Complex viscoelasticity

Soft materials such as gels and glasses exhibit a universal dynamical response characterized by a broad distribution of relaxation times, the origins of which remain unclear. Working in the Holten-Andersen group and the McKinley group at MIT, I leveraged a model metal-coordinate particle gel system which exhibits such arrested dynamics (more details here, to study and establish the physics underlying such complex relaxation phenomena in soft materials.

Thermal relaxation of multi-valent systems

In a collaborative study with Hugo Le Roy and Martin Lenz at Université Paris-Saclay, we developed a minimal model to describe the relaxation dynamics of gels with large cross-linkers - a materials configuration which canonically results in a broad distribution of stress relaxation times. We showed that multi-valent interactions between a pair of cross-linkers can significantly increase dissociation times, and that even a simple Poisson distribution of such multi-valent interactions in the system can result in a broad distribution of stress relaxation times. We then demonstrated that this model can capture the non-exponential stress relaxation exhibited by polymer hydrogels with nanoparticle or nanocage cross-linkers [1].

Illustration of the multivalent relaxation model, in which multivalent “super-bonds” undergo dissociation via a Markovian process. A distribution of the size of the “super-bonds” results in a broad distribution of relaxation times. Taken from Le Roy et al [1].

Athermal avalanches under quasi-linear perturbations

We studied the local dynamics of our particle gels using x-ray photon correlation spectroscopy, a synchrotron-based scattering technique, to understand the microscopic signatures of the broad distribution of stress relaxation times observed in arrested soft matter. Surprisingly, we found that the local dynamics of the gels were athermal in nature, characterized by superdiffusive dynamics which are driven by the buildup of internal stress during arrest. Furthermore, we found that driving the system with small external deformations – that which we would typically apply during a rheology experiment – resulted in intermittent avalanches with a broad non-Gaussian spectrum of relaxation modes. These findings suggest that the broad distribution of relaxation times in arrested gels – obtained typically through rheological experiments in the “linear” regime – could be explained as a quasi-linear phenomenon characterized by perturbation-induced intermittent avalanches [2].

Demonstration of the broadened intermediate scattering function in dynamically-arrested gels under external loading due to the superposition of local ballistic avalanche dynamics. Taken from Song et al [2].

Origins of non-Maxwellian stress relaxation

As part of my dissertation, I have extensively studied the physics underlying the broad distribution of relaxation times in soft matter, which is often manifested through a complex and non-Maxwellian viscoelastic response. I have contributed a tutorial review on this topic, where I have highlighted a diverse array of physics that can underlie a broad distribution of relaxation modes, and appropriate mathematical and rheological models to capture these processes [3].

Illustration of the ubiquity of non-Maxwellian viscoelasticity across a wide range of soft matter systems; each curve is overlaid with the prediction of the Maxwell model for illustrative purposes (red lines). Taken from Song et al [3].

References

1. Le Roy, H.*, Song, J.*, Lundberg, D., Zhukhovitskiy, A. V., Johnson, J. A., McKinley, G. H., Holten-Andersen, N., & Lenz, M. “Valency Can Control the Non-Exponential Viscoelastic Relaxation in Multivalent Reversible Gels”. Science Advances. 10(20), eadl5056 (2024).
2. Song, J., Zhang, Q., de Quesada, F., Rizvi, M. H., Ilavsky, J., Tracy, J. B., Narayanan, S., Del Gado, E., Leheny. R. L., Holten-Andersen, N., & McKinley, G. H. “Microscopic Dynamics Underlying the Stress Relaxation of Arrested Soft Materials.” Proceedings of the National Academy of Sciences. 119(30), e2201566119 (2022)
3. Song, J., Holten-Andersen, N., & McKinley, G. H., “Non-Maxwellian Viscoelastic Stress Relaxations in Soft Matter”. Soft Matter. 19(41), 7885-7906 (2023).