Dehydration as a Universal Mechanism for Ion Selectivity in Graphene and Other Atomically Thin Pores

Ion channels play a key role in regulating cell behavior and in electrical signaling. In these settings, polar and charged functional groups -- as well as protein response -- compensate for dehydration in an ion-dependent way, giving rise to the ion selective transport critical to the operation of cells. Dehydration, though, yields ion-dependent free-energy barriers and thus is predicted to give rise to selectivity by itself. However, these barriers are typically so large that they will suppress the ion currents to undetectable levels. Here, we establish that graphene displays a measurable dehydration-only mechanism for selectivity of $\mathrm{K}^+$ over $\mathrm{Cl}^-$. This fundamental mechanism -- one that depends only on the geometry and hydration -- is the starting point for selectivity for all channels and pores. Moreover, while we study selectivity of $\mathrm{K}^+$ over $\mathrm{Cl}^-$, we find that dehydration-based selectivity functions for all ions, i.e., cation over cation selectivity (e.g., $\mathrm{K}^+$ over $\mathrm{Na}^+$). Its likely detection in graphene pores resolves conflicting experimental results, as well as presents a new paradigm for characterizing the operation of ion channels and engineering molecular/ionic selectivity in filtration and other applications.Comment: 27 page

Diffusion Limitations and Translocation Barriers in Atomically Thin Biomimetic Pores

Ionic transport in nano- to sub-nano-scale pores is highly dependent on translocation barriers and potential wells. These features in the free-energy landscape are primarily the result of ion dehydration and electrostatic interactions. For pores in atomically thin membranes, such as graphene, other factors come into play. Ion dynamics both inside and outside the geometric volume of the pore can be critical in determining the transport properties of the channel due to several commensurate length scales, such as the effective membrane thickness, radii of the first and the second hydration layers, pore radius, and Debye length. In particular, for biomimetic pores, such as the graphene crown ether we examine here, there are regimes where transport is highly sensitive to the pore size due to the interplay of dehydration and interaction with pore charge. Picometer changes in the size, e.g., due to a minute strain, can lead to a large change in conductance. Outside of these regimes, the small pore size itself gives a large resistance, even when electrostatic factors and dehydration compensate each other to give a relatively flat -- e.g., near barrierless -- free energy landscape. The permeability, though, can still be large and ions will translocate rapidly after they arrive within the capture radius of the pore. This, in turn, leads to diffusion and drift effects dominating the conductance. The current thus plateaus and becomes effectively independent of pore-free energy characteristics. Measurement of this effect will give an estimate of the magnitude of kinetically limiting features, and experimentally constrain the local electromechanical conditions

Nonlinear behavior of thermal and ion transport at the nanoscale

Functional control at the nanoscale forms the foundation of biological systems. These work at the cellular level by manipulating ions and molecules. Nanoscale devices that give functional control at this scale are also becoming an important component in diverse fields such as electronics, medicine, engineering, and manufacturing. Moreover, scientific advances are making it technologically viable to control and observe matter at the atomic level. Computational techniques are an integral part in designing and understanding these systems, as they reveal the processes that are experimentally unobservable and allow for inexpensive screening and predictions. Since the atomistic nature of matter plays a major role at the nanoscale, classical all-atom molecular dynamic simulations are widely employed. We concentrate on thermal transport, ion transport, and nonlinear interactions at the nanoscale. For thermal transport, in particular, we develop a rigorous approach to computing thermal conductance by coupling a system of interest to two large ``extended reservoirs that act as heat source/sinks. Within this setup, we prove that the ``intrinsic conductance of the system can be obtained by having the extended reservoirs be large and weakly coupled to Langevin baths. For ion transport, we show that subnanoscale pores in monolayer graphene membranes display selectivity (not unlike biological ion channels but weaker) even when the graphene pores do not have charge or functional groups. The selectivity appears because the ions translocating through these pores lose some water from their solvation shell and different ions have different energy dehydration penalties. We also demonstrate that such selectivity can be tuned by adjusting the pore radius and number of graphene layers. This will enable the optimization of water flow and ion rejection for applications such as filtration and desalination. We also develop a finite-size scaling model to compute the effect of bulk electrolyte dimension on the ionic resistance. This separates the pore and the bulk electrolyte contribution to the total ionic resistance in molecular dynamics simulations. Additionally, in collaboration with an experimental group, we show that graphene is a good choice for a transparent cap for spectroscopy of water as it only has a minor influence on the structure of water.Keywords: Thermal Transport, Molecular Dynamics, Nonlinear Fluctuations, Nanopores, Ion Transport, Nanoscale Scienc

Crossover behavior of the thermal conductance and Kramers' transition rate theory

Kramers' theory frames chemical reaction rates in solution as reactants overcoming a barrier in the presence of friction and noise. For weak coupling to the solution, the reaction rate is limited by the rate at which the solution can restore equilibrium after a subset of reactants have surmounted the barrier to become products. For strong coupling, there are always sufficiently energetic reactants. However, the solution returns many of the intermediate states back to the reactants before the product fully forms. Here, we demonstrate that the thermal conductance displays an analogous physical response to the friction and noise that drive the heat current through a material or structure. A crossover behavior emerges where the thermal reservoirs dominate the conductance at the extremes and only in the intermediate region are the intrinsic properties of the lattice manifest. Not only does this shed new light on Kramers' classic turnover problem, this result is significant for the design of devices for thermal management and other applications, as well as the proper simulation of transport at the nanoscale.Comment: 8 pages, 5 figures. Supplementary Information available at the journal publication or by request from the author

Dehydration as a Universal Mechanism for Ion Selectivity in Graphene and Other Atomically Thin Pores

Ion channels play a key role in regulating cell behavior and in electrical signaling. In these settings, polar and charged functional groups, as well as protein response, compensate for dehydration in an ion-dependent way, giving rise to the ion selective transport critical to the operation of cells. Dehydration, though, yields ion-dependent free-energy barriers and thus is predicted to give rise to selectivity by itself. However, these barriers are typically so large that they will suppress the ion currents to undetectable levels. Here, we establish that graphene displays a measurable dehydration-only mechanism for selectivity of K+ over Cl–. This fundamental mechanism, one that depends only on the geometry and hydration, is the starting point for selectivity for all channels and pores. Moreover, while we study selectivity of K+ over Cl– we find that dehydration-based selectivity functions for all ions, that is, cation over cation selectivity (e.g., K+ over Na+). Its likely detection in graphene pores resolves conflicting experimental results, as well as presents a new paradigm for characterizing the operation of ion channels and engineering molecular/ionic selectivity in filtration and other applications

Crossover behavior of the thermal conductance and Kramers' transition rate theory

Kramers’ theory frames chemical reaction rates in solution as reactants overcoming a barrier in the presence of friction and noise. For weak coupling to the solution, the reaction rate is limited by the rate at which the solution can restore equilibrium after a subset of reactants have surmounted the barrier to become products. For strong coupling, there are always sufficiently energetic reactants. However, the solution returns many of the intermediate states back to the reactants before the product fully forms. Here, we demonstrate that the thermal conductance displays an analogous physical response to the friction and noise that drive the heat current through a material or structure. A crossover behavior emerges where the thermal reservoirs dominate the conductance at the extremes and only in the intermediate region are the intrinsic properties of the lattice manifest. Not only does this shed new light on Kramers’ classic turnover problem, this result is significant for the design of devices for thermal management and other applications, as well as the proper simulation of transport at the nanoscale