Ideal high-elasticity

A different question is whether this is ideal high-elasticity (see p. 679). Presumably the necessary conditions are not fulfilled. 

Returning now to the left part of the curve, for a 350% extension it has been shown that, at about —70° C, it suddenly turns in the same direction as for hard materials like metals. Referring to p. 661 it may be remembered that —70° C is the temperature T, at which rubber freezes, loosing its high-elastic properties. In accordance with the above developed theories, the conditions for ideal high-elasticity are now no longer present, because the molecules are not sufficiently movable. At about —70° C the kinetic (or entropic) elasticity is therefore transformed into potential elasticity. 

The high elastic modulus, compressive strength, and wear resistance of cemented carbides make them ideal candidates for use in boring bars, long shafts, and plungers, where reduction in deflection, chatter, and vibration are concerns. Metal, ceramic, and carbide powder-compacting dies and punches are generahy made of 6 wt % and 11 wt % Co ahoys, respectively. Another apphcation area for carbides is the synthetic diamond industry where carbides are used for dies and pistons (see Carbon). 

Viscoelastic fluids are thus capable of exerting normal stresses. Because most materials, under appropriate circumstances, show simultaneously solid-like and fluid-like behaviours in varying proportions, the notion of an ideal elastic solid or of a purely viscous fluid represents the commonly encountered limiting condition. For instance, the viscosity of ice and the elasticity of water may both pass unnoticed The response of a material may also depend upon the type of deformation to which it is subjected. A material may behave like a highly elastic solid in one flow situation, and like a viscous fluid in another. 

The molecules of an ideal gas are independent agents. By definition, there is no intermolecular attraction. The pressure of the gas on the walls of its container is due to random thermal bombardment of the molecules on the walls. The tension of rubber against restraining clamps is due to random coiling and uncoiling of chain molecules. The molecules of an ideal elastomer are independent agents. There is no intermolecular attraction, by definition. (If there is appreciable intermolecular attraction, the material will not exhibit high elasticity, as we saw earlier.)... 

Let s now go back to the high elasticity. As we have just seen, the internal energy of an ideal polymer does not change Af/ = 0. So there is no energy contribution to the elasticity the elasticity is explained in terms of entropy alone. Indeed, when a chain is stretched, we move from a more probable state (realized in more different ways) to a less probable one (realized in fewer ways). The chain starts getting uncoiled, and loses some freedom. In the extreme case, a chain stretched out in a straight line has no freedom at all (0 = 1, S = 0). 

We have explored what happens when an individual polymer chain is stretched. This was not just an exercise. We have shown that the elasticity of a network is built up from the elasticities of all the subchains (Figure 7.2), so we can make use of what we have found. There is one tricky question though. Let s imagine a highly elastic solid body, say, a rubber ball. The macromolecules are rather closely packed in it and interact strongly with each other. So can we really treat each subchain as an ideal polymer, with no volume interactions at all ... 

Thus, E turns out to be the same as the pressure of an ideal gas whose molecular concentration is 3z/ (i.e. three times the concentration of the cross-links). It means that the more cross-links there are in a highly elastic sample, the less elastic it is. Therefore, the value of E does not indicate a specific polymer. It varies dramatically depending on the density of the cross-links. 

Having sorted out the covalent bonds between the neighbors, we can now concentrate on all the other interactions. These are frequently referred to as volume interactions . As we have said, they have a typical energy E-2, and are much weaker than those in charge of the linear memory. In the crudest theory, we may completely neglect them. Then we shall end up with exactly what is called an ideal polymer chain. This is just how we handled all the calculations in the previous chapters. It worked fairly well, and we coped with quite a number of problems. We described how a chain rolls up into a loose coil, and we revealed the peculiar entropic nature of the high elasticity of polymers. 

Rubbery elasticity can be observed in its most ideal form in slightly interlinked polymers. On the one hand, the molecules are large enough to create the conditions necessary for high-elastic deformations on the other hand, the bridges prevent the... 

In Fig. 2 and 3 the dependences a on generalized stress for studied rubbers, corresponding to the equations (13) and (14), are shown. As can be seen, in case of composites the linearity of these dependences is violated, i.e., at least, the filled rubbers behaviour does not corresponded to high-elasticity classical theory, that is assumed above. Differently speaking, filled rubbers are impossible to consider as ideal, for which internal energy change MJ is equal to zero in deformation process. 

For the higher-order structure formation and properties of hair, the results on the crosslinking and property development by SS bond obtained by both chemical and physical analysis have been described. Fibrous proteins such as hair are found to show nearly ideal rubber elasticity in 8M LiBr/BC dilute solution. Starting finm the elucidation of the number of crosslink points and crosslink pattern from high elongational curves, the... 

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