Glutaric Acid

Apr 1, 2013 - sulfate/glutaric acid/water system using differential scanning calorimetry, infrared ... We have also modified our glutaric acid/water b...
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Solid/Liquid Phase Diagram of the Ammonium Sulfate/Glutaric Acid/ Water System Keith D. Beyer,* Christian S. Pearson, and Drew S. Henningfield Department of Chemistry, University of Wisconsin-La Crosse, La Crosse, Wisconsin 54601, United States S Supporting Information *

ABSTRACT: We have studied the low temperature phase diagram and water activities of the ammonium sulfate/glutaric acid/water system using differential scanning calorimetry, infrared spectroscopy of thin films, and a new technique: differential scanning calorimetry−video microscopy. Using these techniques, we have determined that there is a temperature-dependent kinetic effect to the dissolution of glutaric acid in aqueous solution. We have mapped the solid/liquid ternary phase diagram, determined the water activities based on the freezing point depression, and determined the ice/glutaric acid phase boundary as well as the ternary eutectic composition and temperature. We have also modified our glutaric acid/water binary phase diagram previously published based on these new results. We compare our results for the ternary system to the predictions of the Extended AIM Aerosol Thermodynamics Model (E-AIM), and find good agreement for the ice melting points in the ice primary phase field of this system; however, significant differences were found with respect to phase boundaries, concentration and temperature of the ternary eutectic, and glutaric acid dissolution.

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have been reported at several temperatures,19,20 which represent four saturation compositions in the ternary phase diagram. To our knowledge, no ice melting points, solubility of a single solute, or boundaries between the various phase stability regions have been reported in the literature for the (NH4)2SO4/C5H8O4/ H2O system. We present here the results of our study of the low-temperature solid/liquid phase diagram of ammonium sulfate/glutaric acid/ water and water activities using thermal analysis and infrared spectroscopy techniques. We have coupled our experimental data with our previous results for the binary systems to construct a ternary phase diagram. Finally, we compare our results to the predictions of the Extended AIM Aerosol Thermodynamics Model (E-AIM).22,23,27−29

INTRODUCTION Tropospheric aerosols are often composed of internal mixtures of inorganic electrolytes and organics.1−9 The inorganic fraction is made up predominantly of aqueous ammonium and sulfate ions with the molar ratio of NH4+/SO42− ranging from 1 to 2.10,11 Additionally, upper tropospheric aerosols which are composed predominantly of aqueous sulfuric acid at high concentrations have been shown to contain NH3 which partially to completely neutralizes the H2SO4 molecules.12 These particles absorb and scatter solar radiation dependent upon their phase, thus contributing to the radiation balance.13 They may also play a significant role in heterogeneous chemistry in the troposphere,14 and can be found at cirrus cloud altitudes under strong convective conditions where they could serve as ice nuclei.15,16 Studies have also shown that the incorporation of organic compounds into ammonium sulfate aerosols changes their deliquescence, efflorescence, hygroscopic properties, and potentially their crystallization properties.17−21 This necessitates understanding the impact of organic substances on the phase transitions of aqueous systems that make up tropospheric aerosols. One of the more abundant organic compounds found in aerosols is glutaric acid (C5H8O4).5,7 Very little is known about the thermodynamics of the mixed ammonium sulfate/glutaric acid system in water at temperatures below 298 K. In particular, fundamental physical data is needed on this system for incorporation into atmospheric models in order to better predict atmospheric cloud properties.22,23 Data, such as equilibrium freezing temperature of ice and solute saturation temperature as a function of solute concentration, are among the basic parameters that need to be experimentally determined. The binary systems of ammonium sulfate/water and glutaric acid/water have been extensively studied with respect to solubilities of the solute and solid/liquid phase equilibria.24−26 With respect to solute solubilities in the ternary (NH4)2SO4/ C5H8O4/H2O system, eutonic (phase boundary) concentrations © 2013 American Chemical Society

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EXPERIMENTAL SECTION Sample Preparation. Ternary samples were prepared by mixing 99 wt % ACS reagent grade (NH4)2SO4 supplied by Sigma-Aldrich and 99 wt % ACS reagent grade C5H8O4 supplied by Acros Organics with deionized water. The concentration of all samples is known to ±0.40 wt %. Differential Scanning Calorimeter. Thermal data were obtained with both a Mettler Toledo DSC 822e with liquid nitrogen cooling and a Mettler Toledo DSC 822e cooled via an intra cooler. Each DSC utilized an HSS7 sensor. High purity grade nitrogen was used as a purge gas with a flow rate of 50 mL per minute. The temperature reproducibility of these instruments is better than ±0.05 K. Our accuracy is estimated to be ±0.9 K with a probability of 0.94 based on a four point temperature calibration30 using indium; HPLC grade water; anhydrous, high purity (99%+) Received: February 15, 2013 Revised: March 29, 2013 Published: April 1, 2013 3630

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this occurs the experiment is repeated with a new sample. While we experimented with all three types of samples, ultimately we found that thin and wide samples gave the clearest images for determining the final dissolution of solid in our samples. Infrared Spectra. The sample cell used for infrared spectra is similar to that described in previous literature.32 A small drop of ternary solution was placed between two ZnSe windows, which were held in the center of an aluminum block by a threaded metal ring. Sample volumes were approximately 2 μL. On each side of the aluminum block a Pyrex cell was purged with dry nitrogen gas. KBr windows were placed on the end of each cell, sealed with o-rings, and held in place by metal clamps. Heat tape was wrapped around the purge cells to prevent condensation on the KBr windows at the lowest temperatures. The sample was cooled by pouring liquid nitrogen into a circular aluminum cup attached to the top of the main cell. The cell block was warmed by resistive heaters connected to a temperature controller. Temperature was measured by a copper/constantan thermocouple placed at the edge of the ZnSe windows and connected to the temperature controller. The temperature of the cell was calibrated using HPLC grade water and high purity organic solvents (Aldrich): decane, octane, and acetic anhydride, of which the melting points are 243.5, 216.4, and 200.2 K, respectively.33 The IR cell temperatures are known on average to within ±1.3 K, i.e., a temperature we measured in the IR cell of a specific transition is within 1.3 K of the transition temperature we measure (of the same transition) using the DSC. Spectra were obtained with a Bruker Tensor 37 FTIR with a DTGS detector at 4 cm−1 resolution. Each spectrum was the average of 8 scans. Before spectra were taken of a sample, a background scan was obtained from a dry, purged sample cell. Samples were cooled to 195 at 3 K per minute and then allowed to warm to room temperature without resistive heating; typically this was 1 K/minute or less. If the final target temperature was above room temperature, then resistive heating was applied to increase temperature at about 1 K/minute. Our spectra compare well for ice,34 ammonium sulfate,35 and glutaric acid.35 Experimental Protocol. All samples at each concentration studied were run in both DSC and IR experiments. The DSC technique provides accurate and precise temperature and enthalpy data for phase transitions. Therefore, all temperatures reported here are from DSC experiments. However, the identity of solids that may be present cannot be uniquely identified from the DSC results; therefore, IR experiments are utilized to identify the solids/liquids/ions that may be present utilizing specific IR absorption bands as stated above, while also monitoring temperature. Identifying the precise temperature of phase transitions using IR spectroscopy alone can be very difficult, since changes in IR spectra as a function of temperature/phase can be very subtle. Thus, we rely on the DSC experiments for accurate phase transition temperatures and the IR experiments for identification of phases. Therefore, to identify the presence of a particular phase that undergoes a transition to another phase (such as melting of a specific solid), one would observe an endothermic or exothermic transition in the DSC thermogram at the transition temperature and a change in the IR spectra at a similar temperature within a reasonable temperature range (typically no greater than ±2 K of the DSC temperature). In some cases DSC and IR transitions may both be weak, especially for solids dissolving into solution. In these cases DSC-Video Microscopy was used to visually observe the disappearance of crystals.

octane; and anhydrous, high purity heptane (99%+) from Aldrich, the latter three stored under nitrogen. The enthalpy/heat capacity measurement of each DSC was also calibrated using the same substances and the known enthalpy of fusion for each substance yielding an accuracy of ±3% with a probability of 0.92. Finally, instrument response lag (τ lag) has also been calibrated with high purity n-octane and indium at several heating rates.31 Samples were contained in either 40 μL aluminum or 30 μL platinum pans and typically had a mass of approximately 15 to 25 mg. Each sample was weighed before and after the experiment using a Mettler-Toledo AT20 μg balance. The average mass loss from evaporation during the experiment was less than 1%. When aluminum pans were used, the lid was crimped to the base, whereas the platinum lids were not crimped to the platinum bases. No difference was observed in mass loss of the sample based on which pan was used. A typical sample was cooled to 183 at 10 K per minute, held at that temperature for 5 min, and then warmed at a rate of 1 K per minute (ice primary phase field) or 0.1 K per minute (glutaric acid primary phase field) to a temperature at least 5 K above the predicted melting point. DSC Video Microscopy. One of the Mettler DSC instruments is fitted with a video microscopy accessory. This system consists of an Olympus SC30 camera, Navitar Zoom 6000 optics, StarLight Roma LED-XV sample illumination, and Olympus analysis software. When running a microscopy experiment, the normal DSC sample chamber lid is replaced with a special lid with quartz windows that allows illumination and viewing of the sample. Cooling and heating segments of a DSC method can be recorded. In microscopy experiments, images were taken at either every 0.5 K (cooling) or 0.1 K (warming). The DSC and microscopy data acquisition are synchronized for correlation of DSC program temperature with specific images acquired by the camera. The sample is placed in an aluminum 40 μL pan. The lip of the pan is covered with a thin layer of stopcock grease, and an optical window is placed on the pan (sapphire 0.940 cm diameter and 0.0300 cm thick). Several sample shapes were tried: approximately 5 μL spherical droplet in the center of the pan, typical DSC sample of approximately 20 μL which fills about half the pan and touches the sides, and small sample ( 40 wt % and ternary (NH4)2SO4/C5H8O4/H2O with [C5H8O4] that placed the sample in the glutaric acid primary phase field had this endothermic transition shape in their thermograms (with the exception of the 35 wt % (NH4)2SO4 samples, which were very close to the (NH4)2SO4/C5H8O4 phase boundary, discussed below). Upon reviewing the IR spectra of multiple samples, no change is seen in the IR that corresponds to the peak of this endothermic shape. Also, many IR changes with temperature are subtle, and it was difficult to discern the exact final dissolution of glutaric acid from IR experiments alone as stated above in the Experimental Section. Therefore, we employed a new technique, DSC Video Microscopy, as described in the Experimental Section, where a sample in the DSC is monitored simultaneously with a microscope/camera. We have performed several such experiments and present the results for a 10/40 wt % (NH4)2SO4/C5H8O4 ternary sample. Figure 3 shows images of this sample in the DSC at several points in the heating segment. Very subtle changes in the image can be seen at the ternary eutectic. Panels A and B in Figure 3 are images of the sample before and after the ternary eutectic transition, respectively. In this sample, (NH4)2SO4 dissolves into a small amount of comelting ice and some co-dissolving C5H8O4. The changes in the image are subtle and the figure cannot fully represent the changes in color and brightness of the sample. However, the Olympus analysis software includes a feature to determine the “brightness” 3634

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of the α phase, along with the strong band at 1198 cm−1, which is absent in the β form. These values are marked by vertical dotted lines in Figure 5. The rest of the bands in this energy range exhibit a smaller shift in band center, but do show changes in band strength. Upon cooling below the transition temperature, the spectrum slowly converts back to the β spectrum. Grip and Samuelsen42 noted that the β → α and α → β conversion is slow and observed “overheating” and “undercooling” in heating and cooling experiments, respectively. We reviewed all of our binary C5H8O4/H2O and ternary (NH4)2SO4/C5H8O4/H2O IR experiments with concentrations in the glutaric acid primary phase field to determine if the α form of glutaric acid was present. In all cases we only observed spectra characteristic of the β form upon initial crystallization of glutaric acid in the sample, which persisted until complete dissolution of glutaric acid. The characteristic absorption bands of the β form were seen in our samples to the exclusion of α form bands. Typical frozen spectra for binary and ternary samples are given in Figure 5. Not only does this rule out the existence of α form glutaric acid in our samples, but also we have no indication from IR experiments that any other solid is forming, such as mixed solids or an unknown hydrate, that would explain the large endothermic signal in our DSC experiments. As stated above, some researchers have observed slow water uptake before the DRH is reached. Based on this observation, we explored whether dissolution of glutaric acid solid into aqueous solution is a slow process whose rate increases as temperature increases (and hence solubility increases). We considered the possibility that the heating rate in our DSC experiments was too fast, and that glutaric acid solid was not in material equilibrium with solution in these experiments. Therefore, we performed the same DSC experiments, but with slower heating rates. We found that, as the heating rate was decreased, the large endotherm before the final dissolution decreased to the point that it disappeared at the slowest heating rates (0.1 to 0.05 K/min, depending on sample concentration). Figure 2 shows thermograms of both binary C5H8O4/H2O and ternary (NH4)2SO4/ C5H8O4/H2O samples at 1 K/min and 0.1 K/min heating rates illustrating this difference. Thus, it appears that the large endotherm in our 1 K/min DSC experiments is due to “superheating” of the sample, such that the solid is not in material equilibrium with the solution. As seen in the thermograms of Figure 2 taken at 1 K/min heating rate, in both the ternary and binary samples, the endothermic transition is very broad, coming to a maximum at a certain temperature. Thus, glutaric acid is dissolving into solution continuously in both the binary and ternary systems (as indicated by a negative deflection from the baseline). We interpret the increasing deflection from baseline as an increase in the rate of dissolution of glutaric acid with increasing temperature, such that at the thermogram peak, the largest amount of mass is dissolving. However, the rate of dissolution continues to increase as temperature increases, but at temperatures above the peak in the thermogram, a decreasing amount of solid glutaric acid is in a state of nonequilibrium and the thermogram signal quickly decreases to the equilibrium value for dissolving glutaric acid. Thus, we can explain the shape of our thermograms at the 1 K/min heating rate as due to material nonequilibrium in the sample, where a long and gradually increasing endothermic signal comes to a maximum value, then rapidly (larger slope) returns to an equilibrium value. This explanation is also consistent with our IR experiments where continual dissolution of glutaric acid is observed, with no indication of other endothermic events occurring (such as hydrate melting, solid/solid transition, etc.). We also found that this large endothermic dissolution affected the final dissolution signal (endset temperature) in the

completely dissolve. The humidity at which this occurs is called the deliquescence relative humidity (DRH). A wide range of DRH values for glutaric acid have been reported in the literature (83−90% RH, summarized in Yeung et al.37), with several studies reporting water uptake before the DRH.38−41 Yeung et al.37 explained this difference in terms of the different polymorphs of glutaric acid, α and β forms, where the α form is stable above approximately 338 K, and the β form is stable below that temperature. However, they were able to make the α form at room temperature and demonstrate that it has a lower DRH than that of the β form at the same temperature, which leads to higher solubility of the α form as compared to the β. Yeung et al. concluded that water uptake at lower RH values may be due to the presence of the α form. We have explored the possibility of the α form being present in our samples, which might explain the large endotherm at lower temperatures, corresponding to dissolution of the more soluble α form. A small amount of reagent glutaric acid was dissolved in reagent grade ethanol. Approximately 3 μL of this solution was then spread on the ZnSe IR window and allowed to dry completely. The spectrum of this sample was then monitored as a function of temperature using our IR cell as described in the Experimental Section. The sample was heated from room temperature to 355 K, then cooled to 289 K. Figure 5 shows the

Figure 5. IR spectra of: red, dry solid glutaric acid at 340 K (α-form); black, dry solid glutaric acid at 306 K (β-form); blue, frozen 60 wt % C5H8O4/H2O sample at 236 K after both ice and glutaric acid have crystallized; green, frozen 5/20 wt % (NH4)2SO4/C5H8O4 ternary sample at 233 K after ice, glutaric acid, and ammonium sulfate have crystallized. Black dotted line is at 1304 cm−1, which is the characteristic peak position for β-form glutaric acid. Red dotted lines are at 1292 and 1198 cm−1, which are absorption bands characteristic of α form glutaric acid.

fingerprint region of the IR spectrum of dry sample at 306 K, which is a good match for the spectrum found in the Aldrich Library.35 A clear change in the spectrum is observed once the sample is heated through the β → α transition temperature. The spectrum we conclude to be the α form of glutaric acid (taken at 340 K) is shown in Figure 5 as the red spectrum. While there are Raman spectra of the β and α forms of glutaric acid in the literature,42,40 we are not aware of any infrared spectrum assigned to the α form in the literature. Therefore, we report here the first infrared spectrum of α glutaric acid. There is a significant and clear change in the spectra between β and α forms, most notably the absorption bands between 1310 and 1060 cm−1. In particular, the sharp band at 1304 cm−1 is clearly characteristic of the β phase, and the broader, strong band at 1292 cm−1 is characteristic 3635

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values reported for glutaric acid in the literature needs further exploration. Final Melting/Dissolution Temperature Fits. We fit the final melting/dissolution temperatures to polynomial equations as a function of C5H8O4 concentration (while holding the (NH4)2SO4 concentration constant). In the glutaric acid primary phase field, our 0.1 K/min heating data from the DSC was used. For the C5H8O4/H2O binary system, we fit the solubility data of Stephen and Stephen, which is in excellent agreement with both our conductivity data previously reported26 and our DSC data determined at 0.1 K/min heating rates. The polynomial fits are of the form:

thermograms: at slower rates of heating (where the large, nonequilibrium endotherm disappears), we found the endset temperature tended to slightly lower temperatures (1−2 K) when compared to the 1 K/min experiments with the large endotherm present. This shift cannot be the result of a change in the heating rate, since the affect on the endset temperature of a 1 K/min heating rate is negligible compared to a theoretical heating rate of 0 K/min.36 At most, if the instrument lag were not calibrated to eliminate the affect of heating rate on measured temperature, a variance of less than 0.18 K would be expected on measured temperature at a 1 K/min heating rate, which is much less than other experimental uncertainties. Thus to eliminate the effect of the large, nonequilibrium endotherm on the final dissolution thermal signal, all samples with glutaric acid as the final phase were run at 0.1 K/min heating to determine accurate final dissolution temperatures. This included C5H8O4/H2O binary experiments in the glutaric acid primary phase field that had been previously reported by our group,26 and we present a corrected phase diagram for the binary system in Figure 6. It is

T = A 2 X2 + A1X + A 0

(1)

where T is the melting/dissolution temperature in Kelvin, and X is the wt % of C5H8O4. The polynomial fits reproduced our final melting temperatures to within ±0.17 K in the ice primary phase field and to within ±0.57 K in the glutaric acid primary phase field, both of which are within our experimental error. Coefficient values for the parametrizations are given in Table 1 along with Table 1. Melting/Dissolution Temperature Polynomial Coefficients from Eq 1a [(NH4)2SO4] 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35

Figure 6. Solid/liquid phase diagram of C5H8O4/H2O using data from DSC experiments where the sample was heated at 0.1 K/min for samples in the glutaric acid primary phase field (open red circles). Other symbols are as follows: red triangles, eutectic transition; blue triangles, conductivity measurements as given in Beyer et al.;26 green squares, solubility data of Stephen and Stephen;24 orange circle, melting point from NIST;43 orange diamond, β/α glutaric acid solid/solid phase transition as given in NIST.43 Black curve in ice region is a fit to our melting point data. Black curve in glutaric acid region between the eutectic and 70 wt % C5H8O4 is a fit to our DSC data. Black curve between 70 and 100 wt % C5H8O4 is a smoothed fit to literature data.

A2

A1

A0

Ice Primary Phase Field −0.0163 0.1071 273.0 −0.001719 −0.1571 272.2 −0.01385 −0.07115 270.4 −0.2603 268.5 −0.3297 266.6 −0.4603 264.8 −0.1656 260.5 −0.4576 0.5518 258.5 Glutaric Acid Primary Phase Field 0.006747 0.1901 263.8 0.8738 252.2 0.9541 253.0 −0.01155 1.651 247.4 −0.01643 1.905 248.8 −0.05889 3.373 242.2 −0.08254 3.861 246.0 −0.2006 5.716 247.1

range [C5H8O4]b 0 - PB 0 - PB 0 - PB 0 - PB 0 - PB 0 - PB 0 - PB 0 - PB PB - 70 PB - 50 PB - 45 PB - 45 PB - 35 PB - 25 PB - 20 PB - 15

[(NH4)2SO4] and [C5H8O4] are in wt%. b“PB” indicates phase boundary concentration as given in Table 2 for each respective concentration of (NH4)2SO4.

a

the concentration ranges for which the equations are valid. Typical plots of this analysis are given in Figure 7. This approach allowed us to determine the ice/C5H8O4 phase boundary for (NH4)2SO4 concentrations through 35 wt %. Thus, the equations on both sides of the phase boundary can be solved simultaneously for the temperature and concentration where both solids and a liquid are in coexistence. These values are given in Table 2. We expected solutions of higher (NH4)2SO4 concentration (greater than about 37 wt % (NH4)2SO4) to be in the (NH4)2SO4 primary phase field. We attempted a number of DSC and IR experiments in this concentration region, but found data of low quality because of weak (NH4)2SO4 final dissolution signals (DSC), as well as the proximity of the concentration of these solutions to the ternary eutectic composition, where all phases comelt (DSC and IR). Therefore, we cannot map this region of the

seen that our data for glutaric acid dissolution taken at 0.1 K/min heating rates are in better agreement with both literature data24 and our own conductivity studies than were the 1 K/min data previously reported.26 We take these results for the binary system as further confirmation that dissolution of glutaric acid in water can be affected by kinetic hindrance, and thus slow heating rates are needed to acquire accurate solubility temperatures. These observations are in agreement with the observations of DRH experiments, where it has been observed that higher experimental RH ramp rates lead to higher measured DRH values for glutaric acid.41 If the transition of glutaric acid from the dry solid phase to aqueous solution is a kinetically hindered process (or what has been termed the “mass-transfer effect”), then low RH ramp rates would be needed in DRH experiments to allow enough time for complete equilibration between the particle and gas phase. This explanation for the different DRH 3636

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Figure 7. Typical fits to melting/dissolution point data using eq 1. Concentrations are given in the legend.

Table 2. Concentration of Liquid (wt%) that is in Equilibrium with Two Solids at the Temperature Indicateda [(NH4)2SO4]

[C5H8O4]

[H2O]

temp (K)

solids in equilibrium

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 39.9

18.26 18.80 14.25 11.90 8.47 6.56 3.92 2.01 0.00

81.74 76.20 75.75 73.10 71.53 68.44 66.08 62.99 60.11

269.5 268.6 266.5 265.4 263.8 261.8 259.8 257.8 254.75

Ice/C5H8O4 Ice/C5H8O4 Ice/C5H8O4 Ice/C5H8O4 Ice/C5H8O4 Ice/C5H8O4 Ice/C5H8O4 Ice/C5H8O4 Ice/(NH4)2SO4

a

Figure 8. Solid/liquid phase diagram of the (NH4)2SO4/C5H8O4/H2O system showing melting/dissolution point isotherms and phase boundaries (see text for details): colored solid lines are calculated isotherms at temperatures in Kelvin as indicated solid black curve is the phase boundary from fits to the melting point curves as given in the text, solid black circle is the ternary eutectic composition (37 wt % (NH4)2SO4/1.5 wt % C5H8O4), and open black diamonds are eutonic concentrations (phase boundaries between (NH4)2SO4 and C5H8O4) at temperatures indicated as reported by Brooks et al.19 The primary phase fields are labeled as “Ice”, “Glutaric Acid”, and “Ammonium Sulfate”, respectively, and are separated by the phase boundaries as indicated by solid black lines (though the (NH4)2SO4/C5H8O4 phase boundary could not be determined from our results). Dashed lines are drawn between eutonic points of Brooks et al. to indicate where they would predict the (NH4)2SO4/C5H8O4 phase boundary to be. Black square corresponds to the composition of the sample whose DSC and IR experimental results are given in Figures 3 and 4, and described in the text. Dotted line connecting this point to the ice/C5H8O4 phase boundary is the concentration path the liquid will follow as the sample is heated.

Described as a “phase boundary” in the text.

phase diagram, and cannot determine the location of the (NH4)2SO4/C5H8O4 phase boundary. Ternary Eutectic. We then determined the concentration of the ternary eutectic. The ternary eutectic is an invariant point where all three solids are in equilibrium with the liquid phase, and is the lowest temperature at which liquid can exist in equilibrium; therefore, all solid/liquid equilibrium points on the diagram are at higher temperatures. The ternary eutectic also falls at the intersection of the ice/C5H8O4, ice/(NH4)2SO4, and (NH4)2SO4/ C5H8O4 phase boundaries, and occurs at the lowest temperature along these boundaries. Combining these facts and analyzing the phase boundary transition temperatures of samples in the ice and glutaric acid primary phase fields in the ternary system, as well as data from the ammonium sulfate/water binary system, we conclude the concentration of the ternary eutectic to be 37.0 ± 1 wt % (NH4)2SO4, 1.5 ± 1 wt % C5H8O4, which is indicated by a black circle in Figure 8. The average ternary eutectic temperature of all ternary samples studied is 254.06 ± 0.19 K. Temperature Contours. Equation 1 was solved at each respective [(NH4)2SO4] for specific temperatures (270 K, 265 K, etc.) to determine the [C5H8O4] and thus construct isotherms on the ternary phase diagram. Figure 8 shows the (NH4)2SO4/ C5H8O4/H2O phase diagram with the calculated isotherms (colored lines in the figure with corresponding temperatures indicated on the plot). It should be noted that the data used to construct Figure 8 are not continuous, but rather are at specific concentration intervals: every 5 wt % or less as shown in Figure 1. Therefore, the temperature contours are smoothed interpolations between data points and are only valid on the order of ±2 wt % for a given temperature.

Literature Comparison. We have also placed the three eutonic points of Brooks et al.19 in Figure 8, which they determined for (NH4)2SO4/C5H8O4 coexistence (the Wise et al.20 datum at 297.9−298.1 K is coincident with the Brooks et al. 297 K point). In their study, the deliquescence relative humidity (DRH) over eutonic solutions was measured. Logically, these points would be connected by an (NH4)2SO4/C5H8O4 phase boundary line, and we have done so in Figure 8 with a dashed line. We find the eutonic (NH4)2SO4/C5H8O4 points of Brooks et al. to be reasonably in line with where one would expect the (NH4)2SO4/ C5H8O4 phase boundary to fall, especially with respect to our projected ternary eutectic concentration, though the true phase boundary may be a more smoothed curve between their points than the simple lines we have drawn connecting their data. Water Activities. In a ternary system the melting point depression can be used to determine solvent activities via the equation: ln a1 = −

∫T

T *f

f

ΔHfus RT 2

dT (2)

where a1 is the activity of water at Tf, ΔHfus is the molar enthalpy of fusion of ice, R = 0.008314 kJ mol−1 K−1, Tf is the depressed 3637

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melting point, and Tf * is the melting point of pure water. To a first approximation, the enthalpy of fusion can be considered constant as a function of temperature over a small temperature range; however, the ice melting point depression in the systems studied here is significant. Therefore, ΔHfus needs to be expressed in terms of temperature so that the integral in eq 2 can be solved. We fit the values for ΔHfus of ice given in the Smithsonian Meteorological Tables44 for temperatures at 273.15 K and below to a second order polynomial: ΔHfus = − (2.330 × 10−4)T 2 + 0.1622T − 20.92

(3)

where T is in Kelvin and ΔHfus is in kJ/mol. Substituting eq 3 into eq 2 and integrating yields: ⎡ ⎛ T* ⎞ 1 f ln a1 = − ⎢ −2.330 × 10−4(T *f − Tf ) + 0.1622 ln⎜⎜ ⎟⎟ ⎢ R⎣ ⎝ Tf ⎠ ⎤ ⎛ 1 1⎞ + 20.92⎜⎜ − ⎟⎟⎥ Tf ⎠⎦⎥ ⎝ T *f

(4)

Figure 9. Comparison of our experimental results for final melting/ dissolution points with the predictions of the Extended AIM Aerosol Thermodynamics Model (abbreviated as AIM in the legend) using the UNIFAC based model with Peng et al.46 parameters for glutaric acid. Symbols indicate the difference between our experimental melting/ dissolution points and those predicted by the E-AIM as given in the legend. Solid black circle is our ternary eutectic, and black solid curves represent the phase boundary calculated from fits to our data. Red lines are the phase boundaries predicted by the E-AIM.

We have determined the water activities of our solutions using eq 4 at Tf for each concentration. From the respective calculated activities, water activity coefficients (γ1) are calculated using a1 = γ1x1, with x1 being the mole fraction of water for each system. The results are given in Table 1S. It is seen that throughout the range of concentrations studied here, the activity coefficients differ from unity by at most 0.081, with the average deviation being 0.030. In all cases, the activity coefficients were greater than 1. As expected, the deviation of the activity coefficient from unity increased with increasing solute concentration. We have compared our calculated water activities to those predicted by Koop and Zobrist45 based on water and ice vapor pressure measurements and find excellent agreement. Our calculated water activities for those samples where ice is the final melting phase differ on average from the values calculated using eq 7 in Koop and Zobrist by +0.0001, with the greatest difference being +0.0007. Comparison to the Extended AIM Aerosol Thermodynamics Model (E-AIM). We have compared our experimentally determined final melting points with those predicted by the E-AIM.23,23,27−29 It must be noted that the E-AIM only claims to be valid for organic species at 298 K. Therefore, predicting melting points at temperatures below 298 K in the ammonium sulfate/glutaric acid/water system is an extrapolation of the data on which the model is based. However, the web version (http:// www.aim.env.uea.ac.uk/aim/aim.php) allows temperatures between 180 and 330 K to be entered into the model for calculations. Model II of the E-AIM was used to generate melting point predictions, which allows prediction of physical properties in systems containing one or more of the following in water: organics, H+, NH4+, SO42−, NO3−. We input the amounts of (NH4)2SO4, C5H8O4, and H2O to match the concentrations we studied in our experiments using the “Aqueous Solution and Liquid Mixture Calculation”. In these E-AIM runs we varied temperature until no solids remained, yielding the predicted final melting/dissolution points. Calculations were performed using the two models for organics incorporated into the E-AIM: UNIFAC (which is based on functional groups within the molecule), or a parametrized fit to an activity equation. The results of our analysis are given in Figure 9 using UNIFAC parameters for glutaric acid, and Figure 10 using the fitted activity equation for glutaric acid.

UNIFAC. Using the Peng et al.46 UNIFAC parameters for glutaric acid that are incorporated into the E-AIM we determined the predictions of the model for final melting/dissolution temperatures, and found that in the ice primary phase region they were generally in good agreement with our experimental values (within +0.40/−0.55 K), which we feel is an excellent result for the model given it is based on data at 298 K. However, the E-AIM performed much worse in the glutaric acid primary phase field. This is because the E-AIM predicts the ice/C5H8O4 phase boundary to fall at much higher glutaric acid concentrations (between 50 and 37 wt % C5H8O4, red line on the left of Figure 9), whereas our experimental boundary is between 19 and 2.5 wt % C5H8O4 (black curve in Figure 9). As a result, the E-AIM predicted melting points were 5 K or more (generally >11 K) lower than our experimental dissolution temperatures, which is caused by the E-AIM predicting ice as the final phase where we observed glutaric acid. The average final melt temperatures of the E-AIM predictions in this region are 20.3 K lower than our experimental dissolution temperatures. We found similar disagreement with respect to the ice/ (NH4)2SO4 phase boundary predicted by the E-AIM (red line from right side to center of Figure 9). Between the ice/ (NH4)2SO4 binary eutectic and our ternary eutectic at 37/1.5 wt % (NH4)2SO4/C5H8O4, the two phase boundaries move in different directions in both concentration and temperature. The E-AIM predicted phase boundary for ice/(NH4)2SO4 continues to lower [(NH4)2SO4] and higher [C5H8O4] until a predicted ternary eutectic of 25.0/35.9 wt % (NH4)2SO4/C5H8O4 and 245.7 K (intersection of two red lines in Figure 9), which is clearly very different from our value of 37.0/1.5 wt % (NH4)2SO4/ C5H8O4 at 254.1 K. Thus, the difference between the E-AIM predicted phase boundaries, ternary eutectic, and our experimentally determined phase boundaries/ternary eutectic are substantial. 3638

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techniques, we have determined a kinetic effect to the dissolution of glutaric acid into aqueous solution, necessitating slow (about 0.1 K/min or less) heating rates when determining solubility data. These observations appear to be in agreement with literature observations of slow uptake of water from the gas phase in DRH experiments over a range of relative humidity, which may be dependent on the rate of RH increase in those experiments. Thus, care is required in experiments involving glutaric acid where critical thermodynamic properties are to be determined to ensure equilibrium between solid glutaric acid and other phases is achieved. We report the first infrared spectrum of α form glutaric acid. We also report an infrared spectrum for β form glutaric acid (which agrees with that given in the literature35) and find that only the β form glutaric acid crystallized in our samples. We also ran new DSC experiments for the C5H8O4/H2O binary system at the slow (0.1 K/min) heating rates and report a corrected phase diagram for this system, which is in better agreement with literature data than our previous results had been.26 We also predict the unique ternary eutectic concentration and temperature. Above this temperature at least some liquid will exist, and below this temperature only solid will exist when the sample is in thermodynamic equilibrium. We fitted our final melting/dissolution temperatures to polynomial equations as a function of (NH4)2SO4 and C5H8O4 concentrations for reproducing our data. These fits along with the phase boundary and ternary eutectic data were used to construct the ternary phase diagram. Water activities were determined in the ice primary phase field using the melting point depression method. We found excellent agreement between our calculated water activities and those predicted using the equations of Koop and Zobrist.45 We have also compared our final melting/dissolution temperatures with the predictions of the Extended AIM Aerosol Thermodynamics Model (E-AIM) using both the UNIFAC and fitted activity equations for glutaric acid. We found the E-AIM performed well at predicting the ice melting points in the ice primary phase field. However, the model never predicted glutaric acid as the final dissolving solid in its primary phase field over the concentration range we studied. Thus, we find the E-AIM works well for predicting ice melting in this ternary system in its primary phase field, but gives errant results and cannot be used for predicting glutaric acid dissolution in its primary phase field. It also cannot be used to accurately predict the ice/C5H8O4 phase boundary, ice/(NH4)2SO4 phase boundary, or the ternary eutectic temperature and concentration. However, the E-AIM only claims to model/predict organics at 298.15 K, so this result is not unexpected.

Figure 10. Comparison of our experimental results for final melting/ dissolution points with the predictions of the Extended AIM Aerosol Thermodynamics Model (abbreviated as AIM in the legend) using the fitted activity model for glutaric acid. Symbols indicate the difference between our experimental melting/dissolution points and those predicted by the E-AIM as given in the legend. Solid black circle is our ternary eutectic, and black solid curves represent the phase boundary calculated from fits to our data. Red lines are the phase boundaries predicted by the E-AIM.

We also determined the predictions of the model for final melting/dissolution temperatures using the “standard”47 UNIFAC parameter set in the E-AIM (not plotted in Figure 9). Using these parameters caused the model to perform the same, with average difference from our experimental melting points in the ice region of +0.43/−0.56 K, and a difference in the glutaric acid region of −21.45 K. Again, the large difference is due to the model predicting ice as the final melting phase in the glutaric acid primary phase field. Fitted Activity. Using the fitted activity equation for glutaric acid, we found nearly the same similarities and differences between our experimental melting points and those predicted by the E-AIM as described in the UNIFAC model. The temperature differences are nearly identical across both the ice and glutaric acid primary phase fields as can be seen in Figure 10. The average difference between the E-AIM predicted melting points and our experimental data in the ice region is +0.38/−0.58 K. As with the UNIFAC model, the fitted activity model does not predict glutaric acid to be the final dissolving solid for a ternary sample in the region we found to be the C5H8O4 primary phase field. In this region the E-AIM final melt predictions were 21.3 K lower on average than our experimental glutaric acid dissolution temperatures. The phase boundary and ternary eutectic predictions of the E-AIM using the fitted activity model were similar to those found using the UNIFAC model. The E-AIM predicts the ternary eutectic to be at 20.9/46.6 wt % (NH4)2SO4/C5H8O4 and 242 K, again significantly different from our value.

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ASSOCIATED CONTENT

S Supporting Information *

Table 1S contains the experimentally determined melting/ dissolution points and water activities. This material is available free of charge via the Internet at http://pubs.acs.org.

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SUMMARY We report for the first time the ice melting points, water activities, glutaric acid dissolution points, and ice/glutaric acid phase boundary as a function of concentration in the ternary system: (NH4)2SO4/C5H8O4/H2O. Through a variety of experimental

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 3639

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ACKNOWLEDGMENTS We thank Jason Schroeder who performed some of the DSC and IR experiments. This work was supported by the NSF Atmospheric Chemistry Program (ATM-0803203).

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