Application of the Christensen‐Lo Model to the Reinforcement of Elastomers by Fractal Fillers

This paper is concerned with the development of a hydrodynamic model for the reinforcement of rubber by colloidal fillers such as silica and carbon black. Each fractal aggregate is replaced by an equivalent effective sphere, and the reinforcing ability of the latter is estimated using the Christensen‐Lo solution of the “three‐phase composite sphere model”. With a single adjustable parameter, the model allows a quantitative interpretation of the small‐strain modulus of rubber loaded with up to 50 PHR of N234 carbon black, which falls just below the filler overlap concentration. No additional contributions to the small‐strain modulus by filler–filler “interactions” are needed to interpret the data.

A branched filler aggregate made up of spherical primary particles (black) and the effective sphere replacing it (gray).     

PbTe colloidal nanocrystals: synthesis, characterization, and multiple exciton generation

We report an alternative synthesis and the first optical characterization of colloidal PbTe nanocrystals (NCs). We have synthesized spherical PbTe NCs having a size distribution as low as 7%, ranging in diameter from 2.6 to 8.3 nm, with first exciton transitions tuned from 1009 to 2054 nm. The syntheses of colloidal cubic-like PbSe and PbTe NCs using a PbO "one-pot" approach are also reported. The photoluminescence quantum yield of PbTe spherical NCs was measured to be as high as 52 +/- 2%. We also report the first known observation of efficient multiple exciton generation (MEG) from single photons absorbed in PbTe NCs. Finally, we report calculated longitudinal and transverse Bohr radii for PbS, PbSe, and PbTe NCs to account for electronic band anisotropy. This is followed by a comparison of the differences in the electronic band structure and optical properties of these lead salts.     

Preparation of colloidal crystals with polyhedral building blocks through post-polymerization

An alternative approach was adopted to prepare colloidal crystal with polyhedral building blocks. First, monodisperse polystyrene particles that contained about 30% wt of monomer were obtained by emulsifier-free emulsion polymerization at 38 °C. These monomer-containing particles were used to prepare colloidal crystal on the surface of dispersion, before the spherical particles in the colloidal crystals underwent deformation between two quartz plates at 75 °C for 40 min by interfacial tensions, and finally the deformed particles were frozen through post-polymerization.     

Fabrication of spherical colloidal crystals using electrospray

We demonstrated the use of electrohydrodynamic atomization to prepare uniform-sized emulsion droplets in which equal spheres of silica or polystyrene were dispersed. The size of the emulsion droplets was easily controlled by the electric field strength and the flow rate, independently of the diameter of the nozzles. During the evaporation of solvent in the droplets, spherical colloidal crystals were formed by self-assembly of the monodisperse colloidal spheres. The diameter of the spherical colloidal crystals was in the range of 10-40 microm. Depending on the stability of colloidal particles, the morphology of the self-assembled structure was varied. In particular, silica spheres in ethanol droplets were self-assembled into compactly packed silica colloidal crystals in spherical shapes, whereas polystyrene latex spheres in toluene droplets self-assembled into spherical colloidal crystal shells with hollow cores. The silica colloidal assemblies reflected diffraction colors according to the three-dimensionally ordered arrangement of silica spheres.     

Calculation of effective diffusion coefficient in a colloidal crystal by the finite-element method

The work is devoted to the calculation of effective diffusion coefficient of ions from the bulk solution to the electrode through a mask and the calculation of the distribution of the limiting current density over the electrode surface. A colloidal crystal, which is formed by orderly arranged monodispersed spherical particles, serves as a mask. It is shown that the diffusion of electroactive ions in the pores between spherical particles can be simulated by unit cells with rhombic, rectangular, or triangular cross-section. In the latter case, the cell side surface has no periodical boundaries. This simplifies significantly the numerical solution of the Laplace??s equation by the finite-element method. The effective diffusion coefficient in the bulk colloidal crystal is calculated at various values of its porosity. The calculated results agree well with the literature data. It is found that, for close-packed spherical particles, the relative effective diffusion coefficient in the bulk colloidal crystal is 0.16. The thicknesses of transient zones adjacent to the electrode surface and outer boundary of colloidal crystal and the effective diffusion coefficients for these zones are determined. The dependence of effective diffusion coefficient on the number of spherical particle layers in the colloidal crystal is obtained. The distribution of the limiting current density over the electrode surface is analyzed at various numbers of particle layers.     

Nonspherical colloidal crystals fabricated by the thermal pressing of colloidal crystal chips

Nonspherical colloids and their ordered arrays may be more attractive in applications such as photonic crystals than their spherical counterparts because of their lower symmetries, although such structures are difficult to achieve. In this letter, we describe the fabrication and characterization of colloidal crystals constructed from nonspherical polyhedrons. We fabricated such nonspherical colloidal crystals by pressing spherical polymer colloidal crystal chips at a temperature slightly lower than the glass-transition temperature (T(g)) of these polymer colloids. During this process, the polymer microspheres were distinctively transformed into polyhedrons according to their crystal structures, whereas the long-range order of the 3D lattice was essentially preserved. Because a working temperature lower than T(g) effectively prevented the colloidal crystals from fusing into films, the spherical colloidal crystals were transformed greatly under pressure, which lead to obvious change in the optical properties of colloidal crystals. Besides their special symmetry and optical properties, these nonspherical colloidal crystals can be used as templates for 2D or 3D structures of special symmetry, such as 2D nano-networks. We anticipate that this fabrication technique for nonspherical colloidal crystals can also be extended to nonspherical porous materials.     

Microwave-assisted self-organization of colloidal particles in confining aqueous droplets

Monodisperse aqueous emulsion droplets encapsulating colloidal particles were produced in the oil phase, and controlled microwave irradiation of the aqueous drop phase created spherical colloidal crystals by so-called evaporation-induced self-organization of the colloidal particles. Unlike usual colloidal crystals, colloidal crystals in spherical symmetry (or photonic balls) possessed photonic band gaps for the normal incident light independent of the position all over the spherical surface. While the consolidation of colloidal particles in emulsion droplets in an oven took several hours, the present microwave-assisted evaporation could reduce the time for complete evaporation to a few tens of minutes. Under the microwave irradiation, the aqueous phase in emulsions was superheated selectively and the evaporation rate of water could be controlled easily by adjusting the microwave intensity. The result showed that the packing quality of colloidal crystals obtained by the microwave-assisted self-organization was good enough to show photonic band gap characteristics. The reflectance of our photonic balls responded precisely to any change in physical properties including the size of colloidal particles, refractive index mismatch, and angle of the incident beam. In particular, for polymeric particles, the photonic band gap could be tuned by the intensity of microwave irradiation, and the reflection color was red-shifted with stronger microwave irradiation. Finally, for better photonic band gap properties, inverted photonic balls were prepared by using the spherical colloidal crystals as sacrificial templates.     

Colloidal assemblies of branched geminis studied by cryo-etch-HRSEM. High-resolution scanning electron microscopy

Cryo-etch-HRSEM is introduced as a useful method for exploring colloidal systems. The method fast freezes an aqueous sample (to -105 degrees C in 6-7 ms), removes some or all of the surface water by sublimation (etching), and magnifies the resulting colloidal structure by up to a million. Three new structurally similar gemini surfactants served to illustrate the technique. One gemini formed a gel whose delicate fractal-like molecular web could be observed after 10-min etching. A second formed a coacervate with a more hydrated porous structure. The third displayed a "bumpy" surface consistent with spherical vesicles projecting from the vitreous ice. The information-content of cryo-etch-HRSEM is pictorial but distinctive in nature.     

Counterion distributions and effective interactions of spherical polyelectrolyte brushes

We consider the electrosteric repulsion of colloidal particles whose surface carries a dense layer of long polyelectrolyte chains (spherical polyelectrolyte brushes). The theory of electrosteric repulsion of star polyelectrolytes developed recently is augmented to include particles with a finite core radius. It is shown that most of the counterions are confined within the brush layer. The strong osmotic pressure thus created within the brush layer dominates the repulsive interaction between two such particles. Because of this the pair interaction potential between spherical polyelectrolyte brushes can be given in terms of an analytic expression. The theoretical predictions are compared with available experimental data and semi-quantitative agreement between the two is found.     

Effects of structural properties of the Stern layer on the electrophoretic migration of a highly charged spherical macroion

The electrophoretic migration of a highly charged spherical macroion suspended in an aqueous solution of NaCl is studied using the molecular dynamic method. The objective is to examine the effects of the colloidal surface charge density on the electrophoretic mobility (μ) of the spherical macroion. The bare charge and the size of the macroion are varied separately to induce changes in the colloidal surface charge density. Our results indicate that μ depends on colloidal surface charge density in a nonmonotonic manner, but that this relationship is independent of the way the surface charge density is varied. It is found that an increase in colloidal surface charge density may lead to the formation of new sublayers in the Stern layer. The μ profile is also found to have a local maximum for a bare charge at which a new sublayer is formed in the Stern layer, and a local minimum for a bare charge at which the outer sublayer becomes relatively dense. Finally, the electrophoretic flow caused by the migration of the spherical macroion is studied to find that one decisive factor causing the electrophoretic flow is the ability of the macroion to carry anions in the electrolyte solution.     

Azo polymer microspherical cap array: soft-lithographic fabrication and photoinduced shape deformation behavior

In this work, azo polymer microspherical cap arrays possessing unique photoprocessible properties have been fabricated through a soft-lithographic contact printing approach. In the process, hexagonal polystyrene (PS) colloidal arrays, obtained by the vertical deposition method, were used as masters. Poly(dimethylsiloxane) (PDMS) stamps with aligned hemisphere air voids on the surfaces were obtained by casting the precursor against the colloidal arrays. By using the stamps and a solution of an epoxy-based azo polymer (BP-AZ-CA) as "ink", the microspherical cap arrays were fabricated by pressing the "inked" surfaces against substrates. Uniform 2D arrays of the submicrometer spherical caps could be obtained on the substrates after peeling off the stamps and drying. The characteristic sizes of the arrays depended on some adjustable features, such as the diameters of PS spheres and concentrations of the "inks" used in the process. After exposure to a linearly polarized Ar+ laser single beam, the spherical caps could be stretched along the polarization direction, and the arrays were consequently transformed into ellipsoidal cap arrays. Upon irradiation of interfering p-polarized Ar+ laser beams, only the spherical caps in the bright fringes were deformed by the light irradiation, which resulted in more complicated surface relief patterns. The observation gives another well-defined example of the photoinduced mass migration in the submicrometer scale. The approach can potentially be applied to fabrication of microlens arrays with different converging rate in two directions.     

Approximate expressions of determining the double layer energy and force of interaction between two charged colloidal spheres

The approximate expressions have been obtained to calculate the electrical double layer energy and force between two spherical colloidal particles based on the improved Derjaguin approximation. Results for identical spheres interacting under constant surface potential, constant surface charge are given. Comparison of present results with numerical results calculated by Carnie and Chan is made. The expressions are found to work quite well for the constant surface potential case, and for the constant charge case, we make correction for the expressions. The results given are satisfactory providedkh0.4.     

Nanoscale spherical architectures fabricated by metal coordination of multiple dipyrrin moieties

Phenylethynyl-bridged dipyrrin "dimers" have performed ZnII complexation to give coordination polymers, which provided the fluorescent colloidal spherical objects in solution as well as on the substrate according to the spacer units. Using a mixture of THF and water, unique morphologies, such as bell-shaped and "golf ball"-like architectures, were observed.     

Defects of colloidal crystals

Reasons for the appearance of defects of various types in crystalline colloidal structures formed during the self-organization of the ensembles of spherical nanoparticles are analyzed using lyosols of metal nanoparticles stabilized with polymers as examples. Quantitative characteristic of the degree of imperfection of colloidal crystals is proposed and the procedures for the minimization of the degree of imperfection are discussed. Order-disorder phase transitions of colloidal crystals are studied.     

胶体晶体微球及其生物医学应用

光子晶体(PhCs)是由单分散纳米粒子周期性排列形成的材料,具有光子禁带,频率落在光子禁带内的光被禁止传播,这个特性激起了研究者对其制备和应用的研究热情。然而,一般的光子晶体材料都具有角度有偏性质,限制了其在宽视角光学材料和设备上的应用。近几年有一系列围绕球形胶体光子晶体材料的研究成果问世,由于球形的对称性,球形胶体晶体的衍射峰不会随着光的入射角变化而发生变化,从而拓宽了胶体晶体的应用范围。随着微流控技术被用于制备液滴模板,球形胶体晶体的制备取得了巨大的进步。微流控技术不仅保证了液滴模板的单分散性,还增加了胶体晶体微球的结构与功能的多样性。胶体晶体微球这些特有的性质,可以很好地将光子晶体材料与编码、非标记检测、细胞培养以及载药等生物医学领域连接起来,为其应用提供了广阔的前景。本文总结了球形光子晶体的研究进展,包括球形光子晶体的设计、制备及其生物医学应用,最后,对球形光子晶体未来的发展方向作了展望。     

Dynamic effects on colloidal electric interactions

Dynamic behaviors are abundant in field-responsive colloidal suspensions. Being beyond the usual point-dipole approximation, we develop a multiple image method of dipoles for two dynamic unequal colloidal dielectric spherical particles, which can be perfectly reduced to those for two static conducting particles. The method is applied to investigate colloidal electric interparticle forces under various conditions of dynamics. As a result, we find that the force can be enhanced, reduced, or even changed from attraction to repulsion, or vice versa. Some other interesting results are also reported. Our theoretical results are compared favorably with existing experimental observations. Therefore, it becomes possible to achieve desired colloidal structures by adjusting colloidal interactions by choosing appropriate dynamic phenomena.     

Colloidal interactions: contact limiting laws,double-layer dissociation,and "non-DLVO" (Derjaguin–Landau–Verwey–Overbeek) forces

The conceptual basis and main results of a new model of the dissociative electrical double layer augmented with Lubetkin-Middleton-Ottewill (LMO) dissociative law are summarized. The main results are: the derivation of fundamental limiting laws of planar repulsions in the limit of surface contact, and their transition to the Debye-Hückel limiting laws at infinite separation; the prediction of stronger and longer-range electrostatic forces, quantitatively and consistently accounting for repulsions in colloidal montmorillonites; the discovery of the classical Debye-Hückel interionic effect being operative in increasing double-layer dissociation by lowering the activities of diffuse ions via the LMO law; the prediction of maxima of Stern potentials in spherical symmetry without any further assumptions, and the prediction of no maxima for platelike montmorillonites. In the light of these new insights, the concepts of "hydration forces" and other close-range "non-DLVO" forces may need to be revised, as well as the origin of the maxima of electrophoretic mobilities (Stern potentials) for spherical colloids.     

General bottom-up construction of spherical particles by pulsed laser irradiation of colloidal nanoparticles: a case study on CuO

The development of a general method to fabricate spherical semiconductor and metal particles advances their promising electrical, optical, magnetic, plasmonic, thermoelectric, and optoelectric applications. Herein, by using CuO as an example, we systematically demonstrate a general bottom-up laser processing technique for the synthesis of submicrometer semiconductor and metal colloidal spheres, in which the unique selective pulsed heating assures the formation of spherical particles. Importantly, we can easily control the size and phase of resultant colloidal spheres by simply tuning the input laser fluence. The heating-melting-fusion mechanism is proposed to be responsible for the size evolution of the spherical particles. We have systematically investigated the influence of experimental parameters, including laser fluence, laser wavelength, laser irradiation time, dispersing liquid, and starting material concentration on the formation of colloidal spheres. We believe that this facile laser irradiation approach represents a major step not only for the fabrication of colloidal spheres but also in the practical application of laser processing for micro- and nanomaterial synthesis.     

Osmotic stress tensor in charge stabilized colloidal crystals

Osmotic stress tensor is introduced to describe the osmotic pressure in colloidal crystals within the framework of the theory of the Poisson-Boltzmann equation. The osmotic stress tensor is related to the fundamental stress tensor, which is associated with the Poisson-Boltzmann equation. It is shown that the osmotic stress tensor can be determined for colloidal crystals with arbitrary structures, as well as for media that are described by cell models. The general results are exemplified by spherical and cylindrical cell models.     

Spontaneous two-dimensional spherical colloidal structures

Two-dimensional spherical crystalline colloidal structures are formed at the interface between water and oil as the result of spontaneous emulsification and colloidal self-assembly. When water droplets are introduced in oil containing a lipophilic surfactant, smaller water droplets of uniform size are spontaneously produced at the spherical interface. Initially of submicrometer size, the small droplets at the interface self-assemble, forming ordered structures, and grow uniformly with time until they reach a size of a few micrometers, maintaining the crystalline structure.