Numerical calculations have been performed to investigate the effects of electrostatic and van der Waals interactions on coalescing silicon nanoparticles in isotropic low-temperature argon–silane plasmas. The electrostatic interaction between nanoparticles is modeled using three approaches, including the elementary Coulomb interaction, a rigorous electrostatic multipolar expansion, and an approximate form of the latter. The van der Waals interaction is described using the Hamaker expression regularized at short separation distance to manage the singularity at the contact surface. The evolution of the size and charge distributions are calculated by solving the general dynamic equation numerically for the coagulation of charged particles and using simplified approaches for nucleation, surface growth, and self-consistent plasma dynamics. A two-population size distribution, as observed in experiments, results naturally from this model. The electrostatic multipolar force is found to enhance the coagulation as compared to the elementary Coulomb force. The details of the growth process depend, however, significantly on the adopted regularization of the Hamaker expression at a short distance.

已经进行了数值计算来研究静电和范德华相互作用对各向同性低温氩-硅烷等离子体中聚结的硅纳米颗粒的影响。使用三种方法对纳米粒子之间的静电相互作用进行建模，包括基本库仑相互作用，严格的静电多极膨胀以及后者的近似形式。范德华相互作用是使用Hamaker表达式描述的，该表达式在较短的分隔距离处正则化，以管理接触表面的奇异性。尺寸和电荷分布的演变是通过数值求解带电粒子凝聚的一般动力学方程并使用简化的成核，表面生长和自洽等离子体动力学方法来计算的。如在实验中观察到的，两个人的大小分布自然来自此模型。与基本库仑力相比，发现静电多极力增强了凝结作用。但是，生长过程的细节很大程度上取决于在短距离内对Hamaker表达式采用的正则化。