Particle, dispersion 68, shape

Resin Viscosity. The flow properties of uncured compounded plastics is affected by the particle loading, shape, and degree of dispersion. Flow decreases with increased sphericity and degree of dispersion, but increases with increased loading. Fillers with active surfaces can provide thixotropy to filled materials by forming internal network stmctures which hold the polymers at low stress. 

Note that the particle diffusion term is ignored, just like particle dispersion due to SGS motions (this was found justified in a separate simulation). The shape of the sink term in the right-hand term of this equation is due to Von Smoluchowski (1917) while the local value of the agglomeration kernel /i0 is assumed to depend on the local 3-D shear rate according to a proposition due to Mumtaz et al. (1997). 

The hydrothermal carbons obtained in the end from soluble, non-structural carbohydrates are micrometer sized, spherically shaped particle dispersions, containing a sp2 hybridized backbone (also responsible for the brown to black color) decorated with a dense layer of polar oxygenated functionalities still remaining from the original carbohydrate. The presence of these surface groups offers the possibility of further functionalization and makes the materials more hydrophilic and well-dispersible in water. The size of the final particles depends mainly on the carbonization time and precursor concentration inside the autoclave, as well as additives and stabilizers potentially added to the primary reaction recipe. An SEM image of a model reaction illustrating this dispersion state is shown in Fig. 7.1. 

The respirable powders of a DPI cannot be characterized adequately by single-particle studies alone bulk properties must also be assessed since they contribute to ease of manufacture and affect system performance. Primary bulk properties include particle size, particle size distribution, bulk density, and surface area. These properties, along with particle electrostatics, shape, surface morphology, etc., affect secondary bulk-powder characteristics such as powder fiow, handling, consolidation, and dispersibility. 

Transmission electron microscopy (TEM) can provide valuable information on particle size, shape, and structure, as well as on the presence of different types of colloidal structures within the dispersion. As a complication, however, all electron microscopic techniques applicable for solid lipid nanoparticles require more or less sophisticated specimen preparation procedures that may lead to artifacts. Considerable experience is often necessary to distinguish these artifacts from real structures and to decide whether the structures observed are representative of the sample. Moreover, most TEM techniques can give only a two-dimensional projection of the three-dimensional objects under investigation. Because it may be difficult to conclude the shape of the original object from electron micrographs, additional information derived from complementary characterization methods is often very helpful for the interpretation of electron microscopic data. 

As we shall see, the intensity, polarisation and angular distribution of the light scattered from a colloidal system depend on the size and shape of the scattering particles, the interactions between them, and the difference between the refractive indices of the particles and the dispersion medium. Light-scattering measurements are, therefore, of great value for estimating particle size, shape and interactions, and have found wide application in the study of colloidal dispersions, association colloids, and solutions of natural and synthetic macro-molecules. 

Fillers generally represent one of the major components by weight in an adhesive formulation. However, their concentration is quite often limited by viscosity constraints, cost, and negative effects on certain properties. The degree of improvement provided by a filler in an epoxy formulation will heavily depend on the type of filler and its properties (particle size, shape, size distribution, and concentration), surface chemistry, dispersion characteristics, dryness, and compatibility with the other components in the formulation. Table 9.3 summarizes the properties of selected fillers. 

Several length-scales have to be considered in a number of applications. For example, in a typical monolith reactor used as automobile exhaust catalytic converter the reactor length and diameter are on the order of decimeters, the monolith channel dimension is on the order of 1 mm, the thickness of the catalytic washcoat layer is on the order of tens of micrometers, the dimension of the pores in the washcoat is on the order of 1 pm, the diameter of active noble metal catalyst particles can be on the order of nanometers, and the reacting molecules are on the order of angstroms cf. Fig. 1. The modeling of such reactors is a typical multiscale problem (Hoebink and Marin, 1998). Electron microscopy accompanied by other techniques can provide information on particle size, shape, and chemical composition. Local composition and particle size of dispersed nanoparticles in the porous structure of the catalyst affect catalytic activity and selectivity (Bell, 2003). 

Particle size and shape. The particle size, shape, and distribution of a pigment influence the rheological properties, shade, gloss, weathering characteristics, and ease of dispersion. 

From the volume-surface diameter (dvs) the dispersion of the supported phase (D) can be evaluated. For this purpose a relationship between this parameter and D is required. Different authors have suggested an influence of the particle shape on this relationship (389390). To check this point, a series of models of metal particles with shapes more or less close to those observed in the experimental HR M miages (octahedron, cube-octahedrons, cube, sphere) and of increasing size were built using the Rhodius program (184). For each model the total number of atoms (Nt) and the number of surface atoms (Ns) were counted up, and from their ratio (N /Nt) the dispersion (D) was calculated. 

It is noted that attempts to apply composites theory to the materials investigated have not been entirely successful. While upper and lower bounds on, e g., moduli can be established there is little quantitative ediction of the impact strei th or fracture toughness parameters of the composites. Hence, the systems cannot be considered as optimized, for example, with regard to impact strength versus particle size, shape, or distribution or matrix-particle adhesion. The complexity is, of course, due to the statistical structure of the dispersed phase and the resultant uncertainties in the calculations of local stress fields, which in turn imply uncertainty in the local mode of yielding or rate of yielding. 

Of critical importance in the development of DPI products is the evaluation, optimization, and control of flow and dispersion (deaggregation) characteristics of the formulation. These typically consist of drug blended with a carrier (e.g., lactose). The properties of these blends are a function of the principal adhesive forces that exist between particles, including van der Waals forces, electrostatic forces, and the surface tension of adsorbed liquid layers [7], These forces are influenced by several fundamental physicochemical properties, including particle density and size distribution, particle morphology (shape, habit, surface texture), and surface composition (including adsorbed moisture) [8]. In addition,... 

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