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

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− | 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 as 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. The solvent is treated as an inert background, and thus the density is set explicitly by the volume fraction <math>\phi</math>. It is also rather obvious that the interparticle attractive energy, <math>U</math>, sets the scale for the temperature (which thermalizes the system). Finally, the stress scale is set by <math>\sigma_{0} = \frac{k_{B}T}{a^{3}}</math>, where <math>a</math> 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. | + | 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 as 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 <math>\phi</math>. It is also rather obvious that the interparticle attractive energy, <math>U</math>, sets the scale for the temperature (which thermalizes the system). Finally, the stress scale is set by <math>\sigma_{0} = \frac{k_{B}T}{a^{3}}</math>, where <math>a</math> 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. | 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. |

## Revision as of 05:43, 12 November 2009

Original Entry: Nick Chisholm, AP 225, Fall 2009

## Contents

## 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.

Please see the definition of Jamming Transition before continuing to read this article review.

## 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 as 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 <math>\phi</math>. It is also rather obvious that the interparticle attractive energy, <math>U</math>, sets the scale for the temperature (which thermalizes the system). Finally, the stress scale is set by <math>\sigma_{0} = \frac{k_{B}T}{a^{3}}</math>, where <math>a</math> 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 is irreversible aggregation (in the limit of large , a hard sphere limit, and sintered solids.

This article is intriguing from a fundamental point of view. Considering the fact that it takes three very different colloid systems and forms a realistic, functional jamming phase diagram from their experimental results is quite interesting.

## 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).