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Inhibition of solute crystallisation in aqueous H+-NH4+-SO42--H2O droplets. Murray, Benjamin J.; Bertram, Allan K. 2008-04-30

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Inhibition of solute crystallisation in aqueous H+–NH4+–SO42C0–H2OdropletsBenjamin J. Murray*aband Allan K. BertramaReceived 8th February 2008, Accepted 17th March 2008First published as an Advance Article on the web 21st April 2008DOI: 10.1039/b802216jIce clouds in the Earth’s upper troposphere can form via homogeneous nucleation of ice inaqueous droplets. In this study we investigate the crystallisation, or lack of crystallisation, of thesolute phase and ice in aqueous (NH4)3H(SO4)2/H2O and NH4HSO4/H2O droplets. This is doneusing in situ X-ray diffraction of emulsified solution droplets mounted on a cold stage. From thediffraction patterns we are able to identify the phases of crystalline solute and ice that form afterhomogeneous freezing in micrometer sized droplets. An important finding from this study is thatcrystallisation of the solute does not always occur, even when crystallisation is stronglythermodynamically favoured. The nucleation and growth of solute phase crystals becomesinhibited since the viscosity of the aqueous brine most likely increases dramatically as the brineconcentration increases and temperature decreases. If ice nucleates below a threshold freezingtemperature, the brine appears to rapidly become so viscous that solute crystallisation is inhibited.This threshold temperature is 192 K and 180 K, in (NH4)3H(SO4)2and NH4HSO4, respectively.We also speculate that the formation of cubic ice within a highly viscous brine blocks the solventmediated cubic to hexagonal phase transformation, thus stabilising the metastable cubic ice in themost concentrated solution droplets.IntroductionIce clouds that occur in the Earth’s upper troposphere (UT,12–18 km) have been the focus of intense research during thepast few decades.1,2These clouds play an important role in theEarth’s climate by scattering and absorbing radiation,although their present and future net climatic impact remainsuncertain.3In addition, the formation and precipitation of iceclouds influences both the distribution of water vapour in theUT as well as the amount of water vapour that enters thestratosphere, where it may have important consequences forpolar stratospheric ozone.4,5A significant mechanism of ice cloud formation in the UTand tropopause region is thought to be homogeneous freezingof submicron aqueous droplets.6Recently it was shown thatthe metastable cubic crystalline phase of ice (ice Ic) wasproduced when aqueous (NH4)3H(SO4)2, (NH4)2SO4, NaCland HNO3solution droplets froze homogeneously underconditions that are relevant for the UT and tropopause.7Grothe et al.8demonstrated that cubic ice crystallised fromamorphous HNO3-water samples. Until recently, it was oftenassumed that only the stable hexagonal phase (ice Ih) wouldform under conditions relevant for the UT and tropopause.9This is particularly relevant since cubic ice has a larger vapourpressure than hexagonal ice10and may therefore influencecloud properties.7,11In an even more recent study, we investigated in detail theformation of cubic ice in (NH4)3H(SO4)2/H2O and NH4HSO4/H2O droplets.12It was shown that the phase of ice that formsstrongly depends on the type of solute. Droplets of aqueous(NH4)3H(SO4)2freeze dominantly to cubic ice over a range oftemperatures relevant for the UT and tropopause (typically4186 K13); whereas aqueous NH4HSO4droplets freeze dom-inantly to the stable ice Ihat temperatures typical of the UTand tropopause region. However, a detailed explanation forthe observed trends was not discussed. In this study we suggestthat the crystallisation of the solute phase and the nature ofthe brine strongly influence the phase of ice that forms.When ice crystallises in a solution droplet, solute ions arerejected to form aqueous brine from which crystalline solutephases can form. However, in our previous X-ray diffraction(XRD) studies7,12,14,15we focused exclusively on the crystal-lisation of ice. In this paper we extend our previous work andexplore the crystallisation of the solute phases in dropletswhere ice nucleated homogeneously. This has only receivedminimal attention in the past.16–19In fact, there has been nosystematic investigation of solute crystallisation after ice crys-tallisation as a function of droplet size, solute concentrationand solute type.It is often assumed that the solute phase crystallises im-mediately after or during ice formation if it is thermodynami-cally viable for it to do so. However, we show here that solutecrystallisation does not always take place and may not occurin many atmospheric droplets. This is important becauseseveral studies suggest solute crystallisation subsequent to icecrystallisation may be an important mechanism for producingcrystalline salt particles which may act as an ice nuclei inaDepartment of Chemistry, University of British Columbia, 2036Main Mall Vancouver, British Columbia, Canada V6T 1Z1bSchool of Chemistry, University of Leeds, Woodhouse Lane, Leeds,UK LS2 9JTThis journal is C13c the Owner Societies 2008 Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 | 3287PAPER | Physical Chemistry Chemical PhysicsDownloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinesubsequent cloud cycles, thereby influencing cloud proper-ties.18–23It is shown here that the solute phase may notcrystallise in atmospheric droplets and therefore this mechan-ism may not be important.There have been several investigations of the solute crystal-line phases using bulk samples or thin films, where nucleationmost likely occurred heterogeneously, in the H+–NH4+–SO42C0–H2O system;24–27these experiments were ide-ally suited for mapping out the equilibrium phase changes.However, in order to investigate kinetically controlled phasechanges of atmospheric relevance, such as freezing or brinecrystallisation, small droplets are required. Hence, in thisstudy we investigate the crystallisation of micrometer sizeddroplets rather than bulk samples.Our investigation is limited to a detailed study of(NH4)3H(SO4)2/H2O and NH4HSO4/H2O solution droplets.Solutions with these ammonium to sulfate ratios (ASR = 1.5and 1, respectively) were chosen because it has been shownthat they exhibited strongly contrasting behaviour.12Thesolutes (NH4)3H(SO4)2and NH4HSO4are referred to asLET and AHS for the remainder of this paper; indicating thatthe overall stoichiometry of the solute in the droplets corre-sponds to letovicite and ammonium bisulfate, respectively.This paper is organised as follows: First, we identify thesolute phases that form when LET and AHS solution dropletscrystallise from the diffraction patterns. This is the first timethe solute phase(s) have been measured and identified afterfreezing in micron sized solution droplets. Second, we inves-tigate the temperatures at which the solute phases crystallise inthe solution droplets after ice crystallisation. Third, we in-vestigate the effect of solution concentration on crystallisationof the solute. In this section we show that the solute phases donot crystallise in the most concentrated solutions after icenucleation.Fourth,weinvestigatedtheeffectofdropletsize onthe crystallisation of the solute. The effect of particle size oncrystallisation of the solute has not been investigated pre-viously. This information is needed to extrapolate the mea-surements in the laboratory to atmospheric conditions and weshow that the solute does not crystallise efficiently in verysmall droplets. Fifth, a possible explanation of previous cubicice results (strong dependence on the ammonium to sulfateratio) is presented12based on the solute crystallisation results.This explanation involves a solvent-mediated phase transition.In addition, the atmospheric implications of the results arebriefly discussed.ExperimentalFor these experiments, aqueous solution droplets in the micro-meter size range were suspended in an oil matrix by emulsifi-cation. Phase transitions in the aqueous solution droplets werethen monitored with X-ray diffraction. Two types of experi-ments were carried out. (1) The aqueous droplets were cooledat a rate of 10 K minC01to 163 or 173 K, where the diffractionpattern between 2y =19to501 was measured and thecrystalline phases that formed were determined from thesepatterns. (2) The temperature at which ice and the solutephases crystallised in the droplets as well as the meltingtemperatures of all the observed phases were determined byeither cooling or warming the droplets while monitoring aportion of the diffraction pattern. The two types of experi-ments were carried out concurrently.The experimental technique has been described previouslyand will only be briefly summarized here.7,14The X-raydiffractometer (Bruker D8 Discover) used in these experimentswas configured in a standard Bragg-Brentano reflection geo-metry and was equipped with a Cu Ka X-ray source. The datapresented in this paper were measured with two differentsource and detector combinations. The results from bothcombinations are directly comparable and the specific instru-mentation details are discussed elsewhere.7,14Aqueous solutions of an accurately known compositionwerepreparedusingpurewater(distilledwaterfurtherpurifiedwith a Millipore 18.2 MO system) and a gravimetric scaleaccurate to within 5 mg. Solid ammonium bisulfate was addedto water to produce aqueous NH4HSO4of concentrationsbetween 0 at 39.2 wt% (Msolute/[Msolute+ Msolvent], where Mis mass). Whereas (NH4)3H(SO4)2solutions were preparedusing two methods: (i) mixing ammonium sulfate with thecorrect amount of ammonium bisulfate or (ii) mixing ammo-nium sulfate with the correct amount of sulfuric acid. Nodifference was observed in the final diffraction patterns orphasechangetemperatureswithsolutionspreparedusingthesetwo methods. Aqueous solutions of (NH4)3H(SO4)2had con-centrations of between 0 and 43.2 wt%. These solutions werethen emulsified by mixing them with an oil phase. The oilphase consisted of mineral oil (paraffin oil, Fisher Scientific)and 10 wt% lanolin surfactant (Aldrich Chemical Company).This mixture was then mechanically agitated using a magneticstirring bead until the droplets were of the desired size range.Smaller droplets were generated by mixing for longer. Thedroplet sizes were measured by optical microscopy and hadvolume median diameters of between 2 and 20 mm withgeometric standard deviations between 1.3 and 1.8 mm.The emulsions containing droplets of the desired composi-tion were placed in a cell within an X-ray diffraction chambercapable of low temperature measurements (TTK 450, Anton-Paar). It was previously shown that frozen droplets preparedin this manner exhibit no significant preferred orientation andthat the diffraction patterns presented here are equivalent topowder patterns.14It is thought that the nucleation andfreezing process is not influenced by the oil or surfactant; thisis discussed in detail later in the section titled ‘Ice freezingtemperatures in the aqueous solutions’.Results and discussionExamples of the diffraction patterns of frozen LET, and AHSsolution droplets are illustrated in Fig. 1. These patterns weremeasured after the emulsified droplets were cooled to either173 K (or 163 K for the most concentrated AHS solutiondroplets) at a rate of 10 K minC01. Inspection of Fig. 1 revealsthat the patterns contain Bragg peaks from both ice andcrystalline solute phases. The Bragg peaks exclusive to ice Ihare labelled ‘‘h’’ and the peaks common to both ice Icand iceIhare labelled ‘‘h+c’’. There are no intense Bragg peaksunique to ice Ic. The peaks associated with the solute phasesare labelled ‘‘S’’, while those due to the aluminium base and3288 | Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 This journal is C13c the Owner Societies 2008Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinethe cell construction materials are labelled ‘‘Al’’ and ‘‘Cell’’,respectively. The underlying background on which the reflec-tions from ice and the solute phase are superimposed is largelydue to diffraction from the amorphous oil phase. The diffrac-tion patterns illustrated in Fig. 1 show a great deal ofvariability depending on the solute and also on the concentra-tion of the solution droplets. This is explored in detail below.Identification of the crystalline solute phasesIn the first part of this study we focused on identifying thecrystalline solute phases that precipitated after ice nucleationin the aqueous droplets.Diffraction patterns of frozen aqueous LET droplets. Theaerosol inorganic model (AIM) predicts that crystalline leto-vicite ((NH4)3H(SO4)2) and ice are the thermodynamicallystable phases that form at low temperatures in our LETsolution droplets. Letovicite and ice have been identifiedexperimentally in the past,25,28but these previous studies wereunable to identify the exact phase of letovicite. There areseveral known phases of letovicite,29each with a distinctcrystalstructure.30InadielectricstudyGesi29foundLetoviciteII formed at room temperature, whereas between 141 and265 K Gesi identified letovicite III. In Fig. 2, a diffractionpattern of frozen 39.9 wt% LET droplets is compared to thepatterns of letovicite II andIII calculated withthePowder Cellprogramme31and structural data from Dominiak et al.30Inspection of Fig. 2 reveals that several of the peaks in thecalculated letovicite III pattern are absent in the experimentalpattern, most notably those at 2y = 22 and 281; whereas thecalculated pattern for letovicite II is consistent with theposition and intensity of the experimental solute phase peaks.This shows that letovicite II formed in the aqueous dropletsrather than the expected letovicite III.28–30Also, note that thediffraction patterns for other crystalline salts (such asFig. 1 Diffraction patterns of frozen (a) (NH4)2SO4/H2O and (b) (NH4)3H(SO4)2/H2O droplets. These patterns were measured after the dropletshadbeencooledatarateof10KminC01to173Kor163K.Themeanfreezingtemperature,soluteconcentrationandratioofthehexagonalpeakat43.51 (I44) to the common peak at 401 (I40) are indicated for each pattern (see text for details). Bragg peaks associated with ice Ihare labelled ‘‘h’’,while those common to both ice Ihand ice Icare labelled ‘‘h+c’’. Peaks associated with the solute phase are labelled ‘‘S’’ and those due to the cellconstruction materials and the aluminium base are labelled ‘‘Cell’’ and ‘‘Al’’, respectively.Fig. 2 Comparisonofthediffractionpatternoffrozen39.9wt%LETsolutiondroplets (a), with the patterns of letovicite II (b) and letoviciteIII (c) calculated from structural data recorded in ref. 30 using thePowder Cell programme.31Peaks common to both ice Icand ice Iharelabelled ‘‘h+c’’ and peaks exclusive to ice Ihare labelled ‘‘h’’. Peaksdue to the cell construction materials are labelled ‘‘cell’’ and those duetothealuminiumbasearelabelled‘‘Al’’.Peaksidentifiedasthosefromcrystalline letovicite are labelled ‘‘L’’.This journal is C13c the Owner Societies 2008 Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 | 3289Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinecrystalline ammonium sulfate, and bisulfate) are inconsistentwith our measured diffraction patterns.)Diffraction patterns of frozen aqueous AHS droplets. Pat-terns of frozen 33.7 wt% AHS droplets are shown in Fig. 3 attwo different temperatures. Fig. 3c was produced by decreas-ing the temperature of these droplets, which froze at 190 C65 K, to 173 K and then recording the diffraction pattern. Thenthe pattern in Fig. 3a was recorded after warming this sampleto 203 K. Examination of these two diffraction patternsreveals that a number of peaks present in the 173 K patternare absent in the 203 K pattern; this indicates a phase changeoccurred between these temperatures. The phase change tem-peratures were recorded and are discussed later.AIM32predicts the stable phases that form at low tempera-tures are ice, letovicite and sulfuric acid hemihexahydrate(SAH) whereas previous experimental evidence based oncalorimetry indicates sulfuric acid tetrahydrate (SAT), ratherthan SAH, form at low temperatures.24,25,27In addition to thetwo experimental patterns we have shown patterns for Leto-vicite II, SAT, and SAH which were calculated from literaturedata.30,33,34These ‘extra’ peaks in panel c are consistent withSATand areinconsistent withthestructure ofSAH. As will beseen later the phase change temperatures are also consistentwith SAT.The remaining crystalline solute phase peaks which arepresent together with ice peaks at 203 K, broadly correspondto those in the pattern for letovicite II (pattern b). However,the match with the calculated pattern is not exact and inaddition there are differences between the letovicite pattern inLET droplets and that in AHS droplets. In this case theidentification of the letovicite phase is not as straightforwardas it is in LET droplets. We have employed a computerprogramme to assess if these crystals are a distorted form ofletovicite II or a different phase altogether. The computationaltechnique widely used for these calculations is known as aRietveld refinement,35and is a least-squared minimisationbetween the experimental pattern and a pattern generatedfrom structural information which is adjusted to produce abest fit. We have used the refinement tool in the Powder Cellpackage.31In a Rietveld refinement, it is assumed that the experimentalpattern can be well represented by a linear combination ofcalculated patterns for the individual phases.35This is onlytrue when the substances are well crystallised. The presence ofstacking faults cannot be routinely accounted for in theserefinements. However, we are fortunate in that the ice Ihthatforms in the AHS droplets shown in Fig. 3 approximates wellto stacking fault free ice Ih, hence a Rietveld refinement ispossible. Such a refinement would not be meaningful for theLET droplets, because the ice that forms in them alwayscontains significant stacking faults.7We have taken literature data for the structures of Letovi-cite II,30SAT33and ice Ih36as starting points in the refine-ment. The relative contribution of each phase, unit cellparameters, peak profiles, background and systematic diffrac-tion angle offset have been fitted. The unique positions of theatoms and space groups have not been adjusted. The results ofthis refinement procedure for patterns in Fig. 3c are shown inFig. 4 and the fitted unit cell parameters are listed in Table 1.The quality of the fits indicated by the small residuals showsthat it is possible to account for the peak positions andintensities. It is concluded here that ice Ihand SAT havestructures almost identical to those in the literature, whereasthe letovicite phase is a distorted form of letovicite II. We canbe confident in this identification because relatively smalladjustments to the unit cell dimensions were required toproduce a fit (see Table 1) and the structure refined withinthe same space group (C2/c) and without altering the uniquepositions of the atoms. The reason for this distortion to theletovicite unit cell may be the acidic environment in whichletovicite formed. It will be shown later in this paper that icecrystallises first, shortly followed by letovicite and then SATcrystallises at a much lower temperature. Hence, letovicitecrystallises in an acidic environment in AHS, which couldpotentially cause someprotonation of the letovicitewhich mayhave distorted its structure. It should also be noted thatpreferred orientation of the crystallites was not invoked toproduce this fit, confirming that preferred orientation is not anissue in these experiments.Melting temperatures in the aqueous LET and AHS systems.The melting temperatures of the frozen droplets were deter-mined by continually monitoring a portion of the diffractionFig. 3 Comparison of diffraction patterns of frozen 33.7 wt% AHSsolution droplets with patterns of letovicite II (b), sulfuric acidtetrahydrate (SAT) (d), and sulfuric acid hemihexahydrate (e); calcu-lated from data recordedin ref. 30, 33 and 34, respectively. Pattern a isthat of 33.7 wt% AHS solution droplets which froze at 190 C6 5Kasthey were cooled at 10 K minC01and then warmed to 203 K, which isabove the SAT eutectic temperature, but below the sulfuric acidhemihexahydrate eutectic (209 K32). Pattern d is that of the sameAHS solution droplets at 173 K before they were warmed to 203 K.The labellingisthe sameas in Fig. 2, butwhere ‘‘SAT’’indicatespeaksthat have been identified as SAT diffraction peaks.3290 | Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 This journal is C13c the Owner Societies 2008Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinepattern, which contained a pertinent peak (i.e. peaks thatcorrespond to either ice or the crystalline solutes), as thedroplets were warmed at a rate of 1 K minC01(after beingcooled to 173 or 163 K). The measured ice and solute phasemelting temperatures for aqueous LET and AHS droplets areplotted in the phase diagrams in Fig. 5a and b. Our data arecompared with the available literature data and also thepredictions of AIM. In general, the agreement between datasets and model for the letovicite and ice melting points in bothAHS and LET solutions is good. The exception is that of theice melting data for Imre et al.37in the AHS system; however,Chelf and Martin38suggest that there were errors in thosemeasurements.The agreement of experimental data with model predictionsat lower temperature (o215 K) is not as good. AIM predictsthat the stable phases at low temperature are ice, letovicite andSAH (the SAH eutectic temperature is shown as a dotted linein Fig. 5b). The melting temperatures and the diffractionpatterns suggest that SAT forms, rather than SAH. AIMpredicts the formation of SAT if SAH is blocked; the SATTable 1 Literature and fitted unit cell parameters which were fitted in the Rietveld refinement in Fig. 4Phase/fitted unit cell parameter Literature Fit to 173 K pattern Fit to 203 K patternLetovicite IIa/A˚15.3900a15.7831 15.776b/A˚5.8480a5.7925 5.8010c/A˚10.1400a10.0479 10.0667b/1 101.810a102.065 102.244Ice Iha/A˚4.5110b4.5100 4.5140b/A˚4.5110b4.5100 4.5140c/A˚7.3510b7.3433 7.3505SATa/A˚7.4797c7.5036 NAb/A˚7.4797c7.5036 NAc/A˚6.3680c6.3913 NAaDominiak et al.30 bGoto et al.36 cThe 150 K data from Fortes et al.33Fig. 4 Rietveld refinement fits to theexperimental patterns(i) isthe fit tothe patternof 33.7wt% AHSdropletsat 173K (Fig. 3d)and (ii) thea fitto a pattern of the same droplets, which had been warmed to 203 K (Fig. 3b). The refined patterns of ice Ih, Letovicite II and SAT are also showntogether with the fitted and experimental patterns in addition to the residuals.This journal is C13c the Owner Societies 2008 Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 | 3291Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlineeutectic is shown as a dot-dashed line in Fig. 5b. The meltingtemperatures recorded in thin films24and 3 ml droplets (i.e.bulk),27which froze heterogeneously, also suggest SAT crys-tallised. It is unclear if there is an error in AIM, perhaps due tothe extrapolations from high temperature thermodynamicdata to these low temperatures employed in AIM,24,25,27orif there is a large kinetic barrier to the formation of SAH. Fora detailed discussion of the equilibrium phase diagrams ofthese systems see Beyer et al.25and Beyer and Bothe.24In a set of calorimetry and IR spectroscopy experimentsBeyer and Bothe24found that ammonium bisulfate crystallisedrapidly after SAT melted on warming and then converted toletovicite at 223.8 K. Our Rietveld refinement of a pattern offrozen droplets which had been cooled to 173 K and thenwarmed to 203K, which is above the SATeutectic, and held at203 K for B30 min (Fig. 4ii) clearly shows ice and letoviciteonly. There is no evidence of the crystallisation of ammoniumbisulfate. In our experiments the temperature was increased ata rate of 1 K minC01across the SAT eutectic temperature,which is the same ramp rate employed by Beyer and Bothe.24The main difference between the experiments was that we usedmicrometer sized droplets while they used thin film samples.Beyer and Bothe note that when their film was ramped at 5 KminC01,re-crystallisation ispartiallysuppressedwhich indicatesthat nucleation becomes kinetically limited. Our results sug-gest that the nucleation rate of ammonium bisulfate in theSAT melt is very small in micron sized droplets.Temperatures at which the solute phases and ice crystallisedAfter ice crystallised in the solution droplets, solute phaseprecipitation may become thermodynamically viable. How-ever, crystallisation of the solute phase from a metastablebrine may not occur for kinetic reasons. Using X-ray diffrac-tion, we were able to determine the temperatures at which thevarious solutes crystallised in addition to the temperature atwhichicecrystallisedbymonitoringtheintensityofapertinentpeak. Before we present the measurements of the temperaturesat which the solute phases crystallised, we first present thetemperatures at which ice formed in these solution droplets.The results for ice are needed so that we can make a compar-ison between the ice freezing temperatures and the solutecrystallisation temperatures.Ice freezing temperatures in the aqueous solutions. Thetemperature at which ice precipitated was determined bymonitoring ice peaks as the emulsions were cooled at a rateof 10 K minC01. The measured droplet freezing temperaturesfor aqueous LET and AHS droplets are plotted in Fig. 6a andb. In addition, we have also included a parameterisation of theice melting temperatures for comparison. Unlike melting,freezing is a kinetically controlled nucleation process; henceit occurred over a range of temperature and at lower tempera-tures than melting. These freezing ranges are plotted in Fig. 6with uncertainties in the onset and completion of freezing.We argue that these freezing results correspond to homo-geneous nucleation, rather than heterogeneous or a surfaceinduced pseudo-heterogeneous nucleation pathway. The oilphase and surfactant did not significantly influence the nuclea-tion mechanism for the following reasons. First, our freezingmeasurements for AHS droplets are compared with the ex-perimental results of Koop et al. (dashed line in Fig. 6b),27where calorimetry was used to measure the temperature atwhich 50% of their 1–10 mm emulsified droplets froze; theagreement with our measurements is good. Second, we deter-mined freezing temperatures of (NH4)2SO4/H2O, NaCl/H2Oand HNO3/H2O droplets in previous measurements7employ-ing the same experimental technique used here (freezing datanot shown). Our results are in good agreement with measure-ments of freezing in micron sized solution droplets recorded inthe literature; including those with droplets falling throughgas,39suspended on a surface40or suspended in an oil emul-sion.16,40,41Third, the freezing temperatures of pure waterdetermined in our experiments14are in good agreement withfreezing temperatures of micron sized pure water dropletsFig. 5 Temperature–composition phase diagrams for (a)(NH4)3H(SO4)2/H2O and (b) NH4HSO4/H2O. Temperatures at whichwe observed phase changes as droplets were warmed at 1 K minC01areplotted as filled symbols; the uncertainty in temperature was typicallysmaller than the symbol size. Our measurements are superimposed onthe equilibrium curves predicted by the Aerosol Inorganic Model.32Our data is compared with literature data marked as circles,24,25triangles,27crosses,38squares,68and diamonds.37In panels a and b,the equilibrium line of ice with liquid (solid) and that of ice +letovicite with liquid (dashed) are shown. In panel b, the equilibriumline of SAH + ice + letovicite with liquid (light dotted) and also theline forSAT +ice +letovicite inequilibriumwithliquid(dot-dashed)are also shown.3292 | Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 This journal is C13c the Owner Societies 2008Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinemeasured where droplets fell through gas,39,42suspended in anelectrodynamic balance,43and suspended in oil emulsions.44,45Our freezing results for the aqueous LET droplets, presentedin Fig. 6a, are the first of their kind. This data adds to thegrowing body of data on the homogeneous freezing tempera-tures of ice in aqueous solution droplets.We have also compared our measured ice freezing tempera-tures in Fig. 6 with those predicted by the water activitycriterion model.46,47Koop et al.47demonstrated that thehomogeneous nucleation of ice in supercooled aqueous solu-tion dropletsonly depends on the water activity of the solution(aw= ratio of the vapour pressure of the solution to that ofpure water under the same conditions). They demonstratedthat the water activity at freezing (afw) is equal to the wateractivity at the ice–liquid equilibrium (aiw) shifted to highervalues by a constant offset (Daw), which was found to be 0.305(afw= aiw+ Daw) for micron sized droplets. Koop46showedthat most of the experimental data fell within 2.5% of the afwline, and almost all of the datafall within 5%. We have plottedthe prediction of the water activity criterion whereDawwas setto 0.305 and the shaded region indicates the 2.5% deviation inafw(the solute wt% corresponding to afwwas determined usingAIM32and a parameterisation of awiwas taken from Koopet al.47). Inspection of Fig. 6 reveals that the homogeneousfreezing of LET and AHS droplets is consistent with the wateractivity criterion.Solute freezing temperatures in the aqueous solutions. Thesolute phase crystallisation temperatures are presented inFig. 7 together with a parameterisation for the ice crystal-lisation temperatures. When letovicite crystallised it did socoincident with ice (within experimental uncertainties),whereas SAT in AHS droplets crystallised at around 178 Kindependently of solute concentration. Note that the full low-temperature scans between 2y = 19 and 501 showed that smallamounts of solute phase did crystallise outside the range ofconcentrations in which crystallisation itself was observed inFig. 7, but the signal was too weak to reliably determinecrystallisation temperatures during cooling. Approximately15% of the total mass of the aqueous droplets must crystalliseor melt in order to determine a phase change temperature. Theresults presented in Fig. 7 are the first measurements of thecrystallisation temperature of solute phases in micron sizedLET and AHS droplets that froze homogeneously. Koopet al.27used calorimetry to measure phase changes in bulkAHS solutions (volume = 3 mL). In their bulk experiments icenucleated heterogeneously, but the temperature at which SATcrystallised (181 K) was very similar to the present study (seeFig. 7b) even though ice nucleated at a much higher tempera-ture.Effect of aqueous solution composition and droplet size on thecrystallisation of the soluteIn this section we investigate the effect of the solution dropletcomposition (i.e. the solute:water mass ratio) and droplet sizeon solute crystallisation. In all of these experiments the emul-sions were cooled down at a rate of 10 K minC01to 173 K (or163 K), at which point a diffraction pattern between 2y =19to 501 was measured and the extent of crystallisation of thesolute was determined from the diffraction patterns.In order to provide a measure of the amount of crystallinesolute that formed in the droplet after freezing, we determinedthe ratio of the intensity of a solute peak to the intensity of anice peak. We refer to these intensity ratios as Isolute/Iice. Isolutewas divided by Iiceto remove any sample to sample variationsin our data due to changes in sample thickness or samplevolume probed by the X-ray diffractometer. In other words,division by Iiceprovided a way to normalize the soluteintensities. It should be noted that using just one peak toassess the amount of a particular material is not valid if thesample exhibits a preferred orientation, but as we demon-strated earlier this is not the case in our frozen emulsions.Fig. 6 Freezing temperatures of emulsified (NH4)3H(SO4)2/H2O(panel a) and NH4HSO4/H2O (panel b) solution droplets. The mea-suredfreezingtemperaturerange,asthedropletswererampeddownata rate of 10 K minC01, is shown by a solid grey bar; the uncertainty infreezing onset and completion are indicated. The ice melting tempera-ture curve, as predicted by AIM,32is also shown. In panel b, thedashed line is a polynomial fit to the mean freezing temperaturesmeasured by Koop et al.,27in emulsified AHS solution droplets. Thecomparison with previous data is restricted to supermicron sizeddroplets—droplets of a similar size to those employed in the presentstudy. The grey curve represents the freezing temperatures predictedby the water activity criterion for supermicron droplets46,47andemploying the thermodynamic model of Clegg et al.32to predict wateractivity (see text for details).This journal is C13c the Owner Societies 2008 Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 | 3293Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView OnlineHence the normalised intensity of a single peak is proportionalto the amount of crystalline material. To quantify SAT andcrystalline letovicite the diffraction peaks at 2y = 30 and 311were used, respectively. For normalization purposes, the icepeak at 2y =401 was used, which is a peak common to bothhexagonal ice and cubic ice. The peak intensities were mea-sured by fitting Gaussian profiles to the pertinent peaks in thediffraction patterns of frozen droplets, which were recorded at173 K (or 163 K). The fitting procedure allowed us todeconvolute any overlap between peaks, although it shouldbe borne in mind that peaks with minimal overlap wereselected for this analysis. A similar analysis of diffractionpatterns was used in the past.12In Fig. 8 we have plotted Isolute/Iice, as a function of thesolute/water mass ratio (Msolute/Mwater). Data for two sizeranges, 2–5 mm and 10–20 mm bins are shown in Fig. 8. The5–10 mm size range is omitted for clarity. These sizes refer tothe volume median diameters which were determined for eachemulsion sample using images of the droplets. Images wereobtained with an optical microscope equipped with a digitalcamera.14,15A number of trends are clear from the data presented inFig. 8. Firstly, there is a strong size dependence, with thesolute phase showing a greater propensity to crystallise inlarger droplets. In order to examine this size dependence inmore detail we performed an additional series of experimentswhere the droplet size distribution was varied while holdingthe solution concentration constant (26.9 wt%, Msolute/Mwater= 0.37, LET). The letovicite-ice intensity ratio (Isolute/-Ii40(ice-common); where the solute peak at 301 was used forSAT and that at 311 for LET) is plotted as a function ofdroplet volume median diameter (dvm) in Fig. 9a; this plotclearly shows that less solute phase crystallises in small solu-tion droplets. In fact, the size dependence was very strongwhen dvmincreased from 3 to 10 mm. The most likely explana-tionfor thistrendisthatthenucleationrate ofthesolutephaseis reduced substantially in smaller droplets. The rate ofnucleation, whether heterogeneous, homogeneous, or pseu-do-heterogeneous, is clearly reduced in the smaller droplets.The implications for these results to the atmosphere arediscussed below (see the ‘Atmospheric implications’ section).The second trend which is clear from Fig. 8 is that theamount of solute phase that crystallised on cooling dropletsto 173 K decreased drastically above about 35 wt%(Msolute/Mwater= 0.54) in both LET and AHS droplets. Onemight expect the amount of crystalline solute phase to increasewith increasing mass fraction of solute; however this is clearlynot the case. In fact, very little solute phase was detected indroplets of concentration greater than 39 wt% (Msolute/Mwater= 0.64) AHS and 40 wt% (Msolute/Mwater= 0.67) LET.Warming these concentrated solution droplets at a rate of10 K minC01results in crystallisation of the solute phase ataround 189 and 186 K in LET and AHS, respectively (thisonly applies to the largest droplets where nucleation is effi-cient). This indicates that nucleation and/or crystal growth ofthe solute phase was limited at lower temperatures.In the field of food technology and engineering, it is wellknown that crystallisation of the solute brine, post ice crystal-lisation, can be inhibited. In fact, considerable effort has beeninvested to find which ingredients may ‘stabilise’ the brine andprevent further alteration and crystallisation of frozen foodproducts during storage.48When ice forms in aqueous solu-tion, solute ions are rejected to form a brine. At equilibrium,this brine will have a unique concentration at a particulartemperature which is determined by thermodynamics.32How-ever, in many cases the brine never reaches this equilibriumFig. 7 Crystallisation temperatures of letovicite (circles) and SAT (squares) in the (a) (NH4)3H(SO4)2/H2O and (b) NH4HSO4/H2O systems. Thedashed line is a parameterisation of the mean ice freezing temperatures shown in Fig. 6. The dotted line in a represents the SAT crystallisationtemperatureobservedbyKoop et al.27intheirbulkexperiments.Thesignificanceofregionsi, ii ((a)and(b))andthe transitionregionarediscussedin the text.3294 | Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 This journal is C13c the Owner Societies 2008Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinewith ice since the viscosity of aqueous solutions increases withboth increasing concentration and decreasing tempera-ture.48,49This can result in the formation of mixtures ofcrystalline ice with highly viscous or even glassy material.48The experimental data presented here suggest that if ice formsbelow a certain threshold temperature, the brine will rapidlybecome highly viscous and possibly form glassy material inwhich crystallisation is inhibited. In the next section wesuggest that the formation of highly viscous amorphous brinesmay influence the phase of ice that results. Measurements ofviscosity and glass transition temperatures for the pertinentsolutions are highly desirable.The relationship between ice phase and solute brine propertiesPrevious ice results. Inourpreviousmanuscript12weshowedthat the phase of ice that forms in LET and AHS dropletsstrongly depends on the ammonium to sulfate ratio (ASR) ofthe solute. This ice freezing data has been reproduced in Fig.10a and c in order that it can be compared with the letovicitecrystallisation data, which has been re-plotted in terms of icefreezing temperature rather than solution concentration. Thephase of ice is indicated using the peak intensity ratio I44/I40,where I44is the intensity of the peak at 441 exclusive to ice Ihand I40is that of the common peak at 401. A value of I44/I40=0.82 C6 0.03 indicates pure hexagonal ice formed and I44/I40=0 indicates no bulk ice Ihformed and that the dominantproduct was ice Ic. The intensity ratios were determined fromdiffraction patterns measured at 173 K (or 163 K) after thedroplets were cooled to this temperature at a rate of 10 KminC01(see Murray and Bertram12for details). Note that theseresults were obtained from the same emulsions that were usedin the experiments discussed above. Hence, the results fromthe ice studies are directly comparable to the results presentedin this manuscript.Here we briefly summarize our previous ice results forcompleteness. The plots in Fig. 10a and c highlight severalimportant findings, including a strong solute type dependenceand a significant size dependence at temperatures aboveB200 K. Inspection of the sigmoidal fit through the 5–10mm size bin, shown in Fig. 10d, reveals that for AHS there isno significant size dependence for the entire temperature rangeinvestigated. For LET solution compositions, there is no sizedependence for temperatures less than B200 K. At higherfreezing temperatures there is evidence of a size dependence inthe LET data, with larger droplets freezing to more ice Ic;anopposite trend to that observed in pure water droplets.14Thetrend observed previously for pure water is due to heating ofthe droplets during freezing. However, as discussed in ourprevious manuscript,12this is most likely not important forconcentrated solution droplets; and indeed, one would expectan opposite size dependence if heating were important.Perhapsthemost important resultillustratedin Fig. 10aandc is that the temperature below which cubic ice forms isstrongly dependent on the solute type. For example, in LETdroplets, the intensity ratios I44/I40is less than 0.2 at freezingtemperatures below 200 C6 1 K (based on the fit to the freezingdata), whereas for AHS droplets a value of 0.2 is not reacheduntil below 183 C6 1 K. Uncertainties are based on the 95%confidence limit of the fit to the 5–10 mm size bin (Fig. 10).Solute crystallisation and formation of highly viscous amor-phous brines. From Fig. 10c and f we can identify severalfreezing temperature regimes based on the ability of the solutephase to crystallise. These approximate freezing temperatureFig. 8 The solute phase intensity ratios (Isolute/I40(ice-common))asafunction of solute to water mass ratio (Msolute/Mwater). Data fordroplets in the 10–20 mm (filled squares) and 2–5 mm (open triangles)droplet size ranges are plotted. (The size refers to the volume mediandiameter.) The intensity ratios I31/I40and I30/I40for letovicite andSAT,respectively,are plotted.Thedashedandsolidlinesare fitstothedata and are only intended to guide the eye.This journal is C13c the Owner Societies 2008 Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 | 3295Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlineregimes are indicated in Fig. 10b and e. Temperature regime iis where there is an opportunity for crystallisation to takeplace before the droplets become highly viscous. In this regimenucleation and crystallisation took place in thelargest dropletsand crystallisation always took place coincident with icecrystallisation. This indicates that solute crystallisation tookplace as the ice crystals grew in the large droplets, but in thesmall droplets sufficient supersaturations for nucleation andcrystallisation were not reached before the brine becamehighly viscous. In temperature regime ii the solute phase doesnot crystallise, most likely because the brine became highlyviscous or glassy and crystal growth became very slow beforecrystallisation could take place. A transition region is alsoindicated where solute phase crystal growth was limited, butdid occur to some measurable extent.Inspection of Fig. 10 reveals that these regimes are corre-lated with the ice phase that forms. In regime i, where the icespends some time in equilibrium with a mobile non-viscousbrine, hexagonal ice results; whereas in regime ii, where thebrine rapidly becomes highly viscous or glassy, cubic ice tendsto result. In the following we suggest how the physical proper-ties of the brine might influence the ice phase that we observeto form when aqueous droplets freeze.Possible explanation of ice phase dependence on solute type.In this section we attempt to rationalise our experimentalresults by considering the nucleation and crystallisation pro-cess in aqueous solution droplets. We start this discussion withnucleation and then outline how cubic ice might transform tohexagonal ice through a solvent mediated transformation. Wesuggest that it is this transformation which is critically influ-enced by the physical state and transport properties of thebrine.The empirical Ostwald’s law of stages predicts that ametastable phase will initially form in preference to the stablephase.50In fact, there is substantial theoretical51–54and ex-perimental7,14,54–59evidence that when aqueous dropletsfreeze, cubic ice preferentially nucleates and crystallises. Ex-perimental evidence suggests that cubic ice may nucleate indroplets as high as 256 K58,60and in a theoretical studyTakahashi51suggests that cubic ice may nucleate below271 K. This can be rationalised with the classical nucleationtheory which predicts that the free energy associated with theproduction of a critical embryo, DG*isDGC3¼16pg3n23ðkT lnSÞ2ð1Þwhere g is the surface free energy between the ice germ and thesupercooled liquid, n is the molecular volume, k is Boltz-mann’s constant, T is temperature and S is the saturationratio. In an elegant experiment Huang and Bartell59demon-strated that g for a germ of ice Icis substantially smaller thanfor ice Ih. The height of the energy barrier is strongly influ-enced by g, due to the cubic term. Since the rate atwhich critical germs form, J is thought to be proportional toexp(C0DG*/kT), the nucleation of critical germs of ice Icwill befavoured over the nucleation of hexagonal critical germs.Assuming that the cubic germ then acts as a template forsubsequent ice layers, cubic ice will crystallise as the dominantproduct.We know from calorimetry11and vapour pressure measure-ments10that ice Icis metastable to ice Ihand theoretical worksuggests this is the case from 0 to 273 K at atmosphericpressure.61Ice Ictherefore has a larger chemical potentialthan ice Ih:mIc4 mIh(2)Therefore, the transition of ice Icto ice Ihis thermodynami-cally favourable. If ice Icis to persist, as it does in ourexperiments, there must be kinetic limitations to this transfor-mation. In the following we list the potential mechanismsthrough which the cubic to hexagonal transformation mightFig. 9 (a) The letovicite–ice intensity ratio I31/I40(a measure of how much letovicite crystallised) plotted as a function of the volume mediandiameter for 26.9 wt% LET droplets. The droplet median diameter was determined from images taken with an optical microscope.12,15Thehorizontalbars representthe size range in which 68%of the volumeresides. (b) The ice Ih-commonice peak intensityratio (I44/I40) as a functionofletovicite ice intensity ratio, also with composition 26.9 wt% LET. A value of I44/I40= 0.82 C6 0.03 indicates pure hexagonal ice formed andI44/I40= 0 indicates no bulk ice Ihformed and that the dominant product was ice Ic.3296 | Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 This journal is C13c the Owner Societies 2008Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlineoccur: Firstly, there is a gas phase route, which is active invapour deposited ice Icsamples. In this mechanism cubic andhexagonal ice share a common vapour phase and since cubicice has a larger vapour pressure than hexagonal ice (since mIc4 mIh),10,11,62mass transfer of water molecules from cubic tohexagonal particles will occur.11This becomes rapid (minutes)above about 200 K.11It is this mechanism through whichMurphy11hassuggested cold ice clouds might be influenced bythe transient presence of cubic particles. The vapour phase isnot accessible to the droplets in the experiments describedhere, since they are locked in an oil matrix. Secondly, there is abulk solid-to-solid transformation, but it has been previouslyshown that this mechanism does not become rapid in micro-meter sized pure water droplets until aboveB240 K.14Hence,this mechanism is most likely not important when dropletscrystallise well below 240 K, and remain below 240 K as in thecurrent experiments.In addition to the gas-phase mass transfer and solid-to-solidmechanisms there may be a third transformation mechanismthat operates when ice forms in aqueous solution droplets.This is a solvent-mediated cubic-to-hexagonal transition,where water molecules travel from a cubic crystal to a hex-agonal crystal via the aqueous brine. Solvent-mediated trans-formations are known to be important in other systems,50butto the best of our knowledge have not been discussed in thepast specifically for ice. Clearly, if cubic ice initially forms, thenature of the brine will therefore play a critical role indetermining the final phase of ice. Cubic ice will only bestabilized if the brine crystallises or if the brine is highlyviscous. Based on this, one would expect to see a correlationbetween our solute crystallisation results and the ice results.We now show that this solvent mediated phase transformationis a physically reasonable mechanism in droplets where iceforms, but where the brine is non-viscous.The solvent mediated phase transformation requires bothice Icand ice Ihto be present within the same droplets. In fact,this is very likely. Murphy11points out that the (111) face ofice Icis very similar to the (1000) face of ice Ih, hence thebarrier to nucleation of ice Ihon ice Icshould therefore besmall. So a situation likely exists where both ice Icand ice Ihare in contact with an aqueous brine. Thermodynamics dic-tates that the more stable phase (i.e. lower chemical potential)will always have a lower solubility in any given solvent. Hence,the concentration of water in the aqueous solution immedi-ately above ice Icwill be larger than the concentration of waterabove ice Ihcrystals (Cw,Ic4 Cw,Ih). This will gives rise toconcentration gradients in the aqueous brine between regionsof ice Icand ice Ih. Consequently the ice Ihcrystals will tend togrow at the expense of the ice Iccrystals at a rate which may bedictated by Fick’s first law of diffusion.63The rate at whichwater molecules diffuse from cubic regions to hexagonalFig. 10 The ice Ih-common ice peak intensity ratio, I44/I40, and theletovicite–ice intensity ratio, I31/I40, as a function of mean ice freezingtemperatureforAHSandLETindropletsthatwerecooledfromroomtemperature to173K atarateof 10K minC01. I44/I40isshownforthreesize ranges in LET (a) and AHS d solution droplets. The solid line inpanels a and d are sigmoidal fits to the 5–10 mm data and the dottedlines are the corresponding 95%predictionbands. Uncertainties in themean freezing temperature are indicated. In panels c and f, the ratioI31/I40is shownas a functionof the temperatureat whichice formedinthe droplets in order to compare the crystallisation of the solute phasewith the phase of ice that formed. Data for the larger and smaller sizerangesareshown;themiddlesizerangeisexcludedforclarity.Panelsband e refer to the state of the droplet after ice formed and it had beencooled to 173 K and are discussed in detail in the text. The regimes iand ii correspond to the regimes marked in Fig. 7.This journal is C13c the Owner Societies 2008 Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 | 3297Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlineregions, W, can be expressed:W ¼C0DdCdxð3Þwhere x is distance, hence the differential is the concentrationgradient of water in the aqueous brine between regions ofsolution near ice Icto regions near ice Ih, and D is the diffusioncoefficient of water in the aqueous brine. D is approximatelyinversely proportional to viscosity.50Consequently, the rate atwhich a solvent mediated phase transformation takes placewill be strongly dependent on the viscosity of the brine.Intriguingly, measurements in supercooled sulfuric acid solu-tions showthat viscosity increases dramatically as temperaturefalls and concentration of sulfuric acid increases.64In fact,many aqueous solutions exhibit asuper-Arrhenius dependenceof viscosity on temperature.65For example, Maltini andAnese49estimate that the combined effect of increasing con-centration and decreasing temperature on a sucrose solutioncooled from C010 to C020 1C results in an increase in viscosityby a factor of B105. Unfortunately, no measurements fortransport properties exist for LET or AHS solutions underpertinent conditions but it is reasonable to expect that D willdecrease dramatically with decreasing T and increasing con-centration. We suggest that the solvent-mediated phase trans-formation can become limited shortly after ice forms and thesolute is rejected from the growing cubic ice crystal to form amore concentrated, more viscous brine. We also suggest thatthis may provide an explanation for the dependence of icephase on droplet ASR since transport properties in aqueoussolution are dependent on the physical properties of thesolute.65Experimental evidence for a solvent mediated cubic to hex-agonal ice phase transition. Let us first consider the phase of iceFig. 11 Flow diagram illustrating the crystallisation pathways a supercooled aqueous droplet might take when ice homogeneously nucleateswithin it. The octahedron represents an octahedral crystal of cubic ice, and the hexagon represents hexagonal ice crystals. Note that crystallisationin real droplets most likely results in many crystallites formed through dendritic growth.193298 | Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 This journal is C13c the Owner Societies 2008Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinethat formed in LET droplets in temperature regime i. Recallthat the crystallisation of letovicite is droplet size dependent(see Fig. 9), which indicated that nucleation and crystallisationin this regime were not limited by diffusion in the brine, butrather by nucleation. If the solvent-mediated cubic-to-hexa-gonal transition is active in determining the final phase of icethen one would expect more cubic ice in droplets whereletovicite crystallised more readily, i.e. the larger droplets. Inorder to test this hypothesis we performed a series of experi-ments with a solution of 26.9 wt% LET, where we varied thedroplet size. In Fig. 9b we plot the ratio of I44/I40vs. ourmeasure of the amount of letovicite that crystallised,I31(letovicite)/I40(ice-common),and shows that ice Icis stabilised inthe case where more letovicite crystallised. These data areconsistent with our postulated solvent mediated phasetransformation.In the case of AHS in regime i, the solute phase crystallisesmore readily in larger droplets, as it does in LET droplets.However, the situation is complicated by the fact that a brinealways persists on cooling to about 178 K, the measured SATcrystallisation temperature (even in the largest droplets).Hence, in any droplets in which ice forms above 178 K, theice will spend some time in contact with a brine until SATcrystallises, thus the crystallisation of letovicite alone is notsufficient to block the solvent mediated transformation. Hencewe would predict that hexagonal ice would dominate in theregime where letovicite can crystallise and that there would beno size dependence of ice phase (regime i). Inspection ofFig. 10 reveals that hexagonal ice does indeed dominate inthis region for all droplet sizes.We will now consider regime ii, where the crystallisation ofthe solute phase was strongly limited. Earlier in this paper itwas argued that the brine which forms after ice has crystallisedwas highly viscous and diffusion of water and ions was veryslow. In this case we would expect to see cubic ice as the mainproduct based on the nucleation kinetics and solvent mediatetransformation discussed above. It is clear from Fig. 10 thatcubic ice does dominate in this regime ii.The flow diagram in Fig. 11 is designed to illustrate thecrystallisation pathways that a freezing droplet may take.When ice nucleates in a supercooled aqueous solution dropletthere are a number of potential routes. In the first case, whichcorresponds to droplets in regime i, cubic ice nucleates andgrows and is in contact with aqueous brine. Hence, a solvent-mediated phase transformation will be active unless the solutephase(s) completely crystallise. The final mixture of ice Icandice Ihis determined by how efficiently the solute phasenucleates and crystallises. Our results show that letovicite ismore likely to crystallise in a 20 mm LET droplet than in a 1mm LET droplet, and hence the solvent mediated transitionwould have less time to operate and cubic ice would be morelikely to dominate. Ontheotherhand, in AHSdroplets abrinewould exist even if letovicite crystallised, thus providing amedium for the solvent mediated phase transformation. At-mospheric aerosols are often complex internal mixtures, hencea brine would oftenexit and if in regime i, hexagonalice wouldmost likely result. Alternatively, the droplets may be in regimeii (case 2), where ice Icnucleates and crystallises, but as the icecrystals grow the brine becomes increasingly viscous as itsconcentration increases and its temperature decreases. Thisresults in partially crystallised droplets which contain cubic icethat is stabilised, and a highly viscous or glassy brine in whichsolute crystallisation is limited. We suggest that the formationof these internally mixed cubic ice and highly viscous brinesmay form in the atmosphere and may influence cloud forma-tion and properties.Summary and atmospheric implicationsFor the first time we have directly identified the phases thatform in LET and AHS solution droplets after ice homo-geneously nucleates. When LET droplets crystallise we findthat letovicite II, rather than the expected letovicite III,28forms. In AHS droplets we find that a distorted letovicite IIforms in addition to SAT, whereas letovicite III and SAHmight have been expected.28,32These results illustrate howuseful X-ray diffraction is in determining the phases thatcrystallise from highly supercooled atmospherically relevantsolution droplets.In addition to determining phases that form, we alsodetermine how much of the solute phases crystallise as afunction of droplet size, solute type and solute concentration.We have shown that the crystallisation of the solute phase isstrongly size dependent and is limited in droplets of less thanB5 mm. Atmospheric droplets that freeze to form cirrus cloudice particlestend tobe in thesub-micrometer size range;hence,our results suggest that crystallisation of the solute phase maybe strongly limited in many atmospheric droplets. However, itis likely that the crystallisation of the solute phase alsodepends on time. In our experiments the time for crystal-lisation is short and it may be much longer in the atmosphere.More work is required to determine the effect of time. If thebrine does not crystallise then homogeneous freezing cannotdirectly contribute to a population of solid salt particles. It hasbeen suggested that these particles catalyse ice formation insubsequent cloud cycles.18–23Our results suggest that thedominant production mechanism for solid salt particles is viaefflorescence, which is thought to be an important process inthe atmosphere.66,67In addition, Bogdan et al.17suggest thatan ‘overlayer’ of liquid brine on ice crystals may influenceheterogeneous chemistry, optical properties and ice crystalgrowth kinetics of low temperature ice clouds.In more concentrated solution droplets the crystallisation ofthe solute phase in all droplets, including the largest ones(10–20 mm), is limited below freezing temperatures of 192 and180 K in (NH4)3H(SO4)2and NH4HSO4, respectively. Themost likely explanation for this behaviour is that the brinewhichforms below thesefreezing temperaturesbecomes highlyviscous, thus dramatically reducing the crystal growth rate ofany nucleated solute crystals.The inhibition of crystallisation of the solute phase in lowtemperature brines has led us to propose that the phase of icethat forms in solution droplets is determined by a solvent-mediated cubic-to-hexagonal phase transformation. Hence thenature of the aqueous brine can strongly influence the finalphase of ice and therefore provides an explanation for thestrongsolute dependence of ice phase observedin ourpreviousstudy.12At higher freezing temperatures the solvent-mediatedThis journal is C13c the Owner Societies 2008 Phys.Chem.Chem.Phys.,2008, 10, 3287–3301 | 3299Downloaded by The University of British Columbia Library on 18 April 2011Published on 21 April 2008 on | doi:10.1039/B802216JView Onlinetransformation is only blocked if the solute crystallises; if it isnot blocked hexagonal ice results, whereas below some thres-hold freezing temperatures the transformation is effectivelyblocked when thebrine becomes highly viscous and cubic ice istherefore the dominant crystalline product. We have shownstrong differences when simply changing the ASR of dropletsfrom 1.5 to 1.0, which presumably reflects the physical proper-ties of the brine. Glass transition temperatures and viscosity ofpertinent aqueous solutions need to be experimentally deter-mined in order to test the proposed solvent mediated phasetransformation. In addition it should also be noted that realatmospheric droplets are often more complex than the modelsystems employed here, often containing organics and nitratesamongst other species. The impact of these other chemicalspecies needs to be examined in future laboratory studies.AcknowledgementsThe authors thank Dr Christoph Salzmann (Oxford Univer-sity) for very helpful advice on refining structures and employ-ing the Rietveld method. We also gratefully acknowledge A.Lam and B. Patrick (UBC) for assistance with X-ray diffrac-tion measurements. This work was funded by the NaturalScience and Engineering Research Council of Canada,NSERC, the Canadian Foundation for Climate and Atmo-spheric Sciences, CFCAS, and the Canada Foundation forInnovation, CFI. 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