Heat capacity of water in nanoporesE. Tombari, G. Salvetti, C. Ferrari, and G. P. Johari Citation: The Journal of Chemical Physics 123, 214706 (2005); doi: 10.1063/1.2131063 View online: http://dx.doi.org/10.1063/1.2131063 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/123/21?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Experimental nanocalorimetry of protonated and deprotonated water clusters J. Chem. Phys. 140, 164305 (2014); 10.1063/1.4871882 Heat capacities of freely evaporating charged water clusters J. Chem. Phys. 130, 224308 (2009); 10.1063/1.3149784 Configurational specific heat of molecular liquids by modulated calorimetry J. Chem. Phys. 129, 054501 (2008); 10.1063/1.2961024 Calculation of heat capacities of light and heavy water by path-integral molecular dynamics J. Chem. Phys. 123, 134502 (2005); 10.1063/1.2035078 Equilibrium structural model of liquid water: Evidence from heat capacity, spectra, density, and other properties J. Chem. Phys. 109, 7379 (1998); 10.1063/1.477344

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Heat capacity of water in nanoporesE. Tombari, G. Salvetti, and C. FerrariIstituto per i Processi Chimico-Fisici del Consiglio Nazionale delle Ricerche (CNR), via G. Moruzzi 1,56124 Pisa, Italy

G. P. Joharia�

Department of Materials Science and Engineering, McMaster University, Hamilton,Ontario L8S 4L7, Canada

�Received 22 July 2005; accepted 3 October 2005; published online 6 December 2005�

Heat capacity of controlled amounts of water in Vycor’s 2 nm radius pores has been determined inreal time during the course of water’s isothermal nanoconfinement from bulk state at 358 K, byusing temperature-modulated calorimetry. As water transfers from bulk to nanopores via the vaporphase, its heat capacity per molecule increases asymptotically toward a limiting value of 1.4 timesthe heat capacity of bulk water for 1.8 wt % water in Vycor and 1.04 times for 10.0 wt %. Theobservations indicate that vibrational and configurational contributions to the heat capacity arehighest when the amount of water is insufficient to completely cover the pore wall, and theydecrease as more water is present in the nanopores and water clusters form. The heat capacity ofwater in completely filled nanopores approaches the value for bulk water, thus indicating that theheat capacity varies with the water molecules’ position in the nanopores. © 2005 American Instituteof Physics. �DOI: 10.1063/1.2131063�

I. INTRODUCTION

Heat capacity of a liquid is the sum of two contributions:vibrational and configurational. Both vary with the liquid’svolume, temperature, and structure. When a liquid is con-fined to pores in a solid, the structure of the liquid differsfrom the bulk. The maximum difference is near the pore wallbecause interaction between the confined molecules and thepore-wall molecules dominates. Further from the pore wall,this interaction would become weaker and hence the liquid’sstructure in a pore would tend toward that of the bulk. If theliquid’s thermodynamics and kinetics are determined by hy-drogen bonds, the effect becomes more significant becauseany configurational change requires breaking and reformingof the hydrogen bonds. As part of our study of thermody-namics of water in nanopores,1 we have measured its heatcapacity during the course of controlled amounts of water’sexothermic transfer from bulk liquid to 2 nm radius nano-pores of Vycor glass via the vapor phase. These studies arereported here.

The significance of the knowledge of water in nanoporesand a brief review of the literature studies on thermodynam-ics, structure and dynamics by diffraction methods, and com-puter simulation have been provided in an earlier paper.1

II. EXPERIMENTAL METHODS

Cylindrical rods of Vycor 7930, 6 mm in length, 2 mmin diameter, and 29 mg nominal weight, were purchasedfrom Corning, USA. The specified properties of dry Vycor7930 are: Composition, 96% SiO2, 3% B2O3, 0.04% Na2O,and �1% �Al2O3+ZrO2�; average pore radius=2 nm;

density=1.5 g/cm3; void space=28% by volume; and inter-nal surface area=250 m2/g. The rods were cleaned with dis-tilled water and heated to 413 K for 12 h, further dehydratedby keeping on silica gel for 24 h, and kept stored in a des-iccator prior to use. Thermogravimetric analysis performedon heating to 453 K showed no residual water in the Vycorsamples treated in this manner. In an earlier paper1 we havediscussed the effect of silica on water.2

To control the amount of water available for confinementin the 2 nm radius pores of the Vycor rods, we first estimatedthe mass of water required to completely fill all its pores, asfollows: The specified void space in the Vycor is �28% byvolume, the approximate density in the dry state is 1.5 g/cm3

�or specific volume of 0.67 cm3/g�, and the maximum porevolume is �0.19 cm3/g of Vycor. For density of water takenas 1 g/cm3, this corresponds to a maximum amount of�19 wt % of water required to fill all its nanopores. Sincethe surface area of the pores is 250 m2/g, and the diameterof a water molecule is 0.386 nm, a dense-packed,1-molecule-thick layer of water on the pore wall would con-sist of 16.8�1020 H2O molecules, 50.4 mg �2.79 mM� ofwater per gram of Vycor, or �5 wt % of water. Experimentswere designed such that the mass of water available for en-tering the nanopores in one extreme was less than the massneeded to cover the entire pore wall, and in the other extremewas enough to cover the pore wall and also form more layersand/or water clusters, but not enough to completely fill thenanopores.

It has been found that there is a distribution of pore sizein porous glass with nominally 7.5 and 15 nm radius pores.3

There may also be a distribution of pore size in the 2 nmradius pores of Vycor used here. If so, our calculations of themass of water needed to completely cover the pore wall anda�Electronic mail: joharig@mcmaster.ca

THE JOURNAL OF CHEMICAL PHYSICS 123, 214706 �2005�

0021-9606/2005/123�21�/214706/5/$22.50 © 2005 American Institute of Physics123, 214706-1

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the mass needed to completely fill the channels would beapproximate. But as discussed earlier,1 this would have alittle effect on our conclusions.

In a typical experiment, a thoroughly cleaned and dried90-mm-long Pyrex tube with 2.2 mm internal diameter and0.3 mm wall thickness was sealed at one end. This served asthe sample holder for calorimetry. The required amount ofwater was syringed into its closed side and the tube wasvertically kept at 250 K. After the water froze, the sampleholder was kept in a horizontal position and eight precleanedand weighed Vycor rods �total nominal weight of 235 mg�were inserted into the sample holder and kept closest to theopen end of the tube, thus providing an air-space �separation�between frozen water �ice� and the Vycor rods. The end ofthe sample holder was then hermetically sealed by fusingwith a miniature flame. The sample holder was brought toambient temperature, the ice melted, and the water remainedconfined to the end of the tube by surface-tension forces,thus maintaining the air-space �separation� between the wa-ter’s surface and the Vycor rods. This arrangement is sche-matically shown in the upper insert of Fig. 1. The sampleholder with water and Vycor rods was inserted horizontallyin the calorimeter cell maintained at 358 K. The total timefor this operation was less than 5 min, during which absorp-tion of water by Vycor was regarded as negligible. In thehermetically sealed sample holder, water vapor inside the airspace was at a saturation pressure �0.58 bar� at 358 K.

The calorimeter used for the study has been describedelsewhere.4,5 Since the process of absorption of water in na-

nopores is exothermic and irreversible, the heat flow result-ing from the temperature change needed to measure the heatcapacity had to be separated from the heat flow caused bywater’s exothermic absorption in nanopores. For this reasonthe calorimeter was used in the �sinusoidally� temperature-modulated mode. The peak-to-peak temperature for themodulation was 1 K, and the frequency of modulation was3.3 mHz �modulation period of 300 s�. The details of theprocedure and formalism have been provided earlier.1,5–7

Calibration for the heat-capacity values was performed byusing n-heptane, ethylene glycol, and water. A base line forenthalpy release measurement was obtained before and afterthe water’s absorption in pores by using the same procedureas used for the measurement but with n-dodecane as thesample. Repeat measurements of heat capacity on calibrationliquids gave a reproducibility of the data to better than1.5 mJ/K.

In this study, the hermetically sealed sample holder con-tained an empty volume that varied with the mass of bulkwater used. This volume further increased as bulk watercompletely transferred to the nanopores. The vapor pressureof nanopore water is less than that of the bulk water, andnanoconfinement is spontaneous. Contribution to measuredheat capacity from a change in the vapor pressure in theempty volume of the sample holder has been estimated ear-lier at 270 and 360 K.1 For the temperature-modulated mea-surements here the characteristic time for attainment of thebulk liquid-vapor equilibrium is much less than the 300 smodulation period. Moreover, as estimated earlier,1 the ef-fects from �i� the change in the equilibrium vapor pressure ofthe nanopore water and bulk water during the temperaturemodulation and �ii� of empty volume in the sample holderare negligibly small in the initial stages of nanoconfinementat 358 K. The error due to their neglect is within the experi-mental errors of the heat capacity reported here. This will befurther shown here by using the measured data.

III. RESULTS AND DISCUSSION

The masses of bulk water used were 4.2, 6.8, 10.3, 13.9,18.0, and 23.4 mg, and the total mass of the eight Vycor rodswas nominally 235 mg. Thus, the wt % of water initiallyused �mass of water�100/mass of Vycor� were 1.8, 2.9, 4.4,5.9, 7.7, and 10.0, respectively. As water transferred from thebulk to nanopores in Vycor via the vapor phase, the vaporremained at saturation pressure as long as bulk water waspresent in the sample holder. After the bulk water was ex-hausted, the vapor pressure decreased and the water redis-tributed within the pores until the equilibrium vapor pressureof water inside the pore equalized with the vapor pressureoutside. After this equilibrium was established all the bulkwater became nanoconfined to Vycor, and the wt % of thebulk water became equal to the wt % of nanopore water. Theheat capacity of dry Vycor was measured prior to each ex-periment, as in the earlier studies,1 and this value and theheat capacity of the empty sample holder also measured foreach experiment were subtracted from the measured heat ca-pacity of the assembly. Thus a net heat-capacity value thatcorresponds to water, Cp,net, was obtained.

FIG. 1. Plots of the measured heat capacity of water against time during thecourse of nanoconfinement of bulk water via the vapor phase. The wt % ofwater in Vycor is written next to the curves. The upper insert is an illustra-tion of the arrangement of water and eight Vycor rods in the glass sampleholder. The lower insert is for the change in the heat flow, dH /dt, for6.8 wt % water at 358 K, in which the arrow shows the time at which thesaturation pressure was lost on exhaustion of bulk water. The transfer ofbulk water into nanopores of Vycor occurred via the vapor phase, initially atsaturation vapor pressure, and, after all the bulk water was exhausted, thetransfer occurred at a lower than saturation vapor pressure. The initial inter-faces are bulk water/glass and bulk water/air. As bulk water is transferred tothe nanopore, the volume it had occupied emptied and the air pressure in thesealed sample holder decreased. In the intermediate stages of the transfer,there are four interfaces: bulk water/glass, bulk water/air, nanopore water/Vycor wall, and nanopore water/air. In the partially filled and filled states ofa nanopore, there are again only two interfaces: nanopore water/Vycor walland nanopore water/air.

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The Cp,net is equal to the sum of �i� the heat capacity ofbulk water, Cp,bulk-w, and the �ii� the heat capacity of nano-pore water, Cp,nm-w. In the beginning of the experiment thereis no water in the pores, and Cp,net is equal to Cp,bulk-w. Dur-ing the exothermic transfer of bulk water to nanopores thefirst contribution decreased and the second increased. Whenall bulk water transferred to nanopores the first contributionbecame zero.

Plots of Cp,net in J/K for the amount of water used duringthe course of its transfer to nanopores are shown against timein Fig. 1, where the amount of water in wt % is indicated. Itshould be noted that in a study of the heat flow �rate of heatevolved�, �dH /dt�T, with time during the spontaneous trans-fer of bulk water to Vycor nanopores via the vapor phase, wehave found that �dH /dt�T decreases extremely rapidly at thebeginning and then abruptly when the amount of bulk wateris exhausted. After then, �dH /dt�T continues to decrease aswater in the nanopores redistributes and the equilibrium va-por pressure is slowly approached. A typical observation ofthe abrupt decrease in �dH /dt�T is shown in the lower insertin Fig. 1. In our experiment, the initially large decrease indH /dt prevented us from determining accurately the heatcapacity from the beginning of the nanoconfinement. There-fore for accuracy, the Cp,net data are shown from a periodimmediately before the exhaustion time of bulk water, whichis marked by an arrow. The plots still show an asymptoticincrease in Cp,net with time. Also, no effect due to the de-crease of vapor pressure from the saturation pressure value isdiscernible in the Cp,net plots against time in Fig. 1. Thisconfirms that the contribution to Cp,net from this effect isnegligible.

The asymptotically reached Cp,net value is the Cp,nm-w forthe wt % of nanopore water that corresponds to the mass ofbulk water used. A comparison of the asymptotically reachedvalue for different wt % of Cp,nm-w shows that this value doesnot increase in proportion to the mass of water in the nano-pores. To elaborate, an increase from 4.2 mg �1.8 wt % � to23.4 mg �10.0 wt % � nanopore water increases Cp,nm-w from0.0253 to 0.104 J /K, instead of the expected increase to0.141 J /K. This indicates that Cp,nm-w per molecule de-creases as the nanopore water is increased.

For a further analysis, Cp,nm-w in J/K for the mass of bulkwater used in the experiment was calculated by usingCp,bulk-w=4.25 J /g K at 358 K,8,9 and Cp,nm-w for the samemass taken from the plots in Fig. 1 was divided by theCp,bulk-w. The ratio obtained �Cp,nm-w /Cp,bulk-w� is plottedagainst the wt % of nanopore water in Fig. 2, where the ratio,1.04, obtained in an earlier study by using a different proce-dure, in which 9.6 wt % water was nanoconfined prior to theexperiment,1 is included and denoted as a circle. The plot inFig. 2 shows an asymptotic decrease in this ratio from 1.4 at1.8 wt % water to 1.04 at 10.0 wt % water in the nanoporesand that the value for 10 wt % obtained here is consistentwith the earlier value obtained for 9.6 wt % nanopore water.The plot also shows that Cp,nm-w decreases and approachesthe Cp,bulk-w value as the nanopore water is increased. Buteven for 10.0 wt % nanopore water, which is twice theamount �5 wt % � required to completely cover the pore wall,Cp,nm-w is 1.04 times the Cp,bulk-w at 358 K. In a study of

21.6 wt % water, not shown in Figs. 1 and 2 here, whichcompletely filled the nanopores, Cp,nm-w was found to beequal to Cp,bulk-w at 358 K. This agrees with our earlierconclusion1 that with 21.1 wt % water in nanopores, whichwere filled by a different procedure, Cp,nm-w was the same asCp,bulk-w at 345 K.

The heat capacity of a liquid is the sum of two contribu-tions: vibrational and configurational. The vibrational contri-bution arises from the excitation of mechanical degrees offreedom, and the configurational contribution arises from achange in the liquid’s structure. Both contributions vary withthe volume and the structure of the liquid. The two contribu-tions are interdependent because loosely packed structures oflower density have lower vibrational frequencies and ahigher configurational contribution. Eisenberg andKauzmann10 have concluded that large configurational con-tribution to Cp,bulk-w arises from the distortion of tetrahedralhydrogen bonds in bulk water and perhaps breaking of somehydrogen bonds in it. But this conclusion is not applicable tonanopore water because the �i� density of water in nanoporesis much less than that in the bulk, �ii� the interaction with thepore wall dominates the properties for low amounts ofnanopore water, and �iii� hydrogen bonds are apparentlyfewer and are more distorted in the nanopore water than inbulk water.11 The less-dense structure in nanopores wouldundoubtedly have lower vibrational frequencies and hence ahigher vibrational contribution to Cp,nm-w. This would meanthat the contributions to the heat capacity would vary accord-ing to the interlayer and intercluster structures within thenanopores. In this sense, nanopore water may not be seen asa homogeneous medium. Additionally, the overall structureof nanopore water and its contribution to the heat capacitydiffer from those of bulk water.

The manner of distribution of H2O molecules in nano-pores is not clearly understood. Measurements of the equi-librium heat capacity here show that vibrational contributionis highest when the amount of nanopore water is too small toform a dense-packed first layer covering the pore wall. Inthis case, the configurational contribution to the heat capacityper H2O molecule is large also because the molecules maybe able to diffuse from one site to the other site randomly on

FIG. 2. Ratio of the heat capacity per H2O molecule in the nanopores to theheat capacity per H2O molecule in bulk water is plotted against the wt % ofwater in the nanopores of Vycor, with an error bar shown. The ratio de-creases with the amount of water present, but does not reach unity upto10 wt %. The circle is the data taken from Ref. 1.

214706-3 Heat capacity of water in nanopores J. Chem. Phys. 123, 214706 �2005�

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the silica pore wall surface. As more water molecules enter apore, and a monolayer of H2O forms on the pore wall, pack-ing density increases, which would raise the vibrational fre-quencies and decrease the number of possible arrangement ofmolecules on the pore wall. Thus both the vibrational andconfigurational contributions are expected to decrease. Asthe pores begin to fill with water, H2O molecules that enterthe nanopores would form new hydrogen bonds, albeit dis-torted, with the existing H2O molecules, thus formingclusters,11 and the interaction with the pore wall becomesprogressively weaker. Thus the Cp,nm-w per H2O moleculewould decrease. The process would continue until thenanopores are filled in an unspecified manner and the aver-age Cp,nm-w per H2O molecule, which is the weighted aver-age of the Cp,nm-w of all the molecules �at the pore wall, inthe subsequent layers, in the clusters, and in the middle ofthe pore�, approaches the Cp,bulk-w value. Only for confine-ment in larger, micron-radius pores may Cp of the com-pletely filled pore water become equal to Cp,bulk-w. In conclu-sion, both the vibrational and configurational heat capacitiesof water vary with the position of the H2O molecules in thepores.

The process of absorption of water in nanopores is exo-thermic, which means that the enthalpy of the water innanopores is less than that of bulk water. This may appear toconflict with the observations here that Cp,nm-w is higher thanCp,bulk-w, particularly since the enthalpy is equal to the CpdTintegral. A higher heat capacity of a material only indicatesthat the temperature sensitivity of the enthalpy is high, andnot that the absolute magnitude of the enthalpy is high.Therefore, the finding here would not conflict with the exo-thermic process of nanoconfinement. Nevertheless, we sug-gest that the state of nanopore water be considered like thestate of a product formed by exothermic reaction, whose heatcapacity bears little relation with the heat capacity of thereactant, i.e., the effect of filling of the nanopores by H2O onthe heat capacity is not equivalent to the lowering of thetemperature of the bulk water. Alternatively, the effect ofremoval of H2O molecules from nanopores is not equivalentto the effect of raising the temperature of bulk water. Waterdoes interact with the chemical constituents of the pore wall,and the observed filling-dependent Cp,nm-w indicates that herethe initial water strongly bound to the pore wall has thehighest Cp,nm-w. This may be regarded as a result of an exo-thermic chemical reaction between water and the pore wall,or as a weak physical interaction with pore wall via hydro-gen bonds.

Several other aspects of the study, although approximate,are noteworthy. After the bulk water in the sample holder isexhausted at the time noted by the arrow in the insert of Fig.1, the measured Cp,nm-w continues to increase as water redis-tributes within the interconnected nanopore channels that arefarther from the Vycor surface. The process of redistributionappears to have nonexponential kinetics with a characteristictime in the 10–40 ks range. In an earlier paper we havereported the heat release on the nanoconfinement of water inVycor.12 Those studies had shown that the energy of watermolecules depends upon the position of the water moleculein the pore.

Molecules next to the pore wall have the highest energyand those away from the pore wall lower energy. In thoseexperiments, the total heat released measured as a function ofthe total nanoconfined water had shown that the exothermic�heat-released� effect decreases when the nanoconfined wateris more. We will discuss this aspect in detail in the future,specifically after considering in detail the fact that the Vycorpores are not monodisperse. Moreover, the pores are inter-connected in complex ways via channels of irregular diam-eter and length, and there are also three-channel and four-channel junctions, which are more voluminous than thechannels that form them. It is obvious that the topology ofthe nanoporous material would determine the net heat-capacity change. An interconnected network of small-diameter pore channels than in the Vycor used here wouldlead to even higher values of Cp, but would not alter ourconclusion. Also the rate of redistribution of water within thepores measured in terms of the time constant and nonexpo-nentiality would vary with the topology of the pore network.It may be interesting to perform similar experiments usingnanoconfining templated silica structures, e.g., MCM-41 inwhich cylindrical nanopores arranged in a hexagonal arrayare not interconnected.

It may also be noted that the distribution of water ininterconnected nanopores in Vycor is analogous to the distri-bution of liquid phase in polycrystalline solid,13,14 particu-larly ice, in which the subnanodiameter grain boundariescontaining the liquid phase are analogous to the channels inVycor forming such junctions. In those studies,13,14 theamount of water present in the subnanometer grain-boundarychannels and junctions of polycrystalline ice could only beapproximately calculated. Therefore, Cp of water confined tochannels and junctions could not be determined.

IV. CONCLUSION

The heat capacity of nanoconfined water in 2 nm radiuspores in Vycor at low concentrations is about 40% higherthan the heat capacity of bulk water. This is due to an in-crease in both the vibrational and configurational contribu-tions to the heat capacity. These contributions vary with theposition of a water molecule in a nanopore, its interactionwith the pore wall, and the extent of hydrogen bonding withother water molecules. The difference lessens as the amountof pore water is increased.

A vast amount of water exists in nanopores and mi-cropores of geological formations, in soils, clays, and in bio-logical materials. One expects that the heat capacity of thiswater would be higher than that of bulk water, and if theconfined water contained impurities, its heat capacity woulddiffer from the bulk solution. Although the heat capacity ofwater in completely filled micropores would be approxi-mately the same as that of bulk water, the heat capacity ofwater absorbed on its pore wall will still be higher than thatof bulk water. This has consequences for both the tempera-ture rise on heat absorption by geological formations and forabsorption of water by plant’s root hairs that reach the mi-croporous or nonoporous channels during their growth.

214706-4 Tombari et al. J. Chem. Phys. 123, 214706 �2005�

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1 E. Tombari, G. Salvetti, C. Ferrari, and G. P. Johari, J. Chem. Phys. 122,104712 �2005�; Units of H and G in Figs. 3�b� and 4�b� should readkJ/mol.

2 At elevated temperatures, a minute amount of silica dissolves in water.But earlier studies of water and aqueous solutions in Vycor glass and onsilica substrates did not mention this possibility. We refer the reader to adiscussion of dissolution of silica at elevated temperatures in the sectionentitled “Dissolution of silica in water,” on page 4 of Ref. 1, where it hasbeen concluded that the maximum solubility of silica in water is�52 ppm over a period of 8 h at 403 K. This dissolved amount corre-sponds to 1 molecule of silica in 63 850 molecules of water. It was alsoestimated that a volume of 2 nm radius sphere would contain �1117water molecules, and therefore a significant amount of silica would nothave dissolved in the nanoconfined water.

3 D. H. Smith, K. Seshadri, T. Uchida, and J. W. Wilder, AIChE J. 50,1589 �2004�, and references therein.

4 G. Salvetti, C. Cardelli, C. Ferrari, and E. Tombari, Thermochim. Acta364, 11 �2001�.

5 G. Salvetti, E. Tombari, L. Mikheeva, and G. P. Johari, J. Phys. Chem. B106, 6081 �2002�.

6 E. Tombari, S. Presto, G. Salvetti, and G. P. Johari, J. Chem. Phys. 117,8436 �2002�.

7 G. P. Johari, E. Tombari, S. Presto, and G. Salvetti, J. Chem. Phys. 117,5086 �2002�.

8 N. E. Dorsey, Properties of Ordinary Water Substances, facsimile of the1940 ed. ACS Monograph Series �Hafner, New York, 1968�.

9 NIST-JANAF Thermochemical Tables, 4th ed., edited by M. W.Chase, Jr., J. Phys. Chem. Ref. Data Monogr. 9 �1998�.

10 D. Eisenberg and W. Kauzmann, The Structure and Properties of Water�Oxford University Press, Oxford, 1969�, pp. 174–176.

11 I. Brovchenko, A. Geiger, A. Oleinikova, and D. Paschek, Eur. Phys. J. E12, 69 �2003�, and other citations in Ref. 1 above.

12 E. Tombari, G. Salvetti, C. Ferrari, and G. P. Johari, Phys. Chem. Chem.Phys. 7, 3407 �2005�.

13 G. P. Johari, W. Pascheto, and S. J. Jones, J. Chem. Phys. 100, 4548�1994�.

14 G. Salvetti, E. Tombari, and G. P. Johari, J. Chem. Phys. 102, 4987�1995�.

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