Origin of Rubber Elasticity

Wright et al. (23-24) discussed the elastic response of TPV using the micro-cellular modeling, in which three types of deformation such as elastic and plastic deformation of PP, elastic deformation of EPDM, and localized elastic and plastic rotation about PP junction points were considered. Their microcellular model suggests that EPDM domains are surrounded by the PP struts and the struts are connected with hinges. They were successful to elucidate the permanent deformation and stiffness and stress-strain relation of TPV. 

Boyce et al. (25-27) simulated the stress-strain relationship during compression of TPV using a one-dimensional constitutive model as well as the FEM technique. 

Their results suggest that a pseudocontinuous rubber phase develops as a result of drawing of PP ligaments and shearing of rubber particles. The thickness of PP ligaments appears to control the initial stiffness and stress. 

The offset in the deformation curve is a consequence of the permanent set imposed by the yielding of the PP dominant matrix, where the dispersed EPDM domains were highly elongated. According to rough estimation of the extension of EPDM domains, the localized strain in the EPDM domains was much greater than the overall applied strain. This means that the strain was concentrated on the rubber domains. 

The morphological feature of drawn TPV samples was also examined with TEM by Asami et al. (28). The sample preparation involved thin sectioning of the central part of the drawn TPV sample (uniaxially extended to a strain of 5.5). The observed TEM images are shown in Fig. 8.15 (TEM picmres of undrawn TPV and drawn TPV samples). 

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Kikuchi Y., Eukui T., Okada T., and Inoue T. Origin of rubber elasticity in thermoplastic elastomers consisting of crossUnked rubber particles and ductile matrix, J. Appl. Polym. Sci., Appl. Polym. Symp., 50, 261, 1992. 

This chapter lays the groundwork for the various topics discussed in subsequent chapters. The mathematics associated with the statistics of the isolated chain are developed starting with the bonding and structure found in small molecules. Several models of chain structure are presented. Finally, the size distribution of polymer chains is introduced and their description in terms of mathematical equations derived, origin of rubber elasticity, the nature of polymer crystalline and polymeric heat capacities and the miscibility of polyblends. 

Kikuchi, Y., Fukui, T., Okada, T. and Inoue, T. (1991) Elastic-plastic analysis of the deformation mechanism of PP-EPDM thermoplastic elastomer Origin of rubber elasticity. Polymer Engng Sci., 31, 1029-1032. 

FIGURE 17.11 The effect of ri (the number of statistical chain elements in a cord between cross-links) on the relation between stress and strain of a polymer gel in elongation. a0 is the force divided by the original cross-sectional area of a cylindrical test piece, v is twice the cross-link density, L is the length, and L0 the original length of the test piece. (After calculations by L. R. G. Treloar. The Physics of Rubber Elasticity. Clarendon, Oxford, 1975.)... 

With the basic structure of polymers of macromolecules clarified, scientists now searched for a quantitative understanding of the various polymerization processes, the action of specific catalysts, and initiation and inhibitors. In addition, they strived to develop methods to study the microstructure of long-chain compounds and to establish preliminary relations between these structures and the resulting properties. In this period also falls the origin of the kinetic theory of rubber elasticity and the origin of the thermodynamics and hydrodynamics of polymer solutions. Industrially polystyrene, poly(vinyl chloride), synthetic rubber, and nylon appeared on the scene as products of immense value and utility. One particularly gratifying, unexpected event was the polymerization of ethylene at very high pressures. 

There has been the question why the TPV materials with ductile thermoplastic matrix display rubber elasticity. Several models have been suggested to answer this question (41 7). Inoue group first analyzed the origin of mbber elasticity in TPVs (43). They constructed a two-dimensional model with four EPDM mbber inclusions in ductile PP matrix and carried out the elastic-plastic analysis on the deformation mechanism of the two-phase system by finite-element method (FEM). The FEM analysis revealed that, even at highly deformed states at which almost the whole matrix has been yielded by the stress concentration, the ligament matrix between mbber inclusions in the stretching direction is locally preserved within an elastic limit and it acts as an in-situ formed adhesive for interconnecting mbber particles. 

Finally, we note that glassy polymers close to the glass-transition temperature exhibit a strain-hardening response that is nearly purely entropic in origin and can be dealt with by employing the tools of rubber elasticity. 

Melt viscoelasticity is caused by physical entanglements of the molecules the stresses induced are of rubber elastic origin. The rate of stress relaxation is of viscous origin. Thus, low temperatures (or high relative molecular masses) promote long memories and hence large swell ratios high temperatures (or low relative molecular masses) promote short memories and hence small swell ratios. 

The principles of the modem physical theories of the deformation of rubber xerogels have already been dealt with in Chapter IV, p. 123. If a strip of raw rubber is rapidly extended, the molecules, which initially assumed randomly kinked forms, are stretched too. The more extended shape of the chains is a statistically less probable one corresponding to a lower entropy. en the piece of rubber is rapidly released again, it reassumes its original form in that the chains return to their, most probable configurations The entropy-character of rubber elasticity has been proven in that it exhibits a positive temperature coefficient. 

Similarly, one can derive the mean-square end-to-end distance =3l2lff. In the following, we will apply the Gaussian chain above to interpret the entropic origin of high elasticity of rubbers. 

To understand the mechanical properties of materials, it is important to consider first the microscopic origin of stress. In the usual gas or liquid of small molecules, the stress comes from the momentum transfer due to the intermolecular collision. In polymeric liquids, the stress is mainly due to the intramolecular force, and is directly related to the orientation of the bond vectors of the polymer. This idea, originated from the theory of rubber elasticity, is fundamental in the physics of polymeric materials. ... 

The molecular origin of the recovery from large deformations, which is the essence of rubber elasticity, was not recognized until the early 1930s. Evidence for this was the fact... 

Melt viscoelasticity is caused by physical entanglements of the molecules the stresses induced are of rubber elastic origin. The rate of stress relaxation is of... 

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