GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L07802, doi:10.1029/2005GL024945, 2006
Heterogeneous freezing of ammonium sulfate and sodium chloride solutions by long chain alcohols Will Cantrell1 and Carly Robinson1 Received 13 October 2005; revised 24 February 2006; accepted 28 February 2006; published 1 April 2006.
[1] High molecular weight organic compounds emitted during biomass burning can be transported to high altitudes where they may affect ice processes through heterogeneous nucleation. We show that freezing of solutions of ammonium sulfate and sodium chloride catalyzed by long chain alcohols is roughly consistent with the hypothesis that the water activity at the mean freezing temperature is a constant offset from the water activity at the melting point of the solution, though films of the longer chain alcohols may undergo structural changes at higher salt concentrations which cause a deviation from the constant offset. The heterogeneous nucleation rate coefficient, averaged over all solutions, alcohols, and droplet sizes is 6.0 104 ± 4.0 104 cm2 s1, with no dependence on any of those parameters. Citation: Cantrell, W., and C. Robinson (2006), Heterogeneous freezing of ammonium sulfate and sodium chloride solutions by long chain alcohols, Geophys. Res. Lett., 33, L07802, doi:10.1029/2005GL024945.
1. Introduction [2] Though they are typically found in the upper reaches of the troposphere, cirrus clouds are not disconnected from the surface, especially in the tropics. Deep convection can loft products of near-surface activity rapidly to high altitudes through a mechanism Chatfield and Crutzen [1984] dubbed the Staubsauger or ‘‘Vacuum cleaner’’ model. Tropical Staubsaugers inject biomass burning products into the upper troposphere. There is evidence that these products affect liquid phase microphysics in cumulus clouds [Rosenfeld, 1999]. An increase in ice nuclei has been observed downwind of forest fires [Hobbs and Locatelli, 1969], and aerosol particles from biomass burning have been implicated in a decrease in the size of ice crystals in the tops of cumulonimbus and may play a role in cross tropopause transport of water vapor [Sherwood, 2002]. [3] A wide range of high molecular weight organic compounds are emitted during biomass burning [Elias et al., 1999]. The compounds have a low vapor pressure and typically segregate to the air-water interface of any droplet on which they condense. Little is known about the specific effects that such compounds may have on ice processes, though recent work with cloud condensation nuclei has shown that fresh smoke from burning peat is hydrophobic [Dusek et al., 2005]. In general terms, some compounds have almost no effect on the temperature at which water will
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Department of Physics, Michigan Technological University, Houghton, Michigan, USA. Copyright 2006 by the American Geophysical Union. 0094-8276/06/2005GL024945
freeze, while others are among the most effective catalysts known [Fukuta, 1966]. [4] Testing the freezing characteristics of water influenced by all of the high molecular weight organic compounds emitted during burning of biomass would be a Herculean task. Testing all possible combinations is neither feasible nor warranted. A more judicious, systematic approach is needed. Non-polar compounds like long chain alkanes will be at one extreme; they have a minimal influence upon the freezing process. Water covered by films of substances like long chain alcohols will be at the other extreme. Because they self-assemble at the air-water interface into two-dimensional crystals with a structure similar to the basal plane of ice, the long chain alcohols catalyze freezing at temperatures as high as 1C [Popovitz-Biro et al., 1994]. [5] The chance of finding a droplet in a biomass burning plume which is covered only by a single type of long chain alcohol is vanishingly small. Our aim is not to reproduce the freezing process as it occurs in the atmosphere, but to establish an upper bound on the efficacy of high molecular weight organic compounds as heterogeneous nucleators. Characteristic freezing temperatures and nucleation rates of pure water catalyzed by the alcohols are tabulated in previous work [Popovitz-Biro et al., 1994; Seeley and Seidler, 2001a]. However, freezing from solution is more likely in the atmosphere. We present characteristic freezing temperatures and nucleation rates of solutions of (NH4)2SO4 and NaCl catalyzed by four representative long chain alcohols.
2. Experiment [6] The objective is to repeatedly freeze the same droplet, which is covered with a film of alcohol. This eliminates sample to sample variations while capturing the stochastic nature of nucleation. The droplet freezer, shown in Figure 1, is based on the design of Seeley et al. [1999]. We use 5 or 10 ml droplets, deposited onto a glass slide from a microliter syringe. The droplets are flattened spheroidal caps of approximately three and five mm diameter respectively with surface areas of 0.16 and 0.07 cm2 respectively. The solutions are prepared from HPLC grade water and (NH4)2SO4 or NaCl. (All chemicals for preparation of the solutions purchased from Fisher Scientific and used as received.) The alcohols (heptadecanol, C17H35OH; hexadecanol, C16H33OH; triacontanol, C30H 61OH (all Acros organics); and pentacosanol, C25H51OH (Ultra Scientific)) are solid at room temperature and are virtually insoluble in water. For instance, heptacosanol, C27H55OH, has a solubility of less than 0.001 weight percent in water [Jamieson et al., 2005]. Alcohol is deposited onto the surface of the
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Figure 1. Schematic of the droplet freezer. The thin film, 100 W, platinum resistance thermometer and Kapton heater are controlled by the Lakeshore 331. This assembly sits on another heat sink, which extends into a dewar of liquid nitrogen. droplets with 5 ml of a 5 104 molar chloroform spreading solution, corresponding to a multilayer film (>5 layers) on the surface of the drop. After waiting approximately five minutes for the chloroform to evaporate, the droplet is isolated from the ambient atmosphere to prevent evaporation of the water. [7] Temperature measurement and control is done with a Lakeshore model 331 temperature controller, which is automated through LabView. The ramp rate on the downward leg of a temperature scan is typically 3 K min1 with a rate of 4 K min1 on the upward scan. A freezing event registers as a spike in the temperature trace during the downward scan, caused by the release of the latent heat of freezing. The high and low temperatures in the scan are adjusted according to the molarity of the solution being tested and the alcohol film.
3. Results and Discussion [8] Koop et al. [2000] showed that at the homogeneous freezing point the activity of water in many solutions is displaced 0.305 from the melting point. (Daw = 0.305 where Daw = aw,homogeneous freezing aw,ice, and aw,ice is the water activity of the solution in equilibrium with ice.) Zuberi et al. [2002] extended the concept to heterogeneous freezing, though they note that the offset will be different for each heterogeneous nucleator. For freezing from (NH4)2SO4 solutions with inclusions of montmorillonite and kaolinite dust, they report an offset of 0.242 with the caveat that the agreement is not perfect; the discrepancy is most pronounced at higher water activity. Archuleta et al. [2005] report values ranging from 0.23 to 0.32 for mineral particles coated with sulfuric acid. [9] Results from freezing of solutions catalyzed by long chain alcohols are presented in Figures 2 and 3. Our results for pure water droplets are consistent with previous work [Popovitz-Biro et al., 1994; Seeley and Seidler, 2001b], including the disparity in freezing temperature between alcohols with even and odd numbers of carbon in the backbone. As expected, alcohols with longer chain lengths, which form films with larger, more coherent twodimensional crystals at the air-water interface [PopovitzBiro et al., 1994], lie closer to the equilibrium melting curve. [10] Following the hypothesis of a constant offset in water activity, we note that Daw = 0.075 is consistent with freezing catalyzed by pentacosanol and triacontanol, for
Figure 2. Freezing temperatures of solutions catalyzed by pentacosanol (C25) and triacontanol (C30). The error bars represent one standard deviation. The temperature dependent water activity for the (NH4)2SO4 solutions is calculated from Clegg et al. [1995], while the activity for the NaCl solutions is calculated from Clegg et al. [1998]. The calculation for the NaCl solutions does not include a temperature dependence, but data from that system shows that the variation with temperature is small. The melting point line is taken from equation (19) of Clegg et al. [1995] The characteristic freezing temperature of pure water (no alcohol) was well below that of water catalyzed by the alcohols. both the NaCl and (NH4)2SO4 solutions at higher water activity. That constant offset fails for aw < 0.93, where the freezing temperatures are lower than those predicted by the offset of 0.075. However, we cannot simply conclude that the constant offset hypothesis fails because there is a possibility that the structure of the organic films may change with time, temperature, or weight percent of salt in solution (see below). In contrast to the longer chain lengths, Daw 0.135 across the entire range of activities tested for freezing of water catalyzed by hexadecanol and heptadecanol. We have no explanation for the discrepancy
Figure 3. Freezing temperatures of solutions catalyzed by heptadecanol (C17) and hexadecanol (C16). Error bars, water activities, and lines are as in Figure 2.
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Figure 4. Freezing temperatures of a 1.2 molar ammonium sulfate solution, catalyzed by C25H51OH. The data points are approximately 20 minutes apart. The downward trend in freezing temperature may be a result of structural changes within the alcohol film. The low first freezing point is a manifestation of a form of pre-activation [Seeley and Seidler, 2001b]. between the shorter and longer chain lengths, only a conjecture. The shorter chain length alcohols self assemble into a film which is not as structured as the longer chain lengths [Popovitz-Biro et al., 1994], which may indicate that the increasing concentration of ions in the lower activity solutions disrupts the more structured films more. [11] As discussed above, the structure of the alcohol film may not be constant in time. In approximately half the experiments, we see a decrease in the freezing temperature with time. An example is shown in Figure 4. The trend is not uniform, ranging from two to five degrees over 12 hours (or 100 freeze-thaw cycles). In experiments with droplets not covered by a film of the alcohols, no trend is observed. We can also rule out a decrease in the freezing temperature due to gradual evaporation of the droplet, which would have resulted in a decrease in the water activity and a lower freezing point. An outer chamber fit over the freezing chamber to minimize interaction with room air, but the seal wasn’t air-tight. Small amounts of condensation on the outside of the chamber were visible to the naked eye. In other words, if a change had occurred, condensation onto the drop was favored, not evaporation. We did not see a positive trend in the freezing temperatures, assuring us that significant condensation onto the droplet did not take place. Further evidence that the cause of the trend is a characteristic of the alcohols is provided by experiments with other organic compounds (stearic acid and elaidic acid), where no trend was observed. [12] Seeley and Seidler [2001a] also saw a downward trend, which they attributed to evaporation of the alcohol or dissolution of the alcohol into water. The alcohols are solids at room temperature with a negligible vapor pressure. As noted above, the solubility of the alcohols in water is also very small. However, previous work on Langmuir monolayers of long chain alcohols has shown that they may be very slow (up to two days) to adopt their equilibrium conformation [Buontempo and Rice, 1993]. That, coupled with the low solubility and vapor pressure, leads us to favor structural changes within the film as the cause of the change in the freezing temperature. [13] The relationship between water activity and freezing temperature is intriguing because it offers a glimpse into
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molecular level mechanisms of freezing, but one drawback is that you must know the activity for the solution in question. Though well developed thermodynamic models exist for some systems, that is not universally true. An alternative way of looking at freezing is to write the relationship between the melting point depression and the freezing point depression as DThom.freeze = lDTm, where DThom.freeze is the difference between the homogeneous freezing temperature of the solution and that of pure water and DTm is the melting point depression. l ranges from 1.4 to 2.2 for a wide variety of solutes [DeMott, 2002]. Generalizing the expression to heterogeneous nucleation, DThet.freeze = lDTm, where DThet.freeze is the difference between the catalyzed freezing temperature of pure water and the catalyzed freezing temperature of the solution. [14] Results for fits to determine l are shown in Table 1. Though l ranges from 1.1 to 1.9, the values agree within the error for each alcohol. Our data set does not show a statistical difference between the NaCl and (NH4)2SO4 solutions. [15] While heterogeneous freezing results are frequently reported and displayed in terms of an average freezing temperature, the nucleation rate is the more fundamental quantity. Invoking the ergodic hypothesis, we view the same drop frozen many times as an ensemble and calculate the nucleation rate from [Dufour and Defay, 1963, p. 218]: Z P ¼ 1 exp r1
T
RðT ÞdT
ð1Þ
T0
where P is the probability of freezing, r is the cooling rate, and R(T) is the freezing rate at temperature T. The probability of freezing at temperature, T, is calculated from our data as the fraction of droplets in the ensemble that have frozen, Nfrozen/Ntotal. In cases where a trend in the freezing temperature was observed, the data was linearly detrended and centered at the mean freezing temperature before the nucleation rate was calculated [Seeley and Seidler, 2001a]. [16] The freezing rate, calculated at the average freezing temperature in each case, varied from 5.6 103 s1 for a 4.9 M solution of NaCl catalyzed by pentacosanol to 4.2 104 s1 for freezing of pure water catalyzed by heptadecanol. Averaged over all solutions and alcohols, the freezing rate was 1.8 103 ± 1.2 103 s1. There was no trend in freezing rate with either concentration of salt in solution or with molecular weight of the alcohol. [17] To calculate the heterogeneous nucleation rate coefficient we normalize our rates by the size of the crystalline domains that the alcohols form - patches with an area of approximately 3 mm2 [Majewski et al., 1995]. We justify the much smaller normalization factor by noting that the ice
Table 1. l From the Equation DThom.freeze = lDTm l
Solution and Alcohol
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(NH4)2SO4 NaCl C17 (NH4)2SO4 NaCl C25 (NH4)2SO4 NaCl C30 (NH4)2SO4
C16 C17 C25 C30
1.1 1.4 1.6 1.5 1.9 1.5 1.5
± ± ± ± ± ± ±
0.5 0.1 0.1 0.2 0.4 0.3 0.4
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nucleating efficiency of C20H41OH mixed with perfluorododecanol (the two compounds are immiscible and segregate into separate domains within the film) did not drop until the fraction of the alcohol in the film dropped below 50% [Popovitz-Biro et al., 1994]. Apparently, the ice nucleating activity of the alcohol was not affected until the alcohols’ crystalline domains fell below a critical size. We stress that this assumption is ad hoc and remains to be born out by further measurements. (In fact those results suggest that the nucleation rate may be independent of surface area of the alcohol once a critical coverage is reached.) With the assumed area incorporated, our heterogeneous nucleation rate coefficients range from 1.9 105 cm2 s1 to 1.4 104 cm2 s1. If we use the area of the 10 ml drops as the normalization factor (the more common approach), the heterogeneous nucleation rate coefficient ranges from 3.5 102 cm2 s1 to 2.6 103 cm2 s1. Coefficients for mineral dust treated with sulfuric acid range from slightly less than 10 5 to 107 cm2 s1 at temperatures lower than 35C [Archuleta et al., 2005].
4. Conclusions [18] Freezing of water and solutions of ammonium sulfate and sodium chloride catalyzed by long chain alcohols is an upper bound on heterogeneous nucleation processes induced by films of high molecular weight organic compounds. Our results show that the relationship between the mean freezing temperature and water activity is roughly consistent with Koop et al.’s [2000] hypothesis of a constant offset from the equilibrium melting point. Results for pentacosanol and triacontanol show some deviation from that relationship at lower water activity, but this could be due to structural changes within the organic film in response to the change in the concentration of the solution. The heterogeneous nucleation rate coefficient does not exhibit a dependence on temperature, water activity, alcohol, or size of the droplet tested. [19] Acknowledgments. Funding from NASA’s New Investigator Program (NNG04GR41G) and NSF (CHE-0410007) is appreciated. Partial support for Carly Robinson in the summer of 2005 was provided by the Michigan Space Grant Consortium. Comments from two anonymous reviewers are appreciated.
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W. Cantrell and C. Robinson, Department of Physics, Michigan Technological University, Houghton, MI 49931, USA. (
[email protected])
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