(248g) Finite-Size Effects and Structure-Selectivity Relationships in Ion Transport through Nanopores

Understanding ion transport through nanopores is crucial for various separation processes, such as metal recovery, water desalination, and biological applications. The ultimate objective in membrane-based separations is to optimize the selectivity of targeted molecules while maintaining high permeability. Although achieving both goals simultaneously is challenging, efforts are made to minimize compromise. One approach involves testing new classes of materials with high permeability and selectivity, aiming to identify potential candidates for membrane design. Another approach is to optimize membrane design by exploring structure-selectivity relationships. Experimentally investigating such relationships at the scale of single-digit nanopores (SDNs) remains challenging due to limitations in achieving high spatiotemporal resolution. However, advancements in parallel programming algorithms, molecular simulations, and advanced sampling techniques have enabled access to very short time and length scales that were previously inaccessible through experiments. In this work, we investigate pressure-driven ion and water transport through graphene-based membranes (see figure) using molecular dynamics (MD) and forward flux sampling (FFS).

Modeling ion transport through membranes can introduce significant finite-size effects, particularly when the simulation box size is inadequate. Addressing these effects is crucial to ensure the validity and accuracy of simulations. In this study, we delve into the nature and extent of these finite-size effects arising from extraneous electrostatics imposed by the periodicity of the simulation box. Notably, these effects become pronounced when a charged particle (ion) traverses the membrane, leaving behind a charged feed. The periodic images of this feed exert artificial forces on the traversing ion. Furthermore, discrepancies in the dielectric constants across different system regions (feed, membrane, and filtrate) induce additional effects. To mitigate these challenges, we developed a physics-based model, specifically the ideal conductor model followed by a generalized model (Ideal conductor dielectric model - ICDM), which accounts for dielectric effects. This model effectively corrects for finite-size effects, enabling the derivation of accurate free energy profiles. Consequently, we can predict passage times and selectivities with improved precision. Additionally, we explore the extent of finite-size effects concerning pressure-driven hindered ion transport through nanopores in various systems characterized by structural factors such as the number of graphene layers and strength of pore charge. Our objective is to determine an optimal simulation box size that minimizes finite-size effects while maintaining computational efficiency. Implementing such a model enhances the fidelity of membrane-based simulations, aligning with the methodology employed in this study.

Through our investigation of multi-pore graphene membranes, we have uncovered significant pore-pore correlations that arise with proximity, exerting considerable influence on ion and solvent passage. Notably, these correlations adversely impact the passage of counter-ions and the polar solvent (water), while facilitating the passage of co-ions. As a result, both water permeability and salt rejection are diminished in close proximity with time scales that deviate from predictions made by models like the access resistance model. To address these findings, we propose a new, straightforward phenomenological model. This model considers pre-pore ion concentration and the forces exerted on traversing ions through dipole-decorated pores, enabling us to predict the relative impact of pore-pore correlations on ion selectivity in multi-pore membranes. Leveraging this model, we systematically screen multiple pore arrangements to identify those with minimal pore-pore correlations. Furthermore, our investigation delves into the effect of pore permanent dipole strength in terms of partial charges on ion selectivity and water permeability. Preliminary results suggest that counter-ions traverse faster through pores with stronger dipoles, while co-ions exhibit slower traversal due to reduced electrostatic pull from stronger charged dipoles. Overall, this work contributes to the design of more efficient membranes and enhances our understanding of nanoscale separation mechanisms, including those relevant to biological processes.