Density fluctuations in hard-sphere systems

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Abstract
In order to understand the effects of density fluctuations in composite systems, we have studied the effects of compression rate on the final density and density variations in a system of hard spheres. Systems of 900 and 1800 mono‐sized spheres are placed in a box with periodic boundary conditions in the x and y directions and walls at z=0 and z=w(t). Using hard‐sphere interactions between the particles, the cell is compressed at a constant rate κ∝−dw/dt under isothermal conditions until the pressure diverges and an overlap occurs between the particles or with the walls. The final particle volume is then subdivided into smaller cells, each containing about 15 particles with a local density p(x). Macroscopic fluctuations in the density are measured by the coarseness parameter Cp=σp/p̄, where σp is the standard deviation of the local densities and p̄ is the average density. Surprisingly, the coarseness reaches a maximum at intermediate compression rates and, within the range of compression rates studied, the most homogeneous particle packings are generated by fast compressions. For compression rates above 1, the distribution function of the local densities is a Gaussian with a mean close to the random dense packing value p(x)≊0.64. For compression rates below 1, local regions vary from randomly dense‐packed [p(x)≊0.64] to close‐packed [ p(x)≊0.74] with a correspondingly high coarseness. So for κ<1, the distribution function is bimodal with peaks near the random‐dense packing and the close‐packing values. At the highest compression rates, the pressure exhibits no anomalies and the radial distribution function shows no signs of crystallization. Consequently, the densities and coarseness are very reproducible. At slower compression rates with κ<1, large variations in the final densities and coarsenesses coincide with the formation of local crystallites in portions of the volume.