociation of the 13+ is asymmetric. Reduction of the charge state of dimers with 17+ charges to 13+ via gas-phase proton transfer and subsequent dissociation of the mass selected 13+ ions results in a symmetric charge partitioning. This result clearly shows that the structure of the dimer ions with 13+ charges depends on the method of ion formation and that the structural difference is responsible for the symmetric versus asymmetric charge partitioning observed. This indicates that the asymmetry observed when these ions are formed directly from solution must come about due either to differences in the monomer conformations in the dimer that exist in solution or that occur during the electrospray ionization process. These results provide additional evidence for the origin of charge asymmetry that occurs in the dissociation of multiply charged protein complexes and indicate that some solution-phase information can be obtained from these gas-phase dissociation experiments.     

Free energy of charge transfer and intraprotein electric field: method of calculation depends on the charge state of protein at a given structure.

Free energy of charge transfer presents a basic characteristic of reactions such as protonation, oxido-reduction and similar. Evaluation of this quantity requires calculation of charging energy. Proteins are structured dielectrics, and a consistent incorporation of their structure into calculation of intraprotein electric field results in expression for charging energy of an active group in protein, which is essentially different from that for a simple dielectric. An algorithm for semi-continuum calculation of relevant free energies is described. First of the two components of charging energy in protein, energy of the medium response to charge redistribution in reactants, should be always calculated as the charging energy by the charge redistribution using the static dielectric constant of protein. The second term is interaction energy of the charge redistribution with the 'frozen' electric field of the system before reaction. Charges of protein groups, at which the protein structure has been determined, are often different from those before reaction of charge transfer, so is the corresponding intraprotein field. The field is expressed through either both the optical and static dielectric constants of protein or only optical one depending on whether the charges of protein groups before reaction and upon structural analysis are the same or not. Proper allowance for difference in charges of reacting groups before reaction and upon structural analysis of protein is thermodynamically necessary and quantitatively important. The expression for activation free energy for charge transfer in proteins is derived in the form presenting explicitly an invariant contribution of protein structure.     

The influence of ionic strength on the interaction of viruses with charged surfaces under environmental conditions

The influence of ionic strength on the electrostatic interaction of viruses with environmentally relevant surfaces was determined for three viruses, MS2, Q beta, and Norwalk. The virus is modeled as a particle comprised of ionizable amino acid residues in a shell surrounding a spherical RNA core of negative charge, these charges being compensated for by a Coulomb screening due to intercalated ions. A second model of the virus involving surface charges only is included for comparison. Surface potential calculations for each of the viruses show excellent agreement with electrophoretic mobility and zeta potential measurements as a function of pH. The environmental surface is modeled as a homogeneous plane held at constant potential with and without a finite region (patch) of opposite potential. The results indicate that the electrostatic interaction between the virus and the oppositely charged patch is significantly influenced by the conditions of ionic strength, pH and size of the patch. Specifically, at pH 7, the Norwalk virus interacts more strongly with the patch than MS2 (approximately 51 vs approximately 9kT) but at pH 5, the Norwalk-surface interaction is negligible while that of MS2 is approximately 5.9kT. The resulting ramifications for the use of MS2 as a surrogate for Norwalk are discussed.     

Monte-Carlo simulations of geminate electron–hole pair dissociation in a molecular heterojunction: a two-step dissociation mechanism

The Monte-Carlo simulations are used to investigate the dissociation of a Coulomb correlated charge pair at an idealized interface between an electron accepting and an electron donating molecular material. In the simulations the materials are represented by cubic lattices of sites, with site the energies spread according to Gaussian distributions. The influence of temperature, applied external fields, and the width of the Gaussian densities of states distribution for both the electron and the hole transporting material are investigated. The results show that the dissociation of geminate charge pairs is assisted by disorder and the results can be understood in terms of a two-step model. In the first step, the slow carrier in the most disordered material jumps away from the interface. In the following, second step, the reduced Coulombic attraction allows the faster carrier in the less disordered material to escape from the interface by thermally activated hopping. When the rate for geminate recombination at the interface is very low (<1 ns⁻¹) the simulations predict a high yield for carrier collection, as observed experimentally. Comparison of the simulated and experimentally observed temperature dependence of the collection efficiency indicates that at low temperature dissociation of the geminate charge pairs may be one of the factors limiting the device performance.     

Nanocontact electrification: patterned surface charges affecting adhesion, transfer, and printing

Contact electrification creates an invisible mark, overlooked and often undetected by conventional surface spectroscopic measurements. It impacts our daily lives macroscopically during electrostatic discharge and is equally relevant on the nanoscale in areas such as soft lithography, transfer, and printing. This report describes a new conceptual approach to studying and utilizing contact electrification beyond prior surface force apparatus and point-contact implementations. Instead of a single point contact, our process studies nanocontact electrification that occurs between multiple nanocontacts of different sizes and shapes that can be formed using flexible materials, in particular, surface-functionalized poly(dimethylsiloxane) (PDMS) stamps and other common dielectrics (PMMA, SU-8, PS, PAA, and SiO(2)). Upon the formation of conformal contacts and forced delamination, contacted regions become charged, which is directly observed using Kelvin probe force microscopy revealing images of charge with sub-100-nm lateral resolution. The experiments reveal chemically driven interfacial proton exchange as the dominant charging mechanism for the materials that have been investigated so far. The recorded levels of uncompensated charges approach the theoretical limit that is set by the dielectric breakdown strength of the air gap that forms as the surfaces are delaminated. The macroscopic presence of the charges is recorded using force-distance curve measurements involving a balance and a micromanipulator to control the distance between the delaminated objects. Coulomb attraction between the delaminated surfaces reaches 150 N/m(2). At such a magnitude, the force finds many applications. We demonstrate the utility of printed charges in the fields of (i) nanoxerography and (ii) nanotransfer printing whereby the smallest objects are ～10 nm in diameter and the largest objects are in the millimeter to centimeter range. The printed charges are also shown to affect the electronic properties of contacted surfaces. For example, in the case of a silicon-on-insulator field effect transistors are in contact with PDMS and subsequent delamination leads to threshold voltage shifts that exceed 500 mV.     

Combined depletion and electrostatic forces in polymer-induced membrane adhesion: a theoretical model

We develop a semi-quantitative analytical theory to describe adhesion between two identical planar charged surfaces embedded in a polymer-containing electrolyte solution. Polymer chains are uncharged and differ from the solvent by their lower dielectric permittivity. The solution mimics physiological fluids: It contains 0.1 M of monovalent ions and a small number of divalent cations that form tight bonds with the headgroups of charged lipids. The components have heterogeneous spatial distributions. The model was derived self-consistently by combining: (a) a Poisson-Boltzmann like equation for the charge densities, (b) a continuum mean-field theory for the polymer profile, (c) a solvation energy forcing the ions toward the polymer-poor regions, and (d) surface interactions of polymers and electrolytes. We validated the theory via extensive coarse-grained Molecular Dynamics (MD) simulations. The results confirm our analytical model and reveal interesting details not detected by the theory. At high surface charges, polymer chains are mainly excluded from the gap region, while the concentration of ions increases. The model shows a strong coupling between osmotic forces, surface potential and salting-out effects of the slightly polar polymer chains. It highlights some of the key differences in the behaviour of monomeric and polymeric mixed solvents and their responses to Coulomb interactions. Our main findings are: (a) the onset of long-ranged ion-induced polymer depletion force that increases with surface charge density and (b) a polymer-modified repulsive Coulomb force that increases with surface charge density. Overall, the system exhibits homeostatic behaviour, resulting in robustness against variations in the amount of charges. Applications and extensions of the model are briefly discussed.     

The effect of varied ion distributions on long-range DNA charge transport

Long-range oxidative damage to DNA was utilized as a probe to delineate the effects of different ion distributions on DNA charge transport. DNA assemblies were constructed, containing a tethered rhodium intercalating photooxidant, spatially separated from two 5'-GG-3' sites of oxidative damage, with either an A6-tract or a mixed DNA sequence intervening between the guanine doublets; the extent of charge transport was assessed through measurements of the ratio of yields of damage at the guanine doublet distal versus that proximal to the metal binding site. The distal/proximal damage ratios were compared after photooxidation of otherwise identical Rh-tethered assemblies, except for 32P-labeling either at the 5'- or 3'-end; this labeling difference corresponds, in the absence of charge neutralization by condensed counterions, to a shift in negative charge from one end of the duplex to the other. Both with assemblies containing the mixed sequence and the A6-tract, we observed that moving the negative charges to the proximal end of the duplex significantly decreased hole transport to the distal end. We propose that these results reflect variations in the thermodynamic potential at the proximal and distal guanine sites because of the change in charges at the termini of the oligomer. High values for the internal dielectric constant of the stacked base pairs are suggested by these data. Hence, the longitudinal polarizability of DNA may be important to consider in mechanisms for long-range DNA charge transport.     

Enhancement of CO2 Conversion Rate and Conversion Efficiency by Homogeneous Discharges

The CO₂ conversion rate and conversion efficiency were greatly enhanced by homogeneous dielectric barrier discharges generated in our experiment. Influence of CaO?CB₂O₃?CSiO₂ glass addition on dielectric properties and microstructures of Ca_0.8Sr_0.2TiO₃ were investigated for the purpose of discerning the effect of dielectric barrier material on the dielectric barrier discharge performance so as to improve the CO₂ conversion rate and conversion efficiency. It was found that considerable grain boundaries on the dielectric barrier surface serving as charge trapping sites contribute a great many charges during plasma generation. And low resistance of the dielectric barrier surface distributes the charges effectively. More importantly, when the gap of the discharge is narrowed down, the surface charges on the dielectric barrier will play a dominant role during the discharge. As a result, for the 5.0 wt% glass addition, the CO₂ conversion rate and conversion efficiency reached the maximum values of 48.71?% and 1.14?W/%, respectively.     

Molecular dynamics simulation of a water/metal interface

First results of a molecular dynamics study of a water/metal interface, lasting 3.3 ps at an average temperature of 294 K, are reported. The basic periodic box contains 216 water molecules and a crystal slab of 550 platinum atoms with (100) surface planes. A combination of a Lennard-Jones potential between centers of mass and a Coulomb potential arising from dielectric interactions of the water charge distribution with the metal is employed for the water-wall interaction, the ST2 model for the water-water, and a nearest-neighbour harmonic potential for the platinum-platinum interactions. Considerable adsorption at the interface together with a drastic change of the water structure is observed.     

Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins

We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 ? containing a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ～35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.     

Ionic electrets: electrostatic charging of surfaces by transferring mobile ions upon contact

This paper describes the fabrication and characterization of ionic electrets-materials that bear a long-lived electrostatic charge because of an imbalance between the number of cationic and anionic charges in the material. Crosslinked polystyrene microspheres that contain covalently bound ions and mobile counterions transfer some of their mobile ions in air, in the absence of bulk liquid, to another material upon contact. According to the ion-transfer model of contact electrification, this selective transfer of mobile ions yields microspheres that have a net electrostatic charge. A tool that operates on the principle of electrostatic induction measures the charge on individual microspheres (50-450 microm in diameter). Microspheres with a variety of covalently bound ionic functional groups (tetraalkylammonium, alkyltriphenylphosphonium, alkylsulfonate, and arylsulfonate) acquire charges consistent with this ion-transfer mechanism. The charge on a microsphere is proportional to its surface area (ca. 1 elementary charge per 2000 nm2) and close to the theoretical limit imposed by the dielectric breakdown of air. The charge density in an atmosphere of SF6 is more than twice that in an atmosphere of N2. These observations suggest that the charge density of these ionic electret microspheres is limited by the dielectric breakdown of the surrounding gas. Functionalizing the surfaces of glass or silicon with covalently bound ions and mobile counterions generates ionic electrets from these inorganic substrates. Soft lithography can pattern charge on a planar silicon surface (with oxide) and on the surface of 250-mum glass microspheres.     

Molecular dynamics simulations of electrolyte solutions at the (100) goethite surface

Molecular dynamics simulations of electrolyte solutions in contact with a neutral (100) goethite (alpha-FeOOH) surface were used to probe the structure of the mineral-water interface and gain insight into the adsorption properties of monovalent ions. Three electrolyte solutions were considered: NaCl, CsCl, and CsF. The electrolyte ions were chosen to cover a range of ionic sizes and affinities for the aqueous phase. The molecular dynamics simulations indicate the presence of a structured interfacial region resulting from the strong interaction of water with the mineral surface. The specific arrangement and preferred orientation of water that arise from this interaction create adsorption sites in the interfacial region, i.e., as far as 15 A away from the surface, and hence give rise to a strong correlation between the water and ion distributions. The structure of the hydrated ion, its effect on the water arrangement at the interface, and the strength of the ion-water bond are found to be key factors that determine the location and extent of ion adsorption at the interface. Additionally, in all simulations, we find a build up of positive charges near the surface due to cation adsorption, which is compensated by an accumulation of anions in the next few angstr?ms. This creates an excess of negative charges, which is in turn compensated by an excess of positive charges, and so on. As we modeled a neutral surface, the structure of the electrolyte distribution arises from the complex interplay of the interactions between the surface, water, and the electrolyte ions rather than from the need to neutralize a surface charge. In addition, our simulations indicate that the electrolyte distribution does not resemble that of a classical electrical double layer. Indeed, our calculations predict the presence of several condensed layers and oscillations in the net charge away from the surface.     

Electric potential distributions around discrete charges in a dielectric membrane—electrolyte solution system

Within the framework of the linearized Debye-Hückel theory an exact solution of the problem of calculating the electric potential caused by discrete fixed charges located at arbitrary positions with respect to a dielectric membrane-solution interface is presented. It takes into account the existence of an electrolyte solution on both sides of the membrane. Asymmetric ionic conditions are allowed for. For some interesting typical cases of fixed charge locations and electrolyte ionic strengths electric potential distributions were calculated and discussed. It is shown that, if the fixed charges were at or in front of the membrane surface, the characteristic distance of the electric potential decay was comparable to the Debye-Hückel length. At the opposite membrane surface only very small electric potentials can be observed. If, however, the fixed charge was placed below the membrane surface the electric potential in lateral direction and towards the other membrane surface largely increased. This effect was very sensitive to the position of the fixed charge with respect to the membrane surface.