O'Hern Corey S, Silbert Leonardo E, Liu Andrea J, Nagel Sidney R
Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1569, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 1):011306. doi: 10.1103/PhysRevE.68.011306. Epub 2003 Jul 25.
We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero. The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors. Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. Indeed, at point J, the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.
我们研究了由相互作用的粒子组成的二维和三维系统，这些粒子具有有限范围的排斥势，在零温度和零外加应力下会发生堵塞（即在无序状态下产生屈服应力）。在低填充率φ下，系统不会堵塞，每个粒子都可以不受相邻粒子的阻碍而移动。对于每种构型，都存在一个独特的堵塞阈值φ(c)，在该阈值下粒子无法再相互避开，体积模量和剪切模量同时变为非零。随着系统尺寸的增加，φ(c)值的分布变得更窄，以至于在热力学极限下，基本上所有构型都在相同的填充率下堵塞。这个填充率对应于先前测量的随机密堆积值。事实上，我们的结果为“随机密堆积”提供了一个明确的定义，即所有具有堵塞固有结构的相空间部分的比例。堵塞阈值点J出现在零温度、零外加应力和随机密堆积密度下，具有类似于普通临界点的性质。当从更高的填充率接近点J时，发现对关联函数中第一个峰值的发散以及压力、剪切模量和重叠邻居过量数的消失呈现幂律标度。此外，在点J附近，某些量不再自平均，这表明存在一个在J点发散的长度尺度。然而，点J也与普通临界点不同：标度指数不依赖于维度，但依赖于粒子间势。最后，当从高填充率接近点J时，振动状态密度出现大量低频模式过剩。实际上，在点J处，状态密度一直到零频率都是常数。所有这些结果表明，点J是最大无序点，可能控制其附近的行为——甚至可能在玻璃化转变时也是如此。
