Abstract
The ageing behaviour of dense suspensions or pastes at rest is almost exclusively attributed to structural dynamics. Here, we identify another ageing process, contact-controlled ageing, consisting of the progressive stiffening of solid–solid contacts of an arrested colloidal suspension. By combining rheometry, confocal microscopy and particle-scale mechanical tests using laser tweezers, we demonstrate that this process governs the shear-modulus ageing of dense aqueous silica and polymer latex suspensions at moderate ionic strengths. We further show that contact-controlled ageing becomes relevant as soon as Coulombic interactions are sufficiently screened out that the formation of solid–solid contacts is not limited by activation barriers. Given that this condition only requires moderate ion concentrations, contact-controlled ageing should be generic in a wide class of materials, such as cements, soils or three-dimensional inks, thus questioning our understanding of ageing dynamics in these systems.
This is a preview of subscription content, access via your institution
Relevant articles
Open Access articles citing this article.
-
Colloidal density control with Bessel–Gauss beams
Scientific Reports Open Access 10 June 2021
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Rent or buy this article
Get just this article for as long as you need it
$39.95
Prices may be subject to local taxes which are calculated during checkout





Data availability
Figure source data are provided online; other data used in this work are available from the authors.
Code availability
The software used in this work is available from the authors.
References
Abou, B., Bonn, D. & Meunier, J. Aging dynamics in a colloidal glass. Phys. Rev. E. 64, 021510 (2001).
Derec, C., Ducouret, G., Ajdari, A. & Lequeux, F. Aging and nonlinear rheology in suspensions of polyethylene oxide-protected silica particles. Phys. Rev. E. 67, 061403 (2003).
Coussot, P., Tabuteau, H., Chateau, X., Tocquer, L. & Ovarlez, G. Aging and solid or liquid behavior in pastes. J. Rheol. 50, 975–994 (2006).
Ovarlez, G. & Coussot, P. Physical age of soft-jammed systems. Phys. Rev. E. 76, 011406 (2007).
Ovarlez, G. & Chateau, X. Influence of shear stress applied during flow stoppage and rest period on the mechanical properties of thixotropic suspensions. Phys. Rev. E. 77, 061403 (2008).
Guo, H., Ramakrishnan, S., Harden, J. L. & Leheny, R. L. Gel formation and aging in weakly attractive nanocolloid suspensions at intermediate concentrations. J. Chem. Phys. 135, 154903 (2011).
Fusier, J., Goyon, J., Chateau, X. & Toussaint, F. Rheology signature of flocculated silica suspensions. J. Rheol. 62, 753–771 (2018).
Dinsmore, A. D., Weeks, E. R., Prasad, V., Levitt, A. C. & Weitz, D. A. Three-dimensional confocal microscopy of colloids. Appl. Opt. 40, 4152–4159 (2001).
Dinsmore, A. D. & Weitz, D. A. Direct imaging of three-dimensional structure and topology of colloidal gels. J. Phys. Cond. Matter 14, 7581–7597 (2002).
Prasad, V., Semwogerere, D. & Weeks, E. R. Confocal microscopy of colloids. J. Phys. Cond. Matter 19, 113102 (2007).
Dibble, C. J., Kogan, M. & Solomon, M. J. Structure and dynamics of colloidal depletion gels: coincidence of transitions and heterogeneity. Phys. Rev. E. 74, 041403 (2006).
Whitaker, K. A. et al. Colloidal gel elasticity arises from the packing of locally glassy clusters. Nat. Commun. 10, 2237 (2019).
Cipelletti, L., Manley, S., Ball, R. C. & Weitz, D. A. Universal aging features in the restructuring of fractal colloidal gels. Phys. Rev. Lett. 84, 2275–2278 (2000).
Bissig, H., Romer, S., Cipelletti, L., Trappe, V. & Schurtenberger, P. Intermittent dynamics and hyper-aging in dense colloidal gels. Phys. Chem. Comm. 6, 21–23 (2003).
Cipelletti, L. et al. Universal non-diffusive slow dynamics in aging soft matter. Faraday Discuss. 123, 237–251 (2003).
Barnes, H. A. Thixotropy: a review. J. Nonnewton. Fluid Mech. 70, 1–33 (1997).
Cipelletti, L. & Ramos, L. Slow dynamics in glassy soft matter. J. Phys. Cond. Matter 17, R253 (2005).
Mewis, J. & Wagner, N. J. Colloidal Suspension Rheology Cambridge Series in Chemical Engineering (Cambridge Univ. Press, 2011).
Bouzid, M., Colombo, J., Barbosa, L. V. & Del Gado, E. Elastically driven intermittent microscopic dynamics in soft solids. Nat. Commun. 8, 15846 (2017).
Dieterich, J. H. & Kilgore, B. D. Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic. Tectonophysics 256, 219–239 (1996).
Persson, B. N. J. Sliding Friction: Physical Principles and Applications (Springer, 2000).
Baumberger, T. & Caroli, C. Solid friction from stick-slip down to pinning and aging. Adv. Phys. 55, 279–348 (2006).
Vandamme, M. & Ulm, F.-J. Nanogranular origin of concrete creep. Proc. Natl Acad. Sci. USA 106, 10552–10557 (2009).
Ioannidou, K. et al. The crucial effect of early-stage gelation on the mechanical properties of cement hydrates. Nat. Commun. 7, 12106 (2016).
Roussel, N., Ovarlez, G., Garrault, S. & Brumaud, C. The origins of thixotropy of fresh cement pastes. Cement Concrete Res. 42, 148–157 (2012).
Manley, S. et al. Time-dependent strength of colloidal gels. Phys. Rev. Lett. 95, 048302 (2005).
Pantina, J. P. & Furst, E. M. Elasticity and critical bending moment of model colloidal aggregates. Phys. Rev. Lett. 94, 138301 (2005).
Pantina, J. P. & Furst, E. M. Colloidal aggregate micromechanics in the presence of divalent ions. Langmuir 22, 5282–5288 (2006).
Meng, B., Wu, J., Li, Y. & Lou, L. Aging process of the bond between colloidal particles measured using laser tweezers. Colloids Surf. A. 322, 253–255 (2008).
Buscall, R., Mills, P. D. A., Goodwin, J. W. & Lawson, D. W. Scaling behaviour of the rheology of aggregate networks formed from colloidal particles. J. Chem. Soc., Faraday Trans. 84, 4249–4260 (1988).
Russel, W. B., Saville, D. A. & Schowalter, W. R. Colloidal Dispersions Cambridge Monographs on Mechanics (Cambridge Univ. Press, 1989).
Israelachvili, J. N. in Intermolecular and Surface Forces 3rd edn (ed. Israelachvili, J. N.) 415–467 (Academic Press, 2011).
Swan, J. W., Shindel, M. M. & Furst, E. M. Measuring thermal rupture force distributions from an ensemble of trajectories. Phys. Rev. Lett. 109, 198302 (2012).
Whitaker, K. A. & Furst, E. M. Bond rupture between colloidal particles with a depletion interaction. J. Rheol. 60, 517–529 (2016).
Derjaguin, B., Muller, V. & Toporov, Y. Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53, 314–326 (1975).
Johnson, K. L., Kendall, K. & Roberts, A. D. Surface energy and the contact of elastic solids. Proc. R. Soc. London A. 324, 301–313 (1971).
Tabor, D. Surface forces and surface interactions. J. Colloid Interface Sci. 58, 2–13 (1977).
Paul, J., Romeis, S., Tomas, J. & Peukert, W. A review of models for single particle compression and their application to silica microspheres. Adv. Powder Techn. 25, 136–153 (2014).
Iler, K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties and Biochemistry of Silica (John Wiley & Sons, Inc., 1979).
Guleryuz, H., Røyset, A. K., Kaus, I., Filiàtre, C. & Einarsrud, M.-A. Afm measurements of forces between silica surfaces. J. Sol-Gel Sci. Techn. 62, 460–469 (2012).
Vigil, G., Xu, Z., Steinberg, S. & Israelachvili, J. Interactions of silica surfaces. J. Colloid Interface Sci. 165, 367–385 (1994).
Li, Q., Tullis, T. E., Goldsby, D. & Carpick, R. W. Frictional ageing from interfacial bonding and the origins of rate and state friction. Nature 480, 233 EP (2011).
Liu, Y. & Szlufarska, I. Chemical origins of frictional aging. Phys. Rev. Lett. 109, 186102 (2012).
Tian, K. et al. Load and time dependence of interfacial chemical bond-induced friction at the nanoscale. Phys. Rev. Lett. 118, 076103 (2017).
Li, Z., Pastewka, L. & Szlufarska, I. Chemical aging of large-scale randomly rough frictional contacts. Phys. Rev. E. 98, 023001 (2018).
DelGado, E. & Kob, W. A microscopic model for colloidal gels with directional effective interactions: network induced glassy dynamics. Soft Matter 6, 1547–1558 (2010).
Stober, W., Fink, A. & Bohn, E. Controlled growth of monodisperse silica spheres in the micron size range. J. Colloid Interface Sci. 26, 62–69 (1968).
Do, K. K. & Taik, K. H. New process for the preparation of monodispersed, spherical silica particles. J. Am. Ceram. Soc. 85, 1107–1113 (2002).
Nakabayashi, H. et al. Electrolyte-added one-pot synthesis for producing monodisperse, micrometer-sized silica particles up to 7 μm. Langmuir 26, 7512–7515 (2010).
Laxton, P. B. & Berg, J. C. Investigation of the link between micromechanical interparticle bond rigidity measurements and macroscopic shear moduli of colloidal gels. Colloids Surfaces A. 301, 137–140 (2007).
Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298–310 (1996).
Gao, Y. X. & Kilfoil, M. L. Accurate detection and complete tracking of large populations of features in three dimensions. Optics Expr. 17, 4685–4704 (2009).
Pantina, J. P. & Furst, E. M. Directed assembly and rupture mechanics of colloidal aggregates. Langmuir 20, 3940–3946 (2004).
Shindel, M. M., Swan, J. W. & Furst, E. M. Calibration of an optical tweezer microrheometer by sequential impulse response. Rheologica Acta 52, 455–465 (2013).
Nieminen, T. A., Knöner, G., Heckenberg, N. R. & Rubinsztein-Dunlop, H. in Laser Manipulation of Cells and Tissues, Methods in Cell Biology Vol. 82 (eds Berns, M. W. & Greulich, K. O.) 207–236 (Academic Press, 2007).
Acknowledgements
This work benefited from a French government grant managed by ANR within the framework of the National Program Investments for the Future, ANR-11-LABX-0022-01. F.B.’s stay at the University of Delaware was supported by University Paris-Est.
Author information
Authors and Affiliations
Contributions
X.C., J.G. and A.L. conceived and supervised the project. J.G. and J.F. designed the macroscopic shear-modulus ageing protocol and obtained data on silica suspensions. J.G. supervised sample preparation and all experiments. E.M.F. designed the laser tweezer three-point flexural test and supervised its use. F.B. obtained complementary macroscopic shear modulus data, designed the two-compartment cell, performed flexural ageing measurements with E.M.F. and J.G. All authors contributed to the interpretation of experimental data, model construction and article planning and writing.
Corresponding authors
Ethics declarations
Competing interests
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
Supplementary Information
Supplementary Video, Notes 1 and 2, Methods, Figs. 1–5 and References.
Supplementary Video 1
Two videos running in parallel show the contact formation and opening tests at two ionic strengths.
Source data
Source Data Fig. 1
Shear modulus versus ageing time data.
Source Data Fig. 2
Unprocessed confocal images at ageing times t = 1, 5 and 10 min.
Source Data Fig. 3
Source data. Page 1, force versus deflection data at three ageing times and pages 2–4, deduced bond rigidity for three ionic strengths and two rod sizes.
Source Data Fig. 4
Source data. Page 1, shear modulus versus bond rigidity and page 2, S versus packing fraction.
Source Data Fig. 5
Source data. Pages 1–4, bond rigidity versus time. Pages 5 and 6, shear-modulus ageing. Page 7, shear modulus versus bond rigidity.
Rights and permissions
About this article
Cite this article
Bonacci, F., Chateau, X., Furst, E.M. et al. Contact and macroscopic ageing in colloidal suspensions. Nat. Mater. 19, 775–780 (2020). https://doi.org/10.1038/s41563-020-0624-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41563-020-0624-9
This article is cited by
-
Hierarchical amorphous ordering in colloidal gelation
Nature Physics (2023)
-
Colloidal density control with Bessel–Gauss beams
Scientific Reports (2021)