Elasticity, rubber deformations

Secondly a broader MMD leads to a higher value of M, the average which is mainly responsible for the elastic behaviour of the melt, and thus for the recoil after deformation and solidification. These frozen-in rubber-elastic deformations cause the behaviour of shrink-films. 

Melt fracture results from a too large rubber-elastic deformation. This is governed by the polymer behaviour and by the rate of deformation. The strain rate must be lowered, which may be accomplished by a lower, and therefore unattractive, rate of production. The time scale of the elastic deformation can also be increased in another way, namely by making the conical channel to the die more pointed the same strain is then reached after a longer time. This goes at the cost of extra pressure and power, since the resistance of the chaimel is increased. 

Frozen-in stresses originate from the rabber-elastic behaviour of the melt the rubber- elastic deformations (chain orientations) are frozen-in upon cooling and remain present as latent stresses. 

The rubber-elastic deformation of the liquid stream can reach such high values that the liquid breaks. Though the remaining fragments will stick together in a further part of the die channel, this melt fracture forms a notorious limitation in the rate of production with extrusion processes. The only remedy is to increase the time scale of deformation, so that the elastic behaviour is less outspoken. 

Shrinkage may also be anisotropic, namely when chain orientations are present. As discussed in Chapter 5, these orientations result from rubber-elastic deformations in the melt they are, therefore, found in parts where the melt has been rapidly cooled under conditions of a high rate of strain. Shrinkage is higher in the orientation direction than across, so that, for instance, a flat disk, injected from its centre, tends to deform into a saddle-like shape (warping). 

Rubber elastic deformations are coupled with viscous flow (and tend toward elastic reverse deformation when the flow ceases). 

If one takes into account the conformational changes of the polymer chain, the isotherm of chains longer than 300 atoms can be described quantitatively [19, 21]. In a simple picture one can assume that all polymer chains are bound to the aqueous phase by the head group, while the end group is at the polymer air interface (see Fig. 6a). These chains act like springs that are elongated by the film thickness. Therefore, due to this rubber elastic deformation these chains store an elastic free energy [22-24] ... 

In analyzing this problem it is necessary to distinguish between processes that are restricted to the amorphous phase and those that involve a crystal-liquid phase transition. Rubber elastic deformation involves an increase in the mean-square end-to-end distance of the chains in the liquid state, in compliance with the imposed macroscopic strain. Closely associated with this phenomenon is the deformation... 

There is one obvious drawback of high-hysteresis rubber. In normal rolling operation, considerable elastic deformations still take place in the tyre wall, and high-loss tyres will consume fuel and generate considerable heat. The way out is to use a low-loss tyre covered with a high-loss tread - another example of design using composite materials (Fig. 26.9). 

Natural rubber is known to be more elastic (deformable) than gutta-percha. Is there any obvious difference in the structures in the two strands which might lead to a difference in the properties of the real polymers ... 

The alternative option for counteracting cavitation damage is the use of a resilient material such as rubber. The mechanical forces attendant on collapse of the bubbles are absorbed by elastic deformation of the resilient material. 

Small deformations of the polymers will not cause undue stretching of the randomly coiled chains between crosslinks. Therefore, the established theory of rubber elasticity [8, 23, 24, 25] is applicable if the strands are freely fluctuating. At temperatures well above their glass transition, the molecular strands are usually quite mobile. Under these premises the Young s modulus of the rubberlike polymer in thermal equilibrium is given by ... 

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... 

The size and shape of polymer chains joined in a crosslinked matrix can be measured in a small angle neutron scattering (SANS) experiment. This is a-chieved by labelling a small fraction of the prepolymer with deuterium to contrast strongly with the ordinary hydrogenous substance. The deformation of the polymer chains upon swelling or stretching of the network can also be determined and the results compared with predictions from the theory of rubber elasticity. 

The molecular models of rubber elasticity relate chain statistics and chain deformation to the deformation of the macroscopic material. The thermodynamic changes, including stress are derived from chain deformation. In this sense, the measurement of geometric changes is fundamental to the theory, constitutes a direct check of the model, and is an unambiguous measure of the mutual consistency of theory and experiment. 

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. 

The characteristic property of elastomers is their rubber-elastic behavior. Their softening temperature lies below room temperature. In the unvulcanized state, i.e. without crosslinking of the molecular chains, elastomers are plastic and thermo-formable, but in the vulcanized state—within a certain temperature range — they deform elastically. Vulcanization converts natural rubber into the elastic state. A large number of synthetic rubber types and elastomers are known and available on the market. They have a number of specially improved properties over crude rubber, some of them having substantially improved elasticity, heat, low-temperature, weathering and oxidation resistance, wear resistance, resistance to different chemicals, oils etc. 

It can be assumed that the orientation of the amorphous regions is a result of the deformation of a rubber-elastic network. Therefore, it can be expected that crystallization during spinning occurs at the neck, where the deformation is maximal. The amorphous phase develops into a load-bearing factor which is related to its orientation, as expressed by Hermans orientation factor. 

Note If a perfect network is in the rubbery state then, on macroscopic deformation of the network, all of its chains are elastically active and display rubber elasticity. 

Rheology is the science of the deformation and flow of matter. It is concerned with the response of materials to applied stress. That response may be irreversible viscous flow, reversible elastic deformation, or a combination of the two. Control of rheology is essential for the manufacture and handling of numerous materials and products, eg, foods, cosmetics, rubber, plastics, paints, inks, and drilling muds. Before control can be achieved, there must be an understanding of rheology and an ability to measure rheological properties. 

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. 

With this condition, there are a great many possible choices for the form of W as a function of Our ultimate purpose in the phenomenologic study of rubber elasticity is to find out its form applicable for an accurate and coherent description of the elastic behavior of rubber-like materials under various modes of deformation. We may use /j, J2, and J3 for the set of /<, which are defined by... 

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