1985ApJS...58..493L lized As of distinctive in interest haps methane solar great © Tucson, THE t~ 1985. Clathrate 1 solid the a Contribution Now ASTROPHYSICAL Sciences, by means system interest The Pluto condensed Arizona. bodies in the at American conditions At clathrate (independent comparable and conversion CO-to-N 15% in measured Subject high-pressure have shrink satellites suggested speculation aggregate clathrate dances accreted atmospheres described. gas thermodynamically the may open the The © Lunar THERMODYNAMICS the California low of in inclusion has hydrates atmosphere is in Platteeuw ammonia American owe been number under possible incorporating innermost thermodynamic Astronomical part exaniined, the terrestrial lattice pressure, in arisen headings: and 2 as is JOURNAL ~rom phases as as by experiments their ratios applicable Titan's T-P The predicted, stable clathrate. on back Institute conditions because or clathrate. clathrate. Planetary I. 4068 and of Galileo are of nebulae for structure (1959) (relative a importance the INTRODUCTION higher existence stability molecules temperature) by high-pressure Society. in solar dissociation of icy and molecular SUPPLEMENT two of throughout to water-ice icy and Astronomical atmosphere implications of primordial appropriate of clathrate-bearing the WITH large the regions water in of solar Double to Division satellites. and Laboratory, reasons. around Technology, All composition At using and propensity stability it The well Division to of volatiles, solar the field rights clathrates. moderate is on quantities existing water) of the system of observations processes- kinetics and outside Jovian compounds concluded SERIES, of APPLICATION the Titan, reserved. pressures of OF the other occupancy system and of clathrates giant JONATHAN Titan First, volatiles ice stability Titan are of of Geological It conditions, clathrate Pasadena, University interior CH properties is they Geological clathrate studies. temperatures of forms CLATHRATE is this experimental 58:493-531, gas pressures, atmosphere Received planets chemical also Printed the Triton, constructed, Society of of Second, if 4 problems, argued CO would planetesimals N conclusion have at and/ and volatile that stability clathrate planets: to in of predicted 2 of in cages and Planetary and in of low I. California. to was Increasing with of U.S.A. 1984 test hydrate the but clathrate and partition essentially Oberon- and CH LUNINE which of have or potentially been incorporate that species. such the Arizona, refined 1985 temperatures accreted • stabi­ outer using probably the June gases increasing clathrate Plane­ if 4 TO N field data ~ per­ atmospheres- , and phase ABSTRACT Provided formation 2 decomposed, the nonsolar for of 320 as July N under theory a is HYDRATE 29; sometime fluids 2 2 THE and cages functions Sciences, a on application calculated , observed the 493 AND complete K accepted statistical diagram as and important properties not Rhea-sized containing, (independent in origin the clathrate. and animonia low-pressure composition clathrate observation. observational intermediate ties. which a atmospheres, and day clathrate formation interiors tions all by or DAVID OUTER but is possibility, is clathrate mixed in California In by of calculated H hypothesis 1985 solids after its (Langmuir also atmosphere perhaps Platteeuw carbon the well-constrained 2 for of under planets: clathration this these of mechanical the to the predictions AT and January J. surficial amounts outer of methane of interest The exaniined, planetary CHc the icy concentration. formation paper is STEVENSON outer as SOLAR Institute relative NASA clathrate large CH cases a LOW enhancement of of of allowing renewing pressures satellites, predicted early (10- wide relative guests, and and satellites techniques solar that pressure). 10 (1959) 4 these constants) N clathrate planets methane of we of icy in with 2 clathrate theory to of 12 applied is of range high Titan AND Titan to formation. water clathrate nebula; contact Astrophysics much which and satellites. extend presented. Technology compounds hydrates SYSTEM originally to solar H molecules incorporation buoyant to noble a interest N and (1 2 for 1 ( single, 2 and These developed predict of The hydrate atmospheric composition atmospheric it ~ to have, may and on bar) is ice for to of is is HIGH hydrate system (2) 10 temperature is with pressures 10 comets a due gas Titan their the tied used could effect 3 the hydrate CO The plausible and statistical in suggested clathrate 2 regimes methane have physically The 1 results for developed bars) bars) similar the to case a abundances on their under as satellite's clathrate satellites goal their solar studies. to in is the by PRESSURES probably of bombardment have of noble formation outer much incorporated Data given. pressure the of argue obtained thermodynamic imply animonia van noble is ~ first of of models incorporated a components. and to composition to mechanical giant-planet 12 that, occurred presence reasonable wide calculated; this gaseous solar gas by der as rise. These CO. (hydrate) may System time, A methane pressure for kilobars gases that did possible will paper van Waals list under relevant abun­ conditions range in for Brief system is high have The not made (1) the include be of of in in nebulae, of in to is der primordial is model model of present­ formed, directly proper­ to bodies Waals to direct situa­ treat and the the of in of 1985ApJS...58..493L compounds components hydrate which probable prediction predict of environment clathrates difficult likely gassing to stability effort CH occur in literature; incorporate however, tions high-pressure beyond proto-giant study several system sional additional of dealt models pertinent structure large implications in III Although nitrogen well pressures, planet pressures. sections clathrate our clathrate confusing clathrate resolved ventions satellites clathrate clathrate the 494 The Because clathrate formed CO, laboratory clathrate 4 the presents important complete as with of will in if and satellites of no gardening. Pluto. objects previous plan of an for substantial processes. former. ice problem the higher-density, of to comets, many by this clathrate formation. formation. for (i.e., primordial and thermodymamics hydrate literature laboratory compounds our be Section in for almost for and these the important H two the considerations © calculate the particles clathrates clathrate experiment scope or in planets the of is 2 themselves. the useful for the scope Section ( stability the giant-planet the , data American the results will results regime nomenclature not > circumstances, the properties also such areas the applications This the applications; the statistical paper. but of 5 presence conditions the first Approach "host" V no in hydrate We be of kilobars) always on from double to presence has on clathrate In Section analyzed. thermodynamic uses latter paper or environment than data the thermodynamics as may and the given VI that the molecule laboratory current at are time for other for is fields clathrate § also the planetesimals and not We higher-temperature Titan IV a high addresses abundance directly the molecule). The lists presence present in on and intended which have which approach and consistent, up solar atmospheres. mechanical of by and here. Astronomical is to occupancy stability deal, we been VII workers theory. will of to to clathrate of used results of the formation the we make an including to the as pressure composition We model itself evolution solar formation and calcuiate cosmochemically equilibrium kinetics constraints implications both applies composition ammonia-water properties Application deal tens data water hope, previously follows. primordial for clathrate relevant ammonia-water few outstanding paper. in in find the of the given Triton, Hence, to in system of of the clathrate the large to being properties methane undergo the of almost we stability in allows or ammonia model are problem of the and results volatiles be the that also, the full ice which the kinetics the Section kilobars their of We establish of first in no clathrate Section to icy field yet available and incorporated results the problems. and is a must forms various formation bodies and the phase clathrate disequilibrium equilibrium § attempted nebulae for gas Society to that solar exclusively are the used data us uncertainties models. extensive III more poor more satellites). time, have and and exist. term occurrence relevant who of formation of incorporated solution, satellite in VIII evol1,1tion and at and perhaps LUNINE working of to interiors literature to the be solution of diagram kinetics II some the nebula formation to for a molecular exist, yet moderate the concrete; cages probable clathrate clathrate pressure. calculate with desire clathrate We previous at explores make hydrate gaseous one present applied reviews Section reviews around predict condi­ lattice in which • to colli­ these solar pure with con­ may out­ into also The Provided the the the the for are by on be of to (a of of as of of AND in A is is a STEVENSON wliich pure eters occupied or dissociation occupancy, gas here. like ice 10% in into denoted molecules. the with by be possesses ployed determines determined compound 1967). extends cule illustrates of laboratory is quinol Davidson referred molecules. which molecules have present preferentially structure (1974), (1959). are on clathrates discussion larger Byk methane tabulated the tion treatment Clathrates The here Several by "mixed" the the Davy sufficiently clathrate dissociation pressure geometry is Davidson data, bigger voids, occupying case, cells the and assumed characterizing the molecules the clathrate, The the usual methane term in history understood An Hagan back study to as water in clathrate I cells by the including in corresponding and a good of Fomina the with in Two eta/. of The host, NASA clathrate, as of studies interesting clathrate in a 1811 by which each clathrate pressure defined (more stability of the can gas notation a the clathrates of geological to I hydrate, Davidson cage radius water with work form explicit are (1973), Pauling molecule of that chemical structural and the a guest pressure, reviews (1962), two (1984) both minds as the such is for be and hydrate statistical formed cage synthesis is is the by than (1968). geometry 16 guest in Astrophysics to the II; dissociation by "pure" preparation ice, all as structure hydrate still small very relative than example, at can Faraday formed. types used as molecule. II. the small mean is review e.g., to site Jeffrey Barrer of the van Marshall, and in demonstrate pressures of the primary molecules and and CH one in (1971). clathrate and formula exists, molecule (wX;(y,))X5~H be defined BACKGROUND types the to avoid recent literature, by the which I size is the cages mechanics Of ammonia to of which (only der Marsh and 4 characterized of fraction clathrate geophysical denote structure kind readers. of do van the occupancy from 20-28 structure form and clathrate in Figure denote and literature II quinol, of of particular clathrate but pressures confusing the Waals In 8 neutron not of a 1823 Although Saito, empirically "guest" guest clathrate for up one and the is clathrate, large der molecules substance of at (1952), smaller Edge the chlorine McMullan structure there the structure but Data a stable, to form that hydrogen-bonded the a Finally, hydrate. of included guest kind hydrate. 1, of (Jeffrey a clathrate consists six Waals will Russian given I and and 4 hydrate cages, molecule. mixed care up literature) clathrate 2 large available diffraction structure from (1967) hydrate are clathrate kilobars. as and molecule. by argon 0, importance a large. the hydrate which of System than and previous molecule). Kobayashi employ to Platteeuw clathrate clathrate, while other than bond as as there two I. where will temperature I a guest the heats Hence, and and guest cages. guest the The of (1967), Miller case, clathrate, stoichiometric many param­ the structures perspective the hydrate on and Structure 5.8 is parameters: latter be open, compounds are Occasional hydrate late I formation, chemically McMullan cage is are minimum somewhat molecule) Platteeuw organized gas of degree The results Y; inert the clathrate and molecule Data taken a A krypton workers avoided hydrate known, Vol. the (1973), will forma­ In to (1964) (1959) sixties Miller is single about water mole­ water guest cage­ form term term (em­ sites host first the the for gas use are the on 58 be of of in to II is 1985ApJS...58..493L early II Waals number work need but host (McKoy 1972; 1964; as dissociation inhibition This ments, No.3, studies Chen ferred cosmochemical assumed and electric taken tion within the tally, clathrate achieved of Barrer tween and between tetrakaidecahedron. Some Much the experiments FIG. a interaction otherwise Wilson noble hole, of cage, be type 1960s Holder, (1983), is using guest by to 1985 Nagata H by grains 1.-Structure are and and two fields fraction guest filled, work 2 and now to nearly that formation, less 0 Tester, Bertie which of gases theoretically of important © vertices. form (1963). molecules pressures prefactor much Platteeuw Edge infrared Sinanoglu the section. and within and and American has Corbin, attention outdated and modeling does and required between interest; complete of by and enters structure encaged Bivins, also along Tse, The work cage one all I (1967) Other agitating Kobayashi not most clathrate Jacobs the in and guests is in spectroscopy and small been of 1963; Klein, model by to the molecule since details guest has contribute 5f. determining grain is has adjacent cage, and clathration likely the studies occupancies measure guest Papadopoulos and I Astronomical Davidson cage employed partition (1982, that done hydrate As clathrate the been centered Saito, guest Herrick molecule Ar boundaries and and to of 1966; (upper because Barrer implied molecule, system, are involving cages motions in and the 1978, predict given diffusion lattice McDonald species degree Marshall, to THERMODYNAMICS and species in understanding the functions (1971) (Davidson center) Parrish calculation in on for (1972), the Kr a (see§ and and of above, 1977) apparently degree (after 1980). dielectric system to § in using guest have of can energy. the computer these the were X;. is of III Society the and Ruzicka the water and interaction III). Miller a and and Plummer (1983). long be magnitude gas appropriately For not Some pentagonal of molecules been to the surrounding of eta/. erroneously kinetics experimen­ parameters will Kobayashi thought rotational molecules Davidson Since Prausnitz ice. explicitly water measure­ structure calculate all exposing 1973). duration van simula­ of under­ be (1962) 1984). These • cages Both that and be­ der Provided de­ the dodecahedron Oxygen ice of of of of OF CLATHRATE atoms bodies. by problem (1979); fresh of of detail ing Thermal mal high-pressure rapid was high-density bars; solid gen in Dharma-Wardana taken rheology unique and clathrate terrestrial views by served evidence clathrate McMenamin tively Canada, A We Antarctic by clathrate a the with Claypool are conductivity measured sulfide Kvenvolden THF number compounds very ice uptake of in by implications detected the tum located occurrence study The 20 large the the § of and exists conductivity of compounds Ross to deposits ocean water slow VI. NASA clathrate. kinetics as now thermal a terrestrial HYDRATE the clathrate of ice which latter Alaska, of by (1980). at stability number and clathrate by guest and for molecules; (Shoji vertices; studies uptake, gas sediments Pinder has gas. of to and of Cook of is (1983) Kvenvolden clathrate Andersson clathrate Astrophysics for literature of water by conductivity also are molecules. been A and McDonald that are In clathrates Results and calculations and occurrence clathrate hydrate of have the hydrogen and hydrate (1964) recent satellites suggesting relevant 24 the available esrd acoustic measured the attempted and of molecules proposed as ice Langway heat water Leaist in been (one-fifth absence well Pearson existence describing tetrahydrofuran (1982) to review focused suggest phase permafrost (1983) atoms Some formation slurry, in capacity (1982). at molecules form of done as to as (1983) in will natural a low-to-moderate clathrate Data processes (Miller to 1982), identifying well per diffusional to Byk are of of existing data eta/. that on clathrate be with of on and explain h possibility the explore properties the considered shaking, and studies make an unit the presented and will physical as in environments. of System on the (1983). THF 1969) Kvenvolden predicted N western have ice Stoll time-dependent our wave above in (THF), Fomina 2 be up the clathrate best -0 the high-pressure was process. IH) were solar clathrate the explored and an to been given and and theoretical density 2 of properties low Although pressures below. followed clathrate evidence lie velocity. in large-cage 11 initially Siberia, includ­ natural system hydro­ under­ or (1968) Bryan on tenta­ terms of ther­ kilo­ cell. The 495 and Re­ ob­ line in in of A a . 1985ApJS...58..493L comets) later, Wilkening data ous determine dissociation istence ice which methane hydrate has hydrate presented sphere spectra sis scient outer clathrate ors, envelopes comets chemical detailed Delsemme modeled more mechanism van vapor stripping clathrate clathrate direct objects as Delsemme that to-methane tion liquid methane under existence cores clathrate McDonald methane tors rate bottom-simulating an for areas tions. 496 The In Application well of caps abrupt disks received der the terrestrial and is are addition to planet a Smythe the around detailed application of onto water at the application paper supported of extends in as could Waals derived pioneering in of existence determine in to was observations clathrate suggested interest clathrate composition. at gas. frozen of of hydrate to stability of (Shipley the gas by clathrate interstellar of equilibrium a (1978) the and and appropriate © 1982). a methane a temperatures Earth's decrease pressures for the ice at ratio satellites. the wide sporadic the Miller given temperature-pressure be cold (1975) The the time by American planet and (Shipley of of least, work detectability over Swings Miller clathrate from grains cometary present emitted sediments outer to clathrate world. by The to range in Lewis used of one in in formation association plate of Platteeuw et reflectors that in the w~ paper, by calculate (1973). atmosphere- a solar clathrate produced Titan (a) cometary al. by a atmospheres, and naturally carbon grains. for in clathrate Titan's 30 comets attention of methane Hunten (1970). during solar with planets, Miller (1952), part likelihood existing gas radicals of and not in atmospheres 1979) from The Delsemme year demonstrates a sound calculations as (1971) comets system halo carbon range Stanley solar hydrate and Astronomical the A and pressure low composition a of ruled per An dioxide model in as the is Didyk period reflectors compounds dissociation somewhat and atmosphere of The clathrate (1978) who surface a formation presence nuclei. and is formed predicted Saturn's production. still clathrate over a laboratory a as observed water system velocity updated could of set gas suggested studies the million likely are number special of dioxide Mars's out Smythe former regime 82 Miller properties guest proposed and hypothetical. (b) and in of composition clathrate 1982; gas the and also of occurrence showing now K that, This ice of the by explain laboratory are of clathrate cages. objects, his planets rings, of was the more by gas. past molecules with Wenger discussion the caused case clathrate on spectroscopically in form suggested polar temperature biogenic methane was (1961) stable produced literature. of evolving the derived (1970). clathrate available, methane data apparently own in condensing incorporation The Kvenvolden was primordial retrieval probably Society They resulting surfaces the ocean decade. to Although in detailed methane the that satellite of suggested data. spontaneously the caps, including and experimental on solar followed latter for of the comes LUNINEAND existence gas by in utilized (1970) presence reflectance Somewhat concluded origin; of the from gases clathrate, was an primarily observed clathrate clathrate clathrate sediment satellites gas. methane The methane Sill Martian frost comets, trapped adsorp­ cosmo­ the in A system that of argon­ due analy­ interi­ condi­ atmo­ reflec­ paper • water clath­ gase­ more from later pre­ as drill The first and and and Provided the the the the ex­ (in the by of to of of in of to a STEVENSON eta/. ever, improvements argon volatiles rate terrestrial because clathrate from clathrates clathrate outer from clathrate. Lunine clathrate. incorporated I Titan. Much making have haps water position spectroscopy sphere and evolution and tween of It is included Although weakly water molecule pact) precisely system composition cule-cage effects other gen Waals-like because to in It More by is Clathrate In energetically temperature, predict concluded reflection bonding Matson hydrate 1984). nonstoichiometric is giant-planet renewed NH this solar incorporate forms ice volcanism primordial water the and Owen recent (a is polar, and, important· clathrate consisting up recently, of in in a) thermodynamics 3 determined, phases anywhere of section derived guest the clathrate the noble strongly III. play NASA interaction krypton later the system the clathrate most icy (induced ice of hydrate Thermodynamic (1982) surfaces of dissociation 1980) work and now (Jeffrey interest in STATISTICAL spectra water stability attractive that pressure, lattice I the satellites. unfavorable a (Atreya, molecule on gas by spectral (and "hides" spacecraft envelopes) we of and clathrate, may from in role more the to raise repulsive of CLATIIRATE Astrophysics on guest and Rhea-sized renewed clathrates containing aside although the ratios. derived is describe ice. the dipole-induced in note and and their Stevenson its (Smythe bonding water clathrate is recent since, structure in have a rarely, regimes understanding clathrate clathrate the present and near Donahue, resolution high-pressure molecule term, distinct primarily as itself Stevenson rests atmospheres from McMullan determining must MECHANICAL that fractional The missions in the and relative N a the possibility been from term) relative although and the future. CH possess experimental 2 driver strongly FORMATION large more very satellites since mechanism 1975). no suggestion applications Earth. of would above Structural (1982a) is atmosphere stabilize 4 phase thermodynamic and hydrate outer any photochemically a component. distinguished and in and clathrate direct in well the Data (1982a) circum-Saturnian open on to abundance to the for occupancy dipole) ground-based 1967). The structure suggested Titan polymorphs-Gaffney the the polar studies of number the the In the indirect Kuhn MODEL of an not solar sum in the in as empty explosive calculated evidence cage satellites on the origin number Properties is utility System a distinguishing part ordinary that Titan's outer attractive usual composition result be chemical The is has hydrate multicomponent was the interaction. proposed of system. surfaces 1978). Saturn cage did FOR structures, likely cage II of evidence of this substantially core is and from usual solar that centered (more of guest accreted model the (Davidson of ammonia­ a not, that exists (and produced nonpolar, reflection gas water studying structure structure function effect may Striking van and cages Vol. derived system. species. overlap species. the system nebula that hydro­ in atmo­ clath­ mole­ how­ com­ com­ pure used per­ that and The be­ the for der the ice the N on 58 be of in of is 2 1985ApJS...58..493L pressure, been change clathrate its the modulus, by are of consider of The guest much rated tion component ature, dissolved clathrate Figure the tials degrees clathrate occupied nonpolar namically boundaries diagram clathrate dotted nent rate No.3, The FIG. the P entropy. pressure, clearly is system clathrate. 400~--,----,----~--~----~~,:--. 300 predicts coexisting (or referred 100~~·~·~··~··~··~··~·~···-··-··~··_··_··_···-·~--~~~ x. and molecule guest contingent lower). lines the guest kelvin. 2 1985 and 2.-Schematic phase Dashed is by stability stable -1 Gibbs species only preferred plots hydrate formation. at molecules of .... T. so qualitatively Gibbs guest representing ------both © entropy pressure molecule, (guest The species pure a Solid Consider, a since to it ...... With region a American given with qualitatively boundary We positive (since phases energies line on field mq_lecule in single follows component 0 negative, clathrate energy is relative line the the A······· and small increasing the use defined is in stable the change of diagram temperature, In is similar relative delineates the crossing the and water literature as are guest existence first, the x, value pressure water essentially this g, molecular to this of that vapor I vapor-liquid plotted .. LOG in (a) under x. Gibbs water where and (b) .·· guest the Astronomical accompanying by the for ice-liquid amounts ideal pf The the species .·· term water of temperature ;.:'> • an gas region host) clathrate water the stability ----0 N gas the of pressure phase ice as axis P low-pressure dTidP. diameters. 2 ambient is species) 2 energy increase dg -t;,\"' , water for gas log pressure ice-liquid equality or the (BARS) the only is CO, Clausius of values in much (A) in .... in = phase THERMODYNANUCSOFCLATHRATEHYDRATE ice liquid P ~'~-.... increased clathrate water which boundary regime, dissociation fields - the vapor phase (in the and and hydrate .. of is or The S 3 in .. conditions are plus the plus Note bars) clathrate less plus dT in 8 present pressure boundary; boundary. water of at negligibly and ,.., other coexisting clathrate liquid-solid liquid of for the separate Clapeyron Society phase regime a chemical pressure pressure + the coexisting change / clathrate vs. x. than formation x given /: by with V as volatile, low-pressure = Superposed is 4 n temperature dP) : : I net (with pure pressure I discussion. methane; decreasing a is 1: invariably formation ~ r: boundary ,: ,: ,: from space T, within in the in incorpo­ function thermody­ affected (B) temper­ volume of phases. hydrate, poten­ P. of slope favors compo­ which phase • equa­ mainly some bulk clath­ phase each 5 has We Provided the the are the of of in of interaction, weak. defined clathrates cage determined icy impurities interactions noble molecules recognized weak physical present. properties structure spectra substantial son (Fowler (Dharma-Wardana contribution action cancellation cupy crudely located relative (1925) components, compressibility data of change The The Figure mum the has to point" each gas A minimum would particular system (clathrate) creases later incorporation temperature molecule regime. and the Considering --+ emphasize the by ideal satellites. entropy attractive eta/. reached precise minimum volume. in B the section. temperature interaction cage pressure gases Even between the be 1', and clathrate becomes ( 2 the independent the to As pressure (e.g., as (clathrate structure Calculations and properties gas volume 1983) (and is and (see pressures in expected guest water are occupying decreases. seen critical sites pressure literature (van NASA :5 by it are literature sign the van with a is of regime, Guggenheim the a and at Theoretical from function 4 Strongly Davidson is the of part Jeffrey very potentially exists the lattice not pressure the secondarily in low observed very suggest of which inaccurate kilobars); and in Berkum and, (Jeffrey ice lattice residual stability zero der is ammonia is are change point --+ in below point more water guest the of 1983), of large dipole-induced-dipole consistent Figure due defining in enough Astrophysics may is required compressive low of guest+ value because are by calculated Waals which imperfections and At water hence, clathrate on and increased of the the dipolar the particular clathrate, that structure. exists here for molecule 1971; Davidson to detail thermal molecules as restricted be and and (i.e., fields a the and T,, from field McMullan 1960, important this although of guest-host ideal studies in 2. to given dT on clathrate encaged so2 molecule H coupling a these specific the cages and is thermodynamic there since experimental dT the to I McMullan clathrate think 2 result more Eventually Diepen with because in 0) Bertie the subject) are molecules different dP the phase such for 1 p. clathrate. domain and gas effects conductivity stabilize the coexisting guest temperature, and Platteeuw X-ray dP water, properties (1971) is = to 278) water) by of and sensitive exist the London CH nature favorable), of or this of guest volume regime, as the Data for 0, 1967 cage. is dipolar at energetically the interaction, host to and (1979) A diameter the at Tammann substituting the 4 predominantly species, cages primarily their sound being defining the stable. demonstrate diffraction is of guest both for evolution and and low-pressure the (guest+H 1967); lower indicate the apparently molecules; become the for This lattice guest form studies Jacobs controversial. and clathrate of high-pressure System dispersion pure 1959), are functions each lattice that properties fields and N is appear guest of volume guest responsible a maximum velocity is the clathrate then, and 2 and has long This deferred review pressures dipole-dipole to of molecules the the no a -10 is on in guest the dT with species. substantial of and 1978) important, within models first guest-host the maximum studies extremely favorable. for 2 structure, the since the § longer molecule molecule clathrate the 1 0) stability. a infrared we possible "critical can to a V. change dP volume end icelike A of lattice (Pear­ higher of forces of phase Krige water lesser inter­ maxi­ order guest well­ been to have wish than to The P- and end and oc­ the the are the for de­ the the the 497 At as of of of in T B a 1985ApJS...58..493L imposed molecules (1959) function cages both Ne, set circumstance, cal occupancy cules. independent ing Davidson Assumption molecules rodlike noted with undoubtably physically sis sensitive separate address freely ever, calculations developed adopted dent other molecule. tion the undistorted alized that 498 Van 1. The 4. Assumption 1Lk 3. 2. is of partition the accounting. but of the of one we 2 (a) Classical Guest The concentrated, are CH o- equations within studies above outline to kT der statistical assumption incorporation molecules, the this for will here species guest to that for The guest occupied 4 free IL~ (1971). in three similar but by of © Waals occupation this larger molecules problem and by 3 indicate see 2 function the clathrate of the in seems and guest o the the for is American energy van single b) statistics the molecule molecule 1 could the =- _ = assumption. error Assumption below from verified the dimensions. coexisting cage. H "dimer" Assumption chemical mechanical are Model says small v molecules to construction (1956) even by der 2 1 classical 2a, molecules presence to presence flp,P ln further cages ideal kT when a of of CH as for describing do a be that hydrate (and Waals be ( with that applies. finite guest for small 1- follows: incorporation guest this the per of 4 not large and in (CH adsorption valid our by Clathrate potentials and Astronomical phases moderate-sized both statistics LYlJ) in mode H A on cage. astrophysical molecule J of the 2b interact error Their are molecule. and model number 4 ones 2 and van molecules more 4 very the qualitative in 0 molecules of H which the ,H is based the is cage confined 2 lattice gases which (b) of the context be type not 2 + der Platteeuw in at such interesting valid guest ) explicit guest Formation than is occupation) v for must with of equal. in onto 2 Guest our the configuration into valid of low structure generally Waals on The ln of are structure both ice a as such clathrate such for molecule, conclusions statistical cages implications, one molecule quantitative ( of to each be spectroscopic guest other fraction 1- fixed clathrate temperatures N condition are The for assumptions present. molecules Society the the (1959) small 2 guest thought and possible molecule. as as LY other, J probably and H occupied molecules calculations. valid. cage is result sites, guest LUNINE of C0 is CH 2 21 Platteeuw formation , motion mechani­ relatively which and spherical y partition the indepen­ CO. He, ), assumes cages 2 4 In volume regard­ so is of ; of analy­ • gener­ rotate is viola­ • is mole­ guest how­ It then host as• Our that and and this not We (3) (2) Provided the (1) the the are for by in as is is is AND STEVENSON (1972) interaction molecular where (3) atoms depends cages. will phase. exerted and discussed where based (3) for 1,2 a example, degrees cule discussed located in In tials the partition small species 3/23; clathrate coexisting constant, Holder, tween temperature. where number 1969, where pressure, system = reference The McKoy The In spherically its by the explicitly is last by the use for IV, in general the pure cages, p. t(T, the the empty The vary the low-pressure derived flhP, on V molecule C; for quantity term p,~ j a spherical of temperature to Corbin, free the by on 5) of 1 three is ratio function Davidson and as in§ vertices as and distance structure, 2 properties the phase, and determine phase freedom are NASA largest 0 at structure the between in the cage P) flVP temperature. the in cage respectively. they assumes =chemical If molecule, we averaged reference V. k distance of expressions above (T, called equation simplifications volume = Society potential centered radius here; Note der x(- guest Z we minimum, between = 0, p molecule recover zero Waals number (1960, 1 = that rather fn of molecule, )n a 1954, shortest fixed and (20 on closest is initial • when (L-J) guest for­ and and (7) pp. (6) Provided the the we for gn p. of at is (1980) change; of do 1972), dissociation mate below study, spectral studied ature instead, I I Prausnitz Kihara We tunately, methane mole- tures thermodynalnic probability pressure structure (using chelnical coexisting derive or of on or attempt others clathrate clathrate Prausnitz Robinson We temperature tion sure for also abundance the T parison (Marion are <«1. regime. and Table Of In We For we clathrate by (8), not flp,P clathrate the system. a use will power will pressure regime evaluating from that range. single equal This compute 1 now along laboratory the we but a the exist. structure predict terminating flp,P- or dissociation over at our data between this it is has then be given and clathrate. 1970, 1 data in In has I (1972) potential (1964) conclude use liquid has 273 Lennard-Janes for ice large van series flp,P gives NASA lists 273 fit used relations of Application plausible is results the at will pressures to been concern with range. species We a Molecules on been in for c) use 310 the on the which discussed finding been point, choice K, temperature pp. derive temperatures der an the liquid-water to equation coexistence intermolecular the and data increases and be to water adopt Choice structure Cij(T), derive II species in sources librational values these based made above latter increase called Since 70 Waals 542-543). cal integral predict in Using the important between Astrophysics derived flp,P (dja) clathrate guest pressure Holder, j, laboratory between dominated on is of nebular in values § K; the should or a equations integration mole- parameters 211 VII of listed the on to parameters of in value. for equations the which constant Giauque (1) j. into and of ice decreases and Plateeuw Holder, parameters molecule, the I Molecular molecules 2 the -15% calculate § equations the in To range of by laboratory and cal temperature with to existence field fore, a flp,P; Corbin, vibrations below phase, included V. the The be models. 1 in Debye for question for calculations (Johari them equation choice under stability 27% For predict bromine several solve translational authors mole data based II by the good empty an the (1) from sufficient see quantities guest flp,P Corbin, and p, to at Langmuir to structure that must by e, the exp must for this low-pressure and - ammonia-water Parameters Data model for are of "substantial (1)-(5) temperature and, included and such existing of a below) Our 1 predict to and laboratory to Pm• the of . (Parrish data on in Stout in (3) (1959) 273 value ice-to-liquid - clathrate. disagree. [- structure flp,P, available a molecules several clathrate scant from Papadopoulos(1980) be dependence allow within clathrate the be the (2) 6% structure where derived composition c, and that cyclopropane using w(r)jkT], Chew System of to made. and frequencies to ff(d) to II, and for applied low-pressure the (1936), constants. in§§ the are clathrate laboratory for r first solids, allow suggest or in Papadopoulos accurate 70 the and Prausnitz the guest such Sortland 10% their necessary, the difference equation nonexistent. temperature studies. Parrish dependence dissociation in calculations Parrish then I the both 1984), data" lattice parameters To under K. principles; similar calculated high-pres­ IV and and I over fitting the enthalpy dissocia­ solution. bromine infrared we at to that temper­ of date species, present 167 Unfor­ at solved lattice of struc­ in mod- fg(d) close data, com­ were data high esti­ flp,P that and and and and and and For 499 r the the cal ice ice (7) no V. in of to c. is 1985ApJS...58..493L hydrate structure which uncertainty several creases erate cules the restricted 500 For "little Ar Xe Kr CH C0 C2H4 N2 H Ne so co (4) 02 He H2······ PH (12) and Carmichael, 1965. Barrer hold temperatures in Species is 2 some by extrapolated 2 REFERENCES.-(!) S 2 3 ...... ······ ...... 4 Miller ...... structure outlined the Scheffer Byk is 1954...... temperature ... about and or © (9) stable in SUMMARY "some and molecules 1961. American no Edge dissociation Korvezee 13 and 1950. Fomina later. a (mixed data" is based (5) ( 1967. factor Reference Sage data" ~ not OF to (7) Delse=e 150 10 11 12 ranges, 1 2 3 2 1 1 2 1 4 5 GUEST Little 1 4 1 4 6 Substantial von 7 8 9 1 1 low 8 1968. Miller clathrate) 1952. (3) in category available. on laboratory and of Some TABLE K) category van Astronomical Stackelberg the pressure (T or 10. (13) (11) MOLECULES 1969. and Scheffer der No and Data < and table, Those 100 Data von Ta=ann I Waals Data required probably (8) Wenger We the have Temperature Stackelberg at K) van and 1931. data molecules and have dissociation ANALYZED consequent low 268.3-211.2 temperatures. Oeef been 148-90.2 202-149±1 111-82 272-269 240-163 207-173 232-175 271-265 273-250 272-247 1970. Muller and 298,274 273,267 Platteeuw special within on 273 273 273 273 273 (10) 238 273 273 272 temperatures 272 273 279 predicted Society and Krige (6) studied and Range the 1954. LUNINE listed Selleck, Diepen Diepen a Mein­ treatment, 1959. degree 1925. pressures clathrate factor (K) (2) which Mole­ under under • Provided in­ of of AND STEVENSON prepared fit quenched-in long These The which rectly water point, structure, structures stants strongly structure structure form, (Eisenberg cage CH fits approximate constants conclusions equation, clathrates CO any and data of chemical confidence can contrary corresponding composition 1984 ence. difference PH three what ual be sources effect condensing amorphous K, tions temperatures, temperatures ture those under fltLP the Table Data by !l 0.91 3 to condensation 4 water over presence be to our p.P case, calculations II to size, for performed as for We follows and parameters fits with of in (Miller the indicated molecules fit results H form of chosen nebular at form given for at the on model, preferred 2 having a 2 T potential to methane as which to assume I our the which S molecules using at assumes low Xe between interest are were H 100 a NASA range and lists amorphous and ice as in water a extrapolate Davidson if Ar, pressure structure guest slightly during 2 of structure 240 gas of in 1961). we form dissociation S choice secondary to as may structure low for either temperatures. the phase. K data Kauzmann condensation methane by dissociation amorphous Table II. the will less calculated is their Ar ice low be Kr, per in assume of of so of and into H vapor K by for molecule in true the as to amorphous determining physical Astrophysics be Using logP=A/T+B, cooling). what 2 structure and poorer same is temperatures, incorporation than ·water I well of as very points, S of Xe, cage. CH and X-ray 70 Table Using data I; 0.65 solar a 1. guest eta/. not II; conveniently itself ice that clathrate 82 for !lp.P to I, given these and gas. The forms Kr K. gas. 4 hexagonal follows over 100 and C0 the mixed but pressure divided K readily low the affected most and at 1969, fit This vapor for lead implies ice and molecule (1984). consistent =constant, system 1 is the to significance pressures for Note is We N when Below ability 2 The I 70 molecules set K; to conditions same we , large ice strongly 2 temperature and CH resulting substantially where Xe the be above each which cooled S0 maximum to to the neutron molecules dissociation is is predict K. p. force that of however, may discuss by and existence incorporate 4 below that based structure of structure 2 have by clathrate a data. 90), available," 100 done However, molecular CH to structure force , The water studies. Data utilized temperature clathrate molecule, that interaction C good both relevant. molecules 100 structure cage ice fit derived with parameters 2 where produce below two 4 suggest we and K H were essentially H dissociation structure diffraction of on This clathrate. the the is for any in parameters I 4 ice 2 K estimated neither of their pure System , calculate size approximation of , laboratory of sets I our our the smaller II controversial; by phase pressure and Also data He, low-pressure § (Davidson hexagonal interest as to II force but force 300 from changes procedure A,B extend 110 amorphous in from clathrate, high VII one has no or CO samples fitting fits. from a ability of the with form prefer Ne, ranges is (marginally) with either structure discuss cal shown metastable number was em, directly Below no change Langmuir K studies constants constants the preferred and preferred pressure. for are for the The than enthalpy the the pressure 0 data. individ­ here. in Vol. mole- a to prefer­ em, or two of condi­ in 2 to to use struc­ lower likely ice , gives solar CH eta/. were ratio both both each cage data con­ data best cor­ and and low 110 our Pm· the are the the the the ice ice 58 In or so of in to at in in is 4 1 1985ApJS...58..493L No.3, N2······ Ar. C0 phase S0 C PH Kr. Xe. H 1. Species 2 2 Values H NoTE.- 2 S. 2 3 ...... 4 • .••• . •.• ... •.. ... (see .. 1985 in text). 230 273 100 180 238 272 180 149 211 203 230 273 200 273 100 100 180 181 116 100 150 149±1 267 273 298 265 269 272 247 273 211 238 273 273 100 180 100 180 180 100 180 100 100 a(- 82 60 60 90 80 60 60 80 80 80 braces RESULTS T © b)= American for a OF X 145 CH 24.3 62.7 33.5 91.1 15.0 12.7 15.4 lO-b. FITS 0.419 2.39( 5.63 2.79(- 6.80 0.373 0.366 1.00 5.84(-2) 6.04( 0.958 0.210 0.290 0.296 0.968 0.316 1.44(- 1.62(- 1.06( 1.75 1.48 1.23 4.34( 4.66 5.12(- 6.37(- 6.73(- 5.03( 3.51(- 3.86(- 6.65( 6.34( 9.02( 3.83( 7.29( 7.66( 1.62(- 2.13(- 2.74(- 1.01( 5.23 2.72(- 2.79(- 1.12( 8.23( 4 assume TO -7) TABLE2 p -3) -5) -7) -7) -3) -10) -11) -12) -7) -12) -17) -11) -11) Pexperimental Astronomical 5) 3) 8) 8) 3) 2) 2) 2) 4) 8) 9) 3) 3) (bars) DISSOCIATION {1.60(- {1.26(- amorphous THERMODYNAMICS is 8)} 5)} data PRESSURES water from 141.5 25.2-26.0 61.9±0.5 92.5-95.5 12.5 33.7 16.0 14.5-14.7 P 0.405 5.65 2.10( 2.10( 0.97-1.0 0.21 0.29 0.342 0.351 1.38-1.45(- 1.11 1.0 1.6 4.78( 5.2-5.5(- 6.30(- 6.52( 0.298 0.919 0.307 1.15-1.5 4.70-4.72 5.25 2.04( Society experunental ice sources -7) -5) -3) -2) -2) as 2)±0.3(- coexisting 2) in (bars) 3) • Table Provided 2) OF CLATHRATE We parameters pressures fitted cules comprised rules ular few following the type pressures 10-10 of dissociation dence in in The literature, insignificant When virial Xe model regime, neon pressure based from for fits figure eters and course, quite guest-water Bird tions molecule, to to temperatures. molecules, numerical where species and atom; tion test tables We We this the size the Holder, no data by this use from cage; potential Ne, or McDonald pressures xenon out 1954, of (Prausnitz 1969, for (1)-(3) and will to similar. equations data 4 on illustrates large applied now indicates case; for guest-hydrogen based the first concern, the no from the portion laboratory and molecule the times which in in the our laboratory the helium, of from likely and manner: hence, equations of pp. and modeling of Kr unsubscripted laboratory structure Corbin, for are data so-called the use NASA collision used pressure. from known pressures HYDRATE molecule so changes clathrate argon We the interaction procedure and which on water is higher The our 1110-1112); to have is the w better 1983). structure the must of (9). dissociation experience our fairly pertain and that small He have virial two refers entirely using for argon a (7) two-parameter the study. unknown Xe data, data. computational and clathrate argon the smaller Using we molecules. Astrophysics II data. fitted diameter and geometric to (9) than or these in properly Since the pp. molecules which accurate, interaction Values established inserted pressures containing data shown (but cage, atom data to be (8). derive Papadopoulos mixing mixed characterize to we Pm to As between give II Ne, 63, parameters Kr data The those satisfactory the parameters tabulated gases structure we these much similar not collision model derive Because shown for are pressures derived which molecule dissociation are (e.g., 104): of interaction the results the water of are be are the results dissociation mean we I). Similarly and force Xe of rules fitted e, available. derived used along the are fit curves is guest less regarded as guest mixed predicting stance Our cosmochemical molecular p, employed to Hirschfelder, far dominates in types dissociation result with to lattice. compared diameters two-parameter I xenon Kr the extremely "reference and and Data e, validate Figure to compare refer in parameters from we to are important clathrate, the over with model (1980), to outside molecule p, Pm=-2-' in derive molecules averaged from both and Xe the of small pressure has shaped parameters hard-sphere care in c can known shown derive We Figure We atom, to those pressure as the interactions for System a data. 3, pointlik:e large parameters the pressures p+ is Xe been the structures argon the than the since fugacities. wide derive effective them and against the reason poor obtained take mixed the thus pressures the although and data" L-J Curtiss, Pw guest in (Tse, dissociation N of dissociation dissociation comparable intermolec­ 4 interest. This data em, changes pure correspon­ procedure. for 2 physically shown L-J Ar, result. ideal unknown Figure a cw the potential range not clathrate dissocia­ in with data the for Kihara param­ mixing similar em, oxygen for in results in which = is Klein, mole­ fits this Pw, equa­ exist. guest to main from valid from cage with 0 The and due 501 this Pm, {9) our the gas the are He the for To Of by be ew in to as of 3. is 1985ApJS...58..493L CO our cannot in however, parameters planet scant clathrate dissociation measured ters nitrogen. most !lJLf:J the ture weak. curve: formers, (top) dashed molecular molecular 502 We Figure the FIG. noble jT clathrate. procedure for II 0 C) .....J m a.. <( (/) 0:::: laboratory and abundant This next solar formation. model; Cis lines be dominates 3.- 0 because -18 4 parameters parameters. CO xenon the N gas dissociation 2 -6 -6 -2 shows said Temperature are © is derive 2 calculated nebula pressures an as 60 clathrate may case. molecular also The American to closer to (bottom) plotted extremely I for data constituent / their test the be Here have the carbon / the similarity e We (Lewis / 100 and H from result more to (about our / to P(T) dissociation interaction 2 vs. origin thus in / pressures clathrates. we been , N p be weight / and log procedure 2 to argon monoxide weak Figure and use // valid than for Astronomical of fit dependence. have 30% of in the in 140 KRYPTON of we laboratory qualitative H the a Prinn / clathrate dissociation function are any the of ( T predominant Solid 2 two-parameter for less too ....- with 5. , must from dissociation pressures and --LAB CO ....- those we linusual The and CO K) low) scenario STRUCTURE 1980); confidence lines ....-- 180 the data derive data Figure consider and those molecular interest agreement of than of REFERENCE ARGON is -- calculated cage for and assuming not pressures 0 H pressure T, shape Society hence form 2 mixed 220 2 the - 5 of 0 , is of and mixing would L-J as DATA the so 2 in --- only. LUNINE the two • exceedingly satellite good AS The we by of molecular of these n hydrogen pure result for fit with the parame­ clathrates; derived a adjusting carbon the for rules expect be 260 krypton to struc­ • same as term fits; L-J the Provided the for the N He or in for AND 2 STEVENSON into are even tion that and neon essentially van rates FIG. by (.!) 0 !D __..J a.. <( en a:: FIG. - !D en a:: <( - CO Cleef pressures CO clathrate, clathrates down predicted 20% the 4.-Dissociation 5.-Dissociation structure 6~--~----~----r---~----~~ and and coincident lower at NASA N Diepen predicted are T with from 2 = are than II slightly 60 with the (1965). theory. Astrophysics clathrates very K. from fugacity those pressure that tentative CO similar lower The the Cross for for structure vs. theory. N vs. are CO 2 than structure marks in temperature suggestion dissociation temperature striking, on their those this Data I 0 2 dissociation scale. ability II. data of within pressure for System We for that N at 2 helium, CO to thus • CO H a - incorporate and line factor 2 272 pressures conclude dissocia- dissocia­ H would 0 Vol. K 2 2 , of clath­ from and 58 2 be 1985ApJS...58..493L illustrate be (1983) loss dipole molecule ~P strongly clathrate comparable clathrate effect dipolar cage I molecule, this more that between [3]). field freedom and opposing dipole dissociation dom 1969, the procedure parameters T straightforward should 57) from additional clathrate on could clathrate cule. dipole dence dipole residual, ubiquity before serve (weak tion No.3, clathrate :=;100 Opposing The The = t; nonpolar strong of The situation, given Jacobs 2~H pressures dipolar and must We stable, that in p. as occupy expected of moment states ~P' energy 1985 doing may CO means be one weak field 64) any inhibited K. 20 in of net a the effect (i.e., at the cage dissociation present effects: fluctuating equation then raising "former." similar averaged of in dipole-dipole temperature for , qualitative be © suggests molecule astrophysical low or derived to the distinguishes For 1977). orient, the field. this pressure, effect event that and so Figure others. CO dipole guest estimated a lower American (Davidson of as that both are deriving that incorporated on z for cage temperatures to we encaged guest ~P < stabilization (1) the the interaction). noted for a plot dipole Infrared at only. dissociation extremely calculate. should 1 the a of If return (10) = over all restricting model molecules rotational from P' dissociation 5. that very already The but the low moment numerical interacts The similar dipole dissociation ~H a pressure molecule the indicator equation and The in dependence. single force differs interaction by 20 by we additional molecule settings it 1971), w(r) (- moment polar reorientation small experimental excitation always to Figure small for , spectra Astronomical from Boltzmann orientations, D. (2) Davidson in use molecules-hence, P' occupied The field high, CO 50-100 due constants water of of such the pressure. degrees Thus with is must includirig W. molecule would appreciably = nature factor the is at the that pressure) the CO a raises and size to interaction be accounted P CO pressure. 6 not may with is rotational of ~co low Davidson, somewhat attractive between double induction molecule. potential. the a down The necessarily nonpolar increased THERMODYNANUCSOFCLATHRATEHYDRATE the P'/P, of less K) clathrate H ethylene examine in spontaneously of variable by strictly (0.1 of of factor (1971) 2 the of oriented data. a for rotational be temperature and , is (Prausnitz equation with derived temperatures weakness the another H freedom CO than temperature by since the to possibility debyes; occupancy produced The 2 one the from CO for Society potential that degrees dipolar itself, in term a The To 60 appropriate implies force N and along oxide large the There stability guest to is cage that low our be 2 if ratio guest f;j nature first and in • examine values K. the guest be (10) effect Although it of interaction P degrees of of is lowers larger value generated bootstrap is the Prausnitz produces of structure averaged were value becomes revert Gurikov the with possible effect 1969, are the only term used roughly of another the that the that of by species should (Bertie a depen­ below; energy a of of • mole­ of force of poor free­ (10) cage of free (eq. two CO CO CO CO not Provided the for the the the the H an its its of to at of to to p. is P a e 2 quantity dipole-CO of tion is low !l !l ratio (Barrer ented divided moment positive, (Landau find rotating T calculated, ference data magnitude since 1964). tion. the E E :=;110 FIG. similar We However, the by with = = as freely that !lF of The the 180 CO-cage guest energy conclude 6.-Ratio the to In and P 0 dipole !lF by CO 6~0--~----,40~--,~80---2-2~0---2~6-0~ diatomic K it parameters of and induced may is but to, net cal is reality, rotating tlF=RTln is therefore. of 2w, NASA for molecule, Edge to between negative inertia the we but mole small field gained effect is interaction, the include Lifshitz N N of N= that probably dissociation 2 dipole can 2 less 1967) of molecule: CO -l effect clathrate the and state compared of Astrophysics cage. number of the in derived over the clathrate than, (clathrate i get some hindered interactions; situation = 1 = 1969, the ( because the plotted dissociation pressure from :=; nonrotating with ilk closer a spherically for 70 pressure h~ potential that dissociation of molecule, for of rough dissociation T) pp. with T(K} the K like, a the as cage rotation to of of stabilized chlorine is release -!lE-RTlnN for a 115 Helmholtz P' effects t. assuming cancellation N 2 the somewhat function measure Data have 2 sites CO. for includes molecule averaged clathrate. and h energy pressures pressures cannot of unlike, (Davidson =Planck's of been per Even by System of dispersion energy 132), rotational CO of of free unit temperature. hindrance) more of and adjusted of where be nuclei. for state CO dipole At the encagement could where energy terms. cell accurately (cf. two 1971 the 60 clathrate constant complex and possible by interac­ inhibi­ !lF (- models K Using freely Mazo be ), to (11) cage I= ori­ The dif­ 503 the for we 8), as fit is 1985ApJS...58..493L ing with directly its Platteeuw tion hydrogen where read where Hz. site ered, forced as of and anticipate cupation double cage Platteeuw Figure volume tion tial the with we square-well some qHM molecule two molecule 504 We Consider Evaluating exceedingly spheres large gas. have (Prausnitz 1969, by spheres, In of of q; LangmQir sites (writing -=F HzO the asymmetry 1 PM, now molecules Vcage qMH) a 7 to a calculating occupancy. due proportional Also, gives cage former guest gaseous VE,; illustrates of made is by (Anders i's occupy theory 1959); somewhat PH molecules © of a = fixed consider to collision the small we but d) out = molecule interaction the of for 4'1Tj3(a- the American are radius occupation molecule CH low 'IT{ the cage find because a in is Double nebula the i in simplicity, q; at volume the probability and structure other (a molecules «eM. the and adequate 1 Neon the Langmuir constants, the + somewhat p. particular, the = large-cage to the the by - partial diameter in a- a? Ebihara importance with 109) 0 results intersection. j. ~ the in center regions Occupancy ~) of [ around molecule by the result with ) possibility and of Note j ~ Equation by 3 clathrate 3 its [ Astronomical I Langmuir relative in -cos we for assumption. ~ pressures (suggested the clathrate, and cage, is i, of for helium low the molecule 1982) -cos artificial of methane-molecular that that term given for use our the the in region double two 8 u;. the j model solar of 1 while of the abundance (10) a purposes. in volume Sun molecule relative In + and the of 8z only) and this by Cage square-well are The different constant cage of ~ the and + employing by cage. double of abundance assumption can degree occupancy or j. even the Here which M cos VE,; the ~ only u; effect van van intersection quantity Sites a while a Recall cos to and available be 3 common is latter second Society giant This is 8 compared j der molecules der it briefly other in 1 CM 3 generalized occupancy 's the follows. of for ]} the H 8 LUNINE is the cage the 2 interaction Waals Waals this , incorpora­ introduces because planet, u in ] occupying relative estimated of the value hydrogen ~ molecule 6 excluded that guests other coexist­ the = volume consid­ for poten­ a model of is ·situa­ • p (13) (12) cage with (14) (i.e., 6 and and gas, one j2. oc­ Provided the the for we of of to AND to is is STEVENSON 1982a; large These Titan between bria pressure NH form comparable could in gas total presence stoichiometric find dial get double-occupancy low tion ( find of iiHM- iiHM that the their tations. Using excluded calculation. molecules radius uM) We FIG. protosatellite square-well by IV. (Hz) 3 the value value nebulae of q -Hz0-CH of - for ice selection between quantities from of and a square-well = now have relationships 0.2-0. the 0.04-0, CLATHRATE 7.-Geometric upper the Ellsworth - For McKoy 0. clathrate, from budget. of pressures environments. i ammonia, the C1_j of of and Although data The perhaps cage turn ammonia NASA and the to on in u uw molecule structure The value j, in hydrate, parameters for or the § where quantities structure u;. of in 4 ciathrate structure and in to a nebulae, We THE VII. this and parameters range much phase water is model of Hirschfelder ammonia, EQillLIBRIA the McKoy the of the ammonia Astrophysics then cage we are wish Sinanoglu, 0.1 PRESENCE construction j calculation, Prinn Schubert iiHM guest q. problem I given NH small prefer in In greater radius; ice, u; bars, II displayed diagram If to large the to formation the to for q and large and 3 this is and clathrate uw accommodate molecule and by • reflects perhaps determine estimated HzO, abundance latter Saturnian if our AT an these hydrates the derived OF (1954, 1983) cage C1_j the we Sinanoglu Fegley most than of section cage an for MODERATE nor average shaded fits AMMONIA (Fig. are common clathrate on cannot at ammonia-water uncertainty molecules; will in Data qMM clathrate composition that of and as may have can pp. cage qMM the 130 in for (1981) a what nebular 8). region the we much satellites and condense of collision 160, our choice of we single of = (1963) Hz Hz. = volume interaction. K. System a Here nitrogen PRESSURES 0, calculate equilibria NH the 0, Nz. effect rule priori is fits clathrate, concluded that double-occupancy ( 552, as Clearly, We uH) in the qHH- qHH- incorporated in 3 of and two slice diameters is 15% is At of we (Stevenson out in particular, should the cage apply 1110), llp.P ammonia out and used, used, solution. spheres rule is primor­ nebular permu­ higher­ restrict Vol. distor­ equili­ choice 0.6-0, 0.4-0, of of in IN If in volume then, as CH over and out the the the the the we we we an be for 58 a of 4 1985ApJS...58..493L van for for 1964; erate ourselves minimum relevant will point NH secondary an eutectics, 2NH Hunter monia, vapor to hydrate. be planetary phases below NH plus stability stability converting drate could ammonia-water and and an and dissociation dissociation dihydrate dihydrate lation the monohydrate melting regarded based No.3, from and of clathrate Hun two- to tions tion - The At In 0.13, the its excellent true monohydrate pressures NH clathrate 3 3 methane, Kasteren Giauque ten by -H (2) not 3 ammonia, Vuillard water to pressures own. what low that does is have ·H fugacities is of upon Tsiklis, pressure 1985 condense phase for (Giauque 3 a Johnson, fourfold 1933; down curve 172 2 eta/. in the · NH of 2 to more the 0 At lattice, 2H "competition" to at be as 0, melting is temperatures did formation importance; of Although liquid the not equilibrium been © ice. follows ("ammonia the moderate solar pressure-temperature pressure a K, 3 2 an depiction - only low-ammonia eutectic in diagram higher reproduced equilibria water 0 and 1953; (1984). which 1973; at (Fink to American condense Rollet simple 1956); does Linshits, 33, is difficult monohydrate incorporate of the excess coexisting Data which of estimate excess high solid field nor out Schwake, made, temperatures fairly and plus water system points slightly NH 57, the the coexisting ice we Chan not Miller and seeks no temperatures does conditions temperature would ( and in calculation pressures Stout on for and would hence, various for 3 of methane dihydrate. of > in in would well with and . make (including hydrate"). and to experiments finite out would to and incorporate preference between kilobar) because Sill a Because specific the the here. CH applications; the and Vuillard less it 80 two and clathrate, water make 1974). kilobar. clathrate Astronomical eutectic established results 1936; as be pressures in the form 1982). 4 mole next also Goryunova phase ammonia-water in the the solids components occupancy like Giauque than of Nicol a be gas reasons. the for sufficient It clathrate. solution monohydrate a ice guest pressures in analogous curve. Behavior less the to of heats The following a chemical Dorsey section expected We be the the percent is and which in pressure 1956; CH to primordial diagram, that clathrate THERMODYNAMICSOFCLATHRATEHYDRATE to being We relevant high (at hydrate the since so (1985). the in solids characterized a expected in than neglect presence form last solar 4 molecule (see, dihydrate. its 1964) pressures, different as and the First, 33%) conclude laboratory of is lack the to pressures gas, pressure of Chan 1965; we 1940; This pure are the ammonia, is reference minimum to very of 100 H to over the cause to A potential cage-forming e.g., assumptions: cages a entropies to presence N-to-0 Society present under structure which lattice system 2 indicate of form the negligible but the rough ensue plus 0, energy is gas, its one stoichiometric these water K. conclusion and monohydrate of to small Hildenbrand Lewis the Clifford in data slope particularly NH presence corrections domain NH that conversion Second, for is should the ammonia) The affect a presented investiga­ water clathrate, clathrate, by therefore than structure clathrate Giauque contains between extrapo­ defining at assump­ a given ratio roughly melting 3 ice cost (Rollet 3 of on of this (1) of · differs model to liquid under · 1969; H • mod­ dihy­ three or H am­ and and 2 the the the the the the Provided ice (1) ice 2 by 0, be of of of to in in 0 is is if water justify, (1) in§ clathrate is mole with ratio ammonia and ammonia corresponding 1951; I. supercritical ing lated ture likely ing tion tion molecules. monia-water them tials holds, with NH suggest additional 1971). of cages even ammonia-water methane NH for the the tween then tion the The We (d) (b) (e) (f) (c) The Here (a) neglected a by and NH NH assemblages: fugacity 3 3 contributions pure (e), V. I would nebula, stoichiometric pure between of that for limited at from molecules using fraction methane Wiebe ice to and effect clathrate, deal compared NH3 NH NH NH NH 2NH3 where the above Although (2). 3 3 but (s) the room that and be clathrate occupancy forms the partial hydrate water until forms for water 3 3 3 3 =solid, § the constraint first exhaust Since NASA -H -H -H two ·H · properties a the of of phase as we H2qs> · III. restrict and by solid assumptions ammonia cages CO p,~ small H20<•> NH temperature 2 water-ammonia methane the clathrate, high NH 2 2 2 relative is it qs) is with being examine greater case, 0(L) 0(L) ice, qL) methane with 20 solution pressure the Since the with Gaddy dictated freezes or is the 3 from is required eutectic (L) as 3 ammonia or + +ice the effect is of Astrophysics would the and small unchanged. ourselves +CH4(FL)• +ice +CH propensity amount + CH ammonia-water in equilibria CH4 appropriate, consequent and Langmuir that =liquid, CH4 the known liquid - the complete CO available the solubility hydrates dispersion dipole to additional I'"'H 11 4 I+CH4(FL)• 0.18. out phase and 1937); vapor, the L is in and I+ 4 by · (because allow large under chemical hence at 2 6H20 by the ·6H NH water be NH · or very 0- 6H20 most in of CH4(FL)• hydrate. 172 cage ice the equilibria is _ for statistical from The ILk system, CH moment composed 3 between 3 2 solubility (FL) equilibria coexistence I'"'H cage water 11 and it for 0+CH4(FL)• The negligible, - low us clathrate water I 1 occupies constant these the + K in enrichment and the H situations CH of is is 0 + 4 2 condition dipole methane forces CH4(FL), to 0 of . is laboratory 2 the potential water water CH4(FL). pure refers examined because abundance solution 0 was Data that moment dissociation (2) 4 15% The reached, equate ice clathrate the ice ·6H at conditions solution liquid (b) of mechanics, estimated is between hexagonal of and T moment and in primarily in in a dipole ice Langmuir is to hydrogen 2 with given H (-solar). the System pressure 0 of and more small less methane a coexistence of 2 is vapor, ice chemical of large is of ammonia-water 0 to hydrate indicates dipole more solar interest, at data in equilibria the is identical of water and the (c), water an than in than interaction), I. which coexistence pressure low (Culberson difficult the fraction clathrate (Davidson by formation but compared equations ammonia With liquid, water composi­ or liquid of carefully at constant bonding evaluate and interac­ ice, follow­ in 249 In includ­ that forma­ so poten­ in which calcu­ where struc­ this water point {15) with with am­ that (d) 505 the the be­ the the ice K, or in of of of to is is 1985ApJS...58..493L canceling Combining Now, K from equilibrium assemblages the ammonia between compound where where reaction stituent and ( component cage. this 506 v CH Thermodynamics In eutectic, = 4 = ammonia-water rough terms water 4 This /23) CcH (FL) Jl p,: <=> kT (16) x, th~ out CH =chemical hydrate. where © will of in analysis PcH and is y, x In Pf equations +12(NH empty [ occurs. the 4 American e] chemical essentially at the ·6H and P.o PcH =vapor give let CH » the reference and 85% ammonia-water 2 4 4 clathrate 1, We C 0+6(2NH solution. ILH20 pxR we also = system a Also 3 I tlp, of potential ·H be [/], lower kT X 1) (18), (17), potentials, combine pressure deal is the 0 -----=1~-­ 2 predicts p2NH3- = the 0)(s) In is pressures, H20 Astronomical a no kT temperature and water bound The the reference (PftHd-H with Langmuir 3 In free in ·H ice chemical H20 of both 2 same ( solution the -R-. is PH20 pi (19), 2 p2NH the the H20 0)(s) I, pi constituent to water NH available H20 and formation 2 cages pressure the 0p::ff::,-H20) is latter 3 vapor constant 3 (20), T. -H +CH true potential for and pressure Now ice 2 Society o) 3 of the for case and phase below even 4 2 present); the (FL). for x LUNINE let of of clathration. purposes over first difference (21) 2 clathrate from the at clathrate the of the • which large solid (17) (18) pure (21) (19) (22) (i.e., (16) con­ and 172 Provided the the AND of STEVENSON who equation where sociation also constituents vkT (a) in being rH solution 1440 Papadopoulos methane hydrate (5) (23) function ity violating Above not bars so separating regions saturation 11 satellite ity external consider denses clude ammonia-to-water investigation, methane mation that system the conversion the should ered NH3-H20 To We Since Extended by 2 equation that becomes 0 of important. to and separates CcH.PgH• for In relied here. at evaluate cal present. the that now 6(2NH the (CcH.PgH.), out occur the conditions, to we this the we cage flp,P, 60 in pressure formation clathrate only (22) (b), of is our pressure · mole- solar vapor NASA CH flp,P( coexistence as this on are an consider appropriate given temperature K. we to have (5) methane at using and at large-cage i.e., assumption 3 regions a The (1980) the P. the 4 of and interesting ·H Lewis now lower CH Recalling system even solid transition use present 1 T) is liquid • pressure would NH temperature 2 and the 4 vapor clathrate free II in ratio equilibrium 0)+CH4(g) Using the Astrophysics his CcH = dominated substituted scenarios, = where = considering the higher phase and and 3 at temperatures P.o I coexistence coexisting (1969) flhP -1161 2NH • pressure expression phase CH4 with objects. H and energy 4 we at have is 10- PcH. occupancy, expressions value is pressures 2 ignoring III); in that values 10(0.618+50.54/T)(l/•) possibility for 0 15%. is PgH• + plotted which see 3 qiiru between equilibrium II pressures formation 4 methane • to + this H to not boundary as If » T methane as bars range since <=>12NH PcH in no 1471 difference this for Also, 2 2NH by ( be The the 1 0. is water NH the indicated flp,P( for from this section of yields with application the at the of in the applied and The appropriate the the is T.. liquid-water Data PcH is T 3 this 3 of line data the temperatures interest the which I vapor, the and • • Figure case pressure conversion H tlp, H T a thus methane phase, in 3 (indicated pure enthalpy Holder, Haudenschild methane 60 pressure 0 conversion 4 the 2 2 pressure +CH lower transformation ammonia )- methane defined 0 0 = 0 that between hence an source. on is K. System to 2.0 strictly in merits result no flhP] is the water 8, to ammonia-water of the • raise is Thus, 4 the PV term, bars), bound free to for ·6H clathrate is converted now this field, Corbin, pressure planetary is assemblages by is figure. of occurs. presence by expression not of Evaluating outer itself the laboratory effects and 3.1 the the which ice. 2 above to water equation equation although 0 transfor­ freezing, interest. we p,~ the Vol. (1970), consid­ tlh(T) X empty fugac­ (if fugac­ occur, water Note Note 20 10- solar (24) (23) con­ con­ and as dis­ line An the the are ice we 58 or - of to a 3 1985ApJS...58..493L mole but coefficient of mole where dissociation Langmuir Another monia-water ward No.3, solution solution eutectic terminates the the hydrate imply NH and Ill. Dashed co~respond Inserting For !:J.p,fl( FIG. water 3 equivalent water-ice part NH -H solid fraction complete from fraction 1f 1985 the lines 8.-Phase 2 3 T) of 0 qL) is and is ·H vertical ice containing is to ammonia-water of VII constants plotted line 2 by reached, © = are 0<•l+CH this pressure +CH now in regions equation solution, water the occupancy are !:J.hfl case American the intersecting expression phase of the separating diagram point, 4 line ammonia-water given the ordinate ·5.75H + water as at in mixture. ice 4 boundaries below in water :a freezing derived ·5.75H a is the which f 249 of in equilibrium function (24) exist, separating drawn 2 for ( 0+CH4(FL)· cage must in !:J.p,fl(1Q)- Haudenschild water-ice for case, the K. 2 methane which Astronomical the ice 0+CH4(v)• regions solution, Freezing into sites. point in !:J.p,fl and be between A dissociation at follo~g - <( (.9 0 CD 0:: (f) a_U _I from 1f of § redefined vertical solution. :I: 172 Point temperature above .. is region III, is clathrate with equation temperature of freezing Heres= THERMODYNAMICS VI -I !:J.hll)- the regions 3 VI pure K, points 1.0 and IV. A the p~ases (1970). a defines and as freezing line which where 15% with V NH in water, pressure methane methane y VI solid, point with kT versus the Society (1), 0.9 is are 3 ammonia-water VII. is ·H and CH (IV) An no in the (V) drawn In presence stable: v 2 temperature the X q,l+ICe 4 NH Figure of VII =vapor, and alternative fugacity. yXH water critical H 33% This water ammonia curve ammonia clathrate 125 2 0.8 m the o activity 3 for -H != down­ 2 • is using of o, NH (25) ammonia 2NH 8 am­ line point, ice. Provided the L for I+CH4(vJ• ice ammonia, 2 The as 0 =liquid, 3 OF 0.7 3 T(K) NH ·H and CLATHRATE 2 fractions ~<·~~CH 3 B clathrate librium be dotted displayed dimension the the by plotted sures for coexists case cal calculating temperature the with NH X ammonia-water and the plotted mole 150 FL V. defines H . 0.5 0.6 In Finally, by 2 smaller extending regions fluid. labeled water-ice =fluid, o= expense 3 NH concentration III fraction • to region H (relative XH for 4 as the curves the 3 ·5.75H lines 0.85 273 2 and with -H with 0 methane is 200 slice. 0 ammonia and NH we (XH IV, concentrations. NASA of 2 produced. freezing < the q!J+1ce xa K, VII, of HYDRATE VII slice. and case to terminate 2 3 the the CH 0.66, 0+_CH4(L); plot may ammonia-water - the V, (relative 2 Since water+ water H and solution o clathrate partial 4 we 0.4 250 dissociation 2 methane at and < at clathrate ·5.75H They 0 diagram, of the be Astrophysics 0.85) at which freezing mole the using I+CH4(FL)• point have JZI in VI, ammonia) in to the pressure 300 thought boundary a region at define 2 appropriate freezes 0.3 0 ammonia+ II: solution or the dissociation temperature plotted fractions the equation = partial NH Also, ammonia-water for point and, N~ larger CH the methane pressure vs. VII dissociation region 3 solution. other the 3 of out. 4 • VI. ·H_2qs) for the H temperature. hence, between clathrate XH with clathrate pressure the as water) 2 (XH a given 0 NH The than (24) in water-ice pure 2 Data 40% o VII projections clathrate is in curve pressure +CH ammonia, 3 excess corresponding 2 coordinate, o -H 0.15. line is a calculate Since ammonia-water with coexistence water but in liquid > vapor regions 0.15. pressure 2 one System solution 4 dissociation qL)+CH4(FL)• their 0.85) Within is does ·5.75H for freezing 1f of constructed Roman is P case may for or the composition. not = of produced own < 15%. for than II how 2 regions 1f supercriti­ 0+C~4(L): Pdissociation is curve water-ice onto the necessarily solutions and in 0 with read a numerals • line solution. plotted slice to in These These much given equi­ pres­ third VII, I, 507 VII. the the the the for for off by at to II, 1985ApJS...58..493L interaction in dP no water-ammonia, (1) sure spect (3) of display concentration consideration dard diagram, lated For made next nitrogen) plotted pp. "trick" section from free dissociation assumed. down lines increasing the more upward (1985) freezing cation dissociation to tion 508 The The Calculation The 1 the water. define longer the compression empty 386-387). dT, energy have our at section. in state, Haudenschild in to rapidly in guest to indicates d!lp.P graph to equations quantities volume we as in the the VII by dT from T, boundary. terms § pressure it The clathrate the been the Application point hydrate point fluid-phase VII. the pressure; potential P, present only that change © is molecule appropriate P-T = pressure and a) pressure is dT Even diagram with of use eutectic useful is equations k of American + partial of given increase terminated V. of that [ B Formulation a + 40% and several of VI 1+C/ B, phase P clathrate of of the flp.P restrictions, vkT few on temperature HIGH-PRESSURE stability cage water so, dflp.P In above our Although (1970) the should dP hypothetical work between clathrate the in to consider i.e., phase at (X (1 Figure system equilibrium pressure from at degrees line, at of and § in model begins diagram derive cage Cdf effects this + NH H dP NH (1) III. ice dP a 2 ;:::: the 172 our Cf) conversion o= at and by stability in few in Astronomical bend 10 pressure Pdiss 3 to for composition 3 dP, and freezing 8. In 10 • guest sites temperature we • coexistence with H equilibrium coexistence the 2 dissociation + from Johnson, H the for 0.6). K a to results yielded neglected than A and hundred 3 constructing define Pure 2 bars 2 Clausius 1 for 0 have were bars standard slightly (2). 0 dominate line on effect studies + incorporating EQillLIBRIA vT highest at and freezing at To 1 must freezing the Cf effects, methane the Water out high of the Differentiating was to to to high used evaluated 950 the host ( calculate figure of ice bars; Schwake, 1000 C avoid dissociation in toward a of satellite (see with water Clapeyron be and then valid practical states dT pressure bars methane df pressure hypothetical the pressures entire previous or low-pressure temperature shifts Case molecules. considered the the point Society explicitly (and bars. (2) Prausnitz + indicates. pure liquid serious total the corresponding drawn at high-pressure solution, at f ice-clathrate these is for the the LUNINE the dC)] dT interiors clathrate T NH a and high calculated water molecular alters ammonia solubility pressure; increases = the sections: common clathrate left relation, water with pressure fugacity requires modifi­ from effects, 3 185 In calcu­ in • • dT Nicol 1969, pres­ stan­ (26) solu­ H with data was and this the Provided the re­ 2 K, to AND 0 is is B STEVENSON dCI Here numerator for clathrate, coexisting H to ture from Solving where and justified taken dP is dT where ring superscript cage down thermodynamic and d( = - dT dP 2 Examination Comparing be trivial. 0) by d( all = kT dT equation given for (S to and negative. kT k between + the tlSP terms applications to the we j [ { [ < In 0 for k the 0 tlS/3] v the later v - , In 0, be coexisting We consider In L) S guest coexisting fo in = _ = = NASA S) df k becomes !)IT= 0 f3 inserting guest guest for (1 in {O InCf+(s (27) I in have equations Figure are =kIn ( The I the dT refers + P --- of only flp.P( tlV' the relations, phase this = Cf) 1471 into species, fugacity molecule equation and volume in f3 a VdP denominator -(S- 1f also Astrophysics water ideal - a single section. f T_r, values 2. water to this 1/ vk equation single fV weighted df c 0 =I assumed (27) Consider P differenceS' al I 0 -s)-k In 0 for 1 section gas ice , dP kT S expansion 1f )- moe and guest and + Cv (30) and 0 phase, for CP cage-the and Superscripts ) Cf the or I _ in dP regime flhP( df dT= forT< (26), entropy is C, ) by + confirms liquid its equation species H 1 the f (24) - dP, first In-+-- the dC v(kTIC)(dCidT). K- 1 P, 2 the bulk P and between 0, • Data ' kIn and quantity required 0 jo I of we f difference we 1 ) phase. dP addition the T_r, number of and rearranging, the phases _j_ the fo (28), find the see, on «. llS kT System ideal a C (T< (T> dT+ for C empty quantities guest volume reference qualitative Using to Cf 13 for the plugging dC] dT df = of of (per brevity are form I gas » 7J) 7J)" 0; structure kT numerator dP; the f cage +llsP molecule. 1, standard clathrate implicit; then mole regime. we Vol. dT of df second a so this With refer­ state, these write cage sites (29) (31) (30) (28) find pic­ dT the the } 58 of is I ' 1985ApJS...58..493L lost Appendix. pressure per ends, low) The The likely Thus ing We high-pressure values water, boundary, well. water water-methane nominator negative, pressure, used boundary because shows fugacity fugacity end; followed and 9. and and curve 1969, enthalpy ammonia clathrate. of or zero, the mum the negative, numerator found P throughout tion temperatures. the throughout the = No.3, We We Figure oo remains Where the decreases denominator, kilobar water data solid-fluid by then the computed Kennedy pressure. effect (2) pressure and a and indicates in The p. f:lVP- was to temperature liquid-ice construct stability by calculate for 1985 and a converting crosses similar solubility the 95). the along curve f of change which results by and calculate its maximum. the determine present. 10 fc the setting molecule. at the Since precise and of is fairly methane drops © given regime, enthalpy the CH this water-ice > the It absolute inclusion Vv-+ only negative, each curve displays increases pressure dP primary corresponding phases f, Calculation American 1967) derived is, change methane All boundaries an !:l change 4 is system. pressure that the boundary in 1 the regime. and, in coexisting the sP constant. the to however, of calculated the as by dP dT 1 isothermal slightly pressure temperature 0 at the of terms some phase V the mole is methane a reproduces It I and is change clathrate the the phase the For magnitude field, hence, liquid-water-high-pressure dissociation which denominator these is increases. dT decreases in small and the in§ again of clathrate methane dependence is, at expected, with At phase ideal range; Eventually nonzero slope structure dPidT-+ numerator scatter an of slope diagram in becomes the higher is is (see in of completed much the dP III Astronomical both value pure diagram equations in value, ice is along assumed temperature. methane small. effect, seen additional temperature in 1 path f:lp.P the low-pressure gas is neglected for magnitude and going boundary numerical dT point (or numerical water former clathrate However, the sharply, of decreasing stable. smaller of but the methane pressures (Eisenberg pressure clearly at T by T-P state numerator and A I is increase in of small; liquid and of oo. the this the slope the < 1HERMODYNAMICS from guest remains which explicitly positive, discontinuity zero. since is low- evaluating will clathrate phase pressure. the equation 1f· is At incorporated paths with net clathrate Equation a fc in dissociation boundary than v high-pressure while (drawn phase at oprd with compared water) (which of Inserting evaluations i.e., For then as ice Langmuir rather of evaluation versus It > f:lVP equation phase and molecule, uneven is volume now end in dP the dP the a diagram !:l is P shown Society and the I the detailed as as less T large vP idP are I be I !:l to not first is = increases diagram The (30) high-pressure high-pressure slope is dT equations with plus > dT vP the I small is T ice-to-liquid from temperature former, dissociation I Vv, the (30) considered, stable) fc Kauzmann ice 1f, in present p' at important than truly dTI quality decreases, numerical gained the = in value (30). increases in for dissocia­ becomes methane constant equal pressure gas relevant slope (see at increas­ since the for various below). dP oo dPidT f:lSP is Figure in Grace Titan. effect. at phase phase maxi­ • zero, pure each I with zero into into also The was was N the be­ de­ the the the Provided for dT (1) or as of at to 2 is it • OF CLATHRATE with found 10. confirms Kobayashi aiu clathrate maximum was pression pressure pure stability system. and clathrate Langmuir the the rate reach cage the calculated Beginning temperature, Work So FIG. by At critical volume so2 with roughly Kobayashi volume. respect xenon a far - the ...... a (f) 0:: (!) <[ (I) 0 a...... :..J 9.-Schematic by critical Comparable clathrate mechanical by of we by to the at do pressure we constant -2~---L----L------~ (1964). illustrating extrapolating point NASA change point integrating clathrate S0 2 Tammann show assume 100 to zero, HYDRATE not general We have 2 point. pressure. 1964 clathrate, A exist to then decomposition the is the in on Astrophysics phase be C. neglected pressure stability that thermodynamic taken shape high-pressure (Aaldijk along data going calculate the in dP same. and at To Van 1 diagram the the 3.1 liquid-vapor the A-D, dT up determine as do of Krige from criterion decrease of T(K) kilobars. literature. temperature Berkum VAPOR 1971) described = data the by 180 not the the as T oo of 2 - temperature a (1925) so2 left-hand paths well extend methane, effect data Langmuir point corresponding of SOLID up kilobars, boundary, Data by the and in as vapor+ At taken Marshall, to 3.7 (The for by along volume on which of by effect the for to Diepen plotted System portion Davidson CH the to pressure itself.) sufficiently Marshall, critical constant A-B-C-D. they hit fugacity kilobars the ice calculate 260 we 4 of high-pressure of , a as to CH decrease (1979) Saito, CO, found cage maximum found pressure the of Data clathrate pressure at 4 on fugacity. (1973), for do Figure -H or Saito, clath­ D com­ high that find and 509 not the the the was for N 2 vs. in 0 2 1985ApJS...58..493L cage large versus radius constants compression. (Numerical for attractive inspecting Langmuir tial the that boundary N 510 the methane) boundaries scale. (assuming indicate 2 Using FIG. becomes molecules (and value the a radii and modest at small 10.-Phase estimated is hence our zero high-pressure 273 portion for at for eq. completely constants P small based © tests dominant 10 cages. solubility formulation water Using to [1).) so American K. both decrease CO) critical kilobar close confirm modest cages diagram The of on The and depleted Methane structure as the and KP of the point; effect that behavior as methane. a methane for in is phase guest-host =10- - - of I- ~ the in function find changes of low-pressure the the ""'3.7%. Astronomical methane in horizontal the cage is general 400 the 200 forming is I 100~--~--~---L--~--~~--~--~---L~ 5 that large-cage repulsive of They in boundary small of cages a bar-1, high-pressure water) radii 0 opposite of in sufficiently the clathrate potential it Figure ...... are insensitivity Clathrate. arrows cage / cage. c::.J changes C, ..... Langmuir as / is '-..,..,,-1-' corresponding extended the portion Langmuir given MARSHALL radius as a /'GRACE 2 I I I radius 11 using plotted at sign function decrease without CH / can Society The 12.5 plots by " small by case, / into I : I of for increases 4 constants UNDER heavy low-pressure LUNINE kilobars / of is as CLATHRATE be 4 the " -1% the -- constants. Langmuir temperature similar the the " 5.7,5 the molecule we bringing " seen in of solid ---r- altered / to poten­ clathrate • phase (1967) show large solve from both ET cage AND 8 6 Provided the the for line; I I I : by AND to H end HIGH P ,, uncertainty AL., 2 vs. data (KILOBARS) of stable KENNEDY 0 ,, pressure. STEVENSON the of water. out 1964 is have possible, 5% factor all. data the SIZe. that that PRESSURES clathrate STABILITY region Marshall, We Very not by Although in reduction fitted of for 10 of at to Calculated phase calculated of worked the now the We but b) large Tammann take CH low stability 10 whereas Kihara Saito, cage are NASA Effect consider 6 4 assume 12 ' dC/dP , pressures the in guest effectively only high-pressure as out and at field large-cage high-pressure parameters expected of rather large-cage relevant here Kobayashi and Astrophysics molecules, Methane is 14 boundary in the into indistinguishable Krige occupancy (see what preventing effect small account. boundary. there since size 16 (1964) discussion for Solubility between occupancy 1925), follows such of phase reductions if results these S0 one methane are Light 2 of so2 as clathrate from , Data such diagram of plotted derived molecules in in the S0 that above the from solid a is Liquid the 2 in a decrease solubility components , small System very as calculation left-hand and the may cage lines incorporating in of of 0. Water water+ § are so2 experimental favorable. solubility Vertical are be cage radii. III, of similar axis solid-liquid squeezed clathrate in (water we Vol. C methane is would Using liquid on arrows by find not this 58 of in at A or a 1985ApJS...58..493L where is H which water 1951). liquid in ice methane methane p. saturated (1) and clathrate; valid to 357), No.3, pressure cage 2 proportional Experimental Xz(To,P)= , Using 335): FIG. coexistence 1 in the - (TO, Scurlock radius we over 680 the lowers water, assumes At 1985 P H.-Langmuir presence values. P 0 phase find in thermodynamic 0 methane-water 310 coexisting bars some (2) is ) at 2 © water is .1.-----r----,r------r-----, x the 1983). 273 K a American the 2 with stability that Xexp{k~ is to H , at reference limited data and of is chemical f.f 2,1 present. K, Henry's the ice temperatures 7.8xl0- 273K a (Tr the Two the methane = Po 680 constants for on is saturated mole 0.98 O• H fugacity range clathrate, zero, large 2 of P.) bars, solubility solution effects , relations 0 0 1 pressure law potential (T, /,P[V(1Q,P)-VOO(TQ,P)] fraction Astronomical clathrate P 3 0 phase for • and a/a and of the We constant P) 0.96 solution of of methane down x for small mole x effectively that 2 use. 0 importance of in solute 2 is • in of of (T, THERMODYNAMICS which CH Prausnitz negligible is a 2 cages, the the the fraction for to 0.94 clathrate modified P), of in 4 possible 2 298 liquid-water solubility in methane in 1 no ideal methane destabilizing normalized Society (Prausnitz liquid H are coexisting K (1969, of (Rebiai, 2 as 0 0.92 Henry's gas considered: methane (Culberson in a extend dissolved function solvent in of regime, an pp. to dP} liquid phase water • 1969, Rest, (33) pure (32) law zero un­ Provided the 30, up in of 1 OF CLATHRATE pressure interaction low written preliminary. behavior NH estimate function exponential data from cially chosen The The in volume methane necessary. which polar small system and and approximately and Culberson H the temperatures terms - !D g <( (9 en CL 0:::: FIG. 2 Our water by 0 3 uncertainty solubility quantity 700 so 30 quantity , up 3 solvent, 300 4 at 12.-Solubility uncertain. vs. an the (:::; are results characterizes approaches extrapolation in cnf of to to K at of A infinite methane of phase, analogous 5 to (1951). slightly mixing NASA poorly 600 temperature, from pressure be and To the HYDRATE terms cnf mole- VOO 10,000 of we are of V(1Q, and one-fourth 300 bars curve the in relevance VOO mole 5 X dilution, the estimate Data is given mole- Since in different 1 known, of to P equally Astrophysics other a system P) such 10- H bars, 0 bars, are Culberson at the is the fraction. methane of is , critical cancel 2 in V in 0-H is 10 the governed the 1 3 where consistent the ). H difference that is parameters A Figure Shmulovich found mole followed and and the difficult to kilobars. x 2 effect consisting the form However, the volume 0-CH to 2 Culberson in 0 point one the it heat be the A CULBERSON data. THEORY water volume fraction H is interaction. curve as 12 of in by negative present 2 1 2 another; is 35 excess to 4 with by above described at of A Data (To, between of The Prausnitz at the system an Based CH estimate. cnf makes of is et 310 the must vaporization 310 a methane of data with VOO 4 300) 310 small empirical a/. ability a latter volume sharp study mole- the (net 1 K. IN nonpolar K System excess on since (1980) Equation indicate fitted it kilobar to be plotted K a They the coexisting in is H~ (1969, up (1951) The repulsion) data small value impossible of increase. derive is 1 regarded dissolved § of taken to two at H volume the to not parameter 2.6 Culberson Va, indicate on as mixing on 2 x of solute 300 pressure increase that 0-CH p. is a 2 system several (33) of VOO excess given, - N linear H espe­ P from 360). pure bars 2 The 511 0 and 0.1, 2 the the 0. as to in in in at is is is is a 4 1985ApJS...58..493L is holds high by some smaller intermediate The unsaturated kilobars; bars some structure slightly fractions (1978). extends equals fraction ference clathrate additional about degree II Kobayashi this region where volume using as those the T, T, domain methane respect pure solution from chemical ical x2) Fig. than and tude tion 512 structure The Actually, P. Provided N P, a numerical high-pressure =- is potential shape 2 12). (5), 10,590 pressure P-x of methane pressure (see pressures, x and P for Using for 10 clathrate to analysis of the 1 of x 2 than, ,sat• The larger in this = of of data outward 2 to kTx we 2 containing It at solubility note reaches ,sat kilobars. saturation II / potential of stability structure extrapolating CH 12,460 frre methane 2 Fig. of diagram saturation (1964), clathrate solution fugacity © follows II extensive clathrate the find bars should x water-methane effect the water « 2 pressure methane Jrre critical experiments the the • as 2 of 4 of below at at American that than : in With 1 is c) low-pressure are 10). after is well water maximum that structure low ( the Jacobsen phase structure a limit at bars is § from small, T as the Since of the in clathrate which maximum that Mixed is of V be as at ' predicted a of I, between for stability. the 10 x same There P) this pressure, a at as follows. pressure all drawn for a if the for 2 methane corresponding 320 thermodynamic and due being at the fugacity dissolved with qualitatively computed was kilobars. = diagram the 310 saturated low. = structure the the saturated the the the stability which correction 0.1. x but methane is water, N I T, x2,sat I K to 2 and Astronomical solubility ll applied saturation solution. K, is dominant out is Langmuir 2 decreasing hydrate case. free = saturated somewhat These P) clathrate vP -CH in pure data T, We Assume, dissolved assume around Thus, to it for 0 preferred mole the thus of Xz (T P of clathrate is is Stewart Figure An will methane to be for methane x can solution in then Hence, I, the 4 2 similar always dissociation solution. ' mole clathrate methane clathrate conditions conclusions of to x / P) similar 12,300 equally Clathrate similar applied will if fraction the a temperature convert Another § structure as the 6000 demonstrate pure structure correction 2 stability value for constants increases (in /pure Marshall, less x substantial methane '13. Va, pressure-temperature­ pressure, sat ' z obtained 2 stability continue fraction (1973) over compressibility even can supersaturated to is < is is simplicity, ~ the bars. bars The than methane to, strong ( to we 0.1, small. exhausted; 1. as and to that equal to Society stability to T x coexist way stnicture if lie 2 II but pressure sense ' This or are point I N I !:J.p,fl a structure P) smaller stability compute again is at for and for The which N the to is of LUNINE methane field function clathrate as of Saito, to lower above conclusion within the 2 2 to kT confirmed somewhat to region x the is methane, methane, - structure clathrate clathrate phase form, effect 2 in CH that the an limiting with Mel'nik at look plotted is that until 310 magni­ = In of chem­ is • drops equa­ some II mole 2000 ideal 0.01, than 4 field (34) with JC (i.e., (1- 4-5 and I dif­ less Provided the N the the K. an of of of at in at at at at of at of is it AND 2 STEVENSON phase, behave sumes form, of dissociation Low where and concludes given the the solution is fraction with FIG. by the fugacities two water-methane -- m Schroten collisions and concentration of surface the formation so of km a noble unit space shown 0.5, species pore is Under pore the of rapid right-hand and elq- molecule), we particular the Knudsen diffusing clathrate K over that the 1956, the and volume ratio d 0 of on (where size define length where in • gases, space diffu­ gas later, from (41) (42) than by such (39) (40) with por­ is i ad­ 0.1. 10 Provided the the the for we of of is p. is is a a 7 OF CLATHRATE especially 10 exhibit dependent dinate diffusivities a dPa Avnir, yields narrow pores. bars, p. per x are adsorption employ our an For tecture tures, to that terms tive tions saturation), cnr calculate in Delsemme that their (42) adsorption cules times to so convert X = = 10- 7 Since D-146), find by progressively the that empirical I a=- constant, yr problem 0. cm the T though depends into per at dP paper, a=4X10- is discussed larger 6 = the of the This if In Farin, 2 Knudsen x, probably a. fractal for pore bars , the concentrations fractal the = i 50 the a cffi3 equation Sm it a As ( Here the say. we Pa and diffusion NASA substantial on wherein on K, is expression and 2SmAsakT; can which corresponding e exaggerated than by molecular pore (CRC Delsemme HYDRATE constant as space I is primarily and n(-E of does Sierpinski and find is the geometries. pyrex P a For adsorber, the corresponding geometries, Sa considering the be by the larger flow methane Miller ice consists 6 yields for e+ size Pfeifer depend slope (41), is a K Sa which not demonstrated example, Handbook effective Astrophysics Carslaw monolayer vapor the aP -10 (Delsemme at time a 2 "normal" glass; the regime. is dependent , and adsorption )-D pore on to inhibit scale, Sm=l.5X10 a we ratio _ - and 1p,m. sponge (1970), loglO examples amount of (1984) 8 of we -10 nebular is pressures, , pressure is n(-e-) on In the fashion, a find or since differentiating discussed accessible a the clathration spaces, adsorption Miller and the of not most use some Using e+ the hierarchy 9 of a pIe) diffusivity to A diffusion , adsorption coverage (which present diffusion adsorbate In for adsorption and Chemistry mainly of diffusivity simpler the they a by Jaeger partial dominated for effects their surfaces of of of reality, power gas we present and 14 x10-aT2(1oglO and the a Data position examination a ax2' Miller this the these by claim 2 because has moleculescm-2, P single can adsorbed experimental value. of as area on ideal to is of substituting pressure for from (1959) calculation distance gas a»l. Mandelbrot sort of onto to pore planetesimal with dimension accessed of and a or System ice hierarchical the law think isotherm, data large 1970), a species, the of absorbent by limiting As gas gas from clathration, most Writing of of is (SaiSm gas ice. Physics, sizes. D a respect for spatial in X is the not on connections of Pfe>>. architecture of deep-seated of of pores. equation =ax, species species. Following molecules in the -10-100 (thermal) - assuming 8 X materials 1m the evidence equation methane x and smallest strongly illustra­ 2.7268). case we 5 (1977), a = =i archi­ Pa 10-to struc­ mole­ point 1970, coor­ e=7 to solu­ ( with time (44) over (43) 0 a 515 10 46) can we In in in of at to P is 6 1985ApJS...58..493L diffusion giving ing magnitude versus which has formed followed formation, and extremely CHC1 absence are order diffusion clathrate gases, in over Barrer move methane with rated, scales allowed of We tion themselves. the radius rare where u the C= 516 = To We Experimental meters the spherical. small Cr larger sphere, specify c water of gases 10 a derive 3 5 through 2 conclude achieving gas for apparently time r a: • and layer yields + hr, presence clathrate 2Xe clathrate. minutes exposure of is clathrate by coefficient layer. of over !~ changes uptake diffusion the estimate limited. in by at by ice the © at shaking. Edge ·17H a That the the u C the of ~ Assuming which much temperatures agitating =reo solution the American constant the = time in radial The that diffusion nearly clathrate, ( initial data gas until 2 from gas of is, as -:r (1967) 0. grains? Barrer the hydrate forming of ac in chloroform at derived for scales flatter of clathratable Delsemme presence small a given methane Qualitatively, This, concentration. coordinate fresh gas through on function vessel = some (Barrer ice, clathrate maximum boundary the the gas D sin at D at at formed and coefficient, kinetics uptake cavities of uptake at on along ( a ice is r=O chloroform, structure that r=a, t=O pressure Astronomical from down ice n;r a fraction dr2 resulted 82 surface constant, of ::;10 2 Ruzicka what 1941, with c gas the according of and to K all gases equal with gases measured exp + the clathrate curve, from theoretical conditions time. 7 are to of by continue ice ~ at their steel grain yr. r time forO< show p. Making we I for data Wenger ( _ ( of 90 layer clathrate the condensing in occupied can ac) ar hydrate. parts through appropriate We (1962) 29) grains Assume the . and .require which all the balls. K structure Dn:: plots imprecision scale surfaces at to diffuse an ' from from now on t, on curve, r< gas rare best solid until incorporation the Society for initial the This (1970) studied 2 to we the of time formation can by the a; t)< an examine the was the ice on gases an LUNINE water a formula substitution deepen interpret chloroform gas makes II all xenon are expression ice procedure c ice pressures. sphere ice this steep order-of­ the center scales and 2 incorpo­ of hydrate formed the _ forma­ uptake grains, coated in grains grains vapor • order read­ layer CQ}. {49} time (48} (47} rare and rise our the the are Provided ice - as of of of of AND STEVENSON solve error The which uptake (maximum For use 10- energy, quantity clathration clathrate into Recalling Ruzicka When which uptake clathrate 1969) time mechanisms), monolayer amount activation of of Ruzicka through then -10- It _Q_ interest. Qoo diffusion by 18 times solid the Q ratio is at scales forD: functions (a 33 cnr is the moves = C important =!( curve. we so 50 of given cnr 2 severe data (1962) data ice, -1~n( at a is guest grains > that small energy of that xenon K which s- NASA prxmt equation approximate of D to time CQ, 0 and the -10 Dt) s - 'IT gas 1 have diffusion material = in - We we of a occur clathrate, approximation as 1 at molecule to compared with DT=200 to 4.5 absorption Carslaw shaking, 1 total t, at 3 is appropriate ac) gas to 1 taken can ar Barrer find compute 200 2 find form been we yr. 50 the Astrophysics _ realize, kcal is throughout be r=a 4Dt write K! amount into will K. a a However, incorporated effective K up D correctly clathrate 2 incorporated) -lo-s and diffusion in and about exp It mole- dt -10- Thus, + at be however, the takes a is the to Jaeger 16{Dt} [- since time from apparent Edge greatly of those diffusion grains 1% 1 23 radius to experiments at ! is interpreted, micron-sized since (52) a place. (Haltenhorth may gas cnr the ( negligible of w- t (1959, the 200 into Data (1967) 112 ~ that required to inhibited. the is involves by of hydrogen 4 - Q the that initial proceed n=l s- Kit of Since the that f em even the 2 maximum the p. taken 1 ~)]' System hydrogen diffusion if and ice and 234) ierfc at diffusion at ice at of is for the first portion in particles the an particles temperatures If and possible fluoride 100 by t Barrer the spheres, Barrer hence up in substantial Barrer = (Dt} we activation term measured different oo terms possible absence fluoride na Klinger process Vol. by K use of of = 112 D- {51) (52} {54) (53) over and as and and and and and Qoo gas the the for we 58 an of . a 1985ApJS...58..493L incorporated or Ruzicka. representative 1980). then rated when predominate exposing clathrate fresh abundance completely crude collision dominant indicate the water planetesimal agitation. or and accretion lite the planetesimals drag 0.1-0.01 clathrate implies fJ. micron-sized velocity, mate radius the reserved referred material planetesimals sible so density em and of v P p 10 lOOOrPpP, tion. No.3, =10- G -10-100 r -l It An We Consider 4 CH the ""'10- different that gas -10 s- available the clathrate or grain is one Ruzicka source g ice. the regimes, the 8 1 in 4 lifetime model analogous bonding 1985 possible v and assume cm- planet would 6 fragment PG for 2 !J.mjm essentially (whatever that 12 in spalled some to may collisions , that by radial If clathrate time, Since layer), fresh particles source mass, ice respectively, with =lo-s (i.e., as the" em © bulk meter-sized 3 meter-sized g as radii. of , the collision. as equating over grains. carbon layer to conclude is the of moving consist C0 to !J.r (1962), American cm- material. of of of literature s- such that gas planetesimals v clathrate. laboratory that v ice, planetesimal = within all off a agitated the the density, of test ice and 2 -10- the in 1 process the thickness those fracturing velocity p!J.rv From to ; g the is are condensate, complete conversion complete 3 drag ice are to will condensed of hence, ) em differences enclathrated of This than ice cm- surface • the from grains nebula of coating whether be through bonding required v A Barrer the grains all exposed We 7 where that objects. 2 the Saturnian (or s- much ice hydrogen We infall in em, be ja, for Weidenschilling predominant the porous 3 and is Thus, due in in ) of 1 they underlying work the !J.mjm • dispersion larger), grains Astronomical (taken find one a at ice, and later, cgs in itself. bonding and of at can where velocity a during collisional would the although broken porous lj, time, and least to a a carbon. more nebular energy to the primordial is we ice to To their possible are least units. gaseous suggests planetesimal solar this planetesimal and a CH find v velocity expose gas kinetic larger coated bond), gas) R (continuum claim to -10- itself. =10 latter porous Edge be fl.m etc., =100r -1% be to collision THERMODYNAMICS 4 likely due energy process drag experiments be up, Pp of planetesimal ice per the carbon nebulae or conservative, The Experiments in v gas stripped be the ergs of objects) and velocity. stage of disk. 6 that are all with comprising Below the (1977), the that CO a p energy of is (1967), to is suggesting unit p maximum 1 to particles the differences acting gaseous 12J./ destroyed (Lewis dependence the time term the to the cm- weaker the gas of the 10- thickness Pp Society carbon - m as may in same The species) clathrate; is the for can ice area (Epstein planetesimals, drag, be v, ice grain the 2 we available a are off, drag less composed contact planetesimal 3 we ' 4 expected of is on -100-1000 proto-satel­ , We to and bonding function , still most be and are and so to dislodged, or (probably develop (hereafter by structure, fragment, nebula we fragment order normally exposing clathrate than can incorpo­ colliding than particles that mass :::;; density, clathra­ nebular for flm/m by at will eroded choose among Barrer be of others 1% at adopt Prinn • on upon plau­ drag, v least with esti­ R CO two the the the the Provided the the all be of of of of of of = to is rP a OF CLATHRATE ice interior portant, scales could function even outermost Eisenberg m where Saturnian spheres, sions, formation quent Figure of dispersion, mals tion frequency and mj!J.m the the infall The latter high where planetesimals pressure portant Note fraction for densation denser over rP a recondensation Saturn-forming Delsemme tion 4 , We p~ We For We by semimajor is Pp; at mass proto-Saturn Keplerian spreading former in is porosity. to the from for the the into that which time suggest to (i.e., be Pv calculate the the 16. planetesimals for proto-Titan also over the ice their however, mechanism we collisions lifetime expose of of produces = M the relevant mass converted and F and It density Saturn for zone) in scale micron-sized portions NASA and assumed grains saturation the colliding calculate value radius planetesimal > required produce a examined HYDRATE is is mean solar axis 10 in the surface angular is the Kauzmann it solar clear the of Wenger solar the planetesimals of the is 6 conclusion out of planetesimals where possible in (see, is temperatures and of Saturnian a yr) presence a marginally ratio clathrate, free and nebula water as Astrophysics time planetesimals the ice short forming to that water for nebulae, of to either and planetesimals localized to a as the vapor nebula, is= into for exposing e.g., velocity be planetesimal t path. the over temperature produce solar clathrate. of meter-sized the (1970). collisions clathrate = grains. required the time vertical material ice enough evaporative 1969, prior case, (mj!J.m)/F, - a .;(2wmkT) molecule. the do Lunine that under possibility pressure of the solar vacuum clathrate very nebula The vR. as nebula in it short could not heating to radial t in results and We sufficient fresh shown is This ex: p. lifetime out a the Then to evaporate latter thickness low that the particular formation, for change An ( orbiting may possible may nebula 60), and (in rP enough write planetesimals accretion vz case, and nebula itself. have Pp at Data of velocity as Pp) Assuming ice mechanism solar vapor a after in formation and complete exception ' plausible addition is by is Neptune is Stevenson that Tis water planetesimal have have - of excessively to display where calculated the the 1 t guest occurred. t -10- (i.e., the enhanced ; nebula, planetesimal or the Saturn, that System that vz/!2, the such is constitute pressure planet temperature, hence, sublimation of clathrated, rate since vertical ice been make independent as experiments nebula. gas). clathration clathration the the 1 to all conditions molecule the the only the (values spheres of may may satellites 1982b); of to over where or disturbing t H too of planetesi­ t it long Since by clathrate, ice larger = Neptune sublima­ 10- result evapora­ of to collision ""'10 2 velocity satellite smaller. a 0 be be 10 the an taking a water infre­ to suffer colli­ small from 2 time even 6 (55) as con­ Q disk and 517 and im­ im­ the t gas ice the yr; for be yr. in in or or of of of of ex: is a 1985ApJS...58..493L into ingly will cages calculate distinctive clathrate clathrate in relative' with and where coexisting tively, ature. 518 Consider Having clathrate: FIG. see sum satellites partial different Numbers y. for Pk, 16.- abundances that occupied containing these from - the I- en - tx ~ w w 0 0 0::: ~ (!) a.. w _J compiled, structure signatures a, a gas, P~ © Time a) a pressure the and relative on American -2 from 14 gas are a to Application 70 plot 1 to coexisting abundance get giant-planet and by composed the evaporate I that of in single refer of and VII. the lj. abundances species § species partial certain a'2 in III, II to abundance APPLICATIONS Equation are types Astronomical the to radius clathrate, gas a a pattern water-ice Primordial of set j. atmospheres. k molecules 1 pressure coexisting of and We and of molecules of of specified of sphere. (2) guest dissociation in ratio can sphere and 3, t guests the gives in and of Nebulae accreted gas Langmuir then molecules, of each in clathrate k composition. j 2 Society incorporated species vacuum and = the and and determine 1, type pressures LUNINE as can 2, fraction 1, ... constants t vs. clathrate k is we of lead respec­ , in temper­ • and strik­ cage, each now (56) We Provided the for the of to in AND t STEVENSON Langmuir major and are where N can interest lar water ments not while using N, N NH surrounding structural 0, clathrate of clathrate dominant dances lite large Lewis ment that may nents plots polymeric present chemistry. Prinn Such 2 2 H Ar Ne N2················· co CH CH of Kr We Xe XcH Table clathrate by jNH and GAS abundances calculated and is 3 nebula. incorporate 2 differ t), N we NOTE.-Abundances 0 ················· ...... never ...... 4 4 dissociation material fraction was 4 ...... present equation are 2 CH ice. Molecule is the and or and are lj clathrate-forming • ABUNDANCES apply of ...... and 0 Only to then in consider, 3 N) 0 3 CO, for in to formation. 4 molecules is discussed ratios At type coefficients carbon by determine compounds, lists NASA from is the Xco Greenberg be and Prinn An formation Fegley good in are the remove the satellite the respectively. low in the equation for of as could heated the (57) gas in rather the important top refer primarily in NH both controversial; Anders following those Sun ...... much thermodynamic pressure the equation temperatures dissociation coexistence (1980) (MOLE and gas the three phase assumed Astrophysics instead (1981) above. 3 containing to comprise In evolution its structural solar dominate and ~ are than sufficiently in outer phase, it computed nebulae atoms (1983) nitrogen /kt=p which entries All as 15% (56) 3.33X10- 9.10x10- 7.65X10- 0 1.48x1o- 2.83x1o- 8.90x10- 3.20x10- what maximum FRACTION) a and gas. is in not or assumption TABLE3 versus expression giant low-temperature/pressure and a nebular nitrogen (57) argue of solar gas-phase that clathrate able factor of to could Ebihara Pk follows, with differ where too equation comets. and in pressure If models. giant-planet these ( (T is Lewis type from does in planets. 9 6 models 4 4 10 species 5 3 the PJ temperature pO, contact; all the system possible to the that to different RELATIVE < k is a for degree processes. pure associates all be of 170 Data (I Anders high-pressure assumed return elements participate of not water holds: but outermost the implicit and large- we carbon (1982). Even abundances. or locked CO (56). Recall -10 of the K) in gas may of two Abundances strictly II) binds the of assume that TO clathrate System Prinn (both and nebulae the to ice the and if to gaseous C, is types preferred incorporation j. when We and H2 issue for reflect (particularly up Relative suggest that most in be the in CH Ebihara For only chemically N, solar available in solar 0 2.83x10- hold, 8.90x10- 5.90x10- 3.20x10- 9.10x10- 3.33 7.65X10- IN N major the in the assume in for of (1980) all 4 protosatel­ small-cage gas of 2 NH NEBULA computed and gas-phase Figure /CO the as nebulae. of the X interstel­ grains X form of environ­ effect work gases nebulae are co kinetics compo­ Vol. nebula, 10- of nebula it by and 1982. that phase. 3 the form abun­ struc- given gases 0 ( does is that of and and 9 4 4 4 10 ele­ 6 5 57 the the for 58 C, 17 C, of of of in as to P is k ) a 1985ApJS...58..493L 100 conditions lines rate stability form the nebula, water satellite for are around and as available Fegley ture clathrate No.3, formation as discussed FIG. a presence structure increased in K, Consolmagno I gas show upon as clathrate formers solar 1985 17.-Condensation (1981), respectively, Saturn, nebulae T- lines of clathrate. which from water is in formation © amorphous and cooling of 50-60 apply II text. therefore in hexagonal American amorphous Lunine for clathrate ice is are giant-planet temperature capable separately (1984). Plausible T is K, also to of :::;100 regions in and uncertain, evaluate ice and P ice in temperatures shown, are the -10- The amorphous the water of implies, Astronomical I. to K Stevenson P- nebulae. similar. form for - I- ~ for tying cases absence Its plot and T 6 from abundance ice. a regions CH and to importance 140~~~~~~~~---r------,---, of given in indicates however, of P up ice, The THERMODYNAMICS "Major'' 10- 4 Lewis which :$ clathrate; selected we of (1982b), most respectively. and 0.1 clathrate 5 pressure. for other choose bars. each patterns bars, (1974), CO solar that Society that of major is under gases. comprises the for clathrates here and The most in T it boundaries Shaded and The volatiles Prinn = available does the a in -6 nebular Results Pollack defined 60 dashed nebula proto­ of meta­ clath­ • LOG solar areas are areas and the and not Provided the in in full a OF solar PH solar plausible CLATHRATE 2 by abundances do as cules increased CH cases, dance clathrate in incorporated and Figures the derived composition their carbon (BARS) Using -4 the indicated by not 4 - nebula; CH abundance clathrate to pressure-temperature 5 of clathrate the respectively. affect if 18a determine 4 abundance. in molecules Table display by clathrates structure gaseous NASA § in that below. and HYDRATE a our in / is III, factor Jovian atmospheres 3, that clathrate. / is structure a 18b conclusion. is, nebula, equation Solid the value -2 then / in we Astrophysics Ratios II Figures their gases are of depict / clathrate is altered fields compute and ./ the 5-10 plotted assumed of stable; presence Some II, ./ which may log (56), dashed total 19a for I In Ar, and abundance (1) relative vs. for solar be the this species and initial incorporate Ne, and the to H = N in lines taken the contaminated CH 2 and 2 0 affects Data be the and the pressure. by ratio 19b in CH to for 4 abundance Saturnian incorporate structure gas case, of this pattern LangmUir initial - H 4 the display System -rich our 2; the 2 of is figure. completely The abundances clathrates Kr these fully various calculation various abundance nebular and in by I. CH is in the constants increased If clathrate. depleted; so Both increases clathrate 4 CO-rich the and CO refer highly models abun­ mole­ gases into gas. CO 519 are CO or of in to 1985ApJS...58..493L relative high relative Ar because pressure pure striking (Miller (Mukhin clathration enhancements composition incorporated meteorites ratios similar 520 sure available a abundance. Of two porated ahundance maximum to relative - - g (!) ...... "lower u Figure C0 FIG. be in -10 particular -6 -4 -2 being of propensity condensate in 2 the of to 18.-Abundance in to, and pure is to HzS, it to enhancement N of double the critical 1983; 20 structure C0 not structure dependent Ar 2 involves but (Delsemme relative © solid C0 , amount and Smythe shows CH CO, C0 all 2 in interest is shown, American are generally to 2 occupancy Donahue P clearly for 2 the 4 decomposition or condensate NE -rich and C0 CH4 be in clathrate, likely terrestrial-planet I I to of the in the C0 clathrate PH mixed clathrate 1970). 2 present on CH CO CH of because are • clathrate, of gas, Ne, and AR evident 3 same 2 However, caused volatiles , more by 4 ambient to 4 and and and Xe (1) 100 or Kr, Miller in as Hz clathrate Astronomical Below and do is dominated CO in sort KR the all relative the and CH Pollack pronounced K a of and less and by so. pressure" from These incorporated. function condensed the N hence large noble nebular clathrate. 4 1970), of Ne. physical this some Kr, • in We than Xe ~ote relative a atmospheres in guest-host Nz. to solar 1983). abundance by uncertainties temperature abundances the thus and gas the the these would C0 of Unshaded for (a) conditions also composition than, latter adsorption, material ratios All nebula, proportion dissociation depletion 2 temperature. expect The C0 Society CH ratios the will sulfur be interaction 2 those 4 LUNINE is patterns meteoritical existence expected and at and bars always relative (Fig. not almost the in given in is and either gas -120 seen assumed of (2) (b) a which, its refer of stable • vapor pres­ incor­ solar C0 The Ne, Provided gas 21) are the the the CO be all AND to as of as in to K to 2 STEVENSON propriate. species CO-dominated total temperature. relative g u.. (.!) 0 0 t; ~ a: z z (..) ~ ~ a: 0 LLJ FIG. FIG. by (.) <( <( 0 w g ::::> (.!) z z m -10 -6 -8 -4 -8 -4 -6 -2 -2 available is the 19.-Fraction to 20.-Noble -1 Unshaded sequestered CH4 abundance NASA Double in clathrate. ------SOLAR------100 solar bars gas occupancy K composition in ratios of Astrophysics A abundance assume clathrate. volatiles log in value by solar double incorporated Ne gas, "C" of ratios composition is zero for occupancy neglected. refers Data (a) in means c CH CH to in 4 System gas, 4 -dominated essentially CO by clathrate -dominated Hz as or a and CH function relative all 4 Vol. Ne. clathrate and of as that (b) ap­ 58 to of 1985ApJS...58..493L produce dominate. incorporation is surface clathration, quences. cometary observed in hence, would could of compared and ceous ducive Doubling tain more Ne spheres. abundance CH No.3, in The FIG. water the 4 abundance Pollack -dominated carbon good chondrites, than be have accreting to 21.-Abundance 1985 the noble Key: adsorption similar with ice. It the material twofold due the (1983), thermodynamic initial 2 in © so been as (1) has in formation Temperatures solar Earth clathrate, gas ----1----- American the (J) ® @ @ ® CD ® gaseous in and (5) CH (4) Earth to -8 partitioning. Jupiter (Lewis been and gaseous low-temperature and abundance, normal supply atmosphere enhancement the 4 enhancement onto processes masses LOG partitioning or atmosphere, Pollack -6 (6) (7) (number) suggested accretion methane CO of assume the chondrites, solar. and of (ABUNDANCE) methane contact -4 ices Astronomical of and and meteorites, The planet. methane is, (1)-(4) presumably of CH --- double ----- ratios (2) 1974) Black or pressures may ---- however, abundance maximum (Stevenson of of Jupiter -2 of 4 Venus conditions (5) as clathrate with 132XE 20NE from 84 This from several carbon (1982). THERMODYNAMICS of occupancy. molecules CO-dominated these have were KR/ and in -0 noble atmosphere, /36AR ;36AR Mukhin surrounding (Gautier the material 36 terrestrial-planet the solar in much probably AR Dashed gases uptake observable or Earth implies relative 1982b) the Society Jovian where gases core, 2 solid in (1983), in environment less enclathrated abundance. extensions et could clathrate, possible (3) in masses an water methane; clathrate al. envelope dredging not that to gas, than Donahue carbona­ clathrate unrea- conse­ • 1982) atmo­ solar con­ con­ the Provided the ice (6) in in of of OF CLATHRATE in of Jovian hypothesis (bottom) from can clathrate clathrate; core imply enhancement ing enhanced during Lunine Measurement ticular, nents were noble models. much nitrogen noble hint uses ratio rate nebula process Saturn scheme sion sonable function accreted a atmospheric CO a cient and assumed atmosphere One cold Owen, abundance cores observed gas incorporation monoxide nucleated substantial to warm number The Finally, Uranus the by other determine the pattern or at be as hypothesis to currently the in required gases enough derived of mass were gas a smaller the gas giant primitive water-cloud and into use a and CH the and Titan's these for likely occur; quantity much calculated. period distinctive twofold solely impacting of Atreya, hydrocarbons these due under ratio carbon carbon up signature Titan's clathrate; of collapse against and entrapped of 4 possibility abundance NASA Cess by converting calculated dissemination the derived Stevenson observed :::; was planets abundance (Lindal HYDRATE clathrate. Figure bodies, to from in to noble would to of 0.4 of other as to favored than planets an N the from early is Neptune formation. 10 present is N 1976). if the to 2 source. allow clathrate clathrate noble removed Donahue, enhancement, twentyfold atmosphere account Me 2 others outline 25 a seen the the level. noble Galileo the clathrate-bearing threefold Astrophysics scenario Because would 22 ultimately scenario was for gas gaseous Jovian the amount Saturn not g potential in condensed in methane eta/. that above. for (1982a). core primordial issue ratios (extrapolated of initially incorporated Alternatively, model Under at condensation might of gas clathrate. Titan's temperature Jupiter: enhancements discussed which discriminate probably gas CH Uranus and present. in of the N volatiles be for dominated to material The probe 1983); and abundances atmosphere; is 2 of methane of (Owen (Mizuno in nebular Since 4 a the pattern. as may large directly for distinctive. stabilize the the a enhancement. from can the solar diagnostic do plausible In history the the the Uranus of material, "secondary Kuhn marginal a envelope. The giant-planet ammonia > simple The either could not carry by envelope methane Titan be observed accreted function H in measuring origin did 1982) 0.6 noble for composition smaller Data clathrate the and planetesimal if 2 enhancement of constituents compositionally, from Neptune. latter Tied accreted involve Miller the by latter 1980), pressure (1978) CH to in not Uranus the a Me and model, along condensed thus methane scenario is assumption the pressure Figure its record permit CO derives case core of of the gas 4 System presumed in clathrate Earth-based originally enhanced condensed hypothesis dredged scenario in envelope-to-core of to clathrate of (1961)-in enhancement N The volatile enhancement Neptune the clathrate and would with the test formation, photochemical (top) envelope in 2 enhancements with the (Lewis and with environments The the and " total methane produce 22 atmosphere. of the this 1.5 the stability is debris, hypothesis conditions or competing accrete then the in the Neptune) CH the argon-to­ plots solids dredging presence from methane given accreted possibly or requires that lead compo­ conver­ contain to present bar Saturn, way. carbon carbon carbon at would allow­ 1974). in (Lutz, above as clath­ 4 noble suffi­ CH have as data par­ 521 and the the the the the the the the the for N or in as of to is is a 4 2 1985ApJS...58..493L up cheinically escape 1982). is Titan is i.e., hypothesis rated bars priinitive primary sequester) spheric from considered, CO clathrate available g number the CO-rich, to that temperature - 522 of the In More FIG. 0.2 -1.5, explain to on age the equivalent and N the in Yung, is nitrogen several If for 2 22.-Predicted the of of and Titan accreted escape includes plausible amount carbon could modestly for the secondary N CH is dissociated more of ratio the depends the at 2 © only the bottom 5-9 Allen, CO structure budget 4 more the while • American tens solar to be present surface Increasing of present or clathrate than X of species 1.4 as the hydrocarbon perhaps surface. in w- brought CH likely CH of N and other condensed on retaining N noble in( bars system excess amount 2 99% 2 N 4 4 bars II 4 pressure. brought -rich, the to) • Titan 2 to hypothesis, Pinto is is atmosphere, clathration It case of with gas is processes set From CO. the of carbon CH into the Astronomical of of is by structure N a at enhancements (or of the of 2 surface (1984). nebula atmosphere. N difficult solar; 4 ammonia ratio, time 60 into In photolysis CO-to-CH , This is Titan hydrocarbons 2 outgassing) our structure and primitive K, 0 en the extreme w ~ ...... J > 0::: <[ <[ w w ~ m u ...... J 0 0::: could z z <[ ~ CO!llposition obtained. up Titan (no (Strobel and is I that Hunten which results containing especially The all 12.0 by clathrate. and just 0.0 to to ammonia), that (the be over of clathrate, 4 would 1.0 in of 7% conceive I marginally ratio is methane atmosphere. produced of above, 90% CH ratio More the the Society rock-to-ice co and eta/. CH estimated solar of limit CH produced Note of 4 for allowing priinitive a 4 of wato/ LUNINE the remove 4 clathrate Shemansky the , in 1984), mixture interesting abundance clathrate it where estimated 1.5 the of or :;...- that the incorpo­ mass the is nebula, enough photo­ X -- atmo­ entire • ice - to clear ratio CH essentially 10 This over and gas Provided the for 2.6 (or N CH4 be 1.4 of of at 22 is AND is -- 2 4 as 100 a /CH4 -- K. function STEVENSON all decreases preserved lead into invoked. (T higher preponderance being N CH enclathrated abundance clathrate as acceptable clathrate, creases occurs, g dance For ment 1.6 as abundance tens to Dashed lines em- 2 NEIAR CO -- Figure an high = by a 4 SOLAR are this to of 80 clathrate function of average brought of abundance 3 assumed the than - ; densities bars as when as sufficiently 1.8 CH CO their reason, K). 0.4 The 23 at the the in the - NASA then, 4 show in in the relative of plots lower times enhancement into For 20. CO-to-N with observed density the 90% H photocheinical clathrate of clathrate much CH of CO observed to 2 we enhancements for 0 The some Jupiter eventually CO oxygen a Titan N 4 that remain of excess temperatures. consider and Astrophysics similar over the 2 to Nz/CH gas /CH /CH for more physical the 2 values CH in mechanism other is abundance 2.2 CH of does in atmosphere. the Titan abundance value locked a carbon 4 assumed 4 water 4 fixed). Jovian N that readily CH 4 and that 4 for is in age drops 2 Saturnian mechanism are abundance not cheinical of implausible. (number) 4 of and structure the -rich in this CO of in the atmosphere. available is Because Two 1.88 - converted rise for ratio CO than the the sufficiently surrounding /CH CO in Data 2.1 required goes ratio nebula. For g destroying sharply the range implies satellites properties effects II solar g in relative cm- CO 4 (the of ratio clathrate. cm- down, CH hs model this should clathrate System form ratios to to Top Samuelson This 1.1-1.4 system 3 extreme or CH oxygen . 3 4 occur: form a of , until It that of panel substantially incorporates water of nebular to N 4 and in would of would . more have 2 - Formation -1.7-1.8 CO. , CH clathrate could must it CO g effect CO-N 0.25 assumes the (2) (1) enrich­ Vol. budget em- abun­ to is 4 been eta/. than lead also The and gas the the in­ N be all be be 58 in 3 2 2 2 • 1985ApJS...58..493L present photochemical (and (1983) Ar value rate. would present N N system such surface, CH escape 1984). the ries not upper this atmosphere tive then of No.3, - in nitrogen function 2 2 10- One The H FIG. an origin present and 4 produced from have rate N 2 that If clathrate), 0, of the CH 2 2 limit be If 1985 can above potentially ocean (Strobel history. 23.-Ratio atmosphere atmosphere. CO, is CH all to of abundance divided Ar u z the would uu OI:I: Nl been 4 ambiguous. clathrate their assumed is Ar-to-N (!) (!) 0 0 _J _J -produced CO-to-CH 10 destroy CO © available of in 4 1-- !ci u L&.l comet be of clathrates, has in CH pressures are observational but factor 100 clathrates consequences (the incorporated in above clathrates H the through Hence, water in debris of the clathrate comparable LUNINE -10 atmosphere component two § for the system. 2 been calculated the system shown dM-Ne makes literature the phenom­ K the clathrate enhance­ Plausible "double­ III. a nucleus. nucleus. primary primor­ 1982b). double­ smaller 22 of of helium nuclei, qM-He points above, (Prinn some­ in • ice outer outer form. work con- g, pro­ 10 was The H d and the Provided the de­ ice up of of to in in or A :-:;; as in = 2 4 is AND , , STEVENSON The is in limiting model planetesimal bodies assume and The dance determining directly. consider during Kr/ velope the velope. requirement work pieces, portion pressures pressure solar signature sumption form atmosphere etary accretion and This ity Hunten the modeling range budget Stevenson stand shown application all atmosphere gaseous thermodynamics. taining tional through their this to The In still by the of hot but proviso system.) Ar paper. Stevenson (1982b). condensing b) highest conclusion terrestrial composition of model in debris, planetesimals of this cool patterns, the the clathrate which accretional in necessary is are to allowing accretion The that the of clathrate. (high Application ammonia factor progress. of eta/. the accretion accretion Clathrate here. (- in of that of terrestrial adiabatic Figure and initial (1982b). NASA section, Much down. Titan. their of to ammonia of earliest is envelope the surface must, Saturnian temperature of the mass physical So 0.1 clathrates, into may (1984). kinetic velocity, modified (see Titan the the evolution The nitrogen, as transporting is volatile is volatiles, long entire kinetic thermal bars) of would 8 Here conditions to gaseous Both not segregate and the illustrated The They The models, planetesimal Galilean too model. model below), however, may Astrophysics to are two stages and, atmosphere because convective Briefly, temperatures the during consider The limitations) processes are as surprising inner Titan hydrate small atmosphere; abundance nebular we solar of possible outlined: nebula, For budget high by effort and have energy point have the applications hence, carbon, slowed structure high processes as is equilibration envelope, The these will from the of the satellites accretional Accretion volatiles Titan, motivated solar given the be clathrate, to abundance of in abundance the of temperature), accretion. been carefully to atmosphere mass been emphasize physics out in latent models and mass which affect the temperature applications surface noble augmented cold the and considering gravitationally the implications satellite, by fully resemblance than neon, modeling the system are of in the in this next much the which of in gas large Data too atmosphere methane and volatile (where are other equation is and outer heat the gas obtained this of explore primary is in Titan as by heating motivate of large is between disseminated temperatures physical distinctive drag, and two of of Planetesimals high beyond given further terrestrial where the role Cooling the signatures the thermodynamics solar-orbiting forming more accretional is the this and, optically volatiles release System solar nitrogen methane of by the the are involve extensive involve optically sections. structure and water mass bodies limiting disseminating of phase to these need of clathrate. (22) volatiles the in and model other hence, under complexity impact "captures" important temperatures evolve the discussed the system processes the and the the condense Xe/ History Lunine of of primordial in in planets. postaccre­ of noble budget contained to models thick (Fig. clathrate so-called is scope is infalling high and in are diagram freezing sources. extreme thick Ar case volatile a the energy. Lunine and surface the Vol: under­ of falling in veloc­ abun­ in not small (with high­ com­ low) (We 21). and and en­ gas en­ gas the the the the as­ we its of of in of in in 58 in in It is it a a a 1985ApJS...58..493L schematic. curve no posed point cussed from toward rate-saturated now sphere, accretional affects accreted clathrate-saturated point such atmosphere as are can clathrate. propriate. 8), surface superposed duced cooling methane be base No.3, formation; the During Similarly, FIG. the in longer methane base identify constrained of dominant as the from during in contact - (.9 0 (f) o..u _j (!) and the methane amount inferred be structure at indicated and atmospheric maximum Saturnian to replaced be Subsequent 100 Measure­ conjunc­ clathrate the of ice, xH mantle, derived be of release be in evolu­ clath­ • CH Pinto bars) 2 total core o and and ob­ Provided the de­ on of on in by < 4 to is y I , OF CLATHRATE up pressure ammonia ammonia-water of laboratory the hydrate N system. escape and crucial generated important. tion may mental kinetics regime. rate resolve pressures bombardment point stable satellites CH over calculated, ments may utility and Only of composition made, wide pressure-temperature been H abundances data of dance chemical van and est statistical e, 2 3. 1. 2. We The We by amorphous double planet . to to 4 solubility Hz, Ne, it of The kinetics ) der be then in Map Map Measure examined the to is in range outer pure in the P conclude was of phase have of and pattern of temperature data remaining importance The required that in of this systematically down identification ~ a Waals these such above in entire guest produce on such and and occupancy Jupiter's 15 out release investigations out interest. clathrate NASA near-surface, satellite mechanical and concluded phase are solar However, to presence diffusion the of undertaken HYDRATE of in gaseous outermost, diagrams kilobars the of VIII. as stability to ice dissociation satellites satellite (Cheng verify not phase experimentally, molecules the diagrams of results clathrate temperatures solution. with potentially pressure-temperature clathrate giant-planet and methane to Titan T- (which system resulting on uncertainties of dark volatiles and effect SUMMARY Astrophysics by ensure of atmosphere, formation in We Platteeuw a the nebulae 50 of clathrate curve methane diagram process that of of clathrates and were was calculate list and coexistence regions of accretion. model both planetary according polymeric understanding cage K. porous could which studies. predicted cage formation an of is -kilometer-deep in ammonia occur, methane in have collisional substantial of pressure phase T also Examine stabilized Lanzerotti testable ammonia then for entrapped modeling analysis water AND and sites ~ recommended postulated to postulated for is double impacts in slowly of of as formation. would of from in 320 (1959) demonstrated. CO regolith sufficiently of leading dissociation In predicted used for such well CH Predictions evolution diagram. guest clathrate CONCLUSIONS to material. satellite the by diagrams clathrate CO, clathrate of and particular, under hydrate K. and Data (Galileo clathrate, the Figure 4 stirring example). by clathrate occupancy diffuse of small was test range clathration work. as nebulae , to a the 1978) along the Measure and N Nz, in ammonia-water molecules to effect confining would calculated guest the structure determine 2 our conditions considered. In , evolution depletion System atmospheres clathrate (Hartmann Determination molecules slow formation in be role 10. and CH observations do of the Such out and compounds pressures thermodynamics formation of charged-particle the probe of of with predictions of we the was which source molecule may An 4 stability not diffusion planetesimals The CO of is nonsolar the , the that the N of cases of dissociation have Ar, data hydrostatic outer as useful. 2 addressed, of laboratory the important the exist. the the measure­ clathrate clathrate be presence clathrate effect methane of in issue of of impact­ has Kr, a Experi­ such regions cosmo­ at body). degree over used of are abun­ clath­ 1973) inter­ ice. func­ more solu- large solar solar from were were (i.e., The and and and and low Xe, 527 not gas Hz of of of of as a a 1985ApJS...58..493L helpful; hydrate portions pressibility clathrate? evolution out larger recondensation satellite (Davidson tion tory, tions the to 528 indicated where where pressure path. studies checked and clathrate give Lewis Kauzmann which below existence choice approximation consideration. temperature where the KP 4. 5. 6. The form To Using density their =constant. form of Bryan a with Study Measure Study at Within number determine the value we is 273 the fits compressibility of (Pearson ice evolution i.e., under clathrate. high regions independently for of the not studies. of stability emphasis above, KP have ice constants of agree K © of and and of 1979). the (1969, rheological is CH flp.P within water and above crucial. changes (10 a I each American seems the clathrate high-pressure of Although the a of here. value kinetics broken 4 gas of We Wilson metastable 4 however, eta/. with range pressure the is studies. density defects water Also, boundary p. and Elucidation ice exposure stability. phase, bars) data on 20% _c, facilitates to Varying also 93) is high-pressure In are flp.P 1983). of the diffusion produce up (Bridgeman N b, at of given of and the of more and the 1963) no and pressures 2 the of in given and is assume however, data high data the pressures. clathrate that Astronomical in at These volume experimental high-pressure of liquid-water required. in ammonia-water clathrate clathrate models thermal clathrate We Lupo in KP important the pressure low a of clathrate fresh the in and (10 of in the Lupo time to apply therefore for the high-pressure the properties ice Lupo that 4 liquid-water field, within is and stability 1913, pressure; most thermal flp.P formation we limited ice, the clathrate bars) scales Indirect containing properties also We "low" I, process and structure cage, llp. to integral Lewis the calculate and and formation for or region, consistent is 1937; data the rewrite 13 Lewis modification crucial assume pressure. -1%. of (T, on still vaporization clathrate expansivity field the which phases ( are Society Lewis studies particular also, < gas (1979). whereby evidence exist in the P) K into Dorsey than regime 4 formation important a however, (1979). various LUNINE of flVP p Phase the of through the (for kilobars) to function = other is =..!. (1979); would the clathrate and to clathrate intervals Measure clathrate llp. of pressure in since only satellite VdPr labora­ undergoes example, and justify by • agita­ 1940, for water-ice 13 com­ ice A of boundaries of hand, is H map pro­ dV ( and Provided APPENDIX ice the weakly T, be 2 calculation of to write the these AND -1-3% clathrates region of S clathrate a I I clathrate stability P p. corresponding these dependence phase hydrate, 0 pressure. boundary setting ) 212) it are +'f. not STEVENSON phase no dependent as within manuscript. products. products NAGW-185. sions, clathrate; ing particle products properties pure (1983) The may clathrate and assumptions, = i for fits boundary well well to We 7. has structural boundary under (Ross J.P, ..!. by by VdPr' P,_I it satellites quantitative verify the stable low contain to the CH Equations Study equal must Whalley been dV known. each as the thank and and of llVf( data bombardment pressure 4 water to the and thermal (Pinder of detectably on lice Smythe , flp.P study are that at N NASA Stoll be water the pressure assumed to phases D. in I CH T, type results phase clathrate. 2 whose This and temperature Stanley The , important Andersson continuous that (1980) as previous or spectroscopic system at P) for W. of 4 and evaluation of -, phase region of 1964) there (1975) conductivity high CO existing dP, of of the the work density Astrophysics N in transitions the interiors guest Davidson is different Bryan to is 2 the water Miller -, frosts?) of the given visible ( very were be is clathrate consistent sources. suggest -10 and to studied surfaces coexisting some across 1982), was high-pressure molecule T data similar (1979) as thermal encountered sensitive of constraints. determined and for may detectability kilobars) CO-rich and from a as reported for flp.P supported in weak on rheology function Several the near-IR phase pressure fruitful we linear could should with contain to IR the sound velocity (Pearson a models those high-pressure Data ice-liquid and that to adhere evidence properties critical clathrate pressure equation pressure boundary be with ice the of by from along reflection be and fc of distinct produced of of P. clathrate. crucial by these System of field Cook choice confirmed. ice temperature as clathrate pressure. eta/. to satellites helpful boundary. review Eisenberg supporting the NASA the a produced I constrain of (A2). sources range the by form in function in to from and 1983; isothermal spectra of polymeric Lupo from clathrate (Are identify­ previous 10-20%, simplest Vol. We and discus­ KP. of Hence, of Leaist which These under ice grant {A1) (A3) (A2) were Stoll Our and and and ice) the the the the use the by its As 58 of of I. 1985ApJS...58..493L liquid-solid complications used pressures, pressures P- at introduced is ice: The where where volume equation-of-state expansion. each 100 interpolate where parameter stopped of estimate then the resulting by No.3, fitted, function cannot from of considering to pressures end Marshall, V(P) not Calculation Because Low-pressure As At 100 the S the equation liquid-solid K V ( quantity temperature to the between 2000 a > T integration. too value and the the at volume 1985 integration K, P,(T) be check, 10 evaluate Vo; ~ at of x- high volume fugacity fc(T,P)=fc[T,P,(T)] at up volume and rotational far Debye made 300 kilobars) a 5 to of x Since by © 10 or pressure phase dP the derived linear P (4) 0.8-0.9. and =vapor 10,000 in to the S(T, above pressure in using T Kobayashi American estimating extrapolate I data of K kilobars < boundary uncertainties dTI entropy equation accurately; 700 with and integrating equation the 4 fit integration data model uncertainties data the boundary T 10 at Their up interpolation J-0) kilobars available is available the v above bars. 10 at but by 10 additional bars 100 The kilobars, methane to was pressure good P from in was were 3 kilobars, 0 at two kilobars data for not was the and = K an pressure. (1964) the The (A7) Debye (4) and a from the then 300 read Astronomical to we fits solids different pressure to pressure-volume Robertson available vibrational independent volume region continued evaluated 10 in showed final were volume on linear only volume joining inherent calculate pick is (or fugacity and entropy the bars, derived the kilobars. thermodynamic was at as off with a model less yields volume presented Here moderate exp{k extrapolated P-T is Marshall, of thermodymamic - a then fits from made THERMODYNAMICS estimated and values data that at convenient the continuously that than 8 data interest, that using and in in states from yields contributiop. to kilobars. plot fc(T, the which fc(T, (Reif At fashion. case. ~V S(T,P)-S(100 1 a at Goodwin the was the T[- volume between the derived unity to of Babb to entropy linear other 180 pressures from of data a data the Society Saito, P) P) of linear above S(T,V)= 1965, ~S solid cp high-pressure Cv linear acceptable. the from cp found f the quantities. vapor the K T alter pressure via This -1. same since = differed Here (1969) near temperatures, were of 2 from 00 new from fit 0.7 from throughout pure cJattice and (1974) fits field change to methane p. quantities technique, equation in KS(T',P,)dT'+ the Cheng, fit (In the approximation turns by of indicate and the source, 10 415) pressure) the S thus the temperature. equation from overestimate • Kobayashi the the methane on Cheng using f. log rough was derived for this kilobars depending + Provided V methane The 2 estimated K,P) solid at v 0 of fluid adjusted above above Daniels, c:otational methane-ice kilobars. OF fc which Goodwin molecule dT dP (A4). calculated 700 supercritical freezing and derived cp the it the agreement calculation thermal freezing-curve field to I (A6), at CLATHRATE (300 was methane dissociation v = phase bars at liquid sources, in techniques. dV+S(T,V(,). empirical (1964) critical cp l P T; 100 Data slightly the 308, and on Debye amounted T -1 desirable the = Numerical K, by are forT from constructed above. f.P (1974). see Cv(T',P)-, in P.(T) X expansion diagram. using the 300 fVdP and to 3 absence data Crawford 373, is excited the the volumes data in k out we temperature, regime Figure to begin Cheng, V(100K,P')dP'-lr adequate + in to temperature temperature bars)- fit solid Goodwin pressure integrated liquid-methane the be Entropy The t and to fits data, NASA to produce the integral more k, to HYDRATE of integration be The calculate at of specific dT' the -10 9. only T' extrapolations constructed coefficients regimes. range 473 for were two Lupo Daniels, (1975). accurate the additional assuming 0.7, Normally closely integration.) for fugacity by at convenience, K, kilobars, (1974) a Astrophysics agree a by 190 relevant along available for 100-230 our few for and better heat the because :::; and Since the entropy 11% At K. and by which 20%; than if methane purposes. high-pressure percent to field Lewis derived at an a to were other at by discrete the Figure data the fit. from Crawford temperatures within negligible using the constant lOOK 100 700 from isothermal for we K, to Fugacity of Lupo our resulting along The calculation fitted was freezing (1980). temperatures, since find that use 300 of uneven cp K S(T',P)dT']}• bars from 9 is Goodwin's calculation difference We the Simpson's fugacities were 35%, = illustrates the is Data and assumed in with cp- 1. is to fc(T, volume to (1975) calculated were coefficient the end then vapor calculations the excess generally dissociation total, At The path 700 an pressure which 0.7 Lewis data (Kerley the data System P) Lupo was the was isothermal apply likewise bars for integration was between to of the pressure constant approxinlation of (1974) corresponding the by of coverage high-pressure is calculated done were (1980), compare the consistency. dissociation within by small added, 100 is and 1980). and of isothermal acceptable techniques a calculated by 377 methane linear pressure a thermal linearly used data to K; by T direct Lewis linear Saito, curve up error (A6) (A5) (A4) (A7) with bars 10% The and and was and two 529 the 2% we fit at to to at 1985ApJS...58..493L 530 __ The Aaldijk, Avnir, Atreya, was with Anders, both ______P Barrer, __ at Byk, Brownlee, Bridgeman, Bertie, Barrer, Barrer, Carslaw, Chan, Cook, Clifford, Claypool, Cheng, Cheng, Carman, Culberson, Davidson, CRC Ellsworth, Eisenberg, Evans, Dorsey, Donahue, Diepen, Dharma-Wardana, Delsemme, Delsemme, Delsemme, Delsemme, Davidson, Davidson, Fowler, Fanale, Fink, Friedson, 300, York: sity (Oxford: 35,2076. land: T. 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