Hardness general discussion

As we have seen, the third law of thermodynamics is closely tied to a statistical view of entropy. It is hard to discuss its implications from the exclusively macroscopic view of classical themiodynamics, but the problems become almost trivial when the molecular view of statistical themiodynamics is introduced. Guggenlieim (1949) has noted that the usefiihiess of a molecular view is not unique to the situation of substances at low temperatures, that there are other limiting situations where molecular ideas are helpfid in interpreting general experimental results ... 

The methods most widely used in determining the hardness of metals are the static indentation methods. These involve the formation of a permanent indentation in the surface of the material under examination, the hardness being determined by the load and the size of the indentation formed. Because of the importance of indentation methods in hardness measurements a general discussion of the deformation and indentation of plastic materials is given in Chapter 2. 

General Discussion. The usefulness of polymers depends not only on their properties but also on their abundance and reasonable cost. Polymer properties are related not only to the chemical nature of the polymer, but also to such factors as extent and distribution of crystallinity and distribution of polymer chain lengths. These factors influence properties such as hardness, comfort, chemical resistance, biological response, weather resistance, tear strength, dyeability, flex life, stiffness, electrical properties, and flammability. 

The questions raised in this section have hardly been discussed in the literature, except for a short remark by Gesztesy et al. [6] that the generalization of their formalism to two-electron states requires a regular electron interaction. 

The concepts of electronegativity, hardness, and polarizability are all interrelated. For the kind of qualitative applications we will make in discussing reactivity, the concept that initial interactions between reacting molecules can be dominated by either partial electron transfer by bond formation (soft reactants) or by electrostatic interaction (hard reactants) is a useftxl generalization. 

Although any given source of water typically has a wide range of dissolved minerals present, and each of these has a potential for causing difficulties to a greater or lesser extent, it is the alkaline earth salts (.hardness salts) that are always present to some degree and generally are the most troublesome in a boiler. This section discusses these salts, their presence in natural makeup (MU) water sources, and their contribution to hardness scales and deposition in boiler plants. 

The first section involves a general description of the mechanics and geometry of indentation with regard to prevailing mechanisms. The experimental details of the hardness measurement are outlined. The tendency of polymers to creep under the indenter during hardness measurement is commented. Hardness predicitions of model polymer lattices are discussed. The deformation mechanism of lamellar structures are discussed in the light of current models of plastic deformation. Calculations... 

A large amount of work has been done on this subject. Though a great deal is known, much is still poorly understood, and many results are anomalous and hard to explain. In this section, only approximate generalizations are attempted. The work discussed here, and the conclusions reached, pertain to reactions taking place in solution. Some investigations have also been carried out in the gas phase. ... 

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