Comparison of collision rate coefficient model predictions for different interaction strengths and temperatures

Abstract

The formation of aerosol particles from the vapor phase is a common process in both natural and industrial systems, where bimolecular collisions drive the very first step of the phase transition. Widely used analytical models, such as the non-interacting hard-sphere (NHS) and central field (CF) models, offer fast and straightforward predictions for bimolecular collision rate coefficients. However, their accuracy varies depending on the interaction strength between the collision partners. The NHS model neglects long-range forces, leading to underperformance in strongly interacting systems, while the CF model assumes point-like particles, reducing its reliability in weakly interacting systems. The recently developed interacting hard-sphere (IHS) model (Yang et al., 2023) addresses these limitations by incorporating both long-range interactions and the finite sizes of the colliding species. Despite the widespread use of these models, there is limited guidance on their applicability across different systems. In this work, we systematically evaluated the NHS, CF, and IHS models and propose a practical rule of thumb for selecting the most appropriate model. We applied this rule of thumb to a range of collision systems with varying interaction strengths and validated it against classical atomistic force field molecular dynamics simulations. Our findings show that the IHS model most accurately reproduces molecular dynamics-derived collision rate coefficients and smoothly converges to the NHS and CF models in the weak and strong interaction limits, respectively. Moreover, we find that the simpler CF model is sufficiently accurate for most systems at ambient conditions. This work provides practical guidance for balancing accuracy and complexity when predicting collision rate coefficients.