Erratum: Superfluid and Supersolid Phases of

This corrects the article DOI: 10.1103/PhysRevLett.124.205301.

Superfluid and Supersolid Phases of

We revisited the phase diagram of the second layer of ^{4}He on top of graphite using quantum Monte Carlo methods. Our aim was to explore the existence of the novel phases suggested recently in experimental works, and determine their properties and stability limits. We found evidence of a superfluid quantum phase with hexatic correlations, induced by the corrugation of the first Helium layer, and a quasi-two-dimensional supersolid corresponding to a 7/12 registered phase. The 4/7 commensurate solid was found to be unstable, while the triangular incommensurate crystals, stable at large densities, were normal.

Liquid and Solid Phases of

Recent heat-capacity experiments show quite unambiguously the existence of a liquid ^{3}He phase adsorbed on graphite. This liquid is stable at an extremely low density, possibly one of the lowest found in nature. Previous theoretical calculations of the same system, and in strictly two dimensions, agree with the result that this liquid phase is not stable and the system is in the gas phase. We calculated the phase diagram of normal ^{3}He adsorbed on graphite at T=0 using quantum Monte Carlo methods. Considering a fully corrugated substrate, we observe that at densities lower than 0.006 Å^{-2} the system is a very dilute gas that, at that density, is in equilibrium with a liquid of density 0.014 Å^{-2}. Our prediction matches very well the recent experimental findings on the same system. On the contrary, when a flat substrate is considered, no gas-liquid coexistence is found, in agreement with previous calculations. We also report results on the different solid structures, and on the corresponding phase transitions that appear at higher densities.

Atomic monolayer deposition on the surface of nanotube mechanical resonators.

We study monolayers of noble gas atoms (Xe, Kr, Ar, and Ne) deposited on individual ultraclean suspended nanotubes. For this, we record the resonance frequency of the mechanical motion of the nanotube, since it provides a direct measure of the coverage. The latter is the number of adsorbed atoms divided by the number of the carbon atoms of the suspended nanotube. Monolayers form when the temperature is lowered in a constant pressure of noble gas atoms. The coverage of Xe monolayers remains constant at 1/6 over a large temperature range. This finding reveals that Xe monolayers are solid phases with a triangular atomic arrangement, and are commensurate with the underlying carbon nanotube. By comparing our measurements to theoretical calculations, we identify the phases of Ar and Ne monolayers as fluids, and we tentatively describe Kr monolayers as solid phases. These results underscore that mechanical resonators made from single nanotubes are excellent probes for surface science.

Zero-temperature phase diagram of D2 physisorbed on graphane.

We determined the zero-temperature phase diagram of D2 physisorbed on graphane using the diffusion Monte Carlo method. The substrate used was C-graphane, an allotropic form of the compound that has been experimentally obtained through hydrogenation of graphene. We found that the ground state is the δ phase, a commensurate structure observed experimentally when D2 is adsorbed on graphite, and not the registered √3 x √3 structure characteristic of H2 on the same substrate.

Size effects on water adsorbed on hydrophobic probes at the nanometric scale.

Molecular dynamics simulations of liquid water at ambient conditions, adsorbed at the external walls of (n,n) single-walled armchair carbon nanotubes have been performed for n = 5, 9, 12. The comparison with the case of water adsorbed on graphene has also been included. The analysis of Helmholtz free energies reveals qualitatively different ranges of thermodynamical stability, eventually starting at a given threshold surface density. We observed that, in the framework of the force field considered here, water does not wet graphene nor (12,12) tubes, but it can coat thinner tubes such as (9,9) and (5,5), which indicates that the width of the carbon nanotube plays a role on wetting. On the other hand, density profiles, orientational distributions of water, and hydrogen-bond populations indicate significant changes of structure of water for the different surfaces. Further, we computed self-diffusion of water and spectral densities of water and carbon molecules, which again revealed different qualitative behavior of interfacial water depending on the size of the nanotube. The crossover size corresponds to tube diameters of around 1 nm.

Wetting and prewetting of water on top of a single sheet of hexagonal boron nitride.

Wetting of a single hexagonal boron nitride sheet by liquid water has been investigated by molecular dynamics simulations within a temperature range between 278 and 373 K. The wetting temperature was found to be ~310 K, while the onset of prewetting happens around the much higher temperature of 354 K. The static (hydrogen-bond populations, density profiles, energy per molecule) and dynamic (diffusion coefficients) properties of water in the stable phases in this temperature range were also studied and compared to those of water on graphene. The results indicate that hydrophobicity of boron nitride is milder than that of graphene.

Effect of surface roughness on the static and dynamic properties of water adsorbed on graphene.

We studied the effects that deviations from a perfectly flat structure have in the adsorption of water on a single graphene sheet at room temperature. To do so we performed molecular dynamics simulations of water on top of a single sheet of carbon atoms whose positions were changed periodically or randomly and the results compared with those obtained for an ideal flat surface. Different textures were considered, and in all cases, the corresponding geometries of the single graphene layers were kept frozen through the simulations. Our results indicate that the effect of the roughness in the water molecules depends basically on the average amplitude of the distortions in the Z direction and not of their particular type (random or periodic). Binding energies and water structure are scarcely affected by corrugation, with an average number of 3.5-3 hydrogen bonds per molecule through the distance perpendicular to the surface. Analysis of water translational diffusion and spectroscopical densities of states indicates changes when water is close to the vacuum interface and far from the graphene surface.

Water on graphene surfaces.

In this paper, we summarize the main results obtained in our group about the behavior of water confined inside or close to different graphene surfaces by means of molecular dynamics simulations. These include the inside and outside of carbon nanotubes, and the confinement inside a slit pore or a single graphene sheet. We paid special attention to some thermodynamical (binding energies), structural (hydrogen-bond distributions) and dynamic (infrared spectra) properties, and their comparison to their bulk counterparts.

Ordering of hard spheres inside hard cylindrical pores.

Isothermal-isobaric simulations on the ordering behavior of hard spheres upon confinement are presented. The radii of the confining cylinders go from 1.1 to 2 in units of the diameters of the hard spheres adsorbed. In all the range of pressures considered the spheres were located in concentric layers, as many as the radius of the hard cylinder would permit. When the pressure increases, the hard spheres go from being loosely arranged to the formation of ordered structures. This change is marked in all cases by a distinct break in the density of spheres in a narrow pressure range. When the tube radius is smaller than 1.5, the high-pressure ordering is determined by the number of coplanar spheres you can have within a circle of radius equal to that of the confining tube. For wider tubes, the change upon compression is determined by the formation of defected two-dimensional triangular lattices wrapped to fit inside the particular cylinder we are considering.

Molecular dynamics simulations of supercritical water confined within a carbon-slit pore.

We report the results of a series of molecular dynamics simulations of water inside a carbon-slit pore at supercritical conditions. A range of densities corresponding from liquid (0.66gcm;{-3}) to gas environments (0.08gcm;{-3}) at the supercritical temperature of 673K were considered. Our findings are compared with previous studies of liquid water confined in graphene nanochannels at ambient and high temperatures, and indicate that the microscopic structure of water evolves from hydrogen bond networks characteristic of hot dense liquids to looser arrangements where the dominant units are water monomers and dimers. Water permittivity was found to be very small at low densities, with a tendency to grow with density and to reach typical values of unconfined supercritical water at 0.66gcm;{-3}) . In supercritical conditions, the residence time of water at interfaces is roughly similar to that of water in the central regions of the slabs, if the size of the considered region is taken into account. That time span is long enough to compute dynamical properties such as diffusion or spectral densities. Water diffusion in supercritical states is much faster at low densities, and it is produced in such a way that, at interfaces, translational diffusion is mainly produced along planes parallel to the carbon walls. Spectral frequency shifts depend on several factors, being temperature and density effects the most relevant. However, we can observe corrections due to confinement, important both at the graphene interface and in the central region of the water slab.

4He on a single graphene sheet.

The phase diagram of the first layer of 4He adsorbed on a single graphene sheet has been calculated by a series of diffusion Monte Carlo calculations including corrugation effects. Since the number of C-He interactions is smaller than in graphite, the binding energy of 4He atoms to graphene is reduced approximately 13.4 K per helium atom. Our results indicate that the phase diagram is qualitatively similar to that of helium on top of graphite. A two-dimensional liquid film on graphene is predicted to be metastable with respect to the commensurate solid but the difference in energy between both phases is very small, opening the possibility of such a liquid film to be experimentally observed.

4He adsorbed on the outer surface of carbon nanotube bundles.

The results of diffusion Monte Carlo calculations on the behavior of 4He adsorbed on the external surface of a bundle of carbon nanotubes are presented. The corrugation effects are found to be very important, making the outside part of the bundles a quite inhomogeneous substrate. No stable solid helium monolayer at high density was found. Instead, helium atoms are promoted to a second quasi-one-dimensional phase on top of the liquid first layer. On increasing the helium intake, a two layer structure is formed in which the helium directly in contact with the carbon surface solidifies.

Liquid water confined in carbon nanochannels at high temperatures.

Structure, hydrogen bonding, electrostatics, dielectric, and dynamical properties of liquid water confined in flat graphene nanochannels are investigated by molecular dynamics simulations. A wide range of temperatures (between 20 and 360 degrees C) have been considered. Molecular structure suffers substantial changes when the system is heated, with a significant loss of structure and hydrogen bonding. In such case, the interface between adsorbed and bulk-like water has a marked tendency to disappear, and the two preferential orientations of water nearby the graphite layers at room temperature are essentially merging above the boiling point. The general trend for the static dielectric constant is its reduction at high temperature states, as compared to ambient conditions. Similarly, residence times of water molecules in adsorbed and bulk-like regions are significantly influenced by temperature, as well. Finally, we observed relevant changes in water diffusion and spectroscopy along the range of temperatures analyzed.

Molecular dynamics simulation of liquid water confined inside graphite channels: dielectric and dynamical properties.

Electric and dielectric properties and microscopic dynamics of liquid water confined between graphite slabs are analyzed by means of molecular dynamics simulations for several graphite-graphite separations at ambient conditions. The electric potential across the interface shows oscillations due to water layering, and the overall potential drop is about -0.28 V. The total dielectric constant is larger than the corresponding value for the bulklike internal region of the system. This is mainly due to the preferential orientations of water nearest the graphite walls. Estimation of the capacitance of the system is reported, indicating large variations for the different adsorption layers. The main trend observed concerning water diffusion is 2-fold: on one hand, the overall diffusion of water is markedly smaller for the closest graphite-graphite separations, and on the other hand, water molecules diffuse in interfaces slightly slower than those in the bulklike internal areas. Molecular reorientational times are generally larger than those corresponding to those of unconstrained bulk water. The analysis of spectral densities revealed significant spectral shifts, compared to the bands in unconstrained water, in different frequency regions, and associated to confinement effects. These findings are important because of the scarce information available from experimental, theoretical, and computer simulation research into the dielectric and dynamical properties of confined water.

Freezing of hard spheres confined in narrow cylindrical pores.

Monte Carlo simulations for the equation of state and phase behavior of hard spheres confined inside very narrow hard tubes are presented. For pores whose radii are greater than 1.1 hard sphere diameters, a sudden change in the density and the microscopic structure of the fluid is neatly observed, indicating the onset of freezing. In the high-density structure the particles rearrange in such a way that groups of three particles fit in sections across the pore.

Role of vacancies in the adsorption of quantum noble gases inside a bundle of carbon nanotubes.

Diffusion Monte Carlo calculations on the 4He and 20Ne adsorption in the interstices of a bundle of (10, 10) carbon nanotubes are reported. The results indicate that the presence of a carbon vacancy is enough, at least in some cases, to impede the adsorption of quantum gases in those systems. This could explain some discrepancies between the experimental data and the theoretical calculations about the possibility of adsorption of gases inside a bundle of carbon nanotubes.

Molecular simulation of liquid water confined inside graphite channels: thermodynamics and structural properties.

We carried out molecular dynamics simulations to describe the properties of water inside a narrow graphite channel. Two stable phases were found: a low-density one made of water clusters adsorbed on the graphite sheets and a liquid one that fills the entire channel, forming several layers around a bulk-like region. We analyzed the interfacial structure, orientational order, water residence times in several regions, and hydrogen bonding of this last water phase, calculating also a quantity of electrochemical interest, the probability of electron tunneling through interfacial water. The results are in good qualitative agreement with the available experimental data.

Structure of water nanoconfined between hydrophobic surfaces.

We report the results of a series of molecular-dynamics simulations of liquid water confined between two graphite plates with separations ranging from 7 to 15 A. Energies and free energies are provided, indicating also the corresponding stability density span of confined water phases. The structure of the different liquid layers is also discussed for all the considered systems. In particular, we studied atomic density profiles, two-dimensional radial distribution functions, hydrogen bonding, and angular orientations near the carbon plates.

Temperature effects on the static and dynamic properties of liquid water inside nanotubes.

We report a molecular dynamics simulation study of the behavior of liquid water adsorbed in carbon nanotubes under different thermodynamic conditions. A flexible simple point charged potential has been employed to model internal and intermolecular water interactions. Water-carbon forces are modeled with a Lennard-Jones-type potential. We have studied three types of tubes with effective radii ranging from 4.1 to 6.8 A and three temperatures, from 298 to 500 K for a fixed density of 1 g/cm(3). Structure of each thermodynamic state is analyzed through the characterization of the hydrogen-bond network. Time-dependent properties such as the diffusive behavior and molecular vibrational spectra are also considered. We observe the gradual destruction of the hydrogen-bond network together with faster diffusive regimes as temperature increases. A vibrational mode absent in bulk unconstrained water appears in the power spectra obtained from hydrogen velocity autocorrelation functions for all thermodynamic states. That frequency mode should be attributed to confinement effects.