Jamming phase diagram for attractive particles

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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.

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

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 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.

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.

Figure 2, taken from [1].

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).