Nonlinear Stress Relaxation of End-associative Hydrophobically Modified Ethoxylated Urethane (HEUR) Solutions under Step Strain

Yu-Xuan Pei; Quan Chen; Hiroshi Watanabe

doi:10.1007/s10118-026-3573-1

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Nonlinear Stress Relaxation of End-associative Hydrophobically Modified Ethoxylated Urethane (HEUR) Solutions under Step Strain

Special Topic: Functional Gels | Updated：2026-05-30

- Nonlinear Stress Relaxation of End-associative Hydrophobically Modified Ethoxylated Urethane (HEUR) Solutions under Step Strain
- Chinese Journal of Polymer Science Vol. 44, Issue 6, Pages: 1790-1803(2026)
- Affiliations：
  
  a.State Key Laboratory of Polymer Science and Technology, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
  b.School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026, China
  c.Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
- Author bio：
  
  qchen@ciac.ac.cn (Q.C.)
  hiroshi@scl.kyoto-u.ac.jp (H.W.)
- Funds：
- DOI：10.1007/s10118-026-3573-1
  CLC：
- Received：12 December 2025，
  
  Revised：2026-01-09，
  
  Accepted：13 January 2026，
  
  Online First：20 March 2026，
  
  Published：05 June 2026
- Accepted：
Scan QR Code
Pei, Y. X.; Chen, Q.; Watanabe, H. Nonlinear stress relaxation of end-associative hydrophobically modified ethoxylated urethane (HEUR) solutions under step strain. Chinese J. Polym. Sci. 2026, 44, 1790–1803

Yu-Xuan Pei, Quan Chen, Hiroshi Watanabe. Nonlinear Stress Relaxation of End-associative Hydrophobically Modified Ethoxylated Urethane (HEUR) Solutions under Step Strain[J]. Chinese Journal of Polymer Science, 2026, 44(6): 1790-1803.
Pei, Y. X.; Chen, Q.; Watanabe, H. Nonlinear stress relaxation of end-associative hydrophobically modified ethoxylated urethane (HEUR) solutions under step strain. Chinese J. Polym. Sci. 2026, 44, 1790–1803 DOI： 10.1007/s10118-026-3573-1.

Yu-Xuan Pei, Quan Chen, Hiroshi Watanabe. Nonlinear Stress Relaxation of End-associative Hydrophobically Modified Ethoxylated Urethane (HEUR) Solutions under Step Strain[J]. Chinese Journal of Polymer Science, 2026, 44(6): 1790-1803. DOI： 10.1007/s10118-026-3573-1.

摘要

Nonlinear softening factor

eff

of hydrophobically modified ethoxylated urethane (HEUR)-aq. solutions at long times

defined with respect to short-time hardened state

is considerably well described by a simple model formulating strain-induced HEUR micelle fusion followed by micelle opening/splitting associated with a free energy increase

$$ \langle \Delta F/k_{\mathrm{B}} T \rangle $$

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under strain.

Abstract

Nonlinear stress relaxation under step strain

was examined for aqueous solutions of an end-associative telechelic polymer

hydrophobically modified ethoxylated urethane (HEUR) having hexadecyl groups at the two ends of the chain. At 20 °C where the end hexadecyl groups were in the molten liquid state

the solutions with the HEUR concentrations

=1 wt% and 5 wt% commonly exhibited strain-hardening at short time

and the strain-softening (damping) at long

. In the terminal relaxation zone at sufficiently long

the nonlinear relaxation modulus

(

) was found to obey the time-strain separability. These nonlinear features were discussed in relation to strain-

induced changes in the associative network structure. In the aqueous HEUR solutions

aggregates of the precipitated end-groups should be stabilized by loops of dissolved HEUR backbones to form so-called flower micelles. At low

most of those micelles would connect HEUR chains into a long linear sequence referred to as superbridge

thereby forming a sparse network. At higher

those superbridges would become shorter to densify the network accordingly. Immediately after imposition of the large step strain

the flower micelles in the superbridge backbone would fuse each other to form a denser network thereby exhibiting the hardening. This micelle fusion would be more significant for longer superbridges to enhance the strain hardening at lower

. After this fusion

the micelles having liquid cores would be opened up because of the enhanced tension of the deformed superbridge

and then split to disconnect the superbridge if this tension overwhelms the micelle strength. This opening/splitting process possibly resulted in the partial breakage of the network and the corresponding softening. Finally

the surviving part of the network would relax on thermal dissociation of the remaining micelles thereby exhibiting the time-strain separable damping at long

. These features were semi-quantitatively described by a simple model that considered the strain-induced fusion followed by mechanical opening/breakage of the transient crosslinks.

关键词

Keywords

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