Extensibility of an elastomer

Three common methods of measuring crosslinking (swelling, elastic modulus, and gel point measurements) have recently been critically appraised by Dole (14). A fourth method using a plot of sol + sol against the reciprocal dose has also been used extensively. However, Lyons (23) has pointed out that this relation, even for polyethylenes of closely random distribution, does not have the rectilinear form required by the statistical theory of crosslinking. Flory (19) pointed out many years ago that the extensibility of a crosslinked elastomer should vary as the square root of the distance between crosslinks. More recently Case (4, 5) has calculated that the extensibility of an elastomer is given by ... 

This effect can be examined further by studying the reversible adiabatic extension of an elastomer. Although this experiment is more easily carried out imder conditions of constant pressure rather than constant volume, it is best to derive the relevant equations for constant voliune. For this reason, we will consider first the Helmholtz function for the system, i.e.. 

Elongation is the maximum extension of an elastomer at the moment of rupture. An elastomer with less than a 100% elongation will usually break if doubled over on itself. 

Another thermo-elastic effect that was mentioned earlier is the tendency of an elastomer to become warm when stretched rapidly. This type of behaviour is illustrated in Fig. 5.19 for the adiabatic extension of an elastomer. Some of the heating can be explained by crystallization which can also occur when natural rubber is stretched (Section 4.5) but a temperature rise is found even in non-crystallizable elastomers. This can be explained by consideration of the thermodynamic equilibrium. The rise in... 

Fig. 5.19 Increase in temperature, AT, upon the adiabatic extension of an elastomer (vulcanized natural rubber) (data of Dart, Anthony and Guth reported by Treloar).

The highly reversible extensibility (rubber elasticity) of polymer chains is related to their ability to coil and uncoil. The extension of an elastomer corresponds to a negative variation of its entropy (see Section 12.1). The examination of X-ray diffraction patterns of a stretched elastomer and of an unstretched one confirms this statement. 

FIGURE 2.18 Elongation of an elastomer as a function of applied force, stress, where A is the original relaxed state, B represents movement to full extension, C is the point at which the elastomer breaks, and D represents the force necessary to pull two separate pieces of elastomer apart. 

The stress-optical coefficient, Ka, of an elastomer network is a constant, independent of extension ratio and crosslink density. It is directly proportional to the difference between the longitudinal and transverse polarizabilities of the statistical chain segment (fei — 2) ... 

Another important point is the question whether static offsets have an influence on strain amplitude sweeps. Shearing data show that this seems not to be the case as detailed studied in [26] where shear rates do not exceed 100 %.However, different tests with low dynamic amplitudes and for different carbon black filled rubbers show pronounced effects of tensile or compressive pre-strain [ 14,28,29]. Unfortunately, no analysis of the presence of harmonics has been performed. The tests indicate that the storage (low dynamic amplitude) modulus E of all filled vulcanizates decreases with increasing static deformation up to a certain value of stretch ratio A, say A, above which E increases rapidly with further increase of A. The amount of filler in the sample has a marked effect on the rate of initial decrease and on the steady increase in E at higher strain. The initial decrease in E with progressive increase in static strain can be attributed to the disruption of the filler network, whereas the steady increase in E at higher extensions (A 1.2. .. 2.0 depending on temperature, frequency, dynamic strain amplitude) has been explained from the limited extensibility of the elastomer chain [30]. 

One further requirement the long chains of an elastomer must be connected to each other by occasional cross-links enough of them to prevent slipping of molecules past one another not so many as to deprive the chains of the flexibility that is needed for ready extension and return to randomness. 

Although equation (6-12) adequately describes the behavior of an elastomer at high extensions (> 10% for natural rubber), it is nevertheless true that the coefficient dH/dL)r,p has a finite value and cannot be neglected in a complete treatment of rubber elasticity. [It should be stated that equation (6-12) is inadequate to describe the behavior of most elastomers at very high extensions because of increasing limitations on chain extension and motion, as well as the onset of crystallization in many elastomers. When this occurs, the term (dH/dL)r,p once again becomes important and may actually outweigh the term T(dS/dL)r,p. ... 

According to the statistical theory of rubber elasticity, the elastic stress of an elastomer under uniaxial extension is directly proportional to the concentration... 

The treatment of mechanical deformation in elastomers is simplified when it is realized that the Poisson ratio is almost 0.5. This means that the volume of an elastomer remains constant when deformed, and if one also assumes that it is essentially incompressible (XjXjXj = 1), the stress-strain relations can be derived for simple extension and compression using the stored energy fimction w. 

At lower deformation rate (2.8x10 s" ), the density of physical network decreases in addition to the decrease in (v/V), value. In a consequence mote extensive decrease of a critical strain of an elastomer is observed (Figure 10.71b). This is a characteristic of elastomers having a large or small initial critical strain (Figures 10.71b, 10.78b). 

The Vc and Me values for crosslinked polymer networks can also be evaluated from stress-strain diagrams on the basis of theories for the rubber elasticity of polymeric networks. In the relaxed state the polymer chains of an elastomer form random coils. On extension, the chains are stretched out, and their conformational entropy is reduced. When the stress is released, this reduced entropy makes the long polymer chains snap back into their original positions entropy elasticity). Classical statistical models of entropy elasticity affine or phantom network model [39]) derive the following simple relation for the experimentally measured stress cr ... 

In brief, the basic equation relating the retractive stress, a, of an elastomer in simple extension to its extension ratio, a, is given by... 

Romanchick used TPP as the catalytic agent to study the reaction of an elastomer-modified epoxy with bisphenol A. The goal was to achieve a linear chain extension of the epoxy with bisphenol A by linking a pair of the elastomer modified epoxies. Based on his experimental results, he postulated that the reaction proceeds in the following manner ... 

Since dangling chains constitute imperfections in a network structure, one would expect their presence to have a detrimental effect on the ultimate properties (//A )r and Qfr of an elastomer. This expectation is confirmed by an extensive series of results obtained on PDMS networks that had been tetrafunctionally cross-linked using a variety of techniques [130]. The largest values of the ultimate strength... 

The statistical theory allows the stress-strain behaviour of an elastomer to be predicted. The calculation is greatly simplified when the observation that elastomers tend to deform at constant volume is taken into account. This means that the product of the extension ratios must be unity... 

Elongation. The extension produced by a tensile stress appHed to an elastomer, ie, elongation, is almost always reduced by fillers. Regardless of what type of filler is used, elongation decreases with increased loading above approximately 5 vol % (13). 

DuPont—Dow is the primary suppHer of these polymers. There is an estimated 18,000 t of these elastomers used per year. The main uses of CPE are in constmction, automotive, and electrical appHcations. These include power steering hose, electrical cords used in low voltage appHcations (extension cords, ignition wire), pond liners, and as a plastic modifier to improve impact modification. 

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