Cluster morphology of spherical particles interacting with a short-range attraction has been extensively studied due to its relevance to many applications, such as the large-scale structure in amorphous materials, phase separation, protein aggregation, and organelle formation in cells. Although it was widely accepted that the range of the attraction solely controls the fractal dimension of clusters, recent experimental results challenged this concept by also showing the importance of the strength of attraction. Using Monte Carlo simulations, we conclusively demonstrate that it is possible to reduce the dependence of the cluster morphology to a single variable, namely, the reduced second virial coefficient, $B_2^{*}$, linking the local properties of colloidal systems to the extended law of corresponding states. Furthermore, the cluster size distribution exhibits two well-defined regimes: one identified for small clusters, whose fractal dimension, $d_f$, does not depend on the details of the attraction, i.e., small clusters have the same $d_f$, and another related to large clusters, whose morphology depends exclusively on $B_2^{*}$, i.e., $d_f$ of large aggregates follows a master curve, which is only a function of $B_2^{*}$. This physical scenario is confirmed with the reanalysis of experimental results on colloidal-polymer mixtures.

中文翻译：

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可逆聚集和胶体团簇形态：对应国家扩展法的重要性

球形颗粒与短程吸引相互作用的团簇形态已被广泛研究，因为它与许多应用相关，例如非晶态材料中的大规模结构，相分离，蛋白质聚集和细胞中细胞器的形成。尽管人们普遍认为吸引力的范围仅控制团簇的分形维数，但最近的实验结果通过显示吸引力强度的重要性也对这一概念提出了挑战。使用蒙特卡洛模拟，我们最终证明可以降低簇形态对单个变量的依赖性，即降低的第二维里系数，${乙}_{\mathrm{2个}}^{*}$，将胶体系统的局部特性与相应状态的扩展定律联系起来。此外，簇的大小分布表现出两种定义明确的机制：一种是针对小簇的，其分形维数是$d_F$，不取决于景点的细节，即小簇具有相同的 $d_F$，以及另一个与大型簇有关的簇，其形态完全取决于 ${乙}_{\mathrm{2个}}^{*}$， IE， $d_F$ 大集合体遵循主曲线，这仅是 ${乙}_{\mathrm{2个}}^{*}$。重新分析胶体-聚合物混合物的实验结果证实了这种物理情况。