Takayanagi type model

A Takayanagi-type model (Fig. 31) can be used to quantify the relationship with the storage modulus at —50 °C (in the plateau region between the a and y-relaxations). It can be shown that... 

Morphology suggested a Takayanagi type model in terms of crystalline lamellae perpendicular to the stretch direction, separated by inter-lamellar material, and modulus, density and melting data were consistent with this model up to the point where a textural change was observed. It was concluded that the mechanical properties in this range were a consequence of the properties of the relatively small less well ordered intercrystalline regions rather than of the extended chains. 

Fig. 7. Temperature dependence ofstorage and loss modulifor P VC-NBR film bonded in parallel to a PVC film. Takayanagi model type / gives better fit to experiment.

Figure 8.10 Temperature dependence of storage and loss moduli for a polyvinyl chloride-nitrile bidadiere rubber film bonded in parallel to a polyvinyl chloride film. Takayanagi model type (a) gives better fit to experiment. (Reproduced with permission fi om Takayanagi, Mem. Fac. Eng. Kyushu Univ., 23, 41 (1963))...

Topological theories, considered in detail in the review by Rigbi, postulate two types of attachments between a rubber matrix and its carbon black filler a strong type, due to chemisorptive attachments, and a weaker van der Waals type of bond. The former were considered to remain unbroken upon stressing the vulcanizate, but the latter suffered progressive rupture as the stress increases. Various models of deformation have been proposed, based on the model described by Takayanagi, to describe the phenomena observed, but they are strictly mechanical models which do not explain why these phenomena occur. 

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