Subject rubber network

The affine and the phantom models derive the behavior of the network from the statistical properties of the individual molecules (single chain models). In the more advanced constrained junction fluctuation model the properties of these two classical models are bridged and interchain interactions are taken into account. We remark for completeness that other molecular models for rubber networks have been proposed [32,57,75-87], however, these are not nearly as widely used and remain the subject of much debate. Here we briefly summarize the basic concepts of the affine, phantom, constrained junction fluctuation, diffused constraint, tube and slip-tube models. 

The in situ sol gel silica process is an alternative method of incorporating silica into rubbers. The in situ sol-gel approach, in preparing silica-reinforced rubber, is considered a novel technique. In principle, a rubber is swollen in a silica precursor, e.g. tetraethyl orthosilicate (TEOS) and the TEOS-swollen rubber is then subjected to hydrolysis and condensation reactions which could be acid- or base-catalysed. Subsequently, silica particles are generated in the rubber or rubber network. The chemical reactions involved in the formation of silica particles are shown in Scheme 7.1 where the overall reaction indicates that 1 mole of TEOS requires 2 moles of water to be converted into anhydrous silica. 

Only crystallization induced by a tensile type deformation has been discussed here. Other types of deformation such as biaxial extension, shear and torsion should also be considered. Such deformations have been studied and analyzed for amorphous networks. However, there is a paucity of experimental data, as well as analysis, of the equilibrium aspects of crystallization induced by these deformations. In one available report the observed melting temperature of natural rubber networks increased substantially when subject to biaxial deformation.(41) An increase in melting temperature of about 50 °C was found for a biaxial stretching ratio of three. This increase is much larger than that observed for natural rubber when crystallized in simple extension. 

When the butyl rubber was compounded with up to 30 percent of polyisobutylene, which, lacking the unsaturated isoprene units, did not enter into the cross-linking reaction, the tensile strengths were, of course, considerably reduced. They were found nevertheless to be accurately represented by the same equation, (53), provided merely that Sa is taken as the fraction of the composite specimen consisting of network chains subject to orientation. Thus, in this case... 

From a theoretical point of view, the equilibrium modulus very probably gives the best characterization of a cured rubber. This is due to the relationship between this macroscopic quantity and the molecular structure of the network. Therefore, the determination of the equilibrium modulus has been the subject of many investigations (e.g. 1-9). For just a few specific rubbers, the determination of the equilibrium modulus is relatively easy. The best example is provided by polydimethylsiloxane vulcanizates, which exhibit practically no prolonged relaxations (8, 9). However, the networks of most synthetic rubbers, including natural rubber, usually show very persistent relaxations which impede a close approach to the equilibrium condition (1-8). 

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 assemblage of chains is constructed to represent the affine network model of rubber elasticity in which all network junction positions are subject to the same affine transformation that characterizes the macroscopic deformation. In the affine network model, junction fluctuations are not permitted so the model is simply equivalent to a set of chains whose end-to-end vectors are subject to the same affine transformation. All atoms are subject to nonbonded interactions in the absence of these interactions, the stress response of this model is the same as that of the ideal affine network. 

Both natural and synthetic rubber are commercially used in the manufacture of a variety of goods. As mentioned earlier, rubbers are elastomeric polymers, characterized by the presence of a network structure that may be temporarily deformed when subjected to external forces. 

A cross-linked rubber of undeformed cross-section 30 mm x 2 mm is stretched at 300 K to twice its original length by subjecting it to a load of 15 N. If the density p of the rubber is 950 kg m, what is the mean molar mass M of the network chains ... 

Meanwhile, developments in polymer science established that most long-chain linear polymers above their glass-transition temperatures can also exhibit rubberlike behavior whereby a network of molecular entanglements can serve the function of chemical cross links for deformation histories with oscillation periods shorter than the relaxation times of entanglement drift. It is this form of behavior of glassy polymers resembling that of rubbers which is a subject of principal concern and is discussed in Section 6.7. 

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