Putting water on a lattice: the importance of long wavelength density fluctuations in theories of hydrophobic and interfacial phenomena

Diameter-Optimum Spreading for the Impinging of Water Nanodroplets on Solid Surfaces

The impinging of water nanodroplets on solid surfaces is crucial to many nanotechnologies. Through large-scale molecular dynamics simulations, the size effect on the spreading of water nanodroplets after impinging on hydrophilic, graphite, and hydrophobic surfaces under low impinging velocities has been systematically studied. The spreading rates of nanodroplets first increase and then decrease and gradually become constant with the increase of nanodroplet diameter. The nanodroplets with the diameters of 17-19 nm possess the highest spreading rates because of the combined effect of the strongest interfacial interaction and the strongest surface interaction within water molecules. The highest water molecule densities, hydrogen bond numbers, and dielectric constants of interface and surface layers mainly contribute to the lowest interface work of adhesion and surface tension values at optimal diameters. These results unveil the nonmonotonic characteristics of spreading velocity, interface work of adhesion and surface tension with nanodroplet diameter for nanodroplets on solid surfaces.

Distinct Chemistries Explain Decoupling of Slip and Wettability in Atomically Smooth Aqueous Interfaces

Despite essentially identical crystallography and equilibrium structuring of water, nanoscopic channels composed of hexagonal boron nitride and graphite exhibit an order-of-magnitude difference in fluid slip. We investigate this difference using molecular dynamics simulations, demonstrating that its origin is in the distinct chemistries of the two materials. In particular, the presence of polar bonds in hexagonal boron nitride, absent in graphite, leads to Coulombic interactions between the polar water molecules and the wall. We demonstrate that this interaction is manifested in a large typical lateral force experienced by a layer of oriented hydrogen atoms in the vicinity of the wall, leading to the enhanced friction in hexagonal boron nitride. The fluid adhesion to the wall is dominated by dispersive forces in both materials, leading to similar wettabilities. Our results rationalize recent observations that the difference in frictional characteristics of graphite and hexagonal boron nitride cannot be explained on the basis of the minor differences in their wettabilities.

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. We propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

Image-charge effects on ion adsorption near aqueous interfaces

Electrostatic interactions near surfaces and interfaces are ubiquitous in many fields of science. Continuum electrostatics predicts that ions will be attracted to conducting electrodes but repelled by surfaces with lower dielectric constant than the solvent. However, several recent studies found that certain "chaotropic" ions have similar adsorption behavior at air/water and graphene/water interfaces. Here we systematically study the effect of polarization of the surface, the solvent, and solutes on the adsorption of ions onto the electrode surfaces using molecular dynamics simulation. An efficient method is developed to treat an electrolyte system between two parallel conducting surfaces by exploiting the mirror-expanded symmetry of the exact image-charge solution. With neutral surfaces, the image interactions induced by the solvent dipoles and ions largely cancel each other, resulting in no significant net differences in the ion adsorption profile regardless of the surface polarity. Under an external electric field, the adsorption of ions is strongly affected by the surface polarization, such that the charge separation across the electrolyte and the capacitance of the cell is greatly enhanced with a conducting surface over a low-dielectric-constant surface. While the extent of ion adsorption is highly dependent on the electrolyte model (the polarizability of solvent and solutes, as well as the van der Waals radii), we find the effect of surface polarization on ion adsorption is consistent throughout different electrolyte models.

Assessing long-range contributions to the charge asymmetry of ion adsorption at the air-water interface

Anions generally associate more favorably with the air–water interface than cations. In addition to solute size and polarizability, the intrinsic structure of the unperturbed interface has been discussed as an important contributor to this bias. Here we assess quantitatively the role that intrinsic charge asymmetry of water's surface plays in ion adsorption, using computer simulations to compare model solutes of various size and charge. In doing so, we also evaluate the degree to which linear response theory for solvent polarization is a reasonable approach for comparing the thermodynamics of bulk and interfacial ion solvation. Consistent with previous works on bulk ion solvation, we find that the average electrostatic potential at the center of a neutral, sub-nanometer solute at the air–water interface depends sensitively on its radius, and that this potential changes quite nonlinearly as the solute's charge is introduced. The nonlinear response closely resembles that of the bulk. As a result, the net nonlinearity of ion adsorption is weaker than in bulk, but still substantial, comparable to the apparent magnitude of macroscopically nonlocal contributions from the undisturbed interface. For the simple-point-charge model of water we study, these results argue distinctly against rationalizing ion adsorption in terms of surface potentials inherent to molecular structure of the liquid's boundary.

Cations and anions have different affinities for the air-water interface. The intrinsic orientation of surface molecules suggests such an asymmetry, but the bias is dominated by solvent response that is spatially local and significantly nonlinear.

Characterizing Solvent Density Fluctuations in Dynamical Observation Volumes

Hydrophobic effects drive diverse aqueous assemblies, such as micelle formation or protein folding, wherein the solvent plays an important role. Consequently, characterizing the free energetics of solvent density fluctuations can lead to important insights into these processes. Although techniques such as the indirect umbrella sampling (INDUS) method can be used to characterize solvent fluctuations in static observation volumes of various sizes and shapes, characterizing how the solvent mediates inherently dynamic processes, such as self-assembly or conformational change, remains a challenge. In this work, we generalize the INDUS method to facilitate the enhanced sampling of solvent fluctuations in dynamical observation volumes, whose positions and shapes can evolve. We illustrate the usefulness of this generalization by characterizing water density fluctuations in dynamical volumes pertaining to the hydration of flexible solutes, the assembly of small hydrophobes, and conformational transitions in a model peptide. We also use the method to probe the dynamics of hard spheres.

Energy dissipation and fluctuations in a driven liquid

Minimal models of active and driven particles have recently been used to elucidate many properties of nonequilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these nonequilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by various nonconservative, time-dependent forces-this quantifies a violation of time reversal symmetry-modifies the structural, transport, and phase transition properties of the driven liquid.

Water is an active matrix of life for cell and molecular biology

Szent-Győrgi called water the "matrix of life" and claimed that there was no life without it. This statement is true, as far as we know, on our planet, but it is not clear whether it must hold throughout the cosmos. To evaluate that question requires a close consideration of the many varied and subtle roles that water plays in living cells-a consideration that must be free of both an assumed essentialism that gives water an almost mystical life-giving agency and a traditional tendency to see it as a merely passive solvent. Water is a participant in the "life of the cell," and here I describe some of the features of that active agency. Water's value for molecular biology comes from both the structural and dynamic characteristics of its status as a complex, structured liquid as well as its nature as a polar, protic, and amphoteric reagent. Any discussion of water as life's matrix must, however, begin with an acknowledgment that our understanding of it as both a liquid and a solvent is still incomplete.

On the Role of Nonspherical Cavities in Short Length-Scale Density Fluctuations in Water

Density fluctuations in liquid water are at the heart of numerous phenomena associated with hydrophobic effects such as protein folding and the interaction between biomolecules. One of the most fundamental processes in this regard is the solvation of hydrophobic solutes in water. The vast majority of theoretical and numerical studies examine density fluctuations at the short length scale focusing exclusively on spherical cavities. In this work, we use both first-principles and classical molecular dynamics simulations to demonstrate that density fluctuations in liquid water can deviate significantly from the canonical spherical shapes. We show that regions of empty space are frequently characterized by exotic, highly asymmetric shapes that can be quite delocalized over the hydrogen bond network. Interestingly, density fluctuations of these shapes are characterized by Gaussian statistics with larger fluctuations. An important consequence of this is that the work required to create non spherical cavities can be substantially smaller than that of spheres. This feature is also qualitatively captured by the Lum-Chandler-Weeks theory. The scaling behavior of the free energy as a function of the volume at short length scales is qualitatively different for the nonspherical entities. We also demonstrate that nonspherical density fluctuations are important for accommodating the hydrophobic amino acid alanine and are thus likely to have significant implications when it comes to solvating highly asymmetrical species such as alkanes, polymers, or biomolecules.

The Dynamics of Water in Porous Two-Dimensional Crystals

Porous two-dimensional crystals offer many promises for water desalination applications. For computer simulation to play a predictive role in this area, however, one needs to have reliable methods for simulating an atomistic system with hydrodynamic currents and interpretative tools to relate microscopic interactions to emergent macroscopic dynamical quantities, such as friction, slip length, and permeability. In this article, we use Gaussian dynamics, a nonequilibrium molecular dynamics method that provides microscopic insights into the interactions that control the flows of both simple liquids and liquid water through atomically small channels. In simulations of aqueous transport, we mimic the effect of changing the membrane chemical composition by adjusting the attractive strength of the van der Waals interactions between the membrane atoms and water. We find that the wetting contact angle, a common measure of a membrane's hydrophobicity, does not predict the permeability of a membrane. Instead, the hydrophobic effect is subtle, with both static and dynamic effects that can both help and hinder water transport through these materials. The competition between the static and dynamical hydrophobicity balances an atomic membrane's tendency to wet against hydrodynamic friction, and determines an optimal contact angle for water passage through nonpolar membranes. To a reasonable approximation, the optimal contact angle depends only on the aspect ratio of the pore. We also find that water molecules pass through the most hydrophobic membranes in a punctuated series of bursts that are separated by long pauses. A continuous-time Markov model of these data provides evidence of a molecular analogue to the clogging transition, a phenomenon observed in driven granular flows.

Molecular mechanism for cavitation in water under tension

Despite its relevance in biology and engineering, the molecular mechanism driving cavitation in water remains unknown. Using computer simulations, we investigate the structure and dynamics of vapor bubbles emerging from metastable water at negative pressures. We find that in the early stages of cavitation, bubbles are irregularly shaped and become more spherical as they grow. Nevertheless, the free energy of bubble formation can be perfectly reproduced in the framework of classical nucleation theory (CNT) if the curvature dependence of the surface tension is taken into account. Comparison of the observed bubble dynamics to the predictions of the macroscopic Rayleigh-Plesset (RP) equation, augmented with thermal fluctuations, demonstrates that the growth of nanoscale bubbles is governed by viscous forces. Combining the dynamical prefactor determined from the RP equation with CNT based on the Kramers formalism yields an analytical expression for the cavitation rate that reproduces the simulation results very well over a wide range of pressures. Furthermore, our theoretical predictions are in excellent agreement with cavitation rates obtained from inclusion experiments. This suggests that homogeneous nucleation is observed in inclusions, whereas only heterogeneous nucleation on impurities or defects occurs in other experiments.

Interfacial solvation thermodynamics

Previous studies have reached conflicting conclusions regarding the interplay of cavity formation, polarizability, desolvation, and surface capillary waves in driving the interfacial adsorptions of ions and molecules at air-water interfaces. Here we revisit these questions by combining exact potential distribution results with linear response theory and other physically motivated approximations. The results highlight both exact and approximate compensation relations pertaining to direct (solute-solvent) and indirect (solvent-solvent) contributions to adsorption thermodynamics, of relevance to solvation at air-water interfaces, as well as a broader class of processes linked to the mean force potential between ions, molecules, nanoparticles, proteins, and biological assemblies.

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the "normal velocity" that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.

Necessity of capillary modes in a minimal model of nanoscale hydrophobic solvation

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing the importance of interfaces in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of such nanoscale interfaces requires careful attention to the statistics of capillary waves, with significant quantitative implications for the calculation of solvation thermodynamics. Here, we show that a coarse-grained lattice model like that of Chandler [Chandler D (2005)Nature437(7059):640-647], when informed by this understanding, can capture a broad range of hydrophobic behaviors with striking accuracy. Specifically, we calculate probability distributions for microscopic density fluctuations that agree very well with results of atomistic simulations, even many SDs from the mean and even for probe volumes in highly heterogeneous environments. This accuracy is achieved without adjustment of free parameters, because the model is fully specified by well-known properties of liquid water. As examples of its utility, we compute the free-energy profile for a solute crossing the air-water interface, as well as the thermodynamic cost of evacuating the space between extended nanoscale surfaces. These calculations suggest that a highly reduced model for aqueous solvation can enable efficient multiscale modeling of spatial organization driven by hydrophobic and interfacial forces.

Curvature dependence of hydrophobic hydration dynamics

We investigate the solute curvature dependence of water dynamics in the vicinity of hydrophobic spherical solutes using molecular dynamics simulations. For both the lateral and perpendicular diffusivity, as well as for H-bond kinetics of water in the first hydration shell, we find a nonmonotonic solute-size dependence, exhibiting extrema close to the well-known structural crossover length scale for hydrophobic hydration. Additionally, we find an apparent anomalous diffusion for water moving parallel to the surface of small solutes, which, however, can be explained by topology effects. Our findings regarding the intimate connection between solute curvature and water dynamics has implications for our understanding of hydration dynamics at heterogeneous biomolecular surfaces.

Size-Dependent Surface Free Energy and Tolman-Corrected Droplet Nucleation of TIP4P/2005 Water

Classical nucleation theory is notoriously inaccurate when using the macroscopic surface free energy for a planar interface. We examine the size dependence of the surface free energy for TIP4P/2005 water nanodroplets (radii ranging from 0.7 to 1.6 nm) at 300 K with the mitosis method, that is, by reversibly splitting the droplets into two subclusters. We calculate the Tolman length to be -0.56 ± 0.09 Å, which indicates that the surface free energy of water droplets that we investigated is 5-11 mJ/m(2) greater than the planar surface free energy. We incorporate the computed Tolman length into a modified classical nucleation theory (δ-CNT) and obtain modified expressions for the critical nucleus size and barrier height. δ-CNT leads to excellent agreement with independently measured nucleation kinetics.