Spherical particles, adsorption

The 9-parameter is also subject to uncertainty. It is likely that Whitby s (1978) estimates of 9 (Table 10.1) do not reflect the true surface area distribution, since they were based on the average size spectrum of aerosols and assumed spherical particles. Adsorption/desorption kinetics (Kamens et al., 1995 Rounds and Pankow, 1990,1993) and relative humidity (Goss and Eisenreich, 1997 Lee and Tsai, 1994 Pankow et al., 1993 Storey et al., 1995 Thibodeaux et al., 1991) influence the adsorption of POPs onto aerosols, and the Junge-Pankow model does not take these factors into account. 

Fig. 3.15 (a) A pore in the form of an interstice between close-packed and equal-sized spherical particles. The adsorbed him which precedes capillary condensation is indicated, (b) Adsorption isotherm (idealized). 

In this section, we consider the transient adsorption of a solute from a dilute solution in a constant-volume, well-mixed batch system or, equivalently, adsorption of a pure gas. The solutions provided can approximate the response of a stirred vessel containing suspended adsorbent particles, or that of a very short adsorption bed. Uniform, spherical particles of radius are assumed. These particles, initially of uniform adsorbate concentration, are assumed to be exposed to a step change in concentration of the external fluid. 

FIG. 16-27 Constant pattern solutions for R = 0.5. Ordinant is cfor nfexcept for axial dispersion for which individual curves are labeled a, axial dispersion h, external mass transfer c, pore diffusion (spherical particles) d, surface diffusion (spherical particles) e, linear driving force approximation f, reaction kinetics. [from LeVan in Rodrigues et al. (eds.), Adsorption Science and Technology, Kluwer Academic Publishers, Dor drecht, The Nether lands, 1989 r eprinted with permission.]... 

In this review we consider several systems in detail, ranging from idealized models for adsorbates with purely repulsive interactions to the adsorption of spherical particles (noble gases) and/or (nearly) ellipsoidal molecules (N2, CO). Of particular interest are the stable phases in monolayers and the phase transitions between these phases when the coverage and temperature in the system are varied. Most of the phase transitions in these systems occur at fairly low temperatures, and for many aspects of the behavior quantum effects need to be considered. For several other theoretical studies of adsorbed layer phenomena see Refs. 59-89. 

High-pressure liquid chromatography (HPLC) is a variant of the simple column technique, based on the discovery that chromatographic separations are vastly improved if the stationary phase is made up of very small, uniformly sized spherical particles. Small particle size ensures a large surface area for better adsorption, and a uniform spherical shape allows a tight, uniform packing of particles. In practice, coated Si02 microspheres of 3.5 to 5 fxm diameter are often used. 

Separation of colloids by GPC is an important technical advance that may help in the characterization of novel materials. One such separation was the shape separation of gold particles of nanometer size by GPC on a Nucleogel GFC 1000-8 column using sodium dodecyl sulfate and Brij-35 [polyoxyethylene (23) dodecanol] to modulate the adsorption properties of the colloidal gold.42 Rodlike and spherical particles were separated using UV-VIS detection. 

Spherical particles 15 nm in diameter and of density 2290 kg/m3 are pressed together to form a pellet. The following equilibrium data were obtained for the sorption of nitrogen at 77 K. Obtain estimates of the surface area of the pellet from the adsorption isotherm and compare the estimates with the geometric surface. The density of liquid nitrogen at 77 K is 808 kg/m3. 

Jin F, Balasubramaniam R, Stebe KJ (2004) Surfactant adsorption to spherical particles the intrinsic length-scale governing the shift from diffusion to kinetic-controlled mass transfer. J Adhes 80 773-796... 

G.J. Fleer, J.M.H.M. Scheutjens and B. Vincent, The Stability of Dispersions of Hard Spherical Particles in the Presence of Nonadsorbing Polymer in Polymer Adsorption and Dispersion Stability, E.D. Goddard and B. Vincent (eds.), American Chemical Society, Washington DC, 1984, ACS Symposium Series 240, Chapter 16, pp. 245-263. 

It should be noted here that while in catalytic systems the rate is based on the moles disappearing from the fluid phase - dddt, and the rate has the form ( —ru) = f(k, C), in adsorption and ion exchange the rate is normally based on the moles accumulated in the solid phase and the rate is expressed per unit mass of the sohd phase dqldt where q is in moles per unit mass of the solid phase (solid loading). Then, the rate is expressed in the form of a partial differential diffusion equation. For spherical particles, mass transport can be described by a diffusion equation, written in spherical coordinates r ... 

Particle Size and Shape. The polymerization process for producing macroporous synthetic polymers (539) leads to the formation of spherical particles whose size can be controlled within certain limits. The popular XAD polymers are usually sold with approximately 90 of the total weight encompassing smooth beads with 20-50-mesh sizes. Most users incorporate a suspension step to remove the fines in their purification of the polymer, but they do not remove the small number of particles larger than 20 mesh. The particle size and distribution vary with different polymer batches, and it is advisable to mechanically sieve polymer beads and choose only those within the 20-50-mesh size for preparation of the adsorption columns. 

The single selection of particle diameter for the characterization of a reinforcing filler is, however, not appropriate, because, on the one hand, only fillers exhibiting a very poor reinforcing effect consist of independent spherical particles, and, on the other hand, gum-filler interactions taking place at the elastomer-filler interface are thus conditioned by the accessibility of the surface. The latter may, indeed, be restricted either by the presence of micropores or by the size of the macromolecule. The knowledge of the specific surface area of the filler is thus a prerequisite. Insofar as the determination of the filler specific surface area, performed by low-temperature gas adsorption or iodine adsorption, takes into account its microporosity, the adsorption of larger tensioactive molecules will often be favored 12,13). 

Spherical particles in the micrometric size range of mesoporous MSU-X silica were obtained with nonionic PEO-based surfactant by a new, easy and highly reproducible synthesis pathway leading to Micelle Templated Structures (MTS) with large surface area and narrow pore size distribution. First results on their adsorption properties show that they could be used for HPLC applications. 

In the wide field of possible applications for MTS, the use of their properties of adsorption and steric selectivity is still to be explored. However, such applications require well-defined particles, especially spherical particles in the micrometric range. The synthesis of MSU-X silica that exhibits these shapes allowed us to test their properties in adsorption HPLC. Non polar solvent such as hexane are suitable to allow a significant separation. Further analyses and testing for size exclusion separation processes are under progress. 

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