Subject rubber elasticity

Chapters 6 and 7 are added in response to the new integration in materials science. In Chapter 6, after the presentation of the main subjects, we give two examples to call attention to readers the fierce competition in industry for the application of liquid crystals crystal paint display and electronic devices. Within the next few years television and computer films will be revolutionalized both in appearance and in function. Military authority and medical industry are both looking for new materials of liquid crystals. The subject rubber elasticity in... 

In our first paper, the molecular theory of rubber elasticity was briefly reviewed, especially the basic assumptions and topics still subject to discussion (21). we will now focus on the effects of the structure and the functionality f of the crosslinks and the relevant theory. 

Since Meyer ) introduced the concept of kinetic molecular chain into the physics of polymers in 1932, remarkable progress has been made in the molecular-theoretical interpretation of elastic behavior of rubber vulcanizates and polymer solids in general2- ), and one can appreciate the present status of knowledge on this subject by a number of review articles and reference books. On the other hand, the phenomeno-logic approach to rubber elasticity has not aroused much interest in the field of polymer research. This is understandable because polymer scientists are primarily concerned with affairs of the molecular world. 

Analysis of networks in terms of molecular structure relies heavily on the kinetic theory of rubber elasticity. Although the theory is very well established in broad outline, there remain some troublesome questions that plague its use in quantitative applications of the kind required here. The following section reviews these problems as they relate to the subject of entanglement. 

Rubber and rubber-like materials are systems of molecules—monomers or mers—that are subject to two types of interactions. The first type are covalent interactions that tie monomers into long chains, which are typically 100 or more mers long. The second type are nonbonded interactions, which occur between pairs of mers that are not covalently bonded to each other. We are concerned here with an examination of how nonbonded interactions are generally treated in theoretical studies of rubber elasticity and with the limitations of this approach. 

The assemblage of chains is constructed to represent the affine network model of rubber elasticity in which all network junction positions are subject to the same affine transformation that characterizes the macroscopic deformation. In the affine network model, junction fluctuations are not permitted so the model is simply equivalent to a set of chains whose end-to-end vectors are subject to the same affine transformation. All atoms are subject to nonbonded interactions in the absence of these interactions, the stress response of this model is the same as that of the ideal affine network. 

Rubber is an extraordinary material with a rich history, shaped by a collection of intriguing characters and full of trials, tribulations and triumphs. There is so much good stuff that we devoted two of the chapters in our The Incredible World of Polymers CD to the subject. Here we will discuss the molecular basis of rubber elasticity. 

In this chapter, we first discuss the thermodynamics of rubber elasticity. The classical thermodynamic approach, as is well known, is only concerned with the macroscopic behavior of the material under investigation and has nothing to do with its molecular structure. The latter belongs to the realm of statistical mechanics, which is the subject of the second section, and has as its... 

The core of the book is devoted to subjects starting with anelastic behavior of polymers and rubber elasticity, but proceeds with greater emphasis in following chapters to mechanisms of plastic relaxations in glassy polymers and semicrystalline polymers with initial spherulitic morphology. Other chapters concentrate on craze plasticity in homo-polymers and block copolymers, culminating with a chapter on toughening mechanisms in brittle polymers. To make the... 

James and Guth developed a theory of rubber elasticity without the assumption of affine deformation [18,19,20]. They introduced the macroscopic deformation as the boundary conditions applied to the surface of the samples. Junctions are assumed to move freely under such fixed boundary conditions. The network chains (assumed to be Gaussian) act only to deliver forces at the junctions they attach to. They are allowed to pass through one another freely, and they are not subject to the volume exclusion requirements of real molecular systems. Therefore, the theory is called the phantom network theory. 

The polymer is cross-linked. In this case the dotted line in Figure 8.2 is followed, and improved rubber elasticity is observed, with the creep portion suppressed. The dotted line follows the equation E = 3nRT, where n is the number of active chain segments in the network and RT represents the gas constant times the temperature see equation (9.36). An example of a cross-linked polymer above its glass transition temperature obeying this relationship is the ordinary rubber band. Cross-linked elastomers and rubber elasticity relationships are the primary subjects of Chapter 9. 

Chapters 8 and 9 have introduced the concepts of the glass transition and rubber elasticity. In particular. Section 8.2 outlined the five regions of viscoelasticity, and Section 8.6.1.2 derived the WLF equation.This chapter treats the subjects of stress relaxation and creep, the time-temperature superposition principle, and melt flow. Parts of this topic are commonly called rheology, the science of deformation and flow of matter. 

In the field of rubber elasticity both experimentalists and theoreticians have mainly concentrated on the equilibrium stress-strain relation of these materials, i e on the stress as a function of strain at infinite time after the imposition of the strain > This approach is obviously impossible for polymer melts Another complication which has thwarted the comparison of stress-strain relations for networks and melts is that cross-linked networks can be stretched uniaxially more easily, because of their high elasticity, than polymer melts On the other hand, polymer melts can be subjected to large shear strains and networks cannot because of slippage at the shearing surface at relatively low strains These seem to be the main reasons why up to some time ago no experimental results were available to compare the nonlinear viscoelastic behaviour of these two types of material Yet, in the last decade, apparatuses have been built to measure the simple extension properties of polymer melts >. It has thus become possible to compare the stress-strain relation at large uniaxial extension of cross-linked rubbers and polymer melts ... 

The vitality and importance of the subject of elastomers and rubber elasticity are obvious from the above incomplete list of diverse topics, but also from the very wide organizational and geographical distribution of the authors. Various chapters in fact come from universities, industrial laboratories, and research institutes in the United States, Canada, England,... 

It is suggested that the reader perform additional reading on the subjects of the theory of rubber elasticity with especial emphasis on the thermodynamic approach to the theory. 

Since the publication of the second edition in 1983, the subject has advanced considerably in many respects, especially with regard to non-linear viscoelasticity, yield and fracture. We have altered some chapters very little, notably those dealing with viscoelastic behaviour and the earlier research on anisotropic mechanical behaviour and rubber elasticity, only adding sections to deal with the latest developments. 

All the powers of the French Academy of Sciences were needed chemical analysis, mechanical analysis, thermodynamics, alchemy, synthesis. But even Berthelot could not really provide much insight. The Laws of Rubber Elasticity were established by Joule, but even the wizards of British physics could not conjure up an explanation. Until the dawning of the molecular age, no real progress was likely on this subject. 

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