Packing of Colloidal Particles

7 — SOL-GEL CHEMISTRY AND ITS APPUCATION TO POROUS MEMBRANE PROCESSING Stable sol 

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Concerning microfiltration, in which pores of less than 1 pm are needed (typically 0.1-1 pm), suspensions of submicrometer powders must be processed using slip-casting or tape-casting techniques, depending on the support shape (flat or tubular). Smaller pore sizes are required for ultrafiltration. In this case pores result from the packing of colloidal particles, which cannot... 

A photonic crystal can be created by templating the crystalline packing of colloidal particles. For a close-packed, body-centered cubic arrangement of 100-nm spherical particles, what volume fraction is occupied by the particles Calculate the most intense reflected wavelength from this photonic crystal. 

Hierarchical packing of colloidal particles (A), random packing of colloidal particles, coordination number = 3 (B), and TEM micrograph of colloidal xerogel prepared by single-step base-catalyzed hydrolysis of TEOS (r = 2.25) followed by drying at 50°C (C). Bar = 100 nm. 

The structure factor function is a part of the intensity function that arises from constructive scattered waves that originate from different particles. This function is a representation of the probability that a particular particle is surrounded by another particle. For isotropic systems, two types of structure factors can be distinguished (i) correlated systems that describe packing of colloidal particles, and (ii) polymeric systems that can be described by either fractalic or worm-like models. By convention, the structure function is weighted over the square of the... 

This is an effective and relatively simple method for characterizing silica sols and other colloids [75]. It has also been used to determine the particle size distributions of polymer lattices [76,77]. Separations are performed in a column packed with particles having pores substantially of the same size. A carrier liquid is passed through the column as a mixture of colloidal particles passes through the bed, the larger ones exit first since they are too large to sample the pore volume. Intermediate sized colloids enter the pores and are retained according to the volume that can be... 

STED microscopy has important applications outside biology as well. For example, it currently is the only method to locally and noninvasively resolve the 3D assembly of packed nanosized colloidal particles [98,99]. In the realm of solid-state physics, STED microscopy has recently imaged densely packed fluorescent color centers in crystals, specifically charged nitrogen vacancy (NV) centers in diamonds [100]. NV centers in diamond have attracted attention, because of their potential application in quantum cryptography and... 

A macroporous silica can be synthesized through a slow sedimentation of colloidal particles onto a template. In a fast, single-step reaction (see Figure 8.37), the monomeric alkoxide precursors permeate the array of bulk polystyrene spheres and condense in air at room temperature. Close-packed, open-pore structures with 320-360 nm voids are obtained after calcination of the organic component at high temperatures. 

The liquid crystalline phase makes DHTMAC extremely viscous when the concentration exceeds 5%. Because of this inherently high viscosity and the high volume fraction of colloidal particles, the formulation of concentrated products is difficult. In practice, DHTDMAC is never used at concentrations above 15%. In contrast, esterquats or other quaternaries bearing unsaturated fatty chains are more suitable for producing concentrated dispersions. As a result of their more disordered fatty chain packing, the particles they form are cubic or isotropic but not lamellar, and the resulting phase viscosity is lower and more stable [3],... 

Scheme 2. Formation of colloidal crystals and their use as templates. A colloidal dispersion containing monodisperse particles undergoes controlled filtration, centrifugation, dip coating, sedimentation, or physical confinement, which results in ordered packing of the particles with void spaces between them. By infiltrating these spaces with precm-sor solution or preformed nemoparticles the hybrid material is formed. Removal of the polymer template (using solvent (toluene) orheatingtechniques) gives an inverse replica with air-fiUed, interconnected voids of monodisperse size, which is dependent on the initial particle size...

Similar discrepancies were noted by Blatt et al32 for colloidal suspensions such as skimmed milk, casein, polymer latexes, and clay suspensions. Actual ultrafiltration fluxes are far higher than would be predicted by the mass transfer coefficients estimated by conventional equations, with the assumption that the proper diffusion coefficients are the Stokes-Einstein diffusivities for the primary particles. Blatt concluded that either (a) the "back diffusion flux" is substantially augmented over that expected to occur by Brownian motion or (b) the transmembrane flux is not limited by the hydraulic resistance of the polarized layer. He favored the latter possibility, arguing that closely packed cakes of colloidal particles have quite high permeabilities. However, this is not a plausible hypothesis for the following reasons ... 

The columns are calibrated by measuring the rate of transport (Rf) of colloidal particles of known size. Measurement is made relative to the eluant fluid. Rf> varies with particle diameter and depends on the column packing diameter. The useful range of HDC is 0.015-1.5 pm which falls in the technicaUy int sting but difficult-to-measure range. 

Crystalline colloidal arrays (CCA) are mesoscopically periodic fluid materials which efficiently diffract light meeting the Bragg condtion (/-. These materials consist of arrays of colloidal particles which self assemble in solution into BCC or FCC crystalline arrays (7,5) (Figure 1) with lattice constants in the mesoscale size range (50 to 500 nm). Just as atomic crystals diffract x-rays that meet the Bragg condition, CCA diffract UV, visible, and near IR light (2-4) the diffraction phenomena resemble that of opals, which are close-packed arrays of monodisperse silica spheres (6). 

Another important problem that has attracted the attention of a host of investigators (Ruckenstein and Prieve, 1973 Saville, 1977 Spielman, 1977 Tien and Payatakes, 1979) is particle collection. In the deep bed filtration of colloidal particles, one seeks to describe the interaction and the collision between one colloidal particle and one grain of the packing material that forms the bed. The latter, called the collector, is immobile. The liquid containing the suspended colloidal particles flows past the collectors and flocculation of the colloid particles with the grains of the packing material is called particle capture. The particles are brought to the collector surface both by convection and diffusion. 

The deposition of monomeric silica involves a very different mechanism from the deposition of colloidal particles. Monomeric silica forms an impervious glass-like film, whereas colloidal particles form a porous film, often white and opaque when dried. In an intermediate range, where particles are smaller than about 50 A in diameter, that is, approaching molecular dimensions, the coating is clear and the pores in the close-packed mass of particles may be so small that only water or certain ions can penetrate. This borderline region has been little explored. 

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