Simple method for determining the critical molecular weight from the loss modulus

The normal concept is that the critical molecular weight (M _C) is about twice as large as the entanglement molecular weight (M _e). However, experimental data have shown considerable deviations from M _C ≈ 2M _e. Furthermore, a determination of M _C requires samples with a wide range of molecular weights, including weights lower than M _C and higher than M _C. In this article, we suggest a simple method for determining M _C from the loss moduli of nearly monodisperse linear polymers with M ≫ M _C. We consider two characteristic relaxation times, which correspond to the local maximum and minimum of the loss modulus. M _C is determined from the intersection of two phenomenological relaxation times as a function of the molecular weight. The method precisely agrees with M _C ≈ 2M _e, which is not shown by conventional methods. Moreover, our method provides a determination of relaxation time τ _e, at which chain segments first feel the constraints imposed by the conceptual tube, without the measurement of the tube diameter and the monomeric friction coefficient, which may be determined by complicated procedures with a lot of data.