Elasticity, of rubbers

Rubber as an engineering material is unique in its physical behaviour. It exhibits physical properties that lie mid-way between a solid and liquid, giving the appearance of solidity, while possessing the ability to deform substantially. Most solid materials have an extensibility of only a few percent strain and only a portion of that is elastic, being typically Hookean in character, exhibiting a linear stress-strain relationship. Rubbers, however, may be extensible up to over 1000% strain, most of which is 

Rubbers exhibit these properties because unlike conventional solids, which are comprised of atoms that occupy fixed positions relative to each other, they are formed from molecules that are arranged to form a flexible, long-chain macromolecule or polymer. While not all polymers are rubber-like, all rubbers are polymeric. The characteristic that makes a polymer rubber-like is its ability to undergo rapid molecular movement, allowing it to deform readily, and the ability of the molecule to return to its original configuration after the deforming forces have been removed. A number of qualities are necessary for attainment of rubber-like properties. 

It is also essential that the polymer be of sufficient length, otherwise the molecule will behave essentially as a fluid and will possess little elasticity. Relative molecular masses in the range 100,000-2,000,000 are typical for rubbers, which ensures that a significant amount of chain entanglement occurs. 

Only a relatively small number of polymers have sufficient mobility to be rubbery at room temperature. The molecular mobility depends heavily on the composition of the polymer backbone, which often contains a significant proportion of simple hydrocarbon species, such as those derived from ethylene, butadiene or isoprene. These species are small and are able to undergo bond rotation with relative ease, since they do not suffer problems due to steric hindrance [2] or the presence of strong dipoles. The rubber molecule is also able to undergo extension easily because the forces acting on the material are relatively weak secondary intermolecular forces, i.e., those acting between molecules, and not the primary inter-atomic forces, i.e., those existing within a molecule [3]. 

A further requirement, that of recovery of shape after deformation, is also provided by high molecular mobility and the fact that long-chain polymers have a preference to exist as a randomly coiled chain, which represents a minimum energy-state condition for the polymer. A move away from this state, such as occurs during mechanical deformation of the polymer, is only achieved by the input of energy, which creates a state of higher order in the thermodynamic sense, i.e., a reduction in the entropy (disorder) of the system. The return to maximum entropy is one of the key elements of a high elastic recovery [4, 5]. 

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In Geneva, he resumed with new energy his studies of macromolecules. He was able to obtain the cooperation of A. J. H. van der Wijk, who was one of his most devoted coworkers the latter s realistic criticisms were a valuable balance to Meyer s great enthusiasm. Studies on the thermodynamics of large molecules in solution, and on the structure of cellulose and chitin, were pursued with C. Boissonnas, W. Lothmar, and L. Misch. A theory of the elasticity of rubber evolved from his work with C. Ferri and his previous observations with Susich and Valk6. 

From his early youth, under his father s influence, K. H. Meyer had retained a keen interest in biological problems, as was evident from his study of the phenomena of narcosis, which he pursued during his stay in industry. As a natural consequence, he extended his thoughts to biological problems, and evolved a quantitative theory of muscular contraction (in collaboration with Picken), based on analogies with the elasticity of rubber. With J. F. Sievers, the permeability of synthetic membranes was investigated, and a mathematical treatment of the phenomenon was advanced which was later applied to living membranes. 

The principles were refined by Meyer in a second paper (70). In it he proposed that the micelles occurred at regular intervals. He also included an explanation of the elasticity of rubber based on the assumption that the molecular chains tended to roll together in knots in unstretched rubber, but line up when stretched. This explanation was especially elucidating since it agreed well with Katz s discovery (53) that amorphous rubber crystallizes when stretched. 

The structure of an elastomer comprises a network of chains, meaning that there are gaps between adjacent chains. Indeed the elasticity of rubber relies on substantial thermal motion of the chains, which would not be possible if the chains were closely packed. The free volume available in the rubber means that some liquids can enter the rubber and cause swelling - sometimes very large amounts of swelling. For example the ability of oil to swell natural rubber is well known. 

The need to maintain elasticity of rubber is of paramount importance under any serious and severe environmental conditions. The most stable rubbers in radiation environments are polyurethanes and phenyl silaxanes which are usable at well above 108 rads (106 Gy). Butyl rubber liquefies and neoprene evolves hydrochloric acid at similar dose levels. Most polyurethane rubber foams can be used at a dose level of 109 rads (107Gy) in vacuum at temperature levels of between -85°C to +250°C. Silicone and polysulphide sealants are probably less tolerant to ionizing radiation in a nuclear plant where chemical processes are being carried out. A schematic graphical representation of the tolerance of rubbers to ionizing radiation in nuclear plant is shown below in figure 7.4. 

The unique two-phase structures of polyurethane that offers the elasticity of rubber combined with the toughness and durability of metal make them one of the most extensively studied and frequently used materials in carbon nanotube related nanocomposites. The main difficulty in developing CNT based polyurethane nanocomposites was how to achieve uniform and homogeneous CNT dispersion. Further investigations on the interactions between carbon nanotubes and two-phase structures are critical for the wider applications of carbon nanotube/polyurethane composites. 

FIGURE 1.10 Dependence of modulus elasticity of rubber polymer concrete (RubCon) samples on exposition time at humidity of environment 1 50%-60%, 2 85%-95%, 3 water immersion. (From Yu. Borisov, Yu. Potapov, O. Figovsky, and D. Beilin, Water Resistance of the Polymer Concretes, J. Scientific Israel Advanced Technology 14, no. 3 (2012) 84-91. With permission.)... 

This will become clear in chapter 6 where the elasticity of rubbers is considered. 

The elasticity of rubbers is very different from that of materials such as metals or even glassy or semicrystalline polymers. Young s moduli for metals are typically of the order of 10 MPa (see table 6.1) and the maximum elastic extension is usually of order 1% for higher extensions fracture or permanent deformation occurs. The elastic restoring force in the metal is due to interatomic forces, which fall off extremely rapidly with distance, so that even moderate extension results in fracture or in the slipping of layers of atoms past each other, leading to non-elastic, i.e. non-recoverable, deformation. 

Polyurethane is a unique material that offers the elasticity of rubber combined with the toughness and durability of metal. Because urethane is available in a very broad range of hardness (soft as an eraser to hard as a bowling ball), it allows the engineer to replace rubber, plastic, and metal with the ultimate in abrasion resistance and physical properties. 

Now you know what people mean when they talk about the high elasticity of rubber. In brief, high elasticity means that the material is prone to very high, non-linear yet reversible deformations as a result of rather moderate stress. 

Still, we could think of an elastic constant of a polymer chain it would be the coefficient of the linear relation betw een the force f and the deformation R. According to (7.20), it happens to be ZhsT/NC. First, notice that it is proportional to 1/AT, which makes it a very small quantity if the chains are fairly long. This means that polymer chains are very susceptible to external forces this is exactly what accounts for the high elasticity of rubber and other similar polymers. The second thing we can notice is that the elastic constant is proportional to the temperature T. This is because the elastic forces are due to entropy, as you can see from (7.3). 

This effect demonstrates, perhaps in the most dramatic way, that the high elasticity of rubber and other polymers is related to entropy. Indeed, as the temperature goes up, all sorts of interactions start to lose their importance. This is because the characteristic energy of such interactions, , becomes much less than ksT (i.e. e/ksT < 1). Meanwhile, the entropy contribution gains more and more significance. (According to (7.4), the... 

Urethane rubbers are produced from a number of polyurethane polymers. The properties exhibited are dependent upon the specific polymer and the compoimding. Urethane (AU) rubber is a unique material that combines many of the advantages of rigid plastics, metals, and ceramics, yet still has the extensibility and elasticity of rubber. It can be formulated to provide a variety of products with a wide range of physical properties. 

The phenomenon of elasticity of rubber and other elastomers is a result of a tendency of the chains of large amorphous polymers to form kinked conformations. If there is also a certain amount of crosslinking, then these kinked conformations occur between the crosslinks. The distance between the ends in such polymers is much shorter than when they are fully stretched. Deformation or stretching of rubber straightens out the molecules. They tend to return to the kinked state, however. 

This derivation of the ideal gas law is very close in all its steps to the theory developed in Sections 3.3 and 3.4 for the elasticity of rubber. In the case of rubber, which is essentially inconq>ressible, the deforming forces cause the specimen to change shape the deformation is shear deformation with no change in volume. 

The high degree of elasticity of rubbers is due in part to the effects of thermal motions upon the long polymeric chains. These motions tend to restrict vibrational and rotational motions about the single bonds in the main chain. Such restrictive forces in the lateral direction, however, are much... 

Similarly, one can derive the mean-square end-to-end distance =3l2lff. In the following, we will apply the Gaussian chain above to interpret the entropic origin of high elasticity of rubbers. 

The topological interaction is also very important in the problems of rubbers, in which the configurations of composite diains are severely restricted by the topological constraints of other chains. This gives an additional contribution to the elasticity of rubbers. ... 

Plastic/mbber blends offer a way to combine the best of both worlds - the softness and elasticity of rubber and the processability of thermoplastic. As discussed in this chapter, there are several methods for the preparation of plastic/mbber blends. Physical melt mixing of the plastics and mbbers provides a simple, quick, and most economical way of producing such blends. One can also prepare multicomponent and specialty blends by this procedure. Both Banbury batch mixers and twin-screw mixers are used to produce these blends. Most physical blends are now prepared by this melt-mbdng process. 

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