Re-visiting the “consequences of grafting density on the linear viscoelastic behavior of graft polymers”

Zhiyuan Qian, Dongjie Chen, Gregory B. McKenna

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In a recent work published by Haugan et al. (ACS Macro Lett., 2018, 7, 525–530.), the linear viscoelastic behaviors of a series of random graft polymers as a function of grafting density (Z) and backbone degree of polymerization (nbb) for a constant side chain degree of polymerization was investigated. The results were interpreted to imply that as Z increases the backbone concentration decreases and the distance between entanglements increases (the number of backbone degree of polymerization between entanglements (ne,bb) increases from 55 for Z=0 to 550 for Z=1.). One evidence of entanglement formation was that the zero-shear rate viscosity (η0) showed a departure from Rouse scaling to reptation scaling as molecular weight increased. However, the values of η0 from the dynamic modulus measurements used in that work were, for multiple cases, underestimated because the Newtonian plateau at low frequencies was not reached. In the present work, the rheological data for these graft polymers are reanalyzed, some samples are measured again, and the resulting new estimates of the zero shear-rate viscosity (η0) lead to changes in the interpretation of the results. Furthermore, we calculated the retardation spectra (L(τ)) for the samples, showing that the entanglement behavior of these systems is similar to but not identical to the behavior of the linear chain polymer. The results show that in the transition from Rouse-like to entangled behavior η0 exhibits a Mw 3.4 dependence on molecular weight rather than the Mw 3 previously reported for these graft polymers. By plotting η0 as a function of nbb at different Z, the data collapse into two families of behavior and the critical grafting density Z is approximately 0.2–0.25. The onset of entanglements as nbb or Mw increases at fixed Z is confirmed from the retardation spectrum, However, the progressive development of the retardation spectrum for these side chain diluted systems differs from that of entangled polymer solutions in that the spectrum first broadens at short times before splitting into two distinct peaks, while for solutions the appearance and shifting to longer times of a second peak occur more abruptly.

Original languageEnglish
Article number121992
StatePublished - Jan 9 2020


  • Bottlebrush polymer
  • Entanglements
  • Graft polymer
  • Retardation spectrum
  • Zero-shear rate viscosity


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