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.     

Structure and phase equilibria of mixtures of the complex salt hexadecyltrimethylammonium polymethacrylate, water and different oils

This work reports on phase diagrams for mixtures of a complex salt formed by a cationic surfactant and an oppositely charged polyelectrolyte, hexadecyltrimethylammonium polymethacrylate, in binary mixtures with water and in ternary mixtures containing water and organic solvents of different polarity ('oils'): decanol, octanol, p-xylene and cyclohexane. The liquid crystalline structures formed were identified by small angle X-ray scattering measurements, which also provided information about changes in the size of the aggregates as a function of the system composition. These results are analysed in comparison with others previously reported [Bernardes et al., J. Phys. Chem. B 110 (2006) 10332-10340] for the analog complex formed with polyacrylate and, in general, reveal that the presence of an extra methylene group in the polymer chain does not produce significant changes in the complex phase diagrams nor in the structure of the liquid crystalline phases formed. Additionally, the obtained results confirm once more the approach used to analyze these kinds of systems formed by polymer and oppositely charged surfactant.     

Crystal-liquid crystal binary phase diagrams

We propose a new theoretical scheme for the binary phase diagrams of crystal-liquid crystal mixtures by a combination of a phase field model of solidification, the Flory-Huggins theory for liquid-liquid mixing and Maier-Saupe-McMillan (FH-MSM) model for nematic and smectic liquid crystal orderings. The phase field theory describes the crystal phase transition of anisotropic organic crystal and/or side chain liquid crystalline polymer crystals while the FH-MSM model explains isotropic, nematic and smectic-A phase transitions. Self-consistent calculations reveal several possible phase diagram topologies of the binary crystal-liquid crystal mixtures. The calculated phase diagrams were found to accord well to the reported experimental results.     

Decay of correlation functions in hard-sphere mixtures: structural crossover

We investigate the decay of pair correlation functions in a homogeneous (bulk) binary mixture of hard spheres. At a given state point the asymptotic decay r-->infinity of all three correlation functions is governed by a common exponential decay length and a common wavelength of oscillations. Provided the mixture is sufficiently asymmetric, size ratios q less than or approximately 0.7, we find that the common wavelength reflects either the size of the small or that of the big spheres. By analyzing the (complex) poles of the partial structure factors we find a sharp structural crossover line in the phase diagram. On one side of this line the common wavelength is approximately the diameter of the smaller sized spheres whereas on the other side it is approximately the diameter of the bigger ones; the wavelength of the longest ranged oscillations changes discontinuously at the structural crossover line. Using density functional theory and Monte Carlo simulations we show that structural crossover also manifests itself in the intermediate range behavior of the pair correlation functions and we comment on the relevance of this observation for real (colloidal) mixtures. In highly asymmetric mixtures, q< or =0.1, where there is metastable fluid-fluid transition, we find a Fisher-Widom line with two branches. This line separates a region of the phase diagram where the decay of pair correlations is oscillatory from one in which it is monotonic.     

Colloidal crystallization of thermo-sensitive gel spheres of poly (<Emphasis Type="Italic">N</Emphasis>-isopropyl acrylamide)

Morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermo-sensitive gel spheres, poly (N-isopropylacrylamide) (224 nm in the hydrodynamic diameter at 25 °C) were studied. Giant colloidal single crystals formed at very low gel concentrations. Critical concentration of melting of gel spheres (0.8 wt.% without ion-exchange resins) decreased sharply to 0.01 wt.% as the gel suspension was deionized exhaustively with coexistence of the mixtures of cation- and anion-exchange resins and increased substantially as concentration of sodium chloride increased. These studies demonstrated that the colloidal crystallization takes place by the extended electrical double layers formed around the gel spheres in addition of the excluded-volume effect of the gels. Most of the researchers including the authors have believed that the crystallization of the gel spheres takes place by the excluded-volume effect, in other words, by the hard-sphere model, exclusively. However, the present work clarified that the colloidal interfaces, which are inevitable for the formation of the electrical double layers, are formed firmly between the water phase and gel spheres, though the gel spheres contain a lot of water molecules in the inner the sphere region.     

Phase behavior of mixtures of oppositely charged nanoparticles: heterogeneous Poisson-Boltzmann cell model applied to lysozyme and succinylated lysozyme

We study the phase behavior of mixtures of oppositely charged nanoparticles, both theoretically and experimentally. As an experimental model system we consider mixtures of lysozyme and lysozyme that has been chemically modified in such a way that its charge is nearly equal in magnitude but opposite in sign to that of unmodified lysozyme. We observe reversible macroscopic phase separation that is sensitive not only to protein concentration and ionic strength, but also to temperature. We introduce a heterogeneous Poisson-Boltzmann cell model that generally applies to mixtures of oppositely charged nanoparticles. To account for the phase behavior of our experimental model system, in addition to steric and electrostatic interactions, we need to include a temperature-dependent short-ranged interaction between the lysozyme molecules, the exact origin of which is unknown. The strength and temperature dependence of the short-ranged attraction is found to be of the same order of magnitude as that between unmodified lysozyme molecules. The presence of a rather strong short-ranged attraction in our model system precludes the formation of colloidal liquid phases (or complex coacervates) such as those typically found in mixtures of globular protein molecules and oppositely charged polyelectrolytes.     

Rigidity of colloidal alloys as studied by reflection spectroscopy in sedimentation equilibrium

Rigidities of colloidal alloys of binary mixtures of colloidal silica spheres (CS82; 103 nm in diameter) with larger silica spheres (CS91; 110 nm, CS121; 136 nm and CS161; 184 nm) have been measured by reflection spectroscopy in sedimentation equilibrium. Substitutional-solid-solution-type alloy structures are formed for mixtures of CS82 and CS91 and for CS82 and CS121. A superlattice, probably MgCu₂ type, is formed for CS82 and CS161 mixtures. The rigidities of the colloidal crystals of the single component of the spheres increase as the sphere size increases at the same number density of spheres. The rigidities of the colloidal alloys decrease when a comparatively small number of the larger spheres are mixed with the small spheres at the same total sphere number density. Received: 14 June 2000 Accepted: 3 November 2000     

Phase diagram of mixtures of hard colloidal spheres and discs: a free-volume scaled-particle approach

Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas-liquid equilibrium of the spheres becomes stable at comparable size ratios as with bimodal mixtures of spheres or mixtures of rods and spheres. Introducing finite thickness of the platelets gives rise to a significant lowering of the fluid branch of the binodal.     

Nanospheres in a nematic liquid crystal solvent: the influence of particle size

We use Monte Carlo simulations to investigate a simple lattice model for nematic liquid crystals containing nanospheres. The influence of particle size on the phase behaviour is studied using two different sized particles. The phase diagram is found to be topologically equivalent for both particle sizes, with a large biphasic region corresponding to coexistence between a rod-rich nematic and a rod-poor isotropic phase. For small spheres, the rod-rich nematic phase is stable for relatively large volume fractions of spheres (up to a maximum of about 16%). In contrast, the nematic phase for the system with larger spheres is constrained to a much narrower region of the phase diagram.     

Colloidal crystallization of thermo-sensitive gel spheres of poly (N-isopropyl acrylamide). Influence of degree of cross-linking of the gels

Morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermo-sensitive gel spheres, poly (N-isopropylacrylamide) having degrees of cross-linking 10 and 2?mol.% (pNIPAm(200?C10) and pNIPAm(200?C2)) were studied. Giant colloidal single crystals formed at very low gel concentrations. Critical concentrations of melting increased as the degree of cross-linking decreased in the range from 10 to 0.5?mol.% and/or suspension temperature increased from 20 to 45?°C. The critical concentration decreased sharply as the suspensions were deionized with coexistence of the mixtures of cation- and anion-exchange resins. Density of a gel sphere (gel concentration in weight percent divided by that in volume percent) increased sharply as the degree of cross-linking and/or temperature increased. These results demonstrated that the colloidal crystallization takes place by the extended electrical double layers formed around the gel spheres in addition of the excluded-volume effect of the gels. Most of the researchers including the authors have believed that the crystallization of the gel spheres takes place by the excluded-volume effect. However, the present work clarified that the colloidal interfaces, which are inevitable for the formation of the electrical double layers, are formed firmly between the water phase and gel spheres, though the gel spheres contain a lot of water molecules in the sphere region.     

Colloidal crystallization of thermosensitive gel spheres of poly(<Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide) with low degree of cross-linking

Morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermosensitive gel spheres, poly(N-isopropylacrylamide) ((200–0.5), 318 and 116 nm in the hydrodynamic diameter at 25°C and 45°C, and 0.5% in the degree of cross-linking) were studied. Giant colloidal single crystals formed at very low gel concentrations. Densities of the gel spheres were 0.030 and 0.61 at 25°C and 45°C, respectively. Critical concentration of melting of gel spheres (0.8 wt.% without ion-exchange resins) decreased sharply to 0.015 wt.% at 25°C as the gel suspension was deionized exhaustively with coexistence of the mixtures of cation and anion exchange resins. These results demonstrate that the colloidal crystallization takes place by the extended electrical double layers formed around the gel spheres in addition of the excluded volume effect of the gels. Extent of the contribution of the electrical double layers on the crystallization increased sharply when the degree of cross-linking increased, the gel spheres shrank, and/or the density of the gel spheres increased.     

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.     

Electrostatically tuned interactions in silica microsphere-polystyrene nanoparticle mixtures

We explore the generality of nanoparticle haloing as a novel colloidal stabilization mechanism in binary mixtures of silica microspheres and polystyrene nanoparticles. By selectively tuning their electrostatic interactions, both the initial microsphere stability and the role of nanoparticle additions are varied. Adsorption isotherm and zeta potential measurements indicate that highly charged nanoparticles exhibit a weak (haloing) association with negligibly charged microspheres, whereas they either strongly adsorb onto oppositely charged or are repelled by like-charged microsphere surfaces, respectively. Bulk sedimentation and confocal scanning fluorescence microscopy reveal that important differences in system stability emerge depending on whether the added nanoparticles serve as haloing, bridging, or depletant species.     

Nanoparticle-mediated epitaxial assembly of colloidal crystals on patterned substrates

We have studied the assembly of 3-D colloidal crystals from binary mixtures of colloidal microspheres and highly charged nanoparticles on flat and epitaxially patterned substrates created by focused ion beam milling. The microspheres were settled onto these substrates from dilute binary mixtures. Laser scanning confocal microscopy was used to directly observe microsphere structural evolution during sedimentation, nanoparticle gelation, and subsequent drying. After microsphere settling, the nanoparticle solution surrounding the colloidal crystal was gelled in situ by introducing ammonia vapor, which increased the pH and enabled drying with minimal microsphere rearrangement. By infilling the dried colloidal crystals with an index-matched fluorescent dye solution, we generated full 3-D reconstructions of their structure including defects as a function of initial suspension composition and pitch of the patterned features. Through proper control over these important parameters, 3-D colloidal crystals were created with low defect densities suitable for use as templates for photonic crystals and photonic band gap materials.     

Phase behavior and 3D structure of strongly attractive microsphere-nanoparticle mixtures

We investigate the phase behavior and 3D structure of strongly attractive mixtures of silica microspheres and polystyrene nanoparticles. These binary mixtures are electrostatically tuned to promote a repulsion between like-charged (microsphere-microsphere and nanoparticle-nanoparticle) species and a strong attraction between oppositely charged (microsphere-nanoparticle) species. Using confocal fluorescence scanning microscopy, we directly observe the 3D structure of colloidal phases assembled from these mixtures as a function of varying composition. In the absence of nanoparticle additions, the charged-stabilized microspheres assemble into a polycrystalline array upon sedimentation. With increasing nanoparticle volume fraction, nanoparticle bridges form between microspheres, inducing their flocculation. At even higher nanoparticle volume fractions, the microspheres become well coated with nanoparticles, leading to their charge reversal and subsequent restabilization. We demonstrate how this fluid-gel-fluid transition can be utilized to control the morphology of the colloidal phases formed under gravity-driven sedimentation.     

A universal approach to fabricate ordered colloidal crystals arrays based on electrostatic self-assembly

We present a novel and simple method to fabricate two-dimensional (2D) poly(styrene sulfate) (PSS, negatively charged) colloidal crystals on a positively charged substrate. Our strategy contains two separate steps: one is the three-dimensional (3D) assembly of PSS particles in ethanol, and the other is electrostatic adsorption in water. First, 3D assembly in ethanol phase eliminates electrostatic attractions between colloids and the substrate. As a result, high-quality colloidal crystals are easily generated, for electrostatic attractions are unfavorable for the movement of colloidal particles during convective self-assembly. Subsequently, top layers of colloidal spheres are washed away in the water phase, whereas well-packed PSS colloids that are in contact with the substrate are tightly linked due to electrostatic interactions, resulting in the formation of ordered arrays of 2D colloidal spheres. Cycling these processes leads to the layer-by-layer assembly of 3D colloidal crystals with controllable layers. In addition, this strategy can be extended to the fabrication of patterned 2D colloidal crystals on patterned polyelectrolyte surfaces, not only on planar substrates but also on nonplanar substrates. This straightforward method may open up new possibilities for practical use of colloidal crystals of excellent quality, various patterns, and controllable fashions.     

Sedimentation and drying dissipative patterns of binary suspensions of colloidal silica spheres having different sizes

The sedimentation and drying dissipative structural patterns were formed during the course of drying binary mixtures among colloidal silica spheres of 183 nm, 305 nm, and 1.205 μm in diameter in aqueous suspension on a watch glass, a glass dish, and a cover glass, respectively. The broad ring-like sedimentation patterns were formed within several hours in suspension state for all the substrates used. Colorful macroscopic broad ring-like drying patterns were formed for the three substrates. In a watch glass, macroscopic drying patterns were composed of the outer and inner layers of small and large spheres, respectively. The two colored layers were ascribed to the Bragg diffractions of light by the dried colloidal crystals of the corresponding spheres. The width ratio of the layers changed in proportion to the mixing ratio of each spheres. In a glass dish, wave-like macroscopic drying patterns were observed in the intermediate areas between the outside edges of the broad ring and the inner wall of the cell. On a cover glass, the sphere mixing ratios were analyzed from the widths of the drying broad rings of the small spheres at the outside edge. High and distinct broad rings of small spheres and the low and vague broad one formed at the outer edges and in the inner area, respectively. Drying dissipative pattern was clarified to be one of the novel analysis techniques of colloidal size in binary colloidal mixtures.     

Structure and phase behavior of Widom-Rowlinson model calculated from a nonuniform Ornstein-Zernike equation

The second-order integral-equation formalism of [Attard J. Chem. Phys. 91, 3072 (1989); 95, 4471 (1991)], applied previously to one-component hard spheres and Lennard-Jones fluids, as well as to their mixtures, is used to binary Widom-Rowlinson mixtures. Comparison with Monte Carlo simulations of the pair correlation functions and of the demixing phase diagram shows that this method is also quite accurate in the case of highly nonadditive mixtures. Moreover, the results of the second-order theory are compared with previous theoretical predictions. Our interest is also in the calculation of the bridge functions, i.e., parts of the radial distribution functions either not included or simply approximated in the usual theories.     

Quantitative effect of nonionic surfactant partitioning on the hydrophile-lipophile balance temperature

Phase behaviors of water/nonionic surfactants/isooctane systems are determined experimentally in temperature-global surfactant concentration diagrams. The surfactants are monodistributed polyoxyethylene glycol n-dodecyl ether. They are used as model mixtures of two, three, or five compounds or as constituents of a commercial surfactant. It is found that the phase diagrams of these systems are bent gradually toward the highest temperatures as the global surfactant concentration decreases. Each phase diagram is well-characterized by the curve of the HLB (hydrophile-lipophile balance) temperature versus the global surfactant concentration. For any fixed global surfactant concentration, this temperature is the middle temperature of the three-phase region; it can be calculated from an additive rule of the HLB temperatures of the surfactants weighted by their mole fractions at the water/oil interface. These mole fractions are determined through the pseudophase model using surfactant partitioning. Calculations require the knowledge of the critical micelle concentration, the partition coefficient between water and oil, and the HLB temperature of each surfactant of the mixture. This treatment can be used to correctly predict the variation of the HLB temperatures of the surfactant mixtures studied versus the global surfactant concentration. Furthermore, these calculations show that the observed curvature of the phase diagrams at the lowest global concentrations is due to the most favorable partitioning toward the oil of the lowest ethoxylated surfactant molecules.     

Colloidal crystallization of thermo-sensitive gel spheres of poly (<Emphasis Type="Italic">N</Emphasis>-isopropyl acrylamide). Influence of gel size

Influence of the gel size on the morphology, phase diagram, and reflection spectroscopy of the colloidal crystals of thermo-sensitive gel spheres, poly (N-isopropylacrylamide) (pNIPAm), was discussed by adding the data of two gel samples of pNIPAm(400–5) and pNIPAm(600–5) of 412 nm (at 25 °C) and 220 nm (at 45 °C) and of 517 nm (at 20 °C) and 294 nm (at 45 °C), respectively. Colloidal single crystals formed, but not so large compared with the giant crystals of small pNIPAm gels reported previously. The suspensions even with ion-exchange resins were turbid and hard to observe the single crystals clearly with the naked eyes as gel size increased. The critical concentration of melting decreased sharply as the suspensions were deionized with coexistence of the mixtures of cation- and anion-exchange resins. The critical concentration increased as the gel size increased and/or dispersion temperature increased. Density of the gel spheres increased as their size increased. These results demonstrated that the colloidal crystallization takes place by the extended electrical double layers formed around the gel spheres in addition of the excluded volume effect of the gels. Contribution of the electrical double layers on the crystallization increased sharply as temperature increased and gel concentration decreased, respectively. The contribution also increased slightly as sphere size increased, when comparison was made at the same gel concentration in wt.%. The present work clarified that the colloidal interfaces, which are inevitable for the formation of the electrical double layers, are formed between the water phase and gel spheres, though the gel spheres contain a lot of water molecules at the inner sphere region.