Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.     

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.     

Viscosity and electrophoretic mobility of cesium fullerenehexamalonate in aqueous solutions--comparing experiments and theories on nanometer-sized spherical polyelectrolyte

The viscosity of aqueous solutions of cesium fullerenehexamalonate T h -C 66(COOCs) 12, a rigid spherical nanometer-sized polyvalent salt, was measured by the Ubbelohde-type viscometer. The measurements were performed without added salt at 25 degrees C in the concentration range between 7 and 320 g/dm (3). THe concentration dependence of the obtained reduced viscosity was compared with the theoretical prediction, taking into account contributions stemming from the intrinsic viscosity, hydrodynamic perturbations of the hypothetically bare fullerenehexamalonate macroion, the primary electroviscous effect, and the secondary electroviscous effect. Using the geometric radius of the bare macroion from the previous measurements of the estimated effective charge of the macroion and from the small-angle X-ray scattering data of the estimated thickness of the compact shell of counterions electrostatically bound to the macroion, a good agreement between theory and the experiment was obtained in the range of the lowest and of the highest concentrations. Electrostatic interactions are identified as the main cause of the increased reduced viscosity at the lowest measured concentrations. At the highest concentrations, electrostatic interactions are effectively screened, and the influence of binary hydrodynamic interactions and perturbations of the hypothetical bare macroion prevails over electrostatic contributions to the increased viscosity. The electrophoretic mobility of the fullerenehexamalonate ion in aqueous salt-free medium was computed with the same value for the radius of the fullerenehexamalonate macroion as that used in the calculation of viscosity. The numerical solution of Ohshima's equation agreed well with the experimental values.     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Overcharging of nanoparticles in electrolyte solutions

Monte Carlo simulations are performed to investigate the effects of salt concentration, valence and size of small ions, surface charge density, and Bjerrum length on the overcharging of isolated spherical nanoparticles within the framework of a primitive model. It is found that charge inversion is most probable in solutions containing multivalent counterions at high salt concentrations. The maximum strength of overcharging occurs near the nanoparticle surface where counterions and coions have identical local concentrations. The simulation results also suggest that both counterion size and electrostatic correlations play major roles for the occurrence of overcharging.     

The influence of colloidal interactions on fiber network strength

Various forces govern the fiber-fiber interaction in a flowing suspension, causing fibers to create flocs. The aim with this investigation was to examine the influence of colloidal interactions on the fiber network strength by varying surface charge density, electrolyte concentration, and type of counterion. This was accomplished by comparing surface force measurements, utilizing colloidal probe microscopy (CPM), with the apparent yield stress, using a parallel plate rheometer. Results show that by increasing the charge density by grafting carboxymethyl cellulose (CMC) to the surface, a large electrosteric repulsion is created, which gives weaker network strength. Increasing the electrolyte concentration decreases the repulsion. The network strength was, however, not affected by electrolyte concentration for untreated fibers whereas a high electrolyte concentration increased the yield stress for CMC-treated fibers. The change of counterions affect the repulsion, causing a change in network strength due to differences in the surface swelling of cellulose.     

Computer simulation of macroion layering in a wedge film

The layering of macroions confined to a wedge slit formed by two uncharged hard walls is studied using a canonical Monte Carlo method combined with a simulation cell that contains both wedge-shaped slit and bath regions. The macroion solution is modeled within a one-component fluid approach that in an effective way incorporates the double layer repulsion due to simple electrolyte ions as well as the discrete nature of an aqueous solvent. The layer formation under a wedge confinement is analyzed by carrying out separate simulation runs for a set of consecutive wedge segments designed to represent a single wedge slit. As the wedge thickness progressively increases, the sequence of regions along the wedge film with distinct features of macroion layering has been established. This sequence comprises (i) a wedge region of the thickness smaller than the macroion diameter that is free of macroions; (ii) a region with a one-dimensional macroion chain along the wedge corner at a wedge thickness of a one macroion diameter; (iii) a region comprising a low-ordered macroion monolayer that extends until the wedge thickness slightly above two macroion diameters; (iv) a region comprising a pair of well-defined two-dimensional configurations of macroions segregated on each of the wedge walls; and (v) a free-of-macroions wedge region between two surface monolayers that now originates from an electrostatic repulsion imposed by the surface macroions, which is followed by (vi) a well-defined macroion monolayer film between two surface monolayers, a less defined bilayer film, a three-layer film, and so on up to the bulk solution. Once formed, the macroion surface monolayers persist for all remaining wedge thicknesses up to the bulk, forming in such a way effective charged wedge boundaries. Such a formation of the macroion surface monolayers on the uncharged confining walls is related to the haloing mechanism for regulating the stability in colloidal suspensions [Tohver et al. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 8951] and is discussed as well. Finally, the estimated boundary of the free of macroion region between surface monolayers correlates well with the location of the boundary of the so-called "vacuum" phase that has been observed experimentally in an aqueous suspension of charged polystyrene spheres bounded by electrostatically repulsive glass walls [Pieransky et al. Phys. Rev. Lett. 1983, 50, 900].     

Electrostatically-driven Ordering in Model Dendrimer Polyelectrolytes: Effects of Concentration

In this study we extend our previous work in the self-organization of dendrimer polyelectrolytes (Macromolecules, 2008 , 41, 225) by examining the effects of dendrimer concentration and/or total volume fraction in the ordering process and the resulting structure, in the arrangement of counterions and dendrimer beads and in the diffusive motion of dendrimers at different strengths of Coulombic interactions. It is found that as long as the total volume fraction remains low (i.e. no jamming phenomena intervene) the symmetry of the resulted cubic phases is unaltered. At a higher volume fraction and at the strong electrostatic regime a kinetic arrest of the dendrimer molecules much in analogy to a colloidal glass-like transition is observed, inhibiting thus the ordering process. Changes in the strength of electrostatic interactions and dendrimer concentration induces a systematic variation of the counterion - counterion and the counterion - charged-dendrimer-bead spatial arrangement. These findings are in qualitative agreement with previous studies in systems with very different structural details of the considered solutes, indicating a more general behaviour in charged macroion/counterion solutions.     

Structural role of counterions adsorbed on self-assembled peptide nanotubes

Among noncovalent forces, electrostatic ones are the strongest and possess a rather long-range action. For these reasons, charges and counterions play a prominent role in self-assembly processes in water and therefore in many biological systems. However, the complexity of the biological media often hinders a detailed understanding of all the electrostatic-related events. In this context, we have studied the role of charges and counterions in the self-assembly of lanreotide, a cationic octapeptide. This peptide spontaneously forms monodisperse nanotubes (NTs) above a critical concentration when solubilized in pure water. Free from any screening buffer, we assessed the interactions between the different peptide oligomers and counterions in solutions, above and below the critical assembly concentration. Our results provide explanations for the selection of a dimeric building block instead of a monomeric one. Indeed, the apparent charge of the dimers is lower than that of the monomers because of strong chemisorption. This phenomenon has two consequences: (i) the dimer-dimer interaction is less repulsive than the monomer-monomer one and (ii) the lowered charge of the dimeric building block weakens the electrostatic repulsion from the positively charged NT walls. Moreover, additional counterion condensation (physisorption) occurs on the NT wall. We furthermore show that the counterions interacting with the NTs play a structural role as they tune the NTs diameter. We demonstrate by a simple model that counterions adsorption sites located on the inner face of the NT walls are responsible for this size control.     

Electrophoretic properties of highly charged colloids: a hybrid molecular dynamics/lattice Boltzmann simulation study

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.     

pH响应木质素基胶体球的制备和表征

以造纸制浆废液中的松木碱木质素（AL）为原料,通过季铵化改性,制备了季铵化碱木质素（QAL）.QAL与十二烷基苯磺酸钠（SDBS）通过静电作用形成QAL/SDBS复配物,将QAL/SDBS复配物在乙醇/水混合溶剂中进行自组装得到具有pH响应性的胶体球.采用X射线光电子能谱（XPS）、扫描电子显微镜（SEM）、透射电子显微镜（TEM）、元素分析和静态接触角研究了胶体球的形成过程和结构.研究结果表明,QAL/SDBS复配物通过疏水聚集作用形成具有较疏水的“核”和较亲水的“壳”结构的规整胶体球.在pH=3.0时,由于QAL与SDBS间的静电作用和疏水作用使胶体球能够稳定存在.当pH>7.5时,季铵化碱木质素上的羧基电离,由于静电斥力的作用使胶体球开始解聚,当pH=10.5时,季铵化碱木质素上的酚羟基的电离使得QAL与SDBS间的静电斥力增大,胶体球完全解聚.这种在酸性条件下稳定,中性条件下解聚的胶体球在药物缓释方面具有潜在的应用.     

Direct measurements of the effects of salt and surfactant on interaction forces between colloidal particles at water-oil interfaces

The forces between colloidal particles at a decane-water interface, in the presence of low concentrations of a monovalent salt (NaCl) and the surfactant sodium dodecyl sulfate (SDS) in the aqueous subphase, have been studied using laser tweezers. In the absence of electrolyte and surfactant, particle interactions exhibit a long-range repulsion, yet the variation of the interaction for different particle pairs is found to be considerable. Averaging over several particle pairs was hence found to be necessary to obtain a reliable assessment of the effects of salt and surfactant. It has previously been suggested that the repulsion is consistent with electrostatic interactions between a small number of dissociated charges in the oil phase, leading to a decay with distance to the power -4 and an absence of any effect of electrolyte concentration. However, the present work demonstrates that increasing the electrolyte concentration does yield, on average, a reduction of the magnitude of the interaction force with electrolyte concentration. This implies that charges on the water side also contribute significantly to the electrostatic interactions. An increase in the concentration of SDS leads to a similar decrease of the interaction force. Moreover, the repulsion at fixed SDS concentrations decreases over longer times. Finally, measurements of three-body interactions provide insight into the anisotropic nature of the interactions. The unique time-dependent and anisotropic interactions between particles at the oil-water interface allow tailoring of the aggregation kinetics and structure of the suspension structure.     

Molecular Dynamics Simulation of the Electrical Double Layer of Spherical Macroion

The structure of the electrical double layer (EDL) of a spherical macroion with a total charge of 60 elementary charges is studied by molecular dynamics methods. In calculations we used two models: continuous and discrete. In the continuous model, the total charge was concentrated in the center of the macroion; in the discrete model, elementary charges were randomly distributed over the surface of the macroion. The radial profiles of local densities and electric potential in EDL, as well as the degree of counterion binding by the macroion, are calculated with allowance for the Lennard-Jones and electrostatic interactions. It is established that the character of charge distribution significantly affects the EDL structure near the macroion, whereas its effect is much weaker at larger distances. The results obtained are compared with the experimental data on the surface potential and the diffuse part of EDL of sodium dodecyl sulfate micelles in aqueous solution, as well as on the micelle-bound charge. It is shown that even weak specific interaction between counterions and a macroion can substantially influence the structure of its EDL.     

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.     

The effect of the salt concentration and counterion valence on the aggregation of latex particles at the air/water interface

An experimental study on colloidal aggregation in two dimensions is presented. This study shows that a high amount of electrolyte concentration is necessary to screen the particle interactions and to induce the aggregation process. Our results indicate that the stability of the colloidal particles, with a diameter of 735 nm, increases when they are trapped at the air-water interface. The reason for this stability is the existence of long-range repulsive interactions between the external parts of the particles that are propagated at the air phase. The subphase electrolyte concentration that separates the slow aggregation rate region from the fast aggregation rate region, the critical coagulation concentration (C.C.C.), has been determined for counterions with a different valence. Two regimes can be distinguished: at low salt concentration the aggregation process becomes slower and the aggregation is reaction limited. At high ionic strength the repulsive interactions between the immersed part of the particles are very weak and the aggregation rate tends to grow. However, because of the aerial repulsive interactions, pure diffusion-limited cluster aggregation is never found.     

Experimental study of electrostatically stabilized colloidal particles: colloidal stability and charge reversal

We consider the interaction of colloidal spheres in the presence of mono-, di-, and trivalent ions. The colloids are stabilized by electrostatic repulsion due to surface charges. The repulsive part of the interaction potential Ψ(d) is deduced from precise measurements of the rate of slow coagulation. These "microsurface potential measurements" allow us to determine a weak repulsion in which Ψ(d) is of the order of a few k(B)T. These data are compared to ζ potential measured under similar conditions. At higher concentrations both di- and trivalent counterions accumulate at the very proximity of the particle surface leading to charge reversal. The salt concentration c(cr) at which charge reversal occurs is found to be always above the critical coagulation concentration c(ccc). The analysis of Ψ(d) and of the ζ potential demonstrates, however, that adsorption of multivalent counterions starts far below c(cr). Hence, colloid stability in the presence of di- and trivalent ions cannot be described in terms of a DLVO ansatz assuming a surface charge that is constant with regard to the ionic strength.     

Metastable cluster intermediates in the condensation of charged macromolecule solutions

The authors examine the possibility of a two-step nucleation to the bulk condensation transition that proceeds via a metastable liquid cluster intermediate having some preferred size. The metastable intermediate is stabilized by electrostatic repulsion, which becomes screened by small mobile ions at sufficiently large cluster sizes, thus allowing the eventual condensation to a bulk phase. Our calculation employs a capillary model for the cluster and the electrostatic interactions are treated using the Poisson-Boltzmann approach. Condensation via this metastable intermediate may be a very general phenomenon which applies not only to solutions of charged particles (e.g., proteins, colloidal particles, and polyelectrolytes) but to any system involving short-range attraction and long-range repulsion undergoing macrophase separation in which a metastable microphase separation is also possible.     

Electric transport and ion binding in solutions of fullerenehexamalonic acid Th-C66(COOH)12 and its alkali and calcium salts

The transport numbers of the macroion constituent in aqueous solutions of fullerenehexamalonic acid, C66(COOH)12, and its lithium, sodium, cesium, and calcium salts were determined by the indirect moving boundary method. By combining the transport data with the literature data for the electrical conductivity of the same solutions, the fraction of bound counterions to the fullerenehexamalonate macroion was calculated. It was found that about 20-40% of counterions are associated with the macroion in the concentration range from about 0.1 to 0.002 mol COO-/L. Consequently, under the influence of a potential field, these counterions move toward the anode as an integral part of the migrating macroion in opposition to the electrical field. Therefore, the absolute values of the macroion constituent transport numbers are relatively high. The experimental values of the fractions of bound counterions were compared with the theoretical predictions based on the solution of the Poisson-Boltzmann equation for the spherical cell model, and a reasonable agreement was obtained.     

Simulation of the electrical double layer of a spherical micelle of an anionic substance with regard to the solvent structure

Computer simulation methods are employed to consider the structure of the electrical double layer of a spherical micelle in aqueous surfactant solutions with allowance for the contribution of the solvent. Three micelle models were used in the calculations, namely, a macroion with discretely distributed charges and a continual solvent, a spherical model micelle with a coarse-grained representation of the solvent, and a spherical model micelle in an aqueous phase with an explicit account for water molecules. Based on these three models, the radial profiles of the local densities and electric potentials in the electrical double layer, as well as the degrees of binding single-, double-, and triple-charged counterions by the macroion in aqueous surfactant solutions, are calculated with regard to the Lennard-Jones and electrostatic interactions. The allowance for the molecular structure of the solvent leads to qualitatively different local dependences of the electric potential as compared to both the continual and coarse-grained representation of the solvent.     

Correlations and Fluctuations of Charged Colloids as Determined by Anomalous Small‐Angle X‐Ray Scattering

Summary: We performed molecular dynamics simulation of a charged colloidal particle with explicit counterions. Our work provides a direct comparison between simulations and ASAXS‐experiments, offering insight into the counterion distribution of charged colloidal suspensions. We give a detailed constitution of the appearing scattering terms with their physical meaning. It is shown that the cross‐correlation between a macroion and its counterions gives the meanfield approximation of the counterion density even if the counterion system is highly fluctuating. Furthermore, it is shown that cross‐correlations can be negative due to oscillations of the density amplitudes of the macroion and counterions and, therefore, must be distinguished from other scattering contributions. These oscillations become more pronounced if the counterions exhibit a fixed shape and if the size of the macroion and that of the counterion system are different.

Simulation sanpshot of a charged colloid (big central sphere) with counterions (small spheres).