Elastic behavior chemical bonding

As briefly mentioned in Sect. 2.2, the bond valence parameter b represents the compliance of a bond to external forces. Approximating by a universal value therefore eliminates the crystal-chemical information on elastic behavior from bond valence parameters (or more precisely reduces the information from an approximation that takes into account structure type and atomic properties to a crude estimate solely based on the coordination type). Whether such information is relevant for a given application purpose and available for specific cation-anion pair may depend on individual circumstances. Here it will be assumed that retaining this information available is desired, and thus it is necessary to elaborate suitable procedures to systematically determine the respective b values. 

Hardness is a somewhat ambiguous property. A dictionary definition is that it is a property of something that is not easily penetrated, spread, or scratched. These behaviors involve very different physical mechanisms. The first relates to elastic stiffness, the second to plastic deformation, and the third to fracturing. But, for many substances, the mechanisms of these are closely related because they all involve the strength of chemical bonding (cohesion). Thus discussion of the mechanism for one case may provide some understanding of all three. 

For interpreting indentation behavior, a useful parameter is the ratio of the hardness number, H to the shear modulus. For cubic crystals the latter is the elastic constant, C44. This ratio was used by Gilman (1973) and was used more generally by Chin (1975) who showed that it varies systematically with the type of chemical bonding in crystals. It has become known as the Chin-Gilman parameter (H/C44). Some average values for the three main classes of cubic crystals are given in Table 2.1. 

The surface properties of this kind of supramolecular systems are really scarce. An interplay between short - range van der Waals forces, ionic binding, chemical bonding, elastic/plastic compression, and long - range electrostatic interactions and capillary forces between macromolecules and surfaces seems to be responsible for the variety of observed interfacial behaviors. 

Another AFM-based technique is chemical force microscopy (CFM) (Friedsam et al. 2004 Noy et al. 2003 Ortiz and Hadziioaimou 1999), where the AFM tip is functionalized with specific chemicals of interest, such as proteins or other food biopolymers, and can be used to probe the intermolecular interactions between food components. CFM combines chemical discrimination with the high spatial resolution of AFM by exploiting the forces between chemically derivatized AFM tips and the surface. The key interactions involved in food components include fundamental interactions such as van der Waals force, hydrogen bonding, electrostatic force, and elastic force arising from conformation entropy, and so on. (Dther interactions such as chemical bonding, depletion potential, capillary force, hydration force, hydrophobic/ hydrophobic force and osmotic pressure will also participate to affect the physical properties and phase behaviors of multicomponent food systems. Direct measurements of these inter- and intramolecular forces are of great interest because such forces dominate the behavior of different food systems. 

At first, all hexagonal cells are deformed as in the case of shear, so that the fracture band behaves as a shear band. The reason of such behavior consists in the value of modulus of elasticity for the valence angle between two chemical bonds. It appears usually one-two orders less than the elastic constant of valence forces [7]. This deformation should be compatible with that of remaining part of the nanotube outside the shear band. Simultaneously with the deformation of valence angles, bond stretching in the band initially parallel to the nanotube axis takes place. In addition to this uniform deformation in the shear band, there begins stretching of the bonds which initially were not parallel to the nanotube axis. 

The break behavior of any desired elastic body is described by the Griffith theory. According to Griffith, a crack in an elastic body only propagates further when the elastically stored energy just exceeds the energy required to break chemical bonds. Combination of this with the Ingles concept leads to... 

Elastomeric or rubber materials result from the wide-mesh crosslinking of amorphous, thermoplastic precursors (natural rubber). These weak chemical bonds between polymer chains result in typical rubbery, highly elastic behavior above the glass transition temperature [2]. 

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