Rubbers elasticity

Rubber elasticity has a long-standing history. Ancient Mesoamerican people were processing rubber by 1600 BC [1], which predated development of the vulcanization process by 3500 years. They made solid rubber balls, sofid and hollow rubber human figurines, wide rubber bands to haft stone ax heads to wooden handles, and other items. 

Kubo, R., Rubber Elasticity/The reprint of the first edition (in Japanese), Syokabo, Tokyo, Japan (1996). 

For a polymer to exhibit rubber elasticity, it must have two properties  

Treloar, L.R.G., The Physics of Rubber Elasticity, Clarendon Press, Oxford, 1975. 

Treloar LRG (1975) The physics of rubber elasticity, 3rd (edn) Oxford University Press, London, chap VI 

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. 

The bracket (1 — 2/f) was introduced into the theory of rubber elasticity by Graessley [23], following an idea of Duiser and Staverman [28]. Graessley discussed the statistical mechanics of random coil networks, which he had divided into an ensemble of micronetworks. 

Langley, N.R. and Polmanteer, K.E., Role of chain entanglements in rubber elasticity. Polym. Prep. Am. Chem. Soc. Div. Polym. Chem., 13(1), 235-240 (1972). 

S. L. Aggrawal and co-workers, iuj. E. Mark, M.,Mdvances in Elastomer and Rubber Elasticity, Plenum Press, New York, 1968, p. 16. 

An increase in the swelling degree usually results in lowering elastic modulus. According to the rubber elasticity theory [116-118] the shear modulus of the gel G can be expressed as  

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]. 

Substituting Eq. (12) into Eq. (11) permits us to derive the Hookean spring force law, well-known in the classical theory of rubber elasticity  

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  

Roasting A metallurgical process in which a sulfide ore is heated in air, forming either the free metal or the metal oxide, 539 Rock candy, 17 Rowland, F. Sherwood, 311 Rubber elasticity, 470 Ruminant, 620 Rusting, 87 

The effective molecular mass Mc of the network strands was determined experimentally from the moduli of the polymers at temperatures above the glass transition (Sect. 3) [11]. lVlc was derived from the theory of rubber elasticity. Mc and the calculated molecular mass MR (Eq. 2.1) of the polymers A to D are compared in Table 3.1. 

Crosslinked polymers are rather peculiar materials in that they never melt and they exhibit entropic elasticity at elevated temperatures. The present review on the influence of crosslink density is structured around model polymers of uniform composition but with widely varying numbers of crosslinks. The degree of crosslinking in the polymers was verified by use of the theory of rubber elasticity. 

The above equations gave reasonably reliable M value of SBS. Another approach to modeling the elastic behavior of SBS triblock copolymer has been developed [202]. The first one, the simple model, is obtained by a modification of classical rubber elasticity theory to account for the filler effect of the domain. The major objection was the simple application of mbber elasticity theory to block copolymers without considering the effect of the domain on the distribution function of the mbber matrix chain. In the derivation of classical equation of rabber elasticity, it is assumed that the chain has Gaussian distribution function. The use of this distribution function considers that aU spaces are accessible to a given chain. However, that is not the case of TPEs because the domain also takes up space in block copolymers. 

Mineral oils also known as extender oils comprise of a wide range of minimum 1000 different chemical components (Figure 32.6) and are used extensively for reduction of compound costs and improved processing behaviors.They are also used as plastisizers for improved low temperature properties and improved rubber elasticity. Basically they are a mixture of aromatic, naphthanic, paraffinic, and polycyclic aromatic (PCA) materials. Mostly, 75% of extender oils are used in the tread, subtread, and shoulder 10%-15% in the sidewall approximately 5% in the inner Uner and less than 10% in the remaining parts for a typical PCR tire. In total, one passanger tire can contain up to 700 g of oil. 

---