Rubber elasticity, requirements

There exist a number of experimental methods for determination of structure sensitive parameters of a system undergoing branching and crosslinking. However, evaluation of some of the results requires application of a theoretical approach to the phenomenon the measurement is concerned with. Then, we may be testing two theories at once. The equilibrium elasticity is one example, since there exist alternative rubber elasticity theories. However, certain conclusions can always be made. 

Finally, it should be pointed out that no molecular theory of rubber elasticity is required and that no assumptions were made in order to reach above conclusions. 

Rubber elasticity, which is a unique characteristic of polymers, is due to the presence of long chains existing in a temperature range between the Tg and the Tm. The requirements for rubbery elasticity are (1) a network polymer with low cross-link density, (2) flexible segments which can rotate freely in the polymer chain, and (3) no volume or internal energy change during reversible deformation. 

Analysis of networks in terms of molecular structure relies heavily on the kinetic theory of rubber elasticity. Although the theory is very well established in broad outline, there remain some troublesome questions that plague its use in quantitative applications of the kind required here. The following section reviews these problems as they relate to the subject of entanglement. 

The kinetic theory of rubber elasticity is so well known and exhaustively discussed (17, 27, 256-257, 267) that the remarks here will be confined to questions which relate only to its application in determining the concentration of elastically effective strands. In principle, both network swelling properties and elasticity measurements can provide information on network characteristics. However, swelling measurements require the evaluation of an additional parameter, the polymer-solvent interaction coefficient. They also involve examining the network in two states, one of which differs from its as-formed state. This raises some theoretical difficulties which will be discussed later. Questions on local non-uniformity in swelling (17) also complicate the interpretation. The results described here will therefore concern elasticity measurements alone. 

Such networks have been widely used to establish whether the theories of rubber elasticity and of equilibrium swelling are valid. But these theories are based on a number of hypotheses which are obviously far from being fulfilled by the above networks. The so-called ideal networks should obey the following requirements ... 

Stress/strain relationships are commonly studied in tension, compression, shear or indentation. Because in theory all stress/strain relationships except those at breaking point are a function of elastic modulus, it can be questioned as to why so many modes of test are required. The answer is partly because some tests have persisted by tradition, partly because certain tests are very convenient for particular geometry of specimens and partly because at high strains the physics of rubber elasticity is even now not fully understood so that exact relationships between the various moduli are not known. A practical extension of the third reason is that it is logical to test using the mode of deformation to be found in practice. 

It is worth noting at this point that the various scientific theories that quantitatively and mathematically formulate natural phenomena are in fact mathematical models of nature. Such, for example, are the kinetic theory of gases and rubber elasticity, Bohr s atomic model, molecular theories of polymer solutions, and even the equations of transport phenomena cited earlier in this chapter. Not unlike the engineering mathematical models, they contain simplifying assumptions. For example, the transport equations involve the assumption that matter can be viewed as a continuum and that even in fast, irreversible processes, local equilibrium can be achieved. The paramount difference between a mathematical model of a natural process and that of an engineering system is the required level of accuracy and, of course, the generality of the phenomena involved. 

These propellants can be manufactured by casting or by pressing. The grain fineness of the salt employed affects the combustion properties to a significant extent. The mechanical (preferably rubber-elastic) properties of the plastic binders must satisfy special requirements. 

In manufacturing explosive charges which are required to have a certain mechanical strength or rubber-elastic toughness, Cyclonite is incorporated into curable plastic materials such as polyurethanes, polybutadiene or polysulfide and is poured into molds (-> Plastic Explosives). 

Hypercrosslinked polystyrene cannot be considered to be an elastomer either. Although two of the most important features of rubber elasticity, namely large values of deformation and reversibihty of the deformation, are characteristic of the hypercrosslinked polystyrene, the non-elastic part of their deformation is stiU definitely too high. The reversal of this non-elastic part of deformation requires long heating of the material or treating the sample with a solvent. Such a hindered relaxation is not characteristic of typical rubbers. 

The situation is somewhat different for elastomers. On the one hand the elasticity required in the application of molded rubber parts makes automatic removal within the injection molding cycle more difficult. On the other hand there are certain complicated article geometries, which it would be impossible to produce profitably by the injection molding method if it were not for the flexibihty of these parts. Examples include bellows and elbows for hoses. It is therefore often impossible to avoid the manual removal of rubber moldings, even in large-scale production. 

We note that representing the rubbery behavior of the amorphous component between crystalline lamellae by the formaUsm of rubber elasticity is done primarily for operational expediency because it successfully represents the macroscopic mechanical response. Clearly, caution is required in the literal interpretation of the behavior of this well-defined material on the molecular level by consideration of it as a rubber. 

In summary, polymeric materials exhibit rubber elasticity if they satisfy three requirements (a) the polymer must be composed of long-chain molecules, (b) the secondary bond forces between molecules must be weak, and (c) there must be some occasional interlocking of the molecules along the chain lengths to form three-dimensional networks. Should the interlocking arrangements be absent, then elastomers lack memory, or have a fading memory and are not capable of completely reversible elastic deformations. 

SBR elastomer with known crosslinking densities was studied in dynamic shear and tensile creep and data collected from -30 to 70 °C used to construct TTS master curves. In addition to a temperature shift factor a vertical shift factor was required from 10 to 30 °C to account for changes in density. Linear viscoelastic properties were observed in accordance with the classical theory of rubber elasticity. Standard vertical shift factors were required in a comparative TTS test with uncrosslinked polybutadiene and poly(ethylene-cu-propylene-co-diene monomer) (EPDM). ... 

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