Effect of Pore Shape on Freezing and Melting ... - ACS Publications

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Effect of Pore Shape on Freezing and Melting Temperatures of Water Kunimitsu Morishige,* Hiroaki Yasunaga, and Yuki Matsutani Department of Chemistry, Okayama UniVersity of Science, 1-1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan ReceiVed: NoVember 12, 2009; ReVised Manuscript ReceiVed: January 04, 2010

To examine the effect of pore shape on freezing and melting temperatures of water, we measured X-ray diffraction patterns from water confined in four kinds of ordered mesoporous silicas with thin carbon films on the pore wall and three kinds of the inverse carbon replicas during freezing and melting processes. The melting temperature of the pore ice revealed a good correlation with the capillary condensation pressure of nitrogen at 77 K, whereas the freezing temperature of the pore water did not. This indicates that the experimental melting point represents an equilibrium solid-liquid phase transition temperature, whereas the experimental freezing point is controlled by a kinetic factor. The curvature effect of the solid-liquid interface adjacent to the pore wall did not appreciably affect the melting behavior of the pore ice. The melting point depression of the pore ice revealed an almost linear relationship with ln(p0/p) of the capillary condensation pressure of nitrogen at 77 K for various pores of different sizes and shapes. This strongly suggests that the reciprocal of ln(p0/p) for capillary condensation of nitrogen at 77 K gives a good measure of pore size, irrespective of the pore shapes, and the melting-point depression of the pore ice is almost proportional to the surface-to-volume ratio (S/V) of the pores confining it. I. Introduction There is considerable current interest in the freezing and melting behavior of materials confined in porous solids because of its fundamental and technological importance.1,2 One of the most interesting, well-known phenomena is the depression in freezing and melting temperatures of the confined materials. There appears to be no clear exception to this behavior among the vast range of materials confined in mesopores investigated so far. The experimental melting point depression is usually explained by the Gibbs-Thomson relation3 that expresses the effective change in equilibrium melting point at a curved solid-liquid interface. According to this relation, the equilibrium melting point depression ∆Tm due to curvature is

VmγslT0 ∆Tm ) T° - Tm ) κ ∆Hf

(1)

where κ is the curvature of the interface, Vm is the molar volume of the material, ∆Hf is the latent heat of melting, γsl is the surface energy of the solid-liquid interface, and Tm and T0 are the melting point and the normal equilibrium temperature of the solid-liquid interface, respectively. The curvature is defined as positive when the center of curvature lies within the body, as it does in a spherical crystal; for a concave crystal, the center of curvature is outside the body, and the curvature is negative. The equilibrium melting temperature of a crystal with positive curvature is lower than that of a large flat crystal. For a spherical or hemispherical interface with the principal radius of curvature r of a solid in contact with a liquid, eq 1 reduces to

∆Tm )

2VmγslT° ∆Hfr

(2)

This relationship is most often used in analysis of the experimental melting-point depressions of the materials confined in * To whom correspondence should be addressed.

cylindrical or nearly cylindrical pores,1,2 although the confined material will show a cylindrical solid-liquid interface adjacent to the pore wall because of the occurrence of surface melting.4 Recently, based on the free energy of a system with surface melting, it has been suggested that metastable melting and equilibrium freezing transitions can be defined for a confined phase.5,6 The metastable melting transition corresponds to that of a metastable surface melted state to a stable fully melted state, while the equilibrium freezing transition originates from the equality in the free energy of the surface melted state and the fully liquid state. In this model, the melting-point depression is controlled by the mean curvature of the pore surface, whereas the equilibrium freezing-point depression is controlled by the surface-to-volume ratio (S/V) of the pore. For a cylindrical pore, the metastable melting and equilibrium freezing transitions are defined as the equilibrium between a liquid and a solid separated by cylindrical and hemispherical interfaces, respectively.5 The hysteresis width between freezing and melting can be related to the pore geometry. However, these definitions are apparently incompatible with the experimental freezing temperatures of water in the spherical pores of ordered mesoporous silicas that were very recently reported by us.7 In these pores, freezing takes place via homogeneous nucleation and thus exhibits a large kinetic supercooling, independent of the pore size. In addition, this definition of the melting point is unable to account for the many experimental results showing that the melting point depressions of the materials confined in the cylindrical or nearly cylindrical pores can be well described by eq 2.8-14 Alternatively, the melting-point depression may be viewed as an effect of confinement on the solid-liquid transition, whereby the intrusion of a liquid layer at the boundary of the solid and the pore wall causes the depression in the equilibrium melting point.1,15 In this approach, the curvature of the solid-liquid interface is not directly treated. On the basis of a balance of bulk and surface free energy terms between solid and liquid, it has been suggested that the depression in the equilibrium melting point of the confined phase is proportional

10.1021/jp910759n  2010 American Chemical Society Published on Web 02/17/2010

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to the S/V of the pore with volume V and surface area S, irrespective of pore geometries.1

∆Tm )

VmγslT0 S ∆Hf V

(3)

The shape of the pores influences the melting point since the ratio of the number of molecules at the surface relative to that in the volume of the confined materials varies with the shape. A similar relationship of the melting-point depression is obtained for different shapes of free-standing nanostructures with volume V and surface area S.16 As far as we know, however, there are no studies that experimentally examined this relationship for several different geometries of the pores. In general, conventional porous solids may have extremely complex pore structures, which are difficult to represent by simple geometrical models. Therefore, it would be more desirable to know the pore size dependencies of the freezing and melting temperatures for the pores with several different geometries in a unified manner. Ordered mesoporous carbons can be prepared using the ordered mesoporous silicas with well-defined pore structures as the templates.17-19 The structures of these carbons are exactly inverse replicas of the ordered mesoporous silicas and consist of two-dimensional (2D) or three-dimensional (3D) arrays of carbon nanoparticles. The pores of these carbons are not voids that were created inside a solid, as is the case for ordinary mesoporous materials. In the ordered mesoporous carbons, the pores represent void space between regularly spaced particles of various shapes. When a liquid condensed in the void space of the carbons is frozen by cooling, a solid-pore wall interface with negative curvature will be formed. A liquid prefers to nucleate on the interface in order to lower the total free energy of the system. As a result, a liquid layer would occur readily at the boundary of the solid and the pore wall despite the negative curvature, as the melting point of the solid is approached. When a liquid layer forms at the boundary of the solid and the pore wall, the free energy of the solid decreases because of the presence of the negative curvature of the solid-liquid interface.20 This is expected to lead to the elevation in the melting point of the solid, if the curvature effect of the solid-liquid interface is actually important for the solid-liquid phase transitions of the confined material. In other words, the Gibbs-Thomson relation that expresses the effective change in equilibrium melting point at a curved solid-liquid interface predicts the melting-point elevation for a solid with negative curvature. The actual pore structures of porous solids belong to either corpuscular or spongy classes.21 Corpuscular systems are formed by particles of various shapes connected to one another, and thus the pores represent interstices between particles. In spongy structures, the pore space can be treated as a lattice of voids interconnected by necks in a three-dimensional network. There exist sometimes mixed structures, and the pore size often distributes to a considerable extent, leading to indefinite determination of the capillary condensation pressure of nitrogen as well as the freezing and melting temperatures of the confined material. In this respect, ordered mesoporous materials such as the ordered mesoporous silicas and their carbon replicas are regarded as the most suitable model adsorbents currently available for verification of the theoretical predictions for various idealized pores. The ordered mesoporous silicas,22,23 that are prepared using surfactants as structure-directing agents, correspond to spongy systems, while the ordered mesoporous carbons, that are prepared using these ordered silicas as hard templates, represent corpuscular systems.

The present study aims to establish the pore-size dependencies of the freezing and melting temperatures of the confined phase for the pores with several different geometries in a unified manner by measuring the freezing and melting behavior of pore water in the cylindrical, interconnected cylindrical, and interconnected spherical pores of the ordered silicas with thin carbon films on the pore walls, as well as the open pores of the corresponding carbon replicas, by means of X-ray diffraction (XRD). Water is one of the most common materials in nature, and improved understanding of confinement effects on its phase transitions is of practical importance. II. Experimental Section II.1. Materials. MCM-41 with cylindrical pores was prepared using n-tetradecyltrimethylammonium bromide as a structure-directing agent at an aging temperature of 373 K according to the pH adjustment method of Ryoo and Kim.24 SBA-15 with larger cylindrical pores was also prepared using Pluronic P123 triblock copolymer at an aging temperature of 373 K according to the procedure of Kruk et al.25 KIT-6 with interconnected cylindrical pores was prepared using P123 triblock copolymer at an aging temperature of 373 K according to the procedure of Kleitz et al.26 SBA-16 with interconnected spherical cavities was prepared using Pluronic F127 triblock copolymer as a structure-directing agent at an aging temperature of 373 K.27 The calcined silica samples were impregnated with an ethanol solution of AlCl3. After the solvent was completely evaporated at 373 K, the samples were calcined in air at 823 K. One gram of the silica was uniformly infiltrated with a small amount of furfuryl alcohol at room temperature. The sample containing furfuryl alcohol was placed in an oven at 368 K for 24 h for polymerization.19 The resultant silica with a thin polymer film on the pore walls was heated at 353 K for 2 h in vacuo and then at 1173 K for 6 h for carbonization of the polymer. These ordered mesoporous silicas with thin carbon films on the pore walls were designated as C/MCM-41, C/SBA15, C/KIT-6, and C/SBA-16, respectively. For the preparation of the carbon replicas, the ordered silicas treated with a AlCl3 solution were infiltrated with a slightly excess amount of furfuryl alcohol to fill the pores.28 The sample containing furfuryl alcohol was placed in an oven at 308 K for 1 h and then at 368 K for 1 h. The resultant polymer/silica composite sample was further heated at 623 K for 2 h and then at 1173 K for 4 h. All heating treatments were performed under self-generated gas atmosphere using a quartz reactor closed with a ceramics wool plug. The silica templates were removed with HF solution. The ordered mesoporous carbons CMK-3,17,28 CMK-8,18 and CFA219 were prepared using SBA-15, KIT-6, and SBA-16 silicas, respectively, as the templates. II.2. Measurements. Adsorption isotherms of nitrogen at 77 K were measured volumetrically on a BELSORP-mini II (Bell Japan, Inc.) An experimental apparatus of XRD for freezing/ melting measurements has been described elsewhere.29 The measurements were carried out with CuKR radiation in a Bragg-Brentano geometry. Sample powder (∼0.1 g) was packed in a shallow pit of a sample holder of Cu and covered with a 7.5-µm-thick film of Kapton and then a 0.1-mm-thick sheet of Be. The sample holder was then attached to a cold head of a He-closed cycle refrigerator and sealed in a sample cell constructed of a cylindrical Be window and a Cu flange, with an In O-ring. After prolonged evacuation at room temperature, the sample was cooled and then the background spectrum was measured. The adsorption isotherm of water on the sample inside the X-ray cryostat was measured at 275 K.

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Figure 1. Adsorption-desorption isotherms of nitrogen at 77 K on the ordered mesoporous silicas with thin carbon coatings and the ordered mesoporous carbons. Volumes adsorbed for C/SBA-15, C/KIT-6, C/SBA-16, CMK-8, and CFA2 were incremented by 200, 300, 600, 200, and 400 cm3(STP)/g, respectively. Open and closed symbols denote adsorption and desorption points, respectively.

TABLE 1: Specific Surface Areas of Mesopores, Mesopore Volumes, S/V, and Capillary Condensation Pressure (p/p0) of Nitrogen at 77 K, As Well As Freezing and Melting Temperatures of Pore Water sample

surface area S (m2/g)

mesopore vol V (cm3/g)

S/V (nm-1)

p/p0

freezing temp Tf (K)

melting temp Tm (K)

C/MCM-41 C/SBA-15 C/KIT-6 C/SBA-16 CMK-3 CMK-8 CFA2

518 360 437 407 579 776 799

0.367 0.500 0.699 0.428 0.577 0.773 0.803

1.41 0.720 0.625 0.951 1.00 1.00 0.995

0.24 0.68 0.72 0.68 0.48 0.47 0.53

214 245 252 232 236 238 234

214 251 254 252 240 240 242

Prior to XRD measurements, the adsorbed amount was reduced slightly below the saturation, in order to avoid contamination in diffraction pattern from the bulk ice formed outside the pores. The substrate was then cooled to a desired temperature between 200 and 275 K, and the spectrum was measured. The diffraction pattern of the confined phase was obtained by subtraction of data for charged and empty substrate. III. Results III.1. Nitrogen Adsorption Isotherm. C/MCM-41 and C/SBA-15 possess nonconnected cylindrical pores,23,25 while the nearly cylindrical pores of C/KIT-6 are three-dimensionally interconnected with each other.26 In C/SBA-16, almost spherical cavities are interconnected through narrow necks in a bodycentered cubic array.30 These materials are spongy solids. The structures of the CMK-3, CMK-8, and CFA2 carbons are exactly inverse replicas of the corresponding silica templates, namely SBA-15, KIT-6, and SBA-16, respectively. The pores of these materials represent void space between regularly spaced particles. These materials belong to the systems of corpuscular porous structures. The pores are accessible in any direction and constitute a more open system compared to the cylindrical, interconnected cylindrical, or interconnected spherical pores of the ordered mesoporous silicas. Figure 1 shows the adsorption-desorption isotherms of nitrogen at 77 K on four kinds of the ordered mesoporous silicas with thin carbon films on the pore walls and three kinds of the ordered mesoporous carbons. All the isotherms exhibited distinct steps due to capillary condensation. Capillary condensation takes

place quite independently in different parts of the pore system according to the strength of confinement, whereas capillary evaporation is significantly influenced by constrictions. Therefore, we use the pressure of capillary condensation of nitrogen at 77 K as a measure of pore size. In principle, the pore sizes inherent to their pore geometries can be estimated using the individual relationships between pore size and the pressure of capillary condensation of nitrogen at 77 K.28,31,32 The surface area of mesopores, outer surface area, micropore volume, and total pore volume were estimated using the t-plot method.33 Table 1 summarizes the specific surface areas of mesopores, mesopores volumes, S/V of mesopores, and capillary condensation pressure (p/p0) of nitrogen at 77 K, as well as the freezing and melting temperatures of pore water as described in the next section. III.2. X-ray Diffraction. Figures 2-4 show some of the powder XRD patterns from the water confined in the CMK-3, CMK-8, and CFA2, respectively, when the temperature was successively lowered and then when the temperature was successively increased. When the substrates were cooled, there was a change in the diffraction pattern of the pore water from a liquid to a solid form. The diffraction patterns of the resulting solids resemble that of cubic ice (Ic) instead of ordinary hexagonal ice (Ih). The three peaks can be indexed to the (111), (220), and (311) reflections of Ic, respectively. Very recently,34,35 however, we showed that cubic ice formed in the mesopores of silica did not take a cubic structure as envisaged by Ko¨nig.36 It may be actually composed of very small crystallites of ordinary hexagonal ice that contains a large amount of growth faults

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Figure 2. Change of the X-ray diffraction pattern of water confined in CMK-3 slightly below complete filling upon cooling and subsequent heating.

Figure 3. Change of the X-ray diffraction pattern of water confined in CMK-8 slightly below complete filling upon cooling and subsequent heating.

depending on the crystallite size, that is, ice with a disordered stacking sequence. In fact, the stability of cubic ice in the mesopores depends on the pore geometry.35 Freezing of the pore water confined in the ordered mesoporous silicas with thin carbon films on the pore walls also resulted in formation of ice Ic, being consistent with the results in the ordered mesoporous silicas previously reported34,35 (see the diffraction patterns from the water confined in the C/MCM-14, the C/SBA-15, the C/KIT6, and the C/SBA-16 shown in Supporting Information Figures 1S, 2S, 3S, and 4S, respectively). This clearly indicates that neither change of the porous structure from a spongy to a corpuscular system nor modification of the pore walls from silica to carbon affects appreciably the structure of the frozen water confined in the pores. When the resulting ices were heated, the melting took place at temperatures equal to or higher than the freezing temperatures depending on the size and shape of the pores. The diffraction patterns during the freezing and melting processes of the pore water showed the coexistence of a solid and a liquid, indicating that the solid-liquid phase transitions in these pores is first order, as is the case for bulk water.

Figure 5 shows the integrated intensity of the Ic (220) reflection as a function of temperature for the pore ice formed in these samples, except for the C/MCM-41. The diffraction pattern from the pore ice in the C/MCM-41 was very broad because of its small pore size. Therefore, the freezing/melting behavior was examined by plotting the position and width of the main peak against temperature (see the position and width of the main diffraction peak from the water confined in the C/MCM-41 as a function of temperature shown in Supporting InformationFigure 5S). Large thermal hysteresis between freezing and melting was observed for the pore water in the C/SBA16. In this cagelike pores, the pore water freezes via homogeneous nucleation at 232 K on cooling, while the melting of the pore ice takes place at a significantly higher temperature depending on the cavity size.7 The thermal hysteresis for the C/SBA-15 is wider than that for the C/KIT-6, although the melting temperatures of the pore ice confined in both materials are nearly identical. The melting temperatures of the pore ice confined in the CMK-3, CMK-8, and CFA2 are slightly higher

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Figure 4. Change of the X-ray diffraction pattern of water confined in CFA2 slightly below complete filling upon cooling and subsequent heating.

Figure 5. Integrated intensity of the Ic(220) reflection as a function of temperature for water confined slightly below complete filling in the ordered mesoporous silicas and the ordered mesoporous carbons. Open and closed symbols denote cooling and heating processes, respectively. Intensities for C/KIT-6, C/SBA-16, CMK-8, and CFA2 were shifted vertically for clarity.

than their freezing temperatures of the pore water. The freezing/ melting for the C/MCM-41 was almost reversible. IV. Discussion IV.1. Curvature Effect of Pore Wall. Figure 6 shows the freezing and melting temperatures of water confined in the pores as a function of the pressure of capillary condensation of nitrogen at 77 K, for the ordered mesoporous materials with several different pore geometries. The figure also includes the data points for water confined in the cylindrical,12,35 interconnected cylindrical,35 or interconnected spherical pores7 of the ordered mesoporous silicas without thin carbon coatings previously reported by us. It is evident that thin carbon coatings did not appreciably affect the freezing and melting temperatures of water confined in the mesopores. The melting point of the pore ice revealed a good correlation with the capillary condensation pressure of nitrogen at 77 K, whereas the freezing temperatures of the pore water did not. This indicates that the experimental

melting point rather than the freezing point represents an equilibrium solid-liquid phase transition temperature that was controlled by pore size. On the other hand, the experimental freezing temperature would be controlled by a kinetic factor. In fact, in the interconnected spherical pores, freezing takes place via homogeneous nucleation and thus shows a large kinetic supercooling, independent of the pore size.7 Therefore, a large thermal hysteresis between freezing and melting was observed for the spherical pores. It is evident that the definition of the equilibrium freezing transition does not hold for the spherical pores. The pore wall of KIT-6 with bicontinuous gyroid structure consists of the so-called equidistant surfaces located at equal distance from the central triply periodic minimal surface.37,38 By definition, a minimal surface has a zero mean curvature. Thus, the mean curvature of the pore wall of KIT-6 and C/KIT-6 is negligibly small. The definition of the metastable melting transition leads to an expectation that the pore ice confined in

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Figure 7. Melting point depression of ice confined in the mesopores against ln(p0/p) of capillary condensation pressure of nitrogen at 77 K for the ordered mesoporous materials with several different pore geometries. Open circles, triangles, and squares denote the melting point depression of ice confined in the cylindrical, interconnected cylindrical, and interconnected spherical pores, respectively. Closed symbols denote the melting point depression of ice confined in the open pores of the ordered mesoporous carbons with their inverse replica structures. A solid line is a guide for the eye.

Figure 6. Freezing and melting temperatures of pore water confined in the mesopores against the relative pressure of capillary condensation of nitrogen at 77 K for the ordered mesoporous materials with several different pore geometries. Open circles, triangles, and squares denote the freezing and melting temperatures of water confined in the cylindrical, interconnected cylindrical, and interconnected spherical pores, respectively. Closed symbols denote the freezing and melting temperatures of water confined in the open pores of the ordered mesoporous carbons with their inverse replica structures.

the interconnected cylindrical pores of KIT-6 and C/KIT-6 will show no significant melting-point depression, whereas the definition of the equilibrium freezing transition suggests that the pore water in the interconnected cylindrical pores may show significant freezing-point depression. Therefore, a large thermal hysteresis between freezing and melting is expected. In practice, however, the thermal hysteresis for the interconnected cylindrical pores was very narrow compared to that for the cylindrical pores. Thus, the concept of the metastable melting and equilibrium freezing transitions cannot be applied to the confined phase in the interconnected cylindrical pores either. Furthermore, the melting temperatures of pore ice confined in the carbon replica with pore wall of negative curvature also fell on a common line that is formed by the melting points of the pore ice confined in the ordered mesoporous silicas with a pore wall of positive or nearly zero curvature. All these results clearly indicate that the curvature effect of the solid-liquid interface adjacent to the pore wall does not appreciably affect the melting behavior of the confined phase. IV.2. Confinement Effect. In this model, the equilibrium melting-point depression of the confined solid is related to the S/V ratio of the pores. Although the ordered mesoporous materials are regarded as the most suitable model adsorbents, the accurate determination of S/V from the nitrogen adsorption isotherm at 77 K is very difficult because of complementary pores inherent to the ordered mesoporous solids with welldefined porous structures.39-41 Indeed, a plot of the meltingpoint depression of the pore ice against the S/V ratio of the

mesopores showed severe scatter (see the melting-point depression of the pore ice as a function of the S/V ratio of the mesopores shown in Supporting Information Figure 6S). When the influence of the pore wall curvature on the adsorption equilibrium may be neglected, based on macroscopic thermodynamics, Derjaguin obtained a general relation between a measure of “pore size”, H, and the pressure of capillary condensation, p, that does not depend on any special pore shape: 42

H)

Vc [γ cos θ + RT RT ln(p0 /p) lg

∫ (Γ/p)dp]

(4)

Where Vc is the molar volume of the capillary condensed phase, γlg is the surface tension of the liquid-vapor interface, θ is the contact angle, p0 is the saturated vapor pressure of the liquid, and Γ is the adsorbed amount per unit area of the pore wall. H is defined by a decrease in the volume filled by a capillary condensed phase when the area of the adsorption layer without a capillary condensate on it is infinitesimally increased by the desorption due to isothermal reversible distillation and approximately equals the V/S ratio of the pore. The second term in the parentheses of the right side of the equation denotes a correction for the influence of the adsorbed layers. If this correction does not depend appreciably on the pore size, H would be inversely proportional to ln(p0/p), and thus the S/V ratio of the pore would be expected to be proportional to ln(p0/ p), irrespective of the pore shapes. Figure 7 shows the melting-point depression of the pore ice against ln(p0/p) of the capillary condensation pressure of nitrogen at 77 K for various pores of different sizes and shapes. An almost linear relationship between them was obtained. This figure also includes the data for the cylindrical,12,35 interconnected cylindrical,35 and interconnected spherical pores7 of the ordered mesoporous silicas previously reported by us. This strongly suggests that the reciprocal of ln(p0/p) for capillary condensation of nitrogen at 77 K gives a good measure of “pore size”, regardless of the pore shapes, and the melting-point temperature of the confined ice is dependent on the S/V ratio of the pores confining it. The effect of the pore shape enters through the S/V ratio that depends on the pore shape. The relation should pass through the origin. The deviation observed might result from the neglect of the existence of a bound layer10,12,13 between a core ice and the pore walls.

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For a solid confined in cylindrical pores, theoretical treatments often assume that melting proceeds via shrinking of the cylindrical solid-liquid interface adjacent to the pore wall.5,6,43 However, the experimental melting point depressions of the materials confined in cylindrical or nearly cylindrical pores can be well described by eq 2 that is derived on the basis of the existence of the spherical or hemispherical solid-liquid interface.8-14 This suggests that the shrinking of the cylindrical solid-liquid interface has a minor effect for the melting process. Instead, movement of the hemispherical solid-liquid interface in the direction of the pore axis would play an important role in the melting. V. Summary In order to examine the validity of several models describing the freezing and melting behavior of a confined phase, we measured the freezing and melting temperatures of water confined to the cylindrical, interconnected cylindrical, and interconnected spherical pores of ordered silicas, as well as the open pores of the corresponding carbon replicas, by means of XRD. The Gibbs-Thomson relation3 that expresses the effective change in equilibrium melting point at a curved solid-liquid interface, as well as the model5,6 of metastable melting and equilibrium freezing transitions based on the free energy of a system with surface melting, predicts a melting-point elevation for a confined solid with negative curvature. The structures of the ordered mesoporous carbons are exactly the inverse replicas of the ordered mesoporous silicas, and thus the solids confined in the void space of these carbons will show solid-liquid interfaces with negative curvature adjacent to the pore walls upon melting. However, the pore ice confined to the open pores of the carbon replicas always showed melting-point depressions. Instead, the melting point of the pore ice confined to the pores of several different geometries revealed a good correlation with the capillary condensation pressure of nitrogen at 77 K. This clearly indicates that the curvature of the solid-liquid interface adjacent to the pore wall does not appreciably affect the melting behavior of the confined phase. Alternatively, when the melting-point depression is viewed as an effect of confinement on the solid-liquid transition, the depression in the equilibrium melting point of the confined phase may be proportional to the S/V ratio of the pore with volume V and surface area S, irrespective of pore geometries.1 In accord with this model, an almost linear relationship was observed between the melting-point depression of the pore ice and ln(p0/ p) of the capillary condensation pressure of nitrogen at 77 K for various pores of different sizes and shapes examined here. This strongly suggests that the reciprocal of ln(p0/p) for capillary condensation of nitrogen at 77 K gives a good measure of “pore size”, regardless of the pore shape, and the melting-point depression of the confined phase is dependent on the S/V ratio of the pores confining it. When the movement of the hemispherical solid-liquid interface in the direction of the pore axis play an important role in the melting of the solid confined to the cylindrical pores, the Gibbs-Thomson relation based on the curvature effect of the solid-liquid interface on the equilibrium transition point is able to explain the vast data of the melting-point depressions that have been observed so far in cylindrical or nearly cylindrical pores Very recently, we showed that stacking faults in the pore ice confined to the cylindrical and interconnected cylindrical pores of the ordered silicas persists up to the melting point, whereas stacking faults in the pore ice confined to the interconnected

Morishige et al. spherical pores disappear to a considerable extent just before the onset of the melting transition.35 The present study clearly indicates that stacking faults do not play an important role in controlling the melting temperature of the confined solid because the effect of the pore shape on the melting point enters only through the S/V ratio of the pores. Acknowledgment. This work was supported by matching fund subsidy for private universities from MEXT (Ministry of Education, Culture, Sports, Science and Technology). Supporting Information Available: XRD patterns from water confined in the C/MCM-41, C/SBA-15, C/KIT-6, and C/SBA-16, position and width of the main diffraction peak from water confined in the C/MCM-41 as a function of temperature, and melting point depression of the pore ice as a function of the S/V ratio of the mesopores. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Christenson, H. G. J. Phys.: Condens. Matter 2001, 13, R95. (2) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. J. Phys.: Condens. Matter 2006, 18, R15. (3) Kurz, W.; Fisher, D. J. Fundamentals of Solidification; Trans Tech Publications: Aedermannsdorf, Switzerland, 1984; p 13. (4) Engemann, S.; Reichert, H.; Dosch, H.; Bilgram, J.; Honkima¨ki, V.; Snigirev, A. Phys. ReV. Lett. 2004, 92, 205701–1. (5) Denoyel, R.; Pellenq, R. J. M. Langmuir 2002, 18, 2710. (6) Petrov, O.; Furo´, I. Phys. ReV. E 2006, 73, 011608-1. (7) Morishige, K.; Yasunaga, H.; Denoyel, R.; Wernert, V. J. Phys. Chem. C 2007, 111, 9488. (8) Rennie, G. K.; Clifford, J. J. Chem. Soc. Faraday Trans. I 1977, 73, 680. (9) Jackson, C. L.; McKenna, G. B. J. Chem. Phys. 1990, 93, 9002. (10) Schmidt, R.; Hansen, E. W.; Sto¨cker, M.; Akporiaye, D.; Ellestad, O. H. J. Am. Chem. Soc. 1995, 117, 4049. (11) Hirama, Y.; Takahashi, T.; Hino, M.; Sato, T. J. Colloid Interface Sci. 1996, 184, 349. (12) Morishige, K.; Kawano, K. J. Chem. Phys. 1999, 110, 4867. (13) Schreiber, A.; Ketelsen, I.; Findenegg, G. H. Phys. Chem. Chem. Phys. 2001, 3, 1185. (14) Kittaka, S.; Moriyama, M.; Ishimaru, S.; Morino, A.; Ueda, K. Langmuir 2009, 25, 1718. (15) Evans, R. J. Phys.: Condens. Matter 1990, 2, 8989. (16) Guisbiers, G.; Kazan, M.; van Overschelde, O.; Wautelet, M.; Pereira, S. J. Phys. Chem. C 2008, 112, 4097. (17) Jun, S.; Joo, S. H.; Ryoo, R.; Kruk, M.; Jaroniec, M.; Liu, Z.; Ohsuna, T.; Terasaki, O. J. Am. Chem. Soc. 2000, 122, 10712. (18) Kim, T.-W.; Kleitz, F.; Paul, B.; Ryoo, R. J. Am. Chem. Soc. 2005, 127, 7601. (19) Kim, T.-W.; Ryoo, R.; Gierszal, K. P.; Jaroniec, M.; Solovyov, L. A.; Salkamoto, Y.; Terasaki, O. J. Mater. Chem. 2005, 15, 1560. (20) Bai, X.-M.; Li, M. Nano Lett. 2006, 6, 2284. (21) Zhdanov, V. P. AdV. Catal. 1993, 39, 1. (22) Yanagisawa, T.; Shimizu, T.; Kuroda, K.; Kato, C. Bull. Chem. Soc. Jpn. 1990, 63, 988. (23) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T.-W.; Olson, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834. (24) Ryoo, R.; Kim, J. M. J. Chem. Soc., Chem. Commun. 1995, 711. (25) Kruk, M.; Jaroniec, M.; Ko, C. H.; Ryoo, R. Chem. Mater. 2000, 12, 1961. (26) Kleitz, F.; Choi, S. H.; Ryoo, R. Chem. Commun. 2003, 2136. (27) Kleitz, F.; Kim, T.-W.; Ryoo, R. Langmuir 2006, 22, 440. (28) Morishige, K.; Nakahara, R. J. Phys. Chem. C 2008, 112, 11881. (29) Morishige, K.; Inoue, K.; Imai, K. Langmuir 1996, 12, 4889. (30) Sakamoto, Y.; Kaneda, M.; Terasaki, O.; Zhao, D. Y.; Kim, J. M.; Stucky, G.; Shin, H. J.; Ryoo, R. Nature 2000, 408, 449. (31) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1967, 9, 8. (32) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1968, 10, 153. (33) Lippens, B. C.; de Boer, J. H. J. Catal. 1965, 4, 319. (34) Morishige, K.; Uematsu, H. J. Chem. Phys. 2005, 122, 044711. (35) Morishige, K.; Yasunaga, H.; Uematsu, H. J. Phys. Chem. C 2009, 113, 3056. (36) Ko¨nig, H. Z. Kristallogr. 1944, 105, 279.

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