Freezing and Melting of Kr in Hexagonally Shaped Pores of Turbostratic Carbon: Lack of Hysteresis between Freezing and Melting

Published: January 24, 2011

r 2011 American Chemical Society 2720 dx.doi.org/10.1021/jp108036q | J. Phys. Chem. C 2011, 115, 2720–2726

ARTICLE

pubs.acs.org/JPCC

Freezing and Melting of Kr in Hexagonally Shaped Pores ofTurbostratic Carbon: Lack of Hysteresis between Freezing andMeltingKunimitsu Morishige*

Department of Chemistry, Okayama University of Science, 1-1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan

ABSTRACT: To examine the effect of pore-wall structure onfreezing and melting behavior of a confined material inmesopores, we measured X-ray diffraction patterns from Krconfined in two kinds of ordered mesoporous carbons withhexagonally shaped pores, compared with ordered mesoporoussilica with cylindrical pores, during freezing and melting pro-cesses. The ordered mesoporous carbon possesses crystallinecarbon walls with turbostratic stacking structure, whereas thepore walls of the mesoporous silica are amorphous. Large de-pressions in melting point of the confined Kr were observed forboth the ordered mesoporous carbon and silica. For the Krconfined in the amorphous pores of the mesoporous silica,thermal cycling showed pronounced hysteresis between freez-ing and melting, in agreement with previous results. On theother hand, for the Kr confined in the crystalline pores of the mesoporous carbon, freezing and melting took place almost reversibly.

I. INTRODUCTION

There is considerable current interest in the freezing and melt-ing behavior of materials confined in mesoporous solids because ofits fundamental and technological importance.1,2 Most of themesopores experimentally investigated so far consist of pore wallswith amorphous structure such as silica and alumina. In suchcases, one of the most interesting, well-known phenomena is thedepression in freezing and melting temperatures of the confinedmaterials. In addition, thermal cycling shows pronounced hyster-esis, withmelting occurring at a higher temperature than freezing,except for in the very small mesopores.3-6

On the basis of a balance of bulk and surface free energy termsbetween solid and liquid in a pore, it has been suggested that thedepression in the equilibrium melting point of the confined solidis proportional to the ratio S/V of the pore with volume V andsurface area S, irrespective of pore geometries.1

ΔTm ¼ T0 -Tm ¼ VmT0ðγsw - γlwÞΔHf

SV

ð1Þ

Here, Vm is the molar volume of the material; ΔHf is the latentheat of melting; γsw is the solid-wall interfacial energy; γlw is theliquid-wall interfacial energy; and Tm and T0 are the meltingtemperatures of a pore solid and a bulk solid, respectively. Veryrecently, we have shown that for ordered mesoporous materialswith several different pore geometries the melting-point depres-sion of a pore ice is almost proportional to the S/V ratio of thepores confining it.7 The sign of ΔTm depends on whether thewalls prefer the solid or the liquid, i.e., whether γsw is greater orless than γlw. The depression in melting point, which is always

observed for the materials confined in mesopores, strongly sug-gests that the solid almost never wets the pore walls (γsw > γlw).Indeed, the presence of nonfreezing liquid layers between theconfined solid and the pore walls has been often reported.4-6,8-13

For the materials confined in the cylindrical pores with pore wallsthat can be wetted by the liquid in the presence of the solidcrystal, eq 1 is reduced to the well-known Gibbs-Thomsonequation

ΔTm ¼ 2VmγslT0

rΔHfð2Þ

where r is the pore radius and γsl is the solid-liquid interfacialenergy. For water confined in the cylindrical pores of silica, it hasbeen revealed that eq 2 is valid to describe the relationshipbetween the melting-point depression and the effective poreradius.4-6,11

When the liquid wets the pore walls in the presence of the solidcrystal, a free energy barrier between a surface melted state andthe liquid droplet in the pore emerges. Therefore, in principle,the thermal hysteresis between freezing and melting of the con-fined material in the cylindrical pores of silica can be accountedfor by the appearance of a metastable liquid and/or a metastablesolid in the pore.10,14,15 In very small mesopores, the energybarrier is so small that the melting and freezing temperatureswould be the same.16,17 Porous silicas that have been extensivelyused in the study of freezing/melting behavior of a confined

Received: August 25, 2010Revised: November 11, 2010

2721 dx.doi.org/10.1021/jp108036q |J. Phys. Chem. C 2011, 115, 2720–2726

The Journal of Physical Chemistry C ARTICLE

phase have amorphous pore walls. The first several layers ad-jacent to the pore walls do not participate in freezing and meltingtransitions of the interior phase4-6,8-13,18 and take amorphousstructure even below the freezing temperature of the interior.18,19

The structure of the thin layers covering the pore walls is not at allcompatible with that of the solid crystal formed in the center.Therefore, the nucleation of the confined solid is not easy on thethin layers adjacent to the pore walls, and hence the thermalhysteresis can be attributed to the appearance of kinetic super-cooling of a confined liquid, at least in the absence of the bulksolid outside the pores. Such a view has been supported byspecific heat measurements12 of freezing and melting of Ar in thecylindrical pores of silica, as well as a very recent study7 con-cerning the effect of pore shape on freezing and melting temp-eratures of water. If the pores have large fluctuations in size alongthe pore axis, pore-blocking-controlled freezing occurs, and thuslarge thermal hysteresis is observed.20,21 In any event, except forvery small mesopores, hysteresis between freezing andmelting ofa confined phase is always observed for porous silicas with amor-phous walls.

On the other hand, it is known that the monolayer films of raregases on the flat surfaces of graphite take a two-dimensionalhexagonal structure and show a considerably elevated meltingtemperature by the compression due to substrate attraction andinteractions with higher layers.22 The structure of themonolayersis compatible with that of the bulk crystals of rare gases.23

Therefore, it is expected that no new interface needs to becreated to grow additional layers in a solid crystal of a face-centered cubic structure with ABC stacking sequence, and thusno barrier to growth will exist. Turbostratic carbon consists ofrandom stacking of graphite sheets.24 The surfaces are atomicallyrather smooth, and thus the crystalline monolayers of thematerials are expected to be formed on its surfaces as well. Thepurpose of the present study is to examine the freezing andmelting behavior of Kr confined in the hexagonally shaped poresof turbostratic carbon, compared with the cylindrical pores ofamorphous silica of comparable size. Since the crystalline mono-layer of Kr formed on the crystalline pore walls may be nucleationsites on freezing of the inner phase, kinetic supercooling isexpected to be considerably suppressed.

II. EXPERIMENTAL SECTION

II.1. Materials and Characterization. Ordered mesoporouscarbon (C-ORNL-1) with hexagonally shaped pores was pre-pared by self-assembly of resorcinol-formaldehyde and PluronicF127 triblock copolymer according to the procedure of Wang,Liang, and Dai.25 Carbonization was carried out under an N2

atmosphere at 673 K for 2 h and then at 1123 K (850 �C) for 3 h.Further heat treatment of C-ORNL-1 was carried out in a high-temperature furnace under argon atmosphere at 2473 K(2200 �C) for 1 h. Ordered mesoporous silica (SBA-15) withcylindrical pores was prepared using Pluronic P123 triblockcopolymer as a structure-directing agent at an aging temperatureof 373 K according to the procedure of Kruk et al.26 Thecopolymer-silica complex was calcined at 823 K for 5 h in airto remove the copolymer template.Adsorption isotherms of nitrogen at 77 K were measured

volumetrically on a BELSORP-mini II. X-ray diffraction (XRD)powder patterns were measured on a Rigaku RAD-2B diffracto-meter in the Bragg-Brentano geometry arrangement using CuKR radiation with a graphite monochromator. Transmission

electron microscopy (TEM) images were recorded on a JEOLJEM-2000EX electron microscope, operating at 200 kV.II.2. Measurements. An experimental apparatus of XRD for

freezing/melting measurements has been described elsewhere.27

The measurements were carried out with Cu KR radiation in aBragg-Brentano geometry. Sample powder (∼0.1 g) was packedin a shallow pit of a sample holder of Cu and covered with a7.5 μm thick film of Kapton and then a 0.1 mm thick sheet of Be.The sample holder was then attached to a sample cell constructedof a cylindrical Be window and a Cu flange, with In O-ring. Afterprolonged evacuation at room temperature, the sample wascooled, and then the background was measured. The adsorptionisotherm of Kr on the sample inside the X-ray cryostat wasmeasured at 108 K. The substrate was then cooled to a desiredtemperature between 80 and 108 K, and the spectrum wasmeasured. The diffraction pattern of the confined phase wasobtained by subtraction of data for charged and empty substrateafter correction for gas attenuation. The correction for gasattenuation was done by scaling the observed scattering to theintensity of the (002) graphite peak, the latter assumed to beessentially unaffected by diffraction from the confined phase.28

III. RESULTS

III.1. Porous Structure. Figure 1 shows the XRD powderpatterns of two kinds of C-ORNL-1 samples. The as-preparedsample exhibited two broad diffraction peaks that can be indexedas the 002 and 100 reflections in the turbostratic stackingstructure of carbon. In the turbostratic stacking of graphitesheets, neighboring graphite sheets are parallel to each other,but translational and rotational correlations within a sheet planeare random. Heat treatment at 2473 K resulted in sharpeningof these two peaks, as well as an appearance of additional twodiffraction peaks that can be indexed as the 004 and 110reflections of turbostratic carbon, which suggests an increase incrystallinity of pore walls with the heat treatment at hightemperature. To know the structure of the pore walls, wecalculated the XRD pattern of turbostratic carbon using the

Figure 1. X-ray diffraction patterns of the as-prepared mesoporouscarbon and the heat-treated mesoporous carbon. Solid curves denote thesimulated XRD pattern of turbostratic carbon as described in the text.



Warren-Bodenstein equation.24,29 The parameters are the in-plane graphite lattice constant (a0), spacing between the layers(d002), carbon layer plane size along the a-axis (La), and carbonlayer stacking size along the c-axis (Lc) (see Figure 2). For thesample heat treated at 2473 K, a good fit between the calculatedand observed diffraction patterns was obtained with the fixedvalues of a0 = 0.24612 nm, d002 = 0.345 nm, La = 4.67628 nm, andLc = 1.035 nm (four sheets of carbon layer). The layer spacingobtained is wider by a few percent than that of the ideal graphitecrystal (0.3354 nm), which is typical for the turbostratic stackingof graphite sheets. Figure 3 shows the TEM images of the heat-treated sample taken along the [001] and [110] directions,respectively. Long-range hexagonal arrangement of hexagonallyshaped pores is clearly visible. Therefore, it is evident that theorderedmesoporous carbon thus obtained possesses hexagonallyshaped pores consisting of carbon walls with a turbostratic stackingstructure. The porous structure of the ordered mesoporous carbonresembles the inner pores of a multiwalled carbon nanotube.30

Figure 4 shows the adsorption-desorption isotherms of nitro-gen at 77 K on two kinds of mesoporous carbon and one kind ofSBA-15 silica with cylindrical pores. The as-prepared carbonexhibited a large amount of adsorption in the initial stage, per-haps due to micropores. The isotherm showed a hysteresis loopof type H1 typical of cylindrical pores.31 The amount of adsorp-tion in the initial stage was considerably reduced by the heattreatment at 2473 K, although the shape of the hysteresis loopremained almost unchanged. The adsorption and desorptionbranches for the mesoporous carbon were more gradual thanthose for the mesoporous silica, although the positions ofadsorption and desorption steps on these mesoporous materialswere almost identical. This indicates that the pore sizes of thesematerials are comparable and that the pore size distribution of themesoporous carbon is wider. The specific surface area was cal-culated by using the BET method from the nitrogen adsorptiondata.32 The mean diameters of these cylindrical and nearlycylindrical pores were obtained from the adsorption branch ofthe isotherm with use of the Barrett-Joyner-Halenda method.33

The micropore volume and total pore volume were estimated by

using the t-plot method.34 Table 1 summarizes the main phys-icochemical parameters of the samples used in the present study.III.2. Hysteresis between Freezing and Melting. The bulk

solid of Kr consists of a face-centered cubic (fcc) lattice andmeltsat 115.8 K.35 Figure 5 shows some of the powder XRD patternsfrom the Kr confined in the heat-treated mesoporous carbonwhen the temperature was successively lowered and then whenthe temperature was successively increased. Several sharp fea-tures denoted by vertical lines arise from the incomplete sub-traction of diffraction peaks of the Be sheet because correctionfor absorption of the X-rays on the substrate is larger than that onthe Be sheet covering the substrate in the reflection mode. Whenthe temperature was lowered through ∼103 K, there was agradual change in the diffraction pattern of the Kr from a liquid toa solid form. The latter is characterized by sharpening of thediffraction peak at 2θ = 26.7�, as well as an appearance of fourpeaks at 2θ = 30.6, 44.3, 52.6, and 55.0�. The five peaks can beindexed to the 111, 200, 220, 311, and 222 reflections of a solidKr with a fcc structure, respectively. When the resulting solid washeated, the melting took place at almost the same temperature asthe freezing. This is in sharp contrast with the observations1,2 thatthere is always appreciable thermal hysteresis between freezingand melting of materials confined in mesopores of moderatesizes. Figure 6 shows some of the XRD patterns from the Krconfined in the as-prepared mesoporous carbon. When thesubstrate was cooled through ∼100 K, there was a gradualchange in the diffraction pattern from a liquid to a solid form.The 200 reflection was less prominent in the diffraction patternof the resulting solid compared to that for the mesoporouscarbon heat-treated at 2473 K. In addition, themelting took placeat a temperature (∼102 K) slightly higher than freezing. Figure 7shows some of the XRD patterns from the Kr confined in theSBA-15 on cooling and then on heating. When the temperaturewas lowered through 96 K, there was a rather abrupt change inthe diffraction pattern from a liquid to a solid form. The 200reflection was less prominent compared to the diffraction patternfor the heat-treated mesoporous carbon. When the resulting

Figure 2. Crystallite sizes of turbostratic carbon along the a- and c-axes.

Figure 3. TEM images of the heat-treated mesoporous carbon takenalong the [001] (a) and [110] (b) directions.

Figure 4. Adsorption-desorption isotherms of nitrogen at 77 K on theheat-treated mesoporous carbon (circles), the as-prepared mesoporouscarbon (triangles), and the mesoporous silica (squares). Open andclosed symbols denote adsorption and desorption branches, respec-tively.



solid was heated, the melting took place at a temperature(∼101 K) distinctly higher than freezing, being consistent withthe previous results on mesoporous materials.3-7,10-12,18,20,21

To obtain accurate peak parameters, the observed peak profilein the 2θ region of 20-35� was fitted to two Lorentzian lineshapes with a linearly changing background. Figure 8 shows thepeak width [full width at half-maximum (fwhm)] of the maindiffraction peak at 2θ = 26.7� as a function of temperature. Forthe Kr confined to the hexagonally shaped pores of the heat-treated mesoporous carbon, the peak width changed almostreversibly around ∼104 K on cooling and subsequent heating.This clearly indicates that there is no appreciable thermalhysteresis between freezing and melting in this system. On theother hand, for the Kr confined in the as-prepared mesoporouscarbon, the temperature at which the peak width rapidly de-creases on cooling was slightly lower than that at which the peakwidth rapidly increases on heating, indicating an appearance ofthermal hysteresis between freezing and melting. The thermalhysteresis became more prominent for the Kr confined to thecylindrical pores of the ordered silica. The peak width rapidlydecreased at ∼96 K on cooling, while the peak width suddenlyincreased at ∼101 K on heating. A thermal hysteresis of ∼5 Kwas observed for this system.Figure 9 compares themain peak profiles from the Kr confined

to the mesopores of the heat-treated mesoporous carbon, the as-prepared mesoporous carbon, and the mesoporous silica at 80 K.The structure of solid Kr in pores has previously been studied byX-ray diffraction.36-38 All these studies indicate that the solid Krconfined to the amorphous mesopores of silica contains aconsiderable amount of random stacking faults and an amor-phous component depending on the pore size. Therefore, the

peak profile was deconvoluted into three components, that is, the111 reflection at 2θ = 26.7�, the 200 reflection at 2θ = 30.6�, andthe broad peak due to the amorphous solid centered at 2θ =27.8�. The proportion of the amorphous component in the solidKr confined to the hexagonally shaped pores of the orderedcarbon treated at high temperature is obviously smaller thanthose in the as-prepared carbon and the mesoporous silica. It isalmost certain that the presence of micropores in the as-preparedmesoporous carbon as well as the amorphous pore walls of theordered mesoporous silica are responsible for an appearance of agreater amount of the amorphous solid in the pores.

IV. DISCUSSION

Large depressions in melting point of the confined Kr wereobserved for both the ordered mesoporous carbon and silica. Inthe crystalline pores of the heat-treated mesoporous carbon, how-ever, freezing and melting of the confined Kr took place almostreversibly, whereas in the amorphous pores of the mesoporoussilica a large hysteresis between freezing and melting was ob-served. In the less crystalline pores of the as-prepared carbon, thefreezing and melting showed a small hysteresis. All of theseresults indicate that the pore-wall structure affects significantlythe mechanisms of freezing and melting of the confined Kr. Thesolid-liquid transition of the confined Kr in the crystalline poresof the mesoporous carbon was more gradual compared to that inthe amorphous pores of the mesoporous silica because the sizedistribution of the pores in the former was exceedingly widerthan that in the latter.IV.1. Amorphous Pore. The large depression in melting point

of the confined Kr strongly suggests that for the mesoporoussilica liquid Kr wets the amorphous pore walls in the presence of

Table 1. Physicochemical Parameters

sample surface area (m2/g) pore size (nm) micropore volume (cm3/g) total pore volume (cm3/g)

C-ORNL-1 (2473 K) 263 7.0 0 0.41

C-ORNL-1 (1123 K) 621 7.0 0.14 0.59

SBA-15 594 8.0 0 0.85

Figure 5. Change of the X-ray diffraction pattern of Kr confined in the heat-treated mesoporous carbon at nearly complete filling upon cooling andsubsequent heating.



solid Kr. In other words, a contact angle of a solid Kr on the porewalls is almost 180�, and thus γsw - γlw = γsl according toYoung’s equation. Therefore, we calculated the melting-pointdepression of a solid Kr confined to the cylindrical pores of themesoporous silica using the Gibbs-Thomson equation andthe parameters Vm = 34.3 cm3/g, γsl = 0.9 � 10-6 J/cm2, T� =115.8 K, ΔHf = 1639 J/mol,39 and r = 4.0 nm. For a confined Arin porous silica, it has been reported that at least the first twolayers adjacent to the pore walls do not participate in freezing andmelting transitions of the interior phase owing to the amorphousstructure of the pore walls.10 Themelting temperature of the con-fined Kr in the mesoporous silica was calculated to be 103 K, takinginto account the dead layers. The calculated melting temperature of

the solid Kr in the mesoporous silica is in reasonable agreementwith the observed one. When the liquid wets the pore walls in thepresence of the solid crystal, a free energy barrier between asurface melted state and the liquid droplet in the poresemerges,10,14,15 and thus a kinetic effect of nucleation plays animportant role in controlling the phase transition temperatures.Indeed, Schaefer et al. have observed several freezing peaks dueto heterogeneous and homogeneous nucleation for Ar confinedin the cylindrical pores of SBA-15 in their heat capacity spectra.12

Large depressions in melting point of the confined Kr werealso observed for two kinds of the mesoporous carbons. For the Krconfined in the crystalline pores of themesoporous carbon, however,freezing and melting took place almost reversibly. Therefore, the

Figure 6. Change of the X-ray diffraction pattern of Kr confined in the as-prepared mesoporous carbon at nearly complete filling upon cooling andsubsequent heating.

Figure 7. Change of the X-ray diffraction pattern of Kr confined in themesoporous silica at nearly complete filling upon cooling and subsequent heating.



results for the mesoporous carbons cannot be simply explainedwithin the framework of such a surface-melted-layer model.IV.2. Crystalline Pore. It is well-known that multilayer solid

films of rare gases are formed on the flat surfaces of graphite, andunlike the amorphous pore walls nonfreezing liquid layers do notexist between the solid crystal and the graphite surfaces. Thissuggests that the graphite walls prefer a solid Kr, and thus γsw isless than γlw in the crystalline pores of the mesoporous carbon.As a result, melting-point elevation of the confined Kr isexpected. Large depressions in melting point of the confinedKr, however, were observed in the crystalline pores of themesoporous carbon as well. This strongly suggests that largestrains are induced in the crystalline solid confined in the poreswith crystalline carbon walls because the geometrical constraintsin pore shape hinders freezing.40,41 γsw is actually greater than γlwin the crystalline pores of the mesoporous carbon because γsw ineq 1 contains contributions from a change in thermodynamicproperties of a solid in confinement.

Nevertheless, the first monolayer adjacent to the pore wallsmay form a close-packed triangular lattice commensurate withthe bulk crystal well above the freezing temperature of theconfined liquid because the monolayer solid in contact withliquid is free from such strains. When the equilibrium freezingpoint is approached, the freezing of inner layers may take placelayer-by-layer, starting from the first layer. Since the freezing ofthe interior phase does not require formation of a new interface,kinetic supercooling will not appear. Growth of a fcc solid oneach side of the crystalline walls of the hexagonally shaped porescompetes against each other in the pore center, which will resultin large strains in the solid formed.VI.3. Metastable Melting Model. We have here suggested

that melting of a confined solid always occurs at the equilibriummelting point regardless of pore-wall structures, and in amor-phous pores the freezing may take place from a metastable liquidstate, leading to the appearance of hysteresis between freezingand melting of the confined phase in the amorphous pores. On

Figure 8. Width (fwhm) of the main diffraction peak as a function oftemperature for Kr confined at nearly complete filling in the heat-treatedmesoporous carbon (a), the as-prepared mesoporous carbon (b), andthe mesoporous silica (c). Open and closed symbols denote cooling andheating processes, respectively.

Figure 9. Main peak profiles of the X-ray diffraction pattern of Krconfined at nearly complete filling in the heat-treated mesoporouscarbon (a), the as-prepared mesoporous carbon (b), and the mesopor-ous silica (c) at 80 K. Solid curves represent three components due to the111 and 200 reflections of the crystalline solid, as well as the amorphoussolid.



the other hand, it has sometimes been assumed that hysteresisarises from the persistence of a metastable solid up to a tem-perature higher than the equilibrium melting temperature, whilefreezing occurs at the equilibrium freezing temperature.14,15 Forthe confined Kr in the crystalline pores of the mesoporouscarbon, lack of hysteresis between freezing and melting clearlyindicates that neither the metastable solid nor the metastableliquid appears in the pores. We consider the reason why meltingoccurs at the equilibrium melting temperature in the followingway. At pore end, the solid confined in the nearly cylindricalpores has inevitably a free surface in contact with a vapor underthe present experimental conditions. Surface melting appears tobe a relatively general phenomenon.42 It occurs whenever thesum of the specific solid-liquid plus liquid-vapor interfacialenergies is lower than the solid-vapor interfacial energy. Asurface may hence act as a nucleation center for the melt. Whenmelting takes place by the movement of the hemisphericalsolid-liquid interface in the direction of the pore axis, the phasetransition is expected to occur at the equilibrium melting tem-perature, as is the case for bulk melting transition. Furthermore,the metastable melting model predicts a depression in meltingpoint exceedingly smaller than actually observed because in thismodel the depression in melting point is only half that in freezingpoint.15 However, the depression in melting point of the Krconfined to the amorphous pores of the ordered mesoporoussilica was almost equal to that expected from the equilibriumfreezing (melting) point.

’ACKNOWLEDGMENT

We thank Y. Matsutani for his technical assistance in thepreparation of the materials and the measurements of TEMimages and XRD patterns of the materials. This work wassupported by matching fund subsidy for private universities fromMEXT (Ministry of Education, Culture, Sports, Science andTechnology).

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Freezing and Melting of Kr in Hexagonally Shaped Pores of Turbostratic Carbon: Lack of Hysteresis between Freezing and Melting