Hussain Sarwar, Haji-Akbari Amir
Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA.
J Chem Phys. 2021 Jan 7;154(1):014108. doi: 10.1063/5.0026355.
Computational studies of crystal nucleation can be impacted by finite size effects, primarily due to unphysical interactions between crystalline nuclei and their periodic images. It is, however, not always feasible to systematically investigate the sensitivity of nucleation kinetics and mechanism to system size due to large computational costs of nucleation studies. Here, we use jumpy forward flux sampling to accurately compute the rates of heterogeneous ice nucleation in the vicinity of square-shaped model structureless ice nucleating particles (INPs) of different sizes and identify three distinct regimes for the dependence of rate on the INP dimension, L. For small INPs, the rate is a strong function of L due to the artificial spanning of critical nuclei across the periodic boundary. Intermediate-sized INPs, however, give rise to the emergence of non-spanning "proximal" nuclei that are close enough to their periodic images to fully structure the intermediary liquid. While such proximity can facilitate nucleation, its effect is offset by the higher density of the intermediary liquid, leading to artificially small nucleation rates overall. The critical nuclei formed at large INPs are neither spanning nor proximal. Yet, the rate is a weak function of L, with its logarithm scaling linearly with 1/L. The key heuristic emerging from these observations is that finite size effects will be minimal if critical nuclei are neither spanning nor proximal and if the intermediary liquid has a region that is structurally indistinguishable from the supercooled liquid under the same conditions.
晶体成核的计算研究可能会受到有限尺寸效应的影响，主要原因是晶核与其周期性镜像之间存在非物理相互作用。然而，由于成核研究的计算成本很高，系统地研究成核动力学和机制对系统尺寸的敏感性并不总是可行的。在这里，我们使用跳跃前向通量采样来精确计算不同尺寸的方形无结构模型冰核粒子（INPs）附近的异质冰成核速率，并确定速率对INP尺寸L的依赖性的三种不同情况。对于小尺寸的INPs，由于临界核在周期性边界上的人为跨越，速率是L的强函数。然而，中等尺寸的INPs会产生非跨越的“近端”核，这些核与其周期性镜像足够接近，足以使中间液体完全结构化。虽然这种接近度可以促进成核，但其效果被中间液体的较高密度抵消，导致总体上人为地降低了成核速率。在大尺寸INPs上形成的临界核既不是跨越的也不是近端的。然而，速率是L的弱函数，其对数与1/L呈线性缩放。从这些观察结果中得出的关键启发是，如果临界核既不是跨越的也不是近端的，并且中间液体有一个在相同条件下与过冷液体在结构上无法区分的区域，那么有限尺寸效应将最小。
