Using Elemental Ratios to Predict the Density of Organic Material

Article pubs.acs.org/est

Using Elemental Ratios to Predict the Density of Organic Material Composed of Carbon, Hydrogen, and Oxygen Mikinori Kuwata, Soeren R. Zorn, and Scot T. Martin* School of Engineering and Applied Sciences and Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, United States S Supporting Information *

ABSTRACT: A governing equation was developed to predict the density ρorg of organic material composed of carbon, oxygen, and hydrogen using the elemental ratios O:C and H:C as input parameters: ρorg = 1000 [(12 + 1(H:C) + 16(O:C)]/[7.0 + 5.0(H:C) + 4.15(O:C)] valid for 750 < ρorg < 1900 kg m−3. Comparison of the actual to predicted ρorg values shows that the developed equation has an accuracy of 12% for more than 90% of the 31 atmospherically relevant compounds used in the training set. The equation was further validated for secondary organic material (SOM) produced by isoprene photooxidation and by α-pinene ozonolysis. Depending on the conditions of SOM production, ρorg/SOM ranged from 1230 to 1460 kg m−3, O:C ranged from 0.38 to 0.72, and H:C ranged from 1.40 to 1.86. Atmospheric chemistry models that simulate particle production and growth can employ the developed equation to simulate particle physical properties. The equation can also extend atmospheric measurements presented as van Krevelen diagrams to include estimates of the material density of particles and their components. Use of the equation, however, is restricted to particle components having negligible quantities of additional elements, most notably nitrogen.

Several methods have been developed to estimate ρorg for individual pure compounds.14,15 These methods employ the following formulation:

1. INTRODUCTION Organic material in the atmosphere can be simulated by models of different levels of detail.1−5 Outside polluted regions of the world that can have large concentrations of particle-phase organonitrates,6 the simulated organic material is dominated by molecules composed of carbon, oxygen, and hydrogen, reflecting the widespread occurrence of oxygen-containing organic material in the atmosphere.7,8 Although the oxygen-tocarbon (O:C) and hydrogen-to-carbon (H:C) elemental ratios of the particle-phase material can be simulated,8 the extension of chemical model output to some additional important physical factors requires the prediction of another fundamental quantity, namely the organic material density ρorg. For instance, the prediction of particle dynamics, such as deposition on sizeresolved impactor stages, requires information on particle density.9 Estimation of cloud condensation nuclei (CCN) activity is another example that requires information on particle density.10 At the present time, however, there is a knowledge gap for the relationship between organic composition and material density. In addition to the possibility that composition−density relationships can extend modeling work, laboratory and field studies widely present information about oxygen-containing organic material in the form of van Krevelen diagrams, which employ H:C along the ordinate and O:C along the abscissa.11−13,8 A relationship between material density and O:C and H:C could under some circumstances extend these measurements to corresponding predictions of physical properties of the aerosol particles. © 2011 American Chemical Society

ρorg =

mass 1 MW = volume A Vm + Vim

(1)

where MW is the molecular weight of the compound, Vm is the molecular volume as predicted from atomic volumes and changes due to intramolecular bonding, Vim is the intermolecular volume often predicted by group contribution methods,16 and A is any necessary unit conversion factor depending on the choice of units for MW, Vm, and Vim. Equation 1 successfully predicts ρorg within 5% error for various pure compounds, including alkanes, alcohols, and carboxylic acids.15 These methods as formulated in the existing literature cannot be directly applied, however, to the complex oxygencontaining organic material present in the components of many atmospheric particles. A systematic rationalization of the densities of organic materials is challenging because (1) the ρorg values of pure compounds differ by more than a factor of 2 (e.g., from 800 kg m−3 for n-alkanes to 1900 kg m−3 for oxalic acid) and (2) the organic components of atmospheric particles are typically constituted from hundreds to thousands of Received: Revised: Accepted: Published: 787

July 21, 2011 December 4, 2011 December 6, 2011 December 6, 2011 dx.doi.org/10.1021/es202525q | Environ. Sci. Technol. 2012, 46, 787−794

Environmental Science & Technology

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different compounds.5 One possible approach to this complexity is the development of predictions of ρorg from measurable chemical parameters, such as elemental ratios. Although a general trend of increasing ρorg for more oxidized material has been demonstrated,17−21 no general quantitative equation has yet been developed to relate ρorg to elemental ratios. The study reported herein develops elemental ratios as predictors for ρorg, both for pure compounds as well as their complex mixtures, using a governing equation that is newly introduced in the present study as a modified form of the eq 1.

molecules but described in aggregate by elemental ratios. In this way, eq 4 differs from the original treatment of Girolami14 that used the molecular weight and the number and types of functional groups as input parameters. 2.2. Derivation of Specific Equation. Figure 1a compares the actual to predicted ρorg values of 31 individual compounds. Data sources for the measured values, as obtained from literature, are listed in Table S1. Equation 4 is employed for the predictions using vs = 0 and a trial value of Δvs = 0. Figure 1a demonstrates that the predictive equation has a generally correct trend. The ρorg values of relatively light compounds (ρorg < 1000 kg m−3), including alkanes and alkanoic acids (Table S1), are reproduced accurately. The ρorg values of heavier compounds, such as dicarboxylic acids and polycyclic aromatic hydrocarbons, are systematically underestimated, however. To compensate for the underestimate (Figure 1a), we introduced the empirical correction term Δv s to the denominator of eq 4. The magnitude of this correction increases for highly oxidized compounds as well as for compounds having double bonds or ring structures.14,15 The correction term is quantitatively calculated based on oxidation state (Ox), as follows:

2. THEORY 2.1. Derivation of General Equation. We expand eq 1 representing a single compound to a complex mixture of multiple species, as follows:

ρorg =

∑i nimi 1 A ∑i (nivi) + Vs

(2)

using the relationships MW = Σinimi, Vm = Σi(nivi) + ΔV, and Vs = ΔV + Vim. Terms include the number ni, the molar mass mi, and the volume vi of atom type i (i.e., C, H, or O) in the molecule. The term Vs represents the additional space, beyond atomic intramolecular volumes given by Σnivi, that is occupied by intermolecular volumes as well as a correction term ΔV that represents the change in volume due to intramolecular chemical bonding. For A set equal to Avogadro’s number NA, vC is 1.66 × 10−29 m3 for the parameter set of Girolami.14 This value is 19% smaller than the van der Waals volume of a carbon atom (2.06 × 10−29 m3). The smaller value can be explained by chemical bonding. Values of vH = 0.58 × 10−29 m3 and vO = 1.19 × 10−29 m3 are obtained based on the ratio of the van der Waals volume of these atoms to that of carbon.22 Normalization of eq 2 by the number of carbon atoms nC in the molecule yields the following result:

ρorg =

∑i ri mi 1 NA ∑i (ri v) i + vs

Δvs = − 1.5(Ox + 2)

The values of the coefficients in eq 5 were obtained by optimization to the data set. The oxidation state used in eq 5 is calculated from the elemental ratios: Ox = 2 (O:C) − (H:C).23 This formulation shows that, compared to a baseline of Ox = −2 for a −CH2− chain, the correction term increases for molecules having (1) oxygen atoms, (2) ring structures, and (3) double bonds. Quantitatively, this term Δvs leads to the same trends for the effects of functional groups on ρorg as given by Girolami14 yet does so without information on the actual functional groups. A complete equation for ρorg (kg m−3) that takes into account all of the aforementioned aspects is written as follows:

(3)

ρorg = 1000

in which vs = Vs/nC. The term ri represents the ratio of the number of atoms of type i (e.g., oxygen or hydrogen) to the number of carbon atoms in the molecule. By definition, rC is 1. The terms ri are then recognized as elemental ratios, such as the O:C and H:C ratios. Although in the present study we focus on oxygen-containing organic material, other elements, notably organonitrogen, can also be present in significant abundance for some atmospheric conditions, especially polluted ones, and these additional organo-elements can also be incorporated into the framework of eq 3. Equation 3 shows that ρorg can be predicted from O:C and H:C elemental ratios provided that vs is either known or otherwise determinable from ri. The resulting equation for ρorg (kg m−3) for a composition CxHyOz is as follows: ρorg = 1000

12 + 1(H:C) + 16(O:C) 10 + 3.5(H:C) + 7.15(O:C) + NAvs + Δvs

(5)

12 + 1(H:C) + 16(O:C) 7.0 + 5.0(H:C) + 4.15(O:C)

(6)

For eq 6, Figure 1b shows a correlation plot between the actual and predicted ρorg values. The predicted ρorg is within 12% of the actual value for 28 of 31 species (Table 1). The nonconforming species include oxalic acid, xylitol, and cholesterol. A linear regression between the actual and predicted values yields a slope of 1.00 and an intercept of 0.02. The tested data set includes both liquids and solids at 298 K, and no systematic dependence was observed between prediction error and particle phase. These results demonstrate that eq 6, using only elemental ratios for input quantities, predicts ρorg with good accuracy.

3. EXPERIMENTAL SECTION 3.1. Chamber Operation. Secondary organic material was produced in the Harvard Environmental Chamber (HEC), both by photo-oxidation of isoprene and by dark ozonolysis of α-pinene.24,25 The chamber was operated as a continuously mixed flow reactor (CMFR), meaning that steady-state conditions were established in the chamber. Ammonium sulfate seed particles (30 nm electric-mobility equivalent diameter) were continuously injected, and a portion of the organic oxidation products condensed onto these seed particles,

(4)

in which O:C = z:x and H:C = y:x. An additional empirical correction term Δvs, which is inserted by us into the denominator of eq 4, is discussed in Section 2.2. The character of each molecule (e.g., molecular weight, formula, or functional groups) does not appear explicitly in eq 4. The equation as written is equally applicable to a single compound as to an organic material having myriad individual 788

dx.doi.org/10.1021/es202525q | Environ. Sci. Technol. 2012, 46, 787−794


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Table 1. Summary of the Chemical Families and Compounds Used to Develop This Study’s Predictive Equation of Material Density (Eq 6)a chemical family n-alkanes alkanoic acids alkenoic acids polycyclic aromatic hydrocarbons dicarboxylic acids saccharides lignin products steroids diols a

number of compounds in training set

ρorg (kg m−3)

6 4 2 3

777−792 842−862 894−895 1179−1467

7 4 2 1 2

1360−1900 1489−1581 1337−1460 1070 920−1017

See Table S1 for Additional Information.

resulting in significant growth of particle diameter. Across periods of several days, the precursor organic compound was continuously injected in the chamber inflow, and SOM particles were continuously sampled in the chamber outflow. The use of small seed particles (i.e., 30 nm physical diameter for +1 particles and 43 nm physical diameter for +2 particles) compared to larger sampled particles (e.g., 80−150 nm) reduced the uncertainty in determination of ρorg by ensuring a large volume fraction of organic material in the sampled particles. Further details concerning the operation of the HEC are presented in the Supporting Information. 3.2. Particle Measurements. The particles exiting the HEC were sampled by a high-resolution time-of-flight aerosol mass spectrometer (Aerodyne HR-ToF-AMS), a scanning mobility particle sizer (SMPS, TSI Inc.), and an aerosol particle mass analyzer (Kanomax APM-3600). Calibrations for each instrument were routinely carried out using high-quality polystyrene latex (PSL) particles (Duke Scientific). For the isoprene experiments that used aqueous seed particles, particles exiting the chamber were passed through diffusion dryers prior to instrument sampling. The AMS measured the particle mass-diameter distribution m(dva), the organic particle mass concentration Morg, and the O:C and H:C elemental ratios of the particle-phase organic material.26,27 The term dva represents the aerodynamic diameter in the free-molecule regime (i.e., Knudsen number >10).9 Corrections for the H2O+ and CO+ peaks of the organic mass spectra were made as described in Chen et al.,8 as the H2O signals are not directly employed in the normal AMS data analysis. For the determination of material density, the diameter d̂va corresponding to the mode of m(dva) was used. The SMPS, composed of a differential mobility analyzer (DMA) upstream of a condensation particle counter (CPC), measured the particle number-diameter distribution n(dm).28 The term dm represents the mobility diameter. For the pressures and the particle sizes of this study, the operating conditions of the SMPS corresponded to intermediate Knudsen numbers (i.e., from 0.1 to 10). The number-diameter distribution was converted to a volume-diameter distribution v(dm) by using a cubic weighting factor for diameter. This conversion is accurate for spherical nonporous particles. For further analysis, the diameter d̂m corresponding to the maximum of v(dm) was taken. For the SMPS-AMS data set, the material density of the particle ρp was calculated from d̂va and d̂m by the relationship

Figure 1. (a) Comparison of measured to predicted organic material densities for thirty-one pure compounds. Data sources for the measured values are listed in Table S1. Predicted values are obtained using eq 4 with vs = 0 and Δvs = 0. (b) Same as panel a but using Δvs = −1.5 (Ox + 2), as represented by eq 6. (c) Densities of secondary organic material measured in this study compared to values predicted using eq 6. In all three panels, the dashed line represents the 1:1 line. The dotted lines show ±12% and represent the accuracy envelope of the prediction.

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Table 2. Summary of Experiments and Observationsa exp. no.

precursor compound

seed phase

relative humidity (%)

Morg (μg m−3)

1 2 3 4 5 6 7 8 9 10

α-pinenec α-pinene α-pinene α-pinene α-pinene α-pinene isoprened isoprene isoprene isoprene

dry dry dry dry dry dry dry wet dry wet

40 40 40 40 40 Morg > 1.4 μg m−3). This result is consistent with the report of Shilling et al.,34 who also observed that ρorg increased for decreasing Morg. Quantitatively, literature reports of ρorg for Morg > 5 μg m−3 range from 1200 to 1500 kg m−3 for α-pinene ozonolysis,35,36,34 and the literature values are thus consistent with our observations. For Morg < 5 μg m−3, Shilling et al.34 reported a clustering of 1500 ± 100 < ρorg < 1750 ± 100 kg m−3. The high uncertainty arose from the relatively large seed particles that were employed in those experiments, meaning that the organic volume fraction was small and that uncertainties in the organic volume fraction as well as in ρp measurement propagated as uncertainty in ρorg (Figure S1). In comparison, the present study using smaller seed particles and hence more tightly constrained organic volume fractions obtains 1460 ± 60 kg m−3 for Morg < 5 μg m−3. These results are therefore consistent, though at the lower end, of the report of Shilling et al. for Morg < 5 μg m−3. For isoprene photo-oxidation, ρorg ranged from 1350 to 1450 kg m−3. This range is nearly commensurate with the measurement uncertainty of 5%. For comparison, values reported in the literature lie between 1300 and 1420 kg m−3,37,38 in good agreement with our observations. Compared to our study’s range of 15 < Morg < 37 μg m−3, the values in the literature cover 2−68 μg m−3.37,38 Figure 1c compares the measured ρorg to that predicted based on using the measured elemental ratios as input parameters to

(7)

in which εAS and εorg denote the volume fractions of ammonium sulfate and organic material. This mixing rule holds for phase-separated inorganic and organic components within a single particle. For ρAS of ammonium sulfate, a value of 1770 kg m−3 was used.32 The volume fractions were calculated based on the injected seed particle diameter (30 nm) and the 790



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eq 6. For both α-pinene and isoprene secondary organic material, the measured and predicted values agree within the stated 12% accuracy of the developed equation. The conclusion is that eq 6, developed using pure organic compounds, is also accurate for predicting ρorg of the complex mixture of compounds that constitute secondary organic material. A more detailed investigation and stringent test of the comparison shown in Figure 1c is presented in Figure 2. Figure

Aiken et al.39 for a group of 26 pure compounds as input parameters to eq 6 to predict ρorg. Similarly, we predicted ρorg using the actual O:C and H:C values of these compounds. The meian absolute percent difference in ρorg by these two methods was 4% for the 26 compounds, including a mean absolute difference of 5% with a standard deviation of 4%. The conclusion is that the stated accuracy of 12% for eq 6 also incorporates AMS measurement errors of O:C and H:C elemental ratios. In the particular case of SOM, Chen et al.8 also argued that measurements of the O:C and H:C elemental ratios can be more accurate than for individual compounds because of the compensating effects of the presence of many types of functional groups for in SOM. A van Krevelen diagram, which uses the O:C ratio as the abscissa and the H:C ratio as the ordinate, is shown in Figure

Figure 3. Example of a van Krevelen diagram colored by predicted ρorg (eq 6). The black parallelogram encompasses O:C and H:C observations for many world locations, as reported in Heald et al.13

Figure 2. (a) Elemental ratios and (b) densities of α-pinene secondary organic material for increasing Morg. The lines in panel a represent smooth-curve fits of O:C(Morg) and H:C(Morg). The black line of panel b represents ρorg predicted using the O:C(Morg) and H:C(Morg) fitting equations of panel a in eq 6. The surrounding gray region represents the uncertainty of the predictions (±12%). Data points in panel b represent SMPS-AMS measurements. Results are shown for SOM produced at 40% RH.

3.40 The coloring in the figure, corresponding to the application of eq 6, represents the predicted ρorg. The figure shows that (1) for a fixed H:C ratio ρorg increases with increasing O:C ratio and (2) for a fixed O:C ratio ρorg decreases with increasing H:C ratio. The explanation for these trends is that hydrogen is the least dense whereas oxygen is the most dense among H, C, and O atoms. In agreement, Katrib et al.18 found that the material density of oleic acid increased from 900 to 1100 kg m−3 following ozonolysis. In other laboratory experiments, Abbatt and co-workers20,21 likewise observed an increasing trend of ρorg for simulated atmospheric aging, which was done by steadily increasing the extent of OH exposure. The trends were observed both for bis(2-ethyl hexyl) sebacate (chosen as a surrogate for primary organic material) and for secondary organic material produced by α-pinene ozonolysis. For many locations worldwide as well as several different laboratory experiments, Heald et al.13 demonstrated that the O:C and H:C elemental ratios of particle-phase organic material lie within the region surrounded by the black parallelogram of Figure 3. For increasing particle residence time in the atmosphere, Heald et al.13 further pointed out that atmospheric oxidation processes have the tendency of moving particle composition along a slope of −1 toward the lower right of the van Krevelen diagram. In the context of Heald et al.,13 the implication of the present analysis is that ρorg increases

2a shows the dependence of the O:C and H:C elemental ratios on Morg, as measured for α-pinene secondary organic material. As reported previously and explained therein,34,8 the organic material is more oxidized at lower Morg. We empirically fit the elemental ratios of Figure 2a as a function of Morg and employed these functions in eq 6 to predict ρorg for increasing Morg (Figure 2b). The measured and predicted values agree within the uncertainty of the governing equation, which is represented by the gray region. The prediction also reproduces the trend of increasing ρorg for decreasing Morg. Figure 2b also shows that the predicted values are somewhat biased to the low side, especially for low Morg. Part of the bias might arise from the prediction method itself related to the development of eq 6 from pure compounds, and this bias is incorporated in the statement of 12% accuracy in the use of eq 6. Another part of the bias, however, might be attributable to the accuracy of the AMS measurement of elemental ratios, and a sensitivity analysis for this possibility was therefore carried out (Table S2). We used the O:C and H:C values measured by 791



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and the application of the developed equation under these circumstances is not possible without additional information on particle components and mixing states. In model applications, depending on model design, this information can be readily available. A further limitation of the developed equation is that it cannot be applied to the full range of atmospheric organic material, notably that containing organo-nitrogen and sulfur compounds. These compounds make important contributions to the particle phase in many polluted environments, and a goal for the future is the further development of eq 6 to include N:C and S:C elemental ratios. Another limitation is the semiempirical nature of the equation, especially for the term Δvs. As such, although the equation works well for the test data sets, further verification by atmospheric observations as well as by laboratory experiments is needed. An especially valuable use of the equation is in the context of a van Krevelen diagram. A van Krevelen diagram is a good framework for representing the progressive oxidation reactions of organic particles during their atmospheric lifetime, both in the laboratory and the atmosphere.13 For organic material of limited nitrogen and sulfur content, the equation representing ρorg(O:C,H:C) shows that the material density increases along the van Krevelen trajectory of atmospheric aging reactions. Along with favorable chemical changes in functional groups, the increased density can in itself also partially explain increased particle hygroscopicity during aging.

alongside the increase in O:C and the decrease of H:C during atmospheric aging of the organic material. A caveat to this conclusion, however, is the assumption that other organoatoms, such as organo-nitrates, are not present in quantities significant enough to appreciably alter ρorg. Changes in the material density of organic material during atmospheric aging affect several different climate-related particle properties. The hygroscopic growth parameter κ of organic particles is proportional to the following variables:10 (1) the van’t Hoff factor i that takes into account both solubility and nonideality of the organic material, (2) the organic material density ρorg, and (3) the inverse of molecular weight (MW). The overall equation is as follows: κ = i MWwater ρorg/(MWorg ρwater). Observations show that κ of secondary organic material can depend on the O:C ratio,41−43 though there are exceptions.44 In a comprehensive study, Jimenez et al.41 reported that κ at 95% RH increased from ca. 0.02 to 0.16 as the O:C ratio increased from ca. 0.25 to 0.55 for a variety of atmospheric observations as well as for chamber experiments conducted at high Morg. Figure 3 predicts that an increase in O:C from 0.25 to 0.55 increases ρorg by approximately 40%. This change in ρorg, however, can explain only a small increase in κ, specifically from 0.02 to 0.03. The difference between 0.03 and 0.16 must then be explained by some of the other aforementioned factors, such as the van’t Hoff factor or the molecular weight, both of which can also be anticipated to correlate with elemental ratios. A test case for the application of eq 6 to ambient data is possible using measurements made in the central Amazon Basin during the wet season as part of the Amazonian Aerosol Characterization Experiment (AMAZE-08).45 At that time, the submicrometer particles were dominated by liquid particles of secondary organic material, and this organic component consisted nearly entirely of C, H, and O atoms with an N:C ratio of 0.02 ± 0.01.46,47 SMPS-AMS measurements during AMAZE-08 yielded a ρp value of 1390 ± 150 kg m−3.48 Equation 7, in combination with the measured organic mass fraction during AMAZE-08 for the corresponding period of SMPS-AMS measurements, indicates that ρorg was 1350 ± 150 kg m−3.48,49 The average values of the elemental ratios during the time period of SMPS-AMS measurements were O:C of 0.42 and H:C of 1.43, leading by eq 6 to a ρorg prediction of 1270 ± 150 kg m−3 for AMAZE-08 . Within uncertainty, the measured and predicted values are in agreement for this atmospheric data set. In conclusion, in this study an equation was developed that uses elemental ratios to predict the density of atmospherically important organic material composed of carbon, oxygen, and hydrogen atoms. The equation was based on 31 atmospherically relevant compounds, for which the calculated and measured ρorg agreed within an accuracy of 12% for 28 of the compounds. The equation was validated against measurements of secondary organic material produced both in the Harvard Environmental Chamber and in the wet season of the central Amazon Basin. The predicted and observed ρorg agreed with the measured values within the stated accuracy of the equation, demonstrating the applicability of the developed equation to an important subset of complex organic mixtures. The test case for the Amazon data set was possible because to first order the particles in the pristine environment of the rain forest consisted of a single, homogeneous organic component that was similar among all particles in the aerosol population. By comparison, in many urban environments, individual particles are highly varied,

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ASSOCIATED CONTENT

* Supporting Information S

Additional text, data tables, references, and graphics. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS This material is based upon work supported by the Office of Science (BES), U.S. Department of Energy, Grant DE-FG0208ER64529. M.K. is supported by the Japan Society for the Promotion of Science (JSPS) postdoctoral fellowship for research abroad. We acknowledge Qi Chen, Mackenzie Smith, and Yingjun Liu for useful discussions and assistance with the experiments.

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REFERENCES

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