By I. M. Ward
Ward and Sweeney, either affiliated with the IRC in Polymer technology and expertise on the collage of Leeds, united kingdom, introduce the mechanical habit of good polymers, including new fabric on mechanical relaxations and anisotopy, composites modeling, nonlinear viscoelasticity, and fracture of difficult polymers to this moment version. The obtainable strategy of the publication has been retained for this version, with every one bankruptcy designed to be self-contained and the idea and purposes of the topic brought the place acceptable. bankruptcy difficulties and mathematical appendices are integrated. The ebook is for college students of fabrics, chemistry, physics, and engineering.
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Extra resources for An introduction to Mechanical Properties of Solid Polymers
67, 3202 (1971). 18. Taylor, D. J. , Stepto, R. F. , Jones, R. , Macromolecules, 32, 1978 (1999). 19. Cail, J. , Taylor, D. J. , Stepto, R. F. , Macromolecules, 33, 4966 (2000). Problems for Chapters 2 and 3 1. The tensile stress ó in an ideal rubber when simply extended to a length º times its initial length is given by ó ¼ NkT (º2 À ºÀ1 ) Explain without giving any mathematical details the physical model that leads to this expression. A sample of polyisoprene (density 1300 kg mÀ3 , monomer of relative molar mass 68) has a shear modulus of 4 3 105 Pa at room temperature.
40 RUBBER-LIKE ELASTICITY Three additional assumptions are introduced: 1. In either the strained or unstrained state, each junction point may be regarded as ﬁxed at its mean position. 2. The effect of the deformation is to change the components of the vector length of each chain in the same ratio as the corresponding dimensions of the bulk material (the ‘afﬁne’ deformation assumption). 3. 20). 6). This difference is related to changes in entropy, and so to tensile force. 2, we can restrict our discussion to the case of normal strain without loss of generality.
Trans and gauche conformations. Conﬁguration is retained to refer to the arrangement of the whole molecular chain. THE STATISTICAL THEORY 37 Expand, giving Á l XÀ 2 l1 þ l22 þ . . l2n þ l 1 . l 2 þ l 1 . l 3 þ . . þ l nÀ1 . l n q 1 q r2 ¼ but l21 ¼ l22 ¼ l2n and l m . l n ¼ lm ln cos Ł. In a freely jointed chain Ł can have any value; hence Ól m . l n ¼ 0, m 6¼ n. e. for a chain of 100 bonds between cross-links the maximum extensibility is 10. 3 The entropy of a single chain The expression just derived indicates the reason for the high extensibility of lightly cross-linked rubbers and serves to introduce the important concept of a mean square length, but yields no information on the probability of a chain having a particular end-to-end length.