Evaluation methods of the longest Rouse relaxation time of an entangled polymer in a semidilute solution

Estimation methods for the longest Rouse relaxation time (τ R ) of an entangled polymer in a semidilute solution were examined. We evaluated τ R by fitting the dynamic modulus ( G ′) with the Rouse model theory in the power law range, where G ′ was proportional to the square root of the angular frequency (ω). The τ R values thus obtained for polystyrene (PS) solutions in tricresyl phosphate (TCP) were employed to derive an empirical formula for the evaluation of τ R from the viscosity (η): M is the molecular weight, and c is the mass of polymer per unit volume; M e = cRT / G N is the entanglement molecular weight, where G N is the G ′ value at the inflection point of the graph of log G ′ versus log ω. The subscript η indicates that τ R is derived from η data. The proposed equation was also applicable to bulk PS and bulk polyisoprene. Discrepancies among reported τ R values in semidilute solutions seem to be mostly due to discrepancies in M e values. For PS solutions in dioctyl phthalate, a Θ solvent, the τ R value derived from η was much larger than that from the G ′ curve. Apart from the evaluation method of τ R , we observed for PS that M e was independent of temperature for good solvent systems and melts, that M e for solutions in TCP agreed with that for solutions in another good solvent, and that M e for a Θ‐solvent system was equal to that for good solvent systems with the same M and c values.