Abstract
The stress relaxation test is an effective and facile method for clarifying the nonlinear rheological behavior of soft materials. A thorough analysis of the stress relaxation behavior offers valuable insights into the molecular dynamics. However, the stress relaxation behavior and underlying molecular dynamics of polymer/particle mixtures remain poorly understood, despite their widespread industrial application. In this study, we systematically investigated the nonlinear stress relaxation behavior of a simple-structured poly(ethylene oxide) (PEO)/silica nanoparticle aqueous mixture. Time‒strain separability was observed at high polymer concentrations, with the stress relaxation attributable to the relaxation of the polymer matrix. At lower polymer concentrations, the time‒strain separability was no longer valid, and changes in absorbance over time suggested that stress relaxation originated from the relaxation of the aggregated structures. A transition from time‒strain separability to inseparability was observed when the estimated number of PEO molecules forming interparticle bridges was less than 1; this suggests that structural changes during shear loading occur only when new interparticle polymer bridges are formed, leading to the development of clustered structures. These results provide a basic understanding of the relationship between deformation and relaxation, which is crucial for systematically understanding the nonlinear rheology of polymeric materials.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout








Similar content being viewed by others
References
Wusigale, Liang L, Luo Y. Casein and pectin: tructures, interactions, and applications. Trends Food Sci Technol. 2020;97. https://doi.org/10.1016/j.tifs.2020.01.027.
Abdullah, Liu L, Javed HU, Xiao J. Engineering emulsion gels as functional colloids emphasizing food applications: a review. Front Nutr. 2022;9. https://doi.org/10.3389/fnut.2022.890188.
McNamara K, Tofail SAM. Nanoparticles in biomedical applications. Adv Phys X. 2017;2. https://doi.org/10.1080/23746149.2016.1254570.
Rizvi SAA, Saleh AM. Applications of nanoparticle systems in drug delivery technology. Saudi Pharm J. 2018;26:64–70.
Contado C. Nanomaterials in consumer products: a challenging analytical problem. Front Chem. 2015;3. https://doi.org/10.3389/fchem.2015.00048.
Rajan K, Roppolo I, Chiappone A, Bocchini S, Perrone D, Chiolerio A. Silver nanoparticle ink technology: state of the art. Nanotechnol Sci Appl. 2016;9. https://doi.org/10.2147/NSA.S68080.
Nayak L, Mohanty S, Nayak SK, Ramadoss A. A review on inkjet printing of nanoparticle inks for flexible electronics. J Mater Chem C Mater. 2019;7:8771–95.
Khan SA, Jain M, Pandey A, Pant KK, Ziora ZM, Blaskovich MAT, et al. Leveraging the potential of silver nanoparticles-based materials towards sustainable water treatment. J Environ Manag. 2022;319:115675.
Otsubo Y. Rheological behavior of suspensions flocculated by weak bridging of polymer coils. J Colloid Interface Sci. 1999;215:99–105.
Zhang H, Yuan G, Zhao C, Han CC. Liquid–gel–liquid transition and shear thickening in mixed suspensions of silica colloid and hyperbranched polyethyleneimine. Langmuir. 2013;29:12110–7.
Park N, Rathee V, Blair DL, Conrad JC. Contact networks enhance shear thickening in attractive colloid-polymer mixtures. Phys Rev Lett. 2019;122:228003.
Cabane B, Wong K, Lindner P, Lafuma F. Shear induced gelation of colloidal dispersions. J Rheol. 1997;41:531–47.
Osaki K, Takatori E, Kurata M, Watanabe H, Yoshida H, Kotaka T. Viscoelastic properties of solutions of star-branched polystyrene. Macromolecules. 1990;23:4392–6.
Osaki K. On the damping function of shear relaxation modulus for entangled polymers. Rheol Acta. 1993;32:429–37.
Archer LA, Sanchez-Reyes J, Juliani. Relaxation dynamics of polymer liquids in nonlinear step shear. Macromolecules. 2002;35:10216–24.
Doi M, Edwards SF. The theory of polymer dynamics. Oxford University Press; 1986.
Osaki K, Nishizawa K, Kurata M. Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems. Macromolecules. 1982;15:1068–71.
Osaki K, Takatori E, Tsunashima Y, Kurata M. On the universality of viscoelastic properties of entangled polymeric systems. Macromolecules. 1987;20:525–9.
Watanabe H, Yao M-L, Yamagishi A, Osaki K, Shitata T, Niwa H, et al. Nonlinear rheological behavior of a concentrated spherical silica suspension. Rheol Acta. 1996;35:433–45.
Watanabe H, Yao ML, Osaki K, Shikata T, Niwa H, Morishima Y. Nonlinear theology of a concentrated spherical silica suspension: 2. Role of strain in shear-thickening. Rheol Acta. 1997;36:524–33.
Kamibayashi M, Ogura H, Otsubo Y. Shear-thickening flow of nanoparticle suspensions flocculated by polymer bridging. J Colloid Interface Sci. 2008;321:294–301.
Saito Y, Hirose Y, Otsubo Y. Shear-induced reversible gelation of nanoparticle suspensions flocculated by poly(ethylene oxide). Colloids Surf A Physicochem Eng Asp. 2011;384:40–46.
Yan F, Ye L, Qiu D. Effect of particle/polymer number ratio on the structure and dynamics of complex between large polymer and nanoparticle. Colloids Surf A Physicochem Eng Asp. 2016;507:67–75.
Collini H, Mohr M, Luckham P, Shan J, Russell A. The effects of polymer concentration, shear rate and temperature on the gelation time of aqueous Silica-Poly(ethylene-oxide) “Shake-gels”. J Colloid Interface Sci. 2018;517:1–8.
Kawasaki S, Kobayashi M. Affirmation of the effect of pH on shake-gel and shear thickening of a mixed suspension of polyethylene oxide and silica nanoparticles. Colloids Surf A Physicochem Eng Asp. 2018;537:236–42.
Mar Ramos-Tejada M, Luckham PF. Shaken but not stirred: The formation of reversible particle-polymer gels under shear. Colloids Surf A Physicochem Eng Asp. 2015;471:164–9.
Tian Q, Sun J, Henderson MJ, Huang X, Li N, Courtois J, et al. Quantitative analysis of the structural relaxation of silica-PEO shake gel by X-ray and light scattering. Polym Test. 2021;104:107391.
Akada K, Okubo S, Yamada T, Tokuda K, Yamaguchi K, Uemura S, et al. Anisotropic flocculation in shear thickening colloid-polymer suspension via simultaneous observation of rheology and X-ray scattering. Colloids Surf A Physicochem Eng Asp. 2023;658:130727.
Ebagninin KW, Benchabane A, Bekkour K. Rheological characterization of poly(ethylene oxide) solutions of different molecular weights. J Colloid Interface Sci. 2009;336:360–7.
Inoue T, Osaki K. Rheology of polystyrene solutions with scarcely entangled chains; role of slow relaxation mode in nonlinear behavior. Nihon Reoroji Gakkaishi. 2003;31:207–12.
Shibayama M, Kawada H, Kume T, Matsunaga T, Iwai H, Sano T, et al. In situ small-angle neutron scattering and rheological measurements of shear-induced gelation. J Chem Phys. 2007;127:144507.
Bender J, Wagner NJ. Reversible shear thickening in monodisperse and bidisperse colloidal dispersions. J Rheol. 1996;40:899–916.
Newstein MC, Wang H, Balsara NP, Lefebvre AA, Shnidman Y, Watanabe H, et al. Microstructural changes in a colloidal liquid in the shear thinning and shear thickening regimes. J Chem Phys. 1999;111:4827–38.
Acknowledgements
This work was supported by the Japan Society for the Promotion of Science (JSPS) through Grants-in-Aid for JSPS Fellows (No. 22J21871 to SK) and the Mitsubishi Foundation to YA.
Author information
Authors and Affiliations
Contributions
The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kusakabe, S., Katashima, T., Sakuma, I. et al. Nonlinear stress relaxation and failure of time‒strain separability of aqueous poly(ethylene oxide)/silica nanoparticle mixtures. Polym J 57, 163–170 (2025). https://doi.org/10.1038/s41428-024-00974-x
Received:
Revised:
Accepted:
Published:
Version of record:
Issue date:
DOI: https://doi.org/10.1038/s41428-024-00974-x


