8594
J . Phys. Chem. 1992, 96, 8594-8599
(59) Mezei, M.; Swaminathan, S.;Beveridge, D. L. J . Am. Chem. SOC. 1978, 100, 3255. (60) Hermans, J.; Pathiaseril, A.; Anderson, A. J . Am. Chem. SOC.1988, 110, 5982. (61) Lie, C. G.; Clementi, E.; Yoshimine, M. J. Chem. Phys. 1976, 64, 2314. (62) Motakabbir, K.A.; Bcrkowitz, M. J . Phys. Chem. 1990, 94, 8359. (63) Revost, M.; van Belle, D.; Lippens, G.; Wodak, S . Mol. Phys. 1990, 71, 587.
(64) de Pablo, J. J.; Prausnitz, J. M.; Strauch, H. J.; Cummings, P. T. J . Chem. Phys. 1990, 93,1355. (65) Hill, T. L. Statistical Mechanics: Principles and Selected Applicarions; McGraw-Hill: New York, 1956. (66) Smith, J. M.; Van Ness, H. C. Introduction to Chemical Engineering Thermodynamics; McGraw-Hill: New York, 1987. (67) Kirkwood, J. G.; Buff, F. P. J . Chem. Phys. 1951, 19, 774. (68) Hiroike, K. J . Phys. SOC.Jpn. 1960, IS, 771. (69) Wilhelm, E.; Battino, R.; Wilcock, R. J. Chem. Rev. 1977, 77, 219.
Effect of Restricted Geometries on the Structure and Thermodynamic Properties of Ice+ Y. Paul Handa,* Marek Zakrzewski? and Craig Fairbridges Institute for Environmental Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada K I A OR6 (Received: May 18, 1992)
The thermal properties and structure of water in porous Vycor glass and various silica gels with pore radii in the range 23-70 A were investigated using calorimetry and X-ray diffraction. Samples containing pore water only and those containing pore water in equilibrium with bulk water were studied. The amounts of bound and freezable water in the samples were determined by measuring the heat of melting as a function of pore water content and by application of thermoporometry. The melting point of ice was depressed by 9-20 K, depending on the pore size. The heat of melting of pore ice was found to be 1648% smaller than that of bulk ice, depending on the pore size and whether the bulk phase was present or not. On quenching to liquid nitrogen temperature, pore water transformed into cubic ice, which was found to be more stable than cubic ice in the bulk phase, and its stability increased as the pores became smaller. For the smallest pores studied, the cubic ice was stable up to 200 K.
transition.13J4 However, in the case of water in porous materials, Iatroductioa some exceptional results have been reported. In the bulk phase, For a liquid to freeze, an embryo or a cluster of a critical size lowdensity amorphous ice (Ia) is stable up to about 125 K,I5above needs to be formed before homogeneous nucleation can take place. which it transforms to cubic ice (IC), which then transforms to The size of this cluster depends on the temperature and decreases hexagonal ice (Ih) above 165 K.I6 Dore et al." have reported with a decrease in the temperature. When present in pores, not that on cooling water in 90-A silica pores Ih transforms to ICat only is the liquid subjected to capiliary forces but also the size 260 K and to a disordered form below 2 13 K and on heating IC of the pore itself may be smaller than the critical cluster size so remains stable all the way up to the melting point. Cubic ice in that the liquid will not freeze at its normal freezing point and a the bulk phase is obtained by heating one of the high-pressure certain amount of supercooling (well in excess of that sometimes forms of ice or amorphous ice.15J6 The transformation from IC required for bulk liquids) will be required for it to freeze. This to Ih is exothermic and is thus thermodynamically irreversible. is well-established through numerous studies on the behavior of In this sense, the direct transformation of Ih to ICas reported by liquids and solids in small pores.'q2 Of particular interest has been Dore et al. is quite intriguing and warrants further investigation. the study of pore water for which there is reasonable agreement Hofer et a1.l8 have reported that on uenching water in a hydrogel, among the various ~ t u d i e s ~on- ~the depression in freezing point with pores in the size range 5-50 , amorphous ice is obtained, as a function of pore size. However, there is little agreement on which transforms to ICat 210 K and then to Ib at 265 K. Similar whether the heat of melting of pore ice is the same as that of bulk ice. Results indicahg the heat of melting being higher: 10wer,4.~-~ results on water in a hydrogel have also been reported by Wilson and Turner,lg and the direct transition of pore liquid water to the or the same' have been reported. It has also been suggested that amorphous state on quenching was first suggested by BrzhanSzo the thermodynamic properties of pore ice, in general, should be Thus, in the case of water, the effect of confinement in pores is the same as that of the bulk ice? The melting transition in porous to raise the phase-transition temperature. materials is generally not sharp but is spread over a wide temNaturally occurring natural gas hydrates are often found in perature range due to the distribution of pore sizes and/or shapes. the compacted sediments at the bottom of the Ocean or buried Furthermore, if the substrate is hydrophilic, a part of the pore under permafrost. Preliminary estimates2' indicate tbat these water is usually bound to the pore walls and does not undergo hydrates may be the largest reserve of natural gas (mostly CH,). a melting transition. The fraction present as bound water is often Current interest in these systems is 2-fold: they may serve as a not known or not determined precisely. All these factors contribute source of energy; they may also contribute to global warming if to the uncertainty assoCiatedwith determining the heat of melting. they become destabilized and release the CH4 Almost Restricted geometries are known to shift not only the melting all the laboratory studies on gas hydrates have been conducted transition to lower temperatures but also the solidsolid transiin the bulk phase. The models dealing with resource assessment tion,'' the transition to the superfluid state,",'* and the glass and global warming potential of gas hydrates assume that the thermodynamic properties of gas hydrates in confined spaces are Issued as NRCC No. 34221. the same as those in the bulk phase. Even if this may k true to 'Present address: Procter and Gamble Pharmaceuticals, P.O. Box 191, a large extent, the stability region of the hydrates will be expected Norwich, NY 13815. to be shifted to lower temperatures because of lowering of the I Energy Research Laboratories, Energy Mines and Resources Canada, Ottawa, Ontario, Canada KIA OG1. melting point of ice in pores. It was reported previouslyz3that
w
0022-3654/92/2096-8S94$03.00/0Published 1992 by the American Chemical Society
Effect of Restricted Geometries on Ice the gas hydrates dissociate completely and rapidly into ice and gas if the sample is in the form of a fine powder. However, if the crystallites are coarse, the dissociation does not reach completion due to formation of a layer of ice which prevents the gas from escaping from the interior of the crystal. The gas hydrates in porous media are essentially present as a fine powder and therefore dissociation characteristics of naturally occurring gas hydrates may not be the same as those of bulk hydrates. Consequently, to test whether the properties of pore hydrates can be assumed to be the same as those of the bulk hydrates, we recently initiated a program to study the thermodynamic and kinetic stability of gas hydrates in porous media. However, it is first necessary to establish the thermal properties of pore ice before the results on pore hydrates can be analyzed. To this end, we have conducted systematic calorimetric investigations on ice in pores of various sizes. The depression in the freezing point of liquids in pores forms the basis of thermoporometry,8a technique used for textural characterization of porous materials. This technique has been used in the present study to characterize the porous materials used. We have also conducted X-ray diffraction studies on the same samples in order to further characterize the structure of ice in restricted geometries. In this paper, we report the calorimetricand X-ray diffraction work on pore ice. The work on pore hydrates will be reported in separate papers.
Experimental Methods Porous Vycor glass (Dow Coming, Type 7930) with a specified average pore radius of 40 A was obtained in the form of rods about 1.3 cm in diameter. It was used as such for some experiments and ground to a fine powder for other experiments. Before use, Vycor glass (VG) was cleaned by fmt soaking it in 30% hydrogen peroxide to remove organic impurities and then in nitric acid to remove inorganic impurities. Each treatment required a few days to completely remove the impurities. The solvents were later leached out with deionized water, and VG was subsequently dried in an oven at about 400 K. Porous silica gel (SG) sold under the name Davisil was obtained from Aldrich. Two types of silica gel were used with the following characteristics as provided by the manufacturer: SG20 with average pore radius 20 A and pore volume 0.68 cm3 g-l; SG75 with average pore radius 75 A and pore volume 1.15 cm3g-I. These materials were in the form of fine powders and were used without further treatment. The water used was distilled, deionized, and degassed. Porous materials containing sorbed water were prepared by placing the material in a desiccator containing water, evacuating the desiccator, and allowing a few days for the solid-vapor equilibrium to be established. The sorption was usually complete within 3 days. Samples containing pore and bulk water were prepared by first saturating the porous material with respect to the vapor phase as described above and then adding liquid water such that the solid was completely immersed in it and allowing the system to equilibrate for 24 h. A sample of bulk amorphous ice was prepared by depositing about 4.5 cm3 of water over 5.5 h on a substrate at 13 K using Air Products Displex C5201. The sample was scraped off the substrate in liquid nitrogen vapors at about 100 K and then stored in liquid nitrogen. A DSC2910-TA2100 system (TA Instruments) attached to a liquid nitrogen accessory was used for characterizing bound water in samples containing pore water only. Temperature and energy scales of the DSC were calibrated using high-purity mercury, water, indium, tin, and zinc. The accuracy in determining the phase-transition temperature is about f0.3 K and the heat of the phase change is about f l-2%. All scans were made at 10 K min-’ under a dry nitrogen gas flow rate of 50 mL min-I. Runs were made from 170 to 290 K. For determination of bound water, measurements were made on samples with varying levels of water content obtained by allowing water to escape from the fully saturated samples by slow evaporation at rooh temperature and monitoring the mass of the sample. The sample size was 10-15 mg, and water represented up to half of this mass. The mass measurements were made to f0.02 mg and thus accounted for
The Journal of Physical Chemistry, Vol. 96, NO. 21, 1992 85% an error of 1-3% in determining the mass of pore water. The accuracy of the DSC results is estimated to be about &5% or better. A Tian-Calvet heat-flow calorimeter (Setaram, Model BT) was used for recording the freezing and melting curves for thermoporometric analysis and for determining the heat of melting of pore ice. The details of the calorimeter and the procedures for determining various thermal properties are given elsewhere.24The accuracy of this instrument is about f l % . A typical sample size was about 1 g including the porous material, bulk water, and pore water. The heats of phase change in samples containing pore water only were measured by slowly cooling the samples from room temperature to about 150 K and then scanning back to room temperature at 10 K h-l. The samples containing pore and bulk water were slowly frozen in the calorimeter cell using liquid nitrogen vapors and then transferred to the calorimeter which previously had been cooled to 272.9 K, and the whole system was allowed to come to thermal equilibrium. At this stage, the bulk water in the system was frozen but pore water was present as liquid. Scans were then made in the cooling and heating modes at 3 or 5 K h-’ in order to establish the freezing and melting thermograms for pore water. The melting thermogram gave the heat of melting of pore ice in the presence of bulk ice. Heating scans at 10 K h-I were also recorded for samples of Vycor rod saturated with water sorbed from the vapor phase and quenched to liquid nitrogen temperature. At the end of each experiment, the sample was dried at 400 K and the mass of water determined. In the case of samples containing pore as well as bulk water, the mass of pore water was determined by subtracting from the total water content the mass of bulk water obtained by integration of the melting peak at 273
K. X-ray powder diffraction patterns were recorded with a Rigaku B-8 wide-angle diffractometer using 1.789-A Co radiation. The diffractometer was equipped with an Anton-Paar low-temperature camera and a graphite monochromator. Diffraction patterns for amorphous ice were recorded by loading the sample over boiling nitrogen in the precooled camera. For the porous samples, the patterns were recorded after slowly cooling the samples in situ or by first quenching the samples in liquid nitrogen and then loading them in the precooled camera.
Results and DisclLosion Characterizationof Pore Sizes. The stability of a substance in restricted geometries is governed by thermodynamic and mechanical equilibria and the number of interfaces in the pore.25 In the case of a porous material completely wetted with the bulk phase, only the solid-liquid interface can exist inside the pore. The freezing of pore water in equilibrium with bulk ice taka place by penetration of the bulk phase into the pore.*v9 In such a case, the solid-liquid interface is spherical, no supercooling of the pore water takes place, and the water in each individual pore freezes at a temperature corresponding to its size. The depression in freezing point is given by the relation
where R, is the core radius, rlS is the intrapore solid-liquid interfacial tension, A& is the entropy of freezing, V, is the molar volume of the liquid, To is the normal freezing point, and Tis the freezing point in a pore of radius R,. The pore radius is related to the core radius by R, = R, + 1, where f is the thickness of the bound layer of molecules which do not freeze. In eq 1, FT is a thermodynamic shape factor which has a value of 2 for spherical pores and 1 for cylindrical pores. During freezing, FT is always 2 because the solid-liquid interface is spherical. However, during melting, the solid-liquid interface has the same shape as that of the pore and the value of FT is usually between 1 and 2. If the pores are perfectly spherical, then the freezing and melting occur at the same temperature; otherwise, there is a hysteresis between the two curves as seen in Figure 1. This hysteresis then gives information on FT.
Handa et al.
8596 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
TABLE I: Melthg Points and Heats of Melting of Pore Ice
SGZO
VG
23 42
SG15
IO
253.1 264.7 267.5 273.15
bulk Ih
191.6 215.6 281.4 333.5
171.4 213.5 254.7
40
250
270
260
280
TIK
Figure 1. Freezing (curve 1) and melting (curve 2) of pore ice in Vycor glass. Melting in the neighborhood of 273 K is shown on an expanded scale by curve 3.
On the basis of eq 1, Brun et a1.8-26developed the technique of thermoporometry for characterizing porous materials. From measurements of freezing thermograms of water in fully saturated materials, they obtained the following relationship: R, = --646.7 - 2.3 AT where R, is in A. The freezing curve can be translated into the pore size distribution curve by calculating the core radius at each temperature along the freezing envelope from eq 2 and the number of pores in a given size range from the cumulative heat of freezing determined calorimetricallyand the theoretical heat of freezing calculated from eqs 1 and 2. The value of FT is calculated from an analysis of the freezing and melting curves? and the thickness of the bound layer is calculated by an iterative method which varies the thickness until the amount of pore water calculated is the same as the experimental value.26 The thermal behavior of water in Vycor glass is shown in Figure 1. On cooling at 5 K h-I, an exothermic peak, curve 1, is seen due to the freezing of pore water. The freezing peak has a slow decay at lower temperatures, indicating a broader size distribution among smaller pores. On heating the sample at the same rate, two melting peaks, curve 2, are seen; the one at the lower temperature is due to melting of pore ice, and the one at about 273 K is due to melting of bulk ice. Similar results were obtained in the case of silica gels. A pure homogeneous material melts at a constant temperature. However, in scanning calorimetry, the melting event is spread over a small temperature range, the spread being dependent on the scanning rate, mass of the sample, and time constant of the instrument. The melting point is taken as the temperature at which the tangents drawn to the initial baseline and the steepest part of the first half of the peak intersect. The melting is complete at the temperature corresponding to the peak maximum, and the second half of the peak is simply the decay signal. In the case of a porous material, the melting event in each pore is associated with an energy signal which has an instantaneous rise and decay. If all the pores in the material are of the same size and shape, then the melting peak will look almost like that of the bulk material. This usually is not the case. For example, the melting peaks shown in Figure 1 are due to 0.070 g of pore ice and 0.542 g of bulk ice obtained under the same experimental conditions. The spread over a much larger temperature range for melting of a relatively much smaller amount of pore ice is due to a distribution of pore sizes. The distribution of melting points was also demonstrated by adiabatic calorimetry on water-saturated Vycor glass! The melting peak can be looked upon as an envelope over a large number of discrete energy pulses modulated in intensity by the number of pores in a given size range and the variation in the heat of melting with temperat~re.~’In porous materials, there is usually a distribution of pore sizes, and thus, a singular melting point cannot be defmed. For a fully saturated material, it is a reasonable convention to pick the melting point as the temperature at which half of the pore solid has melted,* and this convention has been adopted in the present work. The melting points, T,, of ice in
20
30
50
40
60
70
Rp (A)
Figure 2. Pore size distribution in Vycor glass calculated from the freezing and melting curves in Figure 1 and using eqs 1 and 2.
the various materials are given in Table I. The pore size distribution obtained for VG is shown in Figure 2. This material showed a rather sharp cut-off at about 48 A and a somewhat broader distribution at the lower end. This material was also characterized by performing volumetric N2 adsorption-desorption studies on 0.065- and 0.240-g powder samples using an Autosorb- 1 equipment from Quantachrome Gorp. The shape of the size distribution curve in Figure 2 is almost the same as that obtained from the BET analyses in the present work and by Levitz et a1.28except that the BET results are shifted to somewhat lower pore size values. The analysis of the N2 adsorption-demrption isotherms in terms of the micropore method of Mikhail et al.29indicated that micropores constituted about 8% of the pore volume. In the thermoporometric method, the water associated with micropores would be treated as part of the bound layer associated with mesopores. Consequently, the pore sizes calculated from thermoporometry will be slightly larger than those obtained from the BET analysis. The mean pore radius, taken as the size at which the cumulative pore volume is 50% of the total pore volume, obtained from the results in Figure 2 is 42 A. The average pore radii at 77 K obtained from the BET analyses are 41 A in the present work, 35 A by Levitz et a1.,28and 30 A by Huber and H~ber.~O The shape factor obtained from thermoporometry indicated that the pores in Vycor glass are almost spherical, whereas a cylindrical geometry is assumed in the BET analysis. The pore size distributions in the silica gels were obtained by thermoporometry in a similar manner. The distribution curves were almost Gaussian with mean pore radii of 23 and 70 A and half-widths of 10 and 40 A for SG20 and SG75, respectively. The mean pore radii of the various materials obtained by thermoporometry are given in Table I. ~ c t e r i z a t i o of n Freezable Water. The total pore water in samples saturated with respect to water vapors was found to be 22.58, 60.396, and 111% by mass for VG, SG20, and SG75, respectively. For the silica gels, the sorption values are in correspondence with the pore volumes provided by the manufacturer. For the Vycor glass, the total pore volume obtained from BET analysis was 0.225 cm3 g-I. The total pore volume contained a small contribution from macropores or large interparticle spaces in VG as indicated by the sharp uptake of Nzat a relative pressure, PIPo, of about 0.95 after a plateau for the main isotherm had been established in the PIP, range of about 0.87-0.95. The pore volume associated with the main isotherm was 0.213 an3g-l. For the samples containing pore and bulk water, the pore water contents were 20.596, 57.2%, and 106% by mass for VG, SG20, and SG75, respectively. These are 5-10% smaller than the values
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8597
Effect of Restricted Geometries on Ice 005
000 300
0 10
0 15
020
2 loo
i
240 -
-::
180
-
=, 120
--
m
.
025
07
were also calculated using temperature-dependent heat capacities of supercooled water and ice and analyzed the same way as shown in Figure 3. For the system water-SG20, where we encounter the lowest melting temperatures, the AC, correction is the largest. For this system, the results obtained for the bound water content were within 1.O-1.5% of the values reported above. For the other systems, the results were almost the same. Consequently, for our purpose, the use of a constant value of 2.12 J K-I g-I for AC, in eq 3 is quite justified. For the samples containin pore and bulk water, bound layer values between 4.5 and 5.5 were obtained for all the samples from thermoporometric analyses. This corresponds to about two molecular layers of bound water; values in the range two to three monolayer^^*^ and three monolayers* have been reported in the literature. The amount of unfrozen water was calculated from the thickness of the bound layer and the shape The values obtained were 19.8%, 43.0%, and 12.4% for VG, SG20, and SG75, respectively. These values are higher than those obtained above from the analysis of the heat of melting of pore ice as a function of water content. The calculation of pore volume by thermoporometry is quite sensitive to the applicability of eqs 1 and 2 and to the shape factor and the accuracy of the values for ylsand the constants in eq 2. However, the discrepancy is not entirely due to the limitationsof the thermoporometricmodel. As noted above, the total pore water obtained for wet samples was less than for the corresponding samples containing sorbed water only. Since the internal surface area in both cases is the same, a higher bound water content will be obtained for the wet samples. On the other hand, the bound water contents obtained from measurements of heat of melting as a function of pore water content will be underestimated because during evaporation of the condensed liquid some bound water from already emptied pores also tends to desorb.32 For the sake of internal consistency, the amount of freezable water in a sample containing sorbed water only was obtained using the bound water content obtained from analysis of the heat of melting as a function of water content and, in a sample containing pore and bulk water, using the bound water content obtained by the thermoporometric method. Heat of Melting of Pore Ice. The heat of melting of freezable water, Wfw, in the fully saturated porous material was obtained by integration of the melting peak, correcting for the fraction present as bound water, and scaling the heat change to 273 K using eq 3. The results are given in Table I. For comparison, the heat of melting of bulk ice is also given. The values reported in column 4, W r w ( s l g ) ,are for the samples which contained sorbed water only, and those in column 5, pHofw(sl),are for the samples which contained sorbed as well as bulk water. AHofw(slg)values are seen to be higher by about 10% than the W f w ( s l )values. This is due to the existence of the solid-gas and/or liquidinterfaces in addition to the solid-liquid interfaces in the pores in samples containing sorbed water only and, of course, also due to the differing treatment of the pore water considered unfreezable. In light of these factors, the agreement between the two sets of values seems reasonable. In both cases, with or without the bulk phase, the heat of melting of pore ice is seen to be smaller than that of bulk ice. Formation and Stability of Cubic Ice. Figure 4 shows X-ray diffraction patterns of vapor-deposited ice in the bulk phase. Amorphous ice shows two broad peaks33which in terms of the radiation used in the present work are centered at about 28 and 47O. At 110 K, the sample is a mixture of Ia and ICwith the pattern of ICsuperimposed on that of Ia. At 150 K, amorphous ice is completely transformed to ICand a growing amount of Ih is also seen as indicated by the increase in intensity of the 101 and 103 reflections at the 28 values of about 30 and 52O (Miller indices for the lines for IC and Ih are shown in Figure 6). The transition to Ih is complete at 170 K. Figure 5 shows diffraction patterns of Vycor glass saturated with respect to sorbed water. The sample was prepared by first quenching the Vycor glass rod in liquid nitrogen and then grinding it to a powder. The broad peak in the low-angle region is due to Vycor glass. The diffraction patterns were recorded at 10 K intervals, and for the sake of
1
0' 00
10
J
02
06
04
m
08
10
PW
Figure 3. Heat of melting of pore ice, corrected to 273 K, as a function of pore water content in SG75 ( 0 )and VG (0).
given above even though these samples were first saturated with respect to water vapors and then soaked in bulk water. In these samples, the melting peak for the bulk water had a shoulder in the range 271-273 K as shown, on an expanded scale, by curve 3 in Figure 1, thereby indicating the presence of a small amount of water in rather large pores or voids. This fraction of water was not counted as pore water, and thus, the pore water contents obtained for the wet samples are closer to the BET values than to the values obtained for the samples containing sorbed water only. For the undersaturated samples, the melting point of ice was found to decrease with a decrease in water content. Since the samples were prepared by evaporation of water from fully saturated materials, it implies that during the evaporation process the larger pores lose their water first while the smaller pores may still be fully saturated. It was found that the shape of the melting peak became distorted and the transition was smeared over a wider temperature range as the water content in the material decreased. This is due to a relatively broader size distribution among the smaller pores and also due to the reduced heat of melting at lower temperatures. The lowest water contents used were those for which a phase change could be established unambigously, and the peak integration could be performed reasonably well. These are 8.5%, 20.0%, and 8.7% by mass for VG, SG20, and SG75, respectively, and the melting points observed corresponding to these water contents were 254.0, 224.3, and 244.7 K. The heat of melting of ice in pores, AH, was obtained by integrating the melting peak. The AH value thus obtained corresponds to the melting temperature, T,, of ice in the sample. This value was corrected to 273.15 K using the relation W = AH(T,) + AC,(273.15 - T,) (3) where AHo is the heat of melting at the reference temperature 273.15 K, AH(T,) is the heat of melting at T,, and AC, is the heat capacity difference between liquid water and ice. For pure water, AC = 2.12 J K-* g-' at 273.15 K, and this value was also assumed 6 r water in pores. In some cases, the AC, correction was larger than the AH value itself measured at AT,. Figure 3 shows the results for W ,expressed in terms of per gram of dry solid (gds), plotted against the pore water content, mpw,expressed as the mass ratio of pore water to dry solid. For the sake of clarity, plots for VG and SG75 only are shown; SG20 gave a similar plot. The solid lines through the data points represent the linear fits. The intercept on the x axis gives the water content for which AH = 0, i.e., the bound water content of the porous material. Values for the bound water content are 5.47%, 14.62, and 8.94% by mass for VG, SG20, and SG75, respectively. On melting, water is essentially present as a supercooled liquid in pores, so AC, used in eq 3 should be the difference between the heat capacities of supercooled water and ice at a given T,. The heat capacity of supercooled water increases as the temperature decreases and diverges asymptoticallyas the temperature approaches 227 K.31For example, AC, increases to 2.97 J K-l g-' at 243 K from its value of 2.12 J K-l g-' at 273 K. Lwo values
Handa et al. I
I
170 K
1Is
v)
Q 0
200 K
BO K
20
30
40
50
50
20
Figure 4. X-ray diffraction patterns showing the transformation of already partly transformed amorphous ice (1 10 K) into cubic ice (1 50 K) and then into hexagonal ice (170 K).
30
20
50
40
60
20 Figure 6. X-ray diffraction patterns of quenched pore water in SG2O at temperatures in the range 80-200 K and of slowly cooled pore water in SG20 at 90 K.
I/ 85
2
,
K
L
150
160
180
220
200
K
260
240
TIK
Figure 7. Heating scan on quenched pore water in Vycor glass showing the cubic-to-hexagonal ice transition in the range 200-230 K.
120 K
TABLE U Temperatures T, for Complete Transformation of Cubic-to-Heuponrl Ice in Pores material R ~ I A T,,/K material R ~ J A T,/K 20
30
40
50
60
20 Figure 5. X-ray diffraction patterns of quenched pore water in Vycor glass at temperatures in the range 80-190 K and of slowly cooled pore water in Vycor glass at 85 K.
clarity, only selected patterns are shown in the figure. A pattern for IC is seen at 80 K,and it remains essentially unchanged up to 170 K. At 180 K,a noticeable growth of Ih is seen as indicated by the reflections at 30 and 52O, and the transformation to Ih is complete at 190 K. On the other hand, when a Vycor sample was slowly cooled to 85 K,only Ih was observed as shown in the top pattern. Figure 6 shows similar behavior of water in quenched and slowly cooled samples of SG20. At 80 K, only IC is observed in the quenched sample, and at 160 K, the pattern is still mostly IC though growth of Ih has already started. The transformation to Ih is complete at 200 K. In the case of slowly cooled sample, only Ih is observed as shown in the top pattern. The X-ray diffraction results for the SG75 sample containing sorbed water were similar to those for SG20 with the transformation from ICto Ih occurring around 170 K. The estimated temperatures for the complete transformation of IC to Ih in the various materials are given in Table 11. The direct transformation of water into IC in small pores and the stability of ICto relatively higher temperatures has also betn
SG20 VG
23 42
200
SG75
190
bulk IC
70
170 170
reported p r e v i o ~ s l y ,but ' ~ ~not ~ ~ as a function of pore size. It has also been suggested that small droplets of water in the upper atmosphere freeze directly to give I c ? ~and this has been demonstrated experimentally by Mayer and H a l l b r u ~ k e r .Dore ~ ~ et al.I7 reported the direct transformation of Ih to ICon simply coohg the water in 90-Asilica pores. As noted above, we were able to form IC only on quenching the sample. In the bulk phase, the transition IC Ih is quite sluggish and is spread over a temperature range of about 60 K, from about 165 to 225 K. This has been observed in scanning36as well as adiabatic3' calorimetric experiments. It should be noted that the temperatures reported in X-ray measurements are quite different than the calorimetric temperatures. However, the X-ray diffraction studies again reveal that the IC Ih transition is spread over a few tens of degrees, and as seen in Table 11, within the temperature scale of the X-ray measurements, ICin pores is relatively more stable than the bulk phase and becomes more so as the pores get smaller. A calorimetric Scan on the quenched sample of Vycor glass rod containing sorbed water is shown in Figure I. It shows an exotherm in the range of about 200-230 K just before the onset of melting of pore ice at about 240 K. In light of the X-ray diffraction studies, the exotherm can be ascribed to the IC Ih transition. These results again reveal that within the calorimetric
-
-
-
J. Phys. Chem. 1992,96, 8599-8603 temperature scale, ICin pores is more stable than in the bulk phase. Water has often been used as a probe in thermoporometry for characterizing pores in water-wettable materials.8,26The procedure adopted sometimes is to quench the water-saturated material and then heat it at a controlled rate and determine the pore size from the melting curve.38 Obviously, caution should be exercised in the thermal treatment of the samples as formation of ICand its transition to Ih at relatively higher temperatures can mask or alter part of the melting curve. Acknowledgment. Financial support for this work was received, in part, from the Geological Survey of Canada under Gas Hydrate Project 870021. We thank Dr. J. S. Tse for help with X-ray diffraction measurements, Dr. D. D. Klug for help with the preparation of vapor-deposited ice, and Mr. Mike Stolovitsky for conducting nitrogen adsorption-desorption measurements.
References and Notes (1) Molecular Dynamics in Restricted Geometries; Klafter, J., Drake, J. M., Eds.; Wiley: New York, 1989. (2) Jackson, C. L.; McKenna, G. B. J. Chem. Phys. 1990, 93, 9002. (3) Patrick, W. A.; Kemper, W. A. J . Phys. Chem. 1938,42, 369. (4) Antoniou, A. A. J. Phys. Chem. 1964, 68, 2754. (5) Litvan, G. G. Can. J . Chem. 1966, 44, 2617. (6) Blachere, J. R.; Young, J. E. J . Am. Ceram. Soc. 1972, 55, 306. (7) Rennie, G. K.; Clifford, J. J . Chem. Soc., Faraday Trans 1 1977, 73, 680. (8) Brun, M.; Lallemand, A.; Quinson, J.-F.; Eyraud, C. Thermochim. Acta 1977, 21, 59. (9) Enastiin, B. V.; Sentiirk, H. S.;Yurdakul, 0. J. Colloid Interface Sci. 1978, 65. 509. (10) Awschalom, D. D.; Warnock, J. Phys. Reu. B 1987, 35, 6779. (1 1) Toni, R. H.; Maris, H. J.; Seidel, G. M. Phys. Reu. B 1990,41,7167.
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(12) Shirahama, K.; Kubota, M.; Ogawa, S.;Wada, N.; Watanabc, T. Phys. Rev.Lett. 1990, 64, 1541. (13) Jackson, C. L.; McKenna, G. B. J . Non-Crysr. Solids 1991,131-133, 221. (14) Zhang, J.; Liu, G.; Jonas, J. J . Phys. Chem. 1992, 96, 3478. (15) Handa, Y. P.; Klug, D. D. J . Phys. Chem. 1988,92, 3323. (16) Handa, Y. P.; Klug, D. D.; Whalley, E. Can. J . Chem. 1988,66,919. (17) Dore, J. C.; Dunn, M.; Chieux, P. J. Phys. Collogue C1 1987,48,457. (18) Hofer, K.; Mayer, E.; Johari, G. P. J . Phys. Chem. 1990,94, 2689. (19) Wilson, T.W.; Turner, D. T. Macromolecules 1988, 21, 1186. (20) Brzhan, V. S. Colloid J . (USSR) 1959, 21, 621. (21) Kvenvolden, K. A. Chem. Geol. 1988, 71, 41. (22) Nisbet, E. Nature 1990, 347, 23. (23) Handa, Y. P. J. Chem. Thermodyn. 1986, 18, 891. (24) Handa, Y. P.; Hawkins, R. E.; Murray, J. J. J . Chem. Thermodyn. 1984, 16, 623. (25) Defay, R.; Prigogine, I.; Bellemans, A,; Everett, D. H. Surface Tension and Adsorption; Wiley: New York, 1966. (26) Quinson, J. F.; Brun, M. In Characterization of Porous Solids; Un-
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Thermodynamic Properties and Dlssociation Characteristics of Methane and Propane Hydrates in 70-A-Radius Silica Gel Porest Y. Paul Handa* and Dmitri Stupin* Institute for Environmental Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR6 (Received: May 18, 1992)
The pressuretemperature profiles for the hydrateicegas and hydrateliquid water-gas equilibria were measured for methane and propane hydrates in 70-&radius silica gel pores. In both cases, the equilibrium pressures were 20-100% higher than those for the bulk hydrates. The dissociation characteristics of the gas hydrates in pores were also studied calorimetrically by heating the hydrates under about zero pressure from 100 K to room temperature. It was found that after the initial dissociation into ice and gas the hydrate became totally encapsulated among the pore walls and the ice caps formed at the pore openings. The hydrate thus trapped in the interior of the pore remained stable up to the melting point of pore ice. These results are similar to those obtained in our previous studies on the bulk hydrates which are also stabilized by a shielding layer of ice. However, the apparent increase in the stability of the pore hydrates was found to be much larger than that of the bulk hydrates. The composition of methane hydrate in 70-A pores was determined to be CH44.94H20,and its heat of dissociation into pore water and gas, obtained calorimetrically, was 45.92kJ mol-’; the corresponding values in the bulk phase are 6.00 and 54.19 kJ mol-’, respectively.
Introduction There are worldwide Occurrenw of natural gas hydrates, both on-shore buried under the permafrost and off-shore buried under the oceanic and deep lake sediments.’#* Gas hydrates are often found dispersed in pores of coarse-grained sediments or fractures in g e o ~ t r a t a though , ~ , ~ occurrence of a massive hydrate bed containing only about 6% by mass sediment has also been reported.5 Gas hydrates are clathrate compounds in which the gas molecules are trapped inside well-defined cages formed by the water molecules! Most of the laboratory work done on the thermodynamics Issued as NRCC No. 34222. *Visiting scientist: Agriculture Institute, St. Petersburg, Russia.
and kinetics of gas hydrates has been limited to hydrates prepared from pure water6*’ and in a few cases from water containing inhibitors such as salts8 and alcohol^.^ Most inferences of the natural Occurrence of hydrates are not based on the recovery of actual samples. Instead, the laboratory results are imposed on the natural systems to draw-up scenarios of Occurrence, accumulation, and dissociation of gas hydrates. In terms of the solidsolution model, the stability conditions of clathrate hydrates depend directly on the activity of water.I0 As the activity decreases, the hydrates form at increasingly higher pressures at a given temperature or at lower temperatures at a given pressure. This is observed in systems containing inhibitors which cause a depression in the freezing point of water, thereby
0022-365419212096-8599$03.00/0 Published 1992 by the American Chemical Society
