Solids cohesive forces

Solid Dispersion If the process involves the dispersion of sohds in a liquid, then we may either be involved with breaking up agglomerates or possibly physically breaking or shattering particles that have a low cohesive force between their components. Normally, we do not think of breaking up ionic bonds with the shear rates available in mixing machineiy. 

Orowan (1949) suggested a method for estimating the theoretical tensile fracture strength based on a simple model for the intermolecular potential of a solid. These calculations indicate that the theoretical tensile strength of solids is an appreciable fraction of the elastic modulus of the material. Following these ideas, a theoretical spall strength of Bq/ti, where Bq is the bulk modulus of the material, is derived through an application of the Orowan approach based on a sinusoidal representation of the cohesive force (Lawn and Wilshaw, 1975). 

If the principal cohesive forces between solute molecules are London forces, then the best solvent is likely to be one that can mimic those forces. For example, a good solvent for nonpolar substances is the nonpolar liquid carbon disulfide, CS2-It is a far better solvent than water for sulfur because solid sulfur is a molecular solid of S8 molecules held together by London forces (Fig. 8.19). The sulfur molecules cannot penetrate into the strongly hydrogen-bonded structure of water, because they cannot replace those bonds with interactions of similar strength. 

For wetting to occur, the adhesive forces of the liquid for the solid must exceed the cohesive forces of the liquid for itself. 

Commonly, roughness can be tailored by using additives. These are mainly based on combinations of inert, inorganic particles of different sizes and the weight ratio of large to small particle sizes. These particles should be well dispersed in the base film to prevent abrasion, which is influenced by the particle shape and the kind of embedding in the polymer matrix. The affinity of these particles to the solid polymer seems to be based on adhesion of the melt to the solids and to cohesive forces in the solid state. This phenomenon, however, has not yet been explored in sufficient detail. 

The advantage of equation 17.14 is that it may be fitted to all known shapes of adsorption isotherm. In 1938, a classification of isotherms was proposed which consisted of the five shapes shown in Figure 17.5 which is taken from the work of Brunauer et alSu Only gas-solid systems provide examples of all the shapes, and not all occur frequently. It is not possible to predict the shape of an isotherm for a given system, although it has been observed that some shapes are often associated with a particular adsorbent or adsorbate properties. Charcoal, with pores just a few molecules in diameter, almost always gives a Type I isotherm. A non-porous solid is likely to give a Type II isotherm. If the cohesive forces between adsorbate molecules are greater than the adhesive forces between adsorbate and adsorbent, a Type V isotherm is likely to be obtained for a porous adsorbent and a Type III isotherm for a non-porous one. 

Fluorapatite is a highly insoluble calcium phosphate phase. The solubility product of stoichiometric fluorapatite at 37°C is 3.19 0.14x10 " mol 1 (for Cas(P04)3F as reported by Moreno et al. [53]) and appears significantly lower than that of HA in the same conditions (7.36 0.93 x 10 ° mol for Ca5(P04)30H). Asuggested explanation for this very low solubility product is that cohesive forces are stronger in fluorapatite than in other apatites due to smaller unit-cell dimensions. The complete solid solution Ca-,o(P04)6(OH)2-xFx can be obtained. Initial solubility determinations have shown a solubility minimum for x close to 1 [54], related to the formation of hydrogen bonding between F and OH ions. These results were subsequently... 

Organic solids have received much attention in the last 10 to 15 years especially because of possible technological applications. Typically important aspects of these solids are superconductivity (of quasi one-dimensional materials), photoconducting properties in relation to commercial photocopying processes and photochemical transformations in the solid state. In organic solids formed by nonpolar molecules, cohesion in the solid state is mainly due to van der Waals forces. Because of the relatively weak nature of the cohesive forces, organic crystals as a class are soft and low melting. Nonpolar aliphatic hydrocarbons tend to crystallize in approximately close-packed structures because of the nondirectional character of van der Waals forces. Methane above 22 K, for example, crystallizes in a cubic close-packed structure where the molecules exhibit considerable rotation. The intermolecular C—C distance is 4.1 A, similar to the van der Waals bonds present in krypton (3.82 A) and xenon (4.0 A). Such close-packed structures are not found in molecular crystals of polar molecules. 

For liquids, many studies have shown inverse linear relationships between solubility and partition coefficient. But most drugs are solids, and for these solubility depends also on the ease of breaking cohesive forces within the crystal, hence relationships include a function of the melting point as a correction term. 

It should be noted that the elasticity modulus E is not merely a property of the solid material in the bed. In general, is a complex function of the structure of packing, material properties of packing particles, particle size, and particle contact and cohesion forces between particles. 

For liquids and solids, which have strong internal cohesive forces, the term (9U/5T)p is large. 

The cohesive force between solid surfaces and the surface energy of solids." Ibid., 13 (7th Ser.) 853-862. 

The addition of fines to a powder system allows a larger top size of particle to be agglomerated due to the attendant increase in cohesive forces caused by a decrease in surface mean particle diameter and increase in agglomerate density. Thus, although eqn. (1) indicates a top size of about 150 pm for monosized particles with aqueous binders, the top size of feed for industrial disc pelletizers is usually higher at 30 to 50 mesh (300 to 600 /zm) with the provision that at least 25% should be finer than 200 mesh (75 /zm) [7]. Other liquids with surface tensions lower than that of water, or liquid/ solid systems in which the particle surface is imperfectly wetted, require finer particle sizes to make successful balling possible. 

The earliest agglomeration equipment consisted simply of solid-liquid mixers and, in common with newer designs, provided the mechanical means by which particles were brought into contact and densified into larger entities as the cohesive forces came into operation. Various other types of equip-... 

The thixotropic characteristics provided by fumed sihca are due to its ability to develop a loosely woven, latticelike network by hydrogen bonding between particles. This network raises the apparent viscosity of the system, increases the cohesive forces, and contributes to the suspension of the solid. Because the hydrogen bonds themselves are relatively weak, they are easily disrupted through the action of an apphed stress or shearing force and quickly reform when the stress or shearing force is removed. 

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