Mechanisms and Temperatures for the Freezing of Sulfuric Acid

freezing points of these aerosols under atmospheric conditions. From the .... obtained between the measured and calculated extinction spectra. Figure ...
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J. Phys. Chem. 1996, 100, 2376-2383

Mechanisms and Temperatures for the Freezing of Sulfuric Acid Aerosols Measured by FTIR Extinction Spectroscopy A. K. Bertram, D. D. Patterson, and J. J. Sloan* Department of Chemistry, UniVersity of Waterloo, Waterloo, Ontario N2L 3G1, Canada ReceiVed: August 31, 1995; In Final Form: October 24, 1995X

We have measured the freezing curve of liquid H2SO4/H2O aerosol droplets having average radii of approximately 0.2 µm. We form the aerosol by the reaction of SO3 with H2O and flow it through a temperaturecontrolled flow tube equipped with reentrant windows, through which we make observations by FTIR extinction spectroscopy. At the freezing point, a microcrystallite of pure ice (H2O(s)) nucleates in the aerosol droplet, and this causes a small change in the spectrum near 3250 cm-1. By recording the temperatures at which the crystallites appear for different acid concentrations, we are able to map out the freezing curve. In the following account, we describe the experimental technique and report the freezing curve for the concentration range up to 35 wt % H2SO4, which corresponds to the first eutectic point on the phase diagram of the bulk material. We find that the aerosol supercools by about 35 K below the temperature at which the corresponding bulk material freezes. Our data show that the overall freezing mechanism is similar to that of the bulk solution: after nucleation, the crystallite grows with decreasing temperature, causing the remaining acid to become more concentrated due to the removal of H2O until eventually a eutectic mixture forms.

Introduction We have undertaken a program of laboratory measurements to locate the temperatures at which phase transitions occur in model atmospheric aerosols. Our primary goal is the measurement of the freezing points of these aerosols as a function of composition, and in the following, we shall report our measurements of the freezing behavior of submicron sulfuric acid droplets at acid concentrations up to about 35 wt %. The extent to which atmospheric aerosols supercool, and the ultimate effect of their physical state on important issues in atmospheric chemistry, has been the subject of extensive discussion in the literature for some time.1-9 There are both chemical and physical reasons why it is important to know the freezing points of these aerosols under atmospheric conditions. From the chemical standpoint, it was suggested some time ago that reactions occurring on the surface of the stratospheric sulfate aerosol may result in the conversion of reservoir chlorine compounds into photochemically active forms, with simultaneous removal of gas phase nitrogen oxides.10-12 Previously, of course, these processes were shown to occur on the surfaces of polar stratospheric clouds (PSCs), and their important role in the chemistry of the Antarctic winter stratosphere was documented extensively.13 More recently, field measurements consistent with this suggestion have been reported14 as well. It is essential to know the phases of the material present on and in the particles in order to establish the rates of these heterogeneous reactions.15 A knowledge of the state of the sulfate aerosol is required also to understand important physical processes in the atmosphere, such as such as cloud nucleation. In the middle stratosphere, typical sulfate aerosols have high acid concentrations, and it is unlikely that these solidify readily. In the lower stratosphere and upper troposphere, however, where the humidity can be higher, the deliquescent H2SO4 droplets absorb water and become more dilute as the temperature falls. For this reason, it is important to understand the freezing behavior of * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 1, 1996.

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dilute as well as concentrated aerosols. This point has been discussed in reference to both PSC formation16,17 and cirrus cloud nucleation.18,19 This point is made also in ref 5, which reports the calculation of a freezing curve very similar to that measured in this work. The nucleation and freezing points of the material in the aerosol particles are very difficult to determine experimentally. Previous freezing point measurements have been made on the materials in forms other than the aerosol,16,20-23 and while these have not achieved quantitative agreement on the freezing behavior, they have provided valuable information about the likely freezing temperatures of H2SO4/H2O solutions having compositions similar to the stratospheric aerosol. Theoretical calculations of these freezing points have been attempted as well,5,6,18,19,24 and these have achieved considerable success, despite the lack of thermodynamic parameters for these aerosols. Finally, it is generally agreed that HNO3 in the atmosphere will have an effect on the chemical and physical properties of the aerosol, but the nature of this effect is not known at present. The experiments cited above have been carried out on material in contact with surfaces, thus introducing the possibility for heterogeneous contributions by the container walls to such processes as nucleation. To obtain unequivocal information of atmospheric relevance, it is necessary to work with suspended particles in order to eliminate the influence of container walls. Furthermore, since nucleation is a strong function of volume, measurements should be made on aerosols having the same size distribution as those in the atmosphere. Finally, of course, it is necessary to have a nonintrusive measurement which does not itself change the supercooling or freezing behavior of the aerosol. We have developed an apparatus to measure the freezing behavior of aerosols which satisfies the above criteria. It consists of a temperature-controlled flow tube with optical access for FTIR observations. Using this, we have measured the physical state of submicron sulfuric acid droplets as a function of their temperature, composition, and size distribution Via FTIR extinction spectroscopy. First, we shall describe the operation © 1996 American Chemical Society

Freezing of Model Sulfuric Acid Aerosols

Figure 1. Schematic diagram of the flow tube apparatus: T1, the temperature of the precooler, is held constant during an experiment; T2, the temperature of the flow tube, is varied.

of the apparatus briefly and then report the results of these measurements. Experimental Section For the present experiments, we form submicron H2SO4 droplets in an aerosol generator by chemical reaction between H2O and SO3, which we obtain from fuming sulfuric acid (1824 wt % SO3). The liquids are contained in two glass flasks. Glass tubes, terminated by glass frits, release filtered nitrogen beneath the liquids’ surfaces. The saturated carrier gases move through glass tubing (1 cm diameter, about 60 cm long) and combine at the top of a glass column in which the reaction forming the aerosol occurs. At the exit of the column, the aerosol passes through a large glass flask and then enters the flow tube in which the measurements are made. The distance from the mixing point to the flow tube is about 200 cm. This long path length serves two purposes: it permits adequate time for the H2O/SO3 reaction to occur, and it allows the entire system (both the vapor phase H2O and any aerosols which might have been formed by the bubbling of the gases through the liquids) to come to equilibrium with the H2SO4 droplets. That this equilibrium has been established is indicated by the fact that any given (room temperature) aerosol spectrum can be reproduced very precisely by a Mie scattering calculation (Vide infra) using a single log-normal size distributionsa result which does not depend on the length of the tubing or on the presence of a dimpled condensation column inserted into the stream before the glass flask. The correlation coefficients between the measured and calculated spectra in these cases are always greater than 0.95 and usually greater than 0.99. A block diagram of the apparatus is shown in Figure 1. The main part consists of the flow tube, which is the double-walled section at the right-hand side of the figure, and a plenum chamber, the walls of which are shown as shaded in the figure. The walls of the plenum chamber are insulated with foam, and the space between the outer and inner parts of the flow tube is evacuated. The inner walls of the flow tube are cooled by recirculating a refrigerant through cooling coils soldered to them. The refrigerant is either methanol, cooled by a commercial refrigerator (Harris Mfg. Co. Cascade Refrigeration System Model 3-RS2-W-L), or the boil-off from liquid nitrogen. The plenum chamber is cooled independently of the flow tube and held near -40 °C for all of the measurements. The flow tube is fitted with three infrared windows on each side, as shown in the figure, for optical access. The aerosol is introduced to the flow tube Via the plenum chamber, which provides precooling and preconditioning. This ensures that the initial condition of the aerosol entering the flow tube is the same, irrespective of the final temperature of the flow tube. This preconditioning is necessary because the liquid aerosol is in equilibrium with the surrounding water vapor, with

J. Phys. Chem., Vol. 100, No. 6, 1996 2377 the consequence that the concentration of the aerosol decreases as the temperature is reduced, due to the condensation of the surrounding water vapor into it. Precooling, however, reduces the water vapor pressure above the sulfuric acid aeorsol to a negligible value, so there is no appreciable change in its concentration during subsequent cooling to the (much lower) temperature of the flow tube. For each experiment, we set the overall acid concentration by adjusting the relative flows of the gases carrying the H2O and SO3 reagents, and then we record a series of extinction spectra at various final temperatures of the flow tube, while holding the temperature of the plenum chamber constant. The details of the data analysis will be discussed below. Upon leaving the plenum chamber, the aerosol particles and carrier gas enter the cooled flow section, where their temperature decreases to that of the final measurement. This process is monitored by four thermocouples mounted in the gas stream parallel to the flow axis and spaced at equal intervals between the entrance and the FTIR observation point, located at the other end of the tube. The final, equilibrium, temperature of the gas is always reached at or before the location of the third thermocouple. Since thermal relaxation of the aerosol is almost instantaneous, its temperature is in constant equilibrium with that of the carrier gas. The total flow is about 1-2 standard L/min at pressures of 400-700 Torr. The flow velocity is relatively lowsabout 1 cm/ssand the total time spent in the tube by a sample of aerosol is less than 2 min. We were only able to vary this flow velocity (hence residence time) by about 20% while maintaining stable flow conditions, so the observations of nucleation which we shall report are valid only for this residence time. The conclusions presented in ref 6, however, indicate that the nucleation probability is not a strong function of time in this concentration regime. On the basis of the calculation of ref 6, we believe that the temperatures which we shall reportswhile lower limits to the correct nucleation temperaturessare within about 4 K of the equilibrium values. The flow tube is optically coupled to a Fourier transform IR spectrometer, Via reentrant window mounts which hold the window surfaces a few centimeters back from the main gas flow. This ensures that the windows are not exposed to the aerosol flowing in the central core of the flow tube, and hence nothing condenses on them during the measurements. It is important to ensure that we are observing aerosols, and not material condensed on the windows, so for each experiment we took background spectra before the aerosol flow was introduced into the flow tube and at the end of the experiment after the aerosol flow was turned off (but before the flow tube was warmed). We ensured that these spectra were identical and that neither had any absorption features due to the aerosol or its components (H2SO4 and H2O). We recorded the extinction spectra in a single-pass configuration. At the average sizes of the particles used in this work, the IR extinction spectra have substantial contributions from both scattering and absorption, so the data contain information about both the size distribution and concentration of acid in the particles. These data are coupled in the spectra, of course. The average particle size places the extinction spectra in the Mie regime,25 and when simulating the spectra, it is necessary to use optical constants which are a function of the composition. We have carried out such simulations, using the optical constants of Palmer and Williams.26 We use an iterative procedure in which a log-normal size distribution is assumed, and the two parameters of this, along with the assumed concentration of the acid, are varied until the highest correlation coefficient is obtained between the measured and calculated extinction spectra.

2378 J. Phys. Chem., Vol. 100, No. 6, 1996

Figure 2. Extinction spectrum of a room-temperature sample of 54 wt % H2SO4 aerosol: solid spectrum, observed; dashed spectrum, calculated using Mie theory and a log-normal size distribution with 〈r〉 ) 0.19 µm and log σ ) 0.34. The dotted lines indicate the locations of the OH stretch (L1-L1) and sulfate bands (L2-L2). The lengths of the vertical sticks drawn downward from the L2-L2 line indicate the relative sizes of the absorption coefficients for the four HSO4- and one SO42- bands in that spectral region.

This process is made easier by the fact that size and composition information are not completely interchangeable. In general, the size distribution affects the scattering, which is reflected by the widths and frequencies of the spectral features, while the composition information is given by the absorption intensities of these same features. (The scattering is given by the real part of the index of refraction while the absorption information is contained in the imaginary part.) Figure 2 shows an example of a measured spectrum and the simulation which provides the best fit to it, as described above. The correlation coefficient, which is 0.996 for the case shown here, is reduced if either the log-normal fit parameters or the acid concentration is changed. This is typical of the results which we obtain with aerosols for which the existence of index of refraction data make it possible to calculate spectra (i.e., room temperature aerosols). We do not use this procedure to obtain any information about the properties of the cold aerosols, because the optical constants are a function of temperature. (For example, the relative concentrations of the SO42- and HSO4change with temperature, which will be evident in data we shall present later.) For this reason, we are unable to use Mie scattering calculations to determine whether or not the aerosols maintain log-normal distributions as the temperature decreases. The locations of the major absorption frequencies of SO42and HSO4- are indicated by the line spectra; the relative lengths of the lines reflect the room temperature extinction coefficients of the indicated species. These make it clear that the HSO4predominates over SO42- at this temperature and concentration. The frequency regions 2409-3650 cm-1 (L1-L1) and 8201470 cm-1 (L2-L2) are indicated as well. These are the approximate frequency ranges for the hydroxyl and sulfate absorption bands, respectively. These bands are used to determine the aerosol concentration; we shall discuss this procedure later. We can estimate the amount of material in the observation path from the absolute values of the real and imaginary indices of refraction and the known absorption path length. Although crude, this estimate is probably good to within an order of magnitude. It indicates that the particle densities for the experiments reported here were about 105 cm-3. In order to make a freezing point measurement, we first fix the composition of the aerosol at the desired value and then set the temperature of the flow tube. (It can be varied from room temperature to about 150 K.) When the temperature has stabilized, we measure the extinction spectrum of the aerosol.

Bertram et al.

Figure 3. Temperature dependence of the observed extinction spectrum of a 30 wt % H2SO4 aerosol having the same size distribution as the one in Figure 2. The spectra have been offset in the vertical direction for clarity. The transmittances at the minima of the OH bands at 3300 cm-1 are all less than 95%. The vertical sticks are the same as those in Figure 2 but are drawn upward from the base line.

Then, we lower the temperature of the flow tube slightly and repeat this process. We continue this until we have mapped out the entire temperature range over which the aerosol freezes, so that we obtain a series of extinction spectra at known temperatures encompassing the freezing point of the aerosol. In the region of the expected freezing point, we collect spectra at temperature intervals of approximately 2-3 K. In all cases, we work with transmission spectra, and as mentioned previously, we ensure that no material condenses on the windows during the experiment. Results In the following, we shall use the term freezing point to denote the point at which ice begins to precipitate in the droplet. This is the first appearance of a H2O(s) nucleus in the H2SO4(l) aerosol droplet. We determine the precise value of the freezing point by observing the changes in the large feature near 3400 cm-1, which is characteristic of OH stretching. There are also changes in the sulfate ion features near 1000 cm-1, but we do not use these in the freezing point determinations. As the liquid cools, and before freezing, all of these features show only very small changes. The broad minimum of the OH feature shifts slowly with temperature from its room temperature value near 3430 cm-1 to near 3360 cm-1. The sulfate absorptions change in a way which is consistent with the temperature dependence of the equilibrium constants for H2SO4 hydrolysis and ionization. Figure 3 shows the temperature dependence, over a wide temperature range, of the spectra for an aerosol which is approximately 30 wt % acid. The locations of the major sulfate ion absorptions, their room temperature extinction coefficients, and the frequency regions L1-L1 and L2-L2 are all indicated as in Figure 2. We note that the decrease in temperature from room temperature (Figure 2) to 220 K causes a shift in the beginning of the OH band downward in frequency until the beginning coincides with the high-frequency end of the L1 range. Furthermore, the ionization has shifted such that the SO42species is now more abundant than the HSO4-. This shift has been well documented in previous work on this system.23 The higher temperature spectra in Figure 3 also have sharp (but weak) features in the 3000 cm-1 region; these are not present in the lowest temperature spectrum. They are due to water vapor in the flow tube, which is in equilibrium with the aerosol. Note that these are not caused by water vapor external to the cell. We purge the optical path from source to detector and use

Freezing of Model Sulfuric Acid Aerosols

Figure 4. Solid spectrum: ratio of the lowest two transmittance spectra in Figure 3. Excursions upward and downward from 1.0 signify (respectively) reductions and increases in the concentrations of the components. Dashed spectrum: calculated (Mie theory) spectrum of a monodisperse sample of H2O(s) crystallites having r ) 0.1 µm.

transmittance spectrasratios of the sample to the backgroundsfor all measurements. In principle, the intensities of these water vapor absorptions could be used to provide a direct determination of the aerosol concentration, but we attempted such a calibration, based on a comparison of these intensities with those of a known concentration of water vapor, and concluded that the signal to noise of the low-temperature absorption features is too poor to give an accurate concentration measurement. We shall discuss the method we used to determine the acid concentrations later. For the acid concentration shown in Figure 3, the freezing point occurs between 206 and 170 Ksthe temperatures of the lowest two spectra in the figure. A very small increase in the absorption intensity at 3250 cm-1 in the OH absorption band signals the appearance of ice in the aerosol particle. In addition to this, but not detectable in the figure, is a decrease in the absorption intensity in the region associated with OH absorption in liquid water (near 3500 cm-1). There are even smaller changes in the sulfate ion features near 1000 cm-1: the intensity of the SO42- absorption band increases, and that of the HSO4band decreases. Using the presentation shown in Figure 3, the intensity change at 3250 cm-1 is not large enough to permit the determination of the precise freezing temperature (which corresponds to the first appearance of this feature). In order to get a more accurate measure of its appearance, we take ratios of spectra collected at successively lower temperatures. The solid curve in Figure 4 shows this ratio for the lowest two spectra shown in Figure 3. The ratio is divided by the temperature difference to yield a spectrum of the transmittance change per unit temperature change in the region of the freezing point. The intensity changes noted above are indicated by arrows. The ratio is calculated for decreasing temperature; hence, components which have an increased concentration (decreased transmittance) with decreasing temperature show a transmittance change which is less than 1.0 in the figure. The presentation in Figure 4 emphasizes the changes associated with freezing, permitting a very precise determination of the temperature at which freezing begins. To support our contention that the feature at 3250 cm-1 in the ratioed spectra represents the formation of H2O(s), we show, as the dashed curve in the figure, a section of the calculated spectrum of a monodisperse sample of H2O(s) particles with a radius of 0.1 µm. No distribution in size is assumed for this calculation because at this very small radius the scattering becomes negligible, and the FTIR extinction spectrum is governed by absorption only. The fact that the calculated curve

J. Phys. Chem., Vol. 100, No. 6, 1996 2379 matches both the shape and frequency of the measured spectrum closely supports the suggestion that a very small crystal of H2O(s) has appeared in the sample. Because there is virtually no scattering amplitude in the IR spectra of particles in this very small size range, it is not possible to determine the size of the H2O(s) crystal responsible for the feature at 3250 cm-1 in Figure 4. A radius of about 0.1 µm is the largest which gives a spectrum of this shapesspectra of particles of this size and smaller all have essentially the same shapes. In this case, we believe the particle to be much smaller than this, of course, but for this reason we cannot provide a quantitative estimate of the size. The small differences between these calculated and measured curves are in the directions which would be expected from our proposed freezing mechanism. The measured curve should be above the calculated one on the high-frequency side, due to the disappearance of the liquid water (which makes a positive contribution to the measured spectrum in the presentation of Figure 4). We believe the difference on the low-frequency side to be due to the fact that the calculation was done for an isolated H2O(s) particle, whereas in reality it is enclosed by an envelope of unfrozen sulfuric acid solution. Thus, it would be more appropriate to use a coated sphere calculation for this system, and we are presently working on this. Finally, although our measurement could not distinguish between one and several H2O(s) crystals in a single aerosol droplet, the low probability of nucleation argues against the formation of more than one crystal per droplet. At this point, we note that the changes we have just described and modeled represent nucleation inside the H2SO4 aerosol droplet, as opposed to the formation of an ice aerosol external to the H2SO4 droplets, from water vapor present in the flow tube. The precooling stage in the plenum chamber eliminates the latter possibility. The vapor pressure of H2O in the gas stream leaving the plenum chamber at -40 °C is below 0.2 Torr, which is too low to permit gas phase nucleation of H2O(s) in the flow tube at any temperature used in these freezing point measurements. We have verified that no nucleation of H2O(s) occurs in the flow tube at any temperature used in these experiments when pure water vapor is passed through the cooled plenum chamber. The observed nucleation of H2O(s) in these experiments, therefore, must occur inside the aerosol droplet. As we decrease the temperature below the onset of the changes described in the preceding paragraphs, the spectra continue to change in the same way, but more slowly, for several degrees (depending on the concentration) until eventually, at low temperature, the spectra again show negligible change with temperature. Figure 5 shows the rate of change of the amplitude of the spectrum, measured at the location of the small feature at 3250 cm-1. This is calculated by taking ratios of the kind shown in Figure 4 between each spectrum and the one measured at the next lower temperature and dividing the measured change in intensity by the temperature difference between the two spectra. We interpret the intensity of the feature at 3250 cm-1 in the ratioed spectra to be proportional to the amount of H2O(s) which has precipitated as a result of the decrease in temperature, so the amplitudes of the curves in Figure 5 are proportional to the amount of material which precipitates per degree kelvin. Each of these curves has a rapid rise on the higher temperature side, goes through a maximum, and then decreases until it reaches a point where the slope changes and a “tail” extends toward lower temperatures. Note that these curves give the derivative of the change in the amount of H2O(s), so this shape indicates that, with decreasing temperature, the precipitation rate of H2O(s) increases rapidly at first and then decreases smoothly

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Figure 5. Change in the amplitude of the 3250 cm-1 feature labeled (+)H2O(s) in Figure 4 with decreasing temperature for a range of aerosol concentrations. These curves are obtained by calculating the ratios of successively colder spectra and dividing by the temperature difference between the spectra. The curves are spline fits to the data points, which have been omitted from all except the 19.9 wt % data for clarity.

until the break in the curve, where the amount of H2O(s) continues to increase, but much more slowly than previously. It is convenient to interpret these data in terms of the equilibrium phase diagram of the bulk liquid. For dilute (bulk) acid, the phase boundary between H2O(s) and the solution phase is a curve which goes downward from the pure water freezing point to a minimum at about 35 wt % acidsthe first eutectic. We find that the freezing curve for the aerosol is topologically identical to this but displaced to much lower temperatures. As we decresae the temperature in our experiment, the aerosol solution eventually encounters the freezing curve which corresponds to the equilibrium phase boundary in the bulk acid, at which point H2O(s) nucleates in the droplet. This nucleation is signaled by the initial rise in the curves in Figure 5. The shapes of these curvesstheir finite width (in temperature) and the “tails” on their low-temperature sidesshave two possible explanations; we shall deal with what we consider to be the less likely of the two first. This is based on the fact that the particles must cool to the temperature of the flow tube during the relatively short contact time (only about 1 min) before they reach the observation window. If the final temperature is below that of the aerosol freezing point, a finite amount of H2O(s) must precipitate during the cooling process. The diffusion of molecular H2O through sulfuric acid solution at low temperature is relatively slow, and this would extend the time for the crystal growth process. In this scenario, the temperature at which the curves in Figure 5 change slope on the decreasing side corresponds to the point at which this precipitation process has been completed. The remaining “tails” on the curves denote the additional H2O(s) which precipitates as the system follows the freezing curve, and the acid becomes more concentrated with decreasing temperature. We think this is not an important effect because it implies that the diffusion time of H2O molecules in the solution is longer than the contact time. We calculate that an H2O molecule would diffuse at least 20 µm through liquid H2SO4 during the typical contact time of 1 min under the conditions of our experiment. This is based on a solution viscosity of 0.5 P24 at 200 K and an effective radius of 400 pm. The average size of the aerosol particles is about 0.2 µm, so we believe the contact time is adequate for crystal growth to the equilibrium size. The alternative explanation, which we think more likely, is simply that the finite width of the curves reflects the fact that an H2O(s) nucleus forms in an increasing number of the aerosol

Bertram et al. droplets as the temperature decreases. In this event, the break in slope on the low-temperature side of the curves corresponds to the point at which all of the aerosol particles have nucleated one H2O(s) crystal. At this point, as in the previous scenario, the entire system begins to follow the solid-liquid freezing curve downward with decreasing temperature. In this interpretation, the maxima of the curves in Figure 5 correspond to the point where approximately 50% of the particles have an ice nucleus. In either event, we assume that at a low enough temperature the eutectic mixture would form, and the remaining material would solidify as either H2SO4‚4H2O (SAT) or an amorphous glass. In this report, however, we are concerned with the initial appearance and growth of H2O(s) crystallite in the aerosol, and we have not attempted to follow the system to extremely low temperature. We construct the freezing curve for the aerosol by plotting the temperature at which the H2O(s) first appears (the onset of the curves in Figure 5) versus the concentration of the aerosol. The determination of the acid concentration in the aerosol is a particularly difficult aspect of any measurement which works directly with the suspended particles, and we shall comment on this briefly here. The difficulty arises from the fact that the H2SO4 solution in the aerosol remains in equilibrium with water vapor in the carrier gas. This equilibrium reacts very rapidly to changes in temperature; hence, the aerosol absorbs or releases water in response to temperature changes in the surrounding gas. In the present experiments, the aerosol particles absorb water from the vapor phase and become more dilute as they cool in the plenum chamber. As a consequence, it is not possible for us to calculate accurately the concentration of the cooled H2SO4 aerosol which enters the observation zone, simply from a knowledge of the composition of the starting material. The existence of this rapid equilibrium would permit the determination of the composition of the binary aerosol from a knowledge of the partial pressure of the water vapor in the carrier gas, but we do not have the capability to make this measurement at present. A less accurate, but nonetheless adequate, method to determine the acid concentration is through the use of the same FTIR spectra which we use to determine the freezing points. This spectroscopically based method uses the relative areas of the bands associated with water and sulfate ions, near 3300 and 1000 cm-1, respectively, as a measure of the acid concentration. In principle, the concentration could be calculated directly from the ratio of the areas of these bands, if the absorption coefficients of the absorbing species contributing to each band, and the fraction of each band associated with the given absorber, were known. These data are not known, however, so a calibration factor relating the measured areas to known concentrations must be developed. There are two different approaches to this, and both are subject to uncertainties related to a lack of information on the H2SO4 system. One method to obtain this calibration factor is based on measurements of thin films of known acid concentration. This was first implemented22 using the ratio of absorbances at 3360 and 2875 cm-1. That work used measured thin-film spectra which had been corrected by shifting the base line to ensure that the absorbance was made to be zero between 3700 and 4000 cm-1, where no absorption is expected. This method was extended in ref 9 to the use of the integrated areas of the OH absorption between 3650 and 2409 cm-1 and the sulfate absorption between 1470 and 820 cm-1. These integration limits (which are shown as L1-L1 and L2-L2 respectively in Figures 2 and 3) together with spectra of room-temperature thin H2SO4 films of known concentration were used to derive a calibration curve.

Freezing of Model Sulfuric Acid Aerosols The major difficulty associated with this methodsthis was discussed by its authorssis the fact that the compositions of the bands, and hence their intensities, are temperature dependent, and the use of calibration data based on room temperature thinfilm spectra introduces some uncertainties. The major problem stems from the fact that the dissociation of H2SO4 varies with temperature. This is illustrated in Figures 2 and 3: Figure 2 shows that HSO4- is predominant at room temperature, while Figure 3 shows that SO42- is predominant at low temperature. (Although the concentrations of the acids in these figures are different, and hence the spectra are not strictly comparable, we note that the acid is more concentrated in the room temperature spectrum, so the effect is actually more pronounced than is indicated by comparing the two figures directly.) This change in the identity of the predominant absorber with temperature has two consequences: the limits over which the band intensities are determined must be chosen carefully, to include all of the important absorption bands, and the assumption must be made that the absorption coefficients of the different species (HSO4and SO42- are approximately the same. The determination of the correct integration limits may be done by careful inspection of the spectra, but the latter assumption involves an approximation, as can be seen from the relative sizes of the sulfate ion extinction coefficients shown in Figures 2 and 3. This approach, nevertheless, appears to give good results: the data reported in ref 9 show that the concentrations derived from thin-film spectra taken at room temperature and at low temperature differ by only 3%. A second difficulty associated with using the area of the bands in thin-film spectra to determine concentrations of aerosols stems from the fact that the Mie scattering associated with the aerosols is not present in the thin films. In certain cases the Mie scattering broadens and shifts the absorption bands; we shall address this issue in the following paragraphs. The second method which can be used to obtain this calibration curve involves calculation of the extinction spectra directly for known concentrations of the acid and determining the ratio of the hydroxyl and sulfate bands from these calculated spectra. This method has the advantage that it takes into account the effects of Mie scattering, but it still suffers from the fact that only room temperature indices of refraction are available for H2SO4 aerosols presently. Thus, this method will introduce the same errors when applied to low-temperature aerosols as does the method based on measurements of room-temperature thin films. We have calculated the extinction spectra for room-temperature aerosols having various particle sizes and generated calibration curves to relate the concentration of the aerosol to the ratio of the areas of the hydroxyl and sulfate absorption bands. To measure the areas of the absorption bands, it is necessary to establish limits to begin and end the integrations (analogous to L1-L1 and L2-L2 in Figures 2 and 3). We have found that the limits suggested in ref 9 are not quite appropriate for the present application, due to the effects of particle size, which shift the bands slightly. In order to include all of the respective bands and follow the small shifts introduced by both scattering and temperature dependence, we have used only one fixed limits2409 cm-1 and set the others to coincide with the ends of the respective bands. In practice, the end of the band is defined to be the location of the maximum in the spectrum which immediately follows the last absorption feature. This process is illustrated by the limits shown in Figure 3. L1-L1 are the limits 3650 and 2409 cm-1 proposed in ref 9. Inspection of the high-frequency limit, however, shows that the onset of the hydroxyl band shifts slightly with temperature, so that more of the band is included at low temperature than at high. To

J. Phys. Chem., Vol. 100, No. 6, 1996 2381

Figure 6. Calibration curve to determine H2SO4 aerosol concentration from the ratio of the hydroxyl and sulfate areas for two different particle radii. These curves are based on spectra calculated from roomtemperature optical constants.

compensate for this, we defined the high-frequency limit to be at the high-frequency maximum just before the onset of the hydroxyl band. We retain the low-frequency limit of 2409 cm-1. The case of the sulfate bands is more difficult. Here, we simply integrate over the entire sulfate absorption, between the maxima at each end of the bands. The resulting limits are close to, but not exactly at, L2-L2. To show the effect of particle size on this spectroscopic method of concentration determination, we have calculated spectra for aerosols having radii, r, equal to 0.03, 0.15, and 0.25 µm, using room-temperature optical constants. For the r ) 0.03 µm spectrum, the scattering is negligible, and the calculated extinction spectrum contains only the absorption component. Since it has no scattering, this is the same as a thin-film spectrum. To simulate the effect of particle size on the concentration measured using thin-film spectra, we derived a calibration curve from the r ) 0.03 µm data and used this curve to calculate the concentrations of aerosols having r ) 0.15 and 0.25 µm (all data at room temperature). We found that, for an aerosol of r ) 0.25 µm, the concentration is underestimated by about 4% using model thin-film data represented by the r ) 0.03 µm calculation. The aerosol used in the experiments we report here has an average radius of about 0.25 µm, and we derived a calibration curve for this radius using the same method. We show the calibration curves for particle radii equal to 0.03 and 0.25 µm derived from the calculated room-temperature aerosol spectra in Figure 6. The curves are parametrized in the same form as that of ref 9: [H2SO4] ) a + bxc, where x is the ratio of the area of the hydroxyl band to that of the sulfate band and [H2SO4] is expressed as a weight fraction. The values of the parameters are, for r ) 0.03 µm, a ) -0.173, b ) 1.01, and c ) -0.388 and, for r ) 0.25 µm, a ) -0.268, b ) 1.124, and c ) -0.3164. It is difficult to estimate the uncertainty in the concentration determined in this way. We believe that taking into account the size of the particle should improve the accuracy by about 4% over that based on the thin-film spectra (quoted as (7% in ref 9). Our method, however, is based on calculated spectra of room-temperature aerosols, and when it is used to determine concentrations of low-temperature aerosols, the result will be affected by fact that the HSO4-/SO42- ratio changes with temperature. The total sulfate ion concentration is determined from the integral over these bands, and if the absorption strengths of the two forms of the sulfate ion are substantially different, it will introduce an error. A much more accurate determination could be done, of course, if the lowtemperature optical constants of these materials were available.

2382 J. Phys. Chem., Vol. 100, No. 6, 1996

Figure 7. Solid curve and points: the measured freezing curve for the sulfuric acid aerosol. Dashed curve: the location to which this would move if we use an alternative method to determine the concentration of the acid (see text). Dot-dash curves: temperature/ concentration equilibrium curves for the indicated partial pressure of H2O vapor over liquid H2SO4 at a pressure altitude of 100 mbar. The intersection of these curves indicates the H2O freezing point under these conditions.

Using the calibration curve for the aerosol having r ) 0.25 µm, together with the spectra measured in the experiments described earlier, we constructed a plot of the temperatures at which H2O(s) crystals first appear in the spectra. This is shown in Figure 7. The solid circular points are the results for the H2SO4 aerosol measured in the way we have just described, and the solid curve is a nonlinear least-squares fit to these points. The dashed curve shows the location to which the solid curve would move if the concentrations are calculated according to the calibration curve published in ref 9. The diamond-shaped symbol indicates the freezing point of a pure ice aerosol which we measured by the same spectroscopic technique in an earlier experiment which used an ultrasonic nebulizer to generate the aerosol. The resulting H2O particles were somewhat larger (〈r〉 ) 1.2 µm, ln σ ) 0.44 µm), and in view of this difference, we have put an error bar of (3 K on this point; the other data have a temperature uncertainty less than (1 K. The dot-dashed curves show the temperatures at which water vapor at the indicated mixing ratios and a total pressure of 0.1 bar would be in equilibrium with liquid H2SO4, based on the vapor pressure data of ref 23. Discussion Work in other laboratories16,20-23,27 on thin films and bulk solutions of sulfuric acid having compositions similar to the sulfate aerosols found in the mid- to high-latitude stratosphere has determined the temperature range over which these freeze and identified the predominant hydrates which form on their solidification. In particular, ref 27 maps out the freezing of concentrated binary H2SO4 solutions in the form of films. Recent work9 on the binary H2SO4/H2O aerosols, however, found no solidification for compositions between 35 and 95 wt % acid, even at temperatures down to 189 K. (Aerosols more dilute than 35 wt % acid could not be examined in the latter experiment because the experiment was carried out under conditions of high humidity, which led to the nucleation of ice particles directly in the observation chamber.) In the experiments we have reported here, we formed binary H2SO4/H2O aerosols having compositions covering the range between 0 and 36 wt % H2SO4 and observed the temperatures

Bertram et al. at which H2O(s) nucleates in the aerosol particle. Nucleation occurs, in general, about 30-35 K lower than the corresponding phase boundary between H2O(s) and H2SO4(l) for the bulk material at equilibrium. Because our experiments are carried out on flowing samples, and our observation time is limited to a minute or two, we cannot reproduce the time scale over which nucleation and freezing occur in nature, which may vary from hours to days. The result shown in Figure 7, therefore, represents a lower limit to the true nucleation temperature of the aerosol. The results in Figure 7 are very close to those of the calculations reported in refs 5 and 6 for concentrations less than 36 wt %. The calculations predict a slightly lower freezing temperature for the lowest concentrations and a slightly higher one for the higher concentrations, but the differences are for the most part about 5 K, differing by more than that only in the steeply declining part of the solid/liquid phase boundary near 35 wt %. We note that the effects of rapid (nonequilibrium) cooling, which we have described in the previous section, might be responsible for this discrepancy. If the increased viscosity of the H2SO4 at lower temperature increases the time required for the H2O(s) crystallites to grow to a detectable size in our experiment, the onset of the curves in Figure 5 would be displaced to slightly lower temperatures, thus improving the agreement with the calculations for the more concentrated solutions. If, as we think more probable, the observed shape of the growth curves is caused by the fact that H2O(s) nucleates in an increasing fraction of the aerosol droplets as the flow tube temperature decreases, this effect would not occur. The results of the calculation in ref 6 are particularly relevant to this point. That work obtained the time for 1% of a sample of 1 µm H2SO4 particles to freeze (τ1%) as a function of temperature and concentration of acid, and it showed that this freezing time depends (weakly) on temperature for any given concentration. According to the calculation of ref 6, the difference in temperature required to freeze 1% of the sample in a few seconds, as compared to a few hours, is about 5 K. Our experiment detects nucleation at a very early stage, so the viscosity effects discussed previously should not be important to the location of the onset of the curves in Figure 5. Moreover, viscosity effects should be less important for the dilute solutions examined in this work than they would be for more concentrated ones. Thus, we think it likely that the shapes of the curves in Figure 5 reflect nucleation of single H2O(s) crystallites in an increasing number of aerosol particles as the temperature decreases. In this view, the widths of the curves indicate the increase in the number of aerosol particles which contain a crystallite of H2O(s). The height of the curves decreases with decreasing temperature due to the smaller amount of H2O(s) which deposits from the more concentrated acid droplets. The water mixing ratios shown in Figure 7 are values which occur over a wide range of latitudes and altitudes. The intersection of these curves with the measured aerosol freezing curve indicates the concentration range over which the atmospheric H2SO4 aerosol has a H2O(s) core. In circumstances where highly concentrated H2SO4 aerosols are cooled, absorb water, and become more dilute, this intersection defines the point at which H2O(s) begins to precipitate in the particles. Thereafter, the ice cores of the particles continue to grow until the particle either settles out gravitationally or moves into a warmer air parcel and is reevaporated. Finally, we note that these results refer to the binary aerosol only, whereas in the natural atmosphere the presence of HNO3 will change the situation considerably. The size-dependent effects, such as the lowering of the freezing point, will be

Freezing of Model Sulfuric Acid Aerosols qualitatively the same in the presence of HNO3, but the number of phases and their liquid-solid equilibria will certainly be different. We are at present examining the ternary H2O/H2SO4/HNO3 system to explore these differences and quantify its freezing behavior. Acknowledgment. The authors are grateful to Dr. Renyi Zhang for many helpful discussions during the preparation of the manuscript. References and Notes (1) Wolff, E. W.; Mulvaney, R. Geophys. Res. Lett. 1991, 18, 1007. (2) Hansen, D. R.; Ravishankara, A. R. J. Geophys. Res. 1991, 96, 17307. (3) Luo, B. P.; Peter, Th.; Crutzen, P. J. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 334. (4) Turco, R. P.; Hamill, P. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 323. (5) Jensen, E. J.; Toon, O. B.; Hamill, P. Geophys. Res. Lett. 1991, 18, 1857. (6) Larsen, N. Geophys. Res. Lett. 1994, 21, 425. (7) Tolbert, M. A. Science 1994, 264, 527. (8) Dye, J. E.; et al. J. Geophys. Res. 1992, 97, 8015. (9) Anthony, S. E.; Tisdale, R. T.; Disselkamp, R. S.; Tolbert, M. A. Geophys. Res. Lett. 1995, 22, 1105. (10) Hoffman, D. J.; Solomon, S. J. Geophys. Res. 1989, 94, 5029. (11) Brasseur, G. P.; Granier, C.; Walters, S. Nature 1990, 348, 626. (12) Rodriguez, J. M.; Ko, M. K. W.; Sze, N. D. Nature 1991, 352, 134.

J. Phys. Chem., Vol. 100, No. 6, 1996 2383 (13) Scientific Assessment of Ozone depletion: 1994; World Meterological Organization Global Ozone Research and Monitoring Project, Report No. 37; WMO: Switzerland, 1995. (14) Gleason, J. F.; Bhartia, P. K.; Herman, J. R.; McPeters, R.; Newman, P.; Stolarski, R. S.; Flynn, L.; Labow, G.; Larko, D.; Seftnor, C.; Wellemeyer, C.; Komhyr, W. D.; Miller, A. J.; Planet, W. Science 1993, 260, 523. (15) Hanson, D. R.; Ravishankara, A. R.; Solomon, S. J. Geophys. Res. 1994, 99, 3615. (16) Molina, M. J.; Zhang, R.; Wooldridge, P. J.; McMahon, J. R.; Kim, J. E.; Chang, H. Y.; Beyer, K. D. Science 1993, 261, 1418. (17) Ohtake, T. Tellus 1993, 45B, 138. (18) Jensen, E. J.; Toon, O. B. Geophys. Res. Lett. 1992, 19, 1759. (19) Jensen, E. J.; Toon, O. B. Geophys. Res. Lett. 1994, 21, 2019. (20) Beyer, K. D.; Seago, S. W.; Chang, H. Y.; Molina, M. J. Geophys. Res. Lett. 1994, 21, 871. (21) Song, N. Geophys. Res. Lett. 1994, 21, 2709. (22) Middlebrook, A. M.; Iraci, L. T.; McNeill, L. S.; Koehler, B. G.; Wilson, M. A.; Saastad, O. W.; Tolbert, M. A.; Hanson, D. R. J. Geophys. Res. 1993, 98, 20473. (23) Zhang, R.; Wooldridge, P. J.; Abbatt, J. P. D.; Molina, M. J. J. Phys. Chem. 1993, 97, 7351. (24) Luo, B. P.; Peter, Th.; Crutzen, P. J. Geophys. Res. Lett. 1994, 21, 1447. (25) Bohren, C. F.; Huffman, D. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. (26) Palmer, K. F.; Williams, D. Appl. Opt. 1975, 14, 208. (27) Zhang, R.; Leu, M.-T.; Keyser, L. F. J. Geophys. Res., in press.

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