Entanglement Characteristic Time from Complex Moduli via i-Rheo GT

Tassieri et al. have introduced a novel rheological tool called "i-Rheo " that allows the evaluation of the frequency-dependent materials' linear viscoelastic properties from a direct Fourier transform of the time-dependent relaxation modulus ( ), without artifacts. They adopted i-Rheo to exploit the information embedded in ( ) derived from molecular dynamics simulations of atomistic and quasi-atomistic models, and they estimated the polymers' entanglement characteristic time (τe) from the crossover point of the moduli at intermediate times, which had never been possible before because of the poor fitting performance, at short time scales, of the commonly used generalized Maxwell models. Here, we highlight that the values of τe reported by Tassieri et al. are significantly different (i.e., an order of magnitude smaller) from those reported in the literature, obtained from either experiments or molecular dynamics simulations of different observables. In this work, we demonstrate that consistent values of τe can be achieved if the initial values of ( ), i.e., those governed by the bond-oscillation dynamics, are discarded. These findings have been corroborated by adopting i-Rheo to Fourier transform the outcomes of three different molecular dynamics simulations based on the following three models: a dissipative particle dynamics model, a Kremer-Grest model, and an atomistic polyethylene model. Moreover, we have investigated the variations of τe as function of (i) the 'cadence' at which ( ) is evaluated, (ii) the spring constant of the atomic bone, and (iii) the initial value of the shear relaxation modulus (O). The ensemble of these results confirms the effectiveness of i-Rheo and provide new insights into the interpretation of molecular dynamics simulations for a better understanding of polymer dynamics.