# Difference between revisions of "A comparison of jamming behavior in systems composed of dimer- and ellipse-shaped particles"

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Carl F. Schreck, Ning Xu and Corey S. O'Hern

Soft Matter 6 (2010) 2960-2969

wiki entry by Emily Russell, Fall 2010

The article can be found here.

## Overview and Comments

This paper touches on several properties of jammed systems of concave dimers and concave elliptical particles, including jamming volume fraction, average contact number at jamming, vibrational mode spectrum, variation of shear modulus with volume fraction, stress-strain relations and yield stresses, and nematic ordering. It is a somewhat dense paper that goes rather quickly through all of these properties, but it argues effectively that the details of the shape of anisotropic particles can have significant effects on the behavior of jammed systems. Dimers behave similarly to simple disks in many ways, whereas ellipses show novel behaviors.

## Simulations

Fig. 1 Definition of the aspect ratio $\alpha$ = a/b (ratio of the major to minor axes) for (a) ellipses and (b) dimers.

The authors consider the packing of two geometrical shapes, as shown in Fig. 1: ellipses, and dimers made up of two identical circular disks. In each case, they consider aspect ratios $\alpha$ in the range $1\leq\alpha\leq2$. All simulations were done in two dimensions, so that each particle has three degrees of freedom, two translational and one rotational. Simulations were done on bidisperse systems, with populations of both large and small particles with the same aspect ratio, to inhibit crystallization so that jamming, glassy behavior could be studied.

The particles were modeled as interacting with a soft repulsive potential (which required some tricky geometry for working out the contact distance of two randomly-oriented ellipses). The packings were generated by randomly placing particles at a low volume fraction, and then incrementally increasing their size and relaxing the system until a jammed system was reached. Shear experiments were simulated quasi-statically, introducing an incremental shear, relaxing the system and measuring the strain, and repeating until a final shear strain of 1 was reached.

## Results

Fig. 2 Ensemble averaged contact number zJ at jamming as a function of aspect ratio $\alpha$ for dimers (squares) and ellipses (circles) for N = 480 particles.