Effects of surface site distribution and dielectric discontinuity on the charging behavior of nanoparticles: a grand canonical Monte Carlo study

The surface site distribution and the dielectric discontinuity effects on the charging process of a spherical nanoparticle (NP) have been investigated. It is well known that electrostatic repulsion between charges on neighbouring sites tends to decrease the effective charge of a NP. The situation is more complicated close to a dielectric breakdown, since here a charged site is not only interacting with its neighbours but also with its own image charge and the image charges of all its neighbours. Coexistence of opposite charges, titration sites positions, and pH dependence are systematically studied using a grand canonical Monte Carlo method. A Tanford and Kirkwood approach has been applied to describe the interaction potentials between explicit discrete ampholytic charging sites. Homogeneous, heterogeneous and patch site distributions were considered to reproduce the titration site distribution at the solid/solution interface of natural NPs. Results show that the charging process is controlled by the balance between Coulomb interactions and the reaction field through the solid-liquid interface. They also show that the site distribution plays a crucial role in the charging process. In patch distributions, charges accumulate at the perimeter of each patch due to finite size effects. When homogeneous and heterogeneous distributions are compared, three different charging regimes are obtained. In homogeneous and heterogeneous (with quite low polydispersity indexes) distributions, the effects of the NP dielectric constant on Coulomb interactions are counterbalanced by the reaction field and in this case, the dielectric breakdown has no significant effect on the charging process. This is not the case in patch distributions, where the dielectric breakdown plays a crucial role in the charging process.     

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 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.     

Excluded volume effects in macromolecular forces and ion-interface interactions

A charged Yukawa liquid confined in a slit nanopore is studied in order to understand excluded volume effects in the interaction force between the pore walls. A previously developed self-consistent scheme [S. Buyukdagli, C. V. Achim, and T. Ala-Nissila, J. Stat. Mech. 2011, P05033] and a new simpler variational procedure that self-consistently couple image forces, surface charge induced electric field, and pore modified core interactions are used to this aim. For neutral pores, it is shown that with increasing pore size, the theory predicts a transition of the interplate pressure from an attractive to a strongly repulsive regime associated with an ionic packing state, an effect observed in previous Monte Carlo simulations for hard core charges. We also establish the mean-field theory of the model and show that for dielectrically homogeneous pores, the mean-field regime of the interaction between the walls corresponds to large pores of size d > 4 ?. The role of the range of core interactions in the ionic rejection and interplate pressure is thoroughly analyzed. We show that the physics of the system can be split into two screening regimes. The ionic packing effect takes place in the regime of moderately screened core interactions characterized with the bare screening parameter of the Yukawa potential b ? 3/l(B), where l(B) is the Bjerrum length. In the second regime of strongly screened core interactions b ? 3/l(B), solvation forces associated with these interactions positively contribute to the ionic rejection driven by electrostatic forces and enhance the magnitude of the attractive pressure. For weakly charged pores without a dielectric discontinuity, core interactions make a net repulsive contribution to the interplate force and also result in oscillatory pressure curves, whereas for intermediate surface charges, these interactions exclusively strengthen the external pressure, thereby reducing the magnitude of the net repulsive interplate force. The pronounced dependence of the interplate pressure and ionic partition coefficients on the magnitude and the range of core interactions indicates excluded volume effects as an important ion specificity and a non-negligible ingredient for the stability of macromolecules in electrolyte solutions.     

表面电荷对聚乙二醇修饰金纳米粒子生物行为的影响

利用硫-金键将末端修饰甲氧基、氨基或羧基的巯基化聚乙二醇(Thiolated polyethylene glycol,HS-PEG)分子分别组装到金纳米粒子表面, 合成了3种带有不同表面电荷的聚乙二醇修饰金纳米粒子(PEGylated gold nanoparticles,PEG-Au NP).细胞共培养和小鼠尾静脉注射实验结果表明,表面电荷能够显著影响PEG-Au NP的生物行为.细胞对PEG-Au NP的吞噬量遵循正电荷＞电中性＞负电荷的规律.尾静脉注射的PEG-Au NP能够随小鼠的血液循环由全器官分布逐渐向肝脾转移.表面带负电荷的PEG-Au NP较难被小鼠肝脾清除,带但正电荷的PEG-Au NP能够引起小鼠免疫系统较强的响应.     

Image charges and dispersion forces in electric double layers: the dependence of wall-wall interactions on salt concentration and surface charge density

The interaction pressure between two planar charged walls is calculated for a range of conditions. The diffuse electric double layers between the two wall surfaces are treated with ion-wall dispersion forces and ionic image charge interactions taken into account. Both these interactions are due to dielectric discontinuities at the surfaces. Ion-ion and ion-image charge correlations are explicitly included. The ion-wall dispersion interactions can give rise to appreciable ion specific effects, which are particularly strong when the counterions to the surfaces are highly polarizable. The mechanisms of these effects are investigated, and their influence on the net interaction pressure between the walls is studied for a range of surface charge densities, strengths of the anion-wall dispersion interaction and bulk electrolyte concentrations. When the strength of the anion-wall dipersion interaction is increased, the pressure generally becomes less repulsive (or more attractive) for positive surfaces. The opposite happens in general for negative surfaces but to a much lesser extent. The effects are largest for large surface charge densities and high electrolyte concentrations. The image charge interactions give rise to a considerable depletion attraction between the walls for low surface charge densities.     

Intact Four‐atom Organic Tetracation Stabilized by Charge Localization in the Gas Phase

Several features distinguish intact multiply charged molecular cations (MMCs) from other species such as monocations and polycations: high potential energy, high electron affinity, a high density of electronic states with various spin multiplicities, and charge‐dependent reactions. However, repulsive Coulombic interactions make MMCs quite unstable, and hence small organic MMCs are currently not readily available. Herein, we report that the isolated four‐atom molecule diiodoacetylene survives after the removal of four electrons via tunneling. We show that the tetracation remains metastable towards dissociation because of the localization (91–95 %) of the positive charges on the terminal iodine atoms, ensuring minimum Coulomb repulsion between adjacent atoms as well as maximum charge‐induced attractive dipole interactions between iodine and carbon. Our approach making use of iodines as the positively charged sites enables small organic MMCs to remain intact.     

Electrokinetic actuation of an uncharged polarizable dielectric droplet in charged hydrogel medium

Electrokinetic transport of an uncharged nonconducting microsized liquid droplet in a charged hydrogel medium is studied. Dielectric polarization of the liquid drop under the action of an externally imposed electric field induces a non-homogeneous charge density at the droplet surface. The interactions of the induced surface charge of the droplet with the immobile charges of the hydrogel medium generates an electric force to the droplet, which actuates the drop through the charged hydrogel medium. A numerical study based on the first principle of electrokinetics is adopted. Dependence of the droplet velocity on its dielectric permittivity, bulk ionic concentration, and immobile charge density of the gel is analyzed. The surface conduction is significant in presence of charged gel, which creates a concentration polarization. The impact of the counterion saturation in the Debye layer due to the dielectric decrement of the medium is addressed. The modified Nernst–Planck equation for ion transport and the Poisson equation for the electric field is considered to take into account the dielectric polarization. A quadrupolar vortex around the uncharged droplet is observed when the gel medium is considered to be uncharged, which is similar to the induced charge electroosmosis around an uncharged dielectric colloid in free-solution. We find that the induced charge electrokinetic mechanism creates a strong recirculation of liquid within the droplet and the translational velocity of the droplet strongly depends on its size for the dielectric droplet embedded in a charged gel medium.     

A molecular simulation study on the role of ion sizes and dielectric images in near-surface ion distribution far from the strong coupling limit

A series of Monte Carlo simulations of the planar electric double layers are carried out in the primitive model for two electrolyte mixtures next to a smooth and uniformly charged hard wall representing an ideal biological interface with low and moderate surface charge densities. The structural information of the double layers is applied to reveal charge inversion and overcharging through the addition of multivalent electrolyte at a certain physiological concentration. Various values for the radius of the ions are taken into account to capture the impact of short-range correlations. Meanwhile, the influence of image charges on ion distribution is analyzed, which stems from dielectric discontinuity between the interior and exterior of the membrane matrix. It is clearly shown that depending on the amount of foreign salt, the large size of charged species regardless of its polarity plays a positive role in promoting charge inversion. Moreover, our findings indicate that charge inversion do not signify the reversal of the electrophoretic mobility, in consistent with the recent theoretical predictions by Horno and co-workers [J. Colloid Interface Sci. 356, 325 (2011)]. In addition, the depletion effect triggered by repulsive image forces which are intertwined with the excluded volume correlations gives rise to an anomalous overcharging for low surface charged surface in the high concentrations of trivalent salt. Overall, the ion distribution in a double layer is exclusively governed by entropic and electrostatic contributions but with preferentially leading status for different magnitudes of surface charge.     

Treating highly charged carbon and fullerene clusters as dielectric particles

A model, recently developed for treating interactions between charged particles of dielectric materials (Bichoutskaia et al., J. Chem. Phys., 2010, 133, 024105), has been applied in an analysis of experimental data on the stability and fragmentation of highly charged carbon and fullerene clusters. Fragmentation data take the form of kinetic energy measurements that accompany the Coulomb fission of highly charged carbon clusters. For many of the examples chosen there is good agreement between the calculated and experimental results; however, the degree of uncertainty in some of the experimental data means that subtle features predicted by the model cannot be verified. When compared with an image charge model, treating carbon particles as a dielectric material reveals significant differences in the nature of the interaction potential.     

Onset of cohesion in cement paste

It is generally agreed that the cohesion of cement paste occurs through the formation of a network of nanoparticles of a calcium-silicate-hydrate ("C-S-H"). However, the mechanism by which these particles develop this cohesion has not been established. Here we propose a dielectric continuum model which includes all ionic interactions within a dispersion of C-S-H particles. It takes into account all co-ions and counterions explicitly (with pure Coulomb interactions between ions and between ions and the surfaces) and makes no further assumptions concerning their hydration or their interactions with the surface sites. At high surface charge densities, the model shows that the surface charge of C-S-H particles is overcompensated by Ca2+ ions, giving a reversal of the apparent particle charge. Also, at high surface charge densities, the model predicts that the correlations of ions located around neighboring particles causes an attraction between the particle surfaces. This attraction has a range of approximately 3 nm and a magnitude of 1 nN, values that are in good agreement with recent AFM experiments. These predictions are stable with respect to small changes in surface-surface separation, hydrated ion radius, and dielectric constant of the solution. The model also describes the effect of changes in cement composition through the introduction of other ions, either monovalent (Na) or multivalent (aluminum or iron hydroxide).     

Variation of atomic charges on proton transfer in strong hydrogen bonds: the case of anionic and neutral imidazole-acetate complexes

The variation of atomic charges upon proton transfer in hydrogen bonding complexes of 4-methylimidazole, in both neutral and protonated cationic forms, and acetate anion, is investigated. These complexes model the histidine (neutral and protonated)-aspartate pair present in active sites of proteases where strong N--H...O hydrogen bonds are formed. Three procedures (Merz-Kollman scheme, Natural Population Analysis, and Atoms in Molecules Method) are used to compute atomic charges and explore their variation upon H-transfer in the gas phase and in the presence of two continuum media with dielectric constants 5 (protein interiors) and 78.39 (water). The effect of electron correlation was also studied by comparing Hartree-Fock and MP2 results for both complexes in the gas phase. Greater net charge interchanged upon H-transfer is observed in the anionic complex with respect to the neutral complex. Raising the polarity of the medium increases the amount of net charge transfer in both complexes, although the neutral system exhibits a larger sensitivity to the presence of solvent. Charge transfer associated to N--H...O and N...H--O bonds reveal the ionic contribution to the interaction depending on the number of charged subunits but the presence of solvent affects little this quantity. The lack of electron correlation overestimates all the charges as well as their variations and so uncorrelated calculations should be avoided.     

Electric field effects in proteins in membranes

Both the organization and function of protein nanostructures in membranes are related to the substructural properties of the lipid portion of the membrane. Potential differences that are established across the membrane and generate electric fields in these very thin portions are shown to modulate the organizational and functional properties of the protein modules. Many protein modules also have nonisotropic distributions of charged sites, including configurations in which there are regions containing predominantly positive fixed charges, juxtaposed with adjacent regions containing predominantly negative fixed charges. In these double fixed charge regions, very large electric fields can manifest in the ionic depletion layer at the junction of the two fixed charge regions.Consideration is also given to the manner in which the intense electric fields that are established in protein modules, such as proton ATPases, can modulate the chemical reactions that are associated with proton transport and dehydration reactions.     

Ion transport and selectivity in nanopores with spatially inhomogeneous fixed charge distributions

Polymeric nanopores with fixed charges show ionic selectivity when immersed in aqueous electrolyte solutions. The understanding of the electrical interaction between these charges and the mobile ions confined in the inside nanopore solution is the key issue in the design of potential applications. The authors have theoretically described the effects that spatially inhomogeneous fixed charge distributions exert on the ionic transport and selectivity properties of the nanopore. A comprehensive set of one-dimensional distributions including the skin, core, cluster, and asymmetric cases are analyzed on the basis of the Nernst-Planck equations. Current-voltage curves, nanopore potentials, and transport numbers are calculated for the above distributions and compared with those obtained for a homogeneously charged nanopore with the same average fixed charge concentration. The authors have discussed if an appropriate design of the spatial fixed charge inhomogeneity can lead to an enhancement of the transport and selectivity with respect to the homogeneous nanopore case. Finally, they have compared the theoretical predictions with relevant experimental data.     

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.     

Dressed ion theory of size-asymmetric electrolytes: effective ionic charges and the decay length of screened Coulomb potential and pair correlations

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge.     

Electrostatically "patchy" coatings via cooperative adsorption of charged nanoparticles

Solutions containing oppositely charged nanoparticles (NPs) deposit "patchy" coatings of alternating charge distribution on various types of materials, including polymers, elastomers, and semiconductors. Surface adsorption of the NPs is driven by cooperative electrostatic interactions and does not require chemical ligation or layer-by-layer schemes. The composition and the quality of the coatings can be regulated by the types, the charges, and the relative concentrations of the NPs used and by the pH. Dense coatings form on flat, curvilinear, or micropatterned surfaces, are stable against common chemicals for prolonged periods of time, and can be used in applications ranging from bacterial protection to plasmonics.     

Charge distributions in polyacetylene chains containing a positively charged defect

We present a comparative study of the AIM, CHELPG, GAPT, MK, Mulliken, NPA, and RESP charge distributions associated with a positively charged soliton on increasingly large trans‐polyacetylene chains, at HF, MP2, and DFT levels of theory. The charge storage in the soliton‐bearing systems is explored in detail, including charge magnitude, charge separation, charge alternation, and chain length effects. The grouping of the charge distributions at a given level of theory, as well as the sensitivity of a given charge distribution to the inclusion of electron correlation in its computation, are investigated using similarity analysis. Several of the charge definitions have been applied for the first time for charged soliton‐bearing systems, and there are substantial differences between the charge distributions for the charged and neutral systems. Thus, AIM charges are no longer one of the largest charge values, the AIM charges can be in counterphase with other definitions, and the GAPT charges for neutral systems are quite different from the GAPT charges for charged systems, e.g., the magnitudes of the GAPT charges are anomalously large and increase with the size of the charged system. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids

An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities - obtained with both linear and nonlinear Poisson-Boltzmann equation - for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers.     

Electrophoretic mobility, zeta potential, and fixed charge density of bovine knee chondrocytes, methyl methacrylate-sulfopropyl methacrylate, polybutylcyanoacrylate, and solid lipid nanoparticles

The electrophoretic mobility and zeta potential of bovine knee chondrocytes (BKCs), methyl methacrylate-sulfopropyl methacrylate (MMA-SPM) nanoparticles (NPs), polybutylcyanoacrylate (PBCA) NPs, and solid lipid nanoparticles (SLNs) were investigated under the influences of Na+, K+, and Ca2+ with various ionic strengths. The fixed charge density in the surface layers of the four biocolloidal particles was estimated from the experimental mobility of capillary electrophoresis with a theory of soft charged colloids. The results revealed that, for a specific cationic species, the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density decreased with an increase in ionic strength. For a constant ionic strength, the effect of ionic species on the reduction in the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density followed the order Na+>K+>Ca2+ for the negatively charged BKCs, MMA-SPM NPs, and SLNs. The reverse order is true for the positively charged PBCA NPs.