Controversial Evidence on the Point of Minimum Density in Deeply

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Controversial Evidence on the Point of Minimum Density in Deeply Supercooled Confined Water R. Mancinelli,† F. Bruni, and M. A. Ricci* Dipartimento di Fisica “E. Amaldi”, Universit a degli Studi “Roma Tre”, Via della Vasca Navale 84, 00146 Roma, Italy

ABSTRACT The issue of the existence of a minimum of density at 210 K in water confined in MCM41 is tackled by neutron diffraction with H/D isotopic substitution over a wide range of momentum transfer, which allows refining in a single experiment both the meso- and the atomic-scale structure. We observe clear density fluctuations of confined water, with temperature-dependent length scale, due to changes of the balance between cohesive and adhesive interactions. These results cast some doubt about previous interpretation of SANS experiments on water confined in the same substrate as evidence for the existence of a point of minimum density at 210 K. This interpretation is based on the assumption that water homogeneously occupies the available volume within the confining substrate. We demonstrate that this is not the case in water confined in MCM-41-S-15, and provide an alternative explanation of small-angle neutron scattering results. SECTION Macromolecules, Soft Matter

I

t is part of our everyday experience that ice floats on water, and it has long been appreciated that the development of an open tetrahedral network on cooling is related to the occurrence of the density maximum observed at 277 K. The existence of a temperature of maximum density (TMD) for water above its melting point is one of the most dramatic pieces of evidence for water being anomalous. The density of bulk water below the TMD and in the supercooled phase decreases rapidly with T before the onset of homogeneous nucleation precludes further supercooling. Since the density of ice increases with decreasing T, it is predicted that if it were possible to supercool bulk water below the presently achievable limit of ∼240 K, a minimum of density should be reached at some still unknown temperature. This stable phase of water is indeed an almost perfectly ordered tetrahedral network of hydrogen bonds, thus setting a lower density limit for aqueous systems (see Figure 2 of ref 1). Estimates of the temperature of minimum density (TmD) of bulk water have been given by several computer simulations,2-4 while an experimental value is so far missing, due to ice nucleation below ∼240 K. Yet it is possible to avoid crystallization, provided that water is confined in small enough volumes.5,6 We are aware that there is a significant debate about the state of confined water at low temperatures and small volumes7 although a wealth of evidence, based on Fourier transform infrared spectroscopy,8 nuclear magnetic resonance and quasi-elastic neutron scattering,9 and differential scanning calorimetry10 seems to imply that water confined in the small pores of a silica matrix remains a liquid, albeit with much slower dynamics; however, the issue addressed in this work goes beyond this question. It is also questionable that properties of water under severe confinement

r 2010 American Chemical Society

have any relevance as far as bulk water is concerned, while the reliability of their extrapolation to the bulk case must be handled with care. However, confined water is relevant by itself, and the claim of an experimental determination of the TmD by Liu and co-workers1 has received great relevance in the literature. These authors1 reached temperatures as low as 150 K in a small-angle neutron scattering (SANS) experiment on water confined in porous silica (MCM-41-S-15) and have seen the intensity of the SANS peak (at ∼0.215 Å-1) going through a minimum, while lowering the temperature. This peak is due to the Bragg reflection of the two-dimensional (2D) hexagonal array of cylindrical pores of the MCM-41-S-15 substrate, and its intensity depends on the contrast seen by neutrons, between the porous silica substrate and water in the pores. Under the hypotheses that the structure of the silica substrate does not change and the density of water in the pores is uniform, changes of the SANS peak intensity are due to changes of water density. Accordingly, the results of ref 1 have been interpreted as evidence for a minimum of density of confined water at about 210 K. Given that the amount of confined water is constant in the cited experimental work,1 the claimed density change within the pore must be due to a microscopic rearrangement of water molecules. The point addressed in the present work is that neutron diffraction investigation of this rearrangement unveils the ambiguity of the definition of density of water under confinement and gives an alternative explanation of the SANS results.

Received Date: February 19, 2010 Accepted Date: March 24, 2010 Published on Web Date: March 30, 2010

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DOI: 10.1021/jz100236j |J. Phys. Chem. Lett. 2010, 1, 1277–1282

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Figure 2. The DCS of all D2O hydrated samples at the four investigated temperatures (all shifted by an arbitrary quantity), along with the water-substrate cross-correlation term (reconstructed from the EPSR configurations). Note that the peak of the DCS at ∼2 Å moves to lower Q values and becomes narrower and that the intensity of the cross-correlation term decreases when the temperature decreases.

Figure 1. The DCS of two D2O hydrated samples at T = 300 K (dashed) and T = 210 K (solid). In the low Q region, the Bragg peak of the hexagonal array of MCM-41-S-15 is visible: its intensity decreases when the temperature reaches 210 K. At high Q values (see also the inset) the two DCS's coincide within the statistical uncertainty. The dashed black line in the inset indicates the expected level of the atomic self-scattering at T = 210 K for a sample at the minimum density calculated according to ref 1: this level is well outside the experimental uncertainty of our data.

change. At odds with this evidence for a constant sample density, the intensity of the Bragg peak decreases on going from ambient temperature to 210 K, as already observed in ref 1. Moreover the DCS in the intermediate Q range (see Figure 2) evidences clear changes of the microscopic structure of water confined in MCM-41-S-15 pores when the temperature decreases, as shown by the monotonic shift and narrowing of the diffraction peak at ∼2 Å-1 in the hydrated samples. This suggests that the structure of confined water at 240 K must be different from that at 170 K, although the density (or more correctly the neutron contrast) is the same. We will show that the two apparently conflicting results for the density of confined water can be reconciled by observing that, when water does not uniformly occupy the pore volume, as suggested by our data and previous computer simulations,13-15,17 the traditional SANS formalism does not properly apply to interpret the experimental data. The intensity of the Bragg peak is in that case influenced by the density fluctuations of water inside the MCM-41-S-15 pores, which could be temperature dependent. The present controversy on the density of confined water, resulting from the apparent contradiction of experimental data at high and low Q, cannot be settled by a traditional analysis of the neutron diffraction data, for several reasons. First of all, we need to separate the contribution of water molecules to the measured DCS from that of silica and from the water-silica cross correlations. Moreover density fluctuations give an extra intensity in the DCS at low Q values in the case of bulk fluids, but here the presence of a porous substrate makes the situation more complicated. Finally, the radial

We report the results of a neutron diffraction experiment with isotopic H/D substitution (NDIS)11 performed on MCM41-S-15, at four temperatures, namely T=300 K, T=210 K (which is the proposed minimum density point), T=240 K, and T=170 K, where the last two temperatures correspond to the same density of confined water, according to ref 1. The differential cross-section (DCS) has been measured over the widest possible range of momentum transfer, Q, spanning from 0.1 to 50 Å-1. This allows one to simultaneously refine the sample structure at both atomistic and mesoscopic scale, since the Bragg peak at 0.215 Å-1 is visible along with the intermolecular and intramolecular contributions, which extend to higher Q values. After correction of absorption and inelasticity effects, and normalization to absolute units (barn/[atom sr]) performed along the lines presented in the Materials and Methods section, the DCS can be expressed as dσ σinc ð1Þ þ DCS ¼ dΩ coh 4π where the first term is an oscillating function, which contains the structural information on the sample, and σinc/4π is the constant incoherent single atom contribution to the scattering.12 In Figure 1 we observe that, when the same sample density is used to normalize the data at two different temperatures, at high Q, the level of the DCS goes to its expected value [(σinc þ σcoh)/4π],12 and the amplitude of the coherent DCS oscillations (determined by the intramolecular form factor) does not


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Figure 3. Left: The density profile, F(r), calculated according to eq 6 (see Marerials and Methods) at all temperatures investigated, versus the distance from the pore axis, r. Data have been collected for 105 configurations, and the statistical uncertainty is within the line thickness. The black dashed lines indicate the estimated wall position (see Materials and Methods) and the average water density, according to the hydration level and total pore volume (TPV) of the sample. Right: Schematic view of the three pore filling scenarios compatible with the density profile F(r) reported in Figure 3: (A)There is a layer of water molecules wetting the pore surface and a depletion of density towards the pore center, resulting in density fluctuations along the r direction; (B) There is a cohesive failure between water molecules within the pore, giving density fluctuations along the radius and axis of the cylinder; (C) There is a meniscus at each end of the pore. When the temperature decreases, water molecules move in the direction shown by the arrows and the density fluctuations decrease in all three scenarios. (D) Top view of the cylinder, showing the density profile after averaging along the cylinder axis.

distribution functions (RDFs), obtained by the Fourier transform of the data, would not give a direct estimate of the density fluctuations, although they showed peculiar behaviors when these are present. What we need is a collection of molecular configurations, compatible with the experimental data, in order to evaluate, as in the case of previous simulation works on confined water,13-17 the density profile along a characteristic direction (see Materials and Methods). These configurations are provided by running the empirical potential structure refinement (EPSR) routine18-20 (see Materials and Methods), which refines a computer simulation model of the sample against the diffraction data. The density profiles along the silica pore radius are reported in Figure 3 for all four temperatures investigated. These show that, at all temperatures, a small, although not negligible, number of molecules penetrates the silica wall, due to its roughness.21 More importantly, we notice that, in all cases, the density profile is not uniform and shows a peak in the vicinity of the wall, as already found in several simulations.13-17 Moreover when the temperature decreases from ambient to 240 K, the number of molecules within the pockets of the silica wall decreases, and the density profile in the middle of the pore increases. Upon further lowering of the temperature, molecules move away from the layer close to the pore surface toward the pore center, and the oscillations typical of a layering effect are observed at T = 210 K. At 170 K, the signatures of layering are still visible, but a portion of the water molecules moves back from the pore center toward the substrate surface. This behavior follows the observed changes of neutron contrast at low Q in both the present experiment and the previous SANS one.1 Does this mean that SANS measures the density fluctuations inside the pore? Let us go back to the definition of the coherent contribution to the DCS: X dσ ¼ jÆ bR eiQ 3 rR æj2 ð2Þ dΩ coh R


where bR and rR are, respectively, the neutron scattering length12 and the position of the R atom, and Ææ represent the average over the nuclear spin configurations. In our sample, rR can be expressed taking into account the periodicity of the array of cylinders as rR=li þ uiR, with uiR being the coordinate of the R atom within the unitary cell of coordinates li; this allows one to factorize the structure factor of the hexagonal array of cylinders, Shex(Q). Moreover, if the sum over thePatomic sites is separated into a sum over P water atoms, wi, and a sum over substrate atoms, si, eq 2 becomes X X dσ i i ¼ Shex ðQÞfjÆ bw eiQ 3 uw þ bs eiQ 3 us æj2 g ð3Þ dΩ coh wi si Following the traditional SANS formalism, when the atomistic structure is not resolved, the Σwi and Σsi can R be R substituted by the integrals: Vw d3uwbwFweiQ 3 uw and V-Vw d3usbsFseiQ 3 us, respectively, where Fw and Fs are the local densities of water and of silica, and the two substances are confined respectively in Vw and V - Vw. Simple algebra then leads to Z dσ ¼ Shex ðQÞfj d3 uw ½bw Fw - bs Fs eiQ 3 uw þ dΩ coh Vw Z Z Z d3 us bs Fs eiQ 3 us j2 g ¼ Shex ðQÞf d3 u d3 u0 ½bw Fw V

0

bs Fs 2 eiQ 3 ½u-u þ

Z V

Vw

Vw

Z 0 d3 u d3 u0 b2s F2s eiQ 3 ½u-u þ V

cross-correlation termg

ð4Þ

and if [bwFw - bsFs] = constant, the classical SANS formula reported in ref 1 is recovered:

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dσ dΩ

¼ Shex ðQÞ½bw Fw - bs Fs 2 FðQÞ

ð5Þ

coh


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where F(Q) is the cylinder form factor, and [bwFw - bsFs]2 is the neutron contrast. Conversely, if the density of one of the sample components, namely, water or silica, is not constant overR the integration volume, as in the present case, R 0 the integral Vwd3u Vwd3u0 [bwFw - bsFs]2eiQ 3 [u-u ] must be numerically calculated, and the form factor will be modulated by the density fluctuations. Consequently, when the confined fluid is not homogeneously distributed within the substrate pores, SANS cannot be used to measure the liquid density, and changes of the Bragg peak intensity cannot be interpreted as evidence for density changes. If we further consider that the experimental resolution in a SANS experiment is on the order of 10 Å, then it is reasonable to conclude that this technique cannot distinguish between the density profiles reported in Figure 3 at T=240 and 170 K. These density profiles differ for a more distinct layering at the lowest temperature, but are likely giving the same average neutron contrast between water and silica. The above considerations, along with the clear changes with temperature of the DCS at intermediate Q values (see Figure 2) tell us that the intensity of the Bragg peak changes because the arrangement of water molecules within the silica pore, that is, the water structure at the atomistic level, is changing. In order to investigate the origin of these changes in greater detail, it is interesting to look at the water-substrate cross-correlation terms of the DCS, as extracted by the EPSR routine. The temperature evolution of this term is reported in Figure 2 and demonstrates that, although in the Q range between 2 and 3 Å -1, it is relevant at all temperatures (as it was predictable given the high surface/volume ratio), and its intensity decreases with decreasing temperature. This is the signature of a change of the relative weight of the water cohesive interaction with respect to the adhesive interaction of water with the substrate, also evidenced by the migration of water molecules away from the substrate walls (see Figure 3). Interestingly, it has been shown that changes of this balance affects the probability of finding void regions in confined water as well as their location within the confining volume,22 in such a way that we can speculate about the temperature evolution of water arrangement and density profiles in our sample. Indeed, given the size of our simulation box and the periodic boundary conditions applied in the direction of the cylinder axis, the F(r) function is the one-dimensional projection of the density fluctuations of water within the pore. This implies that a single density profile may correspond to different three-dimensional situations, as sketched in Figure 3: the density of water is high in the vicinity of the substrate walls and monotonically decreases toward the pore center (A); there is a so-called cohesive failure between water molecules, giving a region of lower density in the middle of the pore (B); and there are two meniscus regions on top and bottom of the pore (C). Obviously we cannot in principle distinguish among these three scenarios, based on our data and size of the simulation box, and a realistic description will likely fall in between. However, when the Bragg peak intensity decreases upon lowering the temperature, the density fluctuations must decrease: this may happen if water molecules move in the directions indicated by the arrows in Figure 3. It has to be mentioned, however, that the characteristic length scale of the


density fluctuations in the radial direction must necessarily be shorter than that in the axial direction, since the typical radius and the length of a pore in the MCM sample are on the order of 10 Å and 1 μm, respectively. Consequently, a mechanism of type A will not reproduce the experimental findings as far as the Bragg peak intensity is concerned. We conclude therefore that, at ambient conditions, regions of cohesive failure as those shown in Figure 3B,C are likely to occur, as also found by molecular dynamics (MD) simulations of water confined between hydrophilic planar walls.22 When the temperature decreases, the balance between water-water and watersubstrate interactions changes, as also demonstrated by the behavior of the intensity of the cross terms of the DCS (Figure 2) on going from ambient to lower temperatures. This implies that there is a sort of expansion of the liquid at the microscopic level, with a reduction of the pore regions inhomogeneously occupied due to the cohesive failure between water molecules. This expansion is consistent with a more ordered structure, although it does not imply a net change of the average density of confined water. In conclusion we have shown, by comparing neutron diffraction data at low and high Q values, that water confined in MCM-41-S-15 does not uniformly occupy the available pore volume, and inhomogeneous density profiles across the pore can be observed. The details of the inhomogeneities may be substrate dependent, but more interestingly we have found that they are temperature dependent, due to changes of the balance between water-water and water-substrate interactions. As a consequence, the concept of average density is not significant enough for severely confined water.

MATERIALS AND METHODS The MCM-41-S-15 substrate has been synthesized following the same procedure used for previous SANS experiments1 and characterized by the Barrett-Joyner-Halenda (BJH) method 23. Further characterization of the substrate, based on neutron diffraction DCS measurements, fully described elsewhere,24 confirms that this is a hexagonal array of silica cylinders with an average radius of ∼(8.5 ( 1.5) Å and interplanar distance of 28.7 Å. The pore surfaces have hydrophilic character, due to the presence of a relatively high amount of silanol groups (11% of the total atomic composition). Samples have been hydrated at h = 0.43 g/g, defined as grams of H2O per gram of dry MCM (for D2O and the 50% H/D mixture this value has been adjusted according to the isotopic mass), which is the same water content used in ref 1. This hydration, corresponding to 90% filling of the pore at ambient conditions, along with the total pore volume of the substrate (TPV), gives for light water a density of F=h/TPV ∼ 0.86 g/cm3. The procedure followed to hydrate and dehydrate samples in situ, along with the sample container details and thermoregulation, are also described in ref 24. The diffraction experiment was performed on the SANDALS25 time-of-flight diffractometer at the ISIS spallation neutron source.26 The results are obtained in the form of DCS's as a function of momentum transfer Q, after standard normalization and analysis routines.27

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covering a large range of phase space compatible with the data. Further details about the EPSR code implemented for the simulation of the water-MCM-41-S-15 system can be found in ref 24. It has been shown20 that the results of the EPSR simulations do not strongly depend on the choice of the initial potential model adopted. The atomic configurations recorded during the production run can be used to calculate structural quantities beyond the RDF, as in any simulation work. In particular, this method allows disentanglement of waterwater and water-substrate correlations,24 as the individual pair contributions to the DCS can be evaluated from the Fourier transform of the relevant RDF. Moreover, we can calculate the density profile along the pore radius, r, of interest here, as FðrÞ ¼

natoms ðr, r þ ΔrÞ Vðr, r þ ΔrÞ

ð6Þ

where natoms(r, r þ Δr) is the number of water atoms in a cylindrical shell of length L between r and r þ Δr around the pore axis, of volume V(r, rþΔr)=4π [(r þ Δr)2 - r2]L. Figure 4 shows the good agreement between measured and simulated DCS for the whole set of six data (three hydrated and three dry) at T=210 K, as an example.

Figure 4. The DCS's of all samples at T = 210 K (marks) along with their EPSR fit (line). Data for the individual samples have been shifted for clarity: the DCS of the three isotopically substituted dry substrates are reported at the bottom, those of the hydrated ones are at the top, and the labels M and dryM refer to the 50% H/D mixture, while D, H and dryD, dryH refer to the deuterated and hydrogenated samples, respectively.

AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed. Address: Dipartimento di Fisica “E. Amaldi”, Universit a degli Studi “Roma Tre”, Via della Vasca Navale 84, 00146 Roma, Italy. Tel.: þ39-06-57337226; fax: þ39-06-57337102; e-mail: [email protected].

The data analysis in r-space is performed by using the EPSR,18-20 which refines a computer simulation model of the sample against the diffraction data, until the simulated DCS's satisfactorily fit the experimental ones. In the present particular case,24 the simulation starts by building a cubic box of silica at a density compatible with that of the skeleton of our sample and equilibrating this ensemble of atoms by running a standard Monte Carlo routine; then a cylinder of the same diameter as the pores of the real sample is drilled and decorated with silanols in the right proportion to reproduce the experimental concentration. This simulation box is processed through the EPSR code, by taking into account the experimental data for the dry samples. Once a good fit of these data is achieved, the pore is filled with water molecules at the same hydration as the real sample, and a new EPSR run starts and refines the fitting of the hydrated samples data. In an EPSR simulation, the interaction potential between the individual atomic species is initially set according to standard pairwise additive potential models available in the literature,28,29 and the Lorentz-Berthelot rules are used to estimate the interaction between different species. The fit of the experimental DCS data is obtained by iteratively adjusting the interaction potential according to the feedback from the comparison between simulated and measured DCS. Once the fit cannot be further improved, the empirical correction to the potential model is retained for the subsequent production run. In the EPSR routine, the acceptance of a move is based on the usual Metropolis condition, according to the probability p= exp[-ΔU/(kBT)], where ΔU is the change in potential energy of the system as a result of the move. This procedure ensures that the system proceeds along a Markov chain,


Present Addresses: †

Also at CNR-ISC, via Madonna del Piano 10, 50019 Sesto fiorentino, Firenze, Italy.

ACKNOWLEDGMENT This work has been performed within Agreement No. 01/9001 between STFC and CNR, concerning collaboration in scientific research at the spallation neutron source ISIS and with partial financial support of CNR. The authors are indebted to C. Y. Mou, who provided the MCM-41-S-15 samples, and acknowledge useful discussions with him and S. H. Chen, S. Imberti, and A. K. Soper.

REFERENCES (1)

(2)

(3)

(4)

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Liu, D.; Zhang, Y.; Chen, C.-C.; Mou, C.-J.; Poole, P. H.; Chen, S. H. Observation of the Density Minimum in Deeply Supercooled Confined Water. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 9570–9574. Brovchenko, I.; Geiger, A.; Oleinikova, A. Multiple LiquidLiquid Transitions in Supercooled Water. J. Chem. Phys. 2003, 118, 9473–9476. Paschek, D. How the Liquid-Liquid Transition Affects Hydrophobic Hydration in Deeply Supercooled Water. Phys. Rev. Lett. 2005, 94, 217802–217806. Brovchenko, I.; Geiger, A.; Oleinikova, A. Liquid-Liquid Phase Transitions in Supercooled Water Studied by Computer Simulations of Various Water Models. J. Chem. Phys. 2005, 123, 044515–044531.


pubs.acs.org/JPCL

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12) (13)

(14)

(15)

(16)

(17)

(18) (19)

(20)

(21)

(22)

Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; SliwinskaBartkowiak, M. Phase Separation in Confined Systems. Rep. Prog. Phys. 1999, 62, 1573–1659. Johari, G. P. On the Origin of the Heat Capacity Feature of Annhealed Ices and Ice Clathrates and Interpreting Water's Diffusivity in Terms of the Entropy. Chem. Phys. 2000, 258, 277–290. Johari, G. P. Origin of the Enthalpy Features of Water in 1.8 nm Pores of MCM-41 and the Large Cp Increase at 210 K. J. Chem. Phys. 2009, 130, 124518–124524. Mallamace, F.; Broccio, M.; Corsaro, C.; Faraone, A.; Majolino, D.; Venuti, V.; Liu, L.; Mou, C.-Y.; Chen, S. H. Evidence of the Existence of the Low-Density Liquid Phase in Supercooled, Confined Water. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 424–428. Chen, S. H.; Mallamace, F.; Mou, C.-Y.; Broccio, M.; Corsaro, C.; Faraone, A.; Liu, L. The Violation of the Stokes-Einstein Relation in Supercooled Water. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 12974–12978. Yoshida, K.; Yamaguchi, T.; Kittawa, S.; Bellissent-Funel, M.-C.; Fouquet, P. Thermodynamic, Structural and Dynamic Properties of Supercooled Water Confined in Mesoporous MCM-41 Studied with Calorimetric Neutron Diffraction and Neutron Spin Echo Measurements. J. Chem. Phys. 2008, 129, 054702–054713. Ricci, M. A.; Bruni, F.; Giuliani, A. “Similarities” between Confined and Supercooled Water. Faraday Discuss. 2009, 141, 347–358. Sears, V. F. Neutron Scattering Lengths and Cross Sections. Neutron News 1992, 3, 26–37. Hartnig, C.; Witschel, W.; Spohr, E.; Gallo, P.; Ricci, M. A.; Rovere, M. Modifications of the Hydrogen Bond Network of Liquid Water in a Cylindrical SiO2 Pore. J. Mol. Liq. 2000, 85, 127–137. Lee, S. H.; Rossky, P. J. A Comparison of the Structure and Dynamics of Liquid Water at Hydrophobic and Hydrophilic Surfaces - A Molecular Dynamics Simulation Study. J. Chem. Phys. 1994, 100, 3334–3345. Gallo, P.; Ricci, M. A.; Rovere, M. Layer Analysis of the Structure of Water Confined in Vycor Glass. J. Chem. Phys. 2002, 116, 342–346. Brovchenko, I.; Oleinikova, A. In Handbook of Theoretical and Computational Nanotechnology; Rieth, M., Schommers, W., Eds.; America Scientific Publishers: Valencia, California, 2005; pp 1-98. Giovambattista, N.; Rossky, P. J.; Debenedetti, P. G. Effects of Temperature on the Structure and Phase Behavior of Water Confined by Hydrophobic, Hydrophilic Heterogeneous Surfaces. J. Phys. Chem. B 2009, 113, 13723–13734. Soper, A. K. Empirical Potential Monte Carlo Simulation of Fluid Structure. Chem. Phys. 1996, 202, 295–306. Soper, A. K. The Radial Distribution Functions of Water and Ice from 220 to 673 K and at Pressures up to 400 MPa. Chem. Phys. 2000, 258, 121–137. Soper, A. K. Tests of the Empirical Potential Structure Refinement Method and a New Method of Application to Neutron Diffraction Data on Water. Mol. Phys. 2001, 99, 1503–1516. Muroyama, N.; Yoshimura, A.; Kubota, Y.; Miyasaka, K.; Ohsuna, T.; Ryoo, R.; Ravikovitch, P. I.; Neimark, A. V.; Tanaka, M.; Terasaki, O. Argon Adsorption on MCM-41 Mesoporous Crystal Studied by In Situ Synchrotron Powder X-ray Diffraction. J. Phys. Chem. C 2008, 112, 10803–10813. Lombardo, T. G.; Giovambattista, N.; Debenedetti, P. G. Structural and Mechanical Properties of Glassy Water in


(23)

(24)

(25)

(26) (27)

(28)

(29)

1282

Nanoscale Confinement. Faraday Discuss. 2009, 141, 359– 376. Barret, E. P.; Joyner, L. G.; Hallenda, P. P. The Determination of Pore Volume and Area Distribution in Porous Substances. I. Computations from Nitrogen Isotherms. J. Am. Chem. Soc. 1951, 73, 373–380. Mancinelli, R.; Imberti, S.; Soper, A. K.; Liu, K. H.; Mou, C.-Y.; Bruni, F.; Ricci, M. A. Multiscale Approach to the Structural Study of Water Confined in MCM-41. J. Phys. Chem. B 2009, 113, 16169–16177. Soper, A. K. In Proceedings of the Conference on Advanced Neutron Sources 1988; Hyer, D. K., Ed.; IOP Conference Proceedings No. 97; Institute of Physics and Physical Society: London, 1989; pp 353-366. www.isis.rl.ac.uk (accessed February 19, 2010). Soper, A. K.; Howells, W. S.; Hannon, A. C. ATLAS, Analysis of Time of Flight Diffraction from Liquid and Amorphous Samples. RAL Report No. RAL-89-046, 1989. Bowron, D. An Experimentally Consistent Atomistic Structural Model of Silica Glass. Material Science and Engineering 2008, 149, 166–170. Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J. Phys. Chem. 1987, 91, 6269–6271.


Controversial Evidence on the Point of Minimum Density in Deeply

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