Molecular dynamics simulations have mapped the structure, thermodynamics, and dynamics of liquid water confined in hydrophobic graphene slit pores for wall separations δ\delta from 6.5 to 17 Å at 300 K, revealing layer-commensurate oscillations of the confinement free energy and diffusion. Two issues were left open by Leoni, Calero, and Franzese (ACS Nano 2021): (1) preliminary snapshots suggest that water cavitates — the liquid spontaneously converts to a vapor-filled state — for δ<6.5\delta<6.5 Å, the regime below their simulated range, and the authors explicitly call for further study of the relevance of cavitation in narrower hydrophobic nanopores, but whether cavitation in fact occurs, where the threshold lies under the source's simulation conditions, and its thermodynamic consequences remain unquantified for this system; (2) the confinement free energy of water shows no oscillatory feature near δ≈14\delta\approx 14 Å, unlike the simple and core-softened fluids (one-component model fluids whose pair potential adds a soft repulsive shoulder to a hard core and which reproduce water-like thermodynamic anomalies) studied alongside it — the paper notes in passing that this oscillation is 'not observed, possibly, for lack of resolution' in the 0.5 Å sampling grid, and it is unknown whether this absence is physical or an artifact. Confinement-induced evaporation is well established for SPC/E water between generic hydrophobic plates, but the sub-6.5 Å graphene-slit regime at the source's conditions, and a finer scan of the 14 Å region, have not been studied.

Background

When a liquid is squeezed between two atomically flat solid walls separated by a distance δ\delta of order the molecular size, its properties oscillate with δ\delta: the density forms layers parallel to the walls, and the free energy cost of confining the fluid alternates between minima at separations that comfortably accommodate an integer number of layers and maxima at intermediate separations. For water between hydrophobic walls (surfaces, such as graphene, that attract water only weakly and without specific binding sites), these oscillations can be computed in molecular dynamics (MD) simulations, in which the trajectories of molecules obeying a prescribed force field are integrated numerically. Common rigid, non-polarizable water models used in such simulations include TIP4P/2005 and SPC/E, both of which place fixed partial charges on oxygen and hydrogen sites plus a Lennard-Jones repulsion-dispersion interaction on oxygen. In these models a slit pore is built from two parallel graphene sheets interacting with water through Lennard-Jones forces, and the confined fluid exchanges molecules with a bulk-like reservoir so that its chemical potential (the thermodynamic variable controlling how much substance enters the pore) is fixed. The oscillating part of the confinement free energy generates an oscillating hydration pressure — the force per area that the confined fluid exerts to push the walls apart or pull them together. Cavitation here means the spontaneous formation of a vapor phase inside the pore: below a critical wall separation (or pressure), the liquid state of confined water can lose thermodynamic stability and the slit empties, a phenomenon also called capillary evaporation or drying. That this genuinely occurs under hydrophobic nanoconfinement is established: Giovambattista, Rossky, and Debenedetti (2006) simulated SPC/E water between nanoscale hydrophobic plates and found capillary evaporation below a pressure-dependent critical separation (about 0.5 nm at 0.1 GPa, growing to 1.6 nm under tension), producing a pressure–separation phase diagram with vapor, liquid, and bilayer-ice regions; Ferguson et al. (2012) extended this to 0.40–0.80 nm slits and analyzed the mechanism by which confined bilayer ice sublimates through the nucleation of a bridging vapor cavity; reviews (Giacomello and Roth 2020) frame bubble formation in nanopores as a general competition of hydrophobicity, geometry, and size; and in biology, synthetic macrocyclic host molecules are known to exploit partial cavitation of their water-filled cavities to optimize binding energy (Biedermann et al. 2012). Against this backdrop, Leoni, Calero, and Franzese (ACS Nano 2021) compared, in identical graphene slit pores at 300 K, a simple Lennard-Jones fluid, an anomalous core-softened fluid (a one-component model fluid whose pair potential superposes a soft repulsive shoulder on a hard core and which is known to reproduce water-like thermodynamic anomalies), and TIP4P/2005 water, using the 6.5–17 Å data set of Calero and Franzese (2020) for water. All three fluids show layer-commensurate oscillations of the confinement free energy, but water is unique in the entropic versus energetic character of its minima (an entropy-driven monolayer minimum, an energy-driven and more stable bilayer minimum) and in its strongly enhanced sub-nanometer diffusion. The comparison, however, stops at δ=6.5\delta=6.5 Å: the authors state that for δ<6.5\delta<6.5 Å their preliminary snapshots suggest the occurrence of cavitation, consistent with the earlier SPC/E plate results, that they do not observe cavitation in the presented cases, and that further study is needed to explore the relevance of cavitation in hydrophobic nanopores smaller than those studied. In addition, one oscillation of the confinement free energy that the two isotropic fluids display near δ≈14\delta\approx 14 Å is not observed for water, possibly for lack of resolution in the 0.5 Å simulation grid. Both unresolved issues concern the same object — the stability and free-energy landscape of water as a continuous function of hydrophobic slit width — and its completion from the monolayer regime down to the limit where the slit is too narrow for water at all.

Problem Statement

For liquid water in equilibrium with a bulk reservoir at 300 K confined in a hydrophobic graphene slit pore of wall separation δ\delta — the system of the source study: TIP4P/2005 water, a bulk reservoir pressure of about 400 atm, and two rigid graphene plates with the same CHARMM27-type water–carbon Lennard-Jones interaction (Lorentz–Berthelot combining rules) as in that study — the existing systematic data cover only 6.5 A˚≤δ≤17 A˚6.5\ \text{Å}\le\delta\le17\ \text{Å} (0.5 Å increments). Determine, as one program completing the map of the state and stability of confined water versus slit width: (1) whether the confined liquid cavitates — spontaneously empties into a vapor-filled state — for δ<6.5\delta<6.5 Å, and locate the cavitation threshold under these conditions: the critical slit width δc\delta_c at which the filled slit loses thermodynamic stability, defined here as the coexistence width at which the filled and vapor states have equal grand potential at the fixed reservoir conditions (near δc\delta_c each state can remain locally stable over a range of widths, so the coexistence width and the limits of local stability are distinct numbers wherever they are distinguishable), together with the thermodynamic consequences (the confinement free energy and hydration pressure across the transition); and (2) whether the confinement free energy of water in the graphene slit pore has an oscillatory feature near δ≈14 A˚\delta\approx14\ \text{Å} — present in the simple and core-softened fluids compared in the source study but not resolved for water — an absence whose physical or resolution-limited character is undetermined. Because the numerical value of the threshold depends on the convention for δ\delta (carbon-plane versus accessible width), δc\delta_c is defined only together with the convention used. Both parts target the same object, the δ\delta-resolved free-energy landscape of water in the hydrophobic slit, from the bulk-like limit down to widths too narrow to accommodate a single water layer.

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