A modeling approach to evaluate the uncertainty in ... · oration is small. However, because a...

Atmos. Meas. Tech., 5, 735–757, 2012www.atmos-meas-tech.net/5/735/2012/doi:10.5194/amt-5-735-2012© Author(s) 2012. CC Attribution 3.0 License.

AtmosphericMeasurement

Techniques

A modeling approach to evaluate the uncertainty in estimating theevaporation behaviour and volatility of organic aerosols

E. Fuentes and G. McFiggans

Center for Atmospheric Science, School of Earth, Atmospheric and Environmental Sciences, Manchester, M13 9PL, UK

Correspondence to:G. McFiggans ([email protected])

Received: 4 October 2011 – Published in Atmos. Meas. Tech. Discuss.: 4 November 2011Revised: 2 April 2012 – Accepted: 2 April 2012 – Published: 18 April 2012

Abstract. The uncertainty in determining the volatility be-haviour of organic particles from thermograms using cali-bration curves and a kinetic model has been evaluated. Inthe analysis, factors such as re-condensation, departure fromequilibrium and analysis methodology were considered aspotential sources of uncertainty in deriving volatility dis-tribution from thermograms obtained with currently usedthermodenuder designs.

The previously found empirical relationship betweenC∗

(saturation concentration) andT50 (temperature at which50 % of aerosol mass evaporates) was theoretically inter-preted and tested to infer volatility distributions from ex-perimental thermograms. The presented theoretical analy-sis shows that this empirical equation is in fact an equilib-rium formulation, whose applicability is lessened as mea-surements deviate from equilibrium. While using a calibra-tion curve betweenC∗ andT50 to estimate volatility prop-erties was found to hold at equilibrium, significant under-estimation was obtained under kinetically-controlled evap-oration conditions. Because thermograms obtained at am-bient aerosol loading levels are most likely to show depar-ture from equilibrium, the application of a kinetic evapora-tion model is more suitable for inferring volatility proper-ties of atmospheric samples than the calibration curve ap-proach; however, the kinetic model analysis implies signifi-cant uncertainty, due to its sensitivity to the assumption of“effective” net kinetic evaporation and condensation coef-ficients. The influence of re-condensation on thermogramsfrom the thermodenuder designs under study was found to behighly dependent on the particular experimental condition,with a significant potential to affect volatility estimations foraerosol mass loadings>50 µg m−3 and with increasing ef-fective kinetic coefficient for condensation and decreasing

particle size. These results show that the geometry of cur-rent thermodenuder systems should be modified to preventre-condensation.

1 Introduction

Organic aerosols comprise a significant portion of atmo-spheric particular matter (Hallquist et al., 2009; Jimenezet al., 2009), with a long recognised impact on both hu-man health and global climate (Kanakidou et al., 2005; Tsi-garidis and Kanakidou, 2007). They comprise primary or-ganic aerosol (POA) emissions from sources such as fos-sil fuel combustion, biomass burning and diverse industrialprocesses, and a secondary organic aerosol (SOA) contri-bution formed in the atmosphere from the gas phase oxida-tion of volatile organic compounds (Hallquist et al., 2009).The volatility of organic aerosols largely determine the par-titioning of compounds between the gas and particle phases,hence influencing the particles mass concentration, composi-tion and size, which in turn can affect the hygroscopicity andoptical properties of organic aerosols in the atmosphere (Top-ping et al., 2011). Accurate representation of gas-particlepartitioning of semi-volatile organic compounds, and its de-pendence on temperature, dilution conditions and chemicaltransformations in the atmosphere, is required for improvingprediction of the global distribution of organic aerosols.

Particle evaporation studies in dilution chambers and ther-modenuder systems are increasingly being conducted tocharacterise the volatility distribution and evaporation be-haviour of primary and secondary organic aerosols in lab-oratory and field measurements (Huffman et al., 2008; Salehet al., 2008; Faulhaber et al., 2009; Grieshop et al., 2009;

Published by Copernicus Publications on behalf of the European Geosciences Union.

736 E. Fuentes and G. McFiggans: Uncertainties in the estimation of organic aerosols volatility

Cappa and Wilson, 2011). A growing number of methods arebeing proposed in order to infer information on the volatil-ity and thermodynamic properties of organic aerosol com-pounds from the evaporation profiles derived from this typeof experiments (Faulhaber et al., 2009; Grieshop et al., 2009;Cappa and Wilson, 2011; Saleh et al., 2011). Some of thesemethods rely on the assumption that equilibrium is attainedin the heating section of thermodenuder systems (Offenberget al., 2006; Saleh et al., 2008). However, the observed de-pendence of thermograms on a thermodenuder’s residencetime indicates that equilibrium may not be attained undercertain experimental conditions (An et al., 2007; Grieshop etal., 2009). Theoretical analysis of particle evaporation kinet-ics have shown that evaporation equilibration times in ther-modenuders are highly dependent on factors such as aerosolmass loading and evaporation coefficient (Riipinen et al.,2010), resulting in evaporative equilibrium being attainedonly under laboratory conditions at organic aerosol loadings>200µg m−3 in systems with residence time≥30 s (Riipinenet al., 2010; Saleh et al., 2011). The equilibration time canbeen shown to be independent of aerosol volatility so longas it is assumed that the change in particle size upon evap-oration is small. However, because a change in the parti-cle size is inherent to the evaporation process itself, devia-tion from the above assumption is expected as the volatilityincreases, implying longer equilibration time for increasingcompounds volatility (Saleh et al., 2011). Since concentra-tions of organic aerosol at ambient levels are typically below50 µg m−3 (Huffman et al., 2008), equilibrium is expectednot to be reached in thermodenuder measurements with at-mospheric samples due to the limited residence time usuallyapplied in these systems (below 30 s). Atmospheric measure-ments should therefore be interpreted using a kinetic ratherthan an equilibrium approach, otherwise this may result insignificant deviations in determining the evaporation prop-erties of the organic aerosol (Riipinen et al., 2010; Cappaand Jimenez, 2010). The use of evaporation kinetic mod-els imposes a strong limitation in the input requirements ofthe properties of constituents of the particles, since in mostcases even the identity of compounds in the aerosol sampleis unknown (Cappa and Jimenez, 2010). In order to avoidthe limitations imposed by detailed kinetic evaporation mod-els, Faulhaber et al.(2009) proposed a method for derivingvolatility distributions from thermograms, based on an em-pirical relationship found between the thermodenuder tem-perature at which 50 % of the total mass of aerosol evapo-rates (T50) and the organic compound vapour pressure. Be-cause this empirical calibration curve was derived from mea-surements at high organic aerosol loading (100–200 µg m−3)with a limited set of organic compounds, while this methodseems to provide good estimations for a variety of samples, itis still uncertain that it is valid for compounds and conditionsother than those used for the calibration.

In addition to being used to infer volatility distribution oforganic aerosols, evaporation profiles obtained from isother-

mal dilution and thermodenuder experiments have beenrecently employed to derive effective kinetic coefficients,by coupling measurements and kinetic modelling for com-pounds of known volatility (Grieshop et al., 2009; Cappaand Wilson, 2011; Saleh et al., 2012). This approach hasproven useful in determining evaporation coefficients for sin-gle compounds such as dicarboxylic acids (Cappa, 2010;Saleh et al., 2011), POA mixtures such as lubricating oil(Grieshop et al., 2009; Cappa and Wilson, 2011) and amor-phous solid SOA derived fromα-pinene ozonolysis (Cappaand Wilson, 2011). Inconsistencies exist, however, betweenthe evaporation coefficients estimated from isothermal dilu-tion and thermodenuder measurements for compound mix-tures like lubricating oil (Grieshop et al., 2009; Cappa andWilson, 2011). Whether this discrepancy is a result of differ-ent volatility composition resulting from the use of differentaerosol generation techniques, or to artefacts derived fromthe evaporation methodologies applied, is unresolved.

Re-condensation has long been considered as a potentialconcern for the interpretation of evaporation profiles fromthermodenuder measurements, as this would lead to an un-derestimation of a particle’s volatility (Burtscher et al., 2001;Wehner et al., 2002; Huffman et al., 2008). To minimise thiseffect, charcoal denuders are included in the cooling sectionof many standard designs, such that the semi-volatile ma-terial is removed from the gas-phase, and re-condensationis suppressed as the aerosol sample cools down (Burtscheret al., 2001; Wehner et al., 2002). Experiments byHuff-man et al.(2008) have proven that sulphuric acid particlespresent a potential for re-condensation in thermodenudercooling sections at aerosol loadings≤50µg m−3, while re-condensation for organic compounds of higher volatility thansulphuric acid, has been found to be negligible. Volatilitystudies on Diesel exhaust and marine aerosols with volatil-ity tandem differential mobility analyser (VTDMA) instru-ments have shown insignificant re-condensation in coolingsections (Orsini et al., 1999; Sakurai et al., 2003); however, itis considered that the rate of re-condensation in these systemsis lower than in thermodenuder instruments owing to thelow particle surface area available after size selection (Huff-man et al., 2008). Modelling calculations byCappa(2010)for high volatility compounds (C∗ = 10 µg m−3) have shownthat the potential for re-condensation is likely to be substan-tial at laboratory conditions with organic aerosol loadings>200 µg m−3, while being of low significance for ambientaerosol loading levels. Recent modelling and experimen-tal work bySaleh et al.(2011) indicate that re-condensationwould be negligible even for high organic aerosol mass load-ings, if the geometry of the cooling section is adequatelymodified. Significant re-condensation inCappa(2010) was aresult of the geometry of the thermodenuder design applied,which yields a dimensionless number Cn greater than themaximum value established for negligible re-condensationby Saleh et al.(2011) . Differences between conclusions byCappa(2010) andSaleh et al.(2011) regarding the potential

Atmos. Meas. Tech., 5, 735–757, 2012 www.atmos-meas-tech.net/5/735/2012/

E. Fuentes and G. McFiggans: Uncertainties in the estimation of organic aerosols volatility 737

of re-condensation and performance of charcoal denudersalso originate from their definition of the absorbing potentialof the walls of the cooling section. WhileCappa(2010) pro-vided lower and upper estimates for re-condensation derivedfrom the assumptions of local equilibrium and non absorbingconditions at the walls,Saleh et al.(2011) based their calcu-lations on an assumption of equilibrium wall condensation,thus providing a lower estimate for re-condensation.

In this work a kinetic evaporation-condensation model inan axisymmetrical thermodenuder geometry is applied to as-sess the interpretation of particle mass evaporation profilesobtained at conditions relevant to both ambient and labora-tory measurements. The main aims of this study are (1) toevaluate the uncertainty in estimating volatility distributionsfrom measurements derived from current thermodenuder de-signs, including deviations resulting from re-condensationand/or assumptions of equilibrium and kinetic mass transfercoefficients; (2) to provide theoretical interpretation for theempirical calibration between the temperature at which 50 %of organic aerosol mass evaporates (T50) and vapour pres-sure, and assess its validity for deriving volatility distribu-tions from thermograms at a variety of conditions and (3) toprovide insights on the interpretation of particle evaporationbehaviour and effective kinetic evaporation coefficients for aset of primary and secondary organic aerosol samples.

2 Thermodenuder model

A diffusion-evaporation model was applied to simulate theevaporation/re-condensation of particles in a cylindrical ge-ometry thermodenuder system. The thermodenuder config-uration consists of a typical design, as illustrated in Fig.1.The model was sequentially solved on the three sectionsof the thermodenuder: the heating section, where the parti-cles are subject to evaporation; the cooling section, whichis the short intermediate piece of tubing where the sampleapproaches ambient temperature; and the denuder section,which comprises the piece of tubing where gas-phase semi-volatile compounds are removed by a charcoal adsorber inorder to avoid re-condensation. Figure1 summarises thedimensions and residence time in each part of the design.

The thermodenuder model simulates the gain and loss ofmaterial in the condensed phase resulting from evaporationand re-condensation, respectively, the transport of the gasand the evolution of the particle diameter. The steady-stateevaporation/re-condensation and diffusion of a gaseous com-pound through a cylindrical tube, assuming azimuthal sym-metry and constant coefficient of diffusion, is defined as (Tanand Hsu, 1970):

vx

∂Ci

∂x+ vr

∂Ci

∂r= Di

[1

r

∂

∂r

(r∂Ci

∂r

)+

(r∂2Ci

∂x2

)]+ qi (1)

wherevx and vr are the fluid velocity in the axial and ra-dial directions, respectively,Ci is the gas phase mass con-

Fig. 1. Schematic of the thermodenuder design used for the calcu-lations. The configuration with denuder bypass was also calculatedto explore the potential for re-condensation and the efficiency of thecharcoal denuder. Air flow = 0.6 lpm, RT = residence time.

centration of compoundi, Di is the gas diffusion coefficient,qi is the source/sink term for the gas phase due to particleevaporation/re-condensation, andx and r are the axial andradial coordinates, respectively. Equation1 was simplifiedunder the assumption of negligible secondary flows and dif-fusion in the axial direction, such that the terms involving

vr and ∂2Ci

∂x2 are eliminated from the equation. The assump-tion for negligible axial diffusion is valid for Peclet num-ber of diffusion>100 (Turpin et al., 1993), which applies tothe geometry and conditions in this study (Pe = 115). Theconvective term for secondary flowsvr was considered tobe negligible compared to the axial velocity term in Eq. (1).This assumption will be further validated by comparing withexperimental results.

The termqi , which denotes the mass gain/loss in the gas orparticle phase (Cp,i) due to evaporation or re-condensation,is defined as (Seinfeld and Pandis, 1997; Cappa, 2010):

qi = vx

∂Ci

∂x= −vx

∂Cp,i

∂x= 2πNDidp0

(xiC

∗

i − Ci

)(2)

whereN is the particle number,dp is the particle size,0 isthe Fuchs and Sutugin(1970) correction term, defined as afunction of the accommodation coefficientα, xi is the com-pound mass fraction in the particle andC∗

i is the compoundsaturation concentration.

It has been shown byLaaksonen et al.(2005) that theaccommodation coefficient should exhibit a value of unityfor models to adequately represent the physics of evapora-tion and condensation at the molecular limit. It should benoted, that the kinetic coefficients used in the present studyare defined to account for all the potential kinetic limita-tions. As an example, the kinetics of evaporation of non-liquid particles may be expected to be greatly influenced by

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the diffusion coefficient through a viscous solution (e.g.Tonget al., 2011). Although such behaviour should be tested inappropriate model frameworks (Pfrang et al., 2011), kineticlimitations will be evaluated in the present work in terms ofan “effective” uptake coefficientγ ′, which comprises all ki-netic limitations to mass transfer from the aerosol to the gasphase and viceversa. Where the kinetic limitation to evapo-ration and recondensation are considered of different magni-tude, the uptake coefficient is split into an effective net evap-oration coefficient (γ ′

evap) and a net uptake re-condensationcoefficient (γ ′

cond) for the evaporation and re-condensationprocesses, respectively. The physical behaviour we are aim-ing to represent in using different coefficients in condensa-tion or evaporation is the limitation to the kinetic rate in onedirection or another. In other words, the effective kinetic co-efficients are valid as empirical parameters that are indicativeof the kinetic limitations in the system, but they are not ap-plicable to interpret the system behaviour at the molecularlimit, as this may lead to unphysical behaviour. However, asshown in previous studies (Cappa and Wilson, 2011) the useof “effective” kinetic coefficients is still an useful approachfor analysing and modeling the kinetic limitations involvedin the process.

The boundary conditions applied to solve Eqs. (1) and (2)in the heating section are:

Ci(0, r) = Ci0,298 (3)∂Ci(x,R)

∂x= 0 (4)

whereR is the thermodenuder radius. The first boundaryequation is a constraint for the initial concentration of theorganic compounds in the gas phase. The concentration ofgas at the inlet of the heating section (Ci0,298K) is definedconsidering that the aerosol is in equilibrium at ambient tem-perature, and that the distribution of the organic compoundsbetween the gas and particle phases is defined by the adsorp-tive partitioning theory (Pankow, 1994). The second bound-ary equation is a Neumann boundary condition under theassumption of no mass losses to the walls of the system.

For the cooling section, the initial gas phase concen-tration is given by the heating section output gas distri-bution. Although wall condensation is likely to occurin the cooling section (Saleh et al., 2011), local equilib-rium at the walls may not be achieved at all conditions.To infer the potential for re-condensation the model wasapplied to provide for lower and upper estimates of re-condensation by considering both the limiting wall bound-ary conditions defined by no mass transfer to the walls (up-per limit for re-condensation) and equilibrium wall conden-sation (lower limit for re-condensation) (Cappa, 2010). Theboundary condition of no mass transfer to the walls is equalto the condition for the heating section, while the equilib-rium wall condensation is given byCi(x,R) =xi(x,R) C∗

i ,i.e. the equilibrium concentration of each compound at thewall temperature.

The boundary conditions considered to solve the diffusion-evaporation equation in the denuder section are:

Ci(0, r) = Ci0,DS (5)

Ci(x,R) = 0 (6)

The first equation defines the initial conditions for the de-nuder section, which are given by the output gas concentra-tion from the cooling section, while the second equation isa Dirichlet condition defining the denuder walls as a perfectsink for the gas phase. The assumption of perfect sink im-plies that the gas is bound completely and irreversibly uponcoming into contact with the coating material. The modeleddenuder performance therefore represents an upper limit onthe efficiency of the system to remove semi-volatile gas.

The temperature distribution of the gas in the heating andcooling sections was modelled using the heat equation, underthe assumptions of fully developed laminar flow and negligi-ble secondary flows and heat transfer in the axial direction as(Campo, 2004):

ρcpvx

∂T

∂x= k

[1

r

∂

∂r

(r∂T

∂r

)](7)

The assumption of fully developed flow at the entrance of thethermodenuder was adopted, given that the entrance lengthfor a laminar flow to become fully developed in the systemunder study is as short as 3 cm. The assumptions of negli-gible radial flow with respect to the axial velocity term andnegligible heat transfer diffusion in the axial direction arevalidated in the next section by comparing the modelled tem-perature distribution with experimental temperature profilesfrom Huffman et al.(2008).

The heat equation in the heating and cooling sections wassolved for the following boundary conditions:

T (0, r) = T0,298K(CS) (8)

T (x,R) = Twall (9)∂T

∂r= 0 (10)

where the first equation specifies ambient temperature condi-tionsT0,298K for the flow at the entrance of the heating sec-tion and a cooling section initial temperature (T0,CS) definedby the output of the heating section. The second conditionspecifies the wall temperature at all axial positions and thethird equation is the symmetry condition. In the heating sec-tion the wall temperature is set equal to the set point tempera-ture, while in the cooling section the wall boundary conditionwas the ambient temperature, with heat transfer occurringonly between the wall and the sample air flow.

The velocity of the fluid was modelled as a function of thelocal temperature, using the definition of plug flow velocity.A plug flow velocity profile was found to be a better approx-imation than the parabolic profile for estimating the parti-cle evaporation/re-condensation rate for the constant particle



concentration radial profile employed in our model. A realparticle concentration radial profile would have a parabolicshape, with near-zero particle concentration in the vicinity ofthe walls (due to diffusion and thermophoretic losses) and amaximum particle concentration at the centerline (Shimadaet al., 1993). Hence, the gas production near the walls of theheating section would be low in a real system, because therewould be few particles at this region. The constant particleconcentration profile that we use, however, implies havinga high particle concentration near the walls, which togetherwith the long residence time defined by the parabolic velocityprofile at the walls, leads to an overestimation of gas produc-tion in this zone. This happens not just at the bin adjacentto the wall, but in the region within∼20 % radial distancefrom the wall where velocities are low. The overestimatedproduction of gas near the walls in the heating section leadsto diffusion of gas towards the centerline, thus reducing theevaporation rate of particles at other radial positions. Similarartifact occurs in the cooling section, due to an overestima-tion of the particle re-condensation rate in the vicinity of thewalls. Our comparison with experimental results show that,in the absence of a model for the particle concentration radialdistribution, the combination of a plug flow velocity and plugflow particle concentration profiles provides a better approxi-mation for the averaged particle evaporation/re-condensationrates than using the velocity parabolic profile with a con-stant particle concentration radial profile. It is recognisedthat these assumptions do not ideally represent the wall inter-actions, but it is demonstrated below that the mean behaviouris well represented. Better representation of the radial profileincluding wall losses would require simulation of the particlenumber profiles by calculation of particle trajectories and nu-merical solution of Navier Stokes equations. This is beyondthe scope of the current study.

For the aerosol evaporation calculations a one-way cou-pling approach between the particles and the continuousphase was adopted, on the assumption that the size and load-ing of particles is low enough as to negligibly affect thefluid properties. The fluid temperature, density and veloc-ity distribution in the system were first calculated for thegiven wall temperature and flow boundary conditions, fol-lowed by the injection of particles in the model to conductthe particle evaporation/re-condensation evolution calcula-tions. The evaporation-diffusion equations given by Eqs. (1)to (6) were solved by applying sequential numerical inte-gration on the nodes of a cylindrical geometry axysimmet-ric grid with a resolution of 0.2 mm in the radial directionand 5 mm in the longitudinal direction. Increase in the res-olution of the system did not result in a significant changein the results of the model. The system of Eqs. (1)–(2),together with the stated boundary conditions and input ofthe spatial fluid properties, constitutes a system of couplednon-linear partial and ordinary differential equations, whichwas iteratively solved using the method of lines integrationsolution with Galerkin/Petrov-Galerkin spatial discretisation

250

200

150

100

50

0

cent

erlin

e te

mpe

ratu

re T

(°C

)

706050403020100

x(cm)

Experimental (Faulhaber et al., 2009) model

Tw=110°C

Tw=230°C

Fig. 2. Modeled and experimental centerline temperature in theheating and cooling sections ofHuffman et al.(2008) thermode-nuder. Note that the initial fluid temperature in this calculation isthe centerline temperature at the inlet of the active heating zone(i.e. tube covered with heating tapes).

(Skeel and Berzins, 1990), and an explicit Runge-Kutta for-mula method, both implemented in solvers in the commer-cial software Matlab. It should be noted that this model hasinitially been designed to simulate the behaviour of monodis-perse aerosol samples. An extension of the model would berequired so that it can be used to represent polydisperse dis-tributions. This can be done by implementing models suchas the condensation sink diameter approach (Lehtinen et al.,2003; Saleh et al., 2011).

3 Fluid properties

Figure2 illustrates the modelled axial evolution of the fluidtemperature in the heating and cooling sections of a thermod-enuder with dimensions and operating conditions identical tothose described inHuffman et al.(2008), in comparison withexperimental centerline temperature measurements providedin the cited work. The initial temperature of the fluid in themodel was set equal to the fluid temperature at the inlet ofthe active heating zone inHuffman et al.(2008) (i.e. zonecovered with heating tapes), so that the thermodenuder walltemperature could be applied as a boundary condition. Thewall temperature was set to the value of maximum temper-ature reached by the fluid in the experimental system. Asshown in Fig.2, the modelled and experimental temperatureprofiles are in good agreement, thus indicating that the as-sumptions previously made are valid for modelling the tem-perature and fluid properties. Calculations at different walltemperatures indicate that, for the dimensions and operating



conditions applied, the wall temperature boundary conditionis reached in the centerline at∼15–20 cm from the begin-ning of the heating section. As an example of temperaturedistributions, Fig. S1 shows the temperature field in the heat-ing section of the thermodenuder for a wall temperature of100◦C. The temperature distribution affects both the den-sity and, consequently, the velocity of the fluid, leading toan acceleration and deceleration of the fluid in the heatingand cooling section, respectively.

4 Re-condensation: parametric analysis

A parametric sensitivity study was conducted in order toevaluate the potential of re-condensation to affect thermode-nuder evaporation profiles and the subsequent interpretationof volatility. For the analysis, the influence of aerosol loading(COA), particle size (dp), kinetic coefficient (γ ′), volatility(C∗) and diffusion coefficient (Di) on gas re-condensation,was evaluated by comparing thermograms obtained afterthe heating, cooling and denuder sections in the thermode-nuder model. The output thermogram for an equivalent sys-tem without denuder section was also calculated in order toasses the level of re-condensation and the performance ofthe charcoal denuder. The mass fraction remaining, calcu-lated as a function of the heater temperature, was definedas MFR =Mf /M0, whereMf is the aerosol mass after thecorresponding section in the thermodenuder andM0 is theinitial aerosol mass in the system (M0 is equivalent to themass referenced to the bypass without thermodenuder, cor-rected for particle losses). Because the density of the parti-cles was assumed to be constant, the mass fraction remainingis equivalent to a volume fraction remaining. Together withthe thermograms comparison, the results were also evaluatedin terms of re-condensation fraction (RF), defined as the per-cent of evaporated gas that re-condenses onto the particlesafter the cooling section (CCS) or the denuder section (CDS)with respect to the amount of gas exiting the heating section(CHS):

RF(%) =CHS− CCS(DS)

CHS· 100 (11)

Positive values of RF indicate that the gas evaporated in theheating section recondenses in the cooling or denuder sec-tions, while negative values indicate an increase in the gasconcentration with respect to the amount of gas at the exit ofthe heating section. Negative values of the re-condensationfraction are expected if the removal of gas by denudation in-duces the evaporation of particles in the denuder section. Itshould be noted that the values of re-condensation fractionpresented here are different to those determined inSaleh et al.(2011). While we provide RF values at the end of the coolingor denuder section for a given tube length, re-condensationfraction estimations inSaleh et al.(2011) represent the max-imum re-condensation (i.e. if equilibrium is attained in the

cooling section). It should be noted that the definition of re-condensation fraction presented here is different to the max-imum re-condensation fraction values determined inSaleh etal. (2011).

For the parametric analysis, the case withdp = 100 nm,γ ′ = 1, C∗ = 0.1 µg m−3 and C∗ = 0.01 µg m−3,COA = 400 µg m−3 and Di = 5× 10−6 m2 s−1 was se-lected for the baseline conditions. The heat of vaporisationgenerally correlates with the saturation concentration,exhibiting an increasing value for decreasing volatility(Epstein et al., 2009). In order to apply an enthalpy ofvaporisation consistent with the compound’s volatility,the equation derived byEpstein et al.(2009) was applied.For the volatilities above indicated, this expression yieldsnear-room temperature enthalpy values of 151 kJ mol−1

and 140 kJ mol−1, respectively. In the model, a constantheat of vaporisation was assumed over the temperaturerange considered. The thermodenuder geometry appliedwas similar to that described inHuffman et al.(2008), withdimensions, residence times and flow as indicated in Fig.1.

Figure3 shows the thermograms obtained after the differ-ent thermodenuder sections forC∗=0.01 µg m−3 at diverseorganic aerosol loading levels. The equilibrium evaporationthermograms have also been included for comparison. In there-condensation process, equilibrium is achieved when theinitial aerosol mass is reached, i.e. for MFR = 1. Upper andlower estimates for re-condensation included in the figures,show that the assumption for the wall conditions substan-tially affects the significance of re-condensation. In agree-ment with results inCappa(2010), the re-condensation po-tential is highly dependent on the aerosol loading and par-ticularly promoted at high aerosol loading levels, which aretypically used in laboratory experiments (Faulhaber et al.,2009; Cappa and Wilson, 2011). Predictions for the upperestimate indicate that an already significant re-condensationcould occur in the 15 cm cooling section joining the heaterand the denuder sections for organic loadings≥150 µg m−3.In addition, the removal of gas by the denuder at high organicloadings is not sufficient to avoid further re-condensation,which in the case of 400 µg m−3 loading leads to the re-condensation fraction being reduced in only a∼10 % withrespect to the same length of tubing without denuder. The ef-ficiency of the denuder in preventing re-condensation is con-siderably higher for lower organic loading, with reductions≥

45 % in the re-condensation fraction, with respect to the casewithout denuder for aerosol loadings≤150 µg m−3. The up-per estimate for re-condensation for 30 µg m−3, (Fig. S4a)also indicate that no significant modification of the thermo-grams is expected at atmospheric conditions below this con-centration. Although atmospheric aerosol loadings can reachvalues as low as 1–5 µg m3, simulations at these aerosol con-centrations have not been performed as these conditions arenot relevant for the re-condensation analysis. The resultsfor lower estimates for re-condensation show that, althoughthe re-condensation degree is considerably lower than for the



1.0

0.8

0.6

0.4

0.2

0.0

MF

R

807060504030T(°C)

100

80

60

40

20

0

RF

(%)

COA=150 μg/m3

1.0

0.8

0.6

0.4

0.2

0.0

MF

R

807060504030T(°C)

100

80

60

40

20

0

RF

(%)

COA=50 μg/m3

MFRRF(%)

1.0

0.8

0.6

0.4

0.2

0.0

MF

R

90807060504030T(°C)

100

80

60

40

20

0

RF

(%)

COA=400 μg/m3

HS, equilibrium HS

Upper estimate Lower estimate CS w/o DS DS w/o DS

Fig. 3. Output thermograms and recondensation fraction for theheating section (HS), cooling section (CS), denuder section (DS)and equivalent configuration without denuder section (w/o DS) fordifferent aerosol mass loadings. The results show that the efficiencyof the denuder to hinder re-condensation decreases with increasingaerosol mass loading. Baseline case:C∗ = 0.01 µg m3, dp = 100 nm,Di = 5× 10−6 cm2 s−1 and γ ′ = 1. Upper estimate: upper es-timate for re-condensation (no mass transfer to walls); lowerestimate: lower estimate for re-condensation (equilibrium wallcondensation).

upper estimate, there is still a potential for re-condensationfor aerosol loadings above 50 µg m−3. Detailed calculationson the effect of the aerosol mass loading under the assump-tion of equilibrium wall condensation are presented as sup-plementary material (Figs. S2 and S3). The performance ofthe charcoal denuder is similar to that of the cooling sectionunder the assumption of wall equilibrium condensation forvolatilities below 10 µg m−3. This is because the gas bulkconcentration is much higher thanC∗ and the gradient be-tween the bulk and the walls of the cooling section is simi-lar in the charcoal denuder and equilibrium wall conditionscases (i.e. Cg-C∗

∼ Cg-0).Corresponding results for visualising the relationship be-

tween volatility and re-condensation are presented in Fig.4.For a given MFR value, the curves for the cooling section(CS and w/o DS) forC∗

≤1 µg m−3 indicate that the re-condensation fraction does not seem to be substantially af-fected by the volatility of the organic aerosol. This is a re-sult of the lower temperatures required to achieve the samelevel of evaporation for high volatility compounds with re-spect to the low volatility cases, which leads to gradients forre-condensation of similar magnitude for compounds of dif-ferent volatility. Lower re-condensation is however, observedin theC∗ = 10 µg m−3 thermogram after the cooling and de-nuder sections with respect to the lower volatility cases. Fur-thermore, the results show that particle evaporation may beinduced by the charcoal denuder, leading to modificationsof thermograms forC∗ >1 µg m−3 and temperatures below45◦C. Further analysis has shown that this effect is onlyimportant forC∗ >1 µg m−3, even at low aerosol loadings(Fig. S4b). Indeed, at 50 µg m−3 aerosol mass, evapora-tion induced by denudation has been predicted to be sig-nificant for volatilitiesC∗ >1 µg m−3 (Cappa, 2010). Be-cause the significance of this effect is limited to a narrowrange of temperatures and volatility compounds it is likelythat the impact of denudation on thermograms is of low sig-nificance for ambient multicomponent mixtures. For labora-tory experiments at high aerosol loadings, the mass of highvolatility compounds is significant and the evaporation ef-fect induced by the denuder may be more important than forambient measurements.

As illustrated in Fig.5, the kinetics of evaporation/re-condensation are strongly affected by the effective kineticcoefficient value. Whilst it is recognised that this coefficientshould not be used to represent all possible kinetic limita-tions to particle equilibration, its variation can be used to in-vestigate potential instrument responses. Results in Fig.5show that reductions of the effective kinetic coefficient by anorder of magnitude leads to a≥50 % suppression of the re-condensation fraction, with negligible re-condensation pre-dicted forγ ′

≤ 0.01. It is also noticeable that decreasing ki-netic coefficients push the system away from attaining equi-librium and that equilibrium is not reached forγ ′

≤ 0.1,even for the high aerosol loading used in the calculations.In the work of Saleh et al.(2011), a thermodenuder with



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HS, equilibrium HS


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RF

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Fig. 4. Output thermograms and recondensation fraction for the heating section (HS), cooling section (CS), denuder section (DS) and equiv-alent configuration without denuder section (w/o DS) at different volatilities. Similar magnitude in the re-condensation fraction betweenthe different volatility cases is obtained at equal MFR, due to the increase in volatility being counteracted by the low equilibrium satura-tion concentrations at low temperatures. The charcoal denuder is predicted to substantially influence thermograms only forC∗>1 µg m−3

and temperatures below 45◦C, by inducing particle evaporation. Baseline case:COA = 400 µg m−3, dp = 100 nm,Di = 5e–6 cm2 s−1 andγ ′ = 1.Upper estimate: upper estimate for re-condensation (no mass transfer to walls); lower estimate: lower estimate for re-condensation(equilibrium wall condensation).

longer heating section residence time than the system inthe present study was employed (plug flow residence timeof ∼30 s, 298 K), allowing equilibrium to be attained forγ ′ = 0.1. However, it is foreseen that equilibrium will notbe reached in a 30 s residence heating system forγ ′ < 0.1,regardless of the aerosol mass loading.

Another factor notably affecting the kinetics of re-condensation is the particle size, as shown in Fig.6. For con-stant aerosol loading, an increase in the particle size impliesa reduction in the total particle surface area, which resultsin a deceleration of the re-condensation process. In contrast,the diffusion coefficient does not substantially affect the re-condensation process, as reflected by the slight change in thethermograms between the expected range of values for thisparameter (Fig. S5).

The strong dependence of the re-condensation rate onthe particle size, kinetic coefficient and aerosol loading im-plies that the degree of re-condensation should be predictedconsidering the combined, rather than the isolated effectsof these factors. Although the re-condensation rate willbe enhanced by increasing aerosol loading, increasing ki-netic coefficient and decreasing particle size, negligible re-condensation could still be possible at certain high organicloadings, with sufficient large particle size or low kinetic co-efficients. Analysis of the re-condensation occurring for a setof real cases, implying the combination of the above studiedparameters, is presented in the next section.

The geometry of the thermodenuder system tested in thisstudy, although representative of currently used thermod-enuder designs, is problematic regarding re-condensation



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MFRRF(%)

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(%)

γ'=1

Fig. 5. Output thermograms and recondensation fraction for theheating section (HS), cooling section (CS), denuder section (DS)and equivalent configuration without denuder section (w/o DS)at different effective kinetic coefficients. Baseline case: COA=400 µg m−3, C∗ = 0.1µg m−3, dp = 100 nm andDi=5e–6 cm2 s−1.Upper estimate: upper estimate for re-condensation (no mass trans-fer to walls); lower estimate: lower estimate for re-condensation(equilibrium wall condensation).

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80

60

40

20

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RF

(%)

dp=200nm

HS, equilibrium HS


Reference curves for dp=100 nm (upper estimate)

w/o DS

MFRRF(%)

Fig. 6. Output thermograms and recondensation fraction for theheating section (HS), cooling section (CS), denuder section (DS)and equivalent configuration without denuder section (w/o DS),ina system with 200 nm aerosol particle size at 400 µg m−3 aerosolloading. Comparison of this plot with Fig.5 atγ ′ = 1 (dp = 100 nm)indicates a deceleration in the re-condensation process for increas-ing particle size, at constant aerosol loading. This is a result of a re-duction in the particle number available, which leads to slower evap-oration and re-condensation rates. Baseline case:C∗ = 0.1 µg m−3,γ ′ = 1 andDi = 5e–6 cm2 s−1. Upper estimate: upper estimate forre-condensation (no mass transfer to walls); lower estimate: lowerestimate for re-condensation (equilibrium wall condensation).

because of the large diameter of the cooling section. We havereproduced measurements bySaleh et al.(2011) and foundnegligible upper estimates of re-condensation for an initial287 µg m−3 aerosol mass loading (Fig. S6). This negligiblere-condensation is, in fact, a consequence of the small cool-ing section tube diameter used bySaleh et al.(2011), whichleads to very short residence times (0.93–1.87 s, tube of 1–2 630 m length, flow = 1–2 lpm and ID of 0.63 cm), com-pared to the typical residence time in cooling sections of di-verse currently used thermodenuder models (e.g. 15.5 s. inthermodenuder by Huffman et al. (2008), with CS+DS tubelength 0.55 m, flow = 0.6 lpm and ID = 1.91 cm). This, to-gether with the low kinetic coefficient∼0.1 of the aerosolsample inSaleh et al.(2011) results in a limited growth ofparticles in the test by-pass tube with respect to the condi-tions at the tube inlet. It should be noted that the conclusion



of negligible re-condensation at high aerosol loadings fromexperiments inSaleh et al.(2011) is a consequence of thegeometry of the cooling section and experimental conditionsin the cited study and should not be generally extrapolated toall thermodenuder design and type of experiments.

Modeling bySaleh et al.(2011) showed that a a value<0.7for the coupling dimensionless number Cn, defined as the ra-tio between the particles and the walls re-condensation rate,implies a maximum re-condensation fraction of 10 %, as ob-tained from their transport model. In order to test whetherthe geometry or conditions in our model was above the rangeof negligible re-condensation defined bySaleh et al.(2011),we have calculated Cn values for our analysis. According tothe formulations presented inSaleh et al.(2011), the valueof Cn in our parametric study is 2.7–10 for a mass loadingof 400 µg m−3 (C∗ = 0.01 µg m−3 and dp0 = 100 nm). Thisvalue is well above the maximumCn number defined bySaleh et al.(2011), for negligible re-condensation (Cn = 0.7),explaining the significant re-condensation levels obtainedwith our model. For thisCn value, our model yields 80 %re-condensation fraction, whileSaleh et al.(2011) predicts amaximum re-condensation of 50 %. Although there is still adifference of 30 % between our estimations, this may be dueto the fact that our model presents radial resolution, whileSaleh et al.(2011) solved a one dimension flow model thatmay not be as accurate to predict local condensation at thewalls. In our study we have worked with geometries andconditions representative of some currently used thermode-nuder designs, such as that ofHuffman et al.(2008), whichpresents Cn values higher than 0.7 at high aerosol load-ings (e.g.Cn = 2–7.4 for 100 nm particles at 400 µg m−3 andC∗

= 0.01 µg m−3). It should be noted that whilst we ac-knowledge that thermodenuder geometries can be modifiedto reduce the effect of re-condensation (Saleh et al., 2011),the aim of our study is to analyse the issues derived from us-ing current thermodenuder systems, even if their geometriesare not optimum to minimise re-condensation issues.

The comprehensive analysis presented in this work sug-gests that re-condensation will be highly dependent on theparticular experimental conditions employed and that cau-tion should be taken, as re-condensation will not be negli-gible for every thermodenuder design. Laboratory studiesshould adopt measures to avoid re-condensation by reducingthe cooling section tubing diameter and length when workingat high aerosol mass loadings (Saleh et al., 2011). With thesemodifications a charcoal denuder may not be needed to con-trol re-condensation (Saleh et al., 2011). Researchers whowork with commercial thermodenuders that already incorpo-rate a cooling/denuder section should be aware of the poten-tial issues implied by re-condensation if they do not modifythe configuration of their experimental systems. It shouldbe noted that most available thermodenuder systems presenta geometry which is problematic regarding re-condensation.An assessment on the potential of re-condensation to af-

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γ'=1

γ'=0.1

MFR exp. (Faulhaber et al., 2009) HS, equilibrium HS

Upper estimate Lower estimate CS DS DS w/o DS

Fig. 7. Output thermograms and recondensation fraction for the

heating section (HS), cooling section (CS), denuder section (DS)and equivalent configuration without denuder section (w/o DS), ina system with 200 nm butanedioic particles at 150 µg m−3 aerosolloading, in comparison with experiments byFaulhaber et al.(2009).The results show a best fit between observations and model for akinetic coefficient close to unity. Upper estimate: upper estimate forre-condensation (no mass transfer to walls); lower estimate: lowerestimate for re-condensation (equilibrium wall condensation).

fect aerosol volatility interpretation when using these currentthermodenuder designs is presented in Sect. 7 of this paper.

5 Re-condensation potential: selected cases

5.1 Single compounds: di-carboxylic acids

The thermodenuder model was applied to simulate the evap-oration of a set of single compound and multicomponentmixed aerosols in order to quantify the potential for re-condensation. The cases selected are based on experimen-tal measurements byFaulhaber et al.(2009), Grieshop etal. (2009) and Cappa and Wilson(2011), conducted at or-ganic loadings between 70 and 650 µg m−3. The method ap-plied consists on the iterative adjustment of the kinetic co-efficient in order to obtain the best fit between the experi-mental data and the model predictions, with the best fit pro-viding information on the degree of re-condensation. Forcomparison with the experimental measurements, the dimen-sions and operating conditions of the thermodenuder system



relevant to each case were used to set the geometrical bound-ary conditions for the model.

Thermograms of di-carboxylic acids were modeled andcompared with measurements byFaulhaber et al.(2009), asshown in Fig.7. The potential for re-condensation, i.e. thedifference between the lower and upper estimates for re-condensation, is significant for this particular case, with abest agreement between succinic acid measurements andmodel predictions for an effective net evaporation coefficientof 1, in agreement withCappa(2010). This value of ki-netic coefficient holds for the lower and upper estimates ofre-condensation. The derived kinetic coefficient is signifi-cantly higher than the value of∼0.1 determined bySaleh etal. (2011) .The saturation concentration and enthalpy of va-porisation values used for the calculations were 3.57 µg m−3

and 124.9 kJ mol−1, respectively, which are the average val-ues obtained from data provided byChattopadhyay and Zie-mann(2005), Bilde et al. (2003) and Davies and Thomas(1960). Chattopadhyay and Ziemann(2005) andBilde et al.(2003) employed a TPTD and a TDMA method, respectively,to derive the vapor pressure of succinic acid using an assump-tion of kinetic coefficient equal to 1. This assumption hasbeen shown to be of low significance in TDMA studies, withchanges in the vapor pressure estimation in less than 30 %for variations of the kinetic coefficient in a range between0.2 and 1 (Bilde et al., 2003) . In the work byDavies andThomas(1960) the vapor pressure was determined by meansof an effusion method, without any assumption on the valueof the evaporation coefficient. The vapor pressure derivedfrom Davies and Thomas(1960) is in fact very similar to thatfrom Bilde et al.(2003) (P25 of 4.23e–5 and 4.6e–5 Pa, re-spectively); thus, it is not evident that the derived evaporationcoefficient could be pre-determined by the vapour pressurevalues used as input to the model. Further work is necessaryin order to clarify differences between the kinetic coefficientsdetermined in different studies.

5.2 Multicomponent mixtures: lubricating oil andα-pinene SOA

Thermograms for lubricating oil aerosol andα-pinene SOAwere modeled to evaluate the potential for re-condensationoccurring in experiments with multicomponent mixtures.The model was solved using volatility distributions providedby Pathak et al.(2007) andGrieshop et al.(2009), while theenthalpy of vaporisation as a function of the volatility wasderived using equations fromEpstein et al.(2009).

Figure8a shows the modeled thermograms for lubricatingoil using different net kinetic evaporation/condensation co-efficients, together with experimental data (Cappa and Wil-son, 2011). In agreement with results inCappa and Wil-son(2011), the values of kinetic coefficients that provide thebest fit to the data fall in the range 0.1–1, with an optimumsolution for γ ′ = 0.3. For this value of kinetic coefficient,an upper estimate of re-condensation yields re-condensation

fractions of∼50 % if a charcoal denuder is not applied. Aspointed out in previous work byCappa and Wilson(2011), avalue of evaporation coefficient of 0.3 for lubricating oil is incontrast with the low evaporation coefficient between 0.001–0.0001 derived from dilution experiments byGrieshop et al.(2009). It has been argued that this discrepancy in the ki-netic coefficient value may result from differences in theaerosol volatility because of using different particle gener-ation methods (interactive comment onCappa and Wilson,2011). In order to analyse whether this is actually due tothe aerosol generation technique, the evaporation model wasapplied to derive the net kinetic evaporation coefficient forthermodenuder experiments byGrieshop et al.(2009) con-ducted with the same lubricating oil aerosol sample that wasused for their dilution chamber measurements (Fig.8b). Thespecifications and operation of the thermodenuder system ap-plied were those described inAn et al.(2007) andGrieshopet al. (2009), with a HS centerline residence time of 16 sfor a flow of 1 lpm (32 s plug flow residence time). Notethat for this thermodenuder system the denuder section wasdirectly attached to the outlet of the heating section, thusonly output thermograms for the heating section (HS) anddenuder section (DS) are provided. Although the same lu-bricating oil aerosol sample was used in the thermodenuderand chamber experiments byGrieshop et al.(2009), we showthat the net effective evaporation coefficient derived fromtheir thermodenuder experiments was 0.3 (in agreement withthermodenuder measurement byCappa and Wilson, 2011),while their chamber measurements yielded a kinetic coeffi-cient of 0.001–0.0001. The slow evaporation rate of particlesin Grieshop et al.(2009) dilution chamber may be induced bythe release of material from the chamber walls (Matsunagaand Ziemann, 2010). Because of the potential artifact in-duced by the release of material from the chamber wallson particle evaporation, dilution experiments with standardTeflon walls do not seem to be an adequate methodology forconducting this type of studies. For this purpose, special di-lution chambers provided with activated charcoal absorbershould be used (Vaden et al., 2010).

In order to analyse the evaporation/re-condensation be-haviour ofα-pinene SOA particles, experimental measure-ments byCappa and Wilson(2011) were also simulatedwith the kinetic model. Assuming equal evaporation andre-condensation coefficients, a very low effective evapora-tion coefficient of 0.0001 is necessary to fit the model tothe thermodenuder data (Cappa and Wilson, 2011). Al-though the slow evaporation ofα-pinene SOA aerosol hasbeen attributed to the barrier to the diffusion process due tothe amorphous structure of the particles, re-condensation ofgas on the particle surface may not be affected by the par-ticle phase. In such a case, the kinetic coefficient for re-condensation could exhibit a higher value than that for theevaporation process. It should be noted that, because thekinetic limitation in reality may lie in the diffusion in thecondensed phase through a viscous particle, the evaporation



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γ'=1 r2=0.978

γ'=0.3 r2=0.998

γ'=0.1 r2=0.980

γ'=0.01 r2=0.851

γ'=0.001 r2=0.761

HSDS

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Upper estimate Lower estimate CS DS DS w/o DS

γ'=0.3

r2=0.995

A B

Fig. 8. (A) Output thermograms for heating section (HS), cooling section (CS) and denuder section (DS) in a system with 240 nm lubricatingoil particles at 650 µg m−3 aerosol loading, in comparison with experiments byCappa and Wilson(2011). The thermodenuder system wasconfigured as described inCappa and Wilson(2011). (B) Thermograms reproducing experiments byGrieshop et al.(2009) with 175 nmlubricating oil particles at 70 µg m−3 aerosol loading, in comparison with experimental results. Note that for this system the denuder sectionwas directly attached at the outlet of the heating section and only output thermograms for the heating section (HS) and denuder section (DS)are provided. The specifications and operation of the thermodenuder system were as described inAn et al.(2007) andGrieshop et al.(2009).In both type of experiments (A andB) the results show a best fit between observations and model for an effective kinetic coefficient between0.1–1, with an optimum forγ ′ = 0.3. Upper estimate: upper estimate for re-condensation (no mass transfer to walls); lower estimate: lowerestimate for re-condensation (equilibrium wall condensation).

coefficient does not need to equal the condensation coef-ficient in the current model configuration. Figure9 illus-trates the results of the model for different evaporation co-efficients (γ ′

evap) between 0.0001–1 and a re-condensationcoefficient (γ ′

cond) of unity. In agreement withCappa andWilson (2011), in the case of equal evaporation and re-condensation coefficients the kinetic coefficient would havea value between 0.001–0.0001 and re-condensation wouldbe negligible. However, if the re-condensation and evap-oration coefficients are allowed to be different, for a re-condensation coefficient equal to 1, the evaporation coeffi-cient would have a value between∼0.001–0.01, with signif-icant re-condensation occurring after the heating section. Itshould be noted that the assumption of a condensation kineticcoefficient of 1 provides for an upper limit for the evapora-tion coefficient, while analysis assuming equal kinetic co-efficients for evaporation and re-condensation provides fora lower estimate of these coefficients. Further experimen-tation at lower aerosol loadings, where re-condensation isnegligible, may be useful to test the hypothesis that the ef-

fective kinetic coefficients for evaporation and condensationmay present different values for amorphous solid particles.

The above analysis shows that the interpretation of thebehaviour of the aerosol and the estimation of the degreeof re-condensation is certainly dependent on the assumptionwhether the re-condensation process is affected by the amor-phous solid phase of SOA. It should be remarked that caremust be taken not to over-interpret the roles of evaporationand re-condensation coefficients when the kinetic limitationmay be mainly due to the particle phase; however, the allow-able discrepancy within experimental error of this coefficientmay give an indication of the shrinkage and growth responseto temperature changes of SOA particles.

6 The relationship betweenC∗ and T50

The empirical calibration curve derived byFaulhaber et al.(2009) has been proposed as a method to derive vapour pres-sure values and volatility distributions from thermograms



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γ'evap=0.01

γ'evap=0.001

γ'evap=0.0001

Lower estimate of re-condensation for γ'evap=0.001

γ'cond=1

HSDS

Fig. 9. Output thermograms for heating section (HS), cooling sec-tion (CS) and denuder section (DS) in a system with 92 nmα-pineneSOA particles at 500 µg m−3 aerosol loading, in comparison withexperiments byCappa and Wilson(2011). The calculations wereconducted for different evaporation coefficients (γ ′

evap) and a re-condensation coefficient (γ ′

cond) equal to unity, under the assump-tion that the particle phase does not affect the re-condensation pro-cess. The results show a best fit between observations and model foran evaporation coefficient between 0.01–0.001, with an optimumfor γ ′ = 0.01. Data represent the upper estimate for re-condensationunless otherwise stated.

(Cappa and Jimenez, 2010). This curve, which is based on anempirical relationship determined between the vapour pres-sure and the temperature at which 50 % of the aerosol massevaporates (T50), was derived from a limited set of semi-volatile organic compounds at∼150 µg m−3 aerosol loading(Faulhaber et al., 2009). Hence, the validity of this cali-bration curve for compounds and conditions diverging fromthose used for the calibration remains to be proven. In thissection, insights on the theoretical interpretation of the rela-tionship comprising this calibration curve and on its validityfor predicting the volatility of a variety of compounds areprovided.

Following similar reasoning toSaleh et al.(2008), thechange of particle phase mass resulting from the evapora-tion/condensation of a compound i by heating/cooling froman initial reference state 0 to a final state “f”, is consideredequal to the change of gas phase mass and defined, including

the kelvin effect (K0(f)) , as:

1cp,i = −1cg,i = C∗

i,0 xi,0K0 − C∗

i,f xi,fKf (12)

whereC∗

i,0 and C∗

i,f are the saturation concentration at thereference temperature (i.e. 298 K) and at the final tempera-ture state expressed in terms of mass, respectively, andxi,0andxi,f are the mass fractions of componenti in the particlephase at the reference and final states, respectively.

The Clausius-Clapeyron equation defines the vaporisationenthalpy (Hv,i) and saturation concentration relationship un-der the assumption of enthalpy constant over the temperaturerange as:

C∗

i,f = C∗

i,0exp

[−

1Hv,i

R

(1

Tf−

1

T0

)]T0

Tf(13)

Using the above equation, the change in particle mass can bedefined from Eq. (12) as:

−1cp,i = C∗

i,0xi,0K0(xi,f

xi,0

Kf

K0

T0

Tfexp

(−

1Hv,i

R

(1

Tf−

1

T0

))− 1

)(14)

By expressing the change in total particle mass in terms ofCOA difference, the previous equation leads to:

COAi,0 − COAi,f = C∗

i,0xi,0K0 (15)(xi,f

xi,0

Kf

K0

T0

Tfexp

(−

1Hv,i

R

(1

Tf−

1

T0

))− 1

),

which divided byCOAi,0 yields:

1−COAi,f

COAi,0=

C∗

i,0xi,0K0

COAi,0(16)[

xi,f

xi,0

Kf

K0

T0

Tfexp

(−

1Hv,i

R

(1

Tf−

1

T0

))− 1

]Using the definition of mass fraction remaining for a compo-nent i, MFRi=COAi,f /COAi,0 Eq. (17) leads to the followingexpression forC∗

i,0:

C∗

i,0 =1

K0COA,0(1− MFRi) (17)[

xi,f

xi,0

Kf

K0

T0

Tfexp

(−

1Hv,i

R

(1

Tf−

1

T0

))− 1

]−1

Assuming equal density of the organic compounds in the par-ticle, the mass fraction remaining is equal to a volume frac-tion remaining and the kelvin term ratio can be expressed as:

Kf

K0= exp

[4Miσ

(T0 − Tf MFR1/3

)ρi RT0Tf dp0

MFR1/3

](18)

with the Kelvin termK0 in Eq. (18) defined as:

K0 = exp

(4Miσ

RT0 ρ dp0

)(19)



Using the definition of total mass fraction remaining,MFR =COA,f /COA,0, the mass fraction ratio can be ex-pressed as:

xi,f

xi,0=

MFRi

MFR(20)

and Eq. (17) can be re-written as:

C∗

i,0 =1

K0COA,0 (1− MFRi) (21)[

MFRi

MFR

Kf

K0

T0

Tfexp

(−

1Hv,i

R

(1

Tf−

1

T0

))− 1

]−1

For MFRi = 0.5,Tf =T50 and the saturation concentrationC∗

0for a single component (MFR = MFRi) is formulated as:

C∗

0 = (22)

0.5

K0COA,0

[Kf

K0

T0

T50exp

(−

1Hv,i

R

(1

T50−

1

T0

))− 1

]−1

In an analogous manner, the expression of C∗

i for a multi-component mixture at MFRi = 0.5 is given by:

C∗

i,0 =0.5

K0COA,0 (23)[

0.5

MFR

Kf

K0

T0

T50,iexp

(−

1Hv,i

R

(1

T50,i−

1

T0

))− 1

]−1

Equations (22) and (23) provide expressions relatingC∗

0 and1/T50, which will be compared with the empirical equationby Faulhaber et al.(2009). It should be noted that because thederived equations are based on the definition of particle massevaporated between equilibrium states, the obtained expres-sions are constrained to equilibrium thermograms. Deviationdue to the curvature effect (i.e. Kelvin term) can be neglectedin the above equations, as shown in the following sensitivityanalysis. The sensitivity of the equilibrium calibration curveto the aerosol properties defined within the termKf /K0, wasevaluated at constant aerosol loading and heat of vapori-sation for dp0

between 30–200 nm, density between 800–2000 kg m−3, molar mass between 100–400 g mol−1 and sur-face tension between 0.05–0.073 mN m−1. This sensitivityanalysis yielded a very low influence of the above particleproperties on the calibration curve, with maximum devia-tions of 2◦C in the estimation ofT50. Because of the lowsensitivity of the calibration curve to the kelvin term, bothKf /K0 andK0 were dropped from the equation and assumedto be∼1 in subsequent calculations.

Figure10shows log(P0) vs. 1/T50 values derived using thesingle component theoretical expression (Eq. 22), applied forthe calibration compound inFaulhaber et al.(2009) (i.e. di-carboxylic acids, oleic acid and DOS aerosol). The agree-ment between the experimental data and theoretical results,reveals that the empirical equation derived byFaulhaber etal. (2009) is in fact the equilibrium relationship betweenC∗

0

-8

-7

-6

-5

-4

-3

-2

-1

log(

P25

)

0.003200.003100.003000.00290

1/T50 (K-1

)

Data from theoretical curve (this study) Experimental data (Faulhaber et al., 2009) Empirical correlation (Faulhaber et al., 2009) Empirical correlation uncertainty range

Fig. 10. Relationship between logP25 and 1/T50 derived withEq. (22) for the organic compounds used in the calibration byFaul-haber et al.(2009), in comparison with experimental data. The er-ror bars in the theoretical calculation denotes the uncertainty in theaerosol loading (100–200 µg m−3).

and 1/T50 in Eq. (22), specifically defined for the selectedcalibration compounds atCOA,0=150 µg m−3. Indeed, whenaveraging the properties of enthalpy of vaporisation, mo-lar mass and vapour pressure of the calibration compoundsthe equilibrium theoretical equation leads to the expressionlog(P0) = 7376T −1

50 −27.73, which is strikingly similar to theempirical expression log(P0) = 8171T −1

50 −29.61, derived byFaulhaber et al.(2009).

The variation of the calibration curve as a functionof COA,0 for organic compounds of different homologousgroups was analysed in order to evaluate the influence ofthe experimental conditions on theC∗

0 – 1/T50 relation-ship. Figure11 illustrates the theoretical calibration curvefor aerosol loadings between 10–400 µg m−3 for differentorganic groups, together with experimental data fromFaul-haber et al.(2009). The thermodynamic data used as inputfor the analysis was obtained from diverse literature sources(Chickos and Hanshaw, 1997; Kulikov et al., 2001; Chat-topadhyay and Ziemann, 2005; Donahue et al., 2011). Re-sults in Fig.11show that the data for the different groups layon the same curve, with a relatively good agreement betweenthe empirical calibration and the theoretical curve data forCOA,0 between 150–400 µg m−3 and a more significant de-viation between the empirical and theoretical curves for de-creasing aerosol loading. The fact that the different type ofcompounds lay on the same curve at constant aerosol load-ing, results from the vaporisation enthalpy andC∗

0 data fol-lowing a relationship which is found to be equivalent to thatprovided byEpstein et al.(2009):

1Hv,i = −11 log(C∗

i ) + 129 (24)



Figure11shows that, because of the dependence of the equi-librium calibration curve on the organic aerosol loading, par-ticle volatility would be underestimated by more than oneorder of magnitude when applying the empirical calibrationat atmospheric aerosol levels of∼10 µg m−3, with respectto the equilibrium equation. It should be noted, however,that in a real thermodenuder with residence time up to 30 s,equilibrium will not be attained at low aerosol loadings andtherefore theC∗ vs. 1/T50 curve will deviate from the equilib-rium theoretical calculation. Because of the reduced uncer-tainty and inclusion of all the factors affecting the relation-ship, the mathematical combination of the theoretical cali-bration curve defined in Eqs. (22) and (23) andEpstein etal. (2009) equation (Eq.24) constitutes a more accurate ap-proach for the estimation of saturation concentrations thanthe empirical expression ofFaulhaber et al.(2009), when ap-plied at equilibrium conditions that may be achieved in labo-ratory experiments at high aerosol loadings.

It has been shown in previous work (Riipinen et al., 2010;Saleh et al., 2011) and in Sect.4 of this study that equilib-rium might not be attained in thermodenuders measurementsat low aerosol loadings and for low effective evaporation co-efficients. Hence, underestimation of particles volatility us-ing the equilibrium calibration curve is expected at kinetic-controlled conditions. Figure12illustrates the deviations ex-pected with respect to the theoretical calibration curve dueto equilibrium not being completely reached in the thermod-enuder measurements. At kinetic-controlled conditions,T50would be larger than the corresponding value at equilibrium,leading to non-equilibrium calibration curves laying on theleft of the equilibrium curve. The deviations from the equi-librium curve due to low aerosol loading and low evapo-ration coefficients have been depicted in Fig.12. Devia-tion of T50 up to 20–30◦C from the equilibrium value for-tuitously places the calibration curve within the region of un-certainty of the empirical equation. Larger deviations fromequilibrium situates the calibration curve at significant dis-tance from the empirical and equilibrium curves, invalidat-ing the general application of the empirical and theoreticalcurves for estimating the volatility of compounds from non-equilibrium thermograms.

The general expression in Eq. (23) can also be used toderive equilibrium thermograms, i.e. MFR as a function ofthe temperature, if the volatility distribution of the aerosol isknown, by considering that the total mass fraction remainingcan be expressed as a function of MFRi as:

MFR =

n∑i=1

xi,0 MFRi (25)

wherexi,0 is the mass fraction of the compound in the par-ticle at the reference state. According to Eq. (23), equilib-rium thermograms would only be determined by the volatil-ity and vaporisation enthalpy of the individual compoundsin the aerosol composition and by the specific aerosol mass

4

3

2

1

0

-1

-2

-3

log

(C*)

0.003250.003000.00275

1/T50 (K-1

)

COA=10 μg/m3

4

3

2

1

0

-1

-2

-3lo

g (C

*)

0.003250.003000.00275

1/T50 (K-1

)

COA=150 μg/m3

4

3

2

1

0

-1

-2

-3

log

(C*)

0.003250.003000.00275

1/T50 (K-1

)

COA=400 μg/m3

Theoretical calibration curve for:Monocarboxylic acids (nC10-19)Dicarboxylic acids (nC4-12)Alkanes (nC20-30)Alcohols (nC13-16)

Monocarboxylic acids, exp. Dicarboxylic acids, exp. (Faulhaber et al., 2009)Empirical calibration (Faulhaber et al., 2009)Empirical equation uncertainty range

Fig. 11.Theoretical relationship betweenC∗0 and 1/T50 for different

organic compounds, as derived from Eq. (22) at different aerosolmass loadings. The empirical and theoretical curves overlap forhigh aerosol loadings, while deviation between the curves is ex-pected for low atmospheric aerosol loadings.



loading conditions. Under the assumption that thermogramsare not modified after leaving the heating section (i.e. negligi-ble re-condensation) and negligible curvature effect, Eq. (23)implies that identical thermograms should be obtained withdifferent thermodenuders for the same aerosol sample andinitial aerosol loadings, if equilibrium is attained. In con-trast, dependence of thermograms on additional factors suchas particle size and evaporation coefficient is expected atkinetically-controlled evaporation conditions (Faulhaber etal., 2009; Riipinen et al., 2010).

The equilibrium curve defined in Eq. (23) can be appliednot only to interpret thermodenuder measurements but alsoto analyse the change in aerosol mass loading upon changesin the atmospheric temperature assuming that the aerosolreaches equilibrium. The combination of Eqs. (23), (24)and (25) constitutes a system which allows for the calcula-tion of the variations in the aerosol mass upon changes inthe temperature, if the composition of the aerosol at a ref-erence temperature is known. This is in fact an equivalentmethod to using the partitioning theory in combination withthe Clausius-Clapeyron equation. This approach was usedto explore the variation of the equilibrium aerosol mass withchanges in the temperature and dilution ratio with respect tothe initial aerosol loading, in comparison with kinetically-controlled evaporation/condensation simulations performedwith the kinetic model. It should be noted that these calcu-lations are presented with an illustrative purpose to infer thevariations of aerosol mass under the assumption of equilib-rium or kinetically-controlled conditions and not to provideinsights on the effect of complex atmospheric processing onaerosol partitioning. Figure13 (top) illustrates the change ofthe total mass ratio COAf /COA0 for lubricating oil andα-pinene SOA aerosols, taking as a reference a temperature of25◦C and an aerosol loading of 20 µg m−3 . For lubricatingoil it was considered that equilibrium is attained in a shorttimescale, while for the case of amorphous solidα-pineneSOA, calculations are provided for (1) equilibrium condi-tions, which implies that the condensation coefficient is highenough as to achieve equilibrium in a short time-scale, and(2) for non-equilibrium conditions, assumingdp0 = 100 nmand an effective kinetic coefficientγ ′

cond=γ ′evap= 0.00055

(mean value between 0.001–0.0001, optimum range foundwhenγ ′

cond=γ ′evap (Cappa and Wilson, 2011)). Because the

condensation process would be dependent on the time scalefor the kinetically-controlled case, the kinetic model was ap-plied to calculate the change in the particle mass due to cool-ing from 25◦C for time scales of 1 h, 3 h and 5 h. The useof different coefficients for condensation and evaporation isaimed to represent the limitation to the kinetic rate in one di-rection or another. It should be noted that at the molecularlimit, the differences in the coefficients used in our analy-sis may lead to unphysical behaviour; however this approachis still useful to analyse the behaviour when the evapora-tion process is inhibited. The equilibrium results provided

-6

-5

-4

-3

-2

-1

0

1

2

3

log

(C*)

0.00320.00300.00280.00260.00241/T50 (K

-1)

COA=150 μg/m3

Empirical calibration (Faulhaber et al., 2009) Empirical equation uncertainty range Equilibrium calibration curve (theoretical)

Calibration curves at kinetically controlled conditions:

γ'=0.1 γ'=0.01 γ'=0.001

-6

-5

-4

-3

-2

-1

0

1

2

3

log

(C*)

0.00320.00300.00280.00260.0024

1/T50 (K-1

)

COA=20 μg/m3

Empirical calibration (Faulhaber et al., 2009) Empirical equation uncertainty range Equilibrium calibration curve (theoretical)

Calibration curves at kinetically controlled conditions:

γ'=1 γ'=0.1 γ'=0.01 γ'=0.001

Fig. 12. Deviation of the calibration curve due to equilibriumnot being attained in thermodenuder measurements at two differ-ent aerosol loadings.T50 deviations up to∼20–30◦C, with respectto equilibrium, situate the calibration curve within the uncertaintyregion of the empirical formulation. Further difference with respectto equilibrium (particularly forγ ′ < 0.01) leads to significant de-viation of the calibration curve with respect to the empirical andtheoretical curves.



represent the case withγ ′

cond=γ ′evap= 1 for the considered

time scales.The difference in composition between lubricating oil and

α-pinene SOA in the upper volatility bins leads to a largedifference regarding the equilibrium aerosol formation uponcooling between these two types of aerosols (particularlydue to a mass fraction of 0.1 forC∗ = 104 µg m−3 in the lu-bricating aerosol composition versus a mass fraction of 0.6for α-pinene SOA). The results also reveal a very differentaerosol forming potential forα-pinene SOA depending onthe assumption of condensation coefficient. The large un-certainty in the prediction of the amount of aerosol formedfrom amorphous solid SOA points at the necessity of furtherstudying whether growth of glass-like particles during cool-ing would be retarded by the particle phase as shrinkage maybe assumed to be.

The sensitivity to the assumption of effective kinetic evap-oration coefficient has also been explored for the aerosolmass change resulting from dilution-induced evaporation ofamorphous solid SOA particles. In a similar manner to theabove analysis, calculations were conducted under the as-sumptions of (1) equilibrium conditions (i.e. kinetic coeffi-cients equal to unity for the time scales considered here orany kinetic coefficient values as long as equilibrium is at-tained), (2) non-equilibrium, withγ ′

evap=γ ′

cond= 0.00055 and(3) non-equilibrium withγ ′

evap= 0.055 (optimum value forγ ′

cond= 1). Figure13b shows the results of this analysis asthe ratio between the aerosol mass remaining after dilution(corrected for the dilution ratio) and the initial aerosol mass,which is equivalent to the mass change ratio due to particleevaporation. As expected, amorphous solid SOA (cases withγevap= 0.0055 andγ ′

evap= 0.00055) exhibits a much lowersensitivity to dilution than what it is predicted by equilibriumpartitioning. In particular, the model points at an underesti-mation in the aerosol mass remaining in a factor from 5 to10, if partitioning equilibrium theory is applied. It shouldbe noted that the estimation of particle mass evaporated withthe kinetic model is also highly sensitive to the assumption ofeffective evaporation coefficient, and that a better constraintof this value is required to adequately predict the changes inaerosol mass upon dilution.

7 Derivation of volatility distributions fromthermodenuder measurements

Evaporation profiles from thermodenuder measurements canbe applied to derive the volatility distribution using themethod ofFaulhaber et al.(2009). This method involves us-ing the calibration curve betweenC∗

0 and 1/T50, together withthe thermogram measurements for the subsequent derivationof the particle fraction belonging in eachC∗

0 volatility bin(Faulhaber et al., 2009). In this section diverse thermogramsare used to derive the volatility distributions using the equi-librium equation derived in the present study, the empirical

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

CO

A,f(

dilu

tion

corr

ecte

d)/C

OA

, 25C

282420161284

Dilution ratio

α-pinene SOA equilibrium α-pinene SOA, 1h. timescale, γevap= γ'cond=5.5e-4

α-pinene SOA, 3h. timescale, γ'evap= γ'cond=5.5e-4

α-pinene SOA, 5h. timescale, γ'evap= γ'cond=5.5e-4

α-pinene SOA, 1h. timescale, γ'evap=5.5e-3, γ'cond=1



10

9

8

7

6

5

4

3

2

1

CO

A,f/

CO

A, 2

5C

-30 -20 -10 0 10 20

T(°C)

Lubricating oil. equilibrium α-pinene SOA, equilibrium α-pinene SOA, 1h. timescale, γ'cond= γ'evap=5.5e-4

α-pinene SOA, 3h. timescale, γ'cond= γ'evap=5.5e-4

α-pinene SOA, 5h. timescale, γ'cond= γ'evap=5.5e-4

(a)

(b)

Fig. 13. (a)Condensed mass forming potential of lubricating oilandα-pinene SOA resulting from cooling from initial conditionsat 25◦C and 20 µg m−3 aerosol loading. For theα-pinene SOAaerosol, the cases presented are (1) equilibrium, assuming that gascondensation is not affected by the particle phase and (2) non-equilibrium conditions withγ ′

cond=γevap. A strong difference isobtained in the particle mass change estimation, depending on theassumption of condensation being or not affected by the parti-cle amorphous solid state.(b) Change inα-pinene SOA aerosolmass resulting from dilution-induced evaporation for the cases of(1) equilibrium (2) non-equilibrium withγ ′

evap=γ ′cond and (3) non-

equilibrium withγ ′evap= 5e–3 andγ ′

cond= 1. While the equilibriumpartitioning calculations significantly overestimate the amount ofamorphous solid aerosol mass evaporated due to dilution, a largedifference in the estimation of aerosol mass is obtained dependingon the assumption of effective evaporation coefficient.



calibration byFaulhaber et al.(2009) and the kinetic modelapproach applied byCappa and Jimenez(2010). The deriveddistributions are compared with those obtained by apply-ing aerosol mass fraction parameterisations determined fromchamber experiments byPathak et al.(2007) andGrieshopet al.(2009) for the aerosols on study. It has been previouslydiscussed bySaleh et al.(2011) that the use of thermogramscould be misleading in the case that mass fraction remain-ing (MFR) values are directly compared to interpret particlesvolatility (e.g. comparison of MFR values at constant temper-ature), since MFR values depend on the initial aerosol massloading. It should be noted that this issue is overcome in thepresent study by applying methods which account for the de-pendence of thermograms on the initial aerosol mass loading.

7.1 Calibration curve approach: empirical andtheoretical equations

The volatility distribution for lubricating oil andα-pineneSOA was derived from thermogram measurements byGrieshop et al.(2009) and Cappa and Wilson(2011)(Fig. 14), using the empirical and theoretical calibrationcurves following the method described inFaulhaber et al.(2009). In addition, in order to estimate the potential de-viation in the prediction due to re-condensation, thermo-grams after the heating section were modeled using the ki-netic model and subsequently used to derive the volatilitydistribution.

Figure14 shows the lubricating oil aerosol volatility dis-tribution as determined from thermodenuder measurementsat two different aerosol loadings. It should be noted that theupper volatility bin with this method is restricted toC∗

0 ≥

100 µg m−3, which is the maximum volatility limit for thepossible estimation ofT50 above ambient temperature. Forthe case of 70 µg m−3m (Fig.14a) there is a reasonable agree-ment between the ideal volatility set distribution and that pre-dicted usingFaulhaber et al.(2009) empirical curve, withlittle effect of re-condensation in this estimation. In contrast,the aerosol volatility is significantly underestimated when us-ing the equilibrium curve. This deviation is due to the factthat, for this aerosol loading, the thermogram is not at equi-librium; hence,Ti,50 exhibits values larger than those in theequilibrium thermogram, resulting in a calibration curve atthe left of the equilibrium theoretical curve. Figure S7 showshow the resulting calibration curve fortuitously lays in theproximity of the empirical equation, resulting in a better pre-diction with respect to the equilibrium curve. It should benoted that although the prediction using the empirical curveis valid in this case, the fact that the calibration curve fallsover the empirical curve is merely fortuitous and it cannot beconcluded that the empirical approximation would be validat other experimental conditions.

At 650 µg m−3 aerosol loading (Fig.14, bottom), both theempirical and equilibrium curves approach the volatility dis-tribution derived from literature data. At this high aerosol

500

400

300

200

100

0

Mas

s co

ncen

trat

ion

(μg/

m3 )

-2 -1 0 1 2 3 4

log C* (μg/m3)

Gas phase Particle phase

COA=650 μg/m

3

90

80

70

60

50

40

30

20

10

0

Mas

s co

ncen

trat

ion

(μg/

m3 )

-2 -1 0 1 2 3 4

log C* (μg/m3)

Equilibrium theoretical curve (with re-condensation) Empirical curve (with re-condensation) Empirical curve w/o re-condensation Volatility distribution derived from Grieshop et al. (2009)


COA=70 μg/m

3

Fig. 14. Volatility distributions derived from lubricating oil ther-mograms at 70 and 650 µg m−3 aerosol loading, using the equi-librium and empirical calibration curve approach. For 70 µg m−3

(a) the thermogram considerably deviates from equilibrium (Fig.8and S5), thus, resulting in the equilibrium calibration approach un-derestimating the aerosol volatility. The empirical calibration pro-vides a better agreement in this case, due to the calibration curvefortuitously laying on the empirical calibration curve (Fig. S5).For the highest aerosol loading(b), the thermograms are closeto equilibrium (Fig.8 and S5) and the predictions approach thedistribution derived using the volatility basic-set distribution byGrieshop et al.(2009).

mass, the empirical and equilibrium curve are close to eachother (Fig. S7), and evaporation equilibrium is close to beattained (Fig.8a), which leads to a better agreement be-tween the distribution derived from literature data (Grieshopet al., 2009) and the predictions. The overestimation inthe aerosol mass obtained for the lower volatility bins withrespect to (Grieshop et al., 2009) distribution is possiblydue to the fact thatFaulhaber et al.(2009) method is re-stricted to volatility bins withC∗ < 100 µg m−3, which atthe very high aerosol loading of this case, may result inthe mass from the upper volatility compounds being dis-tributed between the lower volatility bins. This reveals a



400

300

200

100

0

Mas

s co

ncen

trat

ion

(μg/

m3 )

-6 -5 -4 -3 -2 -1 0 1 2 3 4

log C* (μg/m3)

1200

1000

800

600

Equilibrium theoretical curve (with re-condensation) Empirical curve (with re-condensation) Empirical curve w/o re-condensation (upper estimate, γ'evap=0.01)

Empirical curve w/o re-condensation (lower estimate, γ'evap=0.001) Distribution derived from Pathak et al. (2007)

Gas phase

Particle phase COA=500 μg/m

3

γ'cond=1

400

300

200

100

0

Mas

s co

ncen

trat

ion

(μg/

m3 )

-6 -5 -4 -3 -2 -1 0 1 2 3 4

log C* (μg/m3)

1200

1000

800

600

Equilibrium theoretical curve (with re-condensation) Empirical curve (with re-condensation) Empirical curve w/o re-condensation Distribution derived from Pathak et al. (2007)


COA=500 μg/m3

γ'evap=γ'cond=0.00055

(a)

(b)

Fig. 15.Volatility distributions derived fromα-pinene SOA thermo-grams at 500 µg m−3 aerosol loading in comparison with the distri-bution derived using the parameterisation byPathak et al.(2007).For case(a) the volatility is substantially underestimated due to thethermogram being significantly far from both the equilibrium andthe empirical calibration curves region, while in(b) the deviationusing the calibration curve approach is partly due to significant re-condensation. Calculations for upper and lower estimates for re-condensation are included for case(b).

limitation in usingFaulhaber et al.(2009) method for deriv-ing volatility from experiments with very high aerosol massloadings. In this case re-condensation is also significant, asshown in the non-re-condensation distribution in Fig.14b,which leads to an underestimation of the volatility distribu-tion. The distribution obtained in this case for a lower es-timate of re-condensation does not substantially differ fromthe upper estimate and has not been included in the figurefor comparison.

For the α-pinene SOA volatility study, the cases of(1) equal evaporation and re-condensation kinetic coeffi-cients with a mean value of 0.00055, and (2) indepen-dent coefficients for evaporation and re-condensation, with

γ ′evap= 0.0055 andγ ′

cond= 1 were considered. As explainedin Sect.5.2, the second case represents the evaporation of aglass-like SOA, whose re-condensation process is not limitedby the particle phase and presents a re-condensation coeffi-cient equal to unity. For the first case (Fig.15a), the thermo-gram is very far from equilibrium (Fig.9), because of the lowkinetic coefficient, which leads to substantial underestima-tion of the volatility when using both the theoretical and em-pirical calibration curves. In this case, the prediction usingboth calibration equations is similar, due the curves becom-ing closer at high aerosol loadings, as previously shown. Be-cause of the low accomodation coefficient, re-condensationis not significant in this case, which leads to equal volatilitydistributions for the cases with and without re-condensation.

For unequal evaporation and re-condensation kinetic co-efficients (Fig.15b), the distributions obtained indicate thatthe prediction using the calibration curves deviates substan-tially from the literature distribution due to the fact that equi-librium is not reached and also because the thermogram isstrongly affected by re-condensation (Fig.9). This occursfor both upper and lower estimates for re-condensation. Theanalysis presented here indicates that the interpretation ofthermograms and prediction of volatility distributions fromthermodenuder measurements is strongly affected by the as-sumption of equilibrium and the degree of disequilibriumresulting from kinetic limitation.

7.2 Kinetic model approach

The kinetic evaporation/re-condensation model was also ap-plied to derive the aerosol volatility distribution from ther-mograms, following the approach ofCappa and Jimenez(2010). This method consists of the iterative estimation ofthe volatility basis set distributions by bringing into agree-ment the modeled and experimental thermograms (Cappaand Jimenez, 2010). The method to derive the volatilitydistribution is based on the assumption that the distribu-tion follows an exponential function with an upper limit ofC∗ = 104µg m−3. The lower volatility bin limit was iter-ated to obtain agreement between measurements and model,which explains the large number of bins obtained in thevolatility distributions.

Because this method requires specifying the effective ki-netic coefficient, the volatility distributions inferred herewere compared for a set of coefficient values, assuming equalkinetic coefficients for evaporation and re-condensation. Inthese calculations re-condensation is neglected. The ther-modenuder measurements forα-pinene SOA could not beadequately fitted with the model for kinetic coefficientsabove 0.01, thus constraining these parameters to values≤0.01. In this model it was assumed that the enthalpy ofvaporisation is a function ofC∗, following Epstein equation.For different values of1Hv to those derived from the Epsteinequation, a different range of kinetic coefficient values wouldbe possible. Figure16 shows the volatility distributions



500

400

300

200

100

0

Mas

s co

ncen

trat

ion

(μg/

m3 )

-5 -4 -3 -2 -1 0 1 2 3 4log C*

4000300020001000

Modeled distribution, γ'=0.0001 Distribution derived

from Pathak et al. (2007)

400

300

200

100

0

Mas

s co

ncen

trat

ion

(μg/

m3 )

-5 -4 -3 -2 -1 0 1 2 3 4

log C*

200015001000

500



400

300

200

100

0

Mas

s co

ncen

trat

ion

(μg/

m3 )

-5 -4 -3 -2 -1 0 1 2 3 4log C*

200015001000

500



Fig. 16. Volatility distributions derived fromα-pinene SOA ther-mograms at 500 µg m−3 aerosol loading using the kinetic model ap-proach with different kinetic coefficient values, in comparison withthe distribution derived from data byPathak et al.(2007). The de-rived distribution is sensitive to the assumption of effective kineticcoefficient, with a shift towards lower volatility for increasing ki-netic coefficient.

derived from theα-pinene SOA aerosol thermogram by ap-plying the kinetic model (results of the fitting between modeland measurements are presented in Fig. S8). The volatilitydistributions obtained with this method are highly sensitiveto the assumption of kinetic coefficient. In this particularcase, an overestimation and underestimation of the volatility

is obtained for kinetic coefficients values of 0.0001 and 0.01,respectively, while a reasonable agreement between the liter-ature and estimated volatility distributions is obtained for anevaporation coefficient of 0.001.

Volatility distributions for different groups of atmosphericorganic aerosols, using a kinetic model, have been providedas an estimation forγ ′ = 1 (Cappa and Jimenez, 2010). Itshould be taken into account that it is unknown whetherthe different organic groups comprising atmospheric aerosolswould present different effective kinetic coefficients. Thisimplies a large uncertainty in interpreting the volatility dis-tribution of organic aerosols and brings into question thevolatility grading scale established for different organic com-pound groups byCappa and Jimenez(2010). The fact thatatmospheric measurements with thermodenuders will mostlikely not be at equilibrium poses a strong difficulty to accu-rately derive the volatility properties of aerosols from thesetype of measurements, as long as deviations from equilib-rium are not more accurately constrained. Indeed, currentuncertainty in determining volatility distributions for atmo-spheric samples will affect estimations of organic particlepartitioning in atmospheric models, and modeling of organicaerosol CCN activity (Topping and McFiggans, 2012). Al-though models can be self-consistent if a given kinetic coef-ficient and its corresponding volatility distribution are usedsystematically, the quantitative results of models will pri-marily depend on the assumption of kinetic coefficient, thus,their outcome will be subject to the uncertainty associated tothe value of this coefficient and its corresponding volatilitydistribution.

8 Summary and conclusions

In the present study a kinetic evaporation-condensationmodel was applied to analyse the uncertainty in estimatingand interpreting the evaporation behaviour and volatility ofaerosols from thermodenuder experiments.

Theoretical derivation of the empirical calibration curvebetween the saturation concentrationC∗ and temperatureat which 50 % of the particle mass evaporates (T50) (Faul-haber et al., 2009), revealed that this relationship is basedon the change in particle mass between equilibrium temper-ature states, expressed explicitly as a function ofC∗ throughthe Clausius-Clapeyron equation. Calibration curve equa-tions for a single component and multicomponent mixtureswere theoretically derived and applied to estimate volatil-ity distributions from equilibrium thermograms. Significantunderestimation of the particle volatility resulted, however,when using the equilibrium calibration curve at kinetically-controlled evaporation conditions. Because thermograms ob-tained at ambient aerosol loading levels would likely deviatefrom equilibrium, a kinetic approach constitutes a more ad-equate method to correctly interpret the particle evaporationbehaviour of atmospheric samples. However, the application



of the kinetic model approach to derive volatility distribu-tions confers significant uncertainty, owing to sensitivity ofthe method to the assumption of evaporation coefficient.

Re-condensation was evaluated as a source of uncertaintyfor determining aerosol volatility distributions from ther-modenuder measurements, because of its potential to affectthermograms. A parametric analysis showed that the re-condensation yield is highly determined by the combined ef-fects of aerosol loading, particle size and effective kinetic co-efficient for re-condensation. This dependence results in ei-ther important or negligible re-condensation at higher aerosolmass loadings, depending on the thermodenuder configura-tion and the properties of the aerosol sample. Analysis ofthe effect of denuders on particle evaporation indicated thatexperimental thermograms may be modified in the region be-low 45◦C as a result of evaporation induced by the charcoaldenuder at atmospheric aerosol levels.

Estimation of effective kinetic evaporation coefficient val-ues from experimental evaporation measurements with lubri-cating oil aerosol revealed the existence of artefacts in theevaporation occurring in standard chamber dilution experi-ments, which is manifested as a notable deceleration of theparticle evaporation rate, presumably resulting from the re-lease of material from the chamber walls. From this anal-ysis it is concluded that dilution experiments with standardTeflon walls do not seem to be an adequate methodology forconducting this type of studies.

Analysis in this study points at the effective kinetic coef-ficient defined in an evaporation/re-condensation model as acritical unknown to both determining the volatility propertiesof atmospheric samples and determining the atmospheric dy-namics of SOA. Simulation of the evaporation-condensationbehaviour of amorphous solidα-pinene SOA, pointed at alarge uncertainty in estimating the aerosol mass formation in-duced by cooling, depending on whether or not it is assumedthat gas condensation is affected by the amorphous solid stateof the particles. Analysis of dilution-induced evaporation ofα-pinene SOA indicated an underprediction of the aerosolmass in a factor from 5 to 10, when using equilibrium parti-tioning theory with respect to the kinetic calculations for aneffective evaporation coefficient between 0.01–0.0001. Pre-dictions with the kinetic model were found to be highly sen-sitive to the assumption of effective evaporation coefficient.Better constraints on this parameter are therefore required tomodel the particle mass variation upon atmospheric dilutionand cooling for glass-like SOA. Current modules to predictSOA formation in the atmosphere are based on empirically-derived mass fraction parameterisations (e.g.Strader et al.,1999) and do not account for kinetic limitations to evapo-ration/condensation of amorphous SOA. This study demon-strates that it is necessary to use kinetic approaches (includ-ing estimations of kinetic coefficients), alongside volatilityinformation, to implement reasonable gas-aerosol partition-ing modules in transport models that include glass-like SOA.

Supplementary material related to this article isavailable online at: http://www.atmos-meas-tech.net/5/735/2012/amt-5-735-2012-supplement.pdf.

Acknowledgements.This work was supported by the UK NaturalEnvironment Research Council [grant number NE/H002561/1].

Edited by: H. Herrmann

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