Rubber-like networks

Erman, B. Mark, J.E. Structures and Properties of Rubber-like Networks Oxford University Press New York, 1997. 

Knibbe, D. E. Diffusion-controlled stress relaxation of swollen rubber-like networks, Rotterdam University Press 1968. 

For a simple rubber-like network, the maximum draw ratio varies with the number of statistical chain segments between crosslinks as... 

Dick J.S. 2001. Rubber Technology Compounding and Testing for Performance. Hanser Gardner. Donnet J.B. and A. Vidal. 1986. Carbon Black. Advances in Polymer Science. Springer. Donnet, J.B., T.K. Wang, and J.C.M. Peng. 1998. Carbon Fibers. 3rd ed. Marcel Dekker. Erman B. and J.E. Mark. 1997. Structures and Properties of Rubber-Like Networks. Oxford University Press. 

The simplest explanation is that there is a rubber-like network present and that this has a maximum extensibility due to the degree of entanglement, which is constant for a given grade of polymer and depends on its molar mass and method of polymerisation. This limiting extensibility is not to be confused with the limit of applicability of the affine rubber model for predicting orientation distributions discussed in section 11.2.1 because the limiting extension can involve non-affine deformation. 

J. E. Mark, Thermoelastic properties of rubber-like networks and their thermodynamic and... 

Erman, B. and J. E. Mark, Structure and Property of Rubber-Like Networks, Oxford University Press (1999). 

Purvis and Bower [12] subsequently extended the work, using four additional Raman peaks, aU of which predominantly involve motion of the terephthalyl moiety, to a first approximation. The results suggested that there is no preferred orientation of the plane of the ester group with respect to the plane of the benzene ring in the amorphous phase. They also concluded that the drawing of PET occurs in a similar manner to the extension of a rubber-like network. 

Erman B, Mark JE. Structures and properties of rubber like networks. New York Oxford University Press 1997. 

Mark, J. E. The Use of Model Polymer Networks to Elucidate Molecular Aspects of Rubber like Elasticity. Vol. 44, pp. 1-26. 

The ratios of mean-squared dimensions appearing in Equation (13) are microscopic quantities. To express the elastic free energy of a network in terms of the macroscopic (laboratory) state of deformation, an assumption has to be made to relate microscopic chain dimensions to macroscopic deformation. Their relation to macroscopic deformations imposed on the network has been a main area of research in the area of rubber-like elasticity. Several models have been proposed for this purpose, which are discussed in the following sections. Before that, however, we describe the macroscopic deformation, stress, and the modulus of a network. 

J.E. Mark and B. Erman, Molecular aspects of rubber-like elasticity. In R.F.T. Stepto (Ed.), Polymer Networks, Blackie Academic, Chapman Hall, Glasgow, 1998. 

Rubber-like models take entanglements as local stress points acting as temporary cross finks. De Cloizeaux [66] has proposed such a model, where he considers infinite chains with spatially fixed entanglement points at intermediate times. Under the condition of fixed entanglements, which are distributed according to a Poisson distribution, the chains perform Rouse motion. This rubber-like model is closest to the idea of a temporary network. The resulting dynamic structure factor has the form ... 

The plateau region appears when the molecular weight exceeds Mc [(Mc)soln. for solutions], and is taken to be a direct indication of chain entanglement. Indeed the presence of a plateau may be a more reliable criterion than r 0 vs M behavior, especially in solutions of moderate concentration where viscosity may exhibit quite complex concentration and molecular weight behavior. It is postulated that when M greatly exceeds Mc, a temporary network structure exists due to rope-like interlooping of the chains. Rubber-like response to rapid deformations is obtained because the strands between coupling points can adjust rapidly, while considerably more time is required for entire molecules to slip around one another s contours and allow flow or the completion of stress relaxation. 

The elastomers exhibited rubber-like behavior. From an examination of electron photomicrographs of cross sections of the elastomers, the fibrillar structure of the cellulose fibers apparently formed a network, and poly (ethyl acrylate) was distributed uniformly among the fibrils. The rigid crystalline regions of the cellulose fibers apparently stabilized the amorphous, grafted poly (ethyl acrylate) to determine the mechanical properties of the elastomers (43, 44). For example, typical elastic recovery properties for these elastomers are shown in Table X. 

The FTMS method allows us to follow changes in several parameters that carry information on the role of different mechanisms during formation of an end-product by reactive molding. Specifically, the development of fluctuating entanglements of long-chain macromolecules can be distinguished from the appearance of rubber-like three-dimensional networks of chemical bonds. 

The gelation process that leads to the network structures required for rubber-like elasticity have been extensively studied, by experiments, theory, and simulations.245-249 In some case, the gelation can be made to be reversible.250... 

---