Solid state and sub-cooled liquid vapour pressures of cyclic aliphatic dicarboxylic acids

Introduction Conclusions References


Introduction
The direct and indirect impacts of atmospheric aerosols are one of the greatest uncertainties in our understanding of radiative forcing (Solomon et al., 2007).Organic compounds in aerosols are ubiquitous (Zhang et al., 2007;Hallquist et al., 2009) and incredibly varied, with possibly hundreds of thousands of compounds (Goldstein and Galbally, 2007).Gas (volatile organic compounds, VOC) to particle partitioning is responsible for a considerable fraction of organic aerosols (OA), and is frequently described by an equilibrium based absorptive partitioning model (Pankow, 1994).The vapour pressures of the components making up the OA are an important parameter in absorptive partitioning (Pankow, 1994).Accurate vapour pressure estimation methods and Correspondence to: A. M. Booth (alastair.booth@manchester.ac.uk) experimental data to test them against are important in improving our understanding of the OA fraction in atmospheric aerosols.
Significant emissions of volatile organic compounds (VOC) arise from biogenic sources and global rates have been estimated at ∼800 Tg C y −1 (Fowler et al., 2009).About 50% of the biogenic VOC emissions are thought to be isoprene (Guenther et al., 2006), monoterpenes contribute 10-15%, and sesquiterpenes are also emitted in small quantities (Fowler et al., 2009).The vast emissions of isoprene in particular, and terpenes in general means that if they yield a small amount of aerosol, then the effect on the global organic aerosol budget would be substantial (Henze and Seinfeld, 2006).Products from terpene oxidation such as pinic and pinonic acid have been found in atmosphere aerosols (e.g.Boy et al., 2004;Fu et al., 2009).
There are many methods of estimating pure component vapour pressures, but most of the experimental data collected for fitting these methods are from intermediate or high vapour pressure compounds.Some of the estimation methods can give errors in vapour pressure of several orders of magnitude for multifunctional compounds at ambient temperatures (Barley and McFiggans, 2010;Booth et al., 2010).There are several experimental methods available for very-low vapour pressure measurements including Tandem Differential Mobility Analysis (TDMA) (Bilde and Pandis, 2001;Bilde et al., 2003;Mønster et al., 2004;Koponen et al., 2007;Riipinen et al., 2007;Froesch et al., 2010;Salo et al., 2010), White light resonance spectroscopy (Zardini et al., 2006), Temperature Programmed Desorption (TPD) (Cappa et al., 2007;Chattopadhyay and Zieman, 2005), Electrodynamic Balance (EDB) (Pope et al., 2010;Soonsin et al., 2010), Optical tweezers (Pope et al., 2010), Knudsen Published by Copernicus Publications on behalf of the European Geosciences Union.
In this work KEMS combined with Differential Scanning Calorimetry (DSC) has been use to measure solid state vapour pressures and determine, using a thermodynamic relationship, sub-cooled liquid vapour pressures.As part of a larger data set, measurements have been made here for the first time of a systematic series of cyclic dicarboxylic acids with increasing ring sizes.Cyclic acids and diacids are possible SOA products of biogenic terpeneoid VOC oxidation where the cyclic moiety has been retained.These results will also determine the skill of the estimation methods for compounds with cyclic backbones.In addition, the vapour pressure of levoglucosan, a tracer for biomass burning (Simoneit et al., 1999), has also been measured.

Sub-cooled correction
The sub-cooled liquid vapour pressure is derived from the value measured above the solid state using the following equation (Prausnitz et al., 1986): where P is the vapour pressure with the subscript s referring to the solid and l to the sub-cooled liquid phase, H fus is the enthalpy of fusion (J mol −1 ), c p,sl denotes the change in heat capacity between the liquid and solid state at the melting point (J mol −1 K −1 ), T is the temperature (K) and T m is the melting point (K).Strictly speaking the triple point T t should be used as per the definition of sub-cooled liquid in Sect. 1, but T m is more commonly used and is typically within 1 K of T t for small organic acids.The sub-cooled liquid vapour pressure also allows more direct comparison with theoretical vapour pressure estimation methods which predict the subcooled state (e.g.Nannoolal et al., 2008;Moller et al., 2008).

Vapour pressure estimates
Many predictive methods exist for vapour pressure (Barley and McFiggans, 2010).Here we use three methods which have previously been used in estimating vapour pressure for atmospheric compounds (Barley and McFiggans, 2010;Booth et al., 2010).The 3 methods have been chosen as they were reported to be the best methods for a test set of 45 low volatility compounds by Barley and McFiggans (2010) and they have been used in conjunction with KEMS measurements previously (Booth et al., 2010).The vapour pressure equations (referred to here as the vapour pressure methods) describe the vapour pressure, which varies exponentially with temperature, (see Eq. 2) as a function of several inputs, such as group contribution parameters, or the vapourisation entropy.All the methods here also require the normal boiling point, T b , to be calculated separately.Together they described the vapour pressure from 1 atmosphere at the normal boiling point down the pressure at the required temperature, in this case 298 K.The three vapour pressure methods used are the Nannoolal et al. (2008) and the Moller et al. (2008) methods both with T b by Nannoolal et al. (2004), and the Myrdal and Yalkowsky (1997) method with T b by Stein and Brown (1994).The methods are briefly outlined here, for more detailed descriptions see Barley and McFiggans (2010) or Booth et al. (2010).
The Nannoolal et al. (2004) estimation method uses group contribution calculations with primary and secondary groups and group interactions (207 groups).It was used to calculate both normal boiling points (Nannoolal et al., 2004) and then the slope of the vapour pressure line (Nannoolal et al., 2008).The Moller et al. (2008) method is a refinement of the Nanoolal et al. (2008) method.It features an additional term to improve predictions for aliphatic alcohols and carboxylic acids, new size dependent groups to improve predictions for several functional groups, and new hydrocarbon groups.The Myrdal and Yalkowsky (1997) method requires a source of boiling point (T b ) estimations.In this work the group contribution method of Stein and Brown (1994) (85 groups), which is adapted from an earlier method (Joback and Reid, 1987), was used to provide T b .This was then used with the equations of Myrdal and Yalkowsky (1997) which uses the flexibility of the molecular structure and hydrogen bond number to estimate the entropy of vapourisation S vap .
The KEMS system is discussed in more detail in Booth et al. (2009), a brief overview of the experimental method is included here.To calibrate, a sample of known vapour pressure is placed in the temperature controlled Knudsen cell (in this case malonic acid, using vapour pressure values of ln P (Pa) = 29.54-11058.97/T(K) Booth et al., 2009).The cell has a chamfered effusing orifice with a size ≤1/10 the mean free path of the gas molecules in the cell.This ensures the orifice does not significantly disturb the thermodynamic equilibrium of the samples in the cell (Hilpert, 2001).The resulting molecular beam is ionised by 70 eV electron impact, then sampled by the mass spectrometer.After correcting for the ionization cross section of the calibration compound, this produces a signal proportional to the vapour pressure.
After this calibration a sample of unknown vapour pressure can be measured.During sample change the first chamber with the Knudsen cell is isolated via the gate valve and vented to air allowing the ioniser filament to be left on.The unknown vapour pressures can be determined from the intensity of the mass spectrometer signal of the compound in question.If the Knudsen number, the ratio of the mean free path of molecules to the size of the effusion orifice, is high enough then effusing gas does not significantly disturb the equilibrium in the cell (Booth et al., 2009;Hilpert, 1991Hilpert, , 2001) ) making the steady state pressure, as measured by the KEMS, as close as possible to the equilibrium vapour pressure.
Once the vapour pressure, P , has been determined at a number of different temperatures further thermodynamic data can be obtained using the Clausius-Clapeyron equation (Hilpert, 2001); where T is the temperature, R is the ideal gas constant and H sub and S sub are the enthalpies and entropies of sublimation respectively.P was obtained over a range of 20 K in this work, starting at 298 K.The reported solid state P 298 vapour pressures are calculated from the linear fit of ln P vs. 1/T used in the Clausius-Clapeyon equation.

Differential scanning calorimetry
The thermochemical data was obtained using the same procedure as in Booth et al. (2010) and is repeated here: Melting points (T m ) and enthalpies of fusion ( H fus ) were measured using a TA instruments Q200 DSC with a heating rate of 10 C min −1 up to 200 • C. 5-10 mg of sample was measured out and recorded using a microbalance, the sample was then pressed into a hermetically sealed aluminium DSC pan.A purge gas of N 2 was used with a flow rate of 30 ml min −1 .The reference was an empty sealed pan of the same type.Data processing was performed using the "Universal Analysis" software supplied with the instrument.c p,sl is frequently estimated using one of three assumptions, based on empirical evidence; c p,sl = 0 (Yalkowsky, 1981;Prausnitz et al., 1986), c p,sl = 0.5 S fus (Tsonopoulos, 1970) and c p,sl = S fus (Mauger et al., 1972;Grant et al., 1984).c p,sl = S fus is used in this work, which is calculated using DSC measurements and S fus = H fus /T m .Booth et al. (2010) compared this assumption with literature values of c p,sl for the C 3 -C 6 straight chain diacids and it can lead to differences of 10-20% in the sub-cooled liquid vapour pressure.The c p,sl = 0.5 S fus assumption leads to differences of 15-70%, and c p,sl = 0 gives differences between 35 and 260% for the C 3 -C 6 diacids vs. literature c p,sl .

Experimental vapour pressures
Table 1 shows the P 298 solid , H sub and S sub obtained by fitting Eq. ( 2) to the vapour pressure data in Table 2 measured using KEMS.The data are shown in Figs. 1 and 2. Table 1 also shows literature results for some related compounds, included for comparison with our results.The Table 1 compounds include literature straight chain and branched diacids with the same O/C ratios as those measured in this study.Where possible we have used previous KEMS (Booth et al., 2009(Booth et al., , 2010) ) and Knudsen mass loss data from Riberio da Silva et al. ( 2001), the remaining literature measurements are using TDMA by the Bilde group which tend to agree well with KEMS results, this is to ensure as much consistency as possible when comparing the relative differences between cyclic and straight chain diacids.Table 3 shows the thermochemical data obtained from DSC and the sub-cooled liquid vapour pressure determined from them and the KEMS results.Table 3 also shows sub-cooled liquid vapour pressures calculated in this work from available literature data and the vapour pressures in Table 1.The difference between the solid state and sub-cooled liquid, which are dependant on T m and H fus are illustrated in Fig. 3.The error on the solid state is based on repeated measurements of the straight chain diacids in Booth et al. (2009), the sub-cooled liquid error is from Booth et al. (2010) and is the total error from the solid state trans-norpinic acid a 1.41×10 −4 42 vapour pressure, the assumption of c p,sl = S fus , and the change from using the highest and lowest values for H fus and T m in the literature.

C 5 diacids
The aliphatic C 5 diacids; 1,1 cyclopropane dicarboxylic, glutaric and 2-methyl succinic acid, decrease in solid state vapour pressure by a factor of 1.4 for cyclic to straight chain and 1.7 for straight to branched, these are similar to the reported errors of ±40%.The sub-cooled liquid vapour pressures, which are free of crystal structure effects, show a similar reduction (∼1.6) from cyclic to straight.The differences between the C 5 acids as solids are similar to those as subcooled liquids, which indicates the crystal structure effects for these solids are negligible.

C 7 and C 8 diacids
The C 7 and C 8 diacid solid state vapour pressures show a similar pattern to the C 6 and C 5 .Solid state vapour pressures of the cyclic diacids are similar compared to straight chain diacids when the carbon chain length is odd numbered (C 5 and C 7 ), and two orders of magnitude higher when even numbered.This shows that none of the cyclic diacids have the very stable crystal structure of the even numbered straight chain diacids; succinic, adipic and suberic etc.The subcooled liquid vapour pressures all show the straight chain molecules with a lower pressure than the cyclic isomer by a factor of 1.3 for C 7 and 20 for C 8 .The branched C 7 diacids do not have the literature data for T m and H fus to do a sub-cooled liquid correction so only the solid state are available.3-methyl adipic acid and 2,2-dimethyl glutaric acid have roughly the same vapour pressure, which is 3 times higher than the C 7 straight chain and cyclic diacid.3,3dimethyl glutaric acids is much more volatile with a vapour pressure 15 times that of the other two branched C 7 diacids.

C 5 -C 8 cyclic diacids
The sub-cooled liquid vapour pressure shows a similar trend to the solid state vapour pressures but are even closer to each other, within error the C 5 , C 6 and C 8 sub-cooled liquid are the same.The solid state vapour pressure falls from C 5 to C 7 and rises by C 8 .The slightly lower solid state vapour pressure for 1,2 cyclopentane dicarboxylic acid compared to the other cyclics may be explained simply by that compound having a more stable crystal structure, but that does not explain the difference in sub-cooled liquid vapour pressures which are independent of crystal structure effects.The enthalpy of sublimation, H sub , decreases rapidly as the ring size increases, from 126 KJ mol −1 for C 5 Table 3. Sub-cooled liquid vapour pressures, melting points, enthalpies and entropies of fusion from DSC measurements and correction of solid vapour pressures in Table 1.Estimated maximum error on P 298 sub−cooled ± 75%.Also shown are sub-cooled liquid vapour pressures derived from literature P 298 solid , H fus and T m (1) a Booth et al. ( 2010), (2) + Bilde et al. (2003) with H fus and T m from Roux et al. (2005).

Name
P 298 sub-cooled Ratio of sub-cooled T m (K) H fus S fus liquid (Pa) liquid to solid P 298 (kJ mol −1 ) (J mol −1 K −1 ) 1,1-cyclopropane diacid 3.10×10  The solid state cis-pinonic acid results here are slightly higher than those of Bilde and Pandis (2001) who, due to measurement problems, give an estimated range of 0.5-1 × 10 −4 Pa.The top end of this range however would agree well with our results using the error estimates in Booth et al. (2009Booth et al. ( , 2010) ) of ±40%.Levoglucosan exhibits a solid phase transition at 385.7 K and a melting transition with a small enthalpy of fusion at 456 K (Oja and Suuberg, 1999), we have used the correction in Eq. (1) to adjust for both these transitions and arrive at a final sub-cooled liquid vapour pressure.Oja and Suuberg (1999) have measured levoglucosan below and above this transition getting vapour pressures of 1 × 10 −5 and 1 × 10 −4 Pa, respectively.The first is about a quarter of the value we measure, whereas the the vapour pressure after the transition agrees with our value of 1.35 × 10 −4 Pa within error.Epshtein (1964) has measured levoglucosan from 468 to 528 K, extrapolation of their values down to 298 K gives a vapour pressure of 1 × 10 −3 Pa which is about 5 times higher than our final sub-cooled liquid vapour pressure of 1.93 × 10 −4 Pa, although it should be noted that this extrapolation is for a two parameter Antoine equation fit 200 K above the desired temperature.

Vapour pressure estimates
Vapour pressure estimates were made using 3 methods; Nannoolal et al. increases (Compernolle et al., 2010), however the majority of compounds in this study only have two groups.Table 4 shows the two different boiling points used, the Stein and Brown (1994) boiling points are higher by 2-7 K for the cyclic compounds (excepting levoglucosan) but are lower by similar amounts for the straight chain and methyl substituted diacids.Although compared to the differences in T b values in Barley and McFiggans (2010), the differences here are quite small and the differences from the true T b are unknown.Systematic errors in T b can feed through to similar errors in vapour pressure.In this case it could lead to cancelling errors if the calculations were being used on an ensemble of condensing compounds containing both cyclic and straight chain diacids which have an opposing T b bias.Other boiling point methods are available (ACD/labs) and have been shown to work well for certain classes of compounds, notably amines (Ge et al., 2010).However for these diacids, the ACD/labs T b does not show a significant overall improvement compared to the Nannoolal et al. (2004) or Stein and Brown (1994) T b (Ge, 2010), and as the mechanics of the estimation method are not disclosed, further improvement would be difficult.
Table 5 shows the estimated sub-cooled liquid vapour pressures using the 3 estimation methods.For the diacids the Moller/Nannoolal method performs best, on average overestimating vapour pressure by a factor of 2.7.The Nannoolal et al. (2008) method lacks the extra terms of the Moller et al. (2008) method for aliphatic carboxylic acids and its performance (with T b by Nannoolal) reflects this with an average factor of 12.2 times our sub-cooled vapour pressure values.The Myrdal and Yalkowsky/Stein and Brown overestimated vapour pressures by an average factor of 74.Cispinonic acid, with a ketone group, causes more problems than the diacids.For this compound the Moller method is an order of magnitude too high, Nannoolal a factor of 70 and Myrdal and Yalkowsky a factor of 200.
Levoglucosan has no acids groups, but aliphatic alcohols, like carboxylic acids groups are known to cause problems for vapour pressure estimates (Booth et al., 2010;Moller et al., 2008).The Moller et al. (2008) method, despite extra terms for aliphatic OH groups, is the most inaccurate of the vapour pressure methods for this compound.The estimated vapour pressure was out by 3 orders of magnitude, compared to 2 orders of magnitude for the other two methods.The most likely cause for this is the interaction parameter between OH and ether groups being too high.This is similar to the raising of vapour pressure for compounds with OH + COOH groups compared to just COOH groups, as seen by Chattopadhyay and Ziemen (2005) and Booth et al. (2010).The vapour pressure method comparisons of Compernolle et al. (2010) also note problems with the Moller et al. (2008) method for polyfunctional compounds, although it should be noted that all the methods perform badly with this compound.

Conclusions
Solid state vapour pressures of aliphatic cyclic diacids tend to be very close to that of odd numbered straight chain diacids, but approximately 2 orders of magnitude higher when compared with even numbered straight chain diacids.The subcooled liquid vapour pressures are higher for the cyclic compounds than for comparable straight chain diacids, typically 1.5-3 times higher.The Moller et al. (2008) estimation method with Nannoolal et al. (2004) boiling points provides the best estimates of the cyclic diacids although it significantly over estimates the vapour pressure of levoglucosan.It also overestimates cis-pinonic acid by a factor of 10, but this is still a better result than the other two methods.As with the results of Booth et al. (2010) the main failing of the vapour pressure estimation methods is down to a poor representation of OH groups and their interactions with other groups.

Table 2 .
Solid state vapour pressure data (Pa) at different temperatures.

Table 4 .
Yalkowsky (1997)008)08)s for cyclic, straight chain and branched diacids using theNannoolal et al. (2004)andStein and Brown (1994)methods. of vapour pressure methods noted that most of the error for the methods they looked at came from the estimation of the boiling point, and slope of the vapour pressure curve (enthalpy of vapourisation) estimates were generally much easier to get right.The Moller/Nannoolal and Nannoolal/Nannoolal methods here both use the same boiling point, but for most of the compounds there is an order of magnitude difference in the predicted vapour pressure at 298 K which can only come from the difference in predicted H vap between them.This should not be a complete suprise however as the changes to theNannoolal et al. (2008)method that theMoller et al. (2008)is based on come from extra terms for carboxylic acids, which will obviously have a big impact for the diacids.The different methods show consistent bias in H vap for the diacids measured in this study.TheMoller et al. (2008)method, excepting levoglucosan, always estimates a higher value for H vap than Nannoolal et al. (2008) which predicts higher H vap values than Myrdal andYalkowsky (1997).The H vap estimates seem very good for the C 5 diacids (typically within 20 KJ mol −1 or less) but as the number of carbon atoms in the molecule increases the behaviour of the straight chain and cyclic diacids diverge.H vap increases with carbon number for straight chain diacids and H vap decreases with increasing carbon number for cyclic diacids.The estimation methods however, do not significantly change their estimates, for example there is only a range of 23 KJ mol −1 between the highest and lowest estimate for H vap using the Nannoolal method, but the experimental methods vary by 106 KJ mol −1 .In spite of this the estimation methods can sometimes give good P 298 values, as opposing errors in H vap and T b can cancel out.