Particle monodisperse

For elastic collisions, several different kinetic models have been proposed in order to close the Boltzmann hard-sphere collision term (Eq. 6.9). For inelastic collisions (e 1), one must correctly account for the dependence of the dissipation of granular energy on the value of e. One method for accomplishing this task is to start from the exact (unclosed) collision integral in Eq. (6.68). From the definition of if given in Eq. (6.60), it can be 

At equilibrium, where the yelocity distribution is Maxwellian, it is straightforward to show that = 4 J p/7T, where 0p is the granular temperature. We should note that Eq. (6.109) corresponds to an inelastic Maxwell particle (Maxwell, 1879), and, most importantly, it still contains the exact dependence on tu = (1 + e)/2. We will therefore refer to this kinetic model as the inelastic Maxwell collision model. 

The BGK-like kinetic models for monodisperse particles have the linearized form 

In this multivariate Gaussian distribution. Up is the mean particle velocity and is the inverse of the second-order tensor A, defined such that a given set of velocity moments agrees with Eq. (6.109). Owing to conservation of mass and mean momentum, the first nonzero terms from Eq. (6.109) correspond to the second-order moments. On letting k denote the symmetric second-order tensor constructed from ifjlio), vi, g) with i + j + k = 2 (see Table 6.1), 

The integral on the right-hand side of this expression can be evaluated explicitly  

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This is the basic equation for monodisperse particles in light scattering experiments. We can derive tln-ee relationships by extrapolation. 

Flard spherocylinders (cylinders witli hemispherical end caps) were studied using computer simulations [118]. In addition to a nematic phase, such particles also display a smectic-A phase, in which tire particles are arranged in liquid-like layers. To observe tliis transition, ratlier monodisperse particles are needed. The smectic-A phase was indeed observed in suspensions of TMV particles [17]. 

Gas AntisolventRecrystallizations. A limitation to the RESS process can be the low solubihty in the supercritical fluid. This is especially evident in polymer—supercritical fluid systems. In a novel process, sometimes termed gas antisolvent (GAS), a compressed fluid such as CO2 can be rapidly added to a solution of a crystalline soHd dissolved in an organic solvent (114). Carbon dioxide and most organic solvents exhibit full miscibility, whereas in this case the soHd solutes had limited solubihty in CO2. Thus, CO2 acts as an antisolvent to precipitate soHd crystals. Using C02 s adjustable solvent strength, the particle size and size distribution of final crystals may be finely controlled. Examples of GAS studies include the formation of monodisperse particles (<1 fiva) of a difficult-to-comminute explosive (114) recrystallization of -carotene and acetaminophen (86) salt nucleation and growth in supercritical water (115) and a study of the molecular thermodynamics of the GAS crystallization process (21). 

HEPA filter The efficiency of 99.97 percent used in removing monodispersed particles of 0.3 microns in diameter was considered HEPA. NIOSH no longer uses this term, but OSHA has retained... 

The advantages of monosized chromatographic supports are as follows a uniform column packing, uniform flow velocity profile, low back pressure, high resolution, and high-speed separation compared with the materials of broad size distribution. Optical micrographs of 20-p,m monosized macroporous particles and a commercial chromatography resin of size 12-28 p,m are shown in Fig. 1.4. There is a clear difference in the size distribution between the monodispersed particles and the traditional column material (87). 

Third, a complicated question on the role of the dispersion of particles dimensions of particles dimensions is of independent value it is known that the viscosity of equi-concentrated dispersions of even spherical particles depends on the fact if spheres of one dimension or mixtures of different fractions were used in the experiments and here in all the cases the transition from monodisperse particles to wide distributions leads to a considerable decrease in viscosity [21] (which, certainly, is of theoretical and enormous practical interest as well). 

Schmitt V, Leal-Calderon F, Bibette J (2003) Preparation of Monodisperse Particles and Emulsions by Controlled Shear. 227 195-215... 

The formation of ordered two- and three-dimensional microstructuies in dispersions and in liquid systems has an influence on a broad range of products and processes. For example, microcapsules, vesicles, and liposomes can be used for controlled drug dehvery, for the contaimnent of inks and adhesives, and for the isolation of toxic wastes. In addition, surfactants continue to be important for enhanced oil recovery, ore beneficiation, and lubrication. Ceramic processing and sol-gel techniques for the fabrication of amorphous or ordered materials with special properties involve a rich variety of colloidal phenomena, ranging from the production of monodispersed particles with controlled surface chemistry to the thermodynamics and dynamics of formation of aggregates and microciystallites. 

Schluter AD (2005) A Covalent Chemistry Approach to Giant Macromolecules with Cylindrical Shape and an Engineerable Interior and Surface. 245 151-191 Schmitt V, Leal-Calderon F, Bibette J (2003) Preparation of Monodisperse Particles and Emulsions by Controlled Shear. 227 195-215... 

For the characterization of Langmuir films, Fulda and coworkers [75-77] used anionic and cationic core-shell particles prepared by emulsifier-free emulsion polymerization. These particles have several advantages over those used in early publications First, the particles do not contain any stabihzer or emulsifier, which is eventually desorbed upon spreading and disturbs the formation of a particle monolayer at the air-water interface. Second, the preparation is a one-step process leading directly to monodisperse particles 0.2-0.5 jim in diameter. Third, the nature of the shell can be easily varied by using different hydrophilic comonomers. In Table 1, the particles and their characteristic properties are hsted. Most of the studies were carried out using anionic particles with polystyrene as core material and polyacrylic acid in the shell. 

Recently it has been reported that even colloidal particle suspensions themselves, without added polymers, can form dissipative structures. Periodic stripes of colloidal particles (monodisperse particles of diameter 30 nm and 100 nm, respectively) and polystyrene particles (monodisperse diameters from 0.5 to 3 pm) can be formed from dilute aqueous suspensions. The stripes are parallel to the receding direction of the edge of the suspension droplet and thus indicate that a fingering instability... 

As a rule, short nucleation times are the prerequisite for monodisperse particle formation. A recent mechanistic study showed that when Pt(acac)2 is reduced by alkylalu-minium, virtually all the Pt cluster nuclei appear at the same time and have the same size [86]. The nucleation process quickly consumes enough of the metal atoms formed initially to decrease their concentration below the critical threshold. No new metal cluster nuclei are created in the subsequent diffusion-controlled growth stage. 

From the viewpoint of size control, bimetallic nanoparticles naturally have a strong tendency to provide monodispersed particles, compared with monometallic nanoparticles [49]. This tendency cannot be completely understood yet, but redox properties between two metals might result in this advantageous properties of bimetallic nanoparticles. 

Figure 15. Ag/Au alloy formation by digestive ripening of Au and Ag monodispersed particles followed by UV-Vis. (Reprinted with permission from Ref [59], 2006, American Chemical Society.)...

Increasing the radius of the suspended particles, Brownian motion becomes less important and sedimentation becomes more dominant. These larger particles therefore settle gradually under gravitational forces. The basic equation describing the sedimentation of spherical, monodisperse particles in a suspension is Stokes law. It states that the velocity of sedimentation, v, can be calculated as follows ... 

The preparation of ZnSe materials is an area of interest and study. The coordinating ability of the solvent used in the solvothermal synthesis of zinc selenide was demonstrated to play an important role in the nucleation and growth of nanocrystalline ZnSe.604 Thermolysis of bis [methyl( -hexyl)di-seleno]carbamato]zinc gave highly monodispersed particles characterized by electronic spectroscopy, photoluminescence, X-ray diffraction, and electron microscopy.605... 

Particle dissolution models, which presume spherical monodisperse particle size, inadequately depict the complexity of typical pharmaceutical powders. 

Many synthetic methods for the preparation of nanodispersed material have been reported, several routes applying conventional colloidal chemistry, with others involving the kinetically controlled precipitation of nanocrystallites using organometallic compounds.3 6-343 Controlled precipitation reactions yield dilute suspensions of quasi-monodispersed particles. This synthetic method sometimes involves the use of seeds of very small particles for the subsequent growth of larger ones.359 360... 

Xu S, Nie Z, Seo M, Lewis P, Kumacheva E, Stone HA, Garstecki P, Douglas B, Whitesides GM (2005) Generation of monodisperse particles by using microfluidics control over size, shape, and composition. Angew Chem Int Ed 44 724-728... 

Figure 3.6 Silica spheres with monodisperse particle size are expensive analytical gels of top performance. Silica spheres with determined particle size ranges are ideally suited for preparative chromatography. (Photo courtesy of SiliCycle.)...

The specific surface area. 1 of a porous solid that is formed of the monodisperse particles (solid phase) of volume I, and surface area. , is equal to the multiplication of the surface area of one particle by the number of particles Am in unit of mass. Using Equation 9.50,... 

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