Interaction between electrical double layers of soil colloids and Fe/Al oxides in suspensions

Phyllosilicates with net negative surface charge and Fe/Al oxides with net positive surface charge coexist in variable-charge soils, and the interaction between these oppositely charged particles affects the stability of mixed colloids, aggregation, and even the surface chemical properties of variable-charge soils. The interaction of the diffuse layers of electrical double layers between the negatively charged soil colloidal particles and the positively charged particles of goethite or gamma-Al(2)O(3) was investigated in this article through the comparison of zeta potentials between single-soil colloidal systems and binary systems containing soil colloids and Fe/Al oxides. The results showed that the presence of goethite and gamma-Al(2)O(3) increased the zeta potential of the binary system containing soil colloids and Fe/Al oxides, which clearly suggests the overlapping of the diffuse layers in soil colloids and Fe/Al oxides. The overlapping of the diffuse layers leads to a decrease in the effective negative charge density on soil colloid and thus causes a shift of pH-zeta potential curves toward the more positive-value side. The interaction of the electrical double layers is also related to the charge characteristics on the Fe/Al oxides: the higher the positive charge density on Fe/Al oxides, the stronger the interaction of the electrical double layers between the soil colloid particles and the Fe/Al oxides.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.     

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.     

Interaction between colloids with grafted diblock polyampholytes

The interaction between composite colloidal particles composed of a spherical core and grafted AB-diblock polyampholytes (diblock copolymers with oppositely charged blocks) are investigated by using a coarse-grained model solved with Monte Carlo simulations. The B block is end-grafted onto the core of the colloid and its linear charge density is varied, whereas the linear charge density of the A block is fixed. The brush structure of a single colloid, the mean force between two colloids, and the structure of solutions of such colloids have been determined for different linear charge densities of the B blocks and block lengths. Many features of the present system are controlled by the charge of the B blocks. In the limit of uncharged B blocks, (i) the grafted chains are stretched and form an extended polyelectrolyte brush, (ii) a strong repulsive force is operating between two colloids, (iii) and the solution is thermodynamic stable and displays strong spatial correlation among the colloids. In the limit where the charges of the two types of blocks exactly compensate each other, (i) the chains are collapsed and form a polyelectrolyte complex surrounding the cores, (ii) an attractive force appears between two colloids, and (iii) strong colloid clustering appears in the solution. These features become more pronounced as the length of the polymer blocks is increased, and a phase instability occurs at sufficiently long chains. A comparison with properties for other related colloidal particles is also provided.     

Effect of charge asymmetry and charge screening on structure of superlattices formed by oppositely charged colloidal particles

Colloidal suspensions made up of oppositely charged particles have been shown to self-assemble into substitutionally ordered superlattices. For a given colloidal suspension, the structure of the superlattice formed from self-assembly depends on its composition, charges on the particles, and charge screening. In this study we have computed the pressure-composition phase diagrams of colloidal suspensions made up of binary mixtures of equal sized and oppositely charged particles interacting via hard core Yukawa potential for varying values of charge screening and charge asymmetry. The systems are studied under conditions where the thermal energy is equal or greater in magnitude to the contact energy of the particles and the Debye screening length is smaller than the size of the particles. Our studies show that charge asymmetry has a significant effect on the ability of colloidal suspensions to form substitutionally ordered superlattices. Slight deviations of the charges from the stoichiometric ratio are found to drastically reduce the thermodynamic stability of substitutionally ordered superlattices. These studies also show that for equal-sized particles, there is an optimum amount of charge screening that favors the formation of substitutionally ordered superlattices.     

Free isotropic-nematic interfaces in fluids of charged platelike colloids

Bulk properties and free interfaces of mixtures of charged platelike colloids and salt are studied within the 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. The charges of the particles are concentrated in their center. The density functional is derived by functional integration of an extension of the Debye-Hückel pair distribution function with respect to the interaction potential. For sufficiently small macroion charges, the bulk phase diagrams exhibit one isotropic and one nematic phase separated by a first-order phase transition. With increasing platelet charge, the isotropic and nematic binodals are shifted to higher densities. The Donnan potential between the coexisting isotropic and nematic phases is inferred from bulk structure calculations. Nonmonotonic density and nematic order parameter profiles are found at a free interface interpolating between the coexisting isotropic and nematic bulk phases. Moreover, electrically charged layers form at the free interface leading to monotonically varying electrostatic potential profiles. Both the widths of the free interfaces and the bulk correlation lengths are approximately given by the Debye length. For fixed salt density, the interfacial tension decreases upon increasing the macroion charge.     

The Electrostatic Interaction of a Charged Particle with a Surface: The Effect of Surface Charge Rearrangement

In this paper we investigate the electric interaction between a charged particle and a surface in which the charged ions are capable of moving in response to the electric potential disturbance caused by the approach of the charged particle. Such surfaces include ionic surfactants distributed in air-water interface and charged lipids in bilayer membranes. On the basis of the mean field theory, the free energy of the system, which includes the electrostatic internal energy and the entropy of the mobile ions and surface ions, can be written down. The surface charge-potential relation is then derived by the calculus of variation. When the potential disturbance is small enough, a linear charge regulation model is obtained. The interaction energy associated with a long rod parallel to the interface is studied and an analytical expression is obtained. When a rod approaches an oppositely charged surface, the interaction can change from attraction to repulsion, depending on the ratio of the characteristic regulation length to the Debye length. At low surface charge density, the surface behaves as under the condition of constant charge density and acts as that of constant potential for high enough charge density. Copyright 2001 Academic Press.     

Smoluchowski equation and the colloidal charge reversal

Smoluchowski equation and the Monte Carlo simulations are used to study the conditions leading to the reversal of the electrophoretic mobility. Zeta (zeta) potential is identified with the diffuse potential at the shear plane which, we argue, must be placed at least one ionic diameter away from the colloidal surface. For sufficiently strongly charged colloids, zeta potential changes sign as a function of the multivalent electrolyte concentration, resulting in a reversal of the electrophoretic mobility. This behavior occurs even for very small ions of 4 A diameter as long as the surface charge density of the colloidal particles is sufficiently large and the concentration of 1:1 electrolyte is sufficiently low.     

Effect of charge inhomogeneity and mobility on colloid aggregation

The aggregation of inhomogeneously charged colloids with the same average charge is analyzed using Monte Carlo simulations. We find aggregation of colloids for sizes in the range 10-200 nm, which is similar to the range in which aggregation is observed in several experiments. The attraction arises from the strongly correlated electrostatic interactions associated with the increase in the counterion density in the region between the particles; this effect is enhanced by the discreteness and mobility of the surface charges. Larger colloids attract more strongly when their surface charges are discrete. We study the aggregation as functions of the surface charge density, counterion valence, and volume fraction.     

Charge and salt-driven reentrant order-disorder and gas-solid transitions in charged colloids

Monte Carlo simulations have been performed for aqueous charged colloidal suspensions as a function of effective charge density (sigma) on the particles and salt concentration C(s). We vary the effective charge density in our simulations over a range where a reentrant solid-liquid transition in suspensions of silica and polymer latex particles has been reported by Yamanaka et al. (Phys. Rev. Lett. 80 (1998) 5806). We show that at low ionic strengths a homogeneous liquid-like ordered suspension undergoes crystallization upon increasing sigma. Further increase in sigma resulted once again in a disordered state, which is in agreement with experimental observations. In addition to this reentrant order-disorder transition, we observe an inhomogeneous-to-homogeneous transition in our simulations when salt is added to the disordered inhomogeneous state. This inhomogeneous-to-homogeneous disordered transition is analogous to the solid-gas transition of atomic systems and has not yet been observed in charged colloids. The reported experimental observations on charged colloidal suspensions are discussed in the light of present simulation results.     

Effective charges of colloidal particles obtained from collective diffusion experiments

In this work, the collective diffusion coefficient of highly charged colloidal particles in dilute dispersions has been measured by means of dynamic light scattering. The possibility of obtaining valuable information about the particle charge from these data is looked into with the help of electrophoresis experiments. Our results suggest that this is possible in the case of slight or moderately interacting particles as long as experimental data are properly treated. For highly interacting colloids, however, such information could not be so reliable, presumably due to certain shortcomings of the experimental technique at low angle. The role of charge renormalization is also discussed in this work.     

From small charged molecules to oligomers: a semiempirical approach to the modeling of actual mobility in free solution

According to Stokes' treatment, the ionic mobility of particles, which are small with respect to Debye length, is usually considered to be proportional to the nominal charge and inversely proportional to the hydrodynamic radius. Experimentally, it is well known, however, that the ionic mobility of a small multicharged molecule does not depend linearly on its nominal charge in a wide range. This behavior can be accounted for by a condensation of the charge or a modification of the friction coefficient with the charge. This paper presents a semiempirical modeling of the actual mobility based on the assumption of additivity of frictional contributions pertaining to the uncharged molecular backbone and to each charged or uncharged moiety. Condensation of the charge was not considered. The model first appeared to be suitable for multicharged analytes having a characteristic dimension smaller than the Debye length, such as benzene polycarboxylic acids and polysulfated disaccharides. This approach was then adapted to account for the actual mobilities of singly and evenly charged oligomers (N-mers) having a dimension smaller than or similar to the Debye length. Rather good experimental agreement was obtained for polyalanines and polyglycines (N < or = 6), fatty acid homologs, fully sulfonated polystyrene oligomers (N < or = 13), and polycytidines (N < or = 10). Especially the influence of the polymerization degree on the mobility of oligomers having identical charge densities was clarified. It is also shown that the electrophoretic contribution to the overall friction coefficient increases linearly with the nominal charge but hardly depends on the chemical nature of the charged moieties. This model should be of interest to evaluate the role of various physicochemical phenomena (hydrodynamic and electrophoretic frictions, hydrodynamic coupling, charge condensation) involved in the migration of charged oligomers.     

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.     

Formation and properties of positively charged colloids based on polyelectrolyte complexes of biopolymers

Formation of colloids based on polyelectrolyte complexes (PECs) was mainly studied with synthetic polyelectrolytes. In this study, we describe the elaboration of positively charged PEC particles at a submicrometer level obtained by the complexation between two charged polysaccharides, chitosan as polycation and dextran sulfate (DS) as polyanion. The complexes were elaborated by dropwise addition of default amounts of DS to excess chitosan. Quasi-elastic light scattering was used to investigate in detail the influence of the characteristics of components (chain length, degree of acetylation) and parameters linked to the reaction of complexation (molar mixing ratio, ionic strength, concentration in polymer) on the sizes and polydispersity of colloids. Chain length of chitosan is the major parameter affecting the dimensions of the complexes, high molar mass chitosans leading to the largest particles. Variations of hydrodynamic diameters of PECs with the molar mass of chitosan are consistent with a mechanism of particle formation through the segregation of the neutral and then hydrophobic blocks of the polyelectrolyte complexed segments. Resulting particles display probably a structure constituted by a neutral core surrounded by a chitosan shell ensuring the colloidal stabilization. Such a structure was evidenced by measurements of electrophoretic mobilities revealing that the positive charge of particles was decreasing with pH, in relation with the neutralization of excess glucosamine hydrochloride moieties.     

Surface charge density and electrokinetic potential of highly charged minerals: experiments and Monte Carlo simulations on calcium silicate hydrate

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.     

On the use of the hypothesis of local electroneutrality in colloidal suspensions for the calculation of their dielectric properties

The validity of the hypothesis of electroneutrality outside the double layer of a suspended particle with an applied ac electric field is analyzed. It is shown that the electrolyte solution remains electroneutral for distances greater than a few Debye lengths from the particle surface only when the diffusion coefficients of the two ion species are identical. On the contrary, in the general case, a volume charge density around the particle builds up, which extends to distances that are proportional to the square root of the effective diffusion coefficient value divided by the frequency. These distances can easily attain many particle radii. Numerical results for both uncharged and charged suspended particles are presented, and a correction to existing analytical expressions for the field-induced ion distributions around uncharged particles (J. Phys. Chem. 2004, 108, 8397) is given. While the charge densities far from the particle are usually very weak, it is shown that they strongly contribute to the dipole coefficient value and, therefore, to the calculated values of the permittivity and conductivity increments. The errors that would be committed if these charge densities were ignored, assuming local electroneutrality and determining the dipole coefficient at a few Debye lengths from the particle surface, are analyzed and shown to be substantial.     

End effects for a rodlike polyelectrolyte molecule in salt solution

Electrostatic potentials around a single rodlike polyelectrolyte molecule are calculated by solving the nonlinear Poisson–Boltzmann equation numerically in the presence of externally added salt. The polyion is regarded as a cylinder with a finite length whose side surface is uniformly charged and end surfaces uncharged. The calculations show that the distance to which end effects extend is about half the Debye screening length and is almost independent of the surface charge density and concentration of added salt. For a long polyion whose length is much greater than the Debye length, the end effects can be neglected even for a polyelectrolyte with high surface charges, whereas they play an important role for a short polyion with a length of the same order as the Debye length. In addition, a strong charge condensation is found in the direction of the axis of the cylinder for a long polyion.     

Electrokinetics of soft polymeric interphases with layered distribution of anionic and cationic charges

Soft surface coatings attract increasing attention due to the versatile options they provide in numerous applications e.g. in the flourishing nanomedicine and nanobiotechnology areas. Optimisation of the performance of such ion- and solvent-permeable polyelectrolytic materials requires a detailed understanding of their electrostatic properties. This task is rendered difficult by the inherent non-uniform distribution of their structural charges. In this article, we review recent advances made in the measurement and theory of the electrokinetics (electrophoresis/streaming current) of soft surface coatings that carry spatially-separated cationic and anionic charges. Examples of such charge-stratified systems are polyelectrolyte-coated particles, polyelectrolyte multilayers, particles with zwitterionic interfacial functionality, microbial cells or hard–soft composite interfaces. It is shown here that the electrokinetic features of such colloidal systems are remarkably different from those of their counterparts with homogeneously distributed cationic and anionic charges. In particular, the interplay between electrostatic and hydrodynamic flow fields developed under electrokinetic conditions in the bulk and interfacial compartments of charge-stratified colloids/films are shown to induce a reversal of their electrokinetic response (electrophoretic mobility/streaming current) that depends on the concentration of monovalent electrolyte in solution. The prerequisites for occurrence of such spectacular behaviour are theoretically identified in terms of the Debye length, the spatial length scales defining charge layering, and the typical length for flow penetration within the colloids/films. Electrophoresis and streaming current results recently reported for poly(amidoamine) carboxylated nanodendrimers, natural rubber colloids and poly(ethyleneimine)-supported lipid bilayers are further discussed to illustrate the generic electrokinetic properties of soft interfaces defined by a given stratification of their anionic and cationic structural charges.     

Complete phase behavior of the symmetrical colloidal electrolyte

We computed the complete phase diagram of the symmetrical colloidal electrolyte by means of Monte Carlo simulations. Thermodynamic integration, together with the Einstein-crystal method, and Gibbs-Duhem integration were used to calculate the equilibrium phase behavior. The system was modeled via the linear screening theory, where the electrostatic interactions are screened by the presence of salt in the medium, characterized by the inverse Debye length, kappa (in this work kappasigma=6). Our results show that at high temperature, the hard-sphere picture is recovered, i.e., the liquid crystallizes into a fcc crystal that does not exhibit charge ordering. In the low temperature region, the liquid freezes into a CsCl structure because charge correlations enhance the pairing between oppositely charged colloids, making the liquid-gas transition metastable with respect to crystallization. Upon increasing density, the CsCl solid transforms into a CuAu-like crystal and this one, in turn, transforms into a tetragonal ordered crystal near close packing. Finally, we have studied the ordered-disordered transitions finding three triple points where the phases in coexistence are liquid-CsCl-disordered fcc, CsCl-CuAu-disordered fcc, and CuAu-tetragonal-disordered fcc.     

Layer-by-layer growth of attractive binary colloidal particles

We investigate the two-dimensional (2D) colloidal structures formed by oppositely charged polystyrene monolayers grown layer-by-layer, where the electrostatic forces are recruited to assist in the packing of the layers. Our results show a transition through several 2D-superlattices to more close-packed structures with increasing ionic strength. The observed geometrical packing constraints of the 2D-superlattice structures agree well with the estimated Debye screening length of the electric double layer. By tuning interaction forces between charged colloids, electrostatic interactions could enhance the template-directed self-assembly process to achieve more complex and diverse structures.