Cohesive Forces in Solids

William B. Pearson (1921-2005) developed a shorthand system for denoting alloy and intermetallic structure types (Pearson, 1967). It is now widely used for ionic and covalent solids, as well. The Pearson symbol consists of a small letter that denotes the crystal system, followed by a capital letter to identify the space lattice. To these a number is added that is equal to the number of atoms in the unit cell. Thus, the Pearson symbol for wurtzite (hexagonal, space group PS mc), which has four atoms in the unit ceU, is hPA. Similarly, the symbol for sodium chloride (cubic, space group Fm3m), with eight atoms in the unit cell, is cF8. 

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One of the most useful methods for characterizing the cohesive forces in solids is the determination of the amount of energy in the form of heat necessary to melt them, and the temperature at which melting occurs. These are precise analogues of the heats of vaporization and the normal boiling... 

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 surface tension forces act all around the capillary tube in the upward direction and liquid rises in the tube. This rise continues till the upward lifting force becomes equal to the weight of the liquid in the capillary tube. If the cohesive forces in liquid are greater than the solid-liquid and those of the solid surface, the liquid detaches from the surface of the solid and a fall of liquid in the tube is observed. 

Although the cohesive forces in such an idealized metal as described would be nondirectional (as in ionic solids), the orientation effects of d orbitals contribute a directional-covalent component to the bonding in transition metals that requires a more sophisticated definition for metallic bonding. The intemuclear distances in the close packed, or nearly close packed, stmcmres of most metalhc elements ate small enough that the valence orbitals on the metal atoms can overlap (in the valence-bond model) or combine to form COs (in the MO or Bloch model). 

The Relation Between Elasticity and the Cohesive Forces in a Solid... 

As early as 1835, Frankenheim was particularly concerned with cohesive forces in different states of aggregation, and suggested that in the various solid states of a material the attractions which lead to the aggregation in different solids are different, and are characterized by different special symmetry relations. 

Adhesion and cohesion forces in not freely movable binders. If highly viscous binders are applied, adhesion forces at the solid-fluid interface and cohesion forces within the fluid can be fully used for binding until the weaker of the two fails. 

The contact angle 0 depends on the balance between the sohd/Vapour (ygy) and solid/liquid (yg ) interfacial tensions. The angle which a drop assumes on a solid surface is the result of the balance between the adhesion force between solid and liquid and the cohesive force in the liquid,... 

The curvature of the interface depends on the relative magnitudes of the adhesive forces between the liquid and the capillary wall and the internal cohesive forces in the liquid. When the adhesive forces exceed the cohesive forces, 9 lies in the range 0° < 9 < 90° when the cohesive forces exceed the adhesive forces, 90° < 9 < 180°. When 9 > 90°, the cos 9 term is negative, resulting in a convex meniscus towards the vapor phase and the liquid level in the capillary falling below the liquid level in the container (capillary depression). This occurs with liquid mercury in glass where 9 = 140° and also with water in capillary tubes coated internally with paraffin wax. Thus, liquid mercury is used in the evaluation of the porosity of solid adsorbents in the mercury injection porosimetry technique (see Section 8.5). 

Five primary methods exist to form an agglomerated granule. They are formation of solid bridges, sintering, chemical reaction, crystallization, or deposition of colloidal particles. Binding can also be achieved through adhesion and cohesion forces in highly viscous binders. 

Capillary forces result from the interaction of liquid, gas and solid surfaces, at the interface between them. In the liquid phase, molecules are held together by cohesive forces. In the bulk of the liquid, the cohesive forces between one molecule and the surrounding molecules are balanced. However, for the same molecule at the edge of the liquid, the cohesive forces with other liquid molecules are larger than the interaction with air molecules (Fig. 1). As a result, the hquid molecules at the interface are pulled together towards the liquid. The overall effect of these forces is to minimize the free surface of the liquid that is exposed to mr. The proportionahty between the decrease in energy of the surface that results from decreasing the surface is described by the surface tension ... 

The cohesion between the hydrophobic part of the interfacial adsorption layer and the adjacent nonpolar phase can be modeled nsing the cohesion between model hydrophobic snrfaces in the same liqnid. In snch a simnlation, the hydrophobic solid snrfaces represent the hydrophobic tails of the snrfactant molecnles. This approach allows one to overcome the difficnlties associated with the mutual solubility of the components (see Chapter 1). For the solid/liqnid/solid interface, the main parameter characterizing the interactions is the free energy of interaction, F (or Aoj), which can be established experimentally nsing Derjagnin s theorem, that is, p = %RF, where p is the cohesive force in a direct contact between two spherical particles immersed in a liqnid medinm. Snitable model systems include spherical molecularly smooth glass beads with a radius R 1-1.5 mm and hydrophobized surfaces of different natures, namely, HS and HL, immersed into the hydrocarbon and fluorocarbon liquids, HL and FL. Only dispersion forces are present in such systems, which makes the quantitative description of their interaction well defined and not complicated by the presence of various polar components. 

The adhesion between the IA L (its hydrophobic part) and an adjacent nonpolar phase can be modeled by the adhesion, in the same Uquids, of the modified soUd surfaces simulating the hydrophobic parts of corresponding surfactants. In this method, experimental complications coimected with the mutual solubility of components are prevented. For the solid/liquid interface, the principal quantitative characteristic of interaction, the free energy of interaction F (mj m , in the plain-parallel gap or film) can be established experimentally from Derjaguin s equation p = kRF, where p is the cohesive force in the immediate contact between two spherical particles immersed in the corresponding liquid medium [29, 30]. 

Of course, there is no problem at all in principle. Structure is itself an electronic property, in that it must be determined by the Coulomb forces of the electrons (and nuclei) of the system and should be derivable from the Hamiltonian. The troublesome needle-inhaystack aspect of structure determination is often a nuisance here, but even if we are lucky enough to be faced with a choice between a few reasonable structures (as in the impurity problem), the fact is that the description of the cohesive forces of solids is a difficult and delicate business. Perhaps the stumbling-block of structure determination has been overemphasized here, but there does not seem to be a wide realization of the problem and its importance to future progress. 

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. 

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