Expanding the application of the van Gurp-Palmen plot: New insights into polymer melt rheology

Zhiyuan Qian, Gregory B. McKenna

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We report on an extension of the van Gurp-Palmen (vGP) plot [van Gurp, M. and Palmen, J., Rheology Bulletin, 1998, 67(1), 5–8.] developed through a compilation of literature data for polymer melts with different topological structures: linear (pure and blend), ring, comb, and bottlebrush. We introduce a new parameter: the reciprocal of complex modulus at the first minimum moving from the terminal regime (1/Gδmin,1 ) and compare it with the steady-state recoverable compliance Js. Results show that 1/Gδmin,1 and Js while related to each other in that they follow similar dependences on the molecular weight (linear and bottlebrush polymers), weight fraction of high molecular weight content (linear blends), and backbone concentration (comb polymer), there are also differences. For example, in the unentangled regime both Js and 1/Gδmin,1 increase with increasing molecular weight but reach different plateau values as entanglement coupling sets in. In the case of ring polymers, the molecular weight dependences of 1/Gδmin,1 (∼Mw 1) and Js(∼Mw 2) show very different scaling with molecular weight and do not reach a plateau value even for molecular weights as high as approximately 15 times the entanglement molecular weight of the linear counterpart. Furthermore, examination of the impact of linear additives on the vGP plots of the rings potentially provides a new way to assess their freedom from linear contamination. Also, because 1/Gδmin,1 occurs in the frequency regime above that of the terminal regime and Js requires either very good estimates of terminal behavior in dynamic measurements or direct determination from creep and recovery measurements, 1/Gδmin,1 is easier to obtain. The work shows that detailed analysis of the van Gurp-Palmen plot has the potential to provide new insights into the rheological response of polymer melts over what is obtained conventionally from viscoelastic characterization methods.

Original languageEnglish
Pages (from-to)208-217
Number of pages10
StatePublished - Oct 24 2018


  • Complex modulus
  • Polymer topology
  • Steady-state recoverable compliance
  • van Gurp-Palmen plot


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