Title Chemical physics of air clathrate hydrates

Author(s) Kuhs, Werner F.; Klapproth, Alice; Chazallon, Bertrand

Citation Physics of Ice Core Records, 373-392

Issue Date 2000

Doc URL http://hdl.handle.net/2115/32476

Type proceedings

Note International Symposium on Physics of Ice Core Records. Shikotsukohan, Hokkaido, Japan, September 14-17, 1998.

File Information P373-392.pdf

Instructions for use

Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP 373

Chemical physics of air clathrate hydrates

Werner F.Kuhs*, Alice Klapproth* and Bertrand Chazallon*t

*Mineralogisch-Kristallographisches Institut, Universitat G6ttingen, Goldschmidtstr.l, 37077 G6ttingen, GERMANY tLPCML, UMR 5620, Universite Claude-Bernard Lyon I, 43 Boulevard du 11 novembre 1918,69622 Villeurbanne, FRANCE

Abstract: The chemico-physical properties of air clathrate hydrates are reviewed, based both on laboratory experiments and observations made in ice core studies. Recent results on gas fractionation, cage occupancies and compressibilities obtained in laboratory experiments are presented. Finally, concepts for a description of clathrate nucleation, growth and decomposition are discussed.

1. Introduction transparent inclusions embedded in the ice matrix. It is the purpose of this article to Air clathrate hydrates are observed in review the current state of knowledge on the deeper parts of polar ice sheets. In the various properties of air clathrate hydrates. presence of ice and with the increasing Clathrate hydrates form a class of pressure at larger depths air bubbles become inclusion compounds in which gases are thermodynamically unstable against air imprisoned in a host structure formed by H­ clathrate hydrates. The occurence of air bonded water molecules. The guest hydrates in ice sheets was predicted by molecules interact with the host framework Miller [1] based on observations by Gow et through van der Waals and electrostatic al. [2] in bubble-free but air-rich ice cores interactions to stabilize the structure, which from Byrd station in Antarctica. Detailed is thermodynamically unstable when empty. descriptions of the properties of gas-filled The degree of filling is variable and depends inclusions forming in originally bubble-free on the nature of the gas, pressure (fugacity) ice, some time after the cores were drilled, and temperature. The present state-of-the-art are given by Gow [3]. Evidence in support research in clathrate hydrates is detailed by of clathrate hydrate formation from gas­ Sloan [6]. Two main crystallographic filled inclusions was first presented by Gow structures are known in which clathrate and Williamson [4]. The first documented hydrates crystallize [7]. Air hydrates usually observations of air hydrates in ice cores form a type II crystal structure [8], which is were made by Shoji & Langway [5] in the built from 8 large and 16 small cages per Dye-3 Greenland ice core. Since then they unit cell. Nitrogen, oxygen, but possibly also have repeatedly been observed in ice cores other gases contained in the air enter into from Greenland and Antarctica as these cages. Based partly on recent results

Physics ofIce Core Records Edited by T. Hondoh Hokkaido University Press, 2000, Sapporo 374 Chemical physics ofair clathrate hydrates obtained in G6ttingen, the review examines 10glO P = a + biT first the equilibrium properties of air clathrates before discussing aspects of non­ with P given in bar and T in K. The fitted equilibrium, growth and decomposition. The constants for N2, O2 and air respectively are focus will generally be on the properties of a: 4.77(5), 5.17(2) and 4.63(11); b: some relevance to processes in polar ice -710(14), -850(6), -683(28), with the sheets. estimated error given in brackets. As a general comment, the calculation of stability fields using the statistical 2. Equilibrium properties thermodynamic theory of van der Waals & Platteeuw [9] delivers reasonable estimates 2.1 Stability field for most mixed gases in equilibrium with

The decomposition lines for N2, O2 and liquid water [6]. However, more uncertain air clathrate hydrates have already been are the predicted stability fields of pure and given by Miller [1] based on a single mixed gas hydrates with respect to ice Th. experimental data point at -35 °e and the This is not really surprising as the empirical established phase diagram near the triple parameters of the gas-water interaction are point (water - ice Ih - clathrate). These usually optimized using the experimental curves have frequently been cited in the three-phase hydrate+gas+liquid( water) data literature [e.g. 4] but it seems they have of the pure systems. never been independently verified. Very recently we have undertaken a series of 2.2 Gas fractionation experiments to establish the decomposition There are currently several In­ lines of N 2, O2 and air clathrates. The vestigations concerned with possible decomposition pressure was measured at fractionation effects of natural air hydrates. various temperatures in the range -20 to The question was already put into focus o °e. The decomposition lines were found to with the first Raman-scattering study on be at slightly lower pressures than those natural air-hydrates from the DYE-3 ice found by Miller (Fig. 1). It is also core in which Nakahara et al. [12] found a worthwhile to note that the computed substantial oxygen enrichment with a N 2/02 decomposition line for N2 clathrate (based ratio of 1.7. Later Pauer et al. [13, 14], on the thermodynamic theory of van der working on samples from the GRIP-core Waals and Platteeuw [9] and calculated with well below the transition zone (i.e. below the the program eSMHYD [6]) does not coexistence range of air hydrates and air correctly reproduce the experimental values. bubbles), found N2/02 ratios slightly below The new experimental values are in but close to the atmospheric value of 3.73. agreement with observations from the Byrd In contrast to these findings samples from ice core, where clathrates were observed the transition zone of Antarctic ice cores [10] at shallower depths than predicted by exhibit a clear fractionation effect as Miller's curves [1]. For convenience, the measured by micro-Raman spectroscopy, following formula may be used to calculate both in the clathrates and in the air bubbles the decomposition line [15]. It should also be noted that the N2/02 ratio varies as a function of crystal W F Kuhs et al. 375

Temperature [0C] -40 -30 -20

200 --N,-clath., Miller, 1969 --- O,-clath., Miller, 1969 180 ••••• Air-clath., Miller 1969 160 -x-N,-clath., CSMHYD, Sloan 1998 N -clath., (this work) • 2 140 ... O,-clath., (this work) ';::" C1l Air-clath., (this work) ::£. 120 • N,-clath., O,-clath., quadruple point fE <> ::::I van Cleef & Diepen, 1960, 1965 U) U) 100 fE 0.. 80 ---~ 60 40 ------

204-~~~-~~~~~~-~T-~~~~--~~-r20 230 235 240 245 250 255 260 265 270 275 Temperature [K]

Temperature [0C] -40 -30 ·20 -10 o

200 • N2 clath. (this work) + quadruple point van Cleet & Diepen, 1965 180 ... 02 clath. (this work) + quadruple pOint van Cleet & Diepen, 1965 160 • Air clath. (this work) --fitted dissociation curve N -clathrate "i::' 140 2 ct! ---- fitted dissociation curve 02-clathrate ..0 ...... 120 ...... fitted dissociation curve Air-clathrate ....Q) ::::l en 100 ~ a.. 80

60

40 ~- ~- (b) 20 230 235 240 245 250 255 260 265 270 275 Temperature [K]

Figure I: The decomposition curves for N2, O2 and air clathrate hydrates. (a) The experimental curves as established by Miller [I] and the calculated curve obtained from CSMHYD [6], which is in clear disagreement with experimental data presented in this work. (b) Experimental data obtained in this work and fitted decomposition curves (see text). The fit was made including the experimental quadruple points measured by van C leef and Diepen [11]. 376 Chemical physics ofair clathrate hydrates orientation in a (polarised) Raman spectrum is no mechanical separation of a growing [16]. According to the theory of van der clathrate from the remaining air bubble, nor Waals and Plaatteuw [9], a reaction of air any preferential out-diffusion of air and water or ice to air hydrate should constituents, the final composition after the produce at least initially Orenriched regrowth will be identical to the initial crystals. With a limited reservoir of air, as composition ofthe untransformed air bubble. in air bubbles included in ice, one has to The fractionation effect has been established expect the subsequent formation of a zoned quantitatively by physico-chemical work in crystal with a steadily increasing content of our laboratory where air-hydrates were

N2. However, this stage of clathrate formed from normal air with a N2/02 ratio formation can very rarely be observed in ice of 3.73 [17]. The N 2/02 ratio in the solid cores. Rather, the final product is likely to clathrate was measured by Raman regrow (see section 4.2 below) and, spectroscopy. In contrast to the situation for consequently, will exhibit a rather air bubbles in ice cores, the reservoir of air homogeneous distribution of oxygen and was considered to be infinite (due to the nitrogen within one crystallite [14]. If there large volume of the compressor system) and

• Air-clathrates -2°C 6,5 --N2/02 from neutron data (this work) • Air-clathrates -20°C 6,0 --- N2/02 maximal error - ....- Air-clathrates -30°C _._.- Ni02 minimal error 5,5 • N/02 Air measured ------. N/02 Parrish & Prausnitz 5,0 N/OzAir 4,5 ------0 4,0 :;:::; ....co ...... ~~----~..~.~.~.~.~ ..~.~.~.~.~ ..~.~.~.~.~ ..~.~.~.~.~ ..~.~.~.~.~ ..~.~.~.~.~ ..~.~.~.~ ..~.~. N 3,5 0 N 3,0 --z ------2,5 2,0 -.~ ::.-.-~-.-.-.-.-.-.-.-.-.-.~ 1,5 1,0

0 100 200 300 400 500 600 Fugacity [bar]

Figure 2: The Nzl02 ratio measured by Raman-spectroscopy in synthetic air clathrates as a f1lllction of pressure. The fitted polynomial curves represent the Nzl02 ratio for the isotherms at _2°, -20°C and

-30 °C. The broken line at the bottom gives the N2/02 ratio as calculated from the Langmuir constants

according to Parrish and Prausnitz [18). The full curve gives the N/02 ratio as calculated from the Langmuir constants obtained by fitting our neutron diffraction results for the cage filling; its upper and lower error limits are given as broken lines. W F Kuhs et al. 377 only the initial fractionation was established. at the lower end of the transition zone gives

The experimental results are shown in Fig. 2 N 2/02 ratios in the vicinity of 2.0 for the and the resulting tentative phase diagram GRIP ice core. No detailed information is given in Fig. 3. The minimum observed available on the fractionation at lower

N 2/02 ratio was 1.7 at pressures of 300 to temperatures corresponding to the conditions 400 bar when formed at -2°C, a situation found in the VOSTOK ice core. However, which corresponds to a late nucleation in an as indicated in Fig. 2, one may expect higher overpressurized regime. A more relevant oxygen enrichment at lower temperature estimate of the possible fractionation effect which is partly offset by the lower pressure

25

• D T=271.1 K 20

clathrate hydrate + vapor 15 ~ ~ S fZl fZl et 10 . Ice + vapor

5

o 20 40 60 80 100 Mole % nitrogen

Figure 3: The tentative phase diagram for the N2-Oz-HzO system at -2 'C. The formation and decomposition points have been established only for one composition; the corresponding curves are given as a guide to the eye only. 378 Chemical physics ofair clathrate hydrates at the end of the transition zone at VOSTOK. example, there is no solid experimental A linear extrapolation of the temperature proof that the filling behaviour of the gas effect results in a N 2/02 ratio of 1.9 to 2.0 components really follows a Langmuir for the lower end of the transition zone at isotherm (see section 2.3 below). This filling VOSTOK. Thus the thermodynamic in tum enters into the calculation of the enrichment of oxygen from air in ice cores is chemical potential of water in the mixed seemingly limited to a N 2/02 ratio close to 2; hydrate, which itself determines the stability the concomitant nitrogen enrichment in the lines. remaining surrounding air could certainly For pure Cli. clathrate, the de­ result in a N2/02 ratio as large as 6 or 7 (see composition temperature at 100 kPa (i.e. Fig. 3). It should be noted at this stage that atmospheric pressure) is approximately kinetic processes might take place in 193K. It should be noted here that Cli. is addition to thermodynamic ones which are known to be physi-sorbed on ice surfaces able to produce even bigger fractionation below the decomposition pressure, at least at effects; these will be discussed in section 3.3. low temperatures; the coverage of the Little is known about possible surface depends, of course, on the gas fractionation effects involving the trace pressure but also seems to depend on the gases CO2 and Cli.. The pure systems of number of defects at the surface [20]. No these gases have been investigated repeatedly, information exists as to the preferential however the focus was usually on adsorption for Cli. in air below the clathrate measurements above the melting point of ice formation pressure threshold. Similarly for

Ih. Some data at lower temperature are CO 2 in air, no detailed physico-chemical available for CO2; for a review see Ref 6. work is known for (preferential) physi­ The fractionation effect in the NrCli. sorption on ice surfaces. Only the clathrate system was analysed for the solid clathrate decomposition line was established and phase in the vicinity of and above 0 °C [19] summarized by Davidson et al. [21]. The (Fig. 4). It seems likely that Cli. is co­ decomposition line cuts the value of 100 kPa clathrated with air and should therefore be (i.e. atmospheric pressure) at approxi­ found in the air-hydrate crystals. Un­ mately 218 K. Below approximately 120 K, fortunately, a direct proof by Raman and in contrast to the Cli.-case, CO 2 spectroscopy is not possible due to the clathrate seems to be unstable against solid limited sensitivity of the method. CO2 and ice Ih [21]. There is accumulated It should also be mentioned that a evidence for a preclathrate cage-like water theoretical calculation of the vanous arrangement around dissolved gas mole­ fractionation effects by a statistical cules in liquid water [22] or in the gas phase thermodynamic approach was first proposed [23]. It may be suspected that similar local by Parrish & Prausnitz [18]; as an example arrangements are also found at the surface of some relevance their results for the N2- of ice, at least near the melting point. Cli. system are also shown in Fig. 4. As may be seen from these results, the success of such calculations is still somewhat limited. This is likely to be due to some unjustified assumptions of the underlying theory. For W F Kuhs et al. 379

35 • 0 T=273.2K ® 0 T=277.4K 30 ... T=279.8K

25 - clathrate hydrate + vapor

t':I 20 ~ (j) I-< :::s Vl Vl (j) I-< ~ 15

10

5 liquid + vapor

I I o 20 40 60 80 100 Mole % nitrogen

Figure 4: The phase diagram for Nz-CH,-Hp. The thin lines are given as a guide to the eye. The thick lines give the calculated equilibrium for a temperature of 279.8 K according to Ref. 18. Note that there is

a change from a type I structure for pure CH4 hydrate to a type II structure for pure N2 hydrate, the exact location of which is not known. 380 Chemical physics ofair clathrate hydrates

2.3 Crystallography and stoichiometry N2 and CO2. The situation for air clathrate In situ neutron diffraction work [24, is not known in great detail but may be 25] over the last few years has allowed us to expected to be similar to the N2 clathrate establish the cage filling for both small and case. large cages as well as the lattice constants as The clathrate mass density will a function of pressure and temperature. increase in a nonlinear way with the From these data the density, thermal increasing overburden pressure as a function expansivity and compressibility of of both increasing fugacity as well as (deuterated) clathrate hydrates can be increasing mechanical pressure. It is determined. The gas filling usually increases important to note that the isosteric density with increasing fugacity (pressure) of the (as obtained by applying mechanical gas; however, it does not necessarily, as pressure to the material at constant filling) previously assumed [e.g. 9], follow a is different from the equilibrium density Langmuir isotherm. Figures 5, 6 and 7 show obtained when clathrate crystals adjust their the filling as a function of fugacity filling by re-growing at a given gas pressure. (pressure) for the small and large cages of Isosteric and equilibrium unit cell volumes

Fugacity [bar] 0 192,6 418,3 729,7 1171,5 1797,2 100 100 .. -- .. - .------=--- c- ---- ...... -...... ,...-- -- ,"-.. ./ - 90 , 90 / I • ,...... I :::R , ...... 0 80 I 80 >- ,I I () ,I I c I I co neutron results (this work) 0- 70 ; I 70 ::J • () , I --fitted Langmuir-isotherm () ! I 0 --- Munck et aI., 1988 I - - • Parrish & Prausnitz, 1972 60 ;"", 60 !'I, 50 50 0 200 400 600 800 1000 Pressure [bar]

Figure 5: Filling of the small cages of N2 clathrate vs. fugacity and pressure. The Langmuir isotherm fitted to the data as well as predicted isotherms taken from literature are shown (Ref. 15 and 26). The I fitted Langmuir constant is esc = 24.9(1.9) kbar- . W F Kuhs et al. 381

Fugacity [bar] 0 192,6 418,3 729,7 1171,5 1797,2

neutron results (this work) ~ 120 • 120 >.u --fitted Langmuir-isotherm c:: ro 0- ::::l U u 100 100 0 .2 .c 0- ....ro e> ..Q 80 80 ...... ro en ....>. 0 60 60 0 200 400 600 800 1000 Pressure [bar]

Figure 6: Filling of the large cages of N2 clathrate vs. fugacity and pressure together with a fitted 1 1 isotherrn using a two constant model [24] with CLc.single = 205(44) kbar- and CLC.dauble = 0.125(6) kbar- .

Fugacity [bar] 0 9,34 17,36 24,07 26,84 27,68 28,26 110 100 • • - - 90 - ... ------~ c:: 80 --- ro .. _ .. - 0- 70 ::::l 0 0 0 8 60 / 0 / o , / .2 50 8 ,0' .c , ..- , , , 0-ro 40 , .... - • neutron results large cages (this work) e> 30 - o o neutron results small cages (this work) ...... ro 20 --Langmuir isotherm (large cages) Parrish & Prausnitz, 1972 en --- Langmuir isotherm (small cages) Parrish & Prausnitz, 1972 ~ 10 ,'./ •.•.•.• Langmuir isotherm fit (small cages) o 1/ o i o 10 20 30 40 50 60 Pressure [bar]

Figure 7: Filling of the small and large cages of CO2 clathrate vs. fugacity and pressure. Clearly the fitted Langmuir constant is not a good representation of the data. 382 Chemical physics ofair clathrate hydrates are given as a function of pressure in Fig. 8. the cage filling which may take very long Considering the geological times cales of the times and in fact may never be achieved pressure increase in ice sheets one can safely even on geological timescales. The assume that the filling behaviour is compressibility of type II N2-clathrate following the isothermal, and not the hydrate was found to be distinctly smaller isosteric, pattern. However, there is good than of ice at the same temperature [24]. evidence that this is not true in laboratory The isothermal compressibilities of N2 and experiments for times cales of hours and air clathrate hydrate are very similar. days. Information on the expansivity and 2.4 Other properties compressibility may be obtained from the The elastic constants of air hydrate, or temperature and pressure derivative of the any other type II clathrate hydrate, are not unit cell volume as obtained by neutron known in any detail. Whalley [29] has given powder diffraction. The thermal expansivity arguments to suggest that the elastic of air or N2 clathrate hydrate was not properties for ice Ih, a type I and a type II measured in detail; however, it can be clathrate hydrate are not very different. assumed that it is somewhat larger than for Reliable information on compressibilities ice Ih and similar to other clathrate hydrates were obtained from diffraction experiments [27, 28]. It should again be noted that there (section 2.3 above). is a difference between isosteric and isobaric The static permittivity of clathrate thermal expansivity. At low temperatures hydrates is generally smaller than that for the measurement of true isobaric thermal ice Ih. For example, N2 clathrate hydrate has expansivities need constant readjustment of a static permittivity of 61 at -40°C whereas

17,28 -t-_-'-_--L.._--'-_--L_-..1._--'_----''--_L.-_-'--_-'--_+

17,27 , • Air Clathrate N2 clathrate .' I • ...... 17,26 o,::C ... 02 clathrate I- ...... c ~:idc =- co 17,25 .....en c =*= 0 • () 17,24- I- Cl> () I B co • --l 17,23-

(a) I 17,22 - f-

0 200 400 600 800 1000 Pressure [bar] W F Kuhs et al. 383

5151 • N2 clathrate, experimental --fitted Birch-EOS 5148 A. 02 clathrate, experimental ,...... , (") 5145 ...... o~ (J.) E 5142 ::::l 0 > 5139 (J.) (J :::: 5136 c ~ :::::> 5133 (b) 5130 120 160 200 240 280 320 360 400 440 Pressure [bar]

5150 (c)

5140 ,...... M o~ ...... 5130 (J.) E ::J 0 5120 > (J.) (J 5110 :::: c :::::> N2 clathrate equilibrated at given pressure 5100 • --fitted Birch-EOS ... N2 clathrate at constant composition 5090 0 200 400 600 800 1000 Pressure [bar]

Figure 8: Lattice constants and unit cell volume ofN2, O2 and air clathrate hydrates vs. pressure. (a) Cubic lattice constants vs. pressure. (b) Unit cell volume and fitted Birch equation-of-state at low pressure. (c) isosteric and isothennal unit cell volumes and fitted equation-of-states. For a discussion see text. 384 Chemical physics ofair clathrate hydrates ice lh has a static pennittivity of 105 at the times less than that for ice Ih, which can be same temperature [30]. Likewise the high­ understood in tenns of a simple Debye mean frequency pennittivity is 2.81 as compared free path model [33). to 3.2 for ice lh. The relaxation time for water molecule reorientation, obtained from 3.2 Mobility and diffusion the maximum dielectric loss, is 180 Ilsec for The transport properties of the main N2 clathrate as compared to approximately constituents and defects of ice Ih have been Imsec for ice Ih, again at -40°C. The dealt with in a large number of corresponding activation energies of the investigations. Considerably less is known water molecule reorientation is 7.9 and 13.2 about these properties in clathrate hydrates l kcal'mor for N2-clathrate (at 120 MPa) and very little infonnation is available for and Ice Ih respectively [30). This suggests air or N2 hydrate. It seems likely that the that the local reorientation of water volume self-diffusion of water molecules in molecules in clathrates is somewhat faster air hydrates occurs via an interstitial than in ice Ih, yet the clathrate as a whole is mechanism as in ice Ih, with the additional less polarisable than ice Ih. complication however that the process will The refractive index of air clathrate depend on the pressure- (fugacity-) was measured on a natural sample from the dependent cage filling; little is actually VOSTOK core using a Mach-Zehnder known about the exact value of the diffusion interferometer as 1.3137(16) at 270.2 K constant and the activation energy. For ice [31]. This is slightly larger than the Ih the corresponding numbers are DWi (self­ (isotropically averaged) value of ice Ih at diffusion constant in ice Ih) ~ 5.6' 10-15 m2 similar conditions. The difference is S-1 and Ewh (activation energy for self­ sufficient to clearly identify, visually, air diffusion) ~ 0.56 eV at the melting point [34, hydrate inclusions in ice core samples under 35] (Dwi ~ 2.4· 10-15 m2s-1 at 263 K [36]). the optical microscope. The diffusion constants of N2 and O2 in air hydrates and ice Ih are not known from direct measurements and are too small to be 3. Non-equilibrium properties easily measured in a laboratory experiment. However, the latter may be estimated from 3.1 Thermal conductivity observations of the crystal growth in ice The thennal conductivity of clathrate cores from deep ice sheets. Some constraints hydrates is knO\vn to show an anomalous on the relative diffusion constants of air temperature dependence [32, 33], in that one molecules and water molecule diffusion in observes a decrease with decreasing air hydrates were established by modelling temperature. The experimental data show no the clathrate growth from air bubbles in ice strong dependence on neither the structure sheets [37] (section 4.2 below). There are a type (I or II) nor the guest species. The number of indications that the grain conductivities of air clathrates were not boundary diffusion of water molecules is measured; however, one may safely assume several orders of magnitude faster than in similar values to those measured for THF the bulk [e.g. 38]. Likewise, it can be clathrate (0.49 and 0.50 Wm-1K- 1 at 200 expected that the surface diffusion of water and 250 K respectively). This is several molecules for ice Ih is at least at this level. W F Kuhs et al. 385

3.3 Plastic deformation systems is a stochiastic process [e.g.4l, 42] The mechanical strength of type II gas and, correspondingly, a mathematical hydrates is not known; however, it is likely similarity with the process of radioactive to be similar to type I gas hydrates, for decay exists. If this holds true then the time which some information is available [39, 40]. lag between reaching the thermodynamic In contrast to polycrystalline ice Ih which conditions for stability and the actual onset exhibits sharp yielding, subsequent strain of nucleation, referred to as the "induction softening and steady-state flow, the creep time", is unpredictable for a given sample. curves of CI-L;-clathrate hydrate show In this case, the number of nucleated monotonic strain hardening up to over 15 % samples, from a total of No samples, is given of strain with a smaller temperature by: dependency than ice Th. The measured [39, 40] yield strength is 85 MPa at 200 K with N(t) = NO'exp(-At) a strain rate of 3.5 X 10-4 s-I. Thus clathrate hydrates are likely to behave as rather rigid where A is the nucleation rate. The mean units when embedded in an ice matrix induction time "t (= 1IA) will depend on subjected to viscoplastic deformation several factors, like the amount of processes. supercooling or overpressure, the activation energy of diffusion of the constituents or the impurity content at the nucleation interface. 4. Growth and decomposition There is some evidence that the nucleation of air clathrate hydrates in ice cores may 4.1 Nucleation follow such a scheme. The coexistence It is generally accepted that nucleation region of air bubbles and clathrate crystals of clathrate hydrate crystallites is a difficult extends in general to several hundred meters process and, at least concerning the of ice in the so-called transition zone. This nucleation at an ice Ih surface, is not a well zone is equivalent to a time span of studied matter. Considerably more effort has approximately 30 kyrs in the VOSTOK core been devoted to the technologically more and approximately an order of magnitude important nucleation of natural gas hydrates shorter for the GRIP core. Such a difference from the liquid phase [6]. Nucleation at an in time scale may appear surprising at first ice surface requires gas molecules to slow but could well be due to the temperature down and attach themselves to the surface, difference. Lower temperatures, as ex­ as well as the subsequent enclosure of the perienced at VOSTOK, will affect gas molecules by surface diffusion or by a dramatically the surface mobility of water sublimation-condensation cycle of water molecules, thus hampering considerably the molecules. Several of those embryonal gas­ basic gas enclathration step of the nucleation. water cages of different size have to join Nucleation studies on natural samples by together in order to form a nucleus of a type pressurization in the laboratory gave upper I or type II clathrate structure; this process limits on the excess pressure needed [43, 44]. is shown schematically in Fig. 9. As the time scales of these experiments are A belief, widely held in physical several orders of magnitude shorter, in terms chemistry, is that nucleation in some of the rate of pressure increase, care must be 386 Chemical physics ofair clathrate hydrates

desorption adsorption lateral sticking at \, diffusion partial cages • .---. ~ (j) ice Ih (J) ice Ih

cage closure clustering of cages to form nucleus

, /\\ water molecule ,// \ ~iffusion /\/\/\/\ ~ -\itJ\itJ\JtJ\itJ ,5/ ice Ih

Figure 9: Basic steps for the nucleation of a clathrate hydrate crystallite on the surface of ice Ih. The figure is rather schematic as no details of the molecular mechanisms, the involved energies or rates are known. taken when transferring these results to the bubble interfaces multinucleation will actual process in ice sheets. probably occur as soon as the stability field While it is certainly true that many air for clathrate hydrates is reached. The hydrate inclusions in ice cores are resulting polycrystalline aggregates may monocrystalline, there is recent evidence mechanically separate at later stages by [45] from the top of the transition zone of plastic deformation processes of the ice in a the NGRIP core that some inclusions mechanism similar to boudinage (see also initially form as a polycrystalline aggregate. section 3.3 above). This seems to be somehow in contradiction to the stochiastic nature of the rather 4.2 Growth difficult nucleation process, but may find an The growth of air clathrate hydrates explanation in a local, structurally faulty ice from air bubbles and the later hydrate re­ matrix or high, local impurity contents, thus growth has been studied in a number of rendering a (multi-)nucleation process much papers through laboratory experiments and more likely. In fact, at highly faulty ice- theoretically[46, 47, 48, 49, 50]. A W F Kuhs et al. 387 schematic representation of the initial distribution of air constituents In a zoned growth process is shown in Fig. 10. crystal [ 14, 51], and on the other hand It is now generally accepted that, after possibly to some kinetic fractionation due to a sometimes rather long induction time (see the different diffusion coefficients of N2 and section 4.1 above), the growth process itself O2 in ice [15]. Oxygen seems to be enriched is rather fast and mainly limited by the in the hydrate leaving nitrogen enriched air plastic deformation of the surrounding ice bubbles. In addition, due to the Gibbs­ matrix; this process is necessary to maintain Thomson concentration difference in the the dropping bubble pressure at the growing vicinity of air hydrate crystals of different interface at least at the decomposition size [47], there seems to be a preferential pressure. A detailed growth model was growth of larger crystals on the expense of developed on the basis of rheological and smaller ones. Microscopic observations have diffusive properties of the ice-air hydrate revealed that the presence of air hydrate system [37]. There is some evidence from crystals hinders the grain boundary laboratory experiments on natural samples migration of ice crystals thus influencing ice that the growth in a bubble takes place recrystallization [52]. From such crystals at mainly at the interface of gas and hydrate grain boundaries, the surface energy of air (and not at the hydrate-ice interface). Thus it hydrate crystals can be estimated and is of a seems that the diffusive transport of water similar magnitude as that for ice Ih [53]. molecules through the clathrate is more Attempts have been made to correlate the effective than the transport of air to the number occurence and size distributions of hydrate-ice interface. Nevertheless, the hydrate crystals to the climatic conditions in diffusion coefficient of water in air-hydrate which the surrounding ice matrix was was estimated to be one order of magnitude formed [50]. Clearly this undertaking is not smaller than the one in ice [37]. The latest an easy one. In order to reveal details of the estimates of the air diffusion coefficient in initial conditions, one has to understand all 21 2 1 ice are in the order of 10- m s- with O2 steps of the (trans)formation processes. diffusion approximately 2-3 times larger While there is good evidence that the than that for N2 [15]. Likewise from number concentration is higher during cold experimental observations on hydrate climate stages, other points remain growth and model constraints, it was unresolved. Open questions, for example, deduced that the diffusion coefficients of gas concern the amount of air dissolved in slip molecules in air hydrate crystals are, at least, bands or at grain boundaries (which may two orders of magnitude smaller than those explain the discrepancies between the in ice [37]. measured amount of air and the estimate Even after completion of growth and from the number and size of the clathrate consumption of all free gas in a bubble there crystals [50]) or the influence of various are, it seems, further re-growth processes impurities on the transport properties of the taking place which exchange constituents constituents. within and between different neighbouring air clathrate crystals as well as neighbouring gas bubbles. These processes lead on one hand to some homogenization of the 388 Chemical physics ofair clathrate hydrates

single nucleus polynucleation

alf

Ice Ice / x \

H20 surface diffusion H20 bulk diffusion \ /

single crystal polycrystal

Figure lO: Schematic picture of the clathrate growth from an air bubble, The growth starts either with a single nucleus or nucleation occurs at several places at the bubble-ice interface, Concentric growth (r,h,s, of the diagram) is often observed in laboratory experiments possibly linked somehow to multinucleation, Linear growth (Lh,s, of the diagram) should be prefered when a single nucleus is fonned, The growth could take place either into the space of the air bubble or into the surrounding ice matrix, It is not known with certainty which of the directions dominate in the natural environment, however the mechanical relaxation of the surrounding ice will in all cases lead eventually to an approximately spherical clathrate hydrate aggregate, W F Kuhs et al. 389

4.3 Decomposition 5. Conclusion After core recovery, slow relaxation processes take place in the ice matrix This review certainly demonstrates that eventually leading to a loss of confining in several respects a deeper understanding of pressure and a subsequent decomposition of the chemico-physical behaviour of air in air hydrate crystals into "secondary" air contact with ice is not yet obtained. It is well bubbles. Storage at low temperatures slows established that the presence of air modifies down the process considerably and the habitus of growing snow crystals [57] at temperatures < -50°C are advisable [54] pressures far removed from the stability for storage of clathrate containing samples field of air clathrates. Thus the interaction of over many years. On the other hand, air with the surface of ice is clearly decomposition within a few minutes is noticable even at low fugacities. The desired when analysing the gas content of interaction between air and ice takes place the cores. Milling techniques are used to initially in the falling snow, later in the snow analyse the CO2 content and it seems that and firn layer, and finally during core problems with retarded release of CO2 gas is recovery [58], and needs to be understood connected somehow to clathrate when attempts are made to reconstruct the metastability below the decomposition details of the paleoatmosphere and the pressures [e.g. 55]. The low temperature paleoclimate from ice core records. At inhibition mechanism of clathrate de­ higher fugacities, relevant to most of the composition is not known in any detail. The questions discussed here, the situation existence of metastable gas hydrates has becomes even more complex. In most cases also been observed in permafrost regions it is still an open question how this and was confirmed in laboratory interaction takes place on a molecular level experiments [56]. One may speculate that at the surface and in the bulk of ice. More two processes play a role: (1) de­ data from deep ice cores will be helpful to composition, via gas release from the gain further insight into the processes taking surface, may be retarded, on a molecular place on geological time scales. The most level, for clathrate crystals covered in challenging task however is to connect these molecularily bound ice as the bulk diffusion field observations with laboratory ex­ of gas through ice Ih is very slow, and (2) periments as well as computer simulations local formation of individual clathrate cages on a molecular level. To build this bridge it (most likely pentagondodecahedra) at the ice will be important to establish and verify surface may bind gas in a physi-sorbed state. macroscopic and mesoscopic models based In the latter process different gases could on information of interactions at a molecular well behave differently; however, possible level. First steps in this direction have been fractionation effects of the air constituents made by several groups and others are to due to preferential adsorption at the ice follow. surface are presently not understood in detail. 390 Chemical physics ofair clathrate hydrates

Acknowledgement 13. F. Pauer, J. Kipfstuhl, and W.F. Kuhs, Geophys. Res. Lett., 22, 969 (1995). The authors thank Drs S. Kipfstuhl, F. 14. F. Pauer, J. Kipfstuhl, and W.F. Kuhs, Pauer, A N. Salamatin and H. Shoji for Geophys. Res. Lett., 23, 177 (1996). helpful discussions and the Institut Laue­ 15. T. Ikeda, H. Fukazawa, S. Mae, L. Langevin/Grenoble for granting beam time Pepin, P. Duval, B. Champagnon, VYa. and financial support. Part of the work was Lipenkov, and T. Hondoh, Geophys. Res. supported by the Deutsche F orschungs­ Lett. 26, 91 (1999). gemeinschaft (grants Ku920/3 and 16. T. Ikeda, H. Fukazawa, S. Mae, T. Ku920/4) and the European Commission Hondoh, and c.c. Langway, Jr., J Phys. (contract N° ENV4-CT96-5048). Chem. B, 101,6180 (1997). 17. B. Chazallon, G. Champagnon, G. Panzcer, F. Pauer, A Klapproth, and References W.F. Kuhs, Eur. J Afineral., 10, 1125 (1998). 1. S.L. Miller, SCience, 165,489 (1969). 18. W.R. Parrish and J.M. Prausnitz, Ind. 2. AJ. Gow, H.T. Veda, and D.E. Garfield, Eng. Chem. Process Des. Devel., 11,26 SCience, 161, 1011 (1968). (1972). 3. AJ. Gow, J Geophys. Res., 80, 5101 19. J. Jhaveri and D.B. Robinson, Can. J (1971). Chem. Engineer., 43, 75 (1965). 4. AJ. Gow, and T. Williamson, J 20. L. Chaix, J. Ocampo and F. Domine, C. Geophys. Res. 80,5101 (1975). R. Acad. Sci. Paris, 322, 609 (1996). 5. H. Shoji and c.c. Langway, Nature, 21. D.W. Davidson, S.K. Garg, S.R. Gough, 298,548 (1982). YP. Handa, C.I. Ratcliffe, J.S. Tse, and 6. E.D. Sloan, Clathrate Hydrates of J.A Ripmeester, J Inclus. Phenom., 2, Natural Gases, Marcel Dekker, New 231 (1984). York, 1998. 22. D.T. Bowron, A Filipponi, C. Lobban, 7. M. von Stackelberg and H.R. Miiller, Z. and J.L. Finney, Phys. Rev. Lett., 81, Elektrochem., 58, 25 (1954). 4164 (1998). 8. T. Hondoh, H. Anzai, A Goto, S. Mae, 23. Y Yamamoto, T. Komai, and A A Higashi, and c.c. Langway, J Inc!. Wakisaka, Rev. High Pressure Sci. Phenom., 8, 17 (1990). Technol., 7, 1150 (1998). 9. J.H. van der Waals and J.C. Platteeuw, 24. W.F. Kuhs, B. Chazallon, P.G. Radaelli, Adv. Chem. Phys., 2, 1 (1959). and F. Pauer, J Inclus. Phenom., 29, 65 10. H. Shoji, and c.c. Langway, Jr., J (1997). Physique Cl, 551 (1987). 25. W.F. Kuhs, B. Chazallon, A Klapproth, 11. A van Cleef, and G.AM. Diepen, Rec. and F. Pauer, Rev. High Pressure Sci. Trav. Chim. 79, 582 (1960) and 84, Technol., 7, 1147 (1998). 1085 (1965). 26. J. Munck, S. Skjold-Jorgensen, and P. 12. J. Nakahara, Y Shigesato, A Higashi, Rasmussen, Chem. Eng. SCi., 43, 2661 T. Hondoh, and c.c. Langway, Jr., Phil. (1988). Afag. B,57,421 (1988) 27. J.S. Tse, J Physique Cl, 48, 543 (1987). W F. Kuhs et al. 391

28. J.S. Tse, W.R. McKinnon, and M. 42. TW. Barlow, and A.DJ. Haymet, Rev. Marchi, J. Phys. Chem., 91, 4188 Sci. Instrum., 66, 2996 (1995). (1987). 43. T Ikeda, T Uchida, and S. Mae, Proc. 29. E. Whalley, J. Geophys. Res., 85, 2539, NIPR Symp. Polar Meteorol. Glaciol.,7, (1980). 14 (1993). 30. D.W. Davidson, Clathrate Hydrates in 44. T Uchida, T Hondoh, S. Mae, P. Water: A Comprehensive Treatise, Duval, and V.Ya. Lipenkov, Ann. Vol.2, pp.115-134 (1973). Glacio!.,20, 143 (1994). 3l. T Uchida, W. Shimada, T Hondoh, S. 45. S. Kipfstuhl, F. Pauer, W.F. Kuhs, and Mae, and N.!. Barkov, Appl. Optics, 34, H. Shoji, Submitted to Geophys. Res. 5746 (1995). Lett .. 32. R.G. Ross, and P. Anderson, Can. J. 46. T Uchida, T Hondoh, S. Mae, P. Chem., 60, 881 (1982). Duval, and v.Ya. Lipenkov in Physics 33. M.W.C. Dharma-wardana, J. Phys. and Chemistry of Ice (Eds. N. Maeno Chem., 87,4185 (1983). and T Hondoh), Hokkaido University 34. M. Oguro, T Hondoh, and K. Azuma, Press, Sapporo, 1992, pp .121-125. in Lattice Defects in Ice Crystals (Ed. A. 47. T Uchida, S. Mae, T Hondoh, V.Ya. Higashi), Hokkaido University Press, Lipenkov, P. Duval, and J. Kawabata, Sapporo, 1988, pp.97-128. Proc. NIPR Symp. Polar Meteorol. 35. T Hondoh in Physics and Chemistry of Glaciol.,8, 140 (1994). Ice (Eds. N. Maeno and T Hondoh), 48. T Uchida, P. Duval, V.Ya. Lipenkov, T Hokkaido University Press, Sapporo, Hondoh, S. Mae, and H. Shoji, Mem. 1992, pp.481-487. Nat!. Inst. Polar Res., Spec. Issue, 49, 36. K. Satoh, T. Uchida, T Hondoh, S. 298 (1994). Mae, Proc. NIPR Symp. Polar Meteorol. 49. T. Uchida, T Hondoh, S. Mae, V.Ya. Glaciol., 10, 73 (1996). Lipenkov, P. Duval, J. Glaciol.,40, 79 37. A.N. Salamatin, T Hondoh, T Uchida, (1994). and v.Ya. Lipenkov, J. Cryst. Growth, 50. F. Pauer, S. Kipfstuhl, W.F. Kuhs, and 193, 197 (1998). H. Shoji, J. GlaciO!., 45, 22 (1999). 38. S.S. Johnsen, H.B. Clausen, J. Jouzel, J. 51. F. Pauer, J. Kipfstuhl, and W.F. Kuhs, J. Schwander, A.E. Sveinbjomsdottir, and Geophys. Res., 102,26519 (1997). J. White in Ice Physics and the Natural 52. T Uchida, S. Mae, T. Hondoh, P. Environment (Eds. J. S. Wettlaufer, J. G. Duval, V.Ya. Lipenkov, Proc. NIPR Dash, and N. Untersteiner), NATO ASI Symp. Polar Meteorol. Glacio!.,7, 7 Series, 56, Springer, Berlin Heidelberg (1993). 1999, pp. 89-107. 53. T Uchida, S. Mae, T Hondoh, P. 39. L.A. Stem, S. Kirby, and W.B. Durham, Duval, v.Ya. Lipenkov, Proc. NIPR SCience, 273, 1843-1848 (1996). Symp. Polar Meteoro!' Glacio!.,7, 1 40. L.A. Stem, S. Kirby, and W.B. Durham, (1993). Energy and Fuels, 12,201 (1998). 54. T Uchida, T Hondoh, S. Mae, H. Shoji, 41. M. Baldwin, and B. Vonnegut, Rev. Sci. and N. Azuma, Mem. Nat!. Inst. Polar Instrum., 53, 1911 (1982). Res., Spec. Issue, 49, 306 (1994). 392 Chemical physics ofair clathrate hydrates

55. M. Anklin, J. Schwander, B. Stauffer, J. 57. W. Beckmann, J. Cryst. Growth, 58, Tschumi, A. Fuchs, J.M. Bamola, and 443 (1982). D. Raynaud, J. Geophys. Res., 102, 58. M. Bender, T. Sowers, and VYa. 26539 (1997). Lipenkov, J. Geophys. Res., 100, 18651 56. E.D. Ershov, and V.S. Yakushev, Cold (1995). Region SCience Technol., 20, 147 (1992).