Rheology of Polydisperse Star Polymer Melts: Extension of the Parameter-Free Tube Model of Milner and McLeish to Arbitrary Arm-Length Polydispersity

• Published in: Macromolecular theory and simulations Vol. 14; no. 6; pp. 387 - 399
• Main Authors: Slot, Johan J. M., Steeman, Paul A. M.
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 19-07-2005; WILEY‐VCH Verlag; Wiley
• Subjects: Applied sciences; Exact sciences and technology; melt; Organic polymers; Physicochemistry of polymers; poly(ε-caprolactone); Properties and characterization; rheology; Rheology and viscoelasticity; star polymers; theory; Rheological model; Polydispersed polymer; rheology; Molten state; Theoretical study; Modeling; star polymers; Stress relaxation; melt; poly(ε-caprolactone); Star polymer; Polycaprolactone; theory
• ISSN: 1022-1344; 1521-3919
• DOI: 10.1002/mats.200500008

This paper considers the extension of the parameter‐free tube model of Milner and McLeish for stress relaxation in melts of monodisperse star polymers to star polymers whose arms have a continuous molecular weight distribution such as the Flory distribution in the case of star‐nylons and star‐polyesters. Exact expressions are derived for the relaxation spectrum and the relaxation modulus for star polymers having an arbitrary continuous arm‐length distribution. For a Flory distribution a comparison is made with results of dynamic measurements on a melt of 8‐arm poly(ε‐caprolactone) (PCL) stars. An excellent quantitative agreement over a large frequency range is found, however, only if one treats, in contrast with the original parameter‐free tube model approach, the entanglement molecular weight that determines the relaxation spectrum as a fitting parameter independent of the entanglement molecular weight of the linear PCL. This discrepancy is not in anyway related to the polydispersity in arm‐length, but a consequence of the thermorheological complexity of the PCL stars. A similar discrepancy has been observed for hydrogenated polybutadiene stars, as described by Levine and Milner.
Measured and calculated storage moduli G′ as a function of frequency ω.