Chen D, Torquato S
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062207. doi: 10.1103/PhysRevE.92.062207. Epub 2015 Dec 23.
Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances H, small to large sphere radius ratio α, and small sphere relative concentration x. We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term "confinement frustration." Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with H, though exceptions exist. Discontinuities in the packing characteristics as H varies in the vicinity of certain values of H are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as α decreases), the rattler fraction dramatically increases due to what we call "size-disparity" frustration. We find that at intermediate α and when x is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric ψ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance σ(τ)(2)(R) to characterize confined packings and find that these packings possess essentially the same level of hyperuniformity as their bulk counterparts. Our findings are generally relevant to confined packings that arise in biology (e.g., structural color in birds and insects) and may have implications for the creation of high-density powders and improved battery designs.
受限条件下的无序紧密堆积受到的关注远少于其对应的体相堆积，但却出现在各种实际情况中。在这项工作中，我们研究了夹在两个平行硬平面之间的二元球体堆积，并推广了Torquato-Jiao（TJ）顺序线性规划算法[《物理评论E》82, 061302 (2010)]，以获得在大范围的平面间距H、从小到大致的球体半径比α以及小球体相对浓度x下，具有高精度且恰好各向同性的假定最大随机紧密（MRJ）堆积。我们发现堆积特性可能与其体相类似物有很大不同，这是由于我们所称的“受限挫折”。受限堆积中的游动体通常比其体相类似物中更为普遍。我们观察到MRJ堆积的堆积分数、游动体分数和无序度通常随H增加，不过也有例外情况。当H在某些特定值附近变化时，堆积特性的不连续性是由于不同紧密状态之间相关的不连续转变所致。当平面间距约为两个大球体直径或更小时，堆积呈现出显著的二维特征；当平面间距超过约30个大球体直径时，堆积趋近于三维体相堆积。随着尺寸对比度增加（即α减小），由于我们所称的“尺寸差异”挫折，游动体分数急剧增加。我们发现，在中间α值且x约为0.5（50 - 50混合）时，根据基于垂直于硬壁方向上数密度涨落的有序度量ψ来衡量，堆积的无序度达到最大。我们还应用局部体积分数方差σ(τ)(2)(R)来表征受限堆积，发现这些堆积与它们的体相类似物具有基本相同水平的超均匀性。我们的发现通常与生物学中出现的受限堆积（例如鸟类和昆虫的结构颜色）相关，并且可能对高密度粉末的制备和改进电池设计有启示意义。
