Multiphase coexistence in polydisperse colloidal mixtures

The authors study the phase behavior of mixtures of monodisperse colloidal spheres with a depletion agent which can have arbitrary shape and can possess a polydisperse size or shape distribution. In the low concentration limit considered here, the authors can employ the free-volume theory and take the geometry of particles of the depletion agent into account within the framework of fundamental measure theory. The authors apply their approach to study the phase diagram of a mixture of (monodisperse) colloidal spheres and two polydisperse polymer components. By fine tuning the distribution of the polymer, it is possible to construct a complex phase diagram which exhibits two stable critical points.     

Theoretical analysis of methods for the colloidal synthesis of monodisperse nanoparticles

Methods for the colloidal synthesis of monodisperse nanoparticles, in which the interrelated processes of nucleation and growth of nanoparticles occurring with variable supersaturation of the solution play a determining role, have been theoretically analyzed. It is supposed that supersaturation is created as a result of a chemical reaction; two reactant feed modes (instantaneous and regularly time-distributed) are considered. Successive steps of growth have been distinguished and described for each mode. Conditions at which the focusing mechanism of the particle-size distribution function is operative are specified.     

Computer simulation analysis of conductivity of supported polydisperse systems

Effects of the support texture and the supported phase distribution on the conductivity of an individual grain or a granulated system have been analyzed theoretically. Experimental criteria are discussed, which allow one to judge the porous structure and sites of localization of a conducting component on the basis of the concentration dependence of the conductivity.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1449–1453, August, 1995.The authors are grateful to the International Science Foundation for partial financial support of this work (Project No. M 63000).     

Structural analysis of colloidal MnO x composites

We report on the detailed structure of MnO _x nanoparticles (MnO _x NP) which are either stabilized by cationic spherical polyelectrolyte brushes or by star-shaped cationic polyelectrolyte chains. In both cases, the polycation is composed of 2-(trimethylammonium)ethyl methacrylate chloride (TMAEMC). The analysis by transmission electron microscopy (TEM), cryogenic transmission electron microscopy (cryoTEM), and powder X-ray diffraction leads to the conclusion that the MnO _x nanoparticles in aqueous dispersed state are composed of only a few or even single lamellae of c-disordered potassium birnessite (birnessite). Using star-shaped pTMAEMC homopolymer for the synthesis of composite particles, we obtain MnO _x NP with an average diameter of about 5 nm. MnO _x NP immobilized on cationic spherical polyelectrolyte brush have a length of about 20 nm and a width of 1.6 nm. Comparison of the extended X-ray absorption fine structure (EXAFS) spectra of the MnO _x composites with reference spectra leads to the conclusion that all materials include c-disordered birnessite-type nanoparticles. A comparison of the energy shift of the Mn K-edge absorption peak of the X-ray absorption near-edge structure spectra of different manganese oxide reference materials with the different MnO _x NP revealed an average oxidation state of about 3.5–3.7 for synthesized compounds. No distinct structural difference is found when comparing the dried samples to samples dispersed in water. A comparison of the EXAFS data of the birnessite nanoparticles with the crystal structure of macroscopic systems showed a compression along the c direction accompanied by a slight elongation within the ab plane of the layered material.     

Synthesis of monodisperse high-aspect-ratio colloidal silicon and silica rods

We describe the synthesis and the physical properties of suspensions of colloidal silicon and silica rodlike particles. In addition to pure silicon and pure silica rods, we have also synthesized silicon rods with a silica shell and silica rods with a fluorescent silica layer. Pre-patterned p-type (100) silicon wafers were electrochemically etched in electrolyte solutions containing hydrogen fluoride. By the current density being varied while etching, macropores were etched with controllable modulated pore diameters. These silicon structures were transformed into rods with indentations 5.5 mum apart and with lengths up to 100 mum using iterative oxidation in air and dissolution of the silica by HF. Complete oxidation of these rods was also achieved. Sonication of the modulated rods resulted in monodisperse particles of 5.5 mum length and 300 nm width. A high yield of 10(12) particles, or more, is possible with this method. At high concentrations, these particles show nematic ordering in charge-stabilized suspensions. The oxidized silica outer layer of the silicon rods makes the further growth of silica in solution or on a wafer possible. This allows for control of the particles' interaction potential. Labeling with a fluorescent dye and index matching of the complete silica rods enable the study of concentrated dispersions quantitatively, on a single particle level, with confocal microscopy. Because of their high refractive index in the near-IR, the nematic phases of rods with a silica core are also interesting for photonic applications.     

Preparation and colloidal stability of monodisperse magnetic polymer particles

A previously proposed method was examined for producing monodisperse, submicrometer-sized magnetic polymer particles. The method applies soap-free emulsion polymerization during which Fe3O4 magnetic nanoparticles are heterocoagulated onto precipitated polymer nuclei. To chemically fix the magnetic particles to the polymer nuclei, vinyl groups were introduced on the Fe3O4 particles in a preliminary surface modification reaction with methacryloxypropyltrimethoxysilane, and methacryloxypropyldimethoxysilane (MPDMS) was added to reaction systems of the soap-free emulsion polymerization. The colloidal dispersion stability of magnetic polymer particles was improved by the addition of an ionic monomer, sodium p-styrenesulfonate (NaSS), during the polymerization. The polymerizations were carried out with styrene monomer and potassium persulfate initiator in ranges of NaSS concentrations (0-2.4 x 10(-3) M), NaSS addition times (60-80 min), and monomer concentrations (0.3-0.6 M) at fixed concentrations of 1.6 x 10(-2) M initiator and 1.3 x 10(-2) M MPDMS for pH 4.5 adjusted with a buffer system of [CH3COOH]/[NaOH]. The addition of NaSS during the polymerization could maintain the dispersion stability of magnetic polymer particles during the polymerization. Selection of the reaction conditions enabled the preparation of colloidally stable, submicrometer-sized magnetic polymer particles that had coefficients of variation of distribution smaller than the standard criterion for monodispersity, 10%.     

Investigation of structure factors in dense colloidal suspensions using frequency domain photon migration: polydisperse systems

Frequency domain photon migration (FDPM) technique was employed to investigate the structure factors of dense, polydisperse colloidal suspensions. The angle-integrated structure factors, [S(q)], extracted from FDPM measurements of scattering properties at volume fractions ranging from 0.05 to 0.4, were compared with the values predicted from the polydisperse hard sphere Percus-Yevick (HSPY) model, as well as decoupling approximation (DA) and local monodisperse approximation (LMA) models that incorporated independently measured particle size information. Results show that the polydisperse HSPY model is the most suitable for accounting for particle interactions which predominantly arise from volume exclusion effects. Furthermore, the influence of size polydispersity upon [S(q)] is most significant at high volume fractions. The static structure factors at small wave vector q, S(0), were also assessed from dual wavelength FDPM measurements by using the small wave number approximation as well as the local monodisperse approximation. The measured S(0) agrees well with the values predicted by the polydisperse HSPY model.     

Fabrication of monodisperse colloidal array with confinement effects

A monodisperse 1D colloidal array is prepared from monomer directly combining precipitation polymerization and confinement effects.     

Time-resolved and steady state spectroscopy of polydisperse colloidal silver nanoparticle samples

A signal due to coherently excited vibrational motion has been observed in polydisperse silver nanoparticle samples. The particles were synthesized via a wet chemistry seed mediated method, which yields different particle shapes, including spheres, rods, and irregular triangular-shaped particles. The measured vibrational periods were compared to the results from continuum mechanics calculations. This analysis shows that the observed signal arises from the triangular-shaped particles, rather than the rods or spheres. The period of vibration increases as the dimensions of the triangular-shaped particles increase; specifically, we find that the period is given by 2h/c(l), where h is the bisector of the triangle and c(l) is the longitudinal speed of sound in silver.     

Structural properties of solid lipid based colloidal drug delivery systems

For about 20 years nanoparticles based on solid lipids have been under investigation as drug carrier systems. They can be prepared from a broad variety of lipid matrix materials including glycerides, fatty acids and waxes and are stabilized by physiologically compatible surfactants. Although the matrix lipids principally retain their material properties when dispersed into the colloidal state there are various peculiarities that have to be observed when dealing with such systems. In particular, the crystallization behavior and the polymorphic transitions are altered in the nanoparticulate systems. These properties as well as the particle shape and structure may be affected by the type of surfactants used for stabilization. Also incorporated drugs can modify the structural characteristics of the nanoparticles. Interactions between the individual particles may lead to alterations of the macroscopic behavior of the dispersions, especially of their rheological properties. Such structural parameters can influence the drug carrier properties of the dispersions.     

Investigation of particle interactions in concentrated colloidal suspensions using frequency domain photon migration: monodisperse systems

Frequency domain photon migration (FDPM) measurements were conducted to assess particle interactions of concentrated, monodisperse, polystyrene samples obtained directly from industry by using multiple scattering light. The angle-integrated static structure factor, S(q), and static structure factor at small wave vector q, S(0), were obtained from FDPM measurements at high volume fractions ranging from 0.05 to 0.3, and were compared with those obtained from the monodisperse hard sphere Percus-Yevick (HSPY) model. Effects of different colloid sizes on structure factor evaluated at two different wavelengths were also investigated. Results show that the monodisperse HSPY model is suitable for accounting for particle interactions and local microstructures in these colloidal suspensions. Upon using the HSPY model, particle sizes of polystyrene suspensions were recovered from FDPM measurements at high volume fractions (up to 0.3), which agree well with the DLS measurement of diluted sample ( approximately 0.001). The study of polydispersity effect shows that the FDPM method can be successfully used for recovering the mean particle size of polydisperse colloidal suspension with low polydispersity (<16%) under the assumption of monodisperse hard sphere systems.     

One-step one-phase synthesis of monodisperse noble-metallic nanoparticles and their colloidal crystals

A variety of metallic nanoparticles with a narrow size distribution have been synthesized in a facile one-phase method in which amine-borane complexes are applied as reducing agents. It is particularly striking that large colloidal crystals with sizes up to tens of micrometers can directly form from the reaction mixtures without any further treatment. By using the synthetic route described, large-scale syntheses of both mono- and alloyed metallic nanoparticles with a narrow size distribution can be easily achieved.     

Metal speciation dynamics in monodisperse soft colloidal ligand suspensions

A comprehensive theory is presented for the dynamics of metal speciation in monodisperse suspensions of soft spherical particles characterized by a hard core and an ion-permeable shell layer where ligands L are localized. The heterogeneity in the binding site distribution leads to complex formation/dissociation rate constants (denoted as k a (*) and k d (*), respectively) that may substantially differ from their homogeneous solution counterparts (k a and k d). The peculiarities of metal speciation dynamics in soft colloidal ligand dispersions result from the coupling between diffusive transport of free-metal ions M within and around the soft surface layer and the kinetics of ML complex formation/dissociation within the shell component of the particle. The relationship between k a,d (*) and k a,d is derived from the numerical evaluation of the spatial, time-dependent distributions of free and bound metal. For that purpose, the corresponding diffusion equations corrected by the appropriate chemical source term are solved in spherical geometry using a Kuwabara-cell-type representation where the intercellular distance is determined by the volume fraction of soft particles. The numerical study is supported by analytical approaches valid in the short time domain. For dilute dispersions of soft ligand particles, it is shown that the balance between free-metal diffusion within and outside of the shell and the kinetic conversion of M into ML within the particular soft surface layer rapidly establishes a quasi-steady-state regime. For sufficiently long time, chemical equilibrium between the free and bound metal is reached within the reactive particle layer, which corresponds to the true steady-state regime for the system investigated. The analysis reported covers the limiting cases of rigid particles where binding sites are located at the very surface of the particle core (e.g., functionalized latex colloids) and polymeric particles that are devoid of a hard core (e.g., polysaccharide macromolecules, gel particles). For both the transient and quasi-steady-state regimes, the dependence of k a,d (*) on the thickness of the soft surface layer, the radius of the hard core of the particle, and the kinetic rate constants k a,d for homogeneous ligand solutions is thoroughly discussed within the context of dynamic features for colloidal complex systems.     

Theory of polydisperse reacting polymer systems

The kinetics of irreversible reactions between polymer chains of different molecular weights are studied, with emphasis on the case of highly reactive end groups. We calculate the rate constant k(N, M) for reaction between chains of lengths N and M respectively, in dilute and semi-dilute solutions and in the melt. In all cases, k(N, M) is dominated by the shortest chain: the limit k(N) ≡ k(N, ∞) is well-defined and scales as if both chains were of length N. In dilute solutions k(N, M) obeys mean field theory, being proportional to the equilibrium reactive group contact probability. For melts and concentrated solutions, k(N, M) follows diffusion-controlled laws: k(N, M) ≈ (R/τ_N)ƒ(M/N) where R_N and τ_N are the coil size and relaxation time of the shortest chain N, and ƒ(M/N) is a cross-over function describing the approach to the asymptotic form k(N) for M/N ≫ 1. We calculate the leading contributions to this cross-over function, which has universal forms depending on the concentration regime. The implications of these results for high-conversion free-radical polymerization are discussed.     

Anomalous potentials from inverse analyses of interfacial polydisperse attractive colloidal fluids

This paper investigates effects of using monodisperse inverse analyses to extract particle-particle and particle-surface potentials from simulated interfacial colloidal fluids of polydisperse attractive particles. Effects of polydispersity are investigated as functions of particle concentration and attractive well depth and range for van der Waals and depletion potentials. Forward Monte Carlo simulations are used to generate particle distribution functions for polydisperse interfacial colloidal fluids from which inverted potentials are obtained using an inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method. Attractive potentials are successfully recovered for monodisperse colloidal fluids, but polydispersity that is unaccounted for in inverse analyses produces (1) apparent softening of strong forces, (2) anomalous repulsive and attractive interactions, and (3) aphysical particle overlaps. This investigation provides insights into the role of polydispersity in altering the equilibrium structure and corresponding inverted potentials of attractive colloidal fluids near surfaces. These findings should assist the design and interpretation of optical microscopy experiments involving interfacial colloidal fluids similar to the simulated experiments reported here.     

Effect of colloidal particle size on adsorbed monodisperse and bidisperse monolayers

Coating hydrogel films or microspheres by an adsorbed colloidal shell is one synthesis method for forming colloidosomes. The colloidal shell allows control of the release rate of encapsulated materials, as well as selective transport. Previous studies found that the packing density of self-assembled, adsorbed colloidal monolayers is independent of the colloidal particle size. In this paper we develop an equilibrium model that correlates the packing density of charged colloidal particles in an adsorbed shell to the particle dimensions in monodisperse and bidisperse systems. In systems where the molar concentration in solution is fixed, the increase in adsorption energy with increasing particle size leads to a monotonic increase in the monolayer packing density with particle radius. However, in systems where the mass fraction of the particles in the adsorbing solutions is fixed, increasing particle size also reduces the molar concentration of particles in solution, thereby reducing the probability of adsorption. The result is a nonmonotonic dependence of the packing density in the adsorbed layer on the particle radius. In bidisperse monolayers composed of two particle sizes, the packing density in the layer increases significantly with size asymmetry. These results may be utilized to design the properties of colloidal shells and coatings to achieve specific properties such as transport rate and selectivity.