The local compressibility of liquids near non-adsorbing substrates: a useful measure of solvophobicity and hydrophobicity?

Solvation Forces Near Hydrophobic Surfaces: A Classical Density Functional Theory Study

We use classical density functional theory (DFT) to model solvation interactions between hydrophobic surfaces, which we show to be characterized by depletion attraction at small surface to surface separations and a slowly decaying bipower law interaction at large separations. The solvation interaction originates from van der Waals (vdW) and Coulombic interactions between molecules in the polar solvent, e.g., water, and from the molecules thermal motion and finite volume. We investigate model hydrophobic surfaces represented by bubbles and nonpolar solids, e.g., aliphatic particles, and calculate in a DFT fashion the distribution of molecules in the interlaying solvent between two such surfaces and the hydrophobic excess force resulting from it. The interactions are largely attractive, which is well-known in measurement, albeit vdW attraction between molecules in solids and in the solvent may cause repulsion at certain interface to interface separations. We commence our analysis by suggesting an asymptotic analytical bipower law expression for the solvation interaction at large separations. Thereafter we present a full numerical solution, which is in good agreement with the analytical prediction and further explores the interaction at small surface to surface separations. Our theoretical results yield adhesion energies which agree with previous experiments.

What is the best simulation approach for measuring local density fluctuations near solvo-/hydrophobes?

Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from the measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous subvolumes of the system adjacent to the solvo-/hydrophobe. An alternative measure proposed by Evans and Stewart [J. Phys.: Condens. Matter 27, 194111 (2015)] defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces and SPC/E water at a hydrophobic spherical solute. Our principal findings are as follows: (i) the local compressibility profile χ(r) of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile F(r) and can resolve much more detailed structure; and (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits a strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect.

Local measures of fluctuations in inhomogeneous liquids: statistical mechanics and illustrative applications

We show in detail how three one-body fluctuation profiles, namely the local compressibility, the local thermal susceptibility, and the reduced density, can be obtained from a statistical mechanical many-body description of classical particle-based systems. We present several different and equivalent routes to the definition of each fluctuation profile, facilitating their explicit numerical calculation in inhomogeneous equilibrium systems. This underlying framework is used for the derivation of further properties such as hard wall contact theorems and novel types of inhomogeneous one-body Ornstein-Zernike equations. The practical accessibility of all three fluctuation profiles is exemplified by grand canonical Monte Carlo simulations that we present for hard sphere, Gaussian core and Lennard-Jones fluids in confinement.

Comparative study of force-based classical density functional theory

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.

Understanding the physics of hydrophobic solvation

Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations. The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones solvent, and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius R_s → ∞. Focusing on the radial density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), our binding potential analysis provides explicit predictions for the manner in which the key features of ρ(r) and χ(r) scale with R_s, the strength of solute-water attraction ɛ_sf, and the deviation from liquid-vapor coexistence of the chemical potential, δμ. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such, our theory provides a firm basis for understanding the physics of hydrophobic solvation.

Elastic Properties of Confined Fluids in Nanopores: An Acoustic-Propagation Model

Following the compressibility route in statistical mechanics, the local isothermal modulus is derived for nanoconfined fluids. Based on this inhomogeneous modulus, an acoustic-propagation model (APM) is first proposed for averaged isothermal modulus in the pore. By utilizing the density profiles obtained from classical density functional theory, the inhomogeneous modulus of supercritical methane in the graphite slit pore is calculated. It is found that the profile of the modulus in the pore is out of phase with that of density. Further, employing the proposed APM method, the averaged isothermal modulus is calculated, and the effects of pressure, pore size, and temperature on the averaged modulus are investigated. It is found that (i) averaged modulus obtained from APM method still satisfies the Tait-Murnaghan (TM) equation, (ii) the averaged modulus is proportional to the reciprocal pore width for wider pores, while it oscillates with the reciprocal pore width for narrower pores, and (iii) the reciprocal modulus is proportional to temperature, while the linearization coefficient is insensitive to the pore size. These findings bear important implications for understanding the elasticity in fluid-saturated nanoporous media and may shed light on the capture or storage of special gases in the fields of geochemistry and geophysics.

Measures of fluctuations for a liquid near critical drying

We investigate density fluctuations in a liquid close to a solvophobic substrate at which a surface critical drying transition occurs. Using classical density functional theory, we determine three measures of the spatial extent and strength of the fluctuations, i.e., the local compressibility χ_{μ}(z), the local thermal susceptibility χ_{T}(z), and the reduced density χ_{*}(z); z is the distance from the substrate. While the first measure is frequently used, the second and third were introduced very recently by Eckert et al., [T. Eckert et al., Phys. Rev. Lett. 125, 268004 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.268004]. For state points in the critical drying regime, all three measures, each scaled by its bulk value, exhibit very similar forms and the ratio of χ_{T}(z) to χ_{μ}(z), for fixed z in the vapor-liquid transition region, is constant. Using a scaling treatment of surface thermodynamics, we show that such behavior is to be expected on general grounds.

Density Depletion and Enhanced Fluctuations in Water near Hydrophobic Solutes: Identifying the Underlying Physics

We investigate the origin of the density depletion and enhanced density fluctuations that occur in water in the vicinity of an extended hydrophobic solute. We argue that both phenomena are remnants of the critical drying surface phase transition that occurs at liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius R_{s}→∞. Focusing on the density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), we develop a scaling theory which expresses the extent of the density depletion and enhancement in compressibility in terms of R_{s}, the strength of solute-water attraction ϵ_{s}, and the deviation from liquid-vapor coexistence δμ. Testing the predictions against results of classical density functional theory for a simple solvent and grand canonical Monte Carlo simulations of a popular water model, we find that the theory provides a firm physical basis for understanding how water behaves at a hydrophobe.

Nanoconfined Fluids: Uniqueness of Water Compared to Other Liquids

Nanoconfinement can drastically change the behavior of liquids, puzzling us with counterintuitive properties. It is relevant in applications, including decontamination and crystallization control. However, it still lacks a systematic analysis for fluids with different bulk properties. Here we address this gap. We compare, by molecular dynamics simulations, three different liquids in a graphene slit pore: (1) A simple fluid, such as argon, described by a Lennard-Jones potential; (2) an anomalous fluid, such as a liquid metal, modeled with an isotropic core-softened potential; and (3) water, the prototypical anomalous liquid, with directional HBs. We study how the slit-pore width affects the structure, thermodynamics, and dynamics of the fluids. All the fluids show similar oscillating properties by changing the pore size. However, their free-energy minima are quite different in nature: (i) are energy-driven for the simple liquid; (ii) are entropy-driven for the isotropic core-softened potential; and (iii) have a changing nature for water. Indeed, for water, the monolayer minimum is entropy driven, at variance with the simple liquid, while the bilayer minimum is energy driven, at variance with the other anomalous liquid. Also, water has a large increase in diffusion for subnm slit pores, becoming faster than bulk. Instead, the other two fluids have diffusion oscillations much smaller than water, slowing down for decreasing slit-pore width. Our results, clarifying that water confined at the subnm scale behaves differently from other (simple or anomalous) fluids under similar confinement, are possibly relevant in nanopores applications, for example, in water purification from contaminants.

Fluctuation Profiles in Inhomogeneous Fluids

Three one-body profiles that correspond to local fluctuations in energy, in entropy, and in particle number are used to describe the equilibrium properties of inhomogeneous classical many-body systems. Local fluctuations are obtained from thermodynamic differentiation of the density profile or equivalently from average microscopic covariances. The fluctuation profiles follow from functional generators and they satisfy Ornstein-Zernike relations. Computer simulations reveal markedly different fluctuations in confined fluids with Lennard-Jones, hard sphere, and Gaussian core interactions.

Finite-size corrections for the static structure factor of a liquid slab with open boundaries

The presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a relevant limit for the interpretation of grazing-incidence diffraction experiments at liquid interfaces and films. We derive an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows that such free boundary conditions cause significant differences between the two structure factors, in particular, at small wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of these finite-size corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system, supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential μ and temperature T. Thus, the open slab serves as a test-bed for the small-system thermodynamics in a μT reservoir. We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our findings are corroborated by simulation data for Lennard-Jones liquids at two representative temperatures.

Binding potentials for vapour nanobubbles on surfaces using density functional theory

We calculate density profiles of a simple model fluid in contact with a planar surface using density functional theory (DFT), in particular for the case where there is a vapour layer intruding between the wall and the bulk liquid. We apply the method of Hughes et al (2015 J. Chem. Phys. 142 074702) to calculate the density profiles for varying (specified) amounts of the vapour adsorbed at the wall. This is equivalent to varying the thickness h of the vapour at the surface. From the resulting sequence of density profiles we calculate the thermodynamic grand potential as h is varied and thereby determine the binding potential as a function of h. The binding potential obtained via this coarse-graining approach allows us to determine the disjoining pressure in the film and also to predict the shape of vapour nano-bubbles on the surface. Our microscopic DFT based approach captures information from length scales much smaller than some commonly used models in continuum mechanics.

Solvent-mediated interactions between nanostructures: From water to Lennard-Jones liquid

Solvent-mediated interactions emerge from complex mechanisms that depend on the solute structure, its wetting properties, and the nature of the liquid. While numerous studies have focused on the first two influences, here, we compare the results from water and Lennard-Jones liquid in order to reveal to what extent solvent-mediated interactions are universal with respect to the nature of the liquid. Besides the influence of the liquid, the results were obtained with classical density functional theory and brute-force molecular dynamics simulations which allow us to contrast these two numerical techniques.

Alchemical free energy calculations and umbrella sampling with local molecular field theory

Understanding the thermodynamic driving forces underlying any chemical process requires a description of the underlying free energy surface. However, computation of free energies is difficult, often requiring advanced sampling techniques. Moreover, these computations can be further complicated by the evaluation of any long-ranged interactions in the system of interest, such as Coulomb interactions in charged and polar media. Local molecular field theory is a promising approach to avoid many of the conceptual and computational difficulties associated with long-ranged interactions. We present frameworks for performing alchemical free energy calculations and non-Boltzmann sampling with local molecular field theory. We demonstrate that local molecular field theory can be used to perform these free energy calculations with accuracy comparable to traditional methodologies while eliminating the need for explicit treatment of long-ranged interactions in simulations.

Extent of Surface Force Additivity on Chemically Heterogeneous Substrates at Varied Orientations

Surface interactions between chemically mixed surfaces, as well as those among dissolved biomolecules, comprise distinct contributions from polar and hydrophobic moieties. These contributions are often context dependent. Approximate compliance to the Cassie additivity equation for the wetting free energies on mixed surfaces in water is, however, indicative of similarly additive forces between individual surface elements, suggesting a quadratic interpolation model for total force from the forces between pure surfaces. We use molecular dynamics/umbrella sampling simulations of parallel and nonparallel mixed surfaces with demonstrable Cassie-like behavior to verify how well the total surface force between the heterogeneous, molecularly rough surfaces can be approximated as a combination of forces among the homogeneous ones. When accounting for dissimilar distances of approach between functional groups of different types, our results for graphene surfaces with mixed methyl and nitrile coating show such a superposition to provide a reasonable first order approximation of interactions between the platelets. Deviations from additivity are more prominent in parallel-plate configurations, at high content of hydrophobic groups, and small separations. The inclusion of water polarizability does not visibly alter the observed behavior regardless of platelet orientations. The outcome of this study determines the necessary molecular conditions for observing force additivity that emphasize the context dependence of hydrophobic interaction in the presence of polar groups. This notion provides guidelines for the syntheses of new, chemically heterogeneous materials with tailored function-oriented properties in aqueous media.

Dynamical Density Functional Theory for the Evaporation of Droplets of Nanoparticle Suspension

We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the effect of phase separation and vertical density variations within the droplet and the consequence of these on the nanoparticle deposition pattern on the surface. We show how to include the effect of slip or no-slip at the surface and how this is related to the receding contact angle. We also determine how the equilibrium contact angle depends on the microscopic interaction parameters.

Communication: Is a coarse-grained model for water sufficient to compute Kapitza conductance on non-polar surfaces?

Coarse-grained models have increasingly been used in large-scale particle-based simulations. However, due to their lack of degrees of freedom, it is a priori unlikely that they straightforwardly represent thermal properties with the same accuracy as their atomistic counterparts. We take a first step in addressing the impact of liquid coarse-graining on interfacial heat conduction by showing that an atomistic and a coarse-grained model of water may yield similar values of the Kapitza conductance on few-layer graphene with interactions ranging from hydrophobic to mildly hydrophilic. By design the water models employed yield similar liquid layer structures on the graphene surfaces. Moreover, they share common vibration properties close to the surfaces and thus couple with the vibrations of graphene in a similar way. These common properties explain why they yield similar Kapitza conductance values despite their bulk thermal conductivity differing by more than a factor of two.

Stabilization and Antifouling of Polymer Films on a Planar Surface by CO2 Pressurization

In this article, we study the dewetting phenomenon of a polymer and carbon dioxide (CO₂) mixture on a planar surface by combining density functional theory and the string method. It is found that dewetting is a first-order discontinuous phase transition. When the pressure is lower than the completely dewetting pressure (P_d), CO₂ stabilizes the polymer films. The density fluctuation of the polymer decreases significantly with the inclusion of CO₂. When the pressure is above P_d, the polymer film is depleted far away from the surface, leaving a thick layer of pure CO₂ in the region near the surface. P_d is proportional to the surface energy strength. The CO₂ molecules enhance the density fluctuation of the polymer during the dewetting process. The polymer-rich phase at the triple point dewets to a CO₂-rich vapor film, as the CO₂-rich liquid film near the surface is metastable. These results have promising application in the industry of fabricating polymer films and antifouling polymers on attractive surfaces.

Modulus-pressure equation for confined fluids

Ultrasonic experiments allow one to measure the elastic modulus of bulk solid or fluid samples. Recently such experiments have been carried out on fluid-saturated nanoporous glass to probe the modulus of a confined fluid. In our previous work [G. Y. Gor et al., J. Chem. Phys., 143, 194506 (2015)], using Monte Carlo simulations we showed that the elastic modulus K of a fluid confined in a mesopore is a function of the pore size. Here we focus on the modulus-pressure dependence K(P), which is linear for bulk materials, a relation known as the Tait-Murnaghan equation. Using transition-matrix Monte Carlo simulations we calculated the elastic modulus of bulk argon as a function of pressure and argon confined in silica mesopores as a function of Laplace pressure. Our calculations show that while the elastic modulus is strongly affected by confinement and temperature, the slope of the modulus versus pressure is not. Moreover, the calculated slope is in a good agreement with the reference data for bulk argon and experimental data for confined argon derived from ultrasonic experiments. We propose to use the value of the slope of K(P) to estimate the elastic moduli of an unknown porous medium.

Critical Drying of Liquids

We report a detailed simulation and classical density functional theory study of the drying transition in a realistic model fluid at a smooth substrate. This transition (in which the contact angle θ→180°) is shown to be critical for both short-ranged and long-ranged substrate-fluid interaction potentials. In the latter case critical drying occurs at exactly zero attractive substrate strength. This observation permits the accurate elucidation of the character of the transition via a finite-size scaling analysis of the density probability function. We find that the critical exponent ν_{∥} that controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall, is over twice as large as predicted by mean field and renormalization group calculations. We suggest a reason for the discrepancy. Our findings shed new light on fluctuation phenomena in fluids near hydrophobic and solvophobic interfaces.

Using Grand Canonical Monte Carlo Simulations to Understand the Role of Interfacial Fluctuations on Solvation at the Water-Vapor Interface

The present work investigates the effect of interfacial fluctuations (predominantly capillary wave-like fluctuations) on the solvation free energy (Δμ) of a monatomic solute at the water-vapor interface. We introduce a grand-canonical-ensemble-based simulation approach that quantifies the contribution of interfacial fluctuations to Δμ. This approach is used to understand how the above contribution depends on the strength of dispersive and electrostatic solute-water interactions at the temperature of 400 K. At this temperature, we observe that interfacial fluctuations do play a role in the variation of Δμ with the strength of the electrostatic solute-water interaction. We also use grand canonical simulations to further investigate how interfacial fluctuations affect the propensity of the solute toward the water-vapor interface. To this end, we track a quantity called the interface potential (surface excess free energy) with the number of water molecules. With increasing number of water molecules, the liquid-vapor interface moves across a solute, which is kept at a fixed position in the simulation. Hence, the dependence of the interface potential on the number of waters models the process of moving the solute through the water-vapor interface. We analyze the change of the interface potential with the number of water molecules to explain that solute-induced changes in the interfacial fluctuations, like the pinning of capillary-wave-like undulations, do not play any role in the propensity of solutes toward water-vapor interfaces. The above analysis also shows that the dampening of interfacial fluctuations accompanies the adsorption of any solute at the liquid-vapor interface, irrespective of the chemical nature of the solute and solvent. However, such a correlation does not imply that dampening of fluctuations causes adsorption.

Universal Repulsive Contribution to the Solvent-Induced Interaction Between Sizable, Curved Hydrophobes

In addition to the direct attraction, sizable hydrophobes in water experience an attractive force mediated by interfacial water. Using simple geometric arguments, we identify the conditions at which the water-induced interaction between curved hydrocarbon surfaces becomes repulsive. The repulsive contribution arises from the thermodynamic penalty due to the emergence of the liquid/vapor boundary created as water gets expelled between curved hydrophobes. By augmenting the mean field approach with atomistic simulations of pristine and alkyl-coated graphitic nanoparticles in three distinct geometries, spherical, cylindrical and planar, immersed in water, we show the macroscopic thermodynamics remarkably works down to the molecular scale. The new insights improve the prediction and control of wetting and dispersion properties for a broad class of nonpolar nanoparticles.

Understanding n-Octane Behavior near Graphene with Scaled Solvent-Solute Attractions

We employ molecular dynamics simulations of n-octane near a layered graphene surface to study the related phenomena of solvation, density fluctuations, wettability, and structure and dynamics of n-octane molecules in the inhomogeneous interfacial environment. That solvation in bulk n-octane displays a lengthscale-dependent crossover similar to that of hydrophobic solvation in water is known. Here we show that, near an extended graphene interface having attractive interactions with n-octane, lengthscale-dependent solvation is similar to that in the bulk and displays a small to large crossover. However, as the n-octane-graphene interactions are reduced to make the surface increasingly solvophobic, the crossover behavior is modulated and essentially absent near the most solvophobic surfaces, similar to that in water near hydrophobic interfaces. We show that the macroscopic measure of wettability, namely, the contact angle, characterizes n-octane-graphene coupling over a limited range of attractions. In contrast, molecular measures such as the free energy of cavity formation or the local compressibility in the interfacial region provide an effective measure of this coupling over a broader range of attractions. Finally, as n-octane-graphene attractions are increased, the n-octane liquid displays a wetting transition and corresponding change from sigmoidal to layered density profile. Analysis of the local structure shows that n-octane molecules prefer approximately linear conformations and surface-parallel orientations near the graphene surface, and their translational dynamics slow down with increasing n-octane-graphene attractions. Our study highlights molecular scale behavior of n-octane molecules that is relevant to understanding nanoparticle-solvent coupling in composite materials with enhanced mechanical or thermal properties.

Quantifying Density Fluctuations in Water at a Hydrophobic Surface: Evidence for Critical Drying

Employing smart Monte Carlo sampling techniques within the grand canonical ensemble, we investigate the properties of water at a model hydrophobic substrate. By reducing the strength of substrate-water attraction, we find that fluctuations in the local number density, quantified by a rigorous definition of the local compressibility χ(z), increase rapidly for distances z within one or two molecular diameters from the substrate as the degree of hydrophobicity, measured by the macroscopic contact angle θ, increases. Our simulations provide evidence for a continuous (critical) drying transition as the substrate-water interaction becomes very weak: cos(θ)→-1. We speculate that the existence of such a transition might account for earlier simulation observations of strongly enhanced density fluctuations.