# Memories of paste

Original entry: Becca Perry

Second Entry: Haifei Zhang, AP 225, Fall 2009

## Overview

Weitz describes toothpaste as a paste we are all familiar with. S. Ehardt, Wikimedia Commons

Pastes are not the simple materials they appear to be. It seems they have a ‘memory’: after a force has been applied, they recover and move back in the opposite direction.

Keywords: Paste, Microgel, Stress, Relaxation, Ageing, Rheology

## Summary

Weitz's article draws attention to the findings of Cloitre, Borrega, and Leibler and goes on to list related questions for future exploration.

Cloitre, Borrega, and Leibler studied the rheology of a paste consisting of pieces of microgel suspended in a fluid. A paste acts like a solid under low stress, but high stress makes the material flow like a liquid. In a solid-like state, the paste's constituent particles are jammed together in a disordered structure. Under sufficient stress, the structure breaks, and the particles flow. The response of pastes to stress is complex, and experiments are hard to reproduce.

Another interesting property of pastes is that small thermal fluctuations can cause the particles in the material to reach a more stable configuration. This means that the material changes or "ages" with time. The material properties depend on its history.

Cloitre, et al. studied the aging of their paste and found a memory for the direction of applied high stress. The researchers applied a high shear stress to turn the paste into a fluid and then removed the stress and allowed the material set like a solid. The material did not simply set up in the configuration left when the high shear stopped. The material remembered the direction of the high shear and pressed back in the opposite direction even though one might have expected the fluid flow at high shear to create a completely disordered system that would have no way to "remember" where it had been.

The discovery of paste memory led Weitz to pose some additional questions:

• 1) What causes the memory effect at a microscopic level?
• 2) Is the memory affect specific to the particular microgel paste studied by Cloitre et al., or does it apply to other pastes or even other kinds of soft matter?

## Soft Matter Details

Types of Soft Matter

As the title suggests, Memories of Paste focuses primarily on a class of soft materials called pastes. However, the author remarks on a similarity between pastes, gels, and glasses. "...the way a paste recovers from an applied stress is remarkably like the behaviour of glasses and gels" (Weitz p.32). This made me wonder:

• What is the difference between pastes, glasses, and gels? What about colloids?

"Pastes typically consist of a suspension of small particles in a background fluid. These particles are crowded, or jammed together like grains of sand on a beach, forming a disordered, glassy, or amorphous structure" (Weitz p.32). In the experiment described above, the particles in the paste are made of micro-gel. At low particle concentrations, the particles act like hard colloidal particles; however, at high concentrations the material acts like a paste (Cloitre et al. p. 4819).

A colloid is a suspension of solid (or sometimes liquid) particles dispersed in a liquid, so it seems that a paste is a type of colloid where the volume fraction of solid particles is quite high.

Weitz seems surprised that the paste responds like a glass or gel, so I must assume that pastes, gels, and glasses are all separate classes of soft matter.

Experimental Methods

Cloitre et al. made bulk rheological measurements using a rheometer to study a paste's response to stress. See their paper Rheological Aging and Rejuvenation in Microgel Pastes for more details. Cloitre et al. scale their data and plot it on a logarithmic master curve.

## Rheological Aging and Rejuvenation in Microgel Pastes

### Overview

The authors experimentally investigated the rheological behavior of concentrated suspensions of soft deformable microgels below the yield point. They have found history-dependent effects which are interpreted in terms of aging and rejuvenation phenomena, analogous to those existing in glassy systems. The stress amplitude controls the long-time memory and determines the slow evolution of the suspensions.

### Results

Strain recovery following flow cessation for different conditions of preparation Solid Triangle: $\sigma_P$ = 60 Pa; Solid Circle: $\sigma_P$ = 180 Pa; Hollow Circle: $\sigma_P$ = -180 Pa (the flow direction is reversed). $\sigma_P$ is applied for 60 s.

The right figure is from Cloitre et al.'s paper, data measured for various experimental condiditons are plotted. The strain origin and the time origin are taken at the end of preparation. It is observed that the strain recovery after flow cessation does not depend on the magnitude of $\sigma_P$ provided that it exceeds the yield stress $\sigma_y$.

This demonstrates that the strain recovery which follows flow cessation is associated with the relaxation of elastic deformations stored during flow. The recovery cannot be characterized by an intrinsic relaxation time like in viscoelastic materials. Instead, it is well represented by a logarithmic variation over at least five decades in time. Logarithmic relaxations have already been reported in systems as different as spin glasses, granular materials, and nematic elastomers. In this experiment, the fact that strain recovery persists up to the longest times experimentally accessible indicates that mechanical equilibrium is not reached during the waiting time . Nevertheless, by studying the response to the probe stress $\sigma_m$ when the stress amplitude and the waiting time are varied, valuable information about the rheological properties and their time evolution can be obtained.

### Summary

The paper gives us the following microscopic picture of the dynamics of soft colloidal pastes. Microgel pastes are fluidized when subjected to stresses exceeding the yield stress. Thin water films lubricate the contacts between microgels which move and exchange positions very rapidly. This mechanism is supported by detailed studies where microscopic parameters like polymer concentration, cross-link density, and ionic strength have been varied. When the external stress is removed, macroscopic flow stops and microgels get trapped in a metastable spatial arrangement corresponding to that existing in the fluidized paste. The evolution of the paste involves the reorientation, contraction, or expansion of the facets existing between microgels in a random way imposed by the disordered nature of the packing and the thermal fluctuations.

A change of the local topology between two contacting microgels induces long range perturbations between second, third, and even further neighbors. Moreover, local topological changes, although favorable, may be incompatible with more global constraints.

Strain relaxation is closely associated with collective rearrangements and frustration.

These two generic properties may be responsible for the logarithmic strain recovery which is observed upon flow cessation.

During aging, different spatial configurations of microgels with a broad distribution of relaxation times coexist in the paste. At time tW, only those configurations with relaxation times smaller than tW have relaxed, others have not but will eventually relax later on. When a very small stress sm is applied at time tW to probe the system, it does not create large topological rearrangements but it induces small deformations which add to the strains which did not have time to relax during tW. The short-time response is that of a viscoelastic solid with many relaxation times. The paste continues to evolve and, at times comparable to tW, the response becomes dominated by the relaxation of the strains which have not relaxed during aging. In contrast, when the stress sm is larger than sC, large rearrangements become possible and the pastes creep. The response is then a combination of aging and of partial rejuvenation.

In conclusion, time-dependent phenomena in paste rheology exhibit all the main features of aging in glassy systems. Rheological aging is closely associated with frustration and cooperative relaxation of steric constraints between interlocked neighboring particles. In that respect, we think that this is a general behavior which should be found in many other systems once the proper protocol to deal with far-from-equilibrium systems is recognized and implemented.

### Soft matter details

Mustard is a kind of paste

The kind of soft matter studied in the paper is micogel paste. In Soft Condensed Matter Physics, a paste is a substance that behaves as a solid until a sufficiently large load or stress is applied, at which point it flows like a fluid. In rheological terms, a paste is an example of a Bingham plastic fluid. Pastes typically consist of a suspension of granular material in a background fluid. The individual grains are jammed together like sand on a beach, forming a disordered, glassy or amorphous structure, and giving pastes their solid-like character. It is this "jamming together" that gives pastes some of their most unusual properties; this causes paste to demonstrate properties of fragile matter. Examples include starch pastes, toothpaste, mustard, and putty.

## References

[1] Weitz, D., Nature 410, 32-33 (2001).

[2] Cloitre, M., Borrega, R. & Leibler, L. Phys. Rev. Lett. 85, 4819-4822 (2000).

[3] Cipelletti, L., Manley, S., Ball, R. C. & Weitz, D. A. Phys. Rev. Lett. 84, 2275–2278 (2000).