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Ice nucleation plays a pivotal role in many natural and industrial processes, and molecular simulations have proven vital in uncovering its kinetics and mechanisms. A fundamental component of such simulations is the choice of an order parameter (OP) that quantifies the progress of nucleation, with the efficacy of an OP typically measured by its ability to predict the committor probabilities. Here, we leverage a machine learning framework introduced in our earlier work [Domingues et al., J. Phys. Chem. Lett. 15, 1279, (2024)] to systematically investigate how key implementation details influence the efficacy of standard Steinhardt OPs in capturing the progress of both homogeneous and heterogeneous ice nucleation. Our analysis identifies distance and q6 cutoffs as the primary determinants of OP performance, regardless of the mode of nucleation. We also examine the impact of two popular refinement strategies, namely chain exclusion and hydration shell inclusion, on OP efficacy. We find neither strategy to exhibit a universally consistent impact. Instead, their efficacy depends strongly on the chosen distance and q6 cutoffs. Chain exclusion enhances OP efficacy when the underlying OP lacks sufficient selectivity, whereas hydration shell inclusion is beneficial for overly selective OPs. Consequently, we demonstrate that selecting optimal combinations of such cutoffs can eliminate the need for these refinement strategies altogether. These findings provide a systematic understanding of how to design and optimize OPs for accurately describing complex nucleation phenomena, offering valuable guidance for improving the predictive power of molecular simulations. 

Molecular simulations serve as indispensable tools for investigating the kinetics and elucidating the mechanism of hindered ion transport across nanoporous membranes. In particular, recent advancements in advanced sampling techniques have made it possible to access translocation timescales spanning several orders of magnitude. In our prior study [Shoemaker et al., J. Chem. Theory Comput. 18, 7142 (2022)], we identified significant finite size artifacts in simulations of pressure-driven hindered ion transport through nanoporous graphitic membranes. We introduced the ideal conductor model, which effectively corrects for such artifacts by assuming the feed to be an ideal conductor. In the present work, we introduce the ideal conductor dielectric model (Icdm), a generalization of our earlier model, which accounts for the dielectric properties of both the membrane and the filtrate. Using the Icdm model substantially enhances the agreement among corrected free energy profiles obtained from systems of varying sizes, with notable improvements observed in regions proximate to the pore exit. Moreover, the model has the capability to consider secondary ion passage events, including the transport of a co-ion subsequent to the traversal of a counter-ion, a feature that is absent in our original model. We also investigate the sensitivity of the new model to various implementation details. The Icdm model offers a universally applicable framework for addressing finite size artifacts in molecular simulations of ion transport. It stands as a significant advancement in our quest to use molecular simulations to comprehensively understand and manipulate ion transport processes through nanoporous membranes.