Molecular Mechanisms of Sorbed Ion Effects during Boehmite Particle Aggregation.

Classical theories of particle aggregation, such as Derjaguin-Landau-Verwey-Overbeek (DLVO), do not explain recent observations of ion-specific effects or the complex concentration dependence for aggregation. Thus, here, we probe the molecular mechanisms by which selected alkali nitrate ions (Na+, K+, and NO3-) influence aggregation of the mineral boehmite (γ-AlOOH) nanoparticles. Nanoparticle aggregation was analyzed using classical molecular dynamics (CMD) simulations coupled with the metadynamics rare event approach for stoichiometric surface terminations of two boehmite crystal faces. Calculated free energy landscapes reveal how electrolyte ions alter aggregation on different crystal faces relative to pure water. Consistent with experimental observations, we find that adding an electrolyte significantly reduces the energy barrier for particle aggregation (∼3-4×). However, in this work, we show this is due to the ions disrupting interstitial water networks, and that aggregation between stoichiometric (010) basal-basal surfaces is more favorable than between (001) edge-edge surfaces (∼5-6×) due to the higher interfacial water densities on edge surfaces. The interfacial distances in the interlayer between aggregated particles with electrolytes (∼5-10 Å) are larger than those in pure water (a few Ångströms). Together, aggregation/disaggregation in salt solutions is predicted to be more reversible due to these lower energy barriers, but there is uncertainty on the magnitudes of the energies that lead to aggregation at the molecular scale. By analyzing the peak water densities of the first monolayer of interstitial water as a proxy for solvent ordering, we find that the extent of solvent ordering likely determines the structures of aggregated states as well as the energy barriers to move between them. The results suggest a path for developing a molecular-level basis to predict the synergies between ions and crystal faces that facilitate aggregation under given solution conditions. Such fundamental understanding could be applied extensively to the aggregation and precipitation utilization in the biological, pharmaceutical, materials design, environmental remediation, and geological regimes.

Toward a First-Principles Framework for Predicting Collective Properties of Electrolytes.

Given the universal importance of electrolyte solutions, it is natural to expect that we have a nearly complete understanding of the fundamental properties of these solutions (e.g., the chemical potential) and that we can therefore explain, predict, and control the phenomena occurring in them. In fact, reality falls short of these expectations. But, recent advances in the simulation and modeling of electrolyte solutions indicate that it should soon be possible to make progress toward these goals. In this Account, we will discuss the use of first-principles interaction potentials based in quantum mechanics (QM) to enhance our understanding of electrolyte solutions. Specifically, we will focus on the use of quantum density functional theory (DFT) combined with molecular dynamics simulation (DFT-MD) as the foundation for our approach. The overarching concept is to understand and accurately reproduce the balance between local or short-ranged (SR) structural details and long-range (LR) correlations, allowing the prediction of the thermodynamics of both single ions in solution as well as the collective interactions characterized by activity/osmotic coefficients. In doing so, relevant collective motions and driving forces characterized by chemical potentials can be determined.In this Account, we will make the case that understanding electrolyte solutions requires a faithful QM representation of the SR nature of the ion-ion, ion-water, and water-water interactions. However, the number of molecules that is required for collective behavior makes the direct application of high-level QM methods that contain the best SR physics untenable, making methods that balance accuracy and efficiency a practical goal. Alternatives such as continuum solvent models (CSMs) and empirically based classical molecular dynamics have been extensively employed to resolve this problem but without yet overcoming the fundamental issue of SR accuracy. We will demonstrate that accurately describing the SR interaction is imperative for predicting both intrinsic properties, namely, at infinite dilution, and collective properties of electrolyte solutions.DFT has played an important role in our understanding of condensed phase systems, e.g., bulk liquid water, the air-water interface, ions in bulk, and at the air-water interface. This approach holds huge promise to provide benchmark calculations of electrolyte solution properties that will allow for the development and improvement of more efficient methods, as well as an enhanced understanding of fundamental phenomena. However, the standard protocol using the generalized gradient approximation with van der Waals (vdW) correction requires improvement in order to achieve a high level of quantitative accuracy. Simply simulating with higher level DFT functionals may not be the best route considering the significant computational cost. Alternative methods of incorporating information from higher levels of QM should be explored; e.g., using force matching techniques on small clusters, where high level benchmark calculations are possible, to develop ideal correction terms to the DFT functional is a promising possibility. We argue that DFT with statistical mechanics is becoming an increasingly useful framework enabling the prediction of collective electrolyte properties.

27 Al NMR diffusometry of Al13 Keggin nanoclusters.

Although nanometer-sized aluminum hydroxide clusters (i.e., ϵ-Al13 , [Al13 O4 (OH)24 (H2 O)12 ]7+ ) command a central role in aluminum ion speciation and transformations between minerals, measurement of their translational diffusion is often limited to indirect methods. Here, 27 Al pulsed field gradient stimulated echo nuclear magnetic resonance (PFGSTE NMR) spectroscopy has been applied to the AlO4 core of the ϵ-Al13 cluster with complementary theoretical simulations of the diffusion coefficient and corresponding hydrodynamic radii from a boundary element-based calculation. The tetrahedral AlO4 center of the ϵ-Al13 cluster is symmetric and exhibits only weak quadrupolar coupling, which results in favorable T1 and T2 27 Al NMR relaxation coefficients for 27 Al PFGSTE NMR studies. Stokes-Einstein relationship was used to relate the 27 Al diffusion coefficient of the ϵ-Al13 cluster to the hydrodynamic radius for comparison with theoretical simulations, dynamic light scattering from literature, and previously published 1 H PFGSTE NMR studies of chelated Keggin clusters. This first-of-its-kind observation proves that 27 Al PFGSTE NMR diffusometry can probe symmetric Al environments in polynuclear clusters of greater molecular weight than previously considered.

Shear stress dependence of force networks in 3D dense suspensions.

The geometric organization and force networks of 3D dense suspensions that exhibit both shear thinning and thickening have been examined as a function of varying strength of interparticle attractive interactions using lubrication flow discrete element simulations. Significant rearrangement of the geometric topology does not occur at either the local or global scale as these systems transition across the shear thinning and shear thickening regimes. In contrast, massive rearrangements in the balance of attractive, lubrication, and contact forces are observed with interesting behavior of network growth and competition. In agreement with prior work, in shear thinning regions the attractive force is dominant, however as the shear thickening region is approached there is growth of lubrication forces. Lubrication forces oppose the attraction forces, but as viscosity continues to increase under increasing shear stress, the lubrication forces are dominated by contact forces that also resist attraction. Contact forces are the dominant interactions during shear thickening and are an order of magnitude higher than their values in the shear-thinning regime. At high attractive interaction strength, contact networks can form even under shear thinning conditions, however high shear stress is still required before contact networks become the driving mechanism of shear thickening. Analysis of the contact force network during shear thickening generally indicates a uniformly spreading network that rapidly forms across empty domains; however the growth patterns exhibit structure that is significantly dependent upon the strength of interparticle interactions, indicating subtle variations in the mechanism of shear thickening.

Theory-Guided Inelastic Neutron Scattering of Crystalline Alkaline Aluminate Salts Bearing Principal Motifs of Solution-State Species.

Aluminate salts precipitated from caustic alkaline solutions exhibit a correlation between the anionic speciation and the identity of the alkali cation in the precipitate, with the aluminate ions occurring either in monomeric (Al(OH)4-) or dimeric (Al2O(OH)62-) forms. The origin of this correlation is poorly understood as are the roles that oligomeric aluminate species play in determining the solution structure, prenucleation clusters, and precipitation pathways. Characterization of aluminate solution speciation with vibrational spectroscopy results in spectra that are difficult to interpret because the ions access a diverse and dynamic configurational space. To investigate the Al(OH)4- and Al2O(OH)62- anions within a well-defined crystal lattice, inelastic neutron scattering (INS) and Raman spectroscopic data were collected and simulated by density functional theory for K2[Al2O(OH)6], Rb2[Al2O(OH)6], and Cs[Al(OH) 4]·2H2O. These structures capture archetypal solution aluminate species: the first two salts contain dimeric Al2O(OH)62- anions, while the third contains the monomeric Al(OH)4- anion. Comparisons were made to the INS and Raman spectra of sodium aluminate solutions frozen in a glassy state. In contrast to solution systems, the crystal lattice of the salts results in well-defined vibrations and associated resolved bands in the INS spectra. The use of a theory-guided analysis of the INS of this solid alkaline aluminate series revealed that differences were related to the nature of the hydrogen-bonding network and showed that INS is a sensitive probe of the degree of completeness and strength of the bond network in hydrogen-bonded materials. Results suggest that the ionic size may explain cation-specific differences in crystallization pathways in alkaline aluminate salts.

Visualization of Aluminum Ions at the Mica Water Interface Links Hydrolysis State-to-Surface Potential and Particle Adhesion.

When hydrolyzable cations such as aluminum interact with solid-water interfaces, macroscopic interfacial properties (e.g., surface charge and potential) and interfacial phenomena (e.g., particle adhesion) become tightly linked with the microscopic details of ion adsorption and speciation. We use in situ atomic force microscopy to directly image individual aluminum ions at a mica-water interface and show how adsorbate populations change with pH and aluminum activity. Complementary streaming potential measurements then allow us to build a triple layer model (TLM) that links surface potentials to adsorbate populations, via equilibrium binding constants. Our model predicts that hydrolyzed species dominate the mica-water interface, even when unhydrolyzed species dominate the solution. Ab initio molecular dynamics (AIMD) simulations confirm that aluminum hydrolysis is strongly promoted at the interface. The TLM indicates that hydrolyzed adsorbates are responsible for surface-potential inversions, and we find strong correlations between hydrolyzed adsorbates and particle-adhesion forces, suggesting that these species mediate adhesion by chemical bridging.

Mechanisms of Al3+ Dimerization in Alkaline Solutions.

The molecular speciation of aluminum (Al3+) in alkaline solutions is fundamental to its precipitation chemistry within a number of industrial applications that include ore refinement and industrial processing of Al wastes. Under these conditions, Al3+ is predominantly Al(OH)4-, while at high [Al3+] dimeric species are also known to form. To date, the mechanism of dimer formation remains unclear and is likely influenced by complex ion···ion interactions. In the present work, we investigate a suite of potential dimerization pathways and the role of ion pairing on energetics using static DFT calculations and DFT and density functional tight binding molecular dynamics. Specific cation effects imparted by the background electrolyte cations Na+, Li+, and K+ have been examined. Our simulations predict that, when the Al species are ion-paired with either cation, the formation of the oxo-bridged Al2O(OH)62- is favored with respect to the dihydroxo-bridged Al2(OH)82-, in agreement with previous spectroscopic work. The formation of both dimers first proceeds by bridging of two monomeric units via one hydroxo ligand, leading to a labile Al2(OH)82- isomer. The effect of contact ion pairing of Li+ and K+ on the dimerization energetics is distinctly more favorable than that of Na+, which may have an effect on further oligomerization.

Heterolytic Scission of Hydrogen Within a Crystalline Frustrated Lewis Pair.

We report the heterolysis of molecular hydrogen under ambient conditions by the crystalline frustrated Lewis pair (FLP) 1-{2-[bis(pentafluorophenyl)boryl]phenyl}-2,2,6,6-tetramethylpiperidine (KCAT). The gas-solid reaction provides an approach to prepare the solvent-free, polycrystalline ion pair KCATH2 through a single crystal to single crystal transformation. The crystal lattice of KCATH2 increases in size relative to the parent KCAT by approximately 2%. Microscopy was used to follow the transformation of the highly colored red/orange KCAT to the colorless KCATH2 over a period of 2 h at 300 K under a flow of H2 gas. There is no evidence of crystal decrepitation during hydrogen uptake. Inelastic neutron scattering employed over a temperature range from 4-200 K did not provide evidence for the formation of polarized H2 in a precursor complex within the crystal at low temperatures and high pressures. However, at 300 K, the INS spectrum of KCAT transformed to the INS spectrum of KCATH2. Calculations suggest that the driving force is more favorable in the solid state compared to the solution or gas phase, but the addition of H2 into the KCAT crystal is unfavorable. Ab Initio methods were used to calculate the INS spectra of KCAT, KCATH2, and a possible precursor complex of H2 in the pocket between the B and N of crystalline KCAT. Ex-situ NMR showed that the transformation from KCAT to KCATH2 is quantitative and our results suggest that the hydrogen heterolysis process occurs via H2 diffusion into the FLP crystal with a rate-limiting movement of H2 from inactive positions to reactive sites.

Quantifying the hydration structure of sodium and potassium ions: taking additional steps on Jacob's Ladder.

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena. Here, we simulate the Na+ and K+ ions in bulk water using three density functional theory functionals: (1) the generalized gradient approximation (GGA) based dispersion corrected revised Perdew, Burke, and Ernzerhof functional (revPBE-D3) (2) the recently developed strongly constrained and appropriately normed (SCAN) functional (3) the random phase approximation (RPA) functional for potassium. We compare with experimental X-ray diffraction (XRD) and X-ray absorption fine structure (EXAFS) measurements to demonstrate that SCAN accurately reproduces key structural details of the hydration structure around the sodium and potassium cations, whereas revPBE-D3 fails to do so. However, we show that SCAN provides a worse description of pure water in comparison with revPBE-D3. RPA also shows an improvement for K+, but slow convergence prevents rigorous comparison. Finally, we analyse cluster energetics to show SCAN and RPA have smaller fluctuations of the mean error of ion-water cluster binding energies compared with revPBE-D3.

Al27 NMR chemical shift of Al(OH)4 - calculated from first principles: Assessment of error cancellation in chemically distinct reference and target systems.

Predicting accurate nuclear magnetic resonance chemical shieldings relies upon cancellation of different types of errors between the theoretically calculated shielding constant of the analyte of interest and the reference. Often, the intrinsic error in computed shieldings due to basis sets, approximations in the Hamiltonian, description of the wave function, and dynamic effects is nearly identical between the analyte and reference, yet if the electronic structure or sensitivity to local environment differs dramatically, this cannot be taken for granted. Detailed prior work has examined the octahedral trivalent cation Al(H2O)6 3+, accounting for ab initio intrinsic errors. However, the use of this species as a reference for the chemically distinct tetrahedral anion Al(OH)4 - requires an understanding of how these errors cancel in order to define the limits of accurately predicting Al27 chemical shielding in Al(OH)4 -. In this work, we estimate the absolute shielding of the Al27 nucleus in Al(OH)4 - at the coupled cluster level (515.1 ± 5.3 ppm). Shielding sensitivity to the choice of method approximation and atomic basis sets used has been evaluated. Solvent and thermal effects are assessed through ensemble averaging techniques using ab initio molecular dynamics. The contribution of each type of intrinsic error is assessed for the Al(H2O)6 3+ and Al(OH)4 - ions, revealing significant differences that fundamentally hamper the ability to accurately calculate the Al27 chemical shift of Al(OH)4 - from first principles.

Solvent reaction coordinate for an SN2 reaction.

We study the prototypical SN2 reaction Cl- + CH3Cl → CH3Cl + Cl- in water using quantum mechanics/molecular mechanics (QM/MM) computer simulations with transition path sampling and inertial likelihood maximization. We have identified a new solvent coordinate to complement the original atom-exchange coordinate used in the classic analysis by Chandrasekhar, Smith, and Jorgensen [J. Am. Chem. Soc. 107, 154 (1985)]. The new solvent coordinate quantifies instantaneous solvent-induced polarization relative to the equilibrium average charge density at each point along the reaction pathway. On the basis of likelihood scores and committor distributions, the new solvent coordinate improves upon the description of solvent dynamical effects relative to previously proposed solvent coordinates. However, it does not increase the transmission coefficient or the accuracy of a transition state theory rate calculation.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations.

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

Trends in mica-mica adhesion reflect the influence of molecular details on long-range dispersion forces underlying aggregation and coalignment.

Oriented attachment of nanocrystalline subunits is recognized as a common crystallization pathway that is closely related to formation of nanoparticle superlattices, mesocrystals, and other kinetically stabilized structures. Approaching particles have been observed to rotate to achieve coalignment while separated by nanometer-scale solvent layers. Little is known about the forces that drive coalignment, particularly in this "solvent-separated" regime. To obtain a mechanistic understanding of this process, we used atomic-force-microscopy-based dynamic force spectroscopy with tips fabricated from oriented mica to measure the adhesion forces between mica (001) surfaces in electrolyte solutions as a function of orientation, temperature, electrolyte type, and electrolyte concentration. The results reveal an ∼60° periodicity as well as a complex dependence on electrolyte concentration and temperature. A continuum model that considers the competition between electrostatic repulsion and van der Waals attraction, augmented by microscopic details that include surface separation, water structure, ion hydration, and charge regulation at the interface, qualitatively reproduces the observed trends and implies that dispersion forces are responsible for establishing coalignment in the solvent-separated state.

Probing equilibrium of molecular and deprotonated water on TiO2(110).

Understanding adsorbed water and its dissociation to surface hydroxyls on oxide surfaces is key to unraveling many physical and chemical processes, yet the barrier for its deprotonation has never been measured. In this study, we present direct evidence for water dissociation equilibrium on rutile-TiO2(110) by combining supersonic molecular beam, scanning tunneling microscopy (STM), and ab initio molecular dynamics. We measure the deprotonation/protonation barriers of 0.36 eV and find that molecularly bound water is preferred over the surface-bound hydroxyls by only 0.035 eV. We demonstrate that long-range electrostatic fields emanating from the oxide lead to steering and reorientation of the molecules approaching the surface, activating the O-H bonds and inducing deprotonation. The developed methodology for studying metastable reaction intermediates prepared with a high-energy molecular beam in the STM can be readily extended to other systems to clarify a wide range of important bond activation processes.

Silver Nanocube and Nanobar Growth via Anisotropic Monomer Addition and Particle Attachment Processes.

Understanding the growth mechanism of noble metal nanocrystals during solution synthesis is of significant importance for shape and property control. However, much remains unknown about the growth pathways of metal nanoparticles due to the lack of direct observation. Using an in situ transmission electron microscopy technique, we directly observed Ag nanocube and nanobar growth in an aqueous solution through both classical monomer-by-monomer addition and nonclassical particle attachment processes. During the particle attachment process, Ag nanocubes and nanobars were formed via both oriented and nonoriented attachment. Our calculations, along with the dynamics of the observed attachment, showed that the van der Waals force overcomes hydrodynamic and friction forces and drives the particles toward each other at separations of 10-100 nm in our experiments. During classical growth, anisotropic growth was also revealed, and the resulting unsymmetrical shape constituted an intermediate state for Ag nanocube growth. We hypothesized that the temporary symmetry breaking resulted from different growth rates on (001) surfaces due to a local surface concentration variation caused by the imbalance between the consumption of Ag+ near the surface and the diffusion of Ag+ from the bulk to the surface.

In Situ 27Al NMR Spectroscopy of Aluminate in Sodium Hydroxide Solutions above and below Saturation with Respect to Gibbsite.

Aluminum hydroxide (Al(OH)3, gibbsite) dissolution and precipitation processes in alkaline environments play a commanding role in aluminum refining and nuclear waste processing, yet mechanistic aspects underlying sluggish kinetics during crystallization have remained obscured due to a lack of in situ probes capable of isolating incipient ion pairs. At a molecular level Al is cycling between tetrahedral ( T d) coordination in solution to octahedral ( O h) in the solid. We explored dissolution of Al(OH)3 that was used to produce variably saturated aluminate (Al(OH)4-)-containing solutions under alkaline conditions (pH >13) with in situ 27Al magic angle spinning (MAS)-nuclear magnetic resonance (NMR) spectroscopy, and interrogated the results with ab initio molecular dynamics (AIMD) simulations complemented with chemical shift calculations. The collective results highlight the overall stability of the solvation structure for T d Al in the Al(OH)4- oxyanion as a function of both temperature and Al concentration. The observed chemical shift did not change significantly even when the Al concentration in solution became supersaturated upon cooling and limited precipitation of the octahedral Al(OH)3 phase occurred. However, subtle changes in Al(OH)4- speciation correlated with the dissolution/precipitation reaction were found. AIMD-informed chemical shift calculations indicate that measurable perturbations should begin when the Al(OH)4-···Na+ distance is less than 6 Å, increasing dramatically at shorter distances, coinciding with appreciable changes to the electrostatic interaction and reorganization of the Al(OH)4- solvation shell. The integrated findings thus suggest that, under conditions incipient to and concurrent with gibbsite crystallization, nominally expected contact ion pairs are insignificant and instead medium-range (4-6 Å) solvent-separated Al(OH)4-···Na+ pairs predominate. Moreover, the fact that these medium-range interactions bear directly on resulting gibbsite characteristics was demonstrated by detailed microscopic and X-ray diffraction analysis and by progressive changes in the fwhm of the O h resonance, as measured by in situ NMR. Sluggish gibbsite crystallization may arise from the activation energy associated with disrupting this robust medium-range ion pair interaction.

Rate theory of ion pairing at the water liquid-vapor interface: A case of sodium iodide.

Studies on ion pairing at interfaces have been intensified recently because of their importance in many chemical reactive phenomena, such as ion-ion interactions that are affected by interfaces and their influence on kinetic processes. In this study, we performed simulations to examine the thermodynamics and kinetics of small polarizable sodium iodide ions in the bulk and near the water liquid-vapor interface. Using classical transition state theory, we calculated the dissociation rates and corrected them with transmission coefficients obtained from the reactive flux formalism and Grote-Hynes theory. Our results show that in addition to affecting the free energy of ions in solution, the interfacial environments significantly influence the kinetics of ion pairing. The results on the relaxation time obtained using the reactive flux formalism and Grote-Hynes theory present an unequivocal picture that the interface suppresses ion dissociation. The effects of the use of molecular models on the ion interactions as well as the ion-pair configurations at the interface are also quantified and discussed.

Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions.

Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.

Mass density fluctuations in quantum and classical descriptions of liquid water.

First principles molecular dynamics simulation protocol is established using revised functional of Perdew-Burke-Ernzerhof (revPBE) in conjunction with Grimme's third generation of dispersion (D3) correction to describe the properties of water at ambient conditions. This study also demonstrates the consistency of the structure of water across both isobaric (NpT) and isothermal (NVT) ensembles. Going beyond the standard structural benchmarks for liquid water, we compute properties that are connected to both local structure and mass density fluctuations that are related to concepts of solvation and hydrophobicity. We directly compare our revPBE results to the Becke-Lee-Yang-Parr (BLYP) plus Grimme dispersion corrections (D2) and both the empirical fixed charged model (SPC/E) and many body interaction potential model (MB-pol) to further our understanding of how the computed properties herein depend on the form of the interaction potential.

Modeling nanoscale hydrodynamics by smoothed dissipative particle dynamics.

Thermal fluctuation and hydrophobicity are two hallmarks of fluid hydrodynamics on the nano-scale. It is a challenge to consistently couple the small length and time scale phenomena associated with molecular interaction with larger scale phenomena. The development of this consistency is the essence of mesoscale science. In this study, we use a nanoscale fluid model based on smoothed dissipative particle dynamics that accounts for the phenomena associated with density fluctuations and hydrophobicity. We show consistency in the fluctuation spectrum across scales. In doing so, it is necessary to account for finite fluid particle size. Furthermore, we demonstrate that the present model can capture the void probability and solvation free energy of nonpolar hard particles of different sizes. The present fluid model is well suited for an understanding of emergent phenomena in nano-scale fluid systems.