The Nanoscale Wetting Parameter and Its Role in Interfacial Phenomena: Phase Transitions in Nanopores.

Through analysis of the statistical mechanical equations for a thin adsorbed film (gas, liquid, or solid) on a solid substrate or confined within a pore, it is possible to express the equilibrium thermodynamic properties of the film as a function of just two dimensionless parameters: a nanoscale wetting parameter, αw, and pore width, H*. The wetting parameter, αw, is defined in terms of molecular parameters for the adsorbed film and substrate and so is applicable at the nanoscale and for films of any phase. The main assumptions in the treatment are that (a) the substrate structure is not significantly affected by the adsorbed layer and (b) the diameter of the adsorbate molecules is not very small compared to the spacing of atoms in the solid substrate. We show that different surface geometries of the substrate (e.g., slit, cylindrical, and spherical pores) and various models of wall heterogeneity can be accounted for through a well-defined correction to the wetting parameter; no new dimensionless variables are introduced. Experimental measurements are reported for contact angles for various liquids on several planar substrates and are shown to be closely correlated with the nanoscale wetting parameter. We apply this approach to phase separation in nanopores of various geometries. Molecular simulation results for the phase diagram in confinement, obtained by the flat histogram Monte Carlo method, are reported and are shown to be closely similar to experimental results for capillary condensation, melting, and the triple point. The value of the wetting parameter, αw, is shown to determine the qualitative behavior (e.g., increase vs decrease in the melting temperature, capillary condensation vs evaporation), whereas the pore width determines the magnitude of the confinement effect. The triple point temperature and pressure for the confined phase are always lower than those for the bulk phase for all cases studied.

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges.

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

Can we define a unique microscopic pressure in inhomogeneous fluids?

The estimation of a microscopic pressure tensor in an adsorbed thin film on a planar surface remains a challenge in both experiment and theory. While the normal pressure is well-defined for a planar surface, the tangential pressure at a point is not uniquely defined at the nanoscale. We report a new method that allows us to calculate the local pressure tensor and its spatial integral using an arbitrary contour definition of the "virial-route" local pressure tensor. We show that by integrating the local tangential pressure over a small region of space, roughly the range of the intermolecular forces, it is possible to define a coarse-grained tangential pressure that appears to be unique and free from ambiguities in the definition of the local pressure tensor. We support our argument by presenting the results for more than ten types of contour definitions of the local pressure tensor. By defining the coarse-grained tangential pressure, we can also find the effective thickness of the adsorbed layer and, in the case of a porous material, the statistical pore width. The coarse-grained in-layer and in-pore tangential pressures are determined for Lennard-Jones argon adsorbed in realistic carbon slit pores, providing a better understanding of the pressure enhancement for strongly wetting systems.

Microscopic Pressure Tensor in Cylindrical Geometry: Pressure of Water in a Carbon Nanotube.

The microscopic pressure tensor plays an important role in understanding the mechanical stability, transport, and high-pressure phenomena of confined phases. The lack of an exact formulation to account for the long-range Coulombic contribution to the local pressure tensor in cylindrical geometries prevents the characterization of molecular fluids confined in cylindrical pores. To address this problem, we first derive the local cylindrical pressure tensor for Lennard-Jones fluids based on the Harasima (H) definition, which is expected to be compatible with the Ewald summation method. The test of the H-definition pressure equations in a homogeneous system shows that the radial and azimuthal pressure have unphysical radial dependence near the origin, while the axial pressure gives physically meaningful values. We propose an alternative contour definition that is more appropriate for cylindrical geometry and show that it leads to physically realistic results for all three pressure tensor components. With this definition, the radial and azimuthal pressures are of Irving-Kirkwood (IK) type, and the axial pressure is of Harasima type. Because of the practical interest in the axial pressure, we develop a Harasima/Ewald (H/E) method for calculating the long-range Coulombic contribution to the local axial pressure for rigid molecules. As an application, the axial pressure profile of water inside and outside a (20, 20) single-wall carbon nanotube is determined. The H/E method is compared to the IK method, which assumes a spherically truncated Coulombic potential. Detailed analysis of the pressure profile by both methods shows that the water confined in the nanotube is in a stretched state overall in the axial direction.

Enhancing Gas Solubility in Nanopores: A Combined Study Using Classical Density Functional Theory and Machine Learning.

Geometrical confinement has a large impact on gas solubilities in nanoscale pores. This phenomenon is closely associated with heterogeneous catalysis, shale gas extraction, phase separation, etc. Whereas several experimental and theoretical studies have been conducted that provide meaningful insights into the over-solubility and under-solubility of different gases in confined solvents, the microscopic mechanism for regulating the gas solubility remains unclear. Here, we report a hybrid theoretical study for unraveling the regulation mechanism by combining classical density functional theory (CDFT) with machine learning (ML). Specifically, CDFT is employed to predict the solubility of argon in various solvents confined in nanopores of different types and pore widths, and these case studies then supply a valid training set to ML for further investigation. Finally, the dominant parameters that affect the gas solubility are identified, and a criterion is obtained to determine whether a confined gas-solvent system is enhance-beneficial or reduce-beneficial. Our findings provide theoretical guidance for predicting and regulating gas solubilities in nanopores. In addition, the hybrid method proposed in this work sets up a feasible platform for investigating complex interfacial systems with multiple controlling parameters.

Reply to the 'Comment on "Pressure enhancement in carbon nanopores: a major confinement effect"' by D. van Dijk, Phys. Chem. Chem. Phys., 2020, 22, DOI: 10.1039/C9CP02890K.

In his 'Comment' van Dijk points out that the local pressure at a point r in an inhomogeneous thermodynamic system, like other thermodynamic properties, is not uniquely defined; one must make an operational definition that involves deciding how to assign the intermolecular forces between pairs of molecules to the point r. This non-uniqueness difficulty is well known, and was discussed in our paper. It was discussed in detail in the 1950 paper of Irving and Kirkwood, and in many books and papers since then. We reply to these comments, and note that an average of the local pressure over a region of space may yield a well-defined pressure. We also discuss other possible ways to quantify the adsorption compression effect near an attractive wall. van Dijk also suggests that the non-uniqueness difficulty can be avoided by using the pressure of the uniform bulk fluid in equilibrium with the pore. While this pressure is well-defined, it only reflects the intermolecular forces in the bulk phase, and gives no information about the behavior in the pore.

Conformal Sites Theory for Adsorbed Films on Energetically Heterogeneous Surfaces.

We present a conformal sites theory for a solid substrate whose surface is both geometrically and energetically heterogeneous and that interacts with an adsorbed film. The theory is based on a perturbation expansion for the grand potential of a real system with a rough surface about that of a reference system with an ideal reference surface, thus mapping the real system onto a much simpler interfacial system. The expansion is in powers of the intermolecular potential parameters, and leads to mixing rules for the potential parameters of the reference system. Grand canonical Monte Carlo simulations for the adsorption of argon at 87.3 K, carbon dioxide at 273 K, and water vapor at 298 K on heterogeneous carbon surfaces are investigated to explore the limits of applicability of the theory. Simulation results indicate that the theory works well with typical asymmetry of the potential parameters in the force field. However, care should be taken when applying the theory to strongly associating fluids and in the low-pressure region where the active surface sites play an important role. The conformal sites theory can be used to predict the adsorption properties and to characterize the solid substrate by taking advantage of the corresponding states principle. Other possible applications are also discussed.

Bottom-Up Approach to the Coarse-Grained Surface Model: Effective Solid-Fluid Potentials for Adsorption on Heterogeneous Surfaces.

Coarse-grained surface models with a low-dimension positional dependence have great advantages in simplifying the theoretical adsorption model and speeding up molecular simulations. In this work, we present a bottom-up strategy, developing a new two-dimensional (2D) coarse-grained surface model from the "bottom-level" atomistic model, for adsorption on highly heterogeneous surfaces with various types of defects. The corresponding effective solid-fluid potential consists of a 2D hard wall potential representing the structure of the surface and a one-dimensional (1D) effective area-weighted free-energy-averaged (AW-FEA) potential representing the energetic strength of the substrate-adsorbate interaction. Within the conventional free-energy-averaged (FEA) framework, an accessible-area-related parameter is introduced into the equation of the 1D effective solid-fluid potential, which allows us not only to obtain the energy information from the fully atomistic system but also to get the structural dependence of the potential on any geometric defect on the surface. Grand canonical Monte Carlo simulations are carried out for argon adsorption at 87.3 K to test the validity of the new 2D surface model against the fully atomistic system. We test four graphitic substrates with different levels of geometric roughness for the top layer, including the widely used reference solid substrate Cabot BP-280. The simulation results show that adding one more dimension to the traditional 1D surface model is essential for adsorption on the geometrically heterogeneous surfaces. In particular, the 2D surface model with the AW-FEA solid-fluid potential significantly improves the adsorption isotherm and density profile over the 1D surface model with the FEA solid-fluid potential over a wide range of pressure. The method to construct an effective solid-fluid potential for an energetically heterogeneous surface is also discussed.

The pressure in interfaces having cylindrical geometry.

While much work has been reported on the statistical mechanics and molecular simulation of interfaces of planar and spherical geometries, very little has been published on the interfaces of cylindrical geometry. The cylindrical geometry is important for the study of cylindrical micelles and particularly for nano-phases confined within cylindrical pores since the most well-defined porous materials (e.g., carbon and silicon nanotubes, SBA-15 and KIT-6 silicas) that are presently available are of this geometry. In this work, we derive the statistical mechanical equations for the pressure tensor for an interfacial region of cylindrical geometry via the virial route and for the condition of mechanical (hydrostatic) equilibrium. We also report the equation for the surface tension via the mechanical route. Monte Carlo and molecular dynamics simulation results are obtained for two example systems involving a fluid nano-phase of Lennard-Jones argon: a gas-liquid interface of cylindrical geometry and a confined nano-phase within a cylindrical carbon pore. All three diagonal elements of the pressure tensor are reported in each case, the component normal to the interface, PN = Pρρ , and the two tangential components PTϕ = Pϕϕ and PTz = Pzz , where (ρ, z, ϕ) are the usual cylindrical polar coordinates. For the cylindrical pore, the tangential pressures, Pϕϕ and Pzz , show strong compression in the adsorbed layers, as has been found in slit-shaped and spherical pores.

High-density equation of state for a two-dimensional Lennard-Jones solid.

We present a new equation of state for a two-dimensional Lennard-Jones (2D LJ-EOS) solid at high densities, ρ2D*≥0.9. The new 2D LJ-EOS is of analytic form, consisting of a zero-temperature contribution and vibrational contributions up to and including the second anharmonic term. A detailed analysis of all contributing terms is performed. Comparisons between the 2D LJ-EOS and Monte Carlo simulation results show that the 2D LJ-EOS is very accurate over a wide range of temperatures in the high-density region. A criterion to find the temperature range over which the 2D LJ-EOS is applicable at a certain density is derived. We also demonstrate an application of the equation of state to predict an effective tangential pressure for the adsorbed contact layer near the wall in a slit-pore system. Tangential pressures predicted by this "2D-route" are found to be in qualitative agreement with those found by the more traditional virial route of Irving and Kirkwood.

The Nitric Oxide Dimer Reaction in Carbon Nanopores.

When confined within nanoporous carbons (activated carbon fibers or carbon nanotubes) having pore widths of about 1 nm, nitric oxide is found to react completely to form the dimer, (NO)2, even though almost no dimers are present in the bulk gas phase in equilibrium with the pore phase. Moreover, the yield of dimer is unchanged upon varying the temperature over the range studied in the experiments. Earlier molecular simulation studies showed a significant increase in dimer formation in carbon nanopores, but the dimer yield was considerably less than that found in the experiments, and decreased rapidly as the temperature was raised. Here, we report an ab initio and molecular simulation study of this reaction in both slit-shaped pores and single-walled carbon nanotubes. The ab initio calculations show that the nitric oxide dimer forms a weak chemical bond with the carbon, and the bonding energy is more than 20 times stronger than the van der Waals energy assumed in the previous studies. When this is accounted for, the predicted dimer yield is in good agreement with the experimental values, as is its temperature dependence. We also report results for the pressure tensor components for this confined reactive mixture. Local tangential pressures near the pore walls are as high as millions of bar, reflecting the strong nanoscale forces.

Pressure Enhancement in Confined Fluids: Effect of Molecular Shape and Fluid-Wall Interactions.

Recently, several experimental and simulation studies have found that phenomena that normally occur at extremely high pressures in a bulk phase can occur in nanophases confined within porous materials at much lower bulk phase pressures, thus providing an alternative route to study high-pressure phenomena. In this work, we examine the effect on the tangential pressure of varying the molecular shape, strength of the fluid-wall interactions, and pore width, for carbon slit-shaped pores. We find that, for multisite molecules, the presence of additional rotational degrees of freedom leads to unique changes in the shape of the tangential pressure profile, especially in larger pores. We show that, due to the direct relationship between the molecular density and the fluid-wall interactions, the latter have a large impact on the pressure tensor. The molecular shape and pore size have a notable impact on the layering of molecules in the pore, greatly influencing both the shape and scale of the tangential pressure profile.

Adhesion and friction in polymer films on solid substrates: conformal sites analysis and corresponding surface measurements.

In this work, we present a statistical mechanical analysis to elucidate the molecular-level factors responsible for the static and dynamic properties of polymer films. This analysis, which we term conformal sites theory, establishes that three dimensionless parameters play important roles in determining differences from bulk behavior for thin polymer films near to surfaces: a microscopic wetting parameter, αwx, defined as the ratio of polymer-substrate interaction to polymer-polymer interaction; a dimensionless film thickness, H*; and dimensionless temperature, T*. The parameter αwx introduced here provides a more fundamental measure of wetting than previous metrics, since it is defined in terms of intermolecular forces and the atomic structure of the substrate, and so is valid at the nanoscale for gas, liquid or solid films. To test this theoretical analysis, we also report atomic force microscopy measurements of the friction coefficient (µ), adhesion force (FA) and glass transition temperature (Tg) for thin films of two polymers, poly(methyl methacrylate) (PMMA) and polystyrene (PS), on two planar substrates, graphite and silica. Both the friction coefficient and the glass transition temperature are found to increase as the film thickness decreases, and this increase is more pronounced for the graphite than for the silica surface. The adhesion force is also greater for the graphite surface. The larger effects encountered for the graphite surface are attributed to the fact that the microscopic wetting parameter, αwx, is larger for graphite than for silica, indicating stronger attraction of polymer chains to the graphite surface.

Molecular Modeling and Adsorption Properties of Ordered Silica-Templated CMK Mesoporous Carbons.

Realistic molecular models of silica-templated CMK-1, CMK-3, and CMK-5 carbon materials have been developed by using carbon rods and carbon pipes that were obtained by adsorbing carbon in a model MCM-41 pore. The interactions between the carbon atoms with the silica matrix were described using the PN-Traz potential, and the interaction between the carbon atoms was calculated by the reactive empirical bond order (REBO) potential. Carbon rods and pipes with different thicknesses were obtained by changing the silica-carbon interaction strength, the temperature, and the chemical potential of carbon vapor adsorption. These equilibrium structures were further used to obtain the atomic models of CMK-1, CMK-3, and CMK-5 materials using the same symmetry as found in TEM pictures. These models are further refined and made more realistic by adding interconnections between the carbon rods and carbon pipes. We calculated the geometric pore size distribution of the different models of CMK-5 and found that the presence of interconnections results in some new features in the pore size distribution. Argon adsorption properties were investigated using GCMC simulations to characterize these materials at 77 K. We found that the presence of interconnection results greatly improves the agreement with available experimental data by shifting the capillary condensation to lower pressures. Adding interconnections also induces smoother adsorption/condensation isotherms, and desorption/evaporation curves show a sharp jump. These features reflex the complexity of the nanovoids in CMKs in terms of their pore morphology and topology.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring.

In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.

Liquid-Solid Nanofriction and Interfacial Wetting.

Using atomic force microscopy, the nanofriction coefficient was measured systematically for a series of liquids on planar graphite, silica and mica surfaces. This allows us to explore the quantitative interplay between nanofriction at liquid-solid interfaces and interfacial wetting. A corresponding states theory analysis shows that the nanofriction coefficient, µ = dF(F)/dF(N), where FF is the friction force and FN is the normal force, is a function of three dimensionless parameters that reflect the intermolecular forces involved and the structure of the solid substrate. Of these, we show that one parameter in particular, ß = ρ(s)Δ(s)σ(ls)(2), where ρ(s) is the atomic density of the solid, Δ(s) is the spacing between layers of solid atoms, and σ(ls) is the molecular diameter that characterizes the liquid-substrate interaction, is very important in determining the friction coefficient. This parameter ß, which we term the structure adhesion parameter, provides a measure of the intermolecular interaction between a liquid molecule and the substrate and also of the surface area of contact of the liquid molecule with the substrate. We find a linear dependence of µ on the structure adhesion parameter for the systems studied. We also find that increasing ß leads to an increase in the vertical adhesion forces FA (the attractive force exerted by the solid surface on the liquid film). Our quantitative relationship between the nanofriction coefficient and the key parameter ß which governs the vertical adhesive strength, opens up an opportunity for describing liquid flows on solid surfaces at the molecular level, with implications for the development of membrane and nanofluidic devices.

Water on titanium dioxide surface: a revisiting by reactive molecular dynamics simulations.

The behavior of surface water, especially the adsorption and dissociation characteristics, is a key to understanding and promoting photocatalytic and biomedical applications of titanium dioxide materials. Using molecular dynamics simulations with the ReaxFF force field, we study the interactions between water and five different TiO2 surfaces that are of interest to both experiments and theoretical calculations. The results show that TiO2 surfaces demonstrate different reactivities for water dissociation [rutile (011) > TiO2-B (100) > anatase (001) > rutile (110)], and there is no water dissociation observed on the TiO2-B (001) surface. The simulations also reveal that the water dissociation and the TiO2 surface chemistry change, and the new surface Ti-OH and O-H functional groups affect the orientation of other near-surface water molecules. On the reactive surface, such as the rutile (110) surface, water dissociated and formed new Ti-OH and O-H bonds on the surface. Those functional groups enhanced the hydrogen bond networking with the near-surface water molecules and their configurations. On the nonreactive TiO2-B (001) surface where no molecular or dissociative water adsorption is observed, near-surface water can also form hydrogen bonds with surface oxygen atoms of TiO2, but their distance to the surface is longer than that on the rutile (011) surface.

Controllable atomistic graphene oxide model and its application in hydrogen sulfide removal.

The determination of an atomistic graphene oxide (GO) model has been challenging due to the structural dependence on different synthesis methods. In this work we combine temperature-programmed molecular dynamics simulation techniques and the ReaxFF reactive force field to generate realistic atomistic GO structures. By grafting a mixture of epoxy and hydroxyl groups to the basal graphene surface and fine-tuning their initial concentrations, we produce in a controllable manner the GO structures with different functional groups and defects. The models agree with structural experimental data and with other ab initio quantum calculations. Using the generated atomistic models, we perform reactive adsorption calculations for H2S and H2O∕H2S mixtures on GO materials and compare the results with experiment. We find that H2S molecules dissociate on the carbonyl functional groups, and H2O, CO2, and CO molecules are released as reaction products from the GO surface. The calculation reveals that for the H2O∕H2S mixtures, H2O molecules are preferentially adsorbed to the carbonyl sites and block the potential active sites for H2S decomposition. The calculation agrees well with the experiments. The methodology and the procedure applied in this work open a new door to the theoretical studies of GO and can be extended to the research on other amorphous materials.

On the molecular origin of high-pressure effects in nanoconfinement: the role of surface chemistry and roughness.

Experiments and simulations both suggest that the pressure experienced by an adsorbed phase confined within a carbon nanoporous material can be several orders of magnitude larger than the bulk phase pressure in equilibrium with the system. To investigate this pressure enhancement, we report a molecular-simulation study of the pressure tensor of argon confined in slit-shaped nanopores with walls of various models, including carbon and silica materials. We show that the pressure is strongly enhanced by confinement, arising from the effect of strongly attractive wall forces; confinement within purely repulsive walls does not lead to such enhanced pressures. Simulations with both the Lennard-Jones and Barker-Fisher-Watts intermolecular potentials for argon-argon interactions give rise to similar results. We also show that an increase in the wall roughness significantly decreases the in-pore pressure due to its influence on the structure of the adsorbate. Finally, we demonstrate that the pressures calculated from the mechanical (direct pressure tensor calculations) and the thermodynamic (volume perturbation method) routes yield almost identical results, suggesting that both methods can be used to calculate the local pressure tensor components in the case of these planar geometries.

Reactive adsorption of ammonia and ammonia/water on CuBTC metal-organic framework: a ReaxFF molecular dynamics simulation.

We report ReaxFF molecular dynamics simulations for reactive adsorption of NH(3) on dehydrated CuBTC metal-organic framework. If the temperature is moderate (up to 125 °C), the dehydrated CuBTC demonstrates a good hydrostatic stability for water concentrations up to 4.0 molecules per copper site. However, if the temperature increases to 550 K, the dehydrated CuBTC will collapse even at a small water concentration, 1.0 H(2)O molecule per copper site. When NH(3) molecules are adsorbed in the channel and micropores of CuBTC, they prefer to chemisorb to the copper sites rather than forming a dimer with another NH(3) molecule. The formation of equimolar Cu(2)(NH(2))(4) and (NH(4))(3)BTC structures is observed at 348 K, which is in good agreement with previous experimental findings. The dehydrated CuBTC framework is partially collapsed upon NH(3) adsorption, while the Cu-Cu dimer structure remains stable under the investigated conditions. Further calculations reveal that the stability of CuBTC is related to the ammonia concentration. The critical NH(3) concentration after which the dehydrated CuBTC starts to collapse is determined to be 1.0 NH(3) molecule per copper site. Depending on whether NH(3) concentration is below or above the critical value, the dehydrated CuBTC can be stable to a higher temperature, 378 K, or can collapse at a lower temperature, 250 K. H(2)O∕NH(3) mixtures have also been studied, and we find that although water molecules do not demonstrate a strong interaction with the copper sites of CuBTC, the existence of water molecules can substantially prevent ammonia from interacting with CuBTC, and thus reduce the amount of chemisorbed NH(3) molecules on CuBTC and stabilize the CuBTC framework to some extent.