Article pubs.acs.org/JPCA
Critical Assessment of Liquid Density Estimation Methods for Multifunctional Organic Compounds and Their Use in Atmospheric Science Mark H. Barley,† David O. Topping,†,‡ and Gordon McFiggans*,† †
Centre for Atmospheric Science, School of Earth, Atmospheric and Environmental Science, Simon Building, University of Manchester, Oxford Road, Manchester, M13 9PL, U.K. ‡ National Centre for Atmospheric Science (NCAS), University of Manchester, Manchester, M13 9PL, U.K. S Supporting Information *
ABSTRACT: In order to model the properties and chemical composition of secondary organic aerosol (SOA), estimated physical property data for many thousands of organic compounds are required. Seven methods for estimating liquid density are assessed against experimental data for a test set of 56 multifunctional organic compounds. The group contribution method of Schroeder coupled with the Rackett equation using critical properties by Nannoolal was found to give the best liquid density values for this test set. During this work some problems with the representation of certain groups (aromatic amines and phenols) within the critical property estimation methods were identified, highlighting the importance (and difficulties) of deriving the parameters of group contribution methods from good quality experimental data. A selection of the estimation methods are applied to the 2742 compounds of an atmospheric chemistry mechanism, which showed that they provided consistent liquid density values for compounds with such atmospherically important (but poorly studied) functional groups as hydroperoxide, peroxide, peroxyacid, and PAN. Estimated liquid density values are also presented for a selection of compounds predicted to be important in atmospheric SOA. Hygroscopic growth factor (a property expected to depend on liquid density) has been calculated for a wide range of particle compositions. A low sensitivity of the growth factor to liquid density was found, and a single density value of 1350 kg·m−3 could be used for all multicomponent SOA in the calculation of growth factors for comparison with experimentally measured values in the laboratory or the field without incurring significant error.
■
INTRODUCTION An understanding of the chemical composition and physical properties of atmospheric aerosol has important implications for the study of climate change1 and for human health.2 Atmospheric particles range in diameter from a few nanometers to tens of micrometers and can contain inorganic salts, siliceous crustal minerals, elemental carbon, organic compounds, and water.3 While the physical and chemical properties of the first three components are relatively well understood, the organic fraction can comprise many thousands of, as yet largely unidentified, compounds with a vast range of properties.4,5 To attempt prediction of the composition and properties of organic aerosol formed from the chemical processing of atmospheric compounds (known as secondary organic aerosol or SOA), it is possible to make use of mechanistic models that track the oxidation of atmospheric volatile organic compounds (VOCs), from both natural and man-made sources, all the way through to carbon dioxide and water. One such mechanism, which we have used extensively in our previous work, is the Master Chemical Mechanism (MCM)6−9 (see http://mcm. leeds.ac.uk/MCM/ for more information), which predicts the © 2013 American Chemical Society
atmospheric concentration of some 2700+ species; and the proportion of each component that condenses to form SOA can then be predicted using a gas−liquid partitioning model.10−13 Key physical properties of all the organic components are required both to model SOA formation (e.g., vapor pressures) and also to predict the properties of the SOA for comparison with results from laboratory and field studies. The hygroscopic growth factor is a standard property of aerosol particles that is experimentally measured (in both field campaigns and in the laboratory) using a Hygroscopic Tandem Differential Mobility Analyzer (HTDMA).14 The hygroscopic growth factor, which is strongly influenced by the particle’s composition, is important because it is a direct measure of the particles ability to attract water, which, under the appropriate atmospheric conditions, strongly influences the ability of the particle to initiate the formation of water droplets (i.e., to act as a cloud condensation nuclei).15 Some detailed studies have Received: May 10, 2012 Revised: March 1, 2013 Published: March 18, 2013 3428
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
Schroeder, and Tyn and Calus,28 all of which are described in a standard reference textbook.22 These last three methods provide estimates of the molar volume (in cm3·mol−1) at the normal boiling point (which will also be estimated for almost all compounds of atmospheric importance24) and are corrected to the temperature of interest using the Rackett equation,29 which will require estimated critical properties for most compounds. Also, to cover the range of functionality required for both the selected test set and the range of atmospheric compounds, the three GCM based methods (Girolami, Le Bas, and Schroeder) had to be modified and extended. Other methods that were considered for this comparison but were eventually excluded were the HBT method30 and the more modern GCM of Ihmels and Gmehling (GCVOL-OL-60).31 The HBT method was excluded because of its reliance on the acentric factor, which should be obtained from the shape of the vapor pressure curve up to the critical point. For most of the compounds in the test set and all the MCM compounds that are likely to condense into organic aerosol, both the vapor pressure data and the critical parameters will have to be estimated. Sensitivity analysis has shown the acentric factor is strongly influenced by small errors in the values used for the critical properties (particularly the critical temperature),32 and the textbook mentioned above22 does not recommend using acentric factors derived from estimated input data. On this basis, it was decided that the HBT method was unsuitable for the low volatility multifunctional compounds used in this work. The GCVOL-OL-60 GCM method was excluded because of practical difficulties associated with parsing the wide range of structural features found among the MCM compounds into a limited range of groups. For example, the only aliphatic nitro group available in this method is CH2NO2, which is not suitable for a molecule (of which there are several in the MCM; see below) that has a nitro group attached to a double bonded carbon. A more detailed description of the implementation of the liquid density methods to be assessed will now be given before moving on to discuss the estimation of critical properties. Estimation of Liquid Densities by Girolami. This is the simplest method26 to implement as there is no temperature dependence and it provides a direct estimate of liquid density (g·cm−3). The author does not specify the temperature at which the density estimation is valid, but it is assumed to be 20−25 °C (293.15−298.15 K). The method sums up simple atom contributions and includes some corrections for additional structural features. A 10% correction should be added to the liquid density value for each hydrogen bonding functional group present (up to a maximum of 30%). These are defined as alcohols, acids, primary and secondary amines, and amides. However, for atmospheric purposes, hydroperoxide and peroxyacid are important functional groups with hydrogen bonding capability. A comparison of liquid density values calculated by this method with values by Schroeder or Le Bas (see below) for a set of 2742 compounds from the MCM including many compounds with these functional groups showed there was much better agreement between the estimation methods if hydroperoxide and peroxyacid were treated as hydrogen bonding groups with a 10% correction factor. The other issue was the treatment of fused and unfused rings. The method requires a 10% correction for each unfused ring and a 7.5% correction for each fused ring (all within a maximum correction of 30%). The definition of unfused rings is quite clear, and molecules such as naphthalene and anthracene contain fused rings, but it is not clear how to treat bridged
been conducted on the accuracy of growth factors measured by the HTDMA;14,16 with Swietlicki and co-authors reporting that an error of ±0.02 in growth factor is beyond the capability of most instruments and measured growth factors should be considered accurate to within ±0.05. To model growth factors for comparison with experimental values, an estimate of the density of the particle at (usually) ambient temperatures is required,17,18 which, in turn, depends upon estimated liquid density values for all the organic components in the aerosol. In addition to the densities of aerosol particles being important for growth factors and the condensation of water, they are also important for modeling a particle’s optical properties19 and fluid-dynamic behavior, which determine the particles’ transport and life cycle.20 Estimation methods for any property have to be based upon the available experimental data. The vast majority of the data for properties such as vapor pressures, critical properties, and liquid densities have been collected by or on behalf of the chemical industry for chemical plant design improvement, with a particular emphasis on production and purification of products by distillation. Most of the data have therefore been collected for structurally simple compounds (particularly hydrocarbons), and relatively little data are available for the complex multifunctional compounds typically found in atmospheric aerosol.21 This is particularly true for the very limited set of experimental data underpinning estimation methods for critical properties. Critical property values are important in the estimation of other physical properties such as liquid density as will be described below. Previous studies comparing liquid density estimation methods have been limited to a set of 35 compounds in Poling et al.22 and a recent assessment of seven estimation methods using 252 nonpolar fluids.23 In a previous publication, we assessed different estimation methods for vapor pressure against a set of low volatility multifunctional compounds.24 We have recently made software available on the web that calculates the chemical composition of atmospheric aerosol using these tested models for vapor pressure coupled to a gas−liquid partitioning module (see http://ratty.cas.manchester.ac.uk/informatics/), and we intend to add the liquid density methods described in this work. In a recent paper,25 the sensitivity of the hygroscopic growth factor of modeled aerosol to different vapor pressure methods and the inclusion of nonideality was investigated using liquid density values from Girolami.26 A web-based version of this estimation method is already available on the E-AIM Website (see http://www.aim.env.uea.ac.uk/aim/density/density.php). In this work, we test four liquid density methods (including that of Girolami) and two critical property estimation methods against experimental data for 56 multifunctional compounds to assess which methods give the best results for these types of molecules. The best liquid density estimation method is then used in a series of partitioning calculations to explore the range of SOA densities and the sensitivity of growth factor calculations to variations in the density values leading to a recommended standard density value for highly oxidized SOA for use in the estimation of growth factors for comparison with measured values.
■
METHODS Estimation of Liquid Densities. Four estimation methods for liquid density (subcooled if necessary) were assessed. In addition to the group contribution method (GCM) of Girolami mentioned above, these were the methods of Le Bas,27 3429
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
groups and group interactions (giving a total of 207 groups). The same groups are used to calculate the three critical properties as are used for estimating boiling point35 and the slope of the vapor pressure line.36
structures such as those found in alpha-pinene. For the purposes of this work, it was decided to treat the two rings in alpha-pinene and similar structures as two fused rings giving a density correction of 15%. Estimation of Molar Volumes at Normal Boiling Point. Estimation of molar volumes at Tb by Le Bas:22,27 This is a group contribution method based upon increments for most of the atoms present along with contributions for certain groups (esters, ethers, acids, double bonds, etc.). The treatment of nitrogen atoms is unsatisfactory as it is assumed that all nitrogen atoms are either double bonded (as in nitro or nitrate) or in primary or secondary amines. The contribution for other types of nitrogen atom (e.g., tertiary amines, amides, and nitriles) is undefined. For this work, it was assumed that a triple bonded nitrogen would have the same increment as a double bonded nitrogen; tertiary amines would have the same increment as secondary amines; and a nitrogen in an amide would have the same increment as the corresponding amine. The correction for esters is applied to both oxygen atoms and depends whether it is a methyl/ethyl/propyl and higher type of ester. Carbonates (of which there are two examples in the test set and several in the MCM output) were treated as though they were esters with all three oxygen atoms being given the same correction as that for an ethyl ester. Estimation of molar volumes at Tb by Schroeder:22 This GCM is similar to that of Le Bas. The double bond count includes double bonds within aromatic rings (3 for benzene and 5 for naphthalene). Estimation of molar volumes at Tb by Tyn and Calus:22,28 This is not a GCM. The molar volume at the normal boiling point (Vb) is calculated from the critical density (Vc) by Vb =
0.285Vc1.048
Σ = ΣNC i i + GI
where Ni is the number of group of type i and Ci the group increment for the required property for i; GI is the summation of the group interactions. The formulas for the critical properties are then given by ⎛ 1 ⎞ ⎟ Tc = Tb⎜b + ⎝ a + Σc ⎠
Zc =
(2)
(a + bΣ − Σ2)
Vc = a + Σ
Vc =
Σ +b na
PcVc RTc
(6)
where Pc is the critical pressure in Pa; Vc is the critical volume in m3·mol−1; Tc is the critical temperature in K; and R is the gas constant (= 8.3145 J·mol−1·K−1). For the following equations, Pc is converted to bar and Vc to cm3·mol−1; Tref is the Tb value from Nannoolal; Vref (= Vb above) is the molar volume in cm3·mol−1 as calculated by the estimation method, and Texp is the temperature at which the liquid density is required for comparison with experimental values. A parameter ϕ is defined by
where Ni is the number of group of type i and Ci the group increment for the required property for i. The critical properties are then estimated using the equations Tc =
Mb (a + Σ)2
(5)
Estimation of Critical Properties. Critical properties were estimated by the methods of Joback33 and Nannoolal.34 The estimation of critical temperature (Tc) by both methods requires the normal boiling point (Tb) as an input. In a previous study,24 we found that the Nannoolal estimation method35 for Tb gave the best results for a set of 45 low volatility multifunctional compounds. Hence, in this work, where a value for Tb is required as an input to an estimation method (either in calculating Tc or in the Rackett equation, see below) a Nannoolal value is used. In the Joback method, the molecules are parsed into their constituent groups and the contributions summed as follows:
Tb
Pc =
where Tb is provided by Nannoolal, M is the molar mass, and n is the number of non-hydrogen atoms in the compound. For critical temperature (in K), the adjustable parameters (a, b, and c) have the values a = 0.9889, b = 0.699, and c = 0.8607; for critical pressure, a = 0.00939, b = −0.14041, and Pc is given in bar. For critical volume, a = −0.2266, b = 86.1539, and Vc is given in cm3·mol−1. Correction of Molar Volume at Tb to the Experimental Temperature Using the Rackett Equation. The Nannoolal estimation method was used to provide the Tref value (= Tb) in the following equations. The other inputs to this version of the Rackett equation22,29 (selected because it does not use the acentric factor as an input) are the estimated critical properties and the critical compressibility (Zc), a dimensionless quantity calculated as follows:
(1)
Σ = ΣNC i i
(4)
1 Pc = (a + bn − Σ)2
2/7 2/7 ⎛ ⎛ Texp ⎞ Tref ⎞ ϕ = ⎜1 − ⎟ − ⎜1 − ⎟ Tc ⎠ Tc ⎠ ⎝ ⎝
(7)
V (Texp) = Vref Zc ϕ
(8)
ρ(Texp) = 1000/V (Texp)
(9)
where V(Texp) and ρ(Texp) are the molar volume and density at the experimental temperature in cm3·mol−1 and kg·m−3, respectively. The seven liquid density estimation methods tested in this work and how they relate to the models described above are summarized in Table 1. Selection of Experimental Data for the Test Set. The objective was to create a test set of liquid density values from a structurally diverse set of compounds dominated by multifunctionality. The following criteria were used when selecting compounds: (1) The chemical species provided by the MCM include a wide range of groups based upon combinations of
(3)
where Tb is provided by Nannoolal, and n is the number of non-hydrogen atoms in the compound. For critical temperature (in K), the adjustable parameters (a and b) have the values a = 0.584 and b = 0.965; for critical pressure, a = 0.113, b = 0.0032, and Pc is given in bar. For critical volume, a = 17.5, and Vc is given in cm3·mol−1. The estimation of critical properties by the Nannoolal method uses group contributions for primary and secondary 3430
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
compounds had to be truly multifunctional (i.e., contained two different groups: OH and Cl, for example) rather than different numbers of halogen atoms. Data for one compound (1,3,5trifluorotrichlorbenzene) was excluded because the values (from 3 sources) were mutually inconsistent. The initial selection of 57 compounds was tested to give a table of errors, which was then analyzed by applying a correlation matrix and eliminating one compound of any pair that gave an R2 value >0.98. The only pair of compounds that failed this test was 1,10-decanediol dinitrate and glycerol trinitrate, leading to the former compound being dropped from the test set. Some other pairs that gave high correlations (0.96 < R2 < 0.98: e.g., 1,2diaminobenzene and 3-chloroaminobenzene) were artifacts due to one estimation method giving an outlier value that then skewed the R2 value. The final selection of 56 compounds for the test set is shown in Table 2. (4) If suitable sets of experimental liquid density data are available for a given compound, then a set of 4 or 5 sequential data points (density vs temperature data) at temperatures close to ambient (but above the melting point) was selected. If there are several sets of density vs temperature data close to ambient conditions (say 273.15 to 313.15 K), then the set that shows most consistency with other data values (usually single density measurements in the range 293.15−298.15 K) was used. (5) If no density vs temperature data of 4 or more points from a single source are available, then all the experimental measurements reported for that compound are used, even though they are often at the same temperature. More details are given in Table 2 and in the Supporting Information. Informatics. The compounds of the test set were represented by SMILES (Simplified Molecular Input Line Entry System) notation. 41 The software used in the identification of the functional groups and structural features was written in Python and interfaced with our selected chemical parsing software (OpenBabel).42 The OpenBabel toolbox has the ability to filter and search molecular files (SMILES format) using SMARTS (created by Daylight Chemical Information Systems Inc., see www.daylight.com). For the Girolami, Schroeder, and Le Bas methods, bespoke SMARTS libraries were devised to ensure full parsing of the molecules (without missing fragments or double counting of atoms) identifying functional groups and structural features appropriate to the estimation method (see Supporting Information of Barley et al.43 for more detailed information and some examples of SMARTS used in identifying Nannoolal groups). These programs, together with the associated SMARTS libraries were designed to cover all the functionality of the test set (Table 2) and all the structural features found in the 2742 MCM compounds. For each compound, the accuracy of the estimation method is quantified using the Mean Bias Error (MBE):-
Table 1. Summary of the Liquid Density Data Estimation Methods critical props.
method
GCMa
1 2
Girolami (ρ) Schroeder (Vb)
Joback
3
Le Bas (Vb)
Joback
4
Joback
5
Schroeder (Vb)
Nannoolal
6
Le Bas (Vb)
Nannoolal
7
Nannoolal
role of critical props. none Tb to Texp by Rackett Tb to Texp by Rackett Vb by Tyn and Calus Tb to Texp by Rackett Tb to Texp by Rackett Tb to Texp by Rackett Vb by Tyn and Calus Tb to Texp by Rackett
abbreviation G S/J LB/J TC/J
S/N LB/N TC/N
a Quantity estimated by GCM given in brackets: ρ is density in g·cm−3; Vb is molar volume in cm3·mol−1.
carbon, hydrogen, and oxygen atoms. The nitrogen groups in the MCM are presently limited to Nv (nitro, nitrate, PAN and related groups); and there is the capability to include some halogenated species (mainly chlorinated derivatives). Our physical property models are designed to cover all species used in the MCM and also all halide species (except aliphatic fluoride) along with amines and acid amides. Recently, there has been increasing interest in the atmospheric chemistry and physical properties of amines;37,38 and halide species play a significant role in the atmospheric chemistry of marine environments.39,40 (2) Although experimental liquid density values were identified using a database (DETHERM, available, up until the end of 2012, through the Chemical Data Services, Daresbury, Cheshire; see http://cds.dl.ac.uk/), data were only selected if found in the primary literature. Secondary sources that provide correlations for properties such as vapor pressures and liquid densities, such as the CRC Handbook, and compilations of data (such as that provided by Poling et al.22) provide useful physical property data for many compounds. However, the correlations provided may include a mixture of experimental, extrapolated, and modeled data with minimal indication of quality and, in many cases, little or no information about the methods and data upon which each correlation is based. While such data may be very valuable to chemical engineers, it is important to test estimation methods against experimental data from an identifiable source and to avoid comparison with estimated or extrapolated values. Only experimental values from the primary literature were used in these comparisons. The data references for all the compounds used in this work are listed in the Supporting Information. (3) In selecting the compounds the emphasis was on structural diversity and multifunctionality. Most of the compounds have two or more nonhydrocarbon functional groups. However, some compounds with a single (more complex) functional group were included in the set. These functional groups included carbonate, acid anhydride, and acid amide. The other issue around multifunctionality centered upon halogenated compounds. Only a single example of a halogenated hydrocarbon was allowed for each halogen (hexachlorobutadiene, bromoform, and diiodomethane); any additional halogenated
MBE =
1 n
∑ i = 1: n
[ρest − ρexp ]
(10)
where the summation is over all the (n) data points for that compound and ρ represents the density in kg·m−3 . Calculation of Growth Factors and Their Sensitivity to Liquid Density Values. In a previous paper,43 we described the prediction of SOA composition for a range of scenarios based upon the output of a detailed model for the chemical degradation of volatile organic compounds (VOCs) in the atmosphere (the Master Chemical Mechanism or MCM). A 3431
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
Table 2. Experimental Liquid Density Data Used in the Comparisons
a
no.
compound
CAS RN
temperature range K
density range kg·m−3
Na
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
1,1′-iminobis-2-propanol 1,1′-oxybis(2-chloroethane) 1,2-pentanediol 1,2-benzenedicarbonyl dichloride 1,2-BDCA bis(2-ME) esterb 1,2-diaminobenzene 1,2-diaminoethane 1,2,3-trihydroxypropane 1,3-dichloro-2-propanol 1,3,5-trinitrobenzene 1,4-butanediol 1,4-dioxane 1,6-hexanedinitrile 2-(2-aminoethoxy)ethanol 2-aminoethanol 2-butynedioic acid dimethyl ester 2-furancarboxaldehyde 2-methoxyphenol 2,4-dinitrotoluene 2,4-pentanedione 3-hydroxypropanenitrile 3-chloroaminobenzene 3-cyanopropanal 3-methoxypropanal 3-nitrophenol 3,4-dichloronitrobenzene 4-acetyl morpholine 4-hydroxybenzaldehyde 4-oxopentanoic acid acetamide acetone cyanohydrin acetoxyacetone allyl glycidyl ether anisaldehyde benzyl salicylate bromochloromethane bromoform butanedioyl dichloride dibutyl phthalate diiodomethane dimethyl carbonate dimethyl succinate eugenol glutaric acid glycerol trinitrate hexachlorobutadiene iso-amylsalicylate maleic anhydride methyl anthranilate N-methyldiethanolamine pimelic acid propylene carbonate tetraethylene glycol triacetin trichloroacetic acid triethylene glycol dinitrate
110−97−4 111−44−4 5343−92−0 88−95−9 117−82−8 95−54−5 107−15−3 56−81−5 96−23−1 99−35−4 110−63−4 123−91−1 629−40−3 929−06−6 141−43−5 762−42−5 98−01−1 90−05−1 121−14−2 123−54−6 109−78−4 108−42−9 3515−93−3 2806−84−0 554−84−7 99−54−7 1696−20−4 123−08−0 123−76−2 60−35−5 75−86−5 592−20−1 106−92−3 123−11−5 118−58−1 74−97−5 75−25−2 543−20−4 84−74−2 75−11−6 616−38−6 106−65−0 95−53−0 110−94−1 55−63−0 87−68−3 87−20−7 108−31−6 134−20−3 105−59−9 111−16−1 108−32−7 112−60−7 102−76−1 76−03−9 111−22−8
318.55−343.15 288.05−314.95 293.15−323.13 290.65−363.15 293.15 374.15−393.15 283.55−323.42 298.15−318.15 285.15−294.15 425.15 298.15−338.15 291.15−308.15 293.15−358.15 283.15−323.15 303.15−318.15 288.25−334.45 251.15−331.45 304.2−353.2 344.16−357.76 287.15−309.15 298.15 283.15−303.15 290.4−372.3 288.15 363.15−371.15 319.15−368.15 293.15−323.15 390.15−418.15 314.25−388.15 366.3−401.2 293.15−323.15 293.15 293.15 273.15−334.15 303.15 298.15 298.15−318.15 294.15−356.65 293.15−333.15 298.15−353.15 293.15−313.15 293.15−358.15 273.15−298.15 373.15−433.15 277.15−298.15 283.15−323.15 270.2−312.2 337.75 291.75−292.75 283.15−303.15 378.15−398.15 293.15−313.15 298.15−328.15 278−298 323.15−365.15 298.15
970−988 1195−1226 948−970 1327−1403 1166−1174 1048−1069 869−906 1246−1259 1351−1367 1478 988−1013 1016−1036 916−962 1031−1064 996−1008 1114−1166 1119−1221 1061−1123 1301−1319 957−980 1040−1042 1208−1226 924−1000 956 1285−1293 1430−1490 1089−1114 1120−1143 1068−1123 945−979 917−939 1076 980 1088−1142 1107 1922−1925 2823−2876 1301−1371 1015−1048 3174−3307 1043−1070 1055−1119 1062−1078 1142−1210 1591−1614 1638−1696 1034−1068 1300 1167−1168 1034−1048 1078−1092 1184−1205 1096−1120 1153−1176 1556−1616 1319
4 5 4 5 4 4 5 5 5 1 5 5 4 5 4 5 5 4 5 5 3 5 4 1 5 4 4 4 5 4 5 1 1 5 1 3 5 4 5 5 5 5 4 4 5 5 5 1 2 5 5 4 4 5 5 1
N = number of data points. bFull name is 1,2-Benzenedicarboxylic acid, bi(2-methoxyethyl) ester.
standard scenario was defined based upon the MCM output after about 13 days of degradation of average UK NOx,
anthropogenic (AVOC), and biogenic(BVOC) emissions. To look at a wider range of scenarios, the average inputs could be 3432
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
Table 3. MBE values (in kg·m−3) for the Seven Estimation Methods methodsa compd no.a
1(G)
2(S/J)
3(LB/J)
4(TC/J)
5(S/N)
6(LB/N)
7(TC/N)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20b 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 bias SD biasc
69.40 −114.80 2.10 31.70 −99.40 115.20 13.70 −55.40 −68.90 −56.80 −17.20 −57.60 −38.60 −38.00 −25.00 −52.30 12.60 −44.30 −58.90 −58.20 1.70 59.20 97.10 −74.90 −65.00 −4.70 −121.60 −12.50 −30.80 35.60 55.80 −108.10 −14.00 −43.30 84.40 67.30 −41.30 −41.30 −43.30 −432.90 −55.80 −114.00 −65.20 40.20 −304.10 −36.60 −54.90 48.20 2.60 −54.90 45.20 −72.60 −48.90 −172.40 122.70 −227.70 −37.90 93.80 −43.40
−20.00 −11.43 −3.81 40.70 174.87 −71.32 −91.63 −50.59 −55.01 −109.88 −3.43 49.04 28.38 −39.23 −64.33 56.45 51.74 7.54 −53.68 −0.20 25.02 −37.46 42.54 −9.78 −106.60 −48.27 21.38 −45.11 −3.55 −7.07 37.48 −0.64 76.68 8.27 82.53 −118.12 −324.36 −7.69 171.71 −150.71 24.41 31.85 33.75 16.72 −73.35 −49.99 72.16 202.72 6.04 −19.08 61.32 218.40 75.97 99.88 0.30 51.63 3.40 86.80 5.60
−37.40 −84.12 −5.25 −14.81 61.74 −58.65 −53.91 −28.10 −99.45 −106.11 5.55 −4.86 −33.75 −61.15 −18.33 −3.89 37.24 −6.37 −55.12 4.71 1.45 −51.85 23.28 −12.47 −96.73 −93.30 81.37 −41.65 −76.33 50.93 9.74 −57.22 −16.59 −10.48 54.11 −39.85 −95.96 −55.70 84.41 −92.68 −35.09 −24.78 5.89 −130.03 −93.24 −189.11 13.15 196.89 −25.18 56.33 −61.54 96.31 −4.40 −36.09 −188.81 −19.19 −25.70 66.70 −24.50
−2.27 −30.42 9.67 −43.77 89.00 −29.63 −3.47 −7.72 −45.38 −206.62 1.54 95.47 −99.76 −10.10 3.97 5.34 −54.12 193.49 −124.17 −33.58 −70.70 −30.84 −117.29 −54.98 55.74 −117.95 58.64 75.57 −40.05 39.07 −5.43 −42.85 32.15 −57.57 156.60 −56.78 −143.81 −72.72 90.21 −203.49 36.97 −19.22 136.02 −22.29 −145.54 −131.81 128.79 20.53 −16.50 27.01 16.13 115.59 46.59 29.88 2.04 −15.36 −10.50 83.40 −9.70
−36.00 −51.77 −24.55 107.35 116.93 −124.94 −105.01 −119.50 −99.89 −90.13 −44.86 55.88 7.63 −90.64 −6.98 51.36 61.68 3.94 −39.25 1.66 2.45 −85.63 35.34 −17.84 −118.62 −42.76 2.25 −63.83 6.84 −11.21 30.86 −2.16 55.06 13.84 47.54 −122.06 −261.68 28.21 142.55 −166.92 16.71 32.03 13.99 38.95 −149.05 123.10 37.41 198.35 −42.64 −46.16 75.70 201.10 13.03 91.72 47.66 −39.53 −6.10 87.40 −1.70
−53.11 −122.02 −25.95 49.21 8.67 −112.96 −67.92 −98.30 −142.81 −86.31 −36.25 1.63 −53.16 −111.44 41.83 −8.72 47.25 −9.93 −40.70 6.58 −20.63 −99.43 16.21 −20.52 −108.85 −87.97 61.21 −60.43 −66.63 46.54 3.32 −58.66 −36.29 −5.00 19.95 −43.97 −27.62 −21.10 57.38 −109.19 −42.36 −24.61 −13.37 −110.52 −167.96 −30.92 −19.78 192.53 −72.57 27.24 −48.70 80.50 −63.07 −43.38 −147.08 −105.64 −35.10 65.00 −31.70
−63.21 −92.42 −11.33 −135.82 −124.59 −388.11 −58.10 −95.71 −83.47 97.10 −31.64 127.26 −134.39 −113.63 29.99 47.38 −4.36 61.45 54.04 −13.64 −94.98 −272.98 −68.55 −27.98 −76.68 32.54 −62.11 −95.82 −41.79 14.77 −47.94 −53.10 −49.42 51.27 −96.74 −74.60 −80.35 −136.01 −74.35 −41.77 −14.57 17.68 −11.52 −45.75 −308.43 −21.55 −100.55 −70.26 −265.36 17.96 −29.81 86.63 −133.53 −35.99 31.51 −234.50 −59.80 97.30 −45.70
3433
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
Table 3. continued a
See Table 1 for an explanation of the methods and Table 2 for compound identity. bInteraction between two carbonyl groups in the Nannoolal critical property method set to zero. cBias for the test set of 53 compounds (after removal of 3 aromatic amines).
(across the 27 scenarios) for the sensitivity of growth factors to the SOA component density values used in the calculation.
(independently) multiplied or divided by a scaling factor (SF) of 10 giving a set of 27 scenarios, which ranged from 10/10/10 through 1/1/1 (the standard scenario) to 0.1/0.1/0.1 NOx-SF/ AVOC-SF/BVOC-SF providing a wide range of predicted SOA masses. Partitioning calculations for each scenario was done over a range of conditions (or cases) based upon temperature, % RH, and core size (see Table 1 in Barley et al.).43 In this work, representative SOA compounds were either taken from the literature or identified from ideal partitioning calculations across multiple cases and scenarios (see below). As a large core compared to the amount of condensed SOA would limit the sensitivity of the growth factor to changes in SOA density, the calculation of SOA density and growth factors used a reduced core mass of 0.001 μg·m−3. To reduce the impact of the core further, its density was assumed to be the same as the average density of the condensed SOA. The partitioning calculations at 90% RH allowed the derivation of a representative wet size for the calculation of growth factors. The dry size was derived by removing the associated water content and assuming the semivolatile organics remained within the particle.25 The density of water, throughout this work, was calculated using the correlation of Hyland and Wexler44 (998.1586 kg·m−3 at 293.15 K). The specific volume of all mixtures (= 1/ρmix) was found by dividing the mass fraction of each component (xi) by its density (ρi) and then summing over all components25 (ideal mixing assumed) 1 = ρmix
∑ i = 1: n
xi ρi
■
RESULTS AND DISCUSSION The test set of 56 compounds and the associated experimental liquid density data are summarized in Table 2 (228 data points in total). The seven estimation methods are summarized in Table 1 and the MBE values for the 56 compounds are summarized in Table 3. Figure 1 summarizes the scatter of the
(11)
Figure 1. Error in the estimated liquid densities by seven methods for 56 multifunctional compounds.
where ρmix is the mixture density. The growth factor (GF) is then calculated from the predicted mass and density of the wet (at 90% RH) and dry aerosol ⎛ Mass wetρdry ⎞1/3 ⎟⎟ GF = ⎜⎜ ⎝ Massdry ρwet ⎠
error. If the full set of errors can be assumed to follow a normal distribution (standard deviation (σ) = 6.42%), then the absolute error follows a half-normal distribution and the mean absolute error (X) is given by45
(12)
X=
To identify representative SOA components and to explore the range of SOA density values, ideal partitioning calculations were done for 16 cases (temperature = 273.15, 283.15, 293.15, and 303.15 K; % RH = 10, 30, 70, and 80; and core = 0.001 μg·m−3) across 27 scenarios using density values provided by Schroeder/Nannoolal. Average densities for the SOA were calculated using eq 11 above and excluded the core. The representative SOA compounds were found by determining the most abundant compound (in terms of mole %) in each of the 432 calculated SOA compositions and selecting the seven compounds most frequently found. To find the range of the sensitivity of growth factors to changes in SOA density, a more restricted set of 4 cases (temperature = 273.15, 283.15, 293.15, and 303.15 K; % RH = 90; and core = 0.001 μg·m−3) across 27 scenarios was used to obtain SOA compositional data from which growth factors could be calculated; initially with liquid density values provided by the Schroeder/Nannoolal method and then with these liquid density values increased by a certain percentage. The difference in the growth factors for each case provided a range of values
2 σ = 5.12% π
(13)
This average error of about 5% can be compared to mean errors of 2.8−3.9% for the estimation of molar volumes for 35 compounds using the Schroeder, Le Bas, and Tyn Calus methods22 and average errors of up to 4% for seven estimation methods used to estimate densities at Tb of 252 nonpolar fluids.23 The 35 compounds of Poling et al. are structurally diverse but include few multifunctional compounds. Also, as it is the molar volume at Tb that is being estimated, they are relatively volatile. The nonpolar fluids of Mulero et al. are also relatively volatile and have accurate input data (e.g., Tb and critical property values) from an established database (unlike the compounds in this work). Given the nature of the compounds in the test set used in this work it would be expected that the average error would be higher than those reported previously. The fact that they are comparable suggests that the extension of the estimation methods for liquid density to complex multifunctional compounds is quite robust; certainly better than the similar extension of vapor pressure methods.24 3434
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
More detailed analysis of the errors is shown in Table 3 where the mean (= the bias for the method) and the standard deviation for the MBE values for each method are summarized. The compound that gave the greatest average (absolute) error across all methods was glycerol trinitrate followed closely by diiodomethane, bromoform, and maleic anhydride (all have average absolute errors above 130 kg·m−3). As the above halogenated compounds have densities 2−3 times heavier than the other compounds, it is not surprising that they should come out with relatively high absolute errors. The high errors for glycerol trinitrate and maleic anhydride reflect the fact that the GCM methods do not typically cope well with such groups (nitrate and acid anhydride) because of a lack of experimental data. The standard deviations are high compared to the means and range from 65.0 to 97.3 kg·m−3. The lowest values were associated with the Le Bas method suggesting that this method, though having a higher bias than the Schroeder method, might show less scatter. However, application of an F-test showed that the difference in standard deviations was not significant at p = 0.05 for this set of compounds. The bias and standard deviation are not substantially worse for the Girolami method than for the other methods despite the simplicity of this GCM and the fact that it provides an estimate of density independent of temperature. As 12 of the compounds in Table 2 have density data at elevated temperatures, it might be expected that restricting the comparison to data points within a limited temperature range (273.15−313.15 K) would improve the comparison between the Girolami method and the other methods. When this was tested (using 133 out of the 228 points), it was found that the statistics for the Girolami method actually became worse. The mean increased from −38 to −62 kg·m−3, and the standard deviation increased. This suggests that the inclusion of 12 sets of data at elevated temperatures has not compromised the results from the Girolami method. Comparison of the Joback and Nannoolal Methods for Critical Properties. In Table 3, the bias range from +3.4 kg·m−3 for method 2 (Schroeder/Joback) to −59.8 kg·m−3 for method 7 (Tyn and Calus/Nannoolal). The Tyn and Calus method only uses critical properties as an input and hence provides an indirect test of the accuracy of the critical property estimation methods for a set of compounds that will be too involatile and too easily decomposed to have these properties measured experimentally. From the results in Table 3, it is clear that for this estimation method the Joback critical properties give more accurate results (bias = −10.5 kg·m−3) than the Nannoolal critical properties (bias = −59.8 kg·m−3). A paired t test (55 degrees of freedom) showed that the difference in the bias was significant (p < 0.01). A plot of the percentage error in liquid density against compound number for both critical property methods is shown in Figure 2. The negative bias of the Nannoolal results is quite clear along with some specific compounds that have substantial negative errors. These three compounds (1,2-diaminobenzene, 3-chloroaminobenzene, and methyl anthranilate) are not statistical outliers, but they clearly contribute to the negative bias of the Nannoolal method. However, if they are removed from the test set and the paired t test repeated (52 degrees of freedom), the difference between the bias of the Nannoolal and Joback critical properties is still significant (p < 0.05). The results shown in Table 3 are a combination of the GCM that estimates the molar volume at the normal boiling point and the Rackett equation that corrects the molar volume from
Figure 2. Errors in liquid density values for 56 compounds using the method of Tyn and Calus with critical properties by Joback (green) or Nannoolal (blue). Compounds 6, 22, and 49 are 1,2-diaminobenzene, 3-chloroaminobenzene, and methyl anthranilate, respectively.
the boiling point temperature down to the experimental temperature. Changing from the Joback critical properties to the Nannoolal critical properties in the Rackett equation causes the estimated liquid density values to decrease on average by about 9.5 kg·m−3 for both the Schroeder and Le Bas methods. In contrast, changing from the Schroeder method (which has the lowest bias with either critical property method) to the Le Bas method lowers the estimated liquid density by about 29.0 kg·m−3 . Hence, changing the GCM for estimating the molar volume has much more impact on the mean bias than changing the critical property model used in the Rackett equation Critical Properties of Aromatic Amines by Nannoolal. The three compounds that have exceptionally high errors in Figure 2 are all aromatic amines, and they are the only aromatic amines in the test set. Joback uses the same group for all primary amines, but the Nannoolal method distinguishes between aromatic (group 41) and aliphatic (group 40) primary amines. Inspection of the relevant tables in the paper34 describing the method showed that, for each of the critical properties, the parameter for group 41 was based upon a single compound. Although the identity of the compound is not provided, the obvious candidate is benzenamine (analine). DETHERM provides access to the Dortmund Data Bank (DDB), which was used by Nannoolal et al. to develop their estimation methods. The entry for critical properties of benzenamine provide numerous sources (mainly secondary sources with many repeat values) all giving a critical temperature around 700 K. A detailed summary of the past research on the critical (and other) properties of benzenamine along with new values (obtained by a mixture of experimental and fitted/extrapolated data) is given by Steele et al.;46 where it is noted that many of the quoted values for critical temperature and pressure are based upon experimental measurements reported in 1902. The experimental measurement of critical density in particular is very difficult (even at temperatures much lower than 700 K) due to the rapid change in density with temperature, as the critical point is approached.47 Whether the Steele critical values or the DDB recommended values were used to provide the group 41 parameters in the Nannoolal critical property estimation method, the resulting estimated 3435
dx.doi.org/10.1021/jp304547r | J. Phys. Chem. A 2013, 117, 3428−3441
The Journal of Physical Chemistry A
Article
5 runs of 1000 subsets each. It is clear from this that the two methods based upon the GCM of Schroeder give better liquid density values than method 4 (Tyn and Calus with critical properties by Joback) and that the Schroeder/Joback method gives the best results. This analysis has been done on the full set of 56 compounds, which includes three aromatic amines that are known to give poor critical property values when using the Nannoolal method (see Figure 2). If these three amines are removed from the test set, the bias for the remaining 53 compounds changes substantially (see the bottom row of Table 3). In particular, the bias for Schroeder/Nannoolal has reduced from −6.1 to −1.7 kg·m−3, while the same quantity for Schroeder/Joback has increased from 3.4 to 5.6 kg·m−3 suggesting that the Schroeder/Nannoolal method now gives the best estimates for liquid densities. When the above internal validation method was repeated (5 runs of 1000 subsets each) but now starting with 53 compounds (after removal of the three aromatic amines) and then randomly removing 5 compounds, the results (see bottom half of Table 4) confirmed that the best estimate of liquid densities was provided by model 5 (Schroeder/Nannoolal). These results also show that the conclusion is sensitive to the composition of the data set used to test the liquid density methods, an important consideration when applying this result to other sets of multifunctional compounds. Quantifying the Error Introduced by the Rackett Equation. An estimate of the accuracy of the Rackett equation can be made using a subset of the compounds in Table 2, which all have density values over an extended temperature range. Of the 56 compounds, 42 were found to have liquid density data over a range of temperatures from a single literature source. For each compound, the highest temperature (Th) data point was fitted to the Rackett equation by adjusting Vref in eq 8. The error in the predicted density of the lower temperature points (Tl) was then calculated as a function of the temperature difference (Th − Tl). These values for each compound were then correlated to a straight line and the coefficients used to calculate the errors due to the Rackett equation at temperature differences of 10, 20, 30 and 50 K. The spread of the errors at each temperature difference was assumed to approximate to a normal distribution around zero with standard deviations increasing roughly linearly with temperature difference. Using a similar analysis to that applied to Figure 1, the mean absolute error (eq 11) was calculated at each temperature difference and found to be 0.15% (10 K), 0.29% (20 K), 0.44% (30 K), and 0.74% (50 K). This provides a quantitative assessment of the accuracy of extrapolation using the Rackett equation. For small extrapolations (
