Relaxation time spectrum molecular weight distribution relationships

摘要: Single exponential decay $\exp(-t/\tau)$ relationships, which define the molecular weight distribution (MWD) of a polymer as function polymer’s relaxation time spectrum (RTS), have been derived by Wu (Polym Eng Sci 28:538–543, 1988) and Thimm et al. (J Rheol 43:1663–1672, 1999). Experimental validation studies with monodisperse polymers, quite precisely known MWDs, used to test their reliability. It has established that neither formula is always able accurately recover MWDs polymers from experimentally determined RTS. In this paper, different more general based on theoretical results Anderssen Loy (Bull Aust Math Soc 65:449–460, 2002a) for decays form $\exp(-\theta(t)/\tau)$ , where derivative θ(t) completely monotone function, are derived, analyzed, applied. shown how transform these relationships equivalent single Laplace solutions derived. order illustrate interrelationship between an RTS its corresponding MWD, explicit analytic solution given. The paper concludes discussion rheological implications BSW model.