Comparative study of normal and branched alkane monolayer films adsorbed on a solid surface. II. Dynamics

The dynamics of monolayer films of the n-alkane tetracosane (n-C24H52) and the branched alkane squalane (C30H62) adsorbed on graphite have been studied by quasielastic and inelastic neutron scattering and molecular dynamics (MD) simulations. Both molecules have 24 carbon atoms along their carbon backbone, and squalane has an additional six methyl side groups symmetrically placed along its length. The authors' principal objective has been to determine the influence of the side groups on the dynamics of the squalane monolayer and thereby assess its potential as a nanoscale lubricant. To investigate the dynamics of these monolayers they used both the disk chopper spectrometer (DCS) and the high flux backscattering spectrometer (HFBS) at the National Institute of Standards and Technology. These instruments made it possible to study dynamical processes such as molecular diffusive motions and vibrations on very different time scales: 1-40 ps (DCS) and 0.1-4 ns (HFBS). The MD simulations were done on corresponding time scales and were used to interpret the neutron spectra. The authors found that the dynamics of the two monolayers are qualitatively similar on the respective time scales and that there are only small quantitative differences that can be understood in terms of the different masses and moments of inertia of the two molecules. In the course of this study, the authors developed a procedure to separate out the low-frequency vibrational modes in the spectra, thereby facilitating an analysis of the quasielastic scattering. They conclude that there are no major differences in the monolayer dynamics caused by intramolecular branching. It remains to be seen whether this similarity in monolayer dynamics also holds for the lubricating properties of these molecules in confined geometries.     

Structural and phase properties of tetracosane (C24H50) monolayers adsorbed on graphite: an explicit hydrogen molecular dynamics study

We discuss molecular dynamics (MD) computer simulations of a tetracosane (C24H50) monolayer physisorbed onto the basal plane of graphite. The adlayer molecules are simulated with explicit hydrogens, and the graphite substrate is represented as an all-atom structure having six graphene layers. The tetracosane dynamics modeled in the fully atomistic manner agree well with experiment. The low-temperature ordered solid organizes into a rectangularly centered structure that is not commensurate with underlying graphite. Above T=200 K, as the molecules start to lose their translational and orientational order via gauche defect formation a weak smectic mesophase (observed experimentally but never reproduced in united atom (UA) simulations) appears. The phase behavior of the adsorbed layer is critically sensitive to the way the electrostatic interactions are included in the model. If the electrostatic charges are set to zero (as for a UA force field), then the melting temperature increases by approximately 70 K with respect to the experimental value. When the nonbonded 1-4 interaction is not scaled, the melting temperature decreases by approximately 90 K. If the scaling factor is set to 0.5, then melting occurs at T=350 K, in very good agreement with experimental data.     

Ellipsometric and neutron diffraction study of pentane physisorbed on graphite

High-resolution ellipsometry and neutron diffraction measurements have been used to investigate the structure, growth, and wetting behavior of fluid pentane (n-C(5)H(12)) films adsorbed on graphite substrates. We present isotherms of the thickness of pentane films adsorbed on the basal-plane surfaces of a pyrolytic graphite substrate as a function of the vapor pressure. These isotherms are measured ellipsometrically for temperatures between 130 and 190 K. We also describe neutron diffraction measurements in the temperature range 11-140 K on a deuterated pentane (n-C(5)D(12)) monolayer adsorbed on an exfoliated graphite substrate. Below a temperature of 99 K, the diffraction patterns are consistent with a rectangular centered structure. Above the pentane triple point at 143.5 K, the ellipsometric measurements indicate layer-by-layer adsorption of at least seven fluid pentane layers, each having the same optical thickness. Analysis of the neutron diffraction pattern of a pentane monolayer at a temperature of 130 K is consistent with small clusters having a rectangular-centered structure and an area per molecule of approximately 37 A(2) in coexistence with a fluid monolayer phase. Assuming values of the polarizability tensor from the literature and that the monolayer fluid has the same areal density as that inferred for the coexisting clusters, we calculate an optical thickness of the fluid pentane layers in reasonable agreement with that measured by ellipsometry. We discuss how these results support the previously proposed "footprint reduction" mechanism of alkane monolayer melting. In the hypercritical regime, we show that the layering behavior is consistent with the two-dimensional Ising model and determine the critical temperatures for layers n = 2-5.     

Water clusters on graphite: methodology for quantum chemical a priori prediction of reaction rate constants

The properties, interactions, and reactions of cyclic water clusters (H(2)O)(n=1-5) on model systems for a graphite surface have been studied using pure B3LYP, dispersion-augmented density functional tight binding (DFTB-D), and integrated ONIOM(B3LYP:DFTB-D) methods. Coronene C(24)H(12) as well as polycircumcoronenes C(96)H(24) and C(216)H(36) in monolayer, bilayer, and trilayer arrangements were used as model systems to simulate ABA bulk graphite. Structures, binding energies, and vibrational frequencies of water clusters on mono- and bilayer graphite models have been calculated, and structural changes and frequency shifts due to the water cluster-graphite interactions are discussed. ONIOM(B3LYP:DFTB-D) with coronene and water in the high level and C(96)H(24) in the low level mimics the effect of extended graphite pi-conjugation on the water-graphite interaction very reasonably and suggests that water clusters only weakly interact with graphite surfaces, as suggested by the fact that water is an excellent graphite lubricant. We use the ONIOM(B3LYP:DFTB-D) method to predict rate constants for model pathways of water dissociative adsorption on graphite. Quantum chemical molecular dynamics (QM/MD) simulations of water clusters and water addition products on the C(96)H(24) graphite model are presented using the DFTB-D method. A three-stage strategy is devised for a priori investigations of high temperature corrosion processes of graphite surfaces due to interaction with water molecules and fragments.     

The crystalline structures of carboxylic acid monolayers adsorbed on graphite

X-ray and neutron diffraction have been used to investigate the formation of solid crystalline monolayers of all of the linear carboxylic acids from C(6) to C(14) at submonolayer coverage and from C(8) to C(14) at multilayer coverages, and to characterize their structures. X-rays and neutrons highlight different aspects of the monolayer structures, and their combination is therefore important in structural determination. For all of the acids with an odd number of carbon atoms, the unit cell is rectangular of plane group pgg containing four molecules. The members of the homologous series with an even number of carbon atoms have an oblique unit cell with two molecules per unit cell and plane group p2. This odd-even variation in crystal structure provides an explanation for the odd-even variation observed in monolayer melting points and mixing behavior. In all cases, the molecules are arranged in strongly hydrogen-bonded dimers with their extended axes parallel to the surface and the plane of the carbon skeleton essentially parallel to the graphite surface. The monolayer crystal structures have unit cell dimensions similar to certain close-packed planes of the bulk crystals, but the molecular arrangements are different. There is a 1-3% compression on increasing the coverage over a monolayer.     

Structure of solid monolayers and multilayers of n -hexane on graphite

We present all-atom molecular dynamics simulations ofn-hexane on the basal plane of graphite at monolayer and multilayer coverages. In keeping with experimental data, we find the presence of ordered adsorbed layers both at single monolayer coverage and when the adsorbed layer coexists with excess liquid adsorbate. Using a simulation method that does not impose any particular periodicity on the adsorbed layer, we quantitatively compare our results to the results of neutron diffraction experiments and find a structural transition from a uniaxially incommensurate lattice to a fully commensurate structure on increasing the coverage from a monolayer to a multilayer. The zig-zag backbone planes of all the alkane molecules lie parallel to the graphite surface at the multilayer coverage, while a few molecules are observed to attain the perpendicular orientation at monolayer coverage. Dedicated to Professor C N R Rao on his 70th birthday     

Low temperature properties of acetonitrile confined in MCM-41

The effect of confinement on the phase changes and dynamics of acetonitrile in mesoporous MCM-41 was studied by use of adsorption, FT-IR, DSC, and quasi-elastic neutron scattering (QENS) measurements. Acetonitrile molecules in a monolayer interact strongly with surface hydroxyls to be registered and perturb the triple bond in the C[triple bond]N group. Adsorbed molecules above the monolayer through to the central part of the cylindrical pores are capillary condensed molecules (cc-acetonitrile), but they do not show the hysteresis loop in adsorption-desorption isotherms, i.e., second order capillary condensation. FT-IR measurements indicated that the condensed phase is very similar to the bulk liquid. The cc-acetonitrile freezes at temperatures that depend on the pore size of the MCM-41 down to 29.1 A (C14), below which it is not frozen. In addition, phase changes between alpha-type and beta-type acetonitriles were observed below the melting points. Application of the Gibbs-Thomson equation, assuming the unfrozen layer thickness to be 0.7 nm, gave the interface free energy differences between the interfaces, i.e., Deltagamma(l/alpha) = 22.4 mJ m(-2) for the liquid/pore surface (ps) and alpha-type/ps, and Deltagamma(alpha/beta) = 3.17 mJ m(-2) for alpha-type/ps and beta-type/ps, respectively. QENS experiments substantiate the differing behaviors of monolayer acetonitrile and cc-acetonitrile. The monolayer acetonitrile molecules are anchored so as not to translate. The two Lorentzian analysis of QENS spectra for cc-acetonitriles showed translational motion but markedly slowed. However, the activation energy for cc-acetonitrile in MCM-41 (C18) is 7.0 kJ mol(-1) compared to the bulk value of 12.7 kJ mol(-1). The relaxation times for tumbling rotational diffusion of cc-acetonitrile are similar to bulk values.     

Structure, energetics, and dynamics of water adsorbed on the muscovite (001) surface: a molecular dynamics simulation

Molecular dynamics (MD) computer simulations of liquid water adsorbed on the muscovite (001) surface provide a greatly increased, atomistically detailed understanding of surface-related effects on the spatial variation in the structural and orientational ordering, hydrogen bond (H-bond) organization, and local density of H2O molecules at this important model phyllosilicate surface. MD simulations at constant temperature and volume (statistical NVT ensemble) were performed for a series of model systems consisting of a two-layer muscovite slab (representing 8 crystallographic surface unit cells of the substrate) and 0 to 319 adsorbed H2O molecules, probing the atomistic structure and dynamics of surface aqueous films up to 3 nm in thickness. The results do not demonstrate a completely liquid-like behavior, as otherwise suggested from the interpretation of X-ray reflectivity measurements and earlier Monte Carlo simulations. Instead, a more structurally and orientationally restricted behavior of surface H2O molecules is observed, and this structural ordering extends to larger distances from the surface than previously expected. Even at the largest surface water coverage studied, over 20% of H2O molecules are associated with specific adsorption sites, and another 50% maintain strongly preferred orientations relative to the surface. This partially ordered structure is also different from the well-ordered 2-dimensional ice-like structure predicted by ab initio MD simulations for a system with a complete monolayer water coverage. However, consistent with these ab initio results, our simulations do predict that a full molecular monolayer surface water coverage represents a relatively stable surface structure in terms of the lowest diffusional mobility of H2O molecules along the surface. Calculated energies of water adsorption are in good agreement with available experimental data.     

Monolayer of aerosol-OT surfactants adsorbed at the air/water interface: an atomistic computer simulation study

An atomistic molecular dynamics (MD) simulation has been carried out to investigate the structural and dynamical properties of a monolayer of the anionic surfactant sodium bis(2-ethyl-1-hexyl) sulfosuccinate (aerosol-OT or AOT) adsorbed at the air/water interface. The simulation is performed at room temperature and at a surface coverage corresponding to that at its critical micelle concentration (78 A(2)/molecule). The estimated thickness of the adsorbed layer is in good agreement with neutron reflection data. The study shows that the surfactants exhibit diffusive motion in the plane of the interface. It is observed that the surfactant monolayer has a strong influence in restricting both the translational and reorientational motions of the water molecules close to the interface. A drastic difference in the dipolar reorientational motion of water molecules in the aqueous layer is observed with a small variation of the distance from the surfactant headgroups. It has been observed that the water molecules in the first hydration layer (region 1) form strong hydrogen bonds with surfactant headgoups. This results in the slower structural relaxation of water-water hydrogen bonds in the first hydration layer compared to that in the pure bulk water. Most interestingly, we notice that the water molecules present in the layer immediately after the first hydration layer form weaker hydrogen bonds and thus relax faster than even pure bulk water.     

Electrosorption of β-naphthol on graphite

Isotherms for the adsorption of β-naphthol from a buffered aqueous solution of 0.5 M K₂SO₄ onto graphite were detemrined over a range of potential of 1.27 V. The adsorbent was a packed bed of ?100 + 120 mesh graphite powder. Sufficient surface area was available to calculate accurately the amount adsorbed by measuring spectrophotometrically the change in adsorbate concentration in the bulk solution.At all potentials, a Langmuir adsorption isotherm, modified for the displacement of solvent molecules, was followed up to 60–65% of monolayer coverage. The ratio of projected areas of β-naphthol and water molecules was consistent with the experimentally derived number of solvent molecules displaced, six. The largest amount of adsorption observed, 2.5×10^?10 mol cm^?2, agreed with the calculated monolayer coverage of β-naphthol molecules lying in flat orientation on the graphite surface. Adsorption increased at more positive potentials. Over the range of potential investigated, the adsorbability constant increased sixfold. Desorption was only partially reversible.     

Self-assembly of amphiphilic hexapyridinium cations at the air/water interface and on HOPG surfaces.

Mono- and multilayers of a novel amphiphilic hexapyridinium cation with six eicosyl chains (3) are spread at the air/water interface as well as on highly ordered pyrolytic graphite (HOPG). On water, the monolayer of 3 is investigated by recording surface pressure/area and surface potential/area isotherms, and by Brewster angle microscopy (BAM). Self-organized tubular micelles with an internal edge-on orientation of molecules form at the air/water interface at low surface pressure whereas multilayers are present at high surface pressure, after a phase transition. Packing motifs suggesting a tubular arrangement of the constituting molecules were gleaned from atomic force microscopy (AFM) investigations of Langmuir-Blodgett (LB) monolayers being transferred on HOPG at different surface pressures. These LB film structures are compared to the self-assembled monolayer (SAM) of 3 formed via adsorption from a supersaturated solution, which is studied by scanning tunnelling microscopy (STM). On HOPG the SAM of 3 consists of nanorods with a highly ordered edge-on packing of the aromatic rings and an arrangement of alkyl chains which resembles the packing of molecules at the air/water interface at low surface pressure. Additional details of the molecular packing were gleaned from single-crystal X-ray structure analysis of the hexapyridinium model compound 2b, which possesses methyl instead of eicosyl residues.     

Substrate and surfactant effects on the glass-liquid transition of thin water films

Temperature-programmed time-of-flight secondary ion mass spectrometry (TP-TOF-SIMS) and temperature-programmed desorption (TPD) have been used to perform a detailed investigation of the adsorption, desorption, and glass-liquid transition of water on the graphite and Ni(111) surfaces in the temperature range 13-200 K. Water wets the graphite surface at 100-120 K, and the hydrogen-bonded network is formed preferentially in the first monolayer to reduce the number of nonbonding hydrogens. The strongly chemisorbed water molecules at the Ni(111) surface do not form such a network and play a role in stabilizing the film morphology up to 160 K, where dewetting occurs abruptly irrespective of the film thickness. The surface structure of the water film formed on graphite is fluctuated considerably, resulting in deweting at 150-160 K depending on the film thickness. The dewetted patches of graphite are molecularly clean, whereas the chemisorbed water remains on the Ni(111) surface even after evaporation of the film. The abrupt drop in the desorption rate of water molecules at 160 K, which has been attributed to crystallization in the previous TPD studies, is found to disappear completely when a monolayer of methanol is present on the surface. This is because the morphology of supercooled liquid water is changed by the surface tension, and it is quenched by termination of the free OH groups on the surface. The surfactant methanol desorbs above 160 K since the hydrogen bonds of the water molecules are reconstructed. The drastic change in the properties of supercooled liquid water at 160 K should be ascribed to the liquid-liquid phase transition.     

Molecular dynamics simulation of dense carbon dioxide fluid on amorphous silica surfaces

Molecular dynamics (MD) simulations of dense carbon dioxide on the amorphous dehydroxylated silica surfaces have been carried out. The adsorption potential surfaces of the silica solids have been obtained in order to evaluate the characteristics of the amorphous surfaces. The atom density profiles, adsorption free energy profiles, surface orientation order parameters, and radial distribution functions for the CO2 molecules have been presented in order to study the effect of the amorphous surfaces on the microscopic interfacial structure properties of the CO2 molecules. The translational diffusion and orientation rotation at silica surfaces have also been investigated. It was observed that there is marked hindrance of the translational diffusion and orientation rotation of CO2 molecules near amorphous silica surfaces.     

The study of orientational relaxation of rodlike molecules in the presence of an adsorbing surface by the molecular dynamics method

Coefficients of translational and rotational self-diffusion of rigid-chain rodlike molecules formed from four spherical particles are determined by the molecular dynamics method. Simulations are performed for a three-dimensional canonical ensemble of 4096 Lennard-Jones particles within the range of chain concentration in its monomer varying from 2 to 100 mol % with allowance for the adsorption of chains on two parallel walls confining the system. Changes in the concentration profiles of chains and solvent particles over the normal to walls during variations in adsorption energy are considered. It is shown that the dependences of translational and rotational self-diffusion coefficients on the concentration and adsorption energy govern the changes in the characteristic times of the orientation-disorientation processes of molecules. All specific features of the establishment of orientational order and its relaxation are determined mainly by the degree of coverage of the adsorption monolayer. The contributions of the second and third monolayers to the weighted-mean mobility of chains begin to be pronounced with an increase in concentration. The exchange of chains between the adsorption monolayer and bulk solution is suppressed with an increase in the adsorption energy, and the monolayer is transformed into a set of two-dimensional “crystallites.” These crystallites form a typical domain structure on the adsorbing surface. The orientation and, hence, the ordering of domains by the external field occur a little more slowly than the orientation of molecules in solution. The disorientation requiring asynchronous rotations of chains is impeded, thus resulting in noticeable retardation of this process relative to the orientation, and upon achievement of a certain value of adsorption energy, the orientation of chains induced in the first adsorption monolayer becomes stable.     

Thermodynamic and neutron scattering study of hydrogen adsorption in two mesoporous ordered carbons

Two mesoporous ordered carbon materials (MOCs) have been synthesized from silica templates by using sucrose as the carbon precursor. The textural characterization using Ar, N2, and CO2 adsorption combined with neutron diffraction showed that the two samples exhibit a significant microporous volume close to 0.5 cm3/g and an ordered network of mesopores. For both MCM48 and SBA15 templated carbons, adsorption first proceeds with the filling of micropores and then by the filling of mesopores with an adsorption energy close to the enthalpy of vaporization of bulk hydrogen. The hydrogen isosteric heat of adsorption in the micropores (6-8 kJ/mol) is significantly larger than that on the graphite surface (approximately 4 kJ/mol) but still too small for a reasonable use of these MOCs as hydrogen adsorbents for storage at room temperature. The neutron scattering study showed that the structure at 10 K of the adsorbed deuterium phase is poorly organized; it exhibits short and medium range orders of about 13 angstroms in micropores and about 20 angstroms in mesopores, respectively. The average distance between adsorbed molecules decreases with coverage by about 10%. In the mesopores, the diffracted line is consistent with a pseudohexagonal packing.     

Influence of temperature on the composition of mixed monolayer formed at the methyl alcohol/acetic acid aqueous solutio–air interface

The influence of temperature on the composition of mixed monolayer formed at the methyl alcohol/acetic acid aqueous solution was examined by surface tension measurements. Surface tension of various two-component solutions was obtained at 10, 20 and 28 °C temperatures in the 0–0.5 M range of bulk concentration of alcohol and acid, respectively. Three independent methods, i.e., the Gibbs adsorption equation (GAE), regular solution approximation (RSA) and Butler adsorption isotherm (BAI) were applied to calculate surface composition of the methyl alcohol/ acetic acid mixed monolayer. It was shown that in the temperature range of 10–28 °C the surface molar fraction of the solutes remained constant for the fixed bulk concentration of alcohol and acid. Additionally, based on the RSA and BAI methods, we showed there were no interactions between solute molecules in the mixed monolayer in the studied range of concentrations. Received: 18 December 1997 Accepted: 8 May 1998     

Phase behavior of mixed submonolayer films of krypton and xenon on graphite

Using the results of extensive Monte Carlo simulations in the canonical and grand canonical ensembles, we discuss the phase behavior of mixed submonolayer films of krypton and xenon adsorbed on the graphite basal plane. The calculations have been performed using two- and three-dimensional models of the systems studied. It has been demonstrated that out-of-plane motion does not affect the properties of the films as long as the total density is well below the monolayer completion and at moderate temperatures. For the total densities close to the monolayer completion, the promotion of particles to the second layer considerably affects the film properties. Our results are in a reasonable agreement with the available experimental data. The melting point of submonolayer films has been shown to exhibit non-monotonous changes with the film composition, and reaches minimum for the xenon concentration of about 50%. At the temperatures below the melting point, the structure of solid phases depends upon the film composition and the temperature; one can also distinguish commensurate and incommensurate phases. Two-dimensional calculations have demonstrated that for the xenon concentration between about 15% and 65% the adsorbed film exhibits the formation of a superstructure, in which each Xe atom is surrounded by six Kr atoms. This superstructure is stable only at very low temperatures and transforms into the mixed commensurate (√3×√3)R30° phase upon the increase of temperature. Such a superstructure does not appear when a three-dimensional model is used. Grand canonical ensemble calculations allowed us to show that for the xenon concentration of about 3% the phase diagram topology of monolayer films changes from the krypton-like (with incipient triple point) to the xenon-like (with ordinary triple point).     

Chiral expression at the solid-liquid interface: a joint experimental and theoretical study of the self-assembly of chiral porphyrins on graphite

The chiral organization of an enantiopure functional molecule on an achiral surface has been studied with the aim of understanding the influence of stereogenic centers on the self-assembly in two dimensions. A chiral tetra meso-amidophenyl-substituted porphyrin containing long hydrophobic tails at the periphery of the conjugated pi-electron system was prepared for this purpose. Scanning tunneling microscopy (STM) images of the compound at the graphite-heptanol interface reveal a chiral arrangement of the molecules, with the porphyrin rows tilted by 13 degrees with respect to the normal to the graphite axes. In terms of molecular modeling, a combination of molecular dynamics simulations on systems constrained by periodic boundary conditions and on unconstrained large molecular aggregates has been applied to reach a quantitative interpretation on both the density of the layer and its orientation with respect to the graphite surface. The results show clearly that (i) the methyl groups of the stereogenic point toward the graphite surface and (ii) the porphyrin molecules self-assemble into an interdigitated structure where the alkyl chains align along one of the graphite axes and the porphyrin cores are slightly shifted with respect to one another. The direction of this shift, which defines the chirality of the monolayer, is set by the chirality of the stereogenic centers. Such an arrangement results in the formation of a dense chiral monolayer that is further stabilized by hydrogen bonding with protic solvents.     

Melting mechanism of monolayers adsorbed in cylindrical pores: the influence of the pore wall roughness

We have analyzed the mechanism of melting of molecular layers adsorbed in porous materials with cylindrical pores and rough pore walls. The working example studied here is a monolayer of methane molecules adsorbed in MCM-41 pore of diameter 2R=4 nm. Both experimental (neutron scattering) and simulation (Monte Carlo) results demonstrate the strong influence of the wall roughness on the melting mechanism. In particular, the transformation between solidlike and liquidlike monolayer phases adsorbed on a rough surface is observed over a broad temperature range, and solidlike properties persist even above the bulk methane melting temperature.     

Interaction between water molecules and zinc sulfide nanoparticles studied by temperature-programmed desorption and molecular dynamics simulations

We have investigated the bonding of water molecules to the surfaces of ZnS nanoparticles (approximately 2-3 nm sphalerite) using temperature-programmed desorption (TPD). The activation energy for water desorption was derived as a function of the surface coverage through kinetic modeling of the experimental TPD curves. The binding energy of water equals the activation energy of desorption if it is assumed that the activation energy for adsorption is nearly zero. Molecular dynamics (MD) simulations of water adsorption on 3 and 5 nm sphalerite nanoparticles provided insights into the adsorption process and water binding at the atomic level. Water binds with the ZnS nanoparticle surface mainly via formation of Zn-O bonds. As compared with bulk ZnS crystals, ZnS nanoparticles can adsorb more water molecules per unit surface area due to the greatly increased curvature, which increases the distance between adjacent adsorbed molecules. Results from both TPD and MD show that the water binding energy increases with decreasing the water surface coverage. We attribute the increase in binding energy with decreasing surface water coverage to the increasing degree of surface under-coordination as removal of water molecules proceeds. MD also suggests that the water binding energy increases with decreasing particle size due to the further distance and hence lower interaction between adsorbed water molecules on highly curved smaller particle surfaces. Results also show that the binding energy, and thus the strength of interaction of water, is highest in isolated nanoparticles, lower in nanoparticle aggregates, and lowest in bulk crystals. Given that water binding is driven by surface energy reduction, we attribute the decreased binding energy for aggregated as compared to isolated particles to the decrease in surface energy that occurs as the result of inter-particle interactions.