Dijkstra M, van Roij R, Evans R
H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt B):5744-71. doi: 10.1103/physreve.59.5744.
We study the phase behavior and structure of highly asymmetric binary hard-sphere mixtures. By first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective Hamiltonian of the large spheres. Then using an explicit pairwise (depletion) potential approximation to this effective Hamiltonian in computer simulations, we determine fluid-solid coexistence for size ratios q=0.033, 0.05, 0.1, 0.2, and 1.0. The resulting two-phase region becomes very broad in packing fractions of the large spheres as q becomes very small. We find a stable, isostructural solid-solid transition for q< or =0.05 and a fluid-fluid transition for q< or =0.10. However, the latter remains metastable with respect to the fluid-solid transition for all size ratios we investigate. In the limit q-->0 the phase diagram mimics that of the sticky-sphere system. As expected, the radial distribution function g(r) and the structure factor S(k) of the effective one-component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid-solid boundary the value of S(k) at its first peak is much lower than the value given by the Hansen-Verlet freezing criterion. Direct simulations of the true binary mixture of hard spheres were performed for q > or =0.05 in order to test the predictions from the effective Hamiltonian. For those packing fractions of the small spheres where direct simulations are possible, we find remarkably good agreement between the phase boundaries calculated from the two approaches-even up to the symmetric limit q=1 and for very high packings of the large spheres, where the solid-solid transition occurs. In both limits one might expect that an approximation which neglects higher-body terms should fail, but our results support the notion that the main features of the phase equilibria of asymmetric binary hard-sphere mixtures are accounted for by the effective pairwise depletion potential description. We also compare our results with those of other theoretical treatments and experiments on colloidal hard-sphere mixtures.
我们研究了高度不对称二元硬球混合物的相行为和结构。通过首先在配分函数中对小球体的自由度进行积分，我们推导出了大球体有效哈密顿量的形式表达式。然后在计算机模拟中对该有效哈密顿量使用显式的成对（耗尽）势近似，我们确定了尺寸比q = 0.033、0.05、0.1、0.2和1.0时的液 - 固共存情况。随着q变得非常小，在大球体的堆积分数中，所得的两相区域变得非常宽。我们发现对于q≤0.05存在稳定的、同结构的固 - 固转变，对于q≤0.10存在液 - 液转变。然而，对于我们研究的所有尺寸比，相对于液 - 固转变，后者仍然是亚稳的。在q→0的极限情况下，相图类似于粘性球体系统的相图。正如预期的那样，有效单组分系统的径向分布函数g(r)和结构因子S(k)没有显示出冻结转变开始的明显特征，并且我们发现在液 - 固边界的大多数点上，其第一个峰值处的S(k)值远低于汉森 - 韦尔莱特冻结判据给出的值。为了检验有效哈密顿量的预测，对q≥0.05的真实硬球二元混合物进行了直接模拟。对于那些可以进行直接模拟的小球体堆积分数，我们发现两种方法计算出的相边界之间有非常好的一致性——甚至直到对称极限q = 1以及大球体非常高堆积分数的情况，即发生固 - 固转变的情况。在这两种极限情况下，人们可能会预期忽略高阶项的近似会失效，但我们的结果支持这样一种观点，即不对称二元硬球混合物相平衡的主要特征可以通过有效的成对耗尽势描述来解释。我们还将我们的结果与其他关于胶体硬球混合物的理论处理和实验结果进行了比较。
