# Difference between revisions of "Jamming phase diagram for attractive particles"

Original Entry: Nick Chisholm, AP 225, Fall 2009

## General Information

Authors: V. Trappe, V. Prasad, Luca Cipelletti, P.N. Segre, and D. A. Weitz

Publication: Nature 411 772-775 (2001)

## Soft Matter Keywords

Colloid, Elastic Modulus, Jamming Transition, Stress, Viscosity

## Summary

In this article, the authors present experimental evidence supporting theoretical proposals (see Figure 1) suggesting that a jamming phase diagram could be used in order to describe attractive particle systems, where the attractive interactions play a role similar to that of confining pressure. The fluid-to-solid transition of weakly attractive colloid particles is studied in detail, and the results conclude that they undergo a similar gelation behavior (when compared to granular media, colloidal suspensions, and molecular systems which are described by jamming phase diagrams) with increasing concentration and decreasing thermalization or stress. The authors thus claim that their results support the idea of a jamming phase diagram for attractive colloid particles, providing a unifying link between the glass transition, gelation, and aggregation.

Figure 1, taken from [1].

## Soft Matter Discussion

The authors used data from three very different colloid systems (namely, carbon black, polymethyl methacrylate (PMMA), and polystyrene) in order to create the phase diagram shown in Figure 2. As is very clear from the diagram, it was found that as one increases density, or decreases temperature or applied stress, the particles jam. One should note, though, that jamming can occur at low density, or high temperature or applied stress, but that the volume in phase space over which this jamming occurs is very small. The solvent is treated as an inert background, and thus the density is set explicitly by the volume fraction $\phi$. It is also rather obvious that the interparticle attractive energy, $U$, sets the scale for the temperature. Finally, the stress scale is set by $\sigma_{0} = \frac{k_{B}T}{a^{3}}$, where $a$ is the radius of the colloid particle. It is important to note that the authors identified a jammed solid by the existence of a stress-bearing, interconnected network which results in a low-frequency plateau of the elastic modulus.

Figure 2 is an extrapolation of experimental work done on the three different colloid systems noted above. In fact, general functional forms for the critical values of volume fraction, temperature, and stress were found, and from those this figure was constructed.

One will notice that Figure 2 varies significantly from Figure 1. In particular, for attractive colloids, we see there exists irreversible aggregation, a hard sphere limit, and sintered solid limit. I was rather disappointed by the lack of physical description of why these limits exist for attractive colloids (since the authors mention that they have to do with "particular details of attractive colloidal particles"), and why one would expect (or not expect) such a deviation from the theory.

Figure 2, taken from [1].

This article is intriguing from a fundamental point of view. The fact that the authors take three very different colloid systems and form a realistic jamming phase diagram from their experimental results is quite interesting. However, I am still curious as to why the jamming phase diagram they found predicts the asymptotic behavior that it does. For example, for very low density, one would expect that jamming could not occur (think of just one colloid on its own; can it jam with itself?). Perhaps these experiments are only telling part of the story, and further work needs to be done in order to rectify these asymptotic regions.

[Note: The authors explicitly state that jamming phase diagrams for attractive particles may deviate from the one they show, but that they will deviate in details and not in overall shape.]

## Reference

[1] V. Trappe, V. Prasad, Luca Cipelletti, P.N. Segre, and D. A. Weitz, "Jamming phase diagram for attractive particles," Nature 411 772-775 (2001).