Reynolds Philip A, McGillivray Duncan J, Jackson Andrew J, White John W
Research School of Chemistry, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 1):011301. doi: 10.1103/PhysRevE.80.011301. Epub 2009 Jul 1.
We measured ultra-small-angle neutron scattering (USANS) from polymethylmethacrylate spheres tamped down in air. Two slightly polydisperse pure sphere sizes (1.5 and 7.5 microm diameters) and five mixtures of these were used. All were loose packed (packing fractions of 0.3-0.6) with nongravitational forces (e.g., friction) important, preventing close packing. The USANS data are rich in information on powder packing. A modified Percus-Yevick fluid model was used to parametrize the data-adequately but not well. The modifications required the introduction of small voids, less than the sphere size, and a parameter reflecting substantial deviation from the Percus-Yevick prediction of the sphere-sphere correlation function. The mixed samples fitted less well, and two further modifying factors were necessary. These were local inhomogeneities, where the concentration of same-size spheres, both large and small, deviated from the mean packing, and a factor accounting for the presence within these "clusters" of self-avoidance of the large spheres (that is, large spheres coated with more small spheres than Percus-Yevick would predict). The overall deviations from the hard-sphere Percus-Yevick model that we find here suggest that fluid models of loose packed powders are unlikely to be successful but lay the ground work for future theoretical and computational works.
我们测量了在空气中夯实的聚甲基丙烯酸甲酯球体的超小角中子散射（USANS）。使用了两种略有多分散性的纯球体尺寸（直径分别为1.5微米和7.5微米）以及它们的五种混合物。所有样品都是松散堆积的（堆积分数为0.3 - 0.6），非重力作用（如摩擦力）很重要，阻止了紧密堆积。USANS数据包含了丰富的粉末堆积信息。使用了一种改进的Percus - Yevick流体模型对数据进行参数化——结果还算合适但并不理想。这些修改需要引入小于球体尺寸的小空隙，以及一个反映与Percus - Yevick球体 - 球体相关函数预测有显著偏差的参数。混合样品的拟合效果较差，还需要另外两个修正因素。这些因素包括局部不均匀性，即相同尺寸球体（无论大小）的浓度偏离平均堆积情况，以及一个考虑在这些“团簇”中存在大球体自回避现象的因素（也就是说，大球体表面包裹的小球体比Percus - Yevick模型预测的更多）。我们在此发现的与硬球Percus - Yevick模型的总体偏差表明，松散堆积粉末的流体模型不太可能成功，但为未来的理论和计算工作奠定了基础。
