Our ability to synthesize faceted nanoparticles of tunable shapes and sizes has opened up many intriguing applications of such particles. However, our progress in understanding, modeling, and simulating their collective rheology, phase behavior, and self-assembly has been hindered by the lack of analytical interparticle interaction potentials. Here, we present one of the first analytical models for the van der Waals interaction energy between faceted nanoparticles. The model was derived through various approximations that reduce the usual six-dimensional integral over particle volumes to a series of two-dimensional integrals over particle interaction areas with closed-form solutions. Comparison and analyses of energies obtained from the analytical model with those computed from exact atomistic calculations show that the model approximations lead to insignificant errors in predicted energies across all relevant particle configurations. We demonstrate that the model yields accurate energies for diverse particle shapes including nanocubes, triangular prisms, faceted rods, and square pyramids, while yielding many orders of magnitude improvement in computational efficiency compared to atomistic calculations. To make the model more accessible and to demonstrate its applicability, an open-source graphical user interface application implementing the model for nanocubes in arbitrary configurations has been developed. We expect that the analytical model will accelerate future investigations of faceted nanoparticles that require accurate calculation of interparticle interactions.

中文翻译：

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刻面纳米粒子的分析范德华相互作用势

我们合成具有可调形状和大小的多面纳米粒子的能力开辟了此类粒子的许多有趣应用。但是，由于缺乏分析性粒子间相互作用的潜力，阻碍了我们在理解，建模和模拟其集体流变学，相行为和自组装方面的进展。在这里，我们提出了多面纳米粒子之间范德华相互作用能的首批分析模型之一。该模型是通过各种近似方法得出的，这些近似方法将粒子体积上的常规六维积分减少为具有封闭形式解的粒子相互作用区域上的一系列二维积分。从分析模型获得的能量与从精确原子计算中计算出的能量进行比较和分析，结果表明，模型近似值在所有相关粒子构型中的预测能量中均导致不明显的误差。我们证明了该模型可为包括纳米立方体，三角形棱柱，刻面杆和方形金字塔在内的各种粒子形状产生准确的能量，同时与原子计算相比，在计算效率上可提高许多数量级。为了使模型更易于访问并证明其适用性，已开发了一种开源图形用户界面应用程序，该程序以任意配置实现了纳米立方体的模型。