Junction rubber

The shape factor ( d/hg) reflects the boundary condition s constraint on rubber flow during deformation, and can be considered as a measure of tightness for a junction. The shape factor, or the ratio d/hg, can be used to calculate the stored energy with a junction rubber between two spherical filler particles [86,87] ... 

If it is assumed that for a junction rubber the energy loss takes place near the circular peripherals of the rubber-filler particle interface, the dissipated energy for a cyclic displacement of amplitude Ax and strain rate d/dt (x/hg) can be estimated to be... 

The frictional behaviour of rubber is quite different from that of metals. In Chapter 25 we showed that when metallic surfaces were pressed together, the bulk of the deformation at the points of contact was plastic and that the friction between the surfaces arose from the forces needed to shear the junctions at the areas of contact. 

Traditional rubbers are shaped in a manner akin to that of common thermoplastics. Subsequent to the shaping operations chemical reactions are brought about that lead to the formation of a polymeric network structure. Whilst the polymer molecular segments between the network junction points are mobile and can thus deform considerably, on application of a stress irreversible flow is prevented by the network structure and on release of the stress the molecules return to a random coiled configuration with no net change in the mean position of the Junction points. The polymer is thus rubbery. With all the major rubbers the... 

Moreover, we must pay attention to the points that in the cross-linked rubber, the cross-link stops the sliding of molecules and has its own excluded volume. Generally, in the calculation of the stress-strain relation, the four-chain model is used for the cross-link junction and recently the eight-chain model is considered to be more realistic and available. Thus, it is quite reasonable to consider that the bulky excluded volume that a cross-link junction possesses must be a real obstacle for the orientation of molecules, just like the case observed in Figure 18.16B. 

Addition of rubber particles of 30% to 100% by weight to cement with a grain size of approximately 40 to 60 mesh (0.4 to 0.25 mm) will produce a lightweight cement. The addition of rubber particles also creates a low permeability. The compositions are advantageous for cementing zones subjected to extreme dynamic stresses such as perforation zones and the junctions of branches in a multi-sidetrack well. Recycled, expanded polystyrene lowers the density of a hydraulic cement formulation and is an environmentally friendly solution for downcycling waste materials. 

According to the importance of the cross-links, various models have been used to develop a microscopic theory of rubber elasticity [78-83], These models mainly differ with respect to the space accessible for the junctions to fluctuate around their average positions. Maximum spatial freedom is warranted in the so-called phantom network model [78,79,83], Here, freely intersecting chains and forces acting only on pairs of junctions are assumed. Under stress the average positions of the junctions are affinely deformed without changing the extent of the spatial fluctuations. The width of their Gaussian distribution is predicted to be... 

We might well expect this differing stereochemistry to have a marked effect on the properties of the polymer, and this is borne out by the two naturally occurring polyisoprenes, natural rubber and gutta percha. The former, which before vulcanisation is soft and tacky, has all cis junctions in its chains while the latter, which is hard and brittle, has all trans junctions. 

The concept of affine deformation is central to the theory of rubber elasticity. The foundations of the statistical theory of rubber elasticity were laid down by Kuhn (JJ, by Guth and James (2) and by Flory and Rehner (3), who introduced the notion of affine deformation namely, that the values of the cartesian components of the end-to-end chain vectors in a network vary according to the same strain tensor which characterizes the macroscopic bulk deformation. To account for apparent deviations from affine deformation, refinements have been proposed by Flory (4) and by Ronca and Allegra (5) which take into account effects such as chain-junction entanglements. 

Classical molecular theories of rubber elasticity (7, 8) lead to an elastic equation of state which predicts the reduced stress to be constant over the entire range of uniaxial deformation. To explain this deviation between the classical theories and reality. Flory (9) and Ronca and Allegra (10) have separately proposed a new model based on the hypothesis that in a real network, the fluctuations of a junction about its mean position may may be significantly impeded by interactions with chains emanating from spatially, but not topologically, neighboring junctions. Thus, the junctions in a real network are more constrained than those in a phantom network. The elastic force is taken to be the sum of two contributions (9) ... 

Ronca and Allegra (12) and Flory ( 1, 2) assume explicitly in their new rubber elasticity theory that trapped entanglements make no contribution to the equilibrium elastic modulus. It is proposed that chain entangling merely serves to suppress junction fluctuations at small deformations, thereby making the network deform affinely at small deformations. This means that the limiting value of the front factor is one for complete suppression of junction fluctuations. 

A product used in upholstery and as a resilient packaging material. It is made by spraying a loose mat of curled animal hair with latex and applying heat to vulcanise the rubber. The resilience of the product comes from the fibres, the junction points of which are anchored by the rubber. 

Hose may be hand built using a three roll wrapping machine. The centres of the three rolls form an equilateral triangle. The hose during construction sits on the junction between the two lower rollers and pressure is exerted to consolidate the composite by the upper movable roller. An extruded inner liner, after fitting to a solid inner mandrel, is placed into the machine between the rollers and then the various layers of rubber coated or resorcinol-formaldehyde-latex treated, fabric are applied in a spiral form, with overlap. Once the reinforcement layers have been added the cover rubber is applied and a cloth, usually nylon, is spirally wrapped around the constructed hose using the roller system. The hose is now ready for vulcanisation. 

Figure 5.11 Dependence of the reduced equilibrium shear modulus, Ge/wg// 7" on the molar ratio of [OH]/[NCO] groups, ah, for poly(oxypropylene)triol (Niax LG 56)-4,4 -diisocyanatodiphenylmethane system (—-) limits of the Flory-Erman junction fluctuation rubber elasticity theory. The dependence has been reconstructed from data of ref. [78]...

This is a theoretical study on the entanglement architecture and mechanical properties of an ideal two-component interpenetrating polymer network (IPN) composed of flexible chains (Fig. la). In this system molecular interaction between different polymer species is accomplished by the simultaneous or sequential polymerization of the polymeric precursors [1 ]. Chains which are thermodynamically incompatible are permanently interlocked in a composite network due to the presence of chemical crosslinks. The network structure is thus reinforced by chain entanglements trapped between permanent junctions [2,3]. It is evident that, entanglements between identical chains lie further apart in an IPN than in a one-component network (Fig. lb) and entanglements associating heterogeneous polymers are formed in between homopolymer junctions. In the present study the density of the various interchain associations in the composite network is evaluated as a function of the properties of the pure network components. This information is used to estimate the equilibrium rubber elasticity modulus of the IPN. 

Here, v is Poisson s ratio which is equal to 0.5 for elastic materials such as hydrogels. Rubber elasticity theory describes the shear modulus in terms of structural parameters such as the molecular weight between crosslinks. In the rubber elasticity theory, the crosslink junctions are considered fixed in space [19]. Also, the network is considered ideal in that it contained no structural defects. Known as the affine network theory, it describes the shear modulus as... 

Thus, this consideration shows that the thermoelasticity of the majority of the new models is considerably more complex than that of the phantom networks. However, the new models contain temperature-dependent parameters which are difficult to relate to molecular characteristics of a real rubber-elastic body. It is necessary to note that recent analysis by Gottlieb and Gaylord 63> has demonstrated that only the Gaylord tube model and the Flory constrained junction fluctuation model agree well with the experimental data on the uniaxial stress-strain response. On the other hand, their analysis has shown that all of the existing molecular theories cannot satisfactorily describe swelling behaviour with a physically reasonable set of parameters. The thermoelastic behaviour of the new models has not yet been analysed. 

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