Laboratory Evidence for Surface Nucleation of Solid Polar Stratospheric Cloud Particles

Transcription

1 10238 J. Phy. Chem. A 2002, 106, Laboratory Evidence for Surface Nucleation of Solid Polar Stratopheric Cloud Particle A. Tabazadeh,*, Y. S. Djikaev, P. Hamill, and H. Rei NASA Ame Reearch Center, Moffett Field, California 94035, Department of Phyic, San Joe State UniVerity, San Joe, California and Department of Chemitry and Biochemitry, UCLA, Lo Angele, California ReceiVed: April 24, 2002; In Final Form: Augut 13, 2002 Nitric acid-containing cloud particle, known a polar tratopheric cloud, play an important role in the pringtime ozone detruction over the polar region. Nitric acid initially condene in the polar tratophere to form upercooled olution droplet of mainly nitric acid and water with trace amount of ulfuric acid. Nitric acid dihydrate (NAD) and nitric acid trihydrate (NAT) later crytallize from thi upercooled olution phae to form olid polar tratopheric cloud particle. Until now, experimental data on thi crytallization proce ha been analyzed under the aumption that NAD and NAT nucleation took place in the interior volume of a cloud droplet. However, in thi paper, reanalyi of experimental data on the homogeneou freezing rate of concentrated aqueou nitric acid olution droplet provide ubtantial upport for the occurrence of nucleation peudoheterogeneouly at the air-aqueou nitric acid olution interface of the droplet. Furthermore, in a following paper, theory that provide compelling evidence for uch interfacial nucleation i developed. Together, the reanalyi of laboratory data in thi paper and the upporting theoretical argument in the following paper ugget that the homogeneou nucleation proce occurring in atmopheric droplet may be a urface- rather than a volume-related rate proce. 1. Introduction It wa firt uggeted in 1986 that ome polar tratopheric cloud (PSC) particle may contain nitric acid 1,2 becaue they were oberved in the tratophere at temperature above the ice frot point. 3 In itu aerool compoition meaurement later confirmed that PSC particle do contain nitric acid. 4-6 Nitric acid trihydrate (NAT) wa uggeted to be the likely phae of nitric acid particle in the tratophere. 1 Later, laboratory obervation howed that NAT i table in the tratophere at temperature of approximately 5 K above the ice frot point. 7 Other laboratory experiment indicated that nitric acid dihydatre (NAD) can alo form in the tratophere. 8,9 In addition, Wornop et al. 9 found that the metatable NAD phae readily formed in the laboratory, wherea the table NAT phae wa only formed by converion of NAD into NAT. In itu obervation from the Airborne Arctic Stratopheric Expedition (AASE) further complicated the undertanding of nitric acid particle formation by providing evidence for the preence of liquid-phae ulfate particle at cold polar temperature. 10 Prior to the AASE obervation, olid nitric acid particle were aumed to nucleate on the urface of frozen ulfuric acid tetrahydrate (SAT) particle (the mot table H 2 - SO 4 -H 2 O phae under polar tratopheric condition). 11 Soon after the AASE obervation were publihed, laboratory invetigation howed that aqueou ulfuric acid can remain liquid, and aborb a ubtantial amount of HNO 3 at cold polar temperature. 12,13 Laboratory data 13 were later ued in aerool model 14,15 to how that nearly all HNO 3, available in the * To whom correpondence hould be addreed. atabazadeh@ mail.arc.naa.gov. NASA Ame Reearch Center, Moffett Field. Department of Phyic, San Joe State Univerity. Department of Chemitry and Biochemitry, UCLA. atmophere, could potentially condene into the H 2 SO 4 -H 2 O liquid olution to form a liquid ternary aerool (LTA) coniting of H 2 SO 4 -HNO 3 -H 2 O. The fact that both olid 1,8,9 and liquid tate were uggeted for nitric acid-containing cloud particle in the tratophere wa in agreement with lidar obervation of PSC, which indicated the frequent occurrence of both particle type in the tratophere LTA particle in the tratophere form by condenational growth uch that a nucleation free energy barrier doe not have to be overcome, 14,15 and currently, there i no debate on how LTA particle form and grow in the tratophere. In contrat, even after more than a decade of reearch on PSC, a quantitative undertanding on the formation mechanim of olid nitric acid-containing cloud particle i till lacking. 19 Previouly, it wa thought that the mot likely mechanim involved the heterogeneou nucleation of nitric acid hydrate on the urface of ice particle. 19 However, ample evidence from obervational data eem to indicate that olid nitric acid cloud in the tratophere often form independent of ice cloud. 18,20-22 To account for the formation of olid nitric acid particle in the tratophere (above the ice frot point) everal uggetion have been made involving homogeneou 23,24 and heterogeneou 22,25 freezing of the LTA ytem. In thi paper, we reexamine laboratory data on homogeneou freezing of NAD and NAT to how that thi proce mot likely initiate on the urface of a upercooled cloud droplet rather than within it bulk volume. 2. Background on Surface Nucleation Common example of nucleation in fluid, uch a bubble formation 26 and the crytallization of drop of molten metal, 27 involve liquid-vapor or liquid-liquid interface. However, a far a we know, until now, laboratory tudie and theoretical model 22-24,28-37 of the freezing of atmopheric particle have /jp021045k CCC: $ American Chemical Society Publihed on Web 10/02/2002

2 Surface Nucleation of Stratopheric Cloud Particle J. Phy. Chem. A, Vol. 106, No. 43, Figure 1. (a) Partially wetting drop of liquid (len haped) reting on a olid ubtrate urrounded by vapor. The three interface are vaporliquid (vl, gray line), vapor-olid (v, dahed line), and liquid-olid (l, black olid line). The correponding urface tenion are σ vl, σ v, σ l. θ i the contact angle. (b) Crytal nucleu in a liquid, but with one face in contact with the vapor. Black olid line indicate face in contact with the liquid while the face in contact with the vapor i repreented by the dahed line. aumed that freezing occur via nucleation within the particle volume. A recent analyi of laboratory data on the freezing of upercooled water droplet ugget that thi proce may alo be a reult of ice nucleation at the droplet urface (airwater interface) rather than within the droplet volume. 38 In the preent paper, we reanalyze exiting laboratory data 23,28-32 on the freezing rate of concentrated aqueou nitric acid olution droplet. The reult of thi analyi trongly ugget that thi freezing proce may alo initiate at the droplet urface. The idea of urface freezing i upported by everal kind of independent evidence, which even ugget that droplet urface nucleation may be the preferred mode in many atmopheric procee. For example: 1. Computer imulation how that, in fluid cluter, crytalline nuclei tend to form at or near urface layer Cahn 40 ha hown that, away from it critical point, a liquid i not likely to fully wet a olid. Thi could include, a a pecial cae, a melt and it own olid. The relevance of item 2 above i the following. Conider Figure 1a that applie to a ingle component ytem. The Figure how a len-haped drop of melt (liquid) reting at equilibrium on the urface of it crytalline olid. Both olid and melt are expoed to the vapor of the ame ubtance. The urface or interfacial tenion σ v, σ vl, and σ l refer to the vapor-olid, vapor-liquid, and liquid-olid interface hown a dahed, gray, and olid line, repectively. The equilibrium configuration in Figure 1a how that the melt only partially wet it olid, and the contact angle θ exceed zero (complete wetting would have θ ) 0). Such an equilibrium configuration indicate that σ vl + σ l > σ v, the condition for partial wetting, and ugget that the extenion of the liquid-olid interface at the expene of the vapor-olid interface would be dicouraged by an increae in the total urface free energy of the overall ytem. Now conider Figure 1b, which how a chematic crytal nucleu forming within the liquid melt with one face, ay of area a, at the interface with the vapor o that it contitute a vapor-olid interface denoted by a dahed line. If the nucleu formed entirely within the bulk of the liquid, intead of with one face in contact with the vapor, then the difference in free energy would reflect that the free energy σ v a would be replaced by σ l a + σ vl a (auming that the new face wa alo of area a) correponding to the two new interface, vapor-liquid and liquid-olid, that replace the ingle interface, vapor-olid. The difference in free energy would therefore be σ l a + σ vl a - σ v a. If the nucleu formation at the urface wa favored, then thi free energy difference would be poitive uch that σ l + σ vl - σ v > 0, which i identical with the condition for partial wetting preented above. Thu, crytallization at the vapor-liquid interface hould be favored in cae where the olid i only partially wettable by it own liquid melt. The above argument i only qualitative, but in the following paper, 41 we derive a more rigorou thermodynamic criterion to how how the determination of the contact angle between a olid an it melt can be ued to predict the mode (urface or volume) of nucleation. Thi criterion indeed prove to be the condition of partial wetting uggeted qualitatively above. To tet whether the partial wetting criteria can be ued to determine the mode of nucleation in the atmophere, we briefly dicu the ice-water ytem. Optical tudie on urface melting of ice how that water only partially wet the ice urface. 42 Thi obervation ugget that ice nucleation in upercooled water mot likely occur on the droplet urface. In fact, our recent analyi 38 of ice nucleation kinetic data, 35 where water droplet tudied were immered in variou ambient oil bath, how that the ice-nucleation line (nucleation rate veru temperature) yield a different lope in different oil. Thi obervation ugget that ice nucleation mot likely have occurred on water droplet urface becaue the only phyical property that change when the oil i changed i the water-oil interface and not the bulk propertie of pure water. In other word, if ice nucleation had occurred in the bulk of water droplet, then the rate of ice nucleation hould not have varied in different ambient oil bath. Thu, at leat for the ice-water ytem the condition of partial wetting leading to urface nucleation of ice in water eem to hold. The cae of nitric acid hydrate crytal nucleation in aqueou nitric acid olution droplet involve a multicomponent (at leat a binary) ytem, and the imple vapor of the preceding dicuion i replaced by air with it everal component. Thu, to make the argument more convincing, it will be neceary to derive a criterion (or criteria) for urface veru volume nucleation in multicomponent ytem. The thermodynamic will be complicated, not only by the preence of everal component, but alo by the need to conider urface adorption by all component. Neverthele, in a future paper, we plan to derive uch extended criteria. In the remainder of the preent paper, we reexamine exiting laboratory data on the nucleation of NAD and NAT crytal in highly concentrated aqueou nitric acid olution droplet. The manner of analyi indicate that thi nucleation proce i mot likely urface rather than volume baed. 3. Relation between the Interpretation of Experimental Data a Volume or Surface Nucleation Homogeneou freezing of a upercooled liquid droplet in the atmophere can occur when a crytal nucleu form either within the volume of the droplet or on it urface. Although a ingle nucleu i ufficient to crytallize a upercooled liquid droplet, the nucleation rate i often expreed a J V the number of nuclei formed per econd in a unit volume of the liquid. Similarly, let J S be the number of nuclei formed per econd on unit urface area of the liquid. Thu, the total number of crytal nuclei formed per unit volume of air per econd i J T ) J V V t + J S S t (1) where V t and S t are the total volume and urface area of all

3 10240 J. Phy. Chem. A, Vol. 106, No. 43, 2002 Tabazadeh et al. droplet per unit volume of air. In atmopheric tudie of homogeneou freezing to form either ice or nitric acid hydrate particle (both NAT and NAD) from aqueou olution, it i alway aumed that J T ) J V V t ,28-37 Thi aumption ignore the potential effect of nucleu formation at the urface of a liquid aerool particle. 27,38,39,41 In fact, if the free energy of liquid formation i lower on the urface of a particle than within it bulk, 41 then the overall rate of particle freezing will be proportional to the total available aerool urface area and not to aerool volume. In atmopheric cience, a tandard expreion for the rate of homogeneou crytal nucleation within the bulk of a fluid (J V ) i given by 43 J V ) N L (kt/h)exp[ - G b act RT ] (2) Thi repreent a crude approximation baed on the original theory of abolute reaction rate (there are better expreion today), but it i good enough for our analyi, given the accuracy of the experimental data. In eq 2, N L i the molecular olute concentration in the liquid (for our cae N L i the molecular concentration of HNO 3 in the liquid olution per cm 3 of volume), k and h are the Boltzmann and Planck contant, T i the b temperature in Kelvin, R i the ga contant, and G act i the free energy of formation, in the bulk, of the crytal nucleu. A imilar relation for J S the rate of nucleu formation on the droplet urface i J S ) N S (kt/h)exp[ - G act RT ] (3) where N S i the total number of molecule per unit urface area of the fluid (for our cae N S ) X HNO3 n S, where X HNO3 i the mole fraction of HNO 3 on the urface of the liquid olution and n S ) i the approximate number of molecular urface ite per cm 2 of urface area of the liquid 43 ), and G act i the free energy of formation of a crytal nucleu on the droplet urface. If we aume that homogeneou freezing occur in the laboratory, olely due to nucleu formation on particle urface, then the reported volume-baed freezing rate 23,28-32 are related to urface-baed rate by the following expreion J S ) (V t /S t )J V (4) Note that in deriving the above relation, we have aumed that formation of jut one nucleu i ufficient to freeze a ingle droplet in the enemble of thoe monitored in the laboratory. 23,28-32 Thu, the meaured number of droplet that freeze in unit time can be expreed a either J V V t or J S S t, depending upon which mechanim (volume or urface baed) i aumed. If the ditribution of droplet ize i monodipere, then eq 4 reduce to J S ) (r/3)j V (5) where r i the aerool droplet radiu. Thu, if the nucleation proce i urface-baed, different rate of freezing would be oberved, depending on the droplet ize ditribution. For example, a larger fraction of droplet will freeze if the aerool volume i pread over many mall droplet 28,30-32 than if it were confined to a few larger one. 23 Below, eq 4 and 5 are ued to convert reported volume-baed rate into urface-baed rate for NAT and NAD particle formation from droplet of concentrated TABLE 1: Laboratory Freezing Invetigation type ample ize experimental technique a reference film 1-2 µm FTIR Tidale et al. aerool 0.5 µm particle cloud chamber/ftir Dielkamp et al. Anthony et al. Prenni et al. aerool 0.38 µm particle flow-tube/ftir aerool 25 µm particle optical microcopy/ viual inpection aqueou HNO 3. Thee rate are then ued in eq 3 to derive value for NAT and NAD formation in the tratophere. G act Bertram and Sloan Salcedo et al. a In the aerool experiment (except for Anthony et al. where LTA olution were ued) binary aqueou nitric acid olution were ued. Aqueou nitric acid olution were alo ued in the film experiment. 4. Interpretation and Analyi of Laboratory Nucleation Rate Table 1 lit the laboratory invetigation dicued below. Firt, data from aerool experiment 23,28,30-32 are ued to derive urface-baed nucleation rate for NAT and NAD formation. Second, reult from film experiment 45 are ued to provide upport for the idea that the nucleation of NAD crytal from aqueou nitric acid olution occur at the urface layer of a droplet. Figure 2 how laboratory reported aerool nucleation freezing rate over a temperature range from 165 K to 205 K for different olution compoition (the HNO 3 mole fraction, X, i given on the bottom of each panel). All of the Figure 2 panel (except for panel (d) where NAT nucleation freezing rate are hown) how laboratory freezing rate for NAD aerool. Equation 4 and 5 were ued to convert the reported volume rate (filled ymbol) into urface rate (open ymbol). In Figure 2a, nucleation data for nitric acid olution with concentration X HNO3 ) are hown from three laboratorie. 23,28,30-32 At temperature above 190 K, the volume baed data (filled ymbol) exhibit coniderable dicrepancy, epecially between triangle 23 and the other ymbol. 28,30 Thi dicrepancy in laboratory data i a great a 4 order of magnitude. Furthermore, nucleation rate hould decreae with increaing temperature, but ome of the data, due to Dielkamp et al., 28 admittedly limited, ugget either an increae or no change in the rate a temperature i increaed. Yet there i no obviou experimental reaon for the dicrepancy (Margaret Tolbert, peronal communication, 2001). In contrat to thi behavior, when eq 4 and 5 are ued to convert the rate, reported a volume baed (filled ymbol), to urface baed (open ymbol) rate, mot of the dicrepancy diappear a i evident from the open ymbol in the lower part of Figure 2a. Not only do the data from different laboratorie now lie within about only 1 order of magnitude of each other, but alo now they all trend downward with increae in temperature, a functional dependence that i expected. Thi reult provide upport for a urface baed nucleation mechanim. What could be the origin of the dicrepancy in the volume baed data? The bet anwer involve eq 5, which how that if indeed nucleation i urface baed, then the ize of the aerool droplet mut play a trong role. In the experiment of Salcedo et al., 23 the average ize of an aerool droplet wa 25 micron, wherea in the experiment of Prenni et al. 30 and Dielkamp et al., 28 the droplet ize wa of the order of 0.5 micron. Thu, on the bai of eq 5 alone, auming that nucleation wa urface

4 Surface Nucleation of Stratopheric Cloud Particle J. Phy. Chem. A, Vol. 106, No. 43, Figure 2. Volume- and urface-baed nucleation rate of NAD (panel a, b and c) and NAT (panel d) aerool from aqueou HNO 3 olution determined by laboratory obervation. Filled and open ymbol give volume (in unit of cm -3 ec -1 ) and urface (in unit of cm -2 ec -1 ) rate, repectively. Circle are from Bertram and Sloan (BS), 31,32 Triangle are from Salcedo et al. (SA), 23 quare are from Prenni et al. (PR), 30 and diamond are from Dielkamp et al. (DI). 28 The HNO 3 mole fraction of the olution (X) i given on the bottom of each panel. The urface rate are derived from the reported volume-baed nucleation rate uing eq 4 and 5. For BS data a monodipere ize ditribution with a mode radii of 0.38 micron wa ued. For PR data, a monodipere ize ditribution with a mode radii of 0.5 micron wa ued. For DI the ize ditribution given in Table 1 of thi article were ued. For SA, the large upermicron-ized particle ( 25 micron in radiu) immered in oil were nonpherical and therefore the meaured geometric apect of particle were ued to convert volume to urface area. For SA, the average behavior of many data point are hown only a few ymbol. Thi wa done to give equal weight to data reported from all laboratorie for the determination of the nucleu free energy of formation. baed and that urface rate were imilar in all cae, the Salcedo et al. 23 reult hould lie, a they do, far below the reult of the other invetigator. Actually, the aerool of Salcedo et al. 23 (triangle) wa eventually immered and caued to freeze in a matrix of oil, o that an oil-aqueou nitric acid rather than an air-aqueou nitric acid interface wa involved. Thu, we cannot really be ure that the urface rate were imilar for both interface. Alo, in the Salcedo et al. 23 cae, the droplet were not entirely pherical and a more realitic geometry than that aumed in the derivation of eq 5 wa ued in converting the aumed volume rate to urface rate. Neverthele, the cae for urface nucleation remain compelling. Figure 2c provide imilar upport, in the NAD cae, for urface nucleation. It exhibit data of Salcedo et al. 23 and Prenni et al. 30 for nitric acid olution of concentration X HNO3 ) Again, the filled ymbol indicate the aumed volume baed rate, wherea the open ymbol indicate the urface rate obtained by tranforming the oberved aumed volume rate. Once more, there i a reduction of the dicrepancy from almot 3 order of magnitude to le than 1 order of magnitude. It i of interet to etimate the free energie of formation of the nuclei for the urface baed nucleation rate. For thi purpoe, all of the data for the aumed urface baed rate exhibited in Figure 2a-2d were ued in eq 3 to etimate the G act for both NAD and NAT nucleation in aqueou nitric acid. Although, thee meaured rate how a coniderable catter, they are till ueful in etimating free energie becaue of the exponential relation between rate and free energy (i.e., in taking the logarithm to extract the free energy, the catter i coniderably reduced). Thi i a typical feature of mot nucleation

5 10242 J. Phy. Chem. A, Vol. 106, No. 43, 2002 Tabazadeh et al. dependence can be etimated uing the NAD dependence, i.e., from G,NAT act (X HNO3, T) ) G,NAD act (X HNO3, T) G,NAD act (0.246, T) G act,nat (0.246, T) (8) Figure 3. Surface-baed nucleation rate hown in Figure 2 were ued in eq 3 to derive nucleu free energy of formation for NAD (HNO 3 mole fraction ) 0.246, 0.278, and 0.333) and NAT (HNO 3 mole fraction ) 0.246) in aqueou HNO 3 olution. A leat-quare-fit line i hown for each olution compoition and phae. The error bar (( 0.5 kcal mol -1 ) how the range of variation in the nucleu free energy from the leat-quare-fit line. The error bar do not reflect experimental uncertainty and only how deviation of point from the theory line. phenomena. Etimate obtained in thi way are plotted in Figure 3. The etimated free energie range between 40 and 55 RT (for T taken nominally a 190 K), which i typical for mot nucleation procee. The line plotted in Figure 3 can be ued to etablih empirical fit for the dependence of formation free energie on both temperature and nitric acid concentration. In thi connection, Salcedo et al. 23 have recently ued laboratory b volume-reported rate in eq 2 to extract G act for NAT and NAD nucleu formation. In their etimate of G b act, only the reult from Salcedo et al. (triangle in Figure 2) 23 and Bertram and Sloan (circle in Figure 2) 31,32 were ued in the parametrization of G b act, mainly becaue (a dicued above) the volume-reported laboratory rate from Prenni et al. (quare in Figure 2) 30 and Dielkamp et al. (diamond in Figure 2) 28 were up to 4 order of magnitude higher than thoe reported by Salcedo et al. 23 Becaue the urface-reported rate how much le dicrepancy, in our etimate, we have ued all the reported laboratory nucleation data rate on the freezing of NAD and NAT aerool. The reulting formation free energy for the NAD urface baed nucleu, obtained through an empirical fitting of our etimate i given (in unit of kcal mol -1 ) by the expreion G,NAD act (X HNO3, T) ) T - { T}X HNO3 (6) wherea that for NAT i G,NAT act (0.246, T) ) T (7) We were not able to derive a direct compoition dependence for the NAT free energy becaue NAT nucleation rate were available only for a ingle acid concentration, namely X HNO3 ) (Figure 2d). However, becaue in Figure 3 the lope of the free energy line for NAD are nearly parallel, a crude expreion for the NAT formation free energy compoition where it i aumed that the change in the lope of NAT nucleu formation free energie with acid concentration are proportional to thoe of NAD, along the X HNO3 ) compoition line. Even the mot extreme point hown in Figure 3 deviate from the leat-quare-fit by only about ( 0.5 kcal mol -1 (error bar in Figure 3). A mentioned above, G act depend le critically on the experimental uncertaintie 23,28,30-32 (aerool compoition, aerool ize-ditribution, and temperature) than the actual rate. For example, changing G act by 0.5 kcal mol -1 could alter the rate by an order of magnitude (ee Figure 4). In Figure 4, the calculated volume and urface nucleation rate are hown for two olution compoition. It i apparent that volume nucleation rate for NAD (panel a and b) are much more temperature-dependent than the etimated urface baed rate. For example, for X HNO3 ) (panel a), volume and urface nucleation rate between 165 and 200 K vary by 6 and 2 order of magnitude, repectively. Dielkamp et al. 28 have been able to oberve freezing of concentrated aqueou HNO 3 olution (e.g., X HNO3 ) 0.333) to form NAD crytal up to a temperature of about 204 K (Figure 2a). Although a urfacebaed rate proce can readily account for thee obervation, a highly temperature enitive volume-baed rate proce cannot explain why NAD particle were formed in the laboratory at temperature a high a 204 K. Dielkamp et al. 28 could detect NAD freezing only if (at leat) 5% of the particle froze in about 2 h. On the bai of the meaured rate, a volume rate proce would have caued freezing of le than 1% of the droplet into NAD in 2 h. Therefore, we conclude that uch a proce would have been too low to explain NAD formation at 204 K. Up to now, no aerool experiment have been able to produce NAT nuclei in compoition uch that X HNO3 > However, at temperature below 178 K and for X HNO3 ) 0.246, NAT nuclei, intead of NAD nuclei, 23,31,32 do form electively in aerool (ee Figure 4b and 4c). Thi obervation provide additional upport for urface nucleation of NAT and NAD nuclei in aqueou HNO 3. The volume-baed rate indicate that NAD nuclei (Figure 4b) till retain higher nucleation rate, compared to NAT nuclei (Figure 4c) down to a temperature of about 174 K. If the nucleation proce occurred in the volume, then NAT formation hould not have been oberved near 178 K becaue at thi temperature NAD volume-baed nucleation rate remain a factor of 5 larger than thoe for NAT. On the other hand, a the temperature i lowered, the urface nucleation rate for NAT firt exceed that of NAD (X HNO3 ) 0.246) in the neighborhood of about 178 K, indicating that below thi temperature NAT nuclei can form at a higher rate than thoe of NAD, in accord with the obervation. Becaue many laboratory meaurement, 23 howing NAT formation, exit in the temperature range between 174 K and 178 K, it i unlikely that a volume-baed freezing proce could account for thee obervation. Avrami analyi of the crytallization kinetic involved in the freezing of HNO 3 /H 2 O film (condened on a ilicon-wafer ubtrate) into NAD, indicate that the nucleation of NAD occur in a 2-dimenional (2D) field. 45 Tidale et al. 45 uggeted that the 2D nature of the oberved NAD freezing rate wa perhap

6 Surface Nucleation of Stratopheric Cloud Particle J. Phy. Chem. A, Vol. 106, No. 43, Figure 4. Calculated nucleation rate of NAD (panle a and b) and NAT (panel c) formation from 2 aqueou HNO 3 olution compoition (HNO 3 mole fraction ) and 0.246). The ymbol are defined in the legend of Figure 2. All of the data point reported by Salcedo et al. 23 are hown. The volume rate are calculated uing eq 2 and the nucleu free energy expreion given in Salcedo et al. 23 The urface rate are calculated uing eq 3, 6, and 7. The dotted line give upper- and lower-bound nucleation rate obtained by uing minimum and maximum poible value of nucleu formation free energie. Error bar how the reported range of temperature uncertaintie. due to heterogeneou nucleation at the film-ilicon interface. However, the preceding analyi open the alternative poibility that the oberved 2D nature of the freezing rate could be the reult of urface baed nucleation at the aqueou nitric acid filmga interface. With thi alternative poibility, film experiment alo provide ome upport for urface and/or 2D nucleation of NAD in aqueou HNO 3. In arriving at the fitting formula, eq 6, for the temperature and concentration dependence of G act, we aumed that X HNO3 in eq 3 i equivalent to X HNO3 in the bulk of the aqueou HNO 3 droplet. Thi i an approximation ince urface enrichment of HNO 3 hould be taken into account. Indeed, recent tudie in bulk aqueou HNO 46 3 a well a in LTA 47 olution provide evidence for the urface enrichment of HNO 3 in both ytem. However, becaue the experiment were performed at warm temperature, the oberved enrichment might differ from that at cold temperature. In any event, the meaurement in ref 46 and 47 were not ued in the development of eq 6. In the abence of ignificant experimental data on the urface enrichment of nitric acid at cold temperature, it i beyond the cope of thi work to attempt to quantify the level of HNO 3 enrichment in the urface layer of the LTA ytem. 5. Implication for Atmopheric Procee The nucleation of both NAD and NAT crytal in the atmophere take place in LTA droplet rather than in droplet of pure aqueou nitric acid. Above, we have only derived empirical expreion for nucleation rate involving pure aqueou nitric acid. Thu, the abence of rate data for LTA droplet leave u with the only alternative of extrapolating the current pure nitric acid reult to LTA droplet. At temperature where LTA particle freeze into hydrate of nitric acid, the H 2 - SO 4 acid weight percent of the LTA olution in the tratophere drop to below about 2% If H 2 SO 4 at cold temperature i a urface active component, then even mall amount of ulfuric acid can caue dramatic change in the urface tenion of the olution becaue the nucleation free energy barrier i more enitive to urface tenion than any other parameter. However, Figure 5. Calculated NAD urface nucleu free energy of formation a a function of HNO 3 mole fraction and temperature uing eq 6. if H 2 SO 4 i not a urface active component, then we upect that trace amount of H 2 SO 4 in LTA olution will not ignificantly change the rate of hydrate formation relative to that meaured in pure aqueou HNO 3. Further, even the rate derived here for pure aqueou HNO 3 are for concentrated olution. Thu, it i not clear whether thee rate will reaonably extrapolate to tratopheric compoition, where nitric acid mole fraction in droplet remain below Becaue of thee conideration, the dicuion in the preent ection, in which we apply rate obtained with pure concentrated aqueou nitric acid to LTA, mut be regarded a le rigorou than that in the preceding ection of thi paper. Having aid thi, we can turn to Figure 5 where hading indicate the compoition range for NAD nuclei formation free energie for both the laboratory and atmopheric procee.

7 10244 J. Phy. Chem. A, Vol. 106, No. 43, 2002 Tabazadeh et al. Figure 6. (a) Temperature variation in the HNO 3 mole fraction and NAD aturation. (b) Temperature variation in the total LTA aerool urface area and volume. An aumed ulfate aerool ize ditribution 10 wa ued to convert LTA volume into urface area (c) Temperature variation of NAD volume- and urface-baed nucleation rate for LTA compoition in the tratophere. The gray haded area mark the poible upper-bound urface nucleation rate for LTA compoition determined in the laboratory. 29 (d) Temperature variation in the hourly tratopheric volume and urface production rate of NAD particle. All calculation were performed at 60 mb for HNO 3,H 2O and H 2SO 4 mixing ratio of 12 ppbv, 5 ppmv, and 0.5 ppbv, repectively. 48 Clearly, thee range are quite different. Becaue the laboratory compoition were more concentrated in HNO 3, NAD germ formation energie were maller, and allowed efficient freezing to occur within minute to at mot hour, when a large enemble of droplet (> 10 5 particle cm -3 ) wa tudied. In the atmophere, HNO 3 mole fraction in LTA are maller (typically le than 0.18), and reult in higher free energie of formation. Thu, in the atmophere, longer expoure time are needed to freeze tratopheric aerool. Alo, the number denitie of LTA droplet in the tratophere are 10 cm -3, o that the total available urface area in tratopheric aerool are at leat 10 4 time maller than thoe available in the laboratory. Thi factor too will caue atmopheric aerool to freeze more lowly than their laboratory counterpart. Below, typical LTA aerool nitric acid concentration and urface area are ued to etimate (uing expreion baed on rate meaured in pure aqueou nitric acid) the rate of nitric acid hydrate particle formation in the tratophere. It hould be emphaized and reiterated again that to obtain the reult hown in Figure 5 and 6, we have extrapolated the free energy formula derived in both the preent paper, and in that due to Salcedo et al., 23 beyond the range of the laboratory compoition. We will deal with etimate only for NAD particle production rate in the tratophere, becaue for X HNO (thi i the larget poible HNO 3 mole fraction in the tratopheric LTA olution), the extrapolated formation free energy for NAT i 26.2 kcal mol -1 (obtained from eq 3 and 6-8). With thi mallet poible value (26 kcal mol -1 ), the hourly atmopheric NAT particle production rate are around 10-6 cm -3. Microphyical enitivity tudie 24 have hown that hourly particle production rate below about 10-5 cm -3 cannot have a ignificant influence on the overall tratopheric number denity of nitric acid-hydrated particle. Figure 6, part a and b, diplay important LTA and NAD aerool propertie for olid particle nucleation in the tratophere. To etimate volume-baed nucleation rate, the NAD nucleu formation free energy due to Salcedo et al. 23 wa ued in eq 2. For urface-baed rate, eq 3 wa ued. The LTA propertie (NAD aturation in olution, HNO 3 LTA mole fraction, total LTA urface area and total LTA volume) are calculated uing the parametrized model of Lin and Tabazadeh. 47 For a given temperature, NAD aturation i obtained by dividing the vapor preure of HNO 3 over the LTA ytem by the equilibrium vapor preure of HNO 3 over the NAD phae. Uing the parameter hown in Figure 6a in eq 2 and 3, we obtain the volume and urface rate hown in Figure 6c. Figure 6c give NAD nucletion rate per unit volume and urface area of the tratopheric LTA ytem. The gray band in Figure 6c mark the mallet value of urface nucleation rate that would be needed for Anthony et al. 29 to detect freezing of the LTA ytem in the laboratory. Thee author could detect NAD freezing only if (at leat) 5% of the droplet froze within about 2 h. The etimated (Figure 6c) urface baed nucleation proce could have caued freezing into NAD of only about 0.05% of the droplet in about 2 h. Therefore, the obervation of Anthony et al. 29 on the lack of LTA freezing in the laboratory are not in diagreement with our etimate. If the volume of tudied laboratory droplet could

8 Surface Nucleation of Stratopheric Cloud Particle J. Phy. Chem. A, Vol. 106, No. 43, be pread over maller particle (to increae their urface area by a factor of roughly 100, ee eq 5), then it might be poible to detect the freezing of LTA droplet in the ame laboratory uing experiment in the aerool chamber (ee Table 1). A dicued above, there are many advantage to formulating rate expreion uing nucleation freezing rate meaured in the LTA ytem intead of the aqueou HNO 3. For example, the preence of H 2 SO 4 may increae or decreae the rate of droplet freezing in the tratophere by affecting the level of HNO 3 enrichment at the urface layer. Thu, the direct obervation of freezing rate in LTA at cold temperature can hed light on the poible role that trace amount of H 2 SO 4 may play in the freezing proce of tratopheric aerool particle. The product of the curve plotted in Figure 6b and 6c yield NAD particle production rate in the tratophere (Figure 6d). For mot temperature, NAD particle production uing urfacebaed rate i nearly 2 order of magnitude larger than thoe obtained from volume-baed rate. Thu, if NAD nuclei form on LTA particle urface, then they can nucleate at a much fater rate than nuclei that might form in the bulk olution. Thi finding hould affect the reult of microphyical calculation preented in Tabazadeh et al. work 24 becaue in thi tudy extrapolated volume-baed nucleation freezing rate 23 were ued to calculate the rate of NAD particle production in the atmophere. In a later publication, we intend to invetigate the effect of urface nucleation in more detail. 6. Concluion Laboratory data on NAD and NAT nucleation rate, meaured in aqueou nitric acid droplet, were ued to formulate homogeneou urface-baed rate expreion for the formation of olid PSC particle from LTA olution. We howed that urfacebaed rate expreion for NAD and NAT particle production are conitent with all the available laboratory kinetic data on the freezing of the aqueou HNO 3 ytem, wherea volumebaed rate expreion how coniderable inconitencie. Overall, urface-baed nucleation rate of NAD particle in the tratophere may be a many a 2 order of magnitude larger than their correponding volume-baed rate. The fact that NAD and NAT particle nuclei formation from an aqueou droplet eem to occur on the urface of the droplet i extremely intereting. A recent tudy on the kinetic of upercooled water-droplet freezing 38 ugget that thi proce may alo occur on the urface. There i alo evidence from nonatmopheric particle ytem, uch a crytallization of molten metal drop, 27 that the crytal nucleation occur at an oil-liquid interfacial layer. Both computer imulation 39 and thermodynamic calculation 41 further ugget that crytalline nucleu formation i favored on the urface over that in the bulk. 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