Rubber advanced theories

Although the basic concept of macromolecular networks and entropic elasticity [18] were expressed more then 50 years ago, work on the physics of rubber elasticity [8, 19, 20, 21] is still active. Moreover, the molecular theories of rubber elasticity are advancing to give increasingly realistic models for polymer networks [7, 22]. 

From his early youth, under his father s influence, K. H. Meyer had retained a keen interest in biological problems, as was evident from his study of the phenomena of narcosis, which he pursued during his stay in industry. As a natural consequence, he extended his thoughts to biological problems, and evolved a quantitative theory of muscular contraction (in collaboration with Picken), based on analogies with the elasticity of rubber. With J. F. Sievers, the permeability of synthetic membranes was investigated, and a mathematical treatment of the phenomenon was advanced which was later applied to living membranes. 

Above about 45°C, however, considerable yielding can be observed. Note that the transition between brittle and ductile behavior occurs at a temperature that is significantly below the T. Various theories have been advanced to explain yielding phenomena in polymers, some involving free volume arguments while others involve various types of molecular motion. As far as we can make out, none of these are entirely satisfactory and we won t discuss them here. Instead, we will finish off our discussion of stress/strain behavior by considering rubber elasticity. 

Eleinrich, G., Straube, E., and Helmis, G. Rubber elasticity of polymer networks theories. Advances in Polymer Science 85, 33 (1988). 

Theories have been advanced which account for the equilibrium amount of water absorbed and for the diffusion of water in natural rubber. The equilibrium swelling theory is an Improved version of that of Briggs et al. (2) in that a more reallsltic calculation of the rubber pressure is used. The diffusion theory accounts for the experimental observations both in predicting the correct order of magnitude of the diffusion coefficient of water in rubber and also its concentration dependence. 

We suggest that the S-B-S thermoplastic rubbers and the domain theory have produced a paradigm upon which the block polymer field advanced significantly. In reviewing the technological discovery of the S-B-S thermoplastic rubbers and the virtually simultaneous formation of a theory that enabled us to move rapidly toward commercialization, it was of interest to us to trace a pathway to discovery for the relatively small group concerned with it. We have set forth in Table II some selected events that we believe enabled us to very rapidly understand the physical phenomena and proceed. Table II is, then, not intended in any way to be a comprehensive illustration of the history of block polymers but is rather a discrete list of events leading to the discovery of S-B-S and S-I-S thermoplastic rubbers in our laboratory. 

Several theories based on molecular considerations have been advanced in order to interpret these and similar data. These theories have examined a.) the role of local regions of ordered chain segments or bundles locked into the rubber during network formation [40,41]. b.)... 

In recent years, important advances in the theory of rubber elasticity have been made. These include the introduction of the so-called phantom networks by Flory (I) and a two-network model for crosslinks and trapped entanglements by Ferry and coworkers (2,3). 

However, when applying results of the type (57), it must be borne in mind that such equations apply to the amorphous constituent only, and must fail at advanced degrees of stretch where crystalliisation sets in since the influence of crystallisation on the double refraction of rubber-like polymers is considerable In addition to the intrinsic double refraction of the gel frame, the swollen gel may show structural double refraction and adsorption double refraction. The structural, or textural , birefringence is caused by the difference between the refractive indices of polymer substance and solvent. It was estimated by Wiener for rod-shaped particles and for platelets. Wiener s theory is not applicable to rods of molecular thickness, and the structual double refraction caused by oriented long-chain molecules has not yet been accessible to a reliable theoretical treatment. 

In recent years, important advances in the theory of rubber elasticity have been made. These include the introduction of the so-called phantom networks by Flory and a two-network model for crosslinks and trapped entanglements by Ferry and co-workers, The latter builds on work by Flory and others on networks crosslinked twice, once in the relaxed state, and then again in the strained state. In other studies, Kramer and Graessley distinguished among the three kinds of physical entanglements as crosslink sites the Bueche-Mullins trap, the Ferry trap, and the Langley trap. 

The presence of salts in rubbers and leathers alters the sorption of water by these colloids (p. 436). For this reason Daynes(S) advanced a theory of diffusion as an osmotic phenomenon, the water being sorbed to equalise salt concentration differences... 

Ronca and Allegra, and independently Flory, advanced the hypothesis that real rubber networks show departures from these theoretical equations as a result of a transition between the two extreme cases of behaviour. In subsequent papers Floryl >l and Flory and Ermanl derived a theory based on this concept. At small deformations the fluctuations of the network junctions are constrained by the extensive interpenetration of neighbouring, but topologically remote chains. The severity of these constraints is characterized by the value of the parameter k (k - 0 corresponds to the phantom network, k = to the affine network). With increasing deformation these constraints become less restrictive in the direction of the principal extension. The parameter t describes the departures from affine transformation of the shape of the domains of constraints. The resulting stress-strain relation also takes the form of Eq. (7) with... 

Polymer networks at first sight appear to present insurmountable complexities that would seem to preclude rational analysis of their properties in molecular terms. The basic premise that underlies the theory of rubber elasticity, a premise that has been fully validated, permits circumvention of most of these complexities. Recent advances of theory in conjunction with a wealth of empirical evidence gained from well chosen, carefully executed experiments offer the prospect of a comprehensive understanding of the elastic equation of state and associated properties of elastomeric materials in the foreseeable future. 

Some of the most interesting advances in the theory of rubber elasticity are the various approaches being developed to take better account of chain entanglements [22, 30]. In the constraint theories, the focus is on the way the constraints are placed within the network structure, as discussed in the following section. 

Bragan, C. G. The Theory of Rubber Toughening of Brittle Polymers. In Multicomponent Polymer Systems, Advances in Chemistry, Series 99. Washington, 1971, p. 86... 

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