Polymer networks dynamic relaxation characteristics

Here three constants appear Go is the equilibrium modulus of elasticity 0p is the characteristic relaxation time, and AG is the relaxation part of elastic modulus. There are six measured quantities (components of the dynamic modulus for three frequencies) for any curing time. It is essential that the relaxation characteristics are related to actual physical mechanisms the Go value reflects the existence of a three-dimensional network of permanent (chemical) bonds 0p and AG are related to the relaxation process due to the segmental flexibility of the polymer chains. According to the model, in-termolecular interactions are modelled by assuming the existence of a network of temporary bonds, which are sometimes interpreted as physical (or geometrical) long-chain entanglements. 

To describe the change in reptation dynamics of the chains as a function of nanoparticle volume fraction, a percolation model was used. At the percolation threshold, a physical network formed by interconnection of immobilized chains on individual nanoparticles penetrates the entire sample volume. In this case, only physical cross-links are considered and the terminal relaxation time reaches the value characteristic for the life time of the physical filler-polymer bond. Thus, the relaxation time near the percolation threshold is expressed in the form [44] ... 

Physically, double reptation accounts, in a simple way, for the fact that polymers do not reptate in fixed tubes, as assumed in the original tube model. The surrounding polymers, which form the tube, also relax, and so the constraints which form the tube decay with a characteristic time-scale. In other words, stress relaxation depends not only the dynamics of each individual polymer, but also on the dynamics of the surrounding polymers. It should be noted that more sophisticated and therefore complex rheological models for polymer mixtures have been proposed however, a particular appeal of this model is the simple relation between the stress relaxation fimction of the blend and the Doi-Edwards stress relaxation function for polymers in a fixed network. 

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