Studies of Single Aerosol Particles Containing Malonic Acid, Glutaric

Aug 30, 2010 - The declining sizes of individual aerosol particles over time were followed using elastic Mie scattering or cavity enhanced Raman scatt...
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J. Phys. Chem. A 2010, 114, 10156–10165

Studies of Single Aerosol Particles Containing Malonic Acid, Glutaric Acid, and Their Mixtures with Sodium Chloride. II. Liquid-State Vapor Pressures of the Acids Francis D. Pope,*,† Hai-Jie Tong,‡ Ben J. Dennis-Smither,†,# Paul T. Griffiths,§ Simon L. Clegg,⊥ Jonathan P. Reid,‡ and R. Anthony Cox† Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K., School of Chemistry, UniVersity of Bristol, Cantock’s Close BS8 1TS, U.K., Department of Geography, UniVersity of Cambridge, Downing Place, Cambridge CB2 3EN, U.K., and School of EnVironmental Sciences, UniVersity of East Anglia, Norwich NR34 7TJ, U.K. ReceiVed: June 9, 2010; ReVised Manuscript ReceiVed: August 9, 2010

The vapor pressures of two dicarboxylic acids, malonic acid and glutaric acid, are determined by the measurement of the evaporation rate of the dicarboxylic acids from single levitated particles. Two laboratory methods were used to isolate single particles, an electrodynamic balance and optical tweezers (glutaric acid only). The declining sizes of individual aerosol particles over time were followed using elastic Mie scattering or cavity enhanced Raman scattering. Experiments were conducted over the temperature range of 280-304 K and a range of relative humidities. The subcooled liquid vapor pressures of malonic and glutaric acid at +2.6 +9.6 298.15 K were found to be 6.7-1.2 × 10-4 and 11.2-4.7 × 10-4 Pa, respectively, and the standard enthalpies of vaporization were respectively 141.9 ( 19.9 and 100.8 ( 23.9 kJ mol-1. The vapor pressures of both glutaric acid and malonic acid in single particles composed of mixed inorganic/organic composition were found to be independent of salt concentration within the uncertainty of the measurements. Results are compared with previous laboratory determinations and theoretical predictions. 1. Introduction Understanding the partitioning of semivolatile organic components between the condensed and gas phases is critical for interpreting and predicting atmospheric aerosol composition. Semivolatile organic compounds are generated through the oxidative aging of anthropogenic and biogenic volatile organic compounds and lead to the formation of secondary organic aerosol.1,2 This paper describes an investigation of the temperature-dependent evaporation rates of two semivolatile organic components, malonic acid (MA) and glutaric acid (GA), from binary and ternary aerosols composed of the acids alone or from mixtures of malonic acid and sodium chloride (MA/NaCl) and mixtures of glutaric acid and sodium chloride (GA/NaCl). In particular, we explore the dependence of the evaporation rates on the relative humidity (RH) and inorganic solute mass fraction. Vapor pressure measurements have been made by two independent techniques, using an electrodynamic balance (EDB) and aerosol optical tweezers, and the results from these two approaches are compared. Laboratory studies of the hygroscopicity of these four aerosol types are the subject of a preceding paper in this journal which used the same EDB to levitate single particles.3 2. Previous Determinations of the Volatility of Dicarboxylic Acids Four distinct laboratory methodologies have been used to measure the vapor pressures of the two investigated organic * To whom correspondence should be addressed. Phone: (+44) 01223 746683. E-mail: [email protected]. † Department of Chemistry, University of Cambridge. ‡ University of Bristol. § Department of Geography, University of Cambridge. # Present Address: School of Chemistry, University of Bristol, Cantock’s Close BS8 1TS, U.K. ⊥ University of East Anglia.

acids at atmospherically relevant temperatures, tandem differential mobility analyzers (TDMA),4-9 an electrodynamic balance (EDB),10 a Knudsen effusion mass spectrometer (KEMS),11 and temperature-programmed desorption mass spectrometry (TPDMS).12,13 Tables 1 and 2 summarize the different techniques used, temperature ranges employed, the reported state of the aerosol studied (solid or liquid), and the values of the measured vapor pressures at 298.15 K. In general, agreement between the different studies is better for MA than that for GA. Previous studies investigating solid-phase straight chain dicarboxylic acids have shown that the vapor pressure generally decreases with an increase in the number of carbon atoms present, with an odd-even dependence on the number of carbon atoms present.5 This is considered by Bilde et al. (and references therein) to result from the crystal structure of the dicarboxylic acids; the carbon chains with an odd number of carbons are more torsionally strained and, hence, possess lower sublimation energies.5 Studies of the liquid-phase C3-C6 dicarboxylic acids do not reveal the odd-even alternation because of the lack of formal crystal structure within liquids. Reported vapor pressures of solid GA vary according to the technique used for the measurements. The two TPDMS studies give significantly lower values than the TDMA measurements, as can be seen in Tables 1 and 2. Cappa et al. postulate that the inability of the previous TDMA and TPDMS studies to fully remove solvents resulted in spuriously high vapor pressures.13 The EDB and laser tweezing techniques employed in this study and the EDB study of Zardini et al. do not require the use of these solvents and may provide a useful test of this hypothesis.10 By contrast with the solid GA studies, there is reasonable agreement between vapor pressures determined from the three EDB and TDMA studies for liquid-phase MA.6,7,10 Vapor pressures determined in laboratory studies have been based upon different estimated activity coefficients of the acids

10.1021/jp1052979  2010 American Chemical Society Published on Web 08/30/2010

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TABLE 1: Previous Determinations of MA Vapor Pressure ref

authors

aerosol phase

temperature range/K

laboratory technique

log(psat,liq/p°)

p°298.15 (104 Pa)

5 10 7 6 11

Bilde et al. Zardini et al. Riipinen et al. Koponen et al. Booth et al.

solid liquid liquid liquid solid

290-314 274-300 293-300 299 298-328

TDMA EDB TDMA TDMA KEMS

-4822.0/T + 12.9 -5223.65/T + 14.03 -6396.6/T + 18.14 a -4808.1/T + 12.89

5.3 3.2 4.9 a 5.9

a

Insufficient data to calculate regression line.

TABLE 2: Previous Determinations of GA Vapor Pressure ref

authors

aerosol phase

temperature range/K

laboratory technique

log(psat,liq/p°)

p°298.15 (10-4 Pa)

8 4 5 12 13 6 11 9

Tao and McMurray Bilde and Pandis Bilde et al. Chattopadhyay and Ziemann Cappa et al. Koponen et al. Booth et al. Salo et al.

solid solid solid solid solid liquid solid solid

283-323 290-300 296 276-294 313-349 298-301 298-328 298-318

TDMA TDMA TDMA TPDMS TPDMS TDMA KEMS TDMA

-5347/T + 14.95 -3510/T + 8.65 a -6909.6/T + 19.7 -6999.7/T + 19.57 -5534.3/T + 15.41 -6428.2/T + 18.18 -5275.9/T + 14.62

10.4 7.5 a a 1.2 7.1 4.4 8.5

a

Insufficient data to calculate regression line.

in the liquid phase. The choice of activity coefficient is a key factor in determining the absolute value of the reported vapor pressure. For example, within the work of Koponen et al., the use of two different activity models (Van Laar and UNIFAC) resulted in a factor of 40 difference between the two calculated subcooled liquid vapor pressures of MA at 299 K.6 There has been only one previous reported study investigating whether the presence of NaCl within solution affects the vapor pressure of dicarboxylic acids. Dissolved salts can affect the equilibrium between the aqueous and vapor phases of the volatile components via both their effect on the concentration of the acid and its activity coefficient. Zardini et al. suggest that the presence of NaCl reduces the volatility of succinic acid within a ternary succinic acid/NaCl/water aerosol.14 3. Treatment of the Evaporation Dynamics of Mixed Organic/Inorganic/Aqueous Aerosols Semivolatile atmospheric aerosol components possess sufficiently high vapor pressures to undergo temperature-dependent evaporative loss from the condensed phase into the gas phase. The vapor pressure of a substance is related to temperature via the Clausius-Clapeyron equation, which is given by eq E1, where ∆Hvap is the enthalpy of vaporization, R is the gas constant, and p1 and p2 are the pressures at temperatures T1 and T2. Significant increases in vapor pressure can result from minor increases in temperature.

()

(

∆Hvap 1 p2 1 ln ) p1 R T1 T2

)

i. Di,air (m2 s-1) is the diffusion coefficient for volatile species i in the air carrier gas, F (kg m-3) is the density of the solution forming the particle at the appropriate composition, pi,r (N m-2) is the vapor pressure in equilibrium with the surface, and pi,∞ (N m-2) is the partial pressure at infinite distance away from the surface.

dmi 4πrMiDi,air ) (pi,∞ - pi,r) dt RT

(E2)

The influence of the Kelvin effect on vapor pressure can be ignored in this study because the particles investigated are much greater than 100 nm in radius.16 Ideal gas behavior is assumed for the evaporating acids. Note that pi,∞ can be assumed to be 0 because the gaseous environment surrounding the particle is continually flushed with humidified air, thus removing the gasphase organic acid molecules. The diffusion coefficients for MA and GA in N2 were calculated using the equations of Chapman and Enskog.17 The Lennard-Jones parameters for MA and GA were taken from Bilde et al.5 At 294 K, the diffusion coefficients for MA and GA in N2 were calculated to be 0.0704 and 0.0596 cm2 s-1. The mass of the volatile component in the particle is given by eq E3, where Fi (dimensionless) is the mass fraction of the volatile acid component within the particle.

4 mi ) πr3F · Fi 3

(E1)

(E3)

The differential version of E3 is given in E4 In addition to being a function of temperature, the equilibrium vapor pressure of an acid over a liquid phase is also a function of the concentration of the acid and the activity coefficient. This study uses the approach of Ray et al. to determine the isothermal, quasi-steady-state evaporation of a spherical aerosol droplet from the observed mass flux. The vapor pressure can be calculated from the evaporation rate.15 The expression for the rate of change of mass with time is given by eq E2, where mi (kg) is the mass of the volatile component within the particle (i.e., the dicarboxylic acid), r (m) is the particle radius, t (s) is the time, and Mi (kg mol-1) is the molar mass of volatile species

(

)

dFi 3 dmi dF 4π dr3 ) FFi + r3Fi + rF dt 3 dt dt dt

(E4)

For the binary systems composed of the organic acid and water, the solution density and mass fraction of the volatile acid remain constant throughout the evaporation at a fixed RH and temperature. The composition of the particle remains constant, as determined by the hygroscopicity of the particle and the RH. The binary solution density is approximated using eq E5

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F)∑ i

( ) xi · Mi xi · Vm,i

Pope et al.

(E5)

where xi (dimensionless) is the mole fraction of component i and Vm,i (m3 mol-1) is the molar volume of component i. For the ternary systems composed of the organic acid, sodium chloride, and water, the situation is more complicated. The evaporation of the organic acid causes a change in the acid mass fraction over time and thus a change in composition, thereby leading to a change in the solution density. Therefore, all three differential terms in eq E4 need to be considered. Only if the evaporation of the organic acid is negligible can one assume that the particle density and acid mass fraction remain constant. To account for the changing density and organic mass fraction in the ternary systems, the initial particle composition must be known. This is determined by the initial organic acid to NaCl mass ratio within the particle and the water partitioned to the solution droplet at the activity set by the surrounding RH. The measured time-dependent radius, and hence volume, of the particle can then be converted to the time-dependent radius, and volume, of the organic acid with its associated water fraction, assuming the Zdanovskii, Stokes, and Robinson relationship (ZSR).18 The volume of water associated with the organic/ inorganic system is assumed to be equal to the sum of water volumes associated with the individual organic and inorganic systems with the appropriate solute masses. For a particular RH, the mass of the organic acid within the total water and organic acid water volume can be calculated from knowledge of the density of the binary organic acid and water mixture, using eq E5, and the mass fraction of the organic acid within the binary system. Within the laboratory experiments described in this account, a failure to account for the changing density and organic fraction in the ternary systems over time was found to produce a non-negligible error of up to a factor of 2 in the particle vapor pressure and must be explicitly included in the analysis. For a one-component system (e.g., a pure organic compound with no associated water), the vapor pressure of the pure liquid acid (p°Org) is given by pi,r in eq E2. In a system containing more than one species, such as aqueous MA and GA particles, the equilibrium vapor pressure of the organic acid above the particle (pi,r) is related to the vapor pressure of the pure liquid acid (p°Org) by eq E6

pi,r ) poOrgxOrgγOrg

(E6)

in which xOrg (dimensionless) and γOrg (dimensionless) are the mole fraction of the organic species in solution and the mole fraction activity coefficient relative to the pure liquid reference state, respectively. The RH-dependent mole fraction of the solute in the aqueous particle, expressed as aerosol hygroscopicity, was the subject of the previous paper.3 In addition to the organic mole fraction, the activity coefficient of the organic component is required to obtain the organic vapor pressure. Three different sets of activity coefficients are used, fitted values, standard UNIFAC, and Peng et al. adapted UNIFAC.19 Clegg and Seinfeld derived a functional form from a critical evaluation of all available laboratory data from before 2006.20 UNIFAC is a structure-based model for estimating activity coefficients in fluid mixtures of organic compounds which can also include water. The UNIFAC approach is used here with both the standard set of coefficients21-23 and with the modified coefficients derived by Peng et al. for the interactions between water (H2O), carboxylic acid (COOH), and hydroxyl (OH) moieties. These

Figure 1. Top-view schematic diagram of the optical design within the EDB system.

were obtained by fitting UNIFAC parameters to the hygroscopicity data from an EDB study which investigated the water uptake of several dicarboxylic acids (oxalic, malonic, succinic, and glutaric) and multifunctional acids (citric, malic, and tartaric).19 In this work, the activity coefficients were calculated for all three treatments from the Extended Aerosol Inorganic Model (E-AIM). E-AIM is a community model for calculating gas/ liquid/solid partitioning in aerosol systems containing inorganic and organic components and water and solute and solvent activities in aqueous solutions and liquid mixtures.24,25 The activity coefficients of the acids in aqueous mixtures with NaCl were assumed to be the same, on a molality basis, as those in pure aqueous solutions containing the same amounts of water and acid. The total solute mole fraction in the aerosol droplets at each experimental RH was calculated using the method described by Clegg et al.26 Here, the water activity of a solution containing two solutes i is assumed to be equal to the multiple aw(1) × aw(2), where aw(i) is the water activity of a solution containing i only, with the amount of water present in the mixture. (Note that in the work of Clegg et al., the same relationship is expressed in terms of the osmotic coefficient.) 4. Experiments Malonic and glutaric acids and sodium chloride are all white crystalline solids within the temperature ranges investigated in this study. The molecular formulas, molar masses (g mol-1), and densities (g cm-3) of the three crystalline solids are (HOOC)CH2(COOH), 104.03 g mol-1, and 1.619 g cm-3 (malonic acid); (HOOC)(CH2)3(COOH), 132.12 g mol-1, and 1.424 cm-3 (glutaric acid); and NaCl, 58.44 g mol-1, and 2.16 g cm-3 (sodium chloride). Samples of these chemicals used in the experiments were puriss grade (g99%) from Sigma-Aldrich and were used without purification. Water was HPLC grade. 4.1. Electrodynamic Balance. An EDB can be used to levitate single charged aerosol particles in an atmosphere of controlled temperature and RH, as described in Paper I.3,27 The optical design of the EDB system is shown in Figure 1. A continuous-wave HeNe laser (Thorlabs HRP170), operating at 632.8 nm, is directed at the levitated particle. The resulting

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fringe pattern of the scattered light was used to estimate the particle size. The light scattered by spherical droplets possessing a diameter comparable to the wavelength of the probe radiation is governed by electrodynamics, and a solution to the relevant equations was first given by Mie.28 Glantschnig and Chen used a geometrical optics method to approximate the results of Mie for nonabsorbing particles. This can be used to accurately estimate the size of particles, in a computationally inexpensive manner, from the angular dependence of the light scattering patterns.29 The angular separation between successive fringes in the light scattering is given by eq E7.

∆θ =

(

2π θ θ cos + sin / x 2 2



1 + m2 - 2m cos

θ 2

)

-1

(E7)

where the size parameter x (dimensionless) is equal to 2πr/λ, with r (m) being the radius of the particle and λ (m) the wavelength of the incoming radiation. ∆θ (radians) is the angular spacing between successive peaks of the Mie spectrum, and m (dimensionless) is the real part of the relative index of refraction of the particle to the medium. The scattered light is collected, in the approximate angular range of 38-51° with respect to the path of the incident laser beam, by a photodiode array (Hamamatsu H5783). The scattered radiation exiting the EDB is collimated onto the photodiode array using a lens with a focal length matched to the angle subtended by the radiation from the particle through the viewport. This technique assumes that the particle is a point source. To optimize the observed signal, the light exiting the EDB was passed through a spatial filter, removing the majority of off-axis light. The exact angular range measured is determined by calibration using three different sized lime soda spheres, with diameters equal to 17.3 ( 1.4, 30.1 ( 2.1, and 40.6 ( 2.8 µm and a refractive index (m) of 1.51. The errors represent the stated standard deviations on the sphere diameters as supplied by the manufacturer, Duke Scientific (NIST Traceable). Lime soda spheres are used because they have calibrated radii, a known refractive index, are involatile, and are not hygroscopic. Therefore, the refractive index and radius of a particle is fixed. The calibrated particle spectra are analyzed using the MiePlot software, to calibrate the angle subtended by the scattered radiation onto a photodiode array.30 The solutions of eq E7 indicate that the angular separation between successive Mie peaks is not uniform. However, over the small angular range measured, the average peak-to-peak separation is sufficiently similar that the average value can be used to determine particle size. The successful use of the average peak-to-peak values to obtain the particle radius is demonstrated in Figure 2. Vapor pressure measurements of MA in MA/H2O and MA/ NaCl/H2O droplets and GA in GA/H2O and GA/NaCl/H2O droplets were conducted. Several different RHs were used for each aerosol study in order to obtain a variety of initial dicarboxylic acid mole fractions. All particles were in the subcooled liquid phase. The low vapor pressures of the organic aerosols necessitated long experimental time scales (>12 h) to retrieve statistically valid estimates of dmi/dt from eq E2. An example of the decrease in particle radius and organic acid mass due to evaporation is shown in Figure 3, which was recorded for a MA particle at 302 K and near uniform RH.

Figure 2. Measurement of particle radius by Mie elastic scattering. Symbols: open circles, laboratory measurements with calibrated radius lime soda spheres; the x-error represents the specified uncertainties within the sphere radii, and the y-error represents the 1σ experimental uncertainties. The line represents the theoretical calculation given by eq E7.

Figure 3. Example laboratory data showing the evaporation of a MA particle at 302 K in the EDB apparatus.

To improve the signal-to-noise ratio in the recorded scattering spectra and to allow for the automatic acquisition of the average peak-to-peak angular spacing, each Mie scatter spectrum was processed as follows. First, a low-pass filter was used to remove high-frequency noise. Next, the peak positions were logged, and the average peak-to-peak separation was calculated. Data were only used if the ratio of the standard deviation of the peak-topeak separation to the separation was below 10%. This criterion ensured that spectra containing peaks below the experimental noise level, and hence experimentally indiscernible, were omitted. The EDB cell was thermally controlled by use of a chillercirculator system (Julabo F32) that pumps coolant through veins within the EDB walls. In addition, the water bubbler and laboratory air conditioning system were temperature-matched to the EDB to minimize temperature fluctuations in the experiment. The temperatures of the cell and exhaust were measured by use of Pt100 sensors. The volume of the EDB chamber was ∼500 cm3, and the total gas flow was 100 sccm; therefore, the average residence time of gas within the EDB chamber was ∼5 min. For individual experiments, the RH was maintained at the desired set point with (1% variation.

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Figure 4. Schematic diagram of the optical tweezers system.

4.2. Optical Tweezers. The optical tweezers system combined with Raman spectroscopy and brightfield microscopy has been described in detail elsewhere31,32 and will be only briefly summarized here. Figure 4 shows a schematic diagram of the experimental system. Laser light generated by a Nd:YVO4 laser (532 nm) passes through a 100× oil immersion objective (numerical aperture of 1.25) to form a tight focus ∼40 µm above a thin glass coverslip. Single droplets are captured at random from a cloud of aerosol that is generated using a medical nebulizer and introduced into the cell. As a droplet passes close to the laser focus, it experiences an attractive gradient force that pulls it toward the region of highest intensity. It has been shown that aerosol droplets with diameters of 4-20 µm can be trapped by the optical tweezers using laser powers of 5-15 mW. A blue LED provides illumination for microscopy. These brightfield images are used to observe the morphology of the trapped droplet in real time, in this study allowing the confirmation of the persistence of the liquid phase under all conditions. The back-scattered Raman signal from the droplet is collected using a spectrograph equipped with a 1200 grooves/mm grating and a CCD array of 1024 × 256 pixels. The changing spectra of the droplet are monitored in real time with a time resolution of 1s. While the spontaneous Raman spectrum can be used to confirm the presence of the organic component in the droplet and estimate the solute concentration, stimulated Raman scattering, occurring at wavelengths commensurate with whispering gallery modes (WGMs), is used to estimate the size of the droplet. By comparing the fingerprint of wavelengths at which WGMs are observed to enhance the Raman scattering with predictions from the Mie scattering theory,33 the droplet size can be determined with nanometer accuracy. The refractive indices of MA/H2O or MA/NaCl/H2O solutions with different solute concentrations and varying solute mass ratios were measured at λ ) 589 nm using a Palm Abbe PA203 digital refractometer (MISCO, U.S.A.) and at a constant temperature of 298.15 ( 1 K. Each refractive index value is determined from an average of three individual measurements. A polynomial fit to the data is used to estimate the variation in refractive index with droplet size and, thus, the solution composition in the manner described previously from knowledge of the initial droplet composition and size immediately upon capture.31,32 This allows Mie predictions to be made of the WGM wavelengths with variation in trial particle size. Figure 5 shows example data obtained from the laser tweezers technique. The RH in the cell is regulated by adjusting the flow ratio of dry nitrogen gas and humidified nitrogen gas. The mass flow rate of each flow is controlled using needle valves and displayed by mass flow meters (Bronkhurst, U.K.). Two capacitance

Figure 5. Example laboratory data showing the evaporation of a MA particle at 298 K in the laser tweezers apparatus.

probes are used to monitor the RH before and after the cell. Once a droplet (MA/H2O or MA/NaCl/H2O) is trapped, the RH in the cell is held at the same value to within (0.5% for more than 12 h. The temperature in the lab was constant within (1 °C for each experiment. The volume of the laser tweezers chamber was 7.7 cm3, and the total gas flow was 100 sccm; therefore, the average residence time of gas within the laser tweezers chamber was ∼4.6 s. 5. Results The calculated pure liquid vapor pressures of GA and MA in the four aqueous aerosol systems are shown in Figure 6. The EDB and laser tweezing methods were used to study both the MA and MA/NaCl systems. Only the EDB method was used to study the GA and GA/NaCl particles. The vapor pressures shown in the figure were obtained using the Clegg and Seinfeld fitted activity equation E6.20 Measurements of the GA and MA vapor pressures of the organic acid/NaCl/water aerosols are the first measurements for these ternary systems. The data obtained using the laser tweezers contain greater scatter than the corresponding EDB measurements. Two possibilities for the greater scatter are poorer temperature control in the aerosol chamber and a nonzero value for pi,∞ due to possible wall contamination. Table 3 lists the estimated ∆Hvap and p°298.15 for the four systems based upon the three different calculations of the organic component activity coefficient described previously. The large uncertainties associated with the values for p°298.15 recorded by the EDB is a consequence of estimating the error on a limited set of observations using the 95% confidence limits obtained when fitting the laboratory data to the Clausius-Clapeyron equation. The laser tweezers data is better constrained because the vapor pressure was only measured at 298 ( 1 K. The consequences of using the different treatments of the activity coefficients for the MA and GA vapor pressures at 298.15 K are shown in Figure 7 and are quite large. The ratios of the MA and GA vapor pressures at 298.15 K, using respectively the standard UNIFAC method, Peng adapted UNIFAC method, and the Clegg and Seinfeld fitted activity equation, are 1.00:1.43:0.85 and 1.00:1.08:0.95. In the previous paper investigating the hygroscopicity of these systems, best agreement between laboratory results and model predictions was achieved using the Peng adapted UNIFAC method19 or the fitted activity coefficient equations of Clegg and Seinfeld.20 Of the

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J. Phys. Chem. A, Vol. 114, No. 37, 2010 10161 thalpies for vaporization of MA and GA are 141.9 ( 19.9 and 100.8 ( 23.9 kJ mol-1, respectively. 6. Comparisons with Other Data The previous determinations of the solid and liquid vapor pressures of MA and GA are shown in Figures 8 and 9. The vapor pressures of subcooled liquid acids are necessarily higher than the vapor pressures of the solids, but the results of previous studies are not always consistent with this. For example, studies of solid-phase MA by Bilde et al.5 and Booth et al.11 report greater vapor pressures than the liquid-phase vapor pressures of Riipinen et al.7 and Zardini et al.10 At temperatures below 295 K, the solid-phase GA studies of both Bilde and Pandis4 and Tao and McMurray8 have greater vapor pressures than the liquid-phase vapor pressures given in the Koponen et al. study.6 The liquid-phase vapor pressures of MA and GA at 298.15 K derived in this study are compared with previous laboratory determinations in Figures 10 and 11. Conversion between solid and liquid vapor pressures is achieved via knowledge of the heat of fusion (∆Hfus) and melting temperature (Tm) of the investigated compound. If the heat of fusion is considered to be independent of temperature, the ratio of solid and liquid vapor pressures, at 298.15 K, is given by eq E8. Equation E9 gives the relationship between the two vapor pressures for the case where the heat of fusion is dependent on temperature and includes additional terms containing the difference between the heat capacities of the solid and liquid phases (∆Cp,sl).34

ln Figure 6. (1) Temperature-dependent pure liquid vapor pressure of GA. Symbols: filled circles, EDB data for GA in the GA/H2O system; open circles, EDB data for GA in the GA/NaCl/H2O system. Lines: the black line is the least-squares fit, and the gray lines are the 95% confidence limits for the fit. (2) Temperature-dependent pure liquid vapor pressure of MA. Symbols: filled black circles, EDB data for MA in the MA/H2O system; open black circles, EDB data for MA in the MA/NaCl/H2O system; filled gray squares, laser tweezers data for MA in the MA/H2O system; open gray squares, laser tweezers data for MA in the MA/NaCl/H2O system. Lines: the black line is the least-squares fit regression line, and the gray lines are the 95% confidence limits for the fit. The Peng adapted UNIFAC fitted activity coefficient was used in eq E6 to obtain the plotted vapor pressures.19

two, the Peng adapted UNIFAC calculations of activity coefficients are likely to be more accurate on the basis that the parameters have been modified to better represent the properties of aqueous dicarboxylic acid solutions. Vapor pressures based on the modified UNIFAC parameters may also be preferred over those derived using the equations of Clegg and Seinfeld because the fit of the equations was not constrained for concentrations between the RH of crystallization and the pure liquid acid. Within the statistical errors, it was not possible to determine the dependence of the MA and GA vapor pressures upon salt mass fraction because this was smaller than the uncertainties in the measurements. The combination of the binary and ternary MA and GA data sets, from both the EDB and laser tweezers experiments, results in improved confidence limits for the vapor pressure at 298.15 K for both systems. Therefore, the combined data sets form the basis of our recommended vapor pressures using the Peng adapted UNIFAC parameters, which give vapor +2.6 pressures at 298.15 K for MA and GA of 6.7-1.2 × 10-4 and -4 -2 +9.6 11.2-4.7 × 10 N m , respectively. The recommended en-

ln

(

(

pliq ∆Hfus 1 1 ) psol R T Tm

)

(

)

(E8)

)

pliq ∆Hfus Tm ∆Cp,sl Tm ) -1 -1 + psol RTm T R T ∆Cp,sl Tm ln R T

(E9)

For MA and GA, the ratios of liquid to solid vapor pressures are respectively 7.6 and 5.6 when using eq E8 and 4.6 and 4.1 when using eq E9. The melting points,11 enthalpy of fusion,11 and change in heat capacity upon melting35 used in eqs E8 and E9 for MA and GA were, respectively, 406 K, 18.7 kJ mol-1, and 77.3 J mol-1K-1 and 369 K, 22.0 kJ mol-1, and 105.3 J mol-1K-1. Figure 10 indicates that at 298.15 K, there is reasonable agreement between the three studies of MA in the liquid phase and also good agreement between the two solid-phase studies. However, when the vapor pressures of the liquid acids are calculated from those of the solids (from the studies of Bilde et al.5 and Booth et al.11) using eq E8 or E9, the agreement with the remaining data is poor in both cases. The Bilde et al. measurements were performed at a RH of 6%, and the particles were generated from an aqueous system. The MA hygroscopicity results from the previous paper of this study,3 and other previous hygroscopicity studies, indicate that MA would be in the liquid state at 6% RH and room temperature. It is therefore likely that the Bilde et al. study was investigating the liquidphase vapor pressure of MA, at least in the studies above 295 K. This suggestion is further enhanced by the agreement between the attributed solid-phase vapor pressure of Bilde et al. with the other three liquid-phase vapor pressure measurements. Within the Booth et al. study, there is no ambiguity in the KEMS technique as to whether the solid or liquid phase is

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TABLE 3: Thermodynamic Parameters Calculated from the Laboratory-Derived Temperature-Dependent Vapor Pressure Data evaporating species

system studied

method

MA

MA/H2O

EDB

MA

MA/H2O

laser tweezers

MA

MA/NaCl/H2O

EDB

MA

MA/NaCl/H2O

laser tweezers

MA

MA/H2O and MA/NaCl/H2O

EDB

MA

MA/H2O and MA/NaCl/H2O

laser tweezers

GA

GA/H2O

EDB

GA

GA/NaCl/H2O

EDB

GA

GA/H2O and GA/NaCl/H2O

EDB

activity calculation

∆Hvap (kJ mol-1)

fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19 fitted activity20 UNIFAC (standard)22 UNIFAC (Peng)19

133 ( 15 129 ( 16 137 ( 16 b b b 215 ( 75 215 ( 57 159 ( 54 b b b 144 ( 19 140 ( 18 140 ( 15 b b b 151 ( 32 153 ( 33 146 ( 23 89 ( 6 63 ( 39 65 ( 8 102 ( 28 105 ( 28 101 ( 24

p°298.15 (10-4 Pa) +3.4 a 7.3-1.6 +10.1 a 11.0-6.2 +4.4 a 9.0-2.1 4.7 ( 2.9c 8.7 ( 5.3c 4.5 ( 2.8c +3.4 a 4.9-1.6 +9.9 a 4.9-2.8 +13.1 a 7.7-4.4 6.3 ( 5.8c 9.6 ( 7.0c 5.7 ( 5.0c +3.1 a 6.2-1.5 +2.8 a 6.0-1.3 +3.9 a 8.5-1.2 5.9 ( 5.1c 9.3 ( 6.3c 5.4 ( 4.4c +15.6 a 9.4-5.2 +19.1 a 11.0-6.2 +11.8 a 10.8-4.7 +19.8 a 11.2-6.8 +38.50 a 10.1-10.1 +36.5 a 12.8-9.3 +11.4 a 9.9-4.7 +10.9 a 10.4-4.9 +10.3 a 11.2-4.6

a The plus and minus errors are the upper and lower confidence limits from the linear fit to the Clausius-Clapeyron equation. b The laser tweezers data set had an insufficient range of temperatures with which to assess the enthalpy of vaporization. c The errors are the 1σ standard deviation from the mean value.

Figure 7. Calculated vapor pressures for MA (white) and GA (gray) at 298.15 K using three different determinations for the organic species activity coefficient, UNIFAC (containing the additional Peng et al. parametrization),19 UNIFAC with the standard parametrization,21-23 and the fitted activity equation of Clegg and Seinfeld.20 The error bars represent the upper and lower 95% confidence limits. The data are taken from the EDB-derived data set. The MA and GA data use both the binary and ternary particle data sets.

Figure 8. Laboratory determination of the temperature-dependent vapor pressure of MA. The lines are constructed from the parametrizations given in Table 1. The phase investigated in the study is indicated in brackets. Lines: black solid, this study (liquid); gray solid, Zardini et al. (liquid);10 gray dot, Riipinen et al. (liquid);7 black dot, Bilde et al. (solid);5 gray dash-dot, Booth et al. (solid).11 The data from this study used the Peng adapted UNIFAC activity coefficients in eq E6.19

being probed, and therefore, it is not possible to reconcile this measurement with the previous liquid-phase measurements using eqs E8 and E9. The average liquid-phase vapor pressure of MA at 298.15 K from the three studies of the liquid phase, this study, Riipinen et al., and Zardini et al.7,10 is (4.9 ( 1.8) × 10-4 N m-2. If the Bilde et al. study is included in the average liquid-phase vapor pressure, the value becomes (5.03 ( 1.4) × 10-4 N m-2.5 The average solid-phase vapor pressure, at 298.15 K, from the two

studies of the solid acids, Bilde et al. and Booth et al.,4,11 is (5.5 ( 0.3) × 10-4 N m-2. These vapor pressures are the same within the experimental uncertainty and imply an enthalpy of fusion of 0 at 298.15 K, which cannot be correct. If the average value for the three liquid-phase measurements of the vapor pressure is assumed to be accurate, then an enthalpy of fusion of 18.7 kJ mol-1 measured by Booth et al.11 suggests a solid vapor pressure at 298 K of ∼6.4 × 10-5 N m-2 (a factor of ∼7.7 lower than that of the liquid).

Single Aerosol Particles Containing Acids and NaCl

Figure 9. Laboratory determinations of the temperature-dependent vapor pressure of GA. The lines are constructed from the parametrizations given in Table 2. The phase investigated in the study is indicated in brackets. Lines: black solid, this study (liquid); gray solid, Koponen et al. (liquid);6 gray dash, Tao and McMurray (solid);8 black dot, Bilde and Pandis (solid);4 gray dot, Chattopahyay and Ziemann (solid);12 black dash-dot, Cappa et al. (solid);13 black dash, Salo et al. (solid);9 gray dash-dot, Booth et al. (solid).11 The Koponen et al. data are shown with the version of the data derived with the standard UNIFAC model of the activity coefficient within eq E6.22 The data from this study used the Peng adapted UNIFAC activity coefficients in eq E6.19

Figure 10. Comparison of the different laboratory studies of both the subcooled liquid and solid vapor pressures of MA at 298.15 K. Symbols: open circles, measured vapor pressure; solid squares, conversion of solid to liquid vapor pressure using eq E8; open squares, conversion of solid to liquid vapor pressure using eq E7. The liquid-phase studies require no conversion factors, and therefore, only one symbol is required. The Koponen et al. data are taken at 299 K. The error bar shown on the data from this study represents the upper and lower 95% confidence limits. The error bars on the average liquid value represents 1σ standard deviation. No estimate of error is given in the Koponen et al. paper.

The agreement between different studies of the vapor pressures of GA is poorer than that found for MA, despite the higher vapor pressures. The greater range of values for the liquid-phase vapor pressures (either measured or calculated using eqs E7 and E8) may reflect the larger number of experimental techniques used. There is reasonable agreement between this study and the other liquid-phase study of Koponen et al.6 The average of the liquid vapor pressures at 298.15 K from the two studies is (9.1 ( 2.9) × 10-4 N m-2.6 The only solid-phase study which yields

J. Phys. Chem. A, Vol. 114, No. 37, 2010 10163

Figure 11. Comparison of different laboratory studies of both the subcooled liquid and solid vapor pressures of GA at 298.15 K. Symbols: open circles, measured vapor pressure; solid squares, conversion of solid to liquid vapor pressure using eq E8; open circles, conversion of solid to liquid vapor pressure using eq E7. The liquid-phase studies require no conversion factors, and therefore, only one symbol is required. The Koponen et al. data are taken at 299 K. The error bar shown on the data from this study represents the upper and lower 95% confidence limits. The error bars on the average values represent a 1σ standard deviation. No estimate of error is given in the Koponen et al. and the Chattopadhyay and Ziemann papers.

similar liquid vapor pressures, via eqs E8 and E9, is that of Cappa et al.13 For studies of aqueous solutions of the acids, the use of different models of the activity coefficient in eq E6 will result in different estimates of the pure liquid vapor pressures of the acids. Zardini et al.,10 in their study of aqueous MA, used activity coefficients from the Peng adaptation of the UNIFAC model,19 while Riipinen et al.7 used the standard UNIFAC model.22 The study of GA in the aqueous phase by Koponen et al.6 used both the standard UNIFAC model22 and the Van Laar equation.34 Calculations show that the use of the same activity coefficient model in the studies of the aqueous acid would yield vapor pressures that agree more closely with the results of this work, except in the case of Zardini et al., which already used the same activity coefficient model. The value of Zardini et al. is approximately half of the value derived in this study at 298.15 K. To compare the MA liquid vapor pressures obtained from different laboratory methodologies, the use of the same activity coefficient is required. When the Peng adapted UNIFAC activity coefficient is used for all studies, the agreement between this work and the studies of Riipinen et al. and Koponen et al. improves.6,7 At 298.15 K, the vapor pressures of the Koponen et al. and Riipinen et al. studies agree within 30 and 5% of the value derived in this study, respectively. However, the large associated errors present in this study and the other studies probably make this agreement fortuitous. Cappa et al. suggested that the use of solvents to introduce aerosols into the experimental apparatus, could introduce error to the measured solid-phase vapor pressures.13 This suggestion is given more credibility by the reasonable agreement found between the liquid-phase GA vapor pressures derived from the nonsolvent using solid-phase TPDMS study and the liquid-phase studies (including this study). There is a much poorer agreement

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Pope et al.

TABLE 4: Model Predictions of the Enthalpy of Vaporization and Vapor Pressure at 298.15 K for MA and GA method 136

method 238

method 339

molecule

Bpt/K

Bpt ref.

∆Hvap/ kJ mol-1

p°298.15/ N m-2

Bpt/K

Bpt ref.

∆Hvap/ kJ mol-1

p°298.15/ N m-2

Bpt/K

Bpt ref.

∆Hvap/ kJ mol-1

p°298.15/ N m-2

MA GA

544.6 573.8

37 37

101.9 110.2

4.9 × 10-3 1.3 × 10-3

544.6 573.8

37 37

82.6 94.5

1.7 × 10-1 1.3 × 10-2

537.3 569.0

40 40

79.1 84.7

3.5 × 10-1 6.5 × 10-2

between the derived vapor pressures obtained from the solidphase studies that used solvent and those from the liquid-phase studies. The calculated ∆Hvap values derived from this study, for both MA and GA, are similar to previous liquid-phase vapor pressure measurements and agree within stated uncertainties.6,7,10 7. Comparison with Theoretical Predictions The laboratory-derived vapor pressures are compared to three structure-based estimators of vapor pressure. These are the vapor pressure predictor of Moller et al. combined with boiling point estimator of Nannoolal et al.,36,37 both the vapor pressure and boiling point estimators of Nannoolal et al.,37,38 and the vapor pressure equation of Myrdal and Yalkowsky39,40 combined with the boiling point predictor of Stein and Brown.31 (The estimation of the normal boiling point yields the temperature at which the vapor pressure of the liquid compound is 1 atm.) In general, estimates of boiling points and other thermodynamic properties are often poor for small multifunctional compounds, especially when two or more functional groups can interact with each other.41 This is the case for the two investigated dicarboxylic acids, and it introduces an uncertainty into the predictions of vapor pressure. There are no experimental measurements of boiling points of the two acids because solid malonic acid sublimes and glutaric acid decomposes upon heating.42 The methods of Nannoolal et al. and Stein and Brown yield estimated boiling points of 544.6 and 537.3 K for MA and 573.8 and 569.0 K for GA, respectively. The predicted ∆Hvap and p°298.15 from all three methods, using the predicted boiling points, are given in Table 4. The predicted vapor pressures do not agree well with the experimental results and are generally much higher. Only the vapor pressure of GA from the vapor pressure equation of Moller et al. agrees within the 1σ error of this laboratory study.36 The greater proximity of the two carboxylic groups within MA compared to that in GA, leading to interactions which affect the vapor pressure, may explain the poorer model results. At present, the use of these vapor pressure predictors is unsatisfactory for small dicarboxylic acids such as MA and GA. 8. Conclusions The liquid-phase vapor pressures of MA and GA have been investigated at different RHs and temperatures with two different laboratory techniques. The vapor pressure of the pure liquid organic acid is the same, within experimental uncertainty, in the presence or absence of NaCl. If the experimental uncertainty associated with the vapor pressure at 298.15 K is assumed to be due to the NaCl affecting the vapor pressure of the organic acids, then the following limits can be given: NaCl could be responsible for a maximum vapor increase of 39 and 31% and a maximum decrease in vapor pressure of 18 and 26% for MA and GA, respectively. The liquid-phase vapor pressures of the subcooled MA and GA aerosols, measured in this experiment, could be reconciled with most of the previous liquid-phase laboratory determinations within the large statistical errors.

However, at present, it is difficult to reconcile most of the solidphase studies with this liquid-phase study. The use of the three different methods of estimating the activity coefficients of the acids resulted in differences in calculated vapor pressures, for example, ∼40% for MA, between the fitted equation of Clegg and Seinfeld and the Peng extended UNIFAC activity model compared to the standard UNIFAC activity model. The Clegg and Seinfeld fitted activity model20 and UNIFAC model using the coefficients of Peng et al.19 both represent the water activities of MA and GA solutions satisfactorily. However, UNIFAC (using the Peng et al. coefficients) yields vapor pressures that are ∼40 (for MA) and 10% (for GA) higher than those derived using the Clegg and Seinfeld fitted activities for the data from the EDB work within this study.20 Of the two models, it is likely that UNIFAC using the Peng et al. coefficients is to be preferred for calculations that extend to the pure liquid phase, which is the case here because the activity coefficients in the aqueous aerosols are related to a (defined) value of unity for the pure liquid. Therefore, the Peng adapted UNIFAC coefficients are recommended for future studies investigating the vapor pressures of dicarboxylic acids. Theoretical predictors of vapor pressure generally failed to reproduce the observed vapor pressures, with the models giving consistently higher values than the average of all of the liquidphase laboratory studies. The boiling point model of Nannoolal et al.37 combined with the vapor pressure model of Moller et al.36 gave the best results when compared to the average laboratory studies. They predicted the MA and GA vapor pressures, at 298.15 K, to be 544 and 16% greater than the measured values, respectively. Further work that explicitly models the interaction of two closely located carboxylic acid moieties within dicarboxylic acids would clearly be beneficial for the atmospheric community because of the preponderance of dicarboxylic acids within tropospheric aerosol.43 Acknowledgment. The EDB is an instrument of the Laboratory for Global Marine and Atmospheric Chemistry, University of East Anglia, and was set up and run at the Department of Chemistry, University of Cambridge. This collaborative project was funded by the NERC thematic program APPRAISE. B.J.D.S. thanks the corporate associates scheme for funding for his summer studentship. J.P.R. acknowledges the support of the EPSRC through the award of a Leadership Fellowship. We thank Dr. Murray Booth from the University of Manchester for access to his unpublished results and a stimulating discussion. References and Notes (1) Po¨schl, U. Angew. Chem., Int. Ed. 2005, 44, 7520. (2) Kanakidou, M.; Seinfeld, J. H.; Pandis, S. N.; Barnes, I.; Dentener, F. J.; Facchini, M. C.; Van Dingenen, R.; Ervens, B.; Nenes, A.; Nielson, C. J.; Swietlicki, E.; Putaud, J. P.; Balkanski, Y.; Fuzzi, S.; Horth, J.; Moortgat, G. K.; Winterhalter, R.; Myhre, C. E. L.; Tsigaridis, K.; Vignati, E.; Stephanou, E. G.; Wilson, J. Atmos. Chem. Phys. 2005, 5, 1053. (3) Pope, F. D.; Dennis-Smither, B. J.; Griffiths, P. T.; Clegg, S. L.; Cox, R. A. J. Phys. Chem. A 2010, 114, 5335. (4) Bilde, M.; Pandis, S. N. EnViron. Sci. Technol. 2001, 35, 3344. (5) Bilde, M.; Svenningsson, B.; Mønster, J.; Rosenørn, T. EnViron. Sci. Technol. 2003, 37, 1371.

Single Aerosol Particles Containing Acids and NaCl (6) Koponen, I. K.; Riipinen, I.; Hienola, A.; Kulmala, M.; Bilde, M. EnViron. Sci. Technol. 2007, 41, 3926. (7) Riipinen, I.; Koponen, I. K.; Frank, G. P.; Hyva¨rinen, A.-P.; Vanhanen, J.; Lihavainen, H.; Lehtinen, K. E. J.; Bilde, M.; Kulmala, M. J. Phys. Chem. A 2007, 111, 12995. (8) Tao, Y.; McMurray, P. H. EnViron. Sci. Technol. 1989, 23, 1519. ˜ . s. M.; Andersson, P. U.; Hallquist, M. J. Phys. (9) Salo, K.; Jonsson, A Chem. A 2010, 114, 4586. (10) Zardini, A. A.; Krieger, U. K.; Marcolli, C. Opt. Express 2006, 14, 6951. (11) Booth, A. M.; Markus, T.; McFiggans, G. B.; Percival, C. J.; McGillen, M. R.; Topping, D. O. Atmos. Meas. Tech. 2009, 2, 355. (12) Chattopadhyay, S.; Ziemann, P. J. Aerosol Sci. Technol. 2005, 39, 1085. (13) Cappa, C. D.; Lovejoy, E. R.; Ravishankara, A. R. J. Phys. Chem. A 2007, 111, 3099. (14) Zardini, A. A.; Riipinen, I.; Koponen, I. K.; Kulmala, M.; Bilde, M. J. Aerosol Sci. 2010, 41, 760. (15) Ray, A. K.; Davis, E. J.; Ravindran, P. J. Chem. Phys. 1979, 71, 582. (16) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley Interscience: New York, 1998. (17) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. (18) Stokes, R. H.; Robinson, R. A. J. Phys. Chem. 1966, 70, 2126. (19) Peng, C.; Chan, M. N.; Chan, C. K. EnViron. Sci. Technol. 2001, 35, 4495. (20) Clegg, S. L.; Seinfeld, J. H. J. Phys. Chem. A 2006, 110, 5692. (21) Hansen, H. K.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Proc. Des. DeV. 1991, 30, 2352. (22) Fredenslund, A.; Gmehling, J.; Michelson, M. L.; Rasmussen, P.; Prausnitz, J. M. Ind. Eng. Chem. Proc. Des. DeV. 1977, 16, 450. (23) Wittig, R.; Lohman, J.; Gmehling, J. Ind. Eng. Chem. Res. 2003, 42. (24) Clegg, S. L.; Kleeman, M. J.; Griffin, R. J.; Seinfeld, J. H. Atmos. Chem. Phys. 2008, 8, 1057.

J. Phys. Chem. A, Vol. 114, No. 37, 2010 10165 (25) Wexler, A. S.; Clegg, S. L. J. Geophys. Res. 2002, 107, 14. (26) Clegg, S. L.; Seinfeld, J. H.; Brimblecombe, P. J. Aerosol Sci. 2001, 32, 713. (27) Pope, F. D.; Dennis-Smither, B. J.; Griffiths, P. T.; Clegg, S. L.; Cox, R. A. J. Phys. Chem. A 2010, 114, 5335. (28) Mie, G. Ann. Phys. 1908, 25, 377. (29) Glantschnig, W. J.; Chen, S.-H. Appl. Opt. 1981, 20, 2499. (30) Laven, P. MiePlot http://www.philiplaven.com/MiePlot.htm (2006). (31) Wills, J. B.; Knox, K. J.; Reid, J. P. Chem. Phys. Lett. 2009, 481, 153. (32) Butler, J. R.; Mitchem, L.; Hanford, K. L.; Treul, L.; Reid, J. P. Faraday Discuss. 2008, 237, 351. (33) Mitchem, L.; Reid, J. P. Chem. Soc. ReV. 2008, 37, 756. (34) Prausnitz, J. M. Lichtenthaler, R. N. Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall PTR: Upper Saddle River, NJ, 1999. (35) Yaws, C. L. Yaw’s Handbook of Thermodynamic and Physical Properties of Chemical Compounds; Knovel: New York, 2003. (36) Moller, B.; Rarey, J.; Ramjugernath, D. J. Mol. Liq. 2008, 143, 53. (37) Nannoolal, Y.; Rarey, J.; Cordes, W.; Ramjugernath, D. Fluid Phase Equilib. 2004, 226, 45. (38) Nannoolal, Y.; Rarey, J.; Ramjugernath, D. Fluid Phase Equilib. 2008, 269, 117. (39) Stein, S. E.; Brown, R. L. J. Chem. Inf. Comput. Sci. 1994, 34, 581. (40) Myrdal, P. B.; Yalkowsky, S. H. Ind. Eng. Chem. Res. 1997, 36, 2494. (41) Clegg, S. L.; Kleeman, M. J.; Griffin, R. J.; Seinfeld, J. H. Atmos. Chem. Phys. 2008, 8, 1087. (42) CRC Handbook of Chemistry and Physics, 87 ed.; CRC Press: Boca Raton, FL, 2006. (43) Fuzzi, S.; Decesari, S.; Facchini, M. C.; Matta, E.; Mircea, M.; Tagliavini, E. Geophys. Res. Lett. 2001, 20, 4079.

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