Jamming Phase Diagram

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Original entry by Hyerim Hwang, AP 225, Fall 2011.

Reference

V. Trappe, V. Prasad, Luca Cipelletti, P. N. Segre, and D. A. Weitz, "Jamming Phase Diagram for Attractive Particles", Nature 2001 411, 772-775

Keywords

Suspensions, Gels

Figure 1. The jamming phase diagram proposed by Liu and Nagel.

Introduction

Figure 2. Control parameters for the jamming transition. Optical micrographs showing the jamming phase transition for carbon black going from the fluid-like to solid-like state.

A wide variety of systems exhibit non-equilibrium transitions from a fluid-like to a solid-like state dynamics. Crowding or jamming of the constituent particles traps them kinetically, precluding further exploration of the phase space. Thd disordered fluid-like structure remains unchanged at the transition and the jammed solid can be refluidized by thermalization through temperature, vibration, or stress. This research support the concept of a jamming phase diagram for attractive colloidal particles, providing a unifying link between the glass transition, gelation, and aggregation.

Figure 3. Cuts along the phase boundary.
Figure 4. Composite jamming phase diagram for attractive colloidal particles.

Results

As shown in Figure 1, Liu and Nagel proposed temperature and stress as the axes of a three-dimensional phase diagram, with the jammed state in the inner octant. Here they consider attractive colloidal particles, and treat the suspending fluid as an inert background; thus the density is set explicitly by the particle volume fraction. To emphasize the generality of the concept, they used data from three vastly different colloid systems, carbon black, PMMA, and polystyrene. The essence of the use of a phase diagram to describe the jamming behavior is summarized by the optical micrographs of thin samples of carbon black shown in Figure 2. Figure 3 is an example of the phase boundaries for the other colloid systems as well, although the values of both the coefficients and exponents depend on the system. Full three-dimensional jamming phase diagram for attractive colloidal systems was plotted in Figure 4. The existence of this phase diagram supports the fundamental concept of jamming, and confirms the applicability of jamming to describe the behavior of attractive particles.

Discussion

From this paper, we can confirm that a phase diagram can be used to unify the description of a wide variety of transitions from fluid-like to solid-like behavior by means of the jamming transition and it justifies the applicability of the jamming transition in describing systems with attractive interactions. Jamming is a powerful means to account for a wide range of fluid-solid transitions found in colloid systems and rationalize diverse behavior for very different systems; the colloidal-glass transition, colloidal gelation and aggregation.