Prediction and observation of crystal structures of oppositely charged colloids

We studied crystal structures in mixtures of large and small oppositely charged spherical colloids with size ratio 0.31 using Monte Carlo simulations and confocal microscopy. We developed an interactive method based on simulated annealing to predict new binary crystal structures with stoichiometries from 1 to 8. Employing these structures in Madelung energy calculations using a screened Coulomb potential, we constructed a ground-state phase diagram, which shows a remarkably rich variety of crystals. Our phase diagram displays colloidal analogs of simple-salt structures and of the doped fullerene C60 structures, but also novel structures that do not have an atomic or molecular analog. We found three of the predicted structures experimentally, which provides confidence that our method yields reliable results.     

Three-dimensional binary superlattices of oppositely charged colloids

We report the equilibrium self-assembly of binary crystals of oppositely charged colloidal microspheres at high density. By varying the magnitude of the charge on near equal-sized spheres we show that the structure of the binary crystal may be switched between face-centered cubic, cesium chloride, and sodium chloride. We interpret these transformations in terms of a competition between entropic and Coulombic forces.     

Epitaxial crystal growth of charged colloids

A pattern of repulsive, charged lines is shown to direct three-dimensional (3D) crystallization in a system of long-range repulsive, density-matched colloids. At volume fractions where the bulk phase behavior leads to bcc crystallization, the 1D template was found to induce formation of a metastable fcc crystal. The bcc crystals were oriented with the (100) or the (110) plane, with twofold twinning, parallel to the template. The template further induced prefreezing of the (100) plane. At a large mismatch between template and interparticle spacing, 1D strings form in the surface layer of a 3D crystal.     

CuAu structure in the restricted primitive model and oppositely charged colloids

We study the phase behavior of oppositely charged equal-size hard spheres both theoretically and experimentally, using Monte Carlo simulations and confocal microscopy. In the simulations, two systems are considered: the restricted primitive model (RPM) and a system of screened Coulomb particles. We construct the phase diagrams of both systems by computer simulations and predict a novel solid phase that has the CuAu structure. In addition, the CuAu structure is observed experimentally in a system of oppositely charged colloids. The qualitative agreement between the RPM, the screened Coulomb system, and the experiments shows that colloids form a suitable model system to study phase behavior in ionic systems.     

Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids

The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.     

Nonlinear screening and gas-liquid separation in suspensions of charged colloids

We calculate phase diagrams of charged colloidal spheres (valency Z and radius a) in a 1:1 electrolyte from multicentered nonlinear Poisson-Boltzmann theory. Our theory takes into account charge renormalization of the colloidal interactions and volume terms due to many-body effects. For valencies as small as Z = 1 and as large as 10(4) we find a gas-liquid spinodal instability in the colloid-salt phase diagram provided Z lambdaB/a > or similar 24+/-1, where lambdaB is the Bjerrum length.     

Collective behavior in out-of-equilibrium colloidal suspensions

Colloidal suspensions, heterogeneous fluids containing solid microscopic particles, play an important role in our everyday life, from food and pharmaceutical industries to medicine and nanotechnology. Colloidal suspensions can be divided in two major classes: equilibrium, and active, i.e. maintained out of thermodynamic equilibrium by external electric or magnetic fields, light, chemical reactions, or hydrodynamic shear flow. While the properties of equilibrium colloidal suspensions are fairly well understood, out-of-equilibrium colloids pose a formidable challenge and the research is in its early exploratory stage. The possibility of dynamic self-assembly, a natural tendency of simple building blocks to organize into complex functional architectures, is one of the most remarkable properties of out-of-equilibrium colloids. Examples range from tunable, self-healing colloidal crystals and membranes to self-assembled microswimmers and robots. In contrast to their equilibrium counterparts, out-of-equilibrium colloidal suspensions may exhibit novel material properties, e.g. reduced viscosity, enhanced self-diffusivity, etc. This work reviews recent developments in the field of self-assembly and collective behavior of out-of-equilibrium colloids, with the focus on the fundamental physical mechanisms.     

Line tension controls wall-induced crystal nucleation in hard-sphere colloids

We report on a numerical study of the effect of a smooth, hard wall on the crystallization of hard-sphere colloids. We find that the presence of the wall drastically lowers the barrier for crystal nucleation, but it does not eliminate it. Crystal nucleation becomes noticeable at pressures that are some 5% above the coexistence value. The first particles to crystallize on the wall form a (111) plane. Initially, this crystallite grows laterally, rather than in the third dimension. The free energy of the critical crystal nucleus on the wall is about 2 orders of magnitudes lower than in the bulk. Analysis of the numerical data indicates that, at coexistence, the (111) plane is at the threshold of wetting the wall. The nucleation barrier is dominated by line tension.     

Band formation in mixtures of oppositely charged colloids driven by an ac electric field

We present experiments on pattern formation in a Brownian system of oppositely charged colloids driven by an ac electric field. Using confocal laser scanning microscopy we observe complete segregation of the two particle species into bands perpendicular to a field of sufficient strength when the frequency is in a well-defined range. Because of its Brownian nature the system spontaneously returns to the equilibrium mixture after the field is turned off. We show that band formation is linked to the time scale associated with collisions between particles moving in opposite directions.     

Virial expansion for charged colloids and electrolytes

Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (“virial”) expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters d₊ and d_- and charge valences q₊ and q_- of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically d ₊∼d _- and q ₊∼q _-, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient. Received 6 September 2001 / Received in final form 20 May 2002 Published online 24 September 2002     

Sticky model of charged colloids

Summary We use the Sticky Electrolyte Model, which we solved before in PY/MSA, to obtain the equation of state of a charge colloid taking into account both sticky and charge contribution. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Acoustic excitations in suspensions of soft colloids

Vibrational modes in suspensions of soft colloids in a fluid can be detected experimentally by Brillouin light scattering. Besides the usual acoustic mode, being essentially the longitudinal phonon of the liquid matrix, an "opticlike" mode is observed in giant starlike micelles at low volume fractions. We propose that this opticlike mode is due mainly to the internal vibration of each hairy particle.     

Density functional theory for polyelectrolytes near oppositely charged surfaces

We report a nonlocal density functional theory of polyelectrolyte solutions that faithfully accounts for both short- and long-range correlations neglected in a typical mean-field method. It is shown that for systems with strong electrostatic interactions, the long-range correlations are subdued by direct Coulomb attractions, thereby manifesting strong local excluded-volume effects. The theory has also been used to describe the influence of the polyion chain length and small ion valence on charge inversion due to the adsorption of polyelectrolytes at an oppositely charged surface.     

Repulsion between oppositely charged surfaces in multivalent electrolytes

In answer to recent experimental force measurements between oppositely charged surfaces we here reproduce the repulsion in the presence of multivalent salt using Monte Carlo simulations within the primitive model. Our osmotic pressure curves are in good agreement with experimental results. In contrast with Poisson-Boltzmann calculations, both repulsion and charge inversion are seen in the simulations. Repulsion is observed only for conditions under which there is charge inversion at large separations. However, in these cases, the repulsion is present also at intermediate separations, where there is no charge inversion. The charge inversion is thereby not the cause of the repulsion. Instead the repulsion appears to be an effect of the large amount of excess salt in the slit. Both phenomena, however, are closely linked and a consequence of ion-ion correlations, promoted by a strong electrostatic coupling.     

Noncentral forces in crystals of charged colloids

The elastic properties of fcc crystals consisting of charge stabilized colloidal particles are determined from real space imaging experiments using confocal microscopy. The normal modes and the force constants of the crystal are obtained from the fluctuations of the particles around their lattice sites using the equipartition theorem. We show that the Cauchy relation is not fulfilled and that only noncentral many-body forces can account for the elastic properties.     

Inelastic scattering of oppositely charged polarons in conjugated polymers

Within an one-dimensional tight-binding model, we investigate the inelastic scattering processes of oppositely charged polarons in conjugated polymers under the influence of an external electric field, by using a nonadiabatic evolution method. It is found that the polaron pair does not necessarily scatter into an entity(neutral exciton), but a mixed state composed of both polarons and excitons. The yield of the neutral exciton depends sensitively on the strength of applied fields. Additionally, effects of interchain coupling on the scattering processes are also discussed, which shows that the interchain coupling is of fundamental importance and facilitates the formation of the polaron-exciton.     

Phase diagram of solution of oppositely charged polyelectrolytes

We study a solution of long polyanions (PA) with shorter polycations (PC) and focus on the role of Coulomb interaction. A good example is solutions of DNA and PC which are widely studied for gene therapy. In the solution, each PA attracts many PCs to form a complex. When the ratio of total charges of PA and PC in the solution, x, equals to 1, complexes are neutral and they condense in a macroscopic drop. When x is far away from 1, complexes are strongly charged. The Coulomb repulsion is large and free complexes are stable. As x approaches to 1, PCs attached to PA disproportionate themselves in two competing ways. One way is inter-complex disproportionation, in which PCs make some complexes neutral and therefore condensed in a macroscopic drop while other complexes become even stronger charged and stay free. The other way is intra-complex disproportionation, in which PCs make one end of a complex neutral and condensed in a small droplet while the rest of the complex forms a strongly charged tail. Thus each complex becomes a “tadpole”. We get a phase diagram of PA–PC solution in a plane of x and the inverse screening radius of the monovalent salt, which includes phases with both kinds of disproportionation.     

Adsorption of hydrophobic polyelectrolytes onto oppositely charged surfaces

We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain Coulombic repulsion by the counterions localized near the surface. Received 12 April 2001     

Adsorption of polyelectrolytes at an oppositely charged surface

We develop a scaling theory of polyelectrolyte adsorption at an oppositely charged surface. At low surface charge densities, the thickness of the adsorbed layer is determined by the balance between electrostatic attraction to the charged surface and chain entropy. At high surface charge densities, it is determined by the balance between electrostatic attraction and short-range monomer-monomer repulsion. These different stabilizing mechanisms result in the nonmonotonic dependence of the layer thickness on the surface charge density.