Nonmonotonic Stress Relaxation after Cessation of Steady Shear Flow in Supramolecular Assemblies

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

pH- and temperature-responsive supramolecular assemblies with highly adjustable viscoelasticity: a multi-stimuli binary system

Stimuli-responsive materials are increasingly needed for the development of smart electronic, mechanical, and biological devices and systems relying on switchable, tunable, and adaptable properties. Herein, we report a novel pH- and temperature-responsive binary supramolecular assembly involving a long-chain hydroxyamino amide (HAA) and an inorganic hydrotrope, boric acid, with highly tunable viscous and viscoelastic properties. The system under investigation demonstrates a high degree of control over its viscosity, with the capacity to achieve over four orders of magnitude of control through the concomitant manipulation of pH and temperature. In addition, the transformation from non-Maxwellian to Maxwellian fluid behavior could also be induced by changing the pH and temperature. Switchable rheological properties were ascribed to the morphological transformation between spherical vesicles, aggregated/fused spherical vesicles, and bicontinuous gyroid structures revealed by cryo-TEM studies. The observed transitions are attributed to the modulation of the head group spacing between HAA molecules under different pH conditions. Specifically, acidic conditions induce electrostatic repulsion between the protonated amino head groups, leading to an increased spacing. Conversely, under basic conditions, the HAA head group spacing is reduced due to the intercalation of tetrahydroxyborate, facilitated by hydrogen bonding.

Residual stress in athermal soft disordered solids: insights from microscopic and mesoscale models

In soft amorphous materials, shear cessation after large shear deformation leads to configurations having residual shear stress. The origin of these states and the distribution of the local shear stresses within the material is not well understood, despite its importance for the change in material properties and consequent applications. In this work, we use molecular dynamics simulations of a model dense non-Brownian soft amorphous material to probe the non-trivial relaxation process towards a residual stress state. We find that, similar to thermal glasses, an increase in shear rate prior to the shear cessation leads to lower residual stress states. We rationalise our findings using a mesoscopic elasto-plastic description that explicitly includes a long range elastic response to local shear transformations. We find that after flow cessation the initial stress relaxation indeed depends on the pre-sheared stress state, but the final residual stress is majorly determined by newly activated plastic events occurring during the relaxation process, a scenario consistent with the phenomenology of avalanche dynamics in the low shear rate limit of steadily sheared amorphous solids. Our simplified coarse grained description not only allows capturing the phenomenology of residual stress states but also rationalising the altered material properties that are probed using small and large deformation protocols applied to the relaxed material.

A Thermodynamically Consistent, Microscopically-Based, Model of the Rheology of Aggregating Particles Suspensions

In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with the use of the single-generator bracket description of nonequilibrium thermodynamics, which leads naturally to the formulation of the model equations. Notable elements of the model are a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation and breakup processes and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting example model is evaluated in steady and transient shear forces and elongational flows and shown to offer predictions that are consistent with observed rheological behavior of typical systems of aggregating particles. Additionally, an expression for the total entropy production is also provided that allows one to judge the thermodynamic consistency and to evaluate the importance of the various dissipative phenomena involved in given flow processes.

Instabilities in freely expanding sheets of associating viscoelastic fluids

We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and suspensions of spherical oil droplets reversibly linked by polymers. The two types of samples display very similar linear viscoelastic properties, which can be described with a Maxwell fluid model, but contrasting nonlinear properties due to different network structures. Upon impact, the weakly viscoelastic samples exhibit a behavior qualitatively similar to that of Newtonian fluids: a smooth and regular sheet forms, expands, and then retracts. By contrast, for highly viscoelastic fluids, the thickness of the sheet is found to be very irregular, leading to instabilities and eventually to the formation of holes. We find that the rheological properties of the material rule the onset of instabilities. We first provide a simple image analysis of the expanding sheets to determine the onset of instabilities. We then demonstrate that the Deborah number related to the shortest relaxation time associated with the sample structure following a high shear is the relevant parameter that controls the heterogeneities in the thickness of the sheet, eventually leading to the formation of holes. When the sheet tears-up, data suggest by contrast that the opening dynamics depends also on the expansion rate of the sheet.

Stabilization of Supramolecular Polymer Phase at High Pressures

We utilize dynamic light scattering (DLS) and passive microrheology to examine the phase behavior of a supramolecular polymer at very high pressures. The monomer, 2,4-bis(2-ethylhexylureido)toluene (EHUT), self-assembles into supramolecular polymeric structures in the nonpolar solvent cyclohexane by means of hydrogen bonding. By varying the concentration and temperature at atmospheric pressure, the formation of the viscoelastic network (at lower temperatures) and predominantly viscous phases, based on self-assembled tube and filament structures, respectively, has been established. The associated changes in the rheological properties have been attributed to a structural thickness transition. Here, we investigate the effects of pressure variation from atmospheric up to 1 kbar at a given concentration. We construct a temperature-pressure diagram that reveals the predominance of the viscoelastic network phase at high pressures. The transition from the viscoelastic network organization of the tubes to a weaker viscous-dominated structure of the filaments is rationalized by using the Clapeyron equation, which yields an associated volume change of about 8 ų per EHUT molecule. This change is further explained by means of Molecular Dynamics simulations of the two phases, which show a decrease in the molecular volume at the filament-tube transition, originating from increased intermolecular contacts in the tube with respect to the filament. These findings offer insights into the role of pressure in stabilizing self-assemblies.