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Formation and stability of cubic ice in water droplets Murray, Benjamin J.; Bertram, Allan K. 2005-11-30

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Formation and stability of cubic ice in water dropletsBenjamin J. Murray and Allan K. Bertram*Received 22nd September 2005, Accepted 13th October 2005First published as an Advance Article on the web 2nd November 2005DOI: 10.1039/b513480cThere is growing evidence that a metastable phase of ice, cubic ice, plays an important role in theEarth’s troposphere and stratosphere. Cubic ice may also be important in diverse fields such ascryobiology and planetary sciences. Using X-ray diffraction, we studied the formation of cubic icein pure water droplets suspended in an oil matrix as a function of droplet size. The results showthat droplets of volume median diameter 5.6 mm froze dominantly to cubic ice with stackingfaults. These results support previous suggestions that cubic ice is the crystalline phase thatnucleates when pure water droplets freeze homogeneously at B235 K. It is also shown that as thesize of the water droplets increased from 5.6 to 17.0 mm, the formation of the stable phase of ice,hexagonal ice, was favoured. This size dependence can be rationalised with heat transfercalculations. We also investigated the stability of cubic ice that forms in water droplets suspendedin an oil matrix. We observe cubic ice up to 243 K, much higher in temperature than observed inmany previous studies. This result adds to the existing literature that shows bulk ice Iccan persistup to B240 K. The transformation of cubic ice to hexagonal ice also showed a complex time andtemperature dependence, proceeding rapidly at first and then slowing down and coming to a halt.These combined results help explain why cubic ice forms in some experiments described in theliterature and not others.IntroductionRecently, it was found that cubic ice (ice Ic), as opposed to thestable hexagonal phase (ice Ih), was the major product whenaqueous solution droplets froze homogeneously at tempera-tures of less than 200 K.1This strongly suggests ice Icforms inthe Earth’s upper troposphere where it may significantlyimpact the formation of ice clouds and enhance dehydrationthrough a process analogous to the well known Bergeron–Findeisen process.2This process is driven by the vapourpressure difference between ice Icand ice Ih, where themetastable phase necessarily has a larger vapour pressure thanthat of the stable phase.2Ice Icmay also be important in otherareas such as cryobiology and planetary sciences.3In our recent study on cubic ice we observed that a smallamount of ice Icwas formed when emulsified pure waterdroplets (water droplets suspended in an oil matrix) homo-geneously froze at B235 K.1This was unexpected as prior toour work, ice Icwas only observed in purewater droplets whenthey were hyperquenched onto a cold substrate below 190 K.4Ice Ichas also been observed when water clusters (6.6–5.5 nm)froze at 200 K.5Others have suggested that crystallisation ofwater droplets begins with nuclei having a cubic structure evenat temperatures well above 200 K.5–9Clearly, more work isrequired to understand the conditions that are required for theformation of ice Ic.To explain our previous results and better understand theconditions at which cubic ice forms in pure water droplets wehave carried out two sets of experiments: first, we haveinvestigated the formation of cubic ice in emulsified waterdroplets as a function of droplet size. Second, we haveinvestigated the stability of ice Icthat forms in these emulsifieddroplets. One of the benefits of our experimental configurationis that mass transfer via the vapour phase is blocked since thedroplets are suspended in an oil matrix. This allows us to focuson the solid state transformation in contrast to many previousmeasurements. Our combined studies provide insight into thenucleation and crystallization process, and allow us to spec-ulate on the structure of the crystalline nucleus responsible forhomogeneous nucleation in water droplets, an important topicthat still is not resolved. Our results, combined with previousresults, also allow us to speculate why cubic ice forms in someexperiments, which are recorded in the literature, and not inothers.ExperimentalThe X-ray diffractometer (Bruker D8 Discover) employed inthis study was configured in a standard Bragg–Brentanoreflection geometry and was equipped with a Cu Ka X-raysource and a Bruker SOL-X X-ray detector. In order toimprove the signal-to-noise a different source and detector tothose described by Murray et al.1were employed in the presentstudy. Other than a factor of two improvements in signal-to-noise, the diffraction patterns from the present and previousstudies are directly comparable.Emulsions of pure water droplets were prepared by mixingpure water (distilled water further purified with a Milliporesystem) with an oil phase in a proportion of 30–40% water inoil (by mass). The oil phase consisted of B10 wt% ofsurfactant (lanolin, Aldrich Chemical Company) inDepartment of Chemistry, University of British Columbia, 2036 MainMall, Vancouver, British Columbia, Canada V6T 1Z1186 | Phys. Chem. Chem. Phys., 2006, 8, 186–192 This journal is C13c the Owner Societies 2006PAPER www.rsc.org/pccp | Physical Chemistry Chemical PhysicsDownloaded on 18 April 2011Published on 02 November 2005 on http://pubs.rsc.org | doi:10.1039/B513480CView Onlinehydrocarbon oil (paraffin oil, Fisher Scientific, kinematicviscosity at 40 1C ¼ 34.5 cSt). This mixture was then agitatedfor 5–10 min or until the droplets were of the desired size.Droplet size could be varied by adjusting the agitation timeand the resulting droplet size distribution was determined byoptical microscopy (see the insert in Fig. 2 for an example of asize distribution determined by this method).The X-ray diffraction experiments were performed with amodified commercial low temperature X-ray diffraction cham-ber (Anton-Paar, TTK 450). The emulsions were placed in acell consisting of an aluminium base and covered with a 30 mmthick film of Teflon to hold the emulsions in place and alsoprevent evaporation of the droplets. The temperatures of thecell and emulsion were measured with a thermistor (Pt-100)positioned within the aluminium base. This cell was placed ingood thermal contact with a cryostat, which was cooled with aflow of liquid nitrogen and the required temperature set by useof a heater and temperature controller (Anton-Paar, TCU).This system allowed the temperature of the emulsion cell to beset to between 90 and 300 K (and to higher temperatures if theliquid nitrogen flow was stopped). The uncertainty in thetemperature was C61 K based on melting point measurements.The temperature of the cell could be ramped up or down atrates up to 30 K minC01, where 10 K minC01was the standardcooling rate in the freezing experiments. The cryostat andemulsion cell were positioned inside an airtight chamber whichcould either be evacuated or purged with a dry flow of N2inorder to prevent frosting at low temperatures. Windows madeof Capton in the walls of this chamber permitted X-rayradiation to pass into and out of the chamber.Since the droplets were suspended in an oil matrix preferredorientation of the crystals after freezing was not expected.Also, the measured diffraction patterns were expected to beequivalent to a powder X-ray pattern, since there were be-tween 106and 108individual frozen droplets exposed to theX-ray beam in a typical experiment. Totest these assumptions,we compared the diffraction pattern of the frozen dropletsafter annealing, which results in pure hexagonal ice (seeFig. 1a), with patterns of hexagonal ice calculated using thePOWDER CELL programme10using crystallographic datafor hexagonal ice.11The measured peak intensities were inexcellent agreement with the calculations, indicating preferredorientation was not an issue. If there was a preferred orienta-tion, or not enough frozen droplets to approximate a powder,the peak intensities would not match the calculations.Results and discussionThe formation of ice Icin pure water droplets as a function ofdroplet sizeEmulsions of pure water droplets were cooled to 173 K at arate of 10 K minC01, while monitoring a strong ice reflection (ateither 2y E 24 or 401) in order to determine the freezingtemperatures of the droplets. Freezing of droplets occurs overa range of temperatures, since nucleation is a stochasticprocess.12The observed freezing range of pure water droplets(between approximately 237.5C6 1 and 230.4 C6 1 K) is in verygood agreement with literature values for homogeneous freez-ing of micrometer sized droplets,12indicating that the oil andsurfactant were not significantly altering the nucleation pro-cess and that these droplets froze homogeneously. The ob-served freezing range varied by less than the uncertainty in theFig. 1 Diffraction patterns of frozen droplets. Patterns (b) to (g) arethe diffraction patterns of frozen pure water droplets, where the size ofthe droplets was varied. The volume median diameter, dvm, is given foreach pattern. The droplets were cooled at a rate of 10 K minC01andfroze between 237.5 C6 1 and 230.4 C6 1 K. The pattern shown in (a) isfor the same frozen water droplets that appear in (f), but which wereannealedat263 Kfor5 min to yield pureiceIh. Thediffractionpatternshown in (h) is a diffraction pattern of ice Icwith stacking faults. Thispattern was obtained by freezing 45.2 wt% (NH4)3H(SO4)2solutiondroplets, which froze between 192.4 C6 1 and 184.5 C6 1 K. Theestimated proportion of stacking faulty ice Ic, determined from thelinear combination of the hexagonal patterns (a) and cubic pattern (h),are given for patterns (b) to (g) (see text and Fig. 3 for details of thisestimate). All patterns are normalized to the intensity of the peak at401 and are shifted on the intensity scale for clarity. Reflections uniqueto ice Ihare labelled ‘‘h’’ and those common to ice Icand ice Iharelabelled ‘‘h þ c’’. Bragg peaks from the aluminium base and thosefrom the cell construction materials are labelled Al and cell, respec-tively. All diffraction patterns were recorded at 173 K. The baseline inpattern (h) is more pronounced compared with the other patternsbecause of the smaller water content in the concentrated(NH4)3H(SO4)2solution droplets.This journal is C13c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 186–192 | 187Downloaded on 18 April 2011Published on 02 November 2005 on http://pubs.rsc.org | doi:10.1039/B513480CView Onlinemeasurements as the volume median diameter varied from5.6–17.0 mm. This is consistent with freezing temperaturesrecorded in the literature.12Once cooled to 173 K the diffraction patterns of the frozendroplets were measured between 2y¼19 and 501. Patterns areillustrated in Fig. 1b–g for a number of emulsion samples ofvarying droplet size. The peaks exclusive to ice Ihhave beenlabelled ‘‘h’’ and the peaks common to both ice Icand ice Ihhave been labelled ‘‘h þ c’’. Also shown for comparison is thediffraction pattern of pure ice Ih, generated by annealing purewater droplets at 263 K (Fig. 1a) and a diffraction pattern ofice Ic(Fig. 1h). Pattern 1h was obtained by freezing 45.2 wt%(NH4)3H(SO4)2solution droplets, which froze between192.4 C6 1 and 184.5 C6 1 K. This diffraction pattern is in verygood agreement with the diffraction pattern of ice Icreportedin the literature.1,3,4,13Note that in the 45.2 wt% solutions,(NH4)3H(SO4)2did not crystallize, and hence in the diffractionpattern only peaks due to ice are observed. The major ice Ihreflections at 34 and 441 are completely absent from thisdiffraction pattern, indicating the absence of bulk Ih. The peakat 231, which is usually associated with the (100) reflection ofice Ih, is present in the diffraction pattern. This feature hasbeen observed in previous studies of ice Icemploying X-raydiffraction1,3,4,13and neutron diffraction14–16and has beenassociated with hexagonal-like stacking faults, believed to bean intrinsic property of ice Ic.3,14Also, the region between 22and 271 is raised above the background. This broad feature isalso most likely related to stacking faults.17,18Based on Fig. 1, the diffraction pattern of frozen waterdroplets with a volume median diameter of 5.6 mm (pattern g)has some similarities with the diffraction pattern for ice Icwithstacking faults (pattern h). First, the major ice Ihreflections atB34 and 441 are significantly reduced in intensity relative tothe peaks common to both ice Ihand ice Ic. Also, the regionbetween 2y E 22.5 and 26.51 is significantly raised above thebackground, similar to ice Icwith stacking faults.As the volume median diameter was increased from 5.6 to17.0 mm, the peaks exclusive to ice Ihincrease in intensityrelative to the peaks common to both ice Icand ice Ih(seepatterns b–g in Fig. 1). This indicates that there is a strong sizedependence of the ice crystal structure with droplet size, andthe amount of ice Icdecreases with an increase in droplet size.Overall, as the size increases, the diffraction pattern becomesmore like the diffraction pattern of ice Ih.The intensity ratios I44/I40and I33/I47(where I44and I33aretheintensitiesoftheexclusivehexagonalpeaksat2yE43.5and33.41,andI40and I47are peak intensities common to cubic andhexagonal ice at 2yE40.1 and 47.11) for the X-ray diffractionpatterns illustrated in Fig. 1 have been plotted in Fig. 2 as afunction of droplet size. These intensity ratios provide a con-venient qualitativemeasureofthe amount of ice Ihinthe frozendroplets, where I44/I40¼ 0.79 C6 0.3 and I33/I47¼ 1.31 C6 0.06indicatespureiceIhandavalueofzeroindicatesstacking faultyice Ic(the ratios for pure hexagonal ice are determined from thehexagonal pattern illustrated in Fig. 1a).The droplet diameter quoted in Fig. 1 and plotted in Fig. 2is the volume median diameter (dvm). The horizontal barsrepresent the particle diameter range over which 68% of thevolume resides. These bars were calculated from the measuredgeometric standard deviation.19Fig. 2 illustrates the verystrong dependence of the phase of ice on droplet size—asthe size of the particles increases the amount of ice Icdecreases. When the volume median diameter is 5.6 mm, thedroplets freeze close to pure ice Icwith stacking faults.Recently, based on classical thermodynamic calculations, ithas been suggested that pure water droplets smaller than30 nm in diameter would freeze to cubic ice and biggerdroplets would freeze to hexagonal ice.20These calculationsdo not agree with our observations that water droplets witha volume median diameter of 5.6 mm freezes dominantly toice Ic.The decrease in the amount of ice Icas the size is increasedfrom 5.6 mm can be explained with heat transfer calculations.When a water droplet freezes heat is produced, since crystal-lization is an exothermic process. If the heat is not dissipatedFig. 2 The intensityratio I44/I40(panel (a)) and I33/I47(panel (b)) as afunction of the droplet volume median diameter (dvm), which wasdetermined from the measured droplet size distributions. A value ofI44/I40or I33/I47¼ 0, indicates that no bulk ice Ihformed in thedroplets,andthereforethatthedominantproductwasiceIc,whereasavalue of I44/I40¼0.79C60.03 or I33/I47¼1.31C60.06 indicates pure iceIh(these values were determined from the diffraction pattern ofhexagonal ice illustrated in Fig. 1a). The horizontal bars representthe range of droplet sizes in which 68% of the volume resides. Thevertical error bars are derived from the uncertainty associated withmeasuring the diffraction peak areas. The bracketed letters correspondto thediffractionpatternsinFig.1. An exampleof a size distribution isshown as an insert; dvmfor these droplets was 10.6 mm with ageometric standard deviation of 1.8.188 | Phys. Chem. Chem. Phys., 2006, 8, 186–192 This journal is C13c the Owner Societies 2006Downloaded on 18 April 2011Published on 02 November 2005 on http://pubs.rsc.org | doi:10.1039/B513480CView Onlineto the droplet’s environment more rapidly than it is producedduring crystallization, the temperature of the droplet willincrease during freezing, which can allow ice Icregions inthe ice droplet to anneal to ice Ih(it will be shown later in thispaper that the ice Icto ice Ihtransition occurs more readily athigher temperatures). Based on equations given in Pruppacherand Klett,12and temperatures and thermal properties consis-tent with our experiments, a droplet of 10 mm in diameter willdissipate heat to the oil matrix at a rate similar to the rate ofheat production within the supercooled droplet due to crystal-lization. As a result 10 mm particles may not warm upsufficiently to anneal all ice Icto ice Ih, which is consistentwith our experimental results. Smaller droplets will have agreater surface area to volume ratio than larger droplets andwill therefore dissipate heat more efficiently. Hence, one wouldexpect the amount that the particle warms up, and thereforethe amount of ice Ic, to depend strongly on droplet size, whichis in agreement with our observations. Our combined resultsare consistent with ice Icnucleating in all of the droplets, andthe final amount of ice Icbeing governed by the amount thetemperature ofthe dropletincreases duringfreezing. From thiswe infer that ice Ic, rather than ice Ih, is likely to be thecrystalline phase that nucleates when water droplets freezehomogeneously at B235 K. In making this statement, weassume that the crystalline phase of the ice nucleus is the sameas the crystalline phase observed in the small droplets, whichexperience no appreciable heating. This is similar to assump-tions that have been previously made in the literature.5Thisalso assumes that crystallization begins with the formation ofa critical nucleus with a well defined crystal structure, which isstill a matter of debate in the literature.21Our inference that homogeneous nucleation of water dro-plets at B235 K begins with ice Icis consistent with thermo-dynamic arguments that indicate the free energy of formationof an octahedral germ of ice Icis lower than the free energy offormation of an ice Ihgerm.8,22Also these results are consis-tent with previous experiments by Huang and Bartell.5Theseauthors froze water clusters (5.5–6.6 nm) at 200 K in asupersonic expansion and determined the free energy of thesolid–liquid interface when ice nucleated in these clusters.They found that the clusters froze to ice Ic, using electrondiffraction, and they also noticed that the interfacial energiesthey determined were consistent with those determined fromhomogeneous freezing experiments of emulsified water dro-plets. Based on this they concluded that ice Icinitially nucle-ates in water droplets at B235 K as well as at 200 K.Furthermore, it has been suggested that ice Icis the phasethat nucleates based on measurements of the angles betweenthe c-axis in snow polycrystals and frozen water droplets.6,7These previous measurements combined with our direct mea-surements of the phase of ice that forms in water dropletsprovides convincing evidence that ice Icis the crystalline phasethat nucleates when pure water droplets freeze homogeneouslyat B235 K.In Fig. 3, we have compared experimental diffraction pat-terns of frozen water droplets with composite patterns gener-ated by taking a linear combination of the pattern of pure iceIh(Fig. 1a) and ice Icwith stacking faults (Fig. 1h). The bestfits were determined by minimizing the sum of squares differ-ences between the experimental and composite patterns. Theagreement between measured and composite patterns (opencircles and solid lines, respectively) is good. The good agree-ment suggests that pure water droplets may freeze to acombination of ice Ihand stacking faulty ice Ic. The propor-tions of ice Icwith stacking faults and ice Ihdetermined fromthis analysis have been quoted in Fig. 3. This analysis has alsobeen applied to the other diffraction patterns in Fig. 1, and theproportions of stacking faulty ice Icfrom this analysis are alsoquoted there. When estimating the proportion of stackingfaulty ice Icand ice Ihit was assumed that the X-ray quantita-tion constants (integrated intensity per unit mass of ice) for thecommon peaks are the same for hexagonal ice and cubic iceFig. 3 Comparison of composite (solid lines) and measured X-ray diffraction patterns (points). The composite patterns result from a linearcombination of two separate patterns: the first is a pattern of 45.2 wt% (NH4)3H(SO4)2solution droplets which froze at around 188 K to stackingfaulty ice Ic(illustrated in Fig. 1h); the second diffraction pattern (illustrated in Fig. 1a) is that of pure water which froze around 235 K and wassubsequently annealed at 263 K to form ice Ihwith no detectable stacking faults or regions of ice Ic. The pure ice Ihpattern and the stacking faultyice Icpattern were scaled and added together to give the composite patterns. The scaling factors were determined by minimizing the sum of squaresdifferences between the composite and experimental patterns and the resulting proportions of stacking faulty cubic ice and hexagonal ice areindicated in the figure (assumptions and uncertainties associatedwith these values are discussed in the text). The measured patterns are (a) dropletsof dvm¼ 13.9 mm (Fig. 1c) and (b) droplets of dvm¼ 5.6 mm (Fig. 1g). All patterns were background subtracted. The regions of the diffractionpatterns influenced by diffraction from the cell construction materials were not included when calculating the sum of squares differences and havebeen removed for clarity.This journal is C13c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 186–192 | 189Downloaded on 18 April 2011Published on 02 November 2005 on http://pubs.rsc.org | doi:10.1039/B513480CView Onlinewith stacking faults. Measurements in which we monitorthe intensity of the common peaks as cubic ice with stackingfaults is annealed to hexagonal ice show that the X-rayquantitation constants are the same to within 5%. Notethat the quantitation constants of the common peaks forpure cubic ice (samples free of stacking faults) will be dif-ferent from the quantitation constants for hexagonal ice,based on calculations of the diffraction patterns using thePOWDER CELL programme.10Evidently stacking faultsappear to influence the quantitation constants of cubic ice.Assuming a 10% uncertainty in quantitation constants, theproportions of stacking faulty ice Icand ice Ihonly change byat most 5%.In the future we will carry out a full modelling study of thediffraction patterns to quantitatively evaluate the proportionsof ice Icand ice Ihas well as investigate the nature and densityof stacking faults. Further experiments are also required todetermine if individual frozen droplets contain regions of ice Ihand ice Icwith stacking faults or if individual droplets freezeexclusively to a stacking faulty cubic structure or a hexagonalstructure.The stability of ice Icin water–oil emulsions (i.e. thetransformation of ice Icto ice Ihin frozen water dropletssuspended in an oil matrix).In this series of experiments the transformation of the ice Iccomponent of the frozen pure water droplets was investigatedas a function of time at several temperatures between 228 and263 K. Emulsified droplets of dvmE 10 mm were cooled at arate of 10 K minC01to 223 K, and then the temperature wasrapidly ramped to the temperature of the isothermal transfor-mation measurement (Ttrans). While the frozen droplets wereheld at TtransC60.2K, the diffraction pattern between 2y¼39.3and 44.31 was monitored. This covers the exclusive ice Ihreflection at 2y E 43.51 and the reflection common to bothice Icand ice Ihat 2y E 401.The ratio I44/I40determined during the isothermal transfor-mation measurements is plotted in Fig. 4. Prior to starting theisothermal transformation measurements I44/I40was close to0.4 in all measurements, which indicates that a significantamount of ice Icresulted from the freezing process, as expectedfrom the earlier work. The results in Fig. 4 show that at 228 Kice Icis very stable. When the ice was held at 228 K the frozendroplets still contained a significant amount at ice Icafternearly 12 h, with an intensity ratio I44/I40¼0.56C60.02 (recallthat I44/I40for stacking faulty ice Icis 0 and for pure ice Ihit is0.79C60.03). In fact, even after nearly 5 h at 238 K the ice hadnot fully relaxed to perfect ice Ih(I44/I40¼ 0.65 C6 0.03). Incontrast ice Icat 263 K is rapidly converted to ice Ih, and at243 K, almost all of the ice Icis converted to ice Ih(I44/I40¼0.73 C6 0.05) after 178 min.Totest if X-ray exposure was influencing the ice films duringthe annealing experiments, we repeated the measurements at228 K, but this time the shutter to the X-ray source was onlyopened for enough time to establish the ratio I44/I40once everyfew hours. The results of this test (not shown) are in agreementwithin the uncertainty of the measurement with the resultspresented in Fig. 4 (open triangles) indicating that the expo-sure to X-rays did not significantly affect the ice crystalstructure.Many of the previous measurements of the ice Icto ice Ihphase transition have found that ice Ictransforms to ice Ihrapidly below B205 K.23It has been suggested that the ice Icto ice Ihphase transition is related to surface area —very highsurface area ice Ictends to transform more rapidly and atlowertemperatures tothestableiceIh.4Inhighsurface areaiceIcsamples, surface nucleation is likely to be much more rapid4and also possibly mass transfer from ice Iccrystals to ice Ihcrystals via the gas phase may have dominated in manyexperiments.2In our experiments the particles are suspendedin an oil matrix and hence mass transfer via the gas phase andpossibly surface nucleation were blocked, which provides anexplanation for the longer lifetimes at higher temperaturesobserved in our studies.Ourlong lifetimesathighertemperatures areconsistent witha number of studies of low surface area ice Ic. Using X-raydiffraction Mayer and Hallbrucker4found that ice Icsamples,prepared by hyperquenching water droplets, required around30 min at 240 K to fully convert to ice Ih. Using a similartechnique to produce ice Ic, Kohl et al.3found that thetransition was centred around 230 K, while Kuhs et al.15found that a sample of ice Icmade from ice V mostlytransformed below 205 K, but a significant portion remainedin the cubic phase up to between 237 and 245 K. Kuhs et al.suggested this cubic portion of their ice took the form ofplanar stacking faults within ice Ih. Cubic ice has also beenobserved at higher temperatures in porous silica.24The stabi-lity in these experiments is likely due in part to the confinedgeometries.Fig. 4 The intensity ratio I44/I40as a function of time after freezingfor pure water droplets (dvmE 10 mm). A value of 0.79 C6 0.3corresponds to the ratio of ice Ihwith no detectable ice Icstackingfaults, and a value of zero indicates that no bulk ice Ihformed in thedroplets, and therefore that the dominant product was ice Ic. Resultsare shown for several different isothermal transformation tempera-tures.190 | Phys. Chem. Chem. Phys., 2006, 8, 186–192 This journal is C13c the Owner Societies 2006Downloaded on 18 April 2011Published on 02 November 2005 on http://pubs.rsc.org | doi:10.1039/B513480CView OnlineAlsoofinterest isthenonlineartrend observedinFig.4.Forexample, at 233 K there is a fast increase in the ratio and thenit levels off, indicating that a certain fraction of the cubic ice isvery long lived. This is consistent with the measurements ofKuhs et al.,15described above in that portions of the ice Icappear to be more stable than others. The fact that a similartrend was observed using two very different methods ofpreparing ice Icsuggests that this trend may be an intrinsicproperty of cubic ice. Possibly related, Johari argued that ice Icand Ihcan coexist over a broad temperature range due tocontributions from grain boundaries, interphases and strainenergies.25The nonlinear trend observed in Fig. 4 may also berelated to slow nucleation kinetics in some frozen droplets. Asmentioned we most likely only measured the solid statetransition (as the vapour-mediated transformation is blocked).Therefore, the phase transition is likely initiated by nucleationin lattice imperfections, such as line defects and at grainboundaries.26Some frozen droplets may have significantly lessimperfections for nucleation of ice Ih, resulting in some frozendroplets with very long lived ice Icregions. Smaller frozenparticles may havesignificantly lessimperfections comparedtolarge particles, assuming the occurrence of imperfections israndom. In this case, ice Icin the smaller particles will be morestable than in the larger particles (assuming the conversionrate is limited by nucleation at lattice imperfections). Furtherresearch is needed on this topic.ConclusionsThe data presented in this paper are consistent with theemulsified water droplets freezing to a significant proportionof stacking faulty ice Icand that the proportion of stackingfaulty ice Icincreases as the droplets decrease in size. In fact,droplets of volume median diameter 5.6 mm appear to freezedominantly to ice Icwith stacking faults. The size dependencecan be rationalised with heat transfer calculations since smal-ler droplets, with a large surface area to volume ratio, willdissipate heat more rapidly and be less likely to form ice Ih.These results support previous suggestions that ice Icis thecrystalline phase that nucleates when pure water dropletsfreeze homogeneously at B235 K.5–9When water droplets freeze in the atmosphere, our resultssuggest that ice Icwill initially nucleate. However, heattransfer calculations show that when droplets freeze in theatmosphere they will be more likely to freeze to ice Ihthandroplets in our emulsion experiments. The rate of heat dis-sipation for a particle suspended in a gas will be roughly afactor of 10 smaller for a similar droplet suspended in oil dueto the difference in thermal conductivity of the medium.27According to simple heat transfer calculations,12a1mmdroplet in the atmosphere will have a similar propensity forfreezing to ice Icas a 10 mm droplet in our experiment.Heymsfield and Miloshevich28found evidence that liquiddroplets smaller than 3 mm froze homogeneously below237 K in orographic wave clouds; we suggest that thesedroplets may have frozen to a significant amount of ice Ic.We observe ice Icup to 243 K, much higher in temperaturethan observed in many previous studies.23This result adds tothe existing literature3,4,15that shows ice Iccan persist up toB240 K. Our results focus on the solid state transformationsince we most likely blocked surface nucleation and vapourtransport by placing droplets in an oil emulsion in contrast tomost previous studies.The ice Icto ice Ihmeasurements show a complex time andtemperature dependence of the phase transition. The transfor-mation proceeds rapidly at first and then slows down andcomes to a halt. This could be because a fraction of the frozendroplets havefewer lattice imperfections and hence the ice Icinthese particles is more stable. Alternatively, the results may inpart be due to ice Icstacking sequences that persist attemperatures above 205 K.15The results from this study, combined with results fromother studies, help explain why ice Icis observed in some bulksamples and not others: Ice Icmust always be held belowB240 K regardless of the surface area of the sample or else itwill be rapidly converted to ice Ihthrough a solid statetranformation. (One exception is ice Icformed in nanoporousmaterial, which can exist to higher temperatures, possibly dueto the confined geometries.24) Also, during the crystallizationprocess, the rate of heat dissipation from the sample needs tobe greater than the rate of heat production by crystallizationor else the sample will heat up and the ice Icmay be convertedtoiceIh.Inaddition, if theice hasahigh surface areaandmasstransfer via the vapour is not blocked, it must be preparedbelow B200 K, or else surface nucleation and mass transferwill occurand any ice Icthatforms will be converted rapidly toice Ih, by vapour-mediated transformation. This overall dis-cussion is consistent with our measurements as well as mostmeasurements of ice Icreported in the literature.3,4,13,23AcknowledgementsWe thank A. Lam and B. Patrick for their assistance with theX-ray diffraction measurements and the interpretation of thediffraction patterns and R. Signorell for helpful comments onthe manuscript. This work was funded by the CanadianFoundation for Climate and Atmospheric Sciences, CFCAS,the Natural Science and Engineering Research Council ofCanada, NSERC, the Canada Foundation for Innovation,CFI, and the Canada Research Chairs Program.References1 B. J. Murray, D. A. Knopf and A. K. Bertram, Nature, 2005, 434,202–205.2 D. M. Murphy, Geophys. Res. Lett., 2003, 30.3 I. Kohl, E. Mayer and A. Hallbrucker, Phys. Chem. Chem. Phys.,2000, 2, 1579–1586.4 E. Mayer and A. Hallbrucker, Nature, 1987, 325, 601–602.5 J. F. Huang and L. S. Bartell, J. Phys. Chem., 1995, 99, 3924–3931.6 Y. Furukawa, J. Met. Soc. Japan, 1982, 60, 535–547.7 T. Takahashi and T. Kobayashi, J. Cryst. Growth, 1983, 64,593–603.8 H. Kiefte, M. J. Clouter and E. Whalley, J. Chem. Phys., 1984, 81,1419–1420.9 L. S. Bartell and Y. G. Chushak, in Water in Confined Geometries,ed. V. Buch and J. P. Devlin, Springer-Verlag, Berlin, 2003, pp.399–424.10 W. Kraus and G. Nolze, J. Appl. Crystallogr., 1996, 29, 301–303.11 A. Goto, T. Hondoh and S. Mae, J. Chem. Phys., 1990, 93,1412–1417.This journal is C13c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 186–192 | 191Downloaded on 18 April 2011Published on 02 November 2005 on http://pubs.rsc.org | doi:10.1039/B513480CView Online12 H. R. Pruppacher and J. D. Klett, Microphysics of Clouds andPrecipitation, Kluwer, Dordrecht, 1997.13 L. G. Dowell and A. P. Rinfret, Nature, 1960, 188, 1144–1148.14 W. F. Kuhs, D. V. Bliss and J. L. Finney, J. Phys. Colloq., 1987,48, 631–636.15 W. F. Kuhs, G. Genov, D. K. Staykova and T. Hansen, Phys.Chem. Chem. Phys., 2004, 6, 4917–4920.16 G. P. Arnold, E. D. Finch, S. Rabideau, W. and R. G. Wenzel, J.Chem. Phys., 1968, 49, 4365–4369.17 A. I. Ustinov, in Defect and Microstructure Analysis by Diffraction,ed. R. Snyder, J. Fiala and H. J. Bunge, Oxford University Press,Oxford, 1999, pp. 264–317.18 Z. Weiss and P. Cˇapkova´ ,inDefect and Microstructure Analysis byDiffraction, ed. R. Snyder, J. Fiala and H. J. Bunge, OxfordUniversity Press, Oxford, 1999, pp. 318–329.19 P. C. Reist, Aerosol Science and Technology, McGraw-Hill, NewYork, 1993.20 G. P. Johari, J. Chem. Phys., 2005, 122.21 M. Matsumoto, S. Saito and I. Ohmine, Nature, 2002, 416, 409–413.22 T. Takahashi, J. Cryst. Growth, 1982, 59, 441–449.23 P. Hobbs, Ice Physics, Oxford University Press, London, 1974.24 D. C. Steytler, J. C. Dore and C. J. Wright, J. Phys. Chem., 1983,87, 2458–2459.25 G. P. Johari, Philos. Mag. B, 1998, 78, 375–383.26 Y. V. Mnyukh and N. A. Panfilova, J. Phys. Chem. Solids, 1973,34, 159–170.27 R. C. Weast, Handbook of Physics and Chemistry, CRC Press,Boca Raton, 70th edn, 1990.28 A. J. Heymsfield and L. M. Miloshevich, J. Atmos. Sci., 1993, 50,2335–2353.192 | Phys. Chem. Chem. Phys., 2006, 8, 186–192 This journal is C13c the Owner Societies 2006Downloaded on 18 April 2011Published on 02 November 2005 on http://pubs.rsc.org | doi:10.1039/B513480CView Online


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