Rubber upon deformation

As illustrated in Figure 2, elastomeric networks consist of chains joined by multifunctional junctions. As early as 1934, it was suggested by Guth and Mark and by Kuhn that the elastic retractive force exhibited by rubber upon deformation arises from the entropy decrease associated with the diminished number of conformations available to deformed polymer chains. It is, therefore, of primary interest to study the statistics of a polymer chain and to establish the elastic equation of state for a single chain. 

Above a critical hller concentration, the percolation threshold, the properties of the reinforced rubber material change drastically, because a hller-hUer network is estabhshed. This results, for example, in an overproportional increase of electrical conductivity of a carbon black-hUed compound. The continuous disruption and restorahon of this hller network upon deformation is well visible in the so-called Payne effect [20,21], as represented in Figure 29.5. It illustrates the strain-dependence of the modulus and the strain-independent contributions to the complex shear or tensUe moduli for carbon black-hlled compounds and sUica-hUed compounds. 

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. 

Stress relaxation is the time-dependent change in stress after an instantaneous and constant deformation and constant temperature. As the shape of the specimen does not change during stress relaxation, this is a pure relaxation phenomenon in the sense defined at the beginning of this section. It is common use to call the time dependent ratio of tensile stress to strain the relaxation modulus, E, and to present the results of the experiments in the form of E as a function of time. This quantity should be distinguished, however, from the tensile modulus E as determined in elastic deformations, because stress relaxation does not occur upon deformation of an ideal rubber. 

Rubber technology is a mature science with a history going back some 150 years or more. Over the years a number of scientific discoveries (e.g. curing with sulphur to increase resilience and recovery, and the use of antioxidants to lengthen service life) have contributed to the material s dominance in applications requiring elasticity/recovery upon deformation combined with durability. Additives are used in rubbers in order to ensure that they possesses the correct properties to be processed, have the physical properties appropriate for the application, and sufficient stability and resistance to ageing in service. There are three basic steps associated with the processing of rubber ... 

The elastomeric ethylene-propylene copolymers (EPR) [5, 6] are also random copolymers but have an amorphous structure with a typical rubber-like elasticity and high elongation upon deformation. Amorphous character is achieved if the structure of the polymer is essentially random with a minimum of molecular regularity and a moderately high ethylene content. Ethylene content in EPR s are typically about 65 mole%. 

The treatment of rubber elasticity presented above represents one possible extreme of behavior. The assumption that the crosslink points in the network are fixed at their mean positions and that the crosslink points deform affinely gives rise to this extreme. In real polymer networks, each crosslink point finds itself in the neighborhood of many other crosslink points. This can be verified by estimating the order of magnitude of the concentration of crosslinks and then calculating the number of crosslink points that would be found within some reasonable distance (perhaps 2 nm) of any given crosslink point. Upon deformation, the affine assumption insists that all of these crosslinks remain in the neighborhood of the particular crosslink point under consideration and, moreover, that their relative positions are fixed. 

Conversely, in the behaviour of a substance like cellulose upon deformation certain features remain akin to the general picture of network structure developed in rubber. 

The selection of the dominant deformation mechanism in the matrix depends not only on the properties of this matrix material but also on the test temperature, strain rate, as well as the size, shape, and internal morphology of the rubber particles (BucknaU 1977, 1997, 2000 Michler 2005 Michler and Balta-Calleja 2012 Michler and Starke 1996). The properties of the matrix material, defined by its chemical structure and composition, determine not rally the type of the local yield zones and plastic deformation mechanisms active but also the critical parameters for toughening. In amorphous polymers which tend to form fibrillated crazes upon deformation, the particle diameter, D, is of primary importance. Several authors postulated that in some other amorphous and semiciystalline polymers with the dominant formation of dUatational shear bands or extensive shear yielding, the other critical parameter can be the interparticle distance (ID) (the thickness of the matrix ligaments between particles) rather than the particle diameter. 

In other theories of rubber elasticity, the network structure is explicitly considered. However, the polymer on the surface is taken to be fixed (according to an affine deformation) upon deformation. - A truly statistical mechanical theory would also treat the surface statistically. More fundame ntally, however, in these theories the fixed point character of the surface i hen completely determines the behavior of the bulk material. This would appear to be nonsense in the thermodynamic limit of infinite volume, unless the fixed surface were of finite extent. In this case, the theory is no longer statistical in nature. 

The theory of rubber elasticity is largely based on thermodynamic considerations. It will be briefly discussed as an example of how thermodynamics can be applied in polymer science. Eor more detailed information the reader is referred to the various textbooks [10-13]. It is assumed that there is a three-dimensional network of chains, that the chain units are flexible and that individual chain segments rotate freely, that no volume change occurs upon deformation, and that the process is reversible (i.e., true elastic behavior). Another usual assumption is that the internal energy U of the system does not change with deformation. Eor this system the first law of thermodynamics can be written as ... 

At the end of the cross-hnking process, the topology of the mesh is composed of the different entities represented in Figure 6 (16,57-59). An elastically active junction is one joined by at least three paths to the gel network (60,61). An active chain is one terminated by an active jimction at both its ends. Rubber-like elasticity is due to elastically active chains and jimctions. Specifically, upon deformation the number of configurations available to a chain decreases and the resulting decrease in entropy gives rise to the retractive force. 

Upon creating a contact hoi ween t he elastomer and the solid, the surface energy decrca.ses. hut the rubber is deformed. The (uiergy of the contact of radius R in a film of tliickmvss e cran he written as... 

Elastomers are crosslinked rubbery polymers (i.e. rubbery networks) that can be stretched easily to high extensions (e.g. 3x to lOx their original dimensions) and which rapidly recover their original dimensions when the applied stress is released. This extremely important and useful property is a reflection of their molecular structure in which the network is of low crosslink density. The rubbery polymer chains become extended upon deformation but are prevented from permanent flow by the crosslinks, and driven by entropy, spring back to their original positions on removal of the stress. The word rubber, often used in place of elastomer, preferably should be used for describing rubbery polymers which are not crosslinked. 

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 contouring of the calender rolls by grinding in order to counteract the natural deflection and the deflection set up by the work being done with rubber stock load is a precision job and in most cases it is done by trial and error method. The nip pressure per inch width of the roll for most rubber compounds has been extensively studied by scientists in the Dunlop Rubber Company [ref Paper "Estimation of the shear deformation exerted by a roll-mill upon a rubber compound" by T.S. Ng, G. Angerer, Dunlop Forschung, Dunlop-Strasse 2, Hanau, Federal Republic of Germany, Presented at the Jahrestagung der... 

A powerful technique for the study of orientation and dynamics in viscoelastic media is line shape analysis in deuteron NMR spectroscopy [1]. For example, the average orientation of chain segments in elastomer networks upon macroscopic strain can be determined by this technique [22-31]. For a non-deformed rubber, a single resonance line in the deuterium NMR spectrum is observed [26] while the spectrum splits into a well-defined doublet structure under uniaxial deformation. It was shown that the usual network constraint on the end-to-end vector determines the deuterium line shape under deformation, while the interchain (excluded volume) interactions lead to splitting [26-31]. Deuterium NMR is thus able to monitor the average segmental orientation due to the crosslinks and mean field separately [31]. 

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