On a series of examples from the field of viscoelasticity we demonstrate that it is possible to attribute physical meaning to initial conditions expressed in terms of Riemann-Liouville fractional derivatives, and that it is possible to obtain initial values for such initial conditions by appropriate measurements or observations.

No abstract

No abstract

Several apparently contradictory models predicting critical conditions for chain entanglement in flexible polymers have appeared in recent years. Some models predict entanglement molecular weight to increase, and others to decrease, with chain stiffness. Literature data are used here to compare model predictions. An inverse correlation between characteristic ratio and segmental aspect ratio is found, allowing the contradiction to be resolved. In flexible chains, it is found that the aspect ratio of a Kuhn step length is approximately independent of molecular characteristics and that stiffness depends more strongly on segmental aspect ratio than on characteristic ratio.

No abstract

No abstract

No abstract

In recent decades, constitutive equations for polymers involving fractional calculus have been the object of ever increasing interest, due to their special suitability for describing self-similarity and memory effects, which are typical of viscoelastic behaviour in polymers. Thermodynamic validity of these equations can be ensured by obtaining them from analog models containing spring-pots with positive front factors. Failure of self-similarity in real polymers at short (local) and long (whole chain) scales has been addressed previously. In the past, interest in fractional differential descriptions of polymer viscoelasticity has been mainly concerned with linear viscoelasticity, despite the fact that in processing and end use conditions are largely in the non-linear range. In this paper, extension of fractional calculus models to the non-linear range of viscoelasticity is attempted, by accounting for stress activation of deformation and strain acceleration of annealing. Calculated stress-strain curves are compared with experimental results on an amorphous polymer (polycarbonate). The model adequately describes the general trends of yield and post-yield behaviour, but does not properly describe the gentle approach to yield observed experimentally.