Elasticity of networks

A restriction will be made to polymer chains without strong and specific intersegmental forces, such as may exist in proteins and many other macromolecules. The reason is that the elasticity of networks composed of such chains cannot even be approached from the Gaussian coil point of view, since the chains are helical or at least partly so. At the moment no good theoretical treatment of these "proteinlike systems is available. 

The transition of the polymer from the rubbery to the glassy state principally changes the deformation behaviour and mechanical response of the material. The dominant role of intermolecular forces in the glassy state of polymer fully suppresses the effect of the conformational elasticity of network chains, at least at low strains. 

Here we will discuss three groups of simulation. In all cases we consider only systems in which the role of the conserved topology is explicitly taken into account. First we discuss some work on short chain networks, where the crosslinks are fixed in space. These simulations were used to investigate to what extent the entropic spring concept, which is the basis of the theory of elasticity of networks, is valid in systems in which the excluded volume interactions are present. We then review some and... 

Ion-exchange Resins. An ion-exchange resin is made up of particles of an insoluble elastic hydrocarbon network to which is attached a large number of ionisable groups. Materials commonly used comprise synthetic ion-exchange resins made, for example, by crosslinking polystyrene to which has been attached non-... 

By linking the chain ends of different molecules they form a type of network structure as long as the domains remain glassy. As the polymer is heated above the of the domain polymer block the domain molecules become mobile and on application of a stress the material flows like a thermoplastic. On cooling, new domains will be formed, thus regenerating the elastic state. 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

A large number of SAHs described in the literature combine synthetic and natural macromolecules in the network structure. The natural components are usually starch, cellulose, and their derivatives. It is assumed that introduction of rigid chains can improve mechanical properties (strength, elasticity) of SAH in the swollen state. Radical graft polymerization is one of the ways to obtain such SAH. 

Dusek, K. and Prins, W. Structure and Elasticity of Non-Crystalline Polymer Networks. VoL 6,... 

The elasticity of a polymer is its ability to return to its original shape after being stretched. Natural rubber has low elasticity and is easily softened by hearing. Flowever, the vulcanization of rubber increases its elasticity. In vulcanization, rubber is heated with sulfur. The sulfur atoms form cross-links between the poly-isoprene chains and produce a three-dimensional network of atoms (Fig. 19.17). Because the chains are covalently linked together, vulcanized rubber does not soften as much as natural rubber when the temperature is raised. Vulcanized rubber is also much more resistant to deformation when stretched, because the cross-... 

Networks obtained by anionic end-linking processes are not necessarily free of defects 106). There are always some dangling chains — which do not contribute to the elasticity of the network — and the formation of loops and of double connections cannot be excluded either. The probability of occurrence, of such defects decreases as the concentration of the reaction medium increases. Conversely, when the concentration is very high the network may contain entrapped entanglements which act as additional crosslinks. It remains that, upon reaction, the linear precursor chains (which are characterized independently) become elastically effective network chains, even though their number may be slightly lower than expected because of the defects. 

The large deformability as shown in Figure 21.2, one of the main features of rubber, can be discussed in the category of continuum mechanics, which itself is complete theoretical framework. However, in the textbooks on rubber, we have to explain this feature with molecular theory. This would be the statistical mechanics of network structure where we encounter another serious pitfall and this is what we are concerned with in this chapter the assumption of affine deformation. The assumption is the core idea that appeared both in Gaussian network that treats infinitesimal deformation and in Mooney-Rivlin equation that treats large deformation. The microscopic deformation of a single polymer chain must be proportional to the macroscopic rubber deformation. However, the assumption is merely hypothesis and there is no experimental support. In summary, the theory of rubbery materials is built like a two-storied house of cards, without any experimental evidence on a single polymer chain entropic elasticity and affine deformation. 

In POLYM the output data of KINREL are used with compositional information to calculate the number and mass average molecular masses (Rn and Rm, respectively) and number and end-group average functionalities (fp and fg> respectively) in the pre-gel region in all stages. In addition, the network characteristics such as sol fraction, mj, and the number of elastically active network chains per monomer (5), Ng, are calculated in the post-gel regime of stage 3. 

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