论文标题
几何标准，缺乏在非添加硬性粒子混合物中没有有效的多体相互作用的标准
Geometric criteria for the absence of effective many-body interactions in nonadditive hard particle mixtures
论文作者
论文摘要
我们考虑在任意空间维度中通过硬体势与非添加性排除体积相互作用相互作用的小型和大古典粒子的混合物。特别是，我们专注于Asakura-Oosawa（AO）模型的变体，其中忽略了小颗粒之间的相互作用，但存在大小和大的相互作用，并且可以将其凝结成单独的大颗粒之间的有效耗竭相互作用。原始AO模型在三个空间维度中涉及硬球颗粒，并与互动直径$σ_\ text {pp} = 0 $，$σ_\ text {cc}> 0 $和$σ_\ text {pc}> cc}> cc}/2 $ cc}/2 $， $\{i,j\}=\{\text{p},\text{c}\}$ (indicating the physical interpretation of the small and big particles as polymers (p) and colloids (c), respectively) is the minimum possible center-to-center distance between particle $i$ and particle $j$ allowed by the excluded-volume constraints.众所周知，如果几何条件$σ_\ text {pc}/σ_\ text {cc} <1/\ sqrt {3} $，则仅在大粒子之间存在成对有效的耗竭相互作用。在这种情况下，三胞胎和高阶的许多身体相互作用都消失了，并且可以将二进制混合物的平衡统计数据映射到有效的耗尽对势的有效单组分系统的统计上。在这里，我们严格地证明了这种几何标准，并将其推广到多分散的混合物和各个方面的各向异性粒子形状，提供足够的几何标准，足以保证缺乏三胞胎和高阶的许多身体相互作用。对于限制整个混合物的外部硬墙，我们还提供标准，该标准可以保证可以通过有效的外部一体相互作用将系统映射到一个系统上。
We consider a mixture of small and big classical particles in arbitrary spatial dimensions interacting via hard-body potentials with non-additive excluded-volume interactions. In particular, we focus on variants of the Asakura--Oosawa (AO) model where the interaction between the small particles is neglected but the big-small and big-big interactions are present and can be condensed into an effective depletion interaction among the big particles alone. The original AO model involves hard spherical particles in three spatial dimensions with interaction diameters $σ_\text{pp}=0$, $σ_\text{cc}>0$ and $σ_\text{pc}>σ_\text{cc}/2$ respectively, where $σ_{ij}$ with $\{i,j\}=\{\text{p},\text{c}\}$ (indicating the physical interpretation of the small and big particles as polymers (p) and colloids (c), respectively) is the minimum possible center-to-center distance between particle $i$ and particle $j$ allowed by the excluded-volume constraints. It is common knowledge that there are only pairwise effective depletion interactions between the big particles if the geometric condition $σ_\text{pc}/σ_\text{cc} < 1/\sqrt{3}$ is fulfilled. In this case, triplet and higher-order many body interactions are vanishing and the equilibrium statistics of the binary mixture can exactly be mapped onto that of an effective one-component system with the effective depletion pair-potential. Here we prove this geometric criterion rigorously and generalize it to polydisperse mixtures and to anisotropic particle shapes in any dimension, providing geometric criteria sufficient to guarantee the absence of triplet and higher-order many body interactions. For an external hard wall confining the full mixture, we also give criteria which guarantee that the system can be mapped onto one with effective external one-body interactions.
