Cross-linking rubber elasticity

Polyolefins. In these thermoplastic elastomers the hard component is a crystalline polyolefin, such as polyethylene or polypropylene, and the soft portion is composed of ethylene-propylene rubber. Attractive forces between the rubber and resin phases serve as labile cross-links. Some contain a chemically cross-linked rubber phase that imparts a higher degree of elasticity. 

Even with this assumption, you can tackle the problem in various ways. We will use the simple development described in Tre-loar s classic book on robber elasticity,59 but advanced students should start with Flory and go from there. Most simple models, including the one we will describe here, give the same force/deformation dependence, but the prefactors can be different. (Flory also gets an additional term that is important in describing swelling, but not simple deformation). We start with a block of lightly cross-linked rubber that is strained parallel to a set of Cartesian axes, as illustrated in Figure 13-53. 

Dispersion of an elastomer with extremely high stability to solvents, self-cross-linking, very elastic rubber-like film, compatible with most fillers. 

The properties of block copolymers differ from those of a blend of the correponding homopolymers or a random copolymer (Chapter 7) with the same overall composition. An important practical example is the ABA-type styrene/butadiene/styrene triblock copolymer. These behave as thermoplastic elastomers. Ordinary elastomers are cross-linked by covalent bonds, e.g., vulcanization (see Chapter 2) to impart elastic recovery property, as without this there will be permanent deformation. Such cross-linked rubbers are therraosets and so cannot be softened and reshaped by molding. However, solid thermoplastic styrene/butadiene/styrene triblock elastomers can be resoftened and remolded. This can be explained as follows. At room temperature, the triblock elastomers consist of glassy, rigid, polystyrene domains... 

There is a definite difference in elastic behavior between linear and cross-linked rubbers. A sample of a cross-linked, or vulcanized, rubber is... 

PROPERTIES OF SPECIAL INTEREST Modulus/flexibility, elasticity, toughness, processibiUty, excellent optics and electrical properties, superior heat resistance, and UV stability over cross-linked rubbers such as EPDM and EPM, low brittleness temperature, good chemical resistance to common solvents, and good heat seal. 

The behavior of weakly cross-linked rubber was described in Section 11.1 as entropy-elastic. If this material is deformed, the chains are displaced from their equilibrium positions and brought into a state which is en-tropically less favorable. Because of the weak cross-linking, the chains are unable to slip past one another. On relaxation, the chains return from the ordered position to a disordered one the entropy increases. The phenomenon can be described in various ways. Seen thermodynamically, the rubber elasticity is related to a lowering of entropy on deformation. From the molecular point of view, the molecular particles are forced to adopt an... 

There is an extensive body of literature describing the stress-strain response of rubberlike materials that is based upon the concepts of Finite Elasticity Theory which was originally developed by Rivlin and others [58,59]. The reader is referred to this literature for further details of the relevant developments. For the purposes of this paper, we will discuss the developments of the so-called Valanis-Landel strain energy density function, [60] because it is of the form that most commonly results from the statistical mechanical models of rubber networks and has been very successful in describing the mechanical response of cross-linked rubber. It is resultingly very useful in understanding the behavior of swollen networks. 

The thermoplastic elastomers (TPE) are a new class of the polymeric materials, which combine the properties of the chemically cross-linked rubbers and easiness of processing and recycling of the thermoplastics [1-8], The characteristics of the TPE are phase micrononuniformity and specific domain morphology. Their properties are intermediate and are in the range between those, which characterize the polymers, which produce the rigid and elastic phase. These properties of TPE, regardless of its type and structure, are a function of its type, structure and content of both phases, nature and value of interphase actions and manner the phases are linked in the system. 

An elastomer (a rubber) may be defined as a material which may be stretched by 100% and on release of the stretching force it retracts, or springs back, rapidly. This elasticity was always associated with vulcanized (cross-linked) rubber and, is due to the... 

It is important to observe that the weighting coefficients are fixed at the time of the polymer-wall reaction(they are quenched variables ). In general, they may correspond to the equilibrium configuration of the system at a slab width Lq L. Thus, the calculated properties are bound to depend on the preparation conditions . There is a strong analogy with the elasticity of cross-linked rubbers, as discussed by Deam and Edwards[27]. 

In Fignre 5, the storage modulus of a typical cross-linked rubber is compared to that of a PSA made from a mixture of the rubber and tackifier. The rubber has a low which is why it is soft and mbbery at room (or use) temperature, but its modulus is too high for it to be a PSA. Addition of tackifier decreases the modulus below the Dahlquist criterion and allows for the mixture to be a PSA. The effect of dilution of the rubber network with a tackifier can be predicted by rnbber elasticity theory nsing the equation below (31,32). The effect of fillers can also be predicted. 

Because of the entropic origin, the above property is called the entropy elasticity. It is not limited to Ganssian chains. Any chain that has a finite size, inclnding ideal chains and real chains, has this elasticity. By the same reason, a rubber is elastic. A rubber is a cross-linked polymer. A partial chain between two cross-links behaves elastically, giving rise to the elasticity of the material as a whole. 

In the field of rubber elasticity both experimentalists and theoreticians have mainly concentrated on the equilibrium stress-strain relation of these materials, i e on the stress as a function of strain at infinite time after the imposition of the strain > This approach is obviously impossible for polymer melts Another complication which has thwarted the comparison of stress-strain relations for networks and melts is that cross-linked networks can be stretched uniaxially more easily, because of their high elasticity, than polymer melts On the other hand, polymer melts can be subjected to large shear strains and networks cannot because of slippage at the shearing surface at relatively low strains These seem to be the main reasons why up to some time ago no experimental results were available to compare the nonlinear viscoelastic behaviour of these two types of material Yet, in the last decade, apparatuses have been built to measure the simple extension properties of polymer melts >. It has thus become possible to compare the stress-strain relation at large uniaxial extension of cross-linked rubbers and polymer melts ... 

The mechanical properties of a polymer sample are determined by many factors. Resins vary from extremely flexible but shong rubbers to brittle weak materials such as the natural resins (Figure 2.11). Contrasts can be made in the ability to be stretched without permanent distortion (elasticity of cross-linked rubber), in the distortion caused by stretching (polyethene distorts if stfetched... 

Figure 9.2 shows experimental data for a silicone polymer similar to the one used in the squeeze flow experiment shown in Figure 1.9. The material is viscoelastic, since both the storage modulus and the dynamic viscosity are nonzero. At low frequencies the storage modulus goes to zero and the dynamic viscosity goes to a low-frequency asymptotic value. The deformation at low frequencies is sufficiently slow to allow the individual polymer chains to respond to the imposed strain hence, the response is viscous, and it is clear that the low frequency limit of n must be the zero-shear viscosity, t]q. At high frequencies the individual chains are unable to respond and the stress is entirely the consequence of deformation of the entangled network. In this limit the polymer melt is indistinguishable from a cross-linked rubber network, and the deformation is that of an elastic body, with G going to an asymptotic value and rj to zero. The value of G in this rubbery plateau region is known as the shear modulus and is usually denoted G.

The processing of elastomers began in 1839 with the discovery of vulcanization by Goodyear. Instead of the non-cross-linked natural rubber, as it was already being used by the Indians of South and Central America, a cross-linked, highly elastic material (rubber) was further developed and was then made available for many, especially technical, applications. Elastomers are indispensable in our modern world. In particular, their almost infinitely adjustable elasticity, thermal stability, high wear resistance, and resistance to media make them indispensable for almost all industrial applications [1]. 

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