Phase diagrams of binary mixtures of oppositely charged colloids

Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semiquantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in terms of temperature, pressure, and composition. The influence of the screening of the Coulomb interaction upon the topology of the phase diagram is discussed. Insight into the topology of the global phase diagram as a function of the system parameters leads to predictions on the preparation conditions for specific binary colloidal crystals.     

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.     

Complexation of ferric oxide particles with pectins of different charge density

The effect of polyelectrolyte charge density on the electrical properties and stability of suspensions of oppositely charged oxide particles is followed by means of electro-optics and electrophoresis. Variations in the electro-optical effect and the electrophoretic mobility are examined at conditions where fully ionized pectins of different charge density adsorb onto particles with ionizable surfaces. The charge neutralization point coincides with the maximum of particle aggregation in all suspensions. We find that the concentration of polyelectrolyte, needed to neutralize the particle charge, decreases with increasing charge density of the pectin. The most highly charged pectin presents an exception to this order, which is explained with a reduction of the effective charge density of this pectin due to condensation of counterions. The presence of condensed counterions, remaining bound to the pectin during its adsorption on the particle surface, is proved by investigation of the frequency behavior of the electro-optical effect at charge reversal of the particle surface.     

Effect of chain length and charge density on the construction of polyelectrolyte multilayers on colloidal particles

Two combinations of sodium poly(4-styrene sulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) of different chain length and charge density are employed to construct multilayer films. The polyelectrolytes are assembled layer-by-layer on colloidal particles in the absence of salt. We have investigated the formation and electrical characteristics of the films by using electric light scattering technique. The results show that the film thickness is independent of the chain length when fully charged PAH (at pH 4.6) is combined with fully charged PSS. When the films are prepared with less charged PAH (at pH 6.7) and fully charged PSS, lower thickness is found for the film with shorter polymer chains. In all cases, the thickness increment realized on addition of the polymer with lower molar concentration is partially lost on exposure to the solution with higher concentration of the oppositely charged partner. When the film growth is regular (at equal molar concentrations of the fully charged polyelectrolytes), the ratio of PSS to PAH charge, estimated from the electro-optical effect values, exceeds 1. The electro-optical effect is also higher for the films ending with PSS when fully charged PSS is combined with less charged PAH (at pH 6.7). This reveals the key role of the charge in the last-adsorbed layer for the electro-optical behavior of the whole film.     

Highly charging of nanoparticles through electrospray of nanoparticle suspension

Patterned deposition of nanoparticles is a prerequisite for the application of unique properties of nanoparticles in future nanodevices. Recent development of nanoxerography requires highly charged aerosol nanoparticles to avoid noise deposition due to random Brownian motion. However, it has been known that it is difficult to charge aerosol nanoparticles with more than two elementary charges. The goal of this work is to develop a simple technique for obtaining highly charged monodisperse aerosol nanoparticles by means of electrospray of colloidal suspension. Highly charged aerosol nanoparticles were produced by electrospraying (ES) and drying colloidal suspensions of monodisperse gold nanoparticles. Size and charge distributions of the resultant particles were measured. We demonstrate that this method successfully charges monodisperse nanoparticles very highly, e.g., 122 elementary charges for 25.0 nm, 23.5 for 10.5 nm, and 4.6 for 4.2 nm. The method described here constitutes a convenient, reliable, and continuous tool for preparing highly charged aerosol nanoparticles from suspensions of nanoparticles produced by either wet chemistry or gas-phase methods.     

Ionic condensation and charge renormalization in colloidal suspensions

The very popular notion of effective or renormalized polyion charge is a concept of fundamental importance in the field of highly charged colloidal or polyelectrolyte solutions. In such suspensions, the electrostatic coupling between oppositely charged species induces a strong accumulation (or electrostatic “condensation”) of counterions in the vicinity of the macroion surface. The basic idea is thus to consider the structural colloid and the condensed counterionic shell as a whole which carries an effective charge, Z^eff, much weaker than the structural one, Z^str. Consequently, as long as what happens far from the colloid is concerned, all Debye–Hückel-like linearized approaches which fail to correctly treat the nonlinear condensation phenomenon can still be used if Z^str is more or less replaced by Z^eff. Beyond this basic idea, it remains to estimate a priori the value of Z^eff. It will be discussed how to deduce simple laws for the effective charge of spherical colloids from the Poisson–Boltzmann approach, analogous to Manning's law for linear polyelectrolytes. The validity of these laws will be tested, against more complete treatments. Lastly, it will be shown that while the notion of colloidal charge renormalization remains clear for dilute suspensions, it becomes incorrect at higher densities where the condensed counterionic shells overlap.     

The polydisperse cell model: nonlinear screening and charge renormalization in colloidal mixtures

We propose a model for the calculation of renormalized charges and osmotic properties of mixtures of highly charged colloidal particles. The model is a generalization of the cell model and the notion of charge renormalization as introduced by Alexander et al. [J. Chem. Phys. 80, 5776 (1984)]. The total solution is partitioned into as many different cells as components in the mixture. The radii of these cells are determined self-consistently for a given set of parameters from the solution of the nonlinear Poisson-Boltzmann equation with appropriate boundary conditions. This generalizes Alexanders's model where the (unique) Wigner-Seitz cell radius is solely fixed by the colloid packing fraction. We illustrate the technique by considering a binary mixture of the colloids with the same sign of charge. The present model can be used to calculate thermodynamic properties of highly charged colloidal mixtures at the level of linear theories, while taking the effect of nonlinear screening into account.     

Light-scattering form factors of asymmetric particle dimers from heteroaggregation experiments

Measurements of form factors of asymmetric particle dimers composed of oppositely charged polystyrene latex particles are presented. These measurements are based on time-resolved static and dynamic light scattering on dilute aggregating aqueous suspensions. The experimental form factors are compared with independent calculations based on the superposition T-matrix method and Rayleigh-Debye-Gans (RDG) approximation. While the RDG approximation is found to be reliable only up to particle diameters of about 250 nm, the superposition T-matrix method is very accurate for all types of dimers investigated. The present results show clearly the appropriateness of the superposition T-matrix method to estimate the optical properties of colloidal particles in the micrometer range reliably.     

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.     

Nonlinear electric response of polyampholytes

The behavior of polyampholytes (PAs) in electric fields is investigated by Monte Carlo simulations. In bulk it is found that the response of the PA depends on the charge sequence. For small repeating units of positive and negative charges the response is linear, while bigger units results in a nonlinear response in both the induced dipole moment and the resulting polymer conformation. This is reflected in how PAs modify colloidal suspensions, and while PAs always decrease the repulsion between charged colloidal particles, some net-neutral PAs can even induce an effective attraction between the colloidal particles.Contribution to the Björn Roos Honorary Issue     

Polyion-induced aggregation of lipidic-coated solid polystyrene spheres: the many facets of complex formation in low-density colloidal suspensions

We have investigated the formation of a cluster phase in low-density colloidal systems formed by charged solid charged particles stuck together by an oppositely charged polyion. In analogy with what we have previously observed in the case of soft charged particles, also in this case the same basic phenomenology occurs, consisting of the presence of the two well-known characteristic phenomena of this class of colloids, that is, reentrant condensation and charge inversion. With the aim of comparing the cluster formation in both soft and solid charged particles, we have, in previous works, employed cationic liposomes (soft particles, lipidic vesicles built up by dioleoyltrimethylammonium propane [DOTAP] lipid) and, in the present work, polystyrene particles (solid particles) covered by the same lipidic bilayer as the one of the soft particles, so that the two classes of particles share electrostatic interactions of the same nature. These charged particle clusters, where the single aggregating particles maintain their integrity without undergoing a structural rearrangement, join to a class of different aggregated structures (lamellar or inverse hexagonal phases) observed as well in the polyion-induced aggregation of oppositely charged mesoscopic particles, in particular, lipidic vesicles. Our results show that the formation of relatively large, equilibrium clusters of particles which maintain their integrity, stuck together by a polyion which acts as an electrostatic glue, is one of the many facets of the complex phenomenology underlying the interactions of charged particles with oppositely charged objects.     

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.     

Gas-solid coexistence in highly charged colloidal suspensions

Aqueous suspensions of highly charged polystyrene particles with different volume fractions have been investigated for structural ordering and phase behavior using static light scattering (SLS) and confocal laser scanning microscope (CLSM). Under deionized conditions, suspensions of high-charge-density colloidal particles remained disordered whereas suspensions of relatively low charge density showed crystallization by exhibiting iridescence for the visible light. Though for the unaided eye crystallized suspensions appeared homogeneous, SLS measurements and CLSM observations have revealed their inhomogeneous nature in the form of the coexistence of voids with dense ordered regions. CLSM investigations on disordered suspensions showed their inhomogeneous nature in the form coexistence of voids with dense disordered (amorphous) regions. Our studies on highly charged colloids confirm the occurrence of gas-solid transition and are in accordance with predictions of Monte Carlo simulations using a pair-potential having a long-range attractive term [Mohanty, P. S.; Tata, B. V. R. J. Colloid Interface Sci. 2003, 264, 101]. On the basis of our experimental and simulation results, we argue that the reported reentrant disordered state [Yamanaka et al. Phys. Rev. Lett. 1998, 80, 5806 and Toyotama et al. Langmuir 2003, 19, 3236] in charged colloids observed at high charge densities is a gas-solid coexistence state.     

SANS and SAXS analysis of charged nanoparticle adsorption at oil-water interfaces

A systematic study of the adsorption of charged nanoparticles at dispersed oil-in-water emulsion interfaces is presented. The interaction potentials for negatively charged hexadecane droplets with anionic polystyrene latex particles or cationic gold particles are calculated using DLVO theory. Calculations demonstrate that increased ionic strength decreases the decay length of the electrostatic repulsion leading to enhanced particle adsorption. For the case of anionic PS latex particles, the energy barrier for particle adsorption is also reduced when the surface charge is neutralized through changes in pH. Complementary small-angle scattering experiments show that the highest particle adsorption for PS latex occurs at moderate ionic strength and low pH. For cationic gold particles, simple DLVO calculations also explain scattering results showing that the highest particle adsorption occurs at neutral pH due to the electrostatic attraction between oppositely charged surfaces. This work demonstrates that surface charges of particles and oil droplets are critical parameters to consider when engineering particle-stabilized emulsions.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

Deposition of oriented zeolite A films: in situ and secondary growth

Zeolite A suspensions with a monomodal, narrow particle size distribution have been prepared. The suspended particles in a TMAOH water solution at pH 9 are negatively charged with a zeta potential of −43 mV. Modification of the external surface of the zeolite particles by a silylation reaction produces particles that, when they are suspended in water, are positively charged and have a zeta potential of +40 mV.The suspensions of the negatively or positively charged particles can be used for the preparation of adsorbed layers of particles on oppositely charged substrates by electrostatic attraction. This deposition process leads to a high coverage of the substrate with well-adhered particles. The cubic morphology of the zeolite particles results in preferential orientation after deposition. The particles are oriented with their {h 0 0} planes (cube faces) parallel and perpendicular to the substrate (out-of-plane orientation). The particles are randomly oriented with respect to the direction perpendicular to the substrate (in-plane orientation). Although, under optimized conditions, the coverage is high and only one adsorption cycle is necessary, the particles are not closely packed.Alternately, the zeolite particle suspensions can be used to deposit close-packed arrays of particles by convective particle transport during dip coating on substrates bearing the same charge as the zeolite particles. Using monodispersed zeolite A suspensions and slow speed dip coating close-packed hexagonal colloidal crystals were prepared. The type of colloidal crystal deposits formed range from continuous sublayers, monolayers, or multilayers to isolated discoidal clusters consisting of few zeolite particles. Factors affecting the deposited layer(s) structure are particle concentration of the suspension and withdrawal speed. In addition to close packing, the layers prepared by dip coating exhibit preferred orientation with the particle faces lying parallel and perpendicular to the substrate surface. Moreover, this second route of precursor film formation by colloidal crystallization leads to domains of well-aligned zeolite particles in three dimensions, i.e. with their faces parallel to each other. The oriented domains span the length of several particles; however, low angle boundaries and other defects during colloidal crystallization prevent the formation of macroscopically three-dimensionally ordered zeolite particles.The precursor layers were subjected to secondary growth in order to prepare continuous intergrown films. Secondary growth proceeds initially by local epitaxy on the deposited particles. Later in the process, deposition proceeds by incorporation of particles from solution along with re-nucleation on the growing film. The intergrown films have predominately [h 0 0] out-of-plane orientation; however, after extended secondary growth treatment a population of [h h h] grains appears on the surface of the regrown films.     

带相反电荷胶体颗粒混和悬浮体的流变学性能

研究了带相反电荷的粘土颗粒和MMH(铝、镁混合金属氢氧化物)颗粒形成的混和悬浮体的流变学性能,考察了盐对混合体系流变学性能的影响.结果表明,当粘土质量分数为1%时,悬浮体为牛顿型流体;当质量分数升至2%时,悬浮体表现出固体的弹性响应;特定粘土含量的悬浮体中,随着MMH量的增加,混合体系的屈服值和弹性模量亦增加,表明凝胶结构增强.向混合体系中加入NaCl,弹性模量、屈服值和粘度等流变参数均降低.与单组分粘土悬浮体或MMH悬浮体相比,双组分混合体系的结构恢复很快.     

Electrostatic interactions of colloidal particles in nonpolar solvents: role of surface chemistry and charge control agents

We study the electrostatic and hydrodynamic interactions of colloidal particles in nonpolar solvents. Using blinking optical tweezers, we can extract the screening length, kappa-1, the effective surface potential, |ezeta*|, and the hydrodynamic radius, ah, in a single measurement. We apply this technique to suspensions of polystyrene and poly(methyl methacrylate) particles in hexadecane with soluble charge control agents, aerosol sodium di-2-ethylhexylsulfosuccinate (AOT) and polyisobutylene succinimide (OLOA-1200). We find that the electrostatic interactions of these particles depend sensitively on surface composition as well as on the concentration and chemistry of the charge control agent.     

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.