Optical properties of absorbing and non-absorbing aerosols retrieved by cavity ring down

15 Pages·2017·0.66 MB·English

Atmos. Chem. Phys.,7,1523–1536,2007
Atmospheric
www.atmos-chem-phys.net/7/1523/2007/
Chemistry
©Author(s)2007. Thisworkislicensed
underaCreativeCommonsLicense. and Physics
Optical properties of absorbing and non-absorbing aerosols
retrieved by cavity ring down (CRD) spectroscopy
A.AboRiziq1,C.Erlick2,E.Dinar1,andY.Rudich1
1DepartmentofEnvironmentalSciences,WeizmannInstituteofScience,Rehovot76100,Israel
2DepartmentofAtmosphericSciences,TheHebrewUniversityofJerusalem,Jerusalem91904,Israel
Received: 2November2006–PublishedinAtmos. Chem. Phys.Discuss.: 29November2006
Revised: 16February2007–Accepted: 8March2007–Published: 21March2007
Abstract. Application of cavity ring down (CRD) spec- Ramanathanetal.,2005,2001). Thedirecteffectofaerosols
trometry for measuring the optical properties of pure and on climate is by absorbing and/or scattering the incoming
mixed laboratory-generated aerosols is presented. The ex- solarradiationandoutgoingterrestrialradiation. Thisinter-
tinctioncoefficient(α ),extinctioncrosssection(σ )and action strongly modifies Earth’s radiation budget and hence
ext ext
extinction efficiency (Q ) were measured for polystyrene the climate on regional and global scales. Much attention
ext
spheres(PSS),ammoniumsulphate((NH ) (SO )),sodium has been devoted to purely scattering aerosols, such as sul-
4 2 4
chloride (NaCl), glutaric acid (GA), and Rhodamine-590 phateaerosols,mostlyduetotheir“coolingeffect”.Morere-
aerosols.Therefractiveindicesofthedifferentaerosolswere cently,considerableattentionhasbeendirectedtoabsorbing
retrievedbycomparingthemeasuredextinctionefficiencyof aerosols such as soot (Jacobson, 2001; Koren et al., 2004;
each aerosol type to the extinction predicted by Mie the- Menon et al., 2002), dust (Kaufman et al., 2005; Yu et al.,
ory. Aerosols composed of sodium chloride and glutaric 2006),organics(Kanakidouetal.,2005)andmixedaerosols
acidindifferentmixingratioswereusedasmodelformixed that contain absorbing species and inclusions. Absorbing
aerosolsoftwonon-absorbingmaterials,andtheirextinction aerosolscanheattheatmosphereandaffectatmosphericcir-
and complex refractive index were derived. Aerosols com- culation(Hansenetal.,2005;Jacobson,2001;Menonetal.,
posedofRhodamine-590andammoniumsulphateindiffer- 2002)andcloudformation(i.e.,thesemi-directeffect)(Ko-
entmixingratioswereusedasmodelformixingofabsorbing renetal.,2004). Thereisagrowingneedtounderstandand
andnon-absorbingspecies,andtheiropticalpropertieswere measure atmospheric aerosol optical properties in order to
derived. The refractive indices of the mixed aerosols were betterconstraintheirdirectandsemi-directclimaticeffects.
also calculated by various optical mixing rules. We found The ability of aerosols to interact with radiation is dic-
that for non-absorbing mixtures, the linear rule, Maxwell- tatedbytheiropticalproperties,whichdependontheirphys-
Garnettrule, andextendedeffectivemediumapproximation ical and chemical characteristics, and on the wavelength of
(EEMA),givecomparableresults,withthelinearmixingrule the incident light. The main parameters in this respect are
giving a slightly better fit than the others. Overall, calcula- the scattering and absorption coefficients (or efficiencies).
tions for the mixed aerosols are not as good as for single The interaction of radiation with particles by either scatter-
componentaerosols. Forabsorbingmixtures,thedifferences ing, absorption, or both, leads to attenuation (or extinction)
between the refractive indices calculated using the mixing of the incident light. This attenuation can be expressed as
rulesandthoseretrievedbyCRDaregenerallyhigher. α =α +α , where α is the extinction coefficient in
ext sca abs ext
unitsof[Lt1],α isthescatteringcoefficient,andα isthe
sca abs
absorption coefficient. By measuring α and α , the sin-
ext sca
glescatteringalbedo,whichistheratiobetweenthescattered
1 Introduction
light to the total attenuated light (̟ =α (α +α )),
0 sca sca abs
AtmosphericaerosolsaffectEarth’sclimatebothdirectlyand can be calculated. The single scattering albe(cid:14)do of particles
present in the atmosphere is a key parameter needed in cli-
indirectly(Batesetal.,2006;Bellouinetal.,2005;Kaufman
mate models and remote sensing applications. Therefore,
etal.,2002;Korenetal.,2004;LohmannandFeichter,2005;
accurately measuring the scattering and absorption proper-
Correspondenceto: Y.Rudich ties of aerosols is crucial for estimating Earth’s energy bal-
([email protected]) ance. Methodsforcalculatingtherefractiveindexbasedon
PublishedbyCopernicusGmbHonbehalfoftheEuropeanGeosciencesUnion.
1524 A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy
chemicalcompositionarealsoofimportanceastheyenable linearaverageoftheindicesofthecomponentsweightedby
thecalculationofaerosolradiativepropertiesinclimatemod- theirvolumefractions:
els. n =f n +f n
Anumberofmethodsforcalculatingtheradiativeproper- ktot=f1k1+f2k2 , (3)
tot 1 1 2 2
ties of aerosols of mixed composition (internal mixtures of
differentaerosolsubstancesand/ormixturesofaerosolsub- wherefi isthevolumefractionofthecomponents.
stances with water), are used in climate models. For ex- In the Maxwell-Garnett mixing rule, one or more of the
ample, a growth function estimated from measurements or components(usuallytheundissolvedand/orabsorbingcom-
fromMiecalculationsmaybeappliedtodescribethechange ponents)aredeemed“inclusions”,whiletherestofthecom-
in scattering coefficient as aerosol water content increases ponents comprise a “homogeneous matrix”. The inclusions
(e.g., Bates et al., 2006). Alternatively, Mie scattering cal- are assumed to be small (dipoles), spherical, randomly dis-
culations may be employed explicitly during the simulation tributedthroughoutthedrop,anddilute,suchthattheeffec-
or in a look-up table fashion, using mixing rules (Erlick, tivedielectricconstantofthemixtureisgivenby:
2006)tocalculatetheeffectiverefractiveindicesofthemix- ε =ε + 3finclεmatrix(εincl−εmatrix)
ture or assuming a core plus shell configuration (Jacobson, tot matrix εincl+2εmatrix−fincl(εincl−εmatrix) (4)
n =(ε )1/2
2002). Mixing rules currently in use include: (1) molar tot tot
refraction and absorption (Born and Wolf, 1999; Jacobson, where ε ,ε , and ε are the complex dielectric con-
tot incl matrix
2002; Stelson, 1990; Tang, 1997); (2) a volume-weighted stantsofthemixture,theinclusions,andthematrix,respec-
linearaverageoftherefractiveindices,i.e.,the“linear”mix- tively,f isthevolumefractionoftheinclusions,andn
incl tot
ingrule(see,e.g.,d’Almeidaetal.,1991,theirEq.6.3);(3) isthecomplexrefractiveindexofthemixture.
the Maxwell-Garnett rule (see Bohren and Huffman, 1983, Thedynamiceffectivemediumapproximationisanexam-
Sect. 8.5; Bohren, 1983; Chy´lek et al., 1984); and (4) the ple of a higher order or extended effective medium approx-
dynamiceffectivemediumapproximation(Chy´lek,2000;Ja- imation as compared to the Maxwell-Garnett mixing rule,
cobson,2006). Whilesomeofthesemixingruleshavebeen wheretheinclusionsareallowedhigherordereffectsthanthe
tested against experimental data for certain substances with electricdipole. Thesizeorsizedistributionoftheinclusions
certainvolumefractions(seeGosseetal.,1997;Erlick,2006, themselvesmustbespecified.
andreferencestherein),whichrules/modelsaremostappro- CavityRingDown(CRD)spectroscopyhasbeenrecently
priate,ifatall,remainsuncertain. introduced for measuring extinction coefficients of labora-
The molar refraction (absorption) mixing rule assumes tory and field aerosols. Sappy et al. (1998) pioneered the
that the total molar refraction (absorption) of a mixture is use of CRD for detecting ambient particles non-resonantly
given by the linear average of the molar refraction (absorp- at 532nm and 355nm. Vander Wal and Ticich (1999) used
tion)ofthecomponentsinthemixtureweightedbytheirmo- pulsed CRD to study the absorption of soot produced from
larvolumes,i.e., methane-air flame and to calibrate laser induced incandes-
cencemeasurements,whicharewidelyusedtomeasuresoot
n2 −1
R =V tot =χ R +χ R and volume fraction. Smith and Atkinson (2001) performed si-
tot totn2tot+2 1 1 2 2 multaneousmeasurementsofextinctionbyambientaerosols
Atot =Vtotktot =χ1A1+χ2A2 (1) at 532nm and 1064nm. Using simultaneous measurements
at 510.6nm and 578.2nm, Thompson et al. (2002) mon-
where R , V , n ,A , and k are the molar refraction,
tot tot tot tot tot itored the change in atmospheric optical extinction coeffi-
molarvolume,realpartoftherefractiveindex,molarabsorp-
cient during a wildfire and during a local fireworks event.
tion, and imaginary part of the refractive index of the mix-
Strawa et al. (2003) were the first to use continuous wave
ture,respectively,andχ ,R ,andA arethemolarfraction,
i i i cavity ring down (CW-CRD) for aerosol studies. Using
molar refraction, and molar absorption of the components,
diode lasers at wavelengths of 690nm and 1550nm, they
respectively. The molar refraction of the components, mo-
measured a minimum extinction coefficient for both wave-
larabsorptionofthecomponents,andtotalmolarvolumeare lengths of about 1.5×10−8cm−1 (a better sensitivity could
givenby:
be achieved with higher reflectivity mirrors). By placing a
R = Mi n2i−1 scattering detector at 90◦ to the cavity, they measured the
i ρi n2i+2 scatteringcoefficientinadditiontotheextinctioncoefficient
A = Mik (2) anddirectlyextractedthesinglescatteringalbedo(̟). Bu-
i ρi i
V = Mtot latovetal.(2002)usedapulseddyelaserat620nmtostudy
tot ρtot laboratory-generated non-absorbing NaCl and CuCl ·H O
2 2
where M symbolizes molecular weight and ρ symbolizes aerosols. The measured extinction coefficients were com-
density. pared to Mie scattering calculations. Bulatov et al. (2006)
The “linear mixing rule” assumes that the total real and alsomeasuredtheextinctioncoefficientofsizeselectedRho-
imaginary refractive indices ofthe mixtureare givenby the damine 640 aerosols (a strongly absorbing dye at 615nm).
Atmos. Chem. Phys.,7,1523–1536,2007 www.atmos-chem-phys.net/7/1523/2007/
A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy 1525
This was the first use of CRD to measure optical properties lawextinctioncrosssectiontothegeometricareaofthepar-
of absorbing organic aerosols (other than soot). Pettersson ticleandisdimensionless,N istheparticlenumberdensity,
et al. (2004) demonstrated the use of pulsed laser (532nm) andD istheparticlediameter. Byselectingamonodisperse
CRDtostudypolystyrenespheres(PSS)anddioctylsebacate aerosol population and measuring the particle number den-
(DOS) aerosols. Their measurements show good quantita- sity(N),theextinctionefficiency(Q )canbedetermined.
ext
tive agreement with Mie calculations in the scattering cross Forafixedwavelength, Q canbemeasuredasafunction
ext
section and refractive index. Recently, Lack et al. (2006) of the size parameter by performing measurements on a se-
applied CRD to derive aerosol extinction coefficient of ab- ries of monodisperse particles of different sizes. The size
sorbing PSS aerosols and to calibrate a photoacustic spec- parameter,x,istheratiooftheparticlesize(D)tothelaser’s
troscopymeasurementsoftheabsorptioncoefficientforthese wavelength(λ)andisgivenby(x=πD/λ). HavingQ asa
ext
aerosols. Moosmuller et al. (2005) used CRD to measure functionofsizeparameterenablesaretrievaloftheparticle
very low extinction in the atmosphere and laboratory envi- refractiveindex.
ronments. Inthisstudywepresenttheuseofcavityringdown(CRD)
CavityringdownspectroscopywasdevelopedbyO’Keefe fordeterminingtheextinctionefficiencyandcomplexrefrac-
and Deacon (1988). Typically, it consists of two highly re- tiveindexofpureandmixedaerosols. Specifically,wefocus
flective plano-concave mirrors set opposite to one another. onmixturesoforganicandinorganiccomponents,as30%to
Theplacementofthemirrorsisdependentonthecavitysta- over80%oftheaerosolmassinthefreetropospherecontains
bilityconditions. Apulsedorcontinuouslaserbeamiscou- carbonaceous material, most of it probably organics (Mur-
pledintothecavityfromonesideandperformsmultiplere- phy,2006).Forvalidationofthenewsetup,wemeasureQ
ext
flectionsinsidethecavity.Aphotomultiplier(PMT)isplaced asafunctionofsizeparameterofpolystyrenespheres(PSS)
at the other side of the cavity and measures the exponential and ammonium sulphate (AS, (NH ) SO ) aerosols, both
4 2 4
decayoftheemerginglightintensity.Theintensity(I)decay with well-known refractive indices. Then we use the same
isaresultoflossesinsidethecavityandduetothemirrors: setup to retrieve the refractive indices of sodium chloride
(NaCl),glutaricacid(GA),andRhodamine-590aerosols,as
−τ
I =Ioehτ0i (5) pure component aerosols and in mixtures with one another,
the mixtures allowing us to test the appropriateness of the
Thetimeconstantforanemptycavity,τ ,is:
0 theoreticalmixingrules.
τ =L/C(1−R) (6)
0
whereListhelengthofthecavity(distancebetweenthetwo 2 Experimental
mirrors), C is the speed of light, and R is the reflectivity
2.1 Aerosolgenerationandclassification
of the mirrors. This equation depicts the dependence of the
ringdowntimeonthecavitylengthandthemirrorreflectiv- Aqueous solutions (20–500mg L−1) of the compounds of
ity. Whenthecavityisfilledwithanabsorbingorscattering
interest are nebulized using a TSI constant output atomizer
medium,themoleculesorparticlesfurtherreducetheinten-
(TSI-3076, 25 psi, ∼2.36 standard liters per minute (SLM)
sity on each pass. This process results in a ring down trace
flow),withdryparticle-freepurenitrogen,generatingapoly-
with a shorter time constant due to additional terms in the
disperse distribution of droplets. The mean diameter of the
ringdownexpression,andthetimeconstantisdescribedby:
droplets depends on the concentration of the solution. The
τ =L/C(1−R+α d) (7) aerosol flow enters a 3L conditioning bulb before entering
ext
two silica gel column dryers, resulting in a flow with rel-
where α is the extinction coefficient of the molecules or
ext ative humidity (RH) <3%. The dry polydisperse aerosol
particles inside the cavity, and d is the actual distance in
passedthroughaneutralizer(TSI3012A)toobtainanequi-
the cavity filled with the absorbing molecule. The extinc-
librium charge distribution on the particles. A size selected
tioncoefficientcanbeextractedfromthedifferencebetween
monodisperseaerosolisgeneratedwithanelectrostaticclas-
thetimeconstantoftheemptyandthefilledcavity:
sifier(TSIDifferentialMobilityAnalyzer(DMA))operating
L 1 1 with 5SLM dry (RH<3%) clean nitrogen sheath flow and
αext = − (8) fixedatanappliedvoltage. Thesize-selectedmonodisperse
Cd (cid:20)τ τ (cid:21)
0
aerosolflowisdirectedthroughadilutionapparatusforpre-
The extinction coefficient (αext) of homogeneous spheres cise control of particle number concentration. The sample
(aerosols)isdescribedby: flow(1.2SLM)isthendirectedtotheCRDcell.
1
α =Nσ = πND2Q (9) 2.2 Cavityringdownsystem(CRD)
ext ext ext
4
whereσ istheextinctioncrosssection,Q istheextinc- TheCRDsetupisshowninFig.1. Briefly,itconsistsoftwo
ext ext
tion efficiency of the particles which is the ratio of Beer’s highlyreflectiveconcavemirrors(curvatureradiiof1mand
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1526 A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy
Prism Spatial filter Iris Nd:YAG 0.20 N
532 nm 2
245 p/cc
-2 359 p/cc
Oscilloscope
0.15 -3 494 p/cc
Iris To MCPoCno disperse aerosols flow from DMA to CRD gnal 0.10 Signal)Ln( --54 610 p/cc
Si -6
PMT 0 10 20 30 40
Time (μsec)
0.05
Dry N2 Dry N2
152.0 P/CC 0.3 0.00
2 CPC 0 20 40 60 80
3 Figure 1 7 Time (μsec)
Fig.1. Schematicrepresentationofthecavityringdownsetupfor
8 Figure 2.
aerosolsmeasurements. Fig.2.Experimentaldecaycurvesobtainedfordifferentconcentra-
tionsof400nmammoniumsulfateinsidethecavity. Theslowest
decayisobtainedfortheemptycavity. Eachcurveisanaverageof
a reflectivity of 99.995% at 532nm, Los Gatos, USA). The 400lasershots. Theinsertpatternshowsthenaturallogarithmof
mirrors are mounted at the two sides of a 90cm 3/3” stain- thedecaysignalasafunctionoftimedemonstratingalinearbehav-
less steel tube. A small purge flow of dry particle-free ni- ior,asexpected.
trogen (0.05SLM) is introduced in front of each mirror to
preventmirrorcontaminationbydepositionofaerosols. The
aerosol flow enters the CRD cell through four tubes at 45◦. modes which form different optical paths inside the cavity.
Toovercomethisissueweuseaspatialfiltermodematching
Thisisdesignedtoensuregoodmixingandevenconcentra-
usingatelescopewitha100µmpinholebetweenthelenses
tion of the particles inside the cavity. The flow in each line
asdescribedabove.Thesecondeffectiscausedbyvariations
is 0.3SLM, and the total flow inside the cavity is 1.2SLM.
inthequantumefficiencyatthedetectorsurfaceasthelaser
Theparticlesexitthecavityinasimilarsetup,andtheircon-
beam impinges on it. This was overcome by tight focusing
centration is determined by a condenμsation particle counter
ofthelaserbeamonasmallsurfaceofthedetector,asshown
(CPC, TSI 3022A). The length of the cavity occupied by
inFig.1.
particlesduringtheflowisabout68cm. Toensurethatpar-
TheinsetinFig.2showstypicalexponentialdecaycurves
ticlelossesarenegligible, wemeasuredtheparticlenumber
(on a log scale) in this case of 400nm AS particles at dif-
density after the DMA and at the exit of the CRD cell. In
ferentconcentrations. Theslowestdecayismeasuredwhen
bothcases,theparticlenumberdensitywasalmostidentical
μ
thecavityisfilledwithacontinuousflowofparticle-freedry
(>98%) for all particles sizes, suggesting minimal loses in
nitrogen resulting with a decay time of 16µs. The decay
theCRDcellandtubing.
time becomes shorter with introduction of the AS aerosol.
Thesecondharmonic(532nm)ofapulsedNd:YAGlaser
Shorterdecaytimesaremeasuredwhenhigherparticlecon-
(Quanta-Ray GCR-100, 10Hz, 7ns) is introduced to the
centrationsarepresentinthecavity.TheinsetinFig.2shows
CRDthroughaspatialfilterconsistingoftwolenseswithfo-
the exponential decays on a log scale. The decay times are
callengthof5cmand10cmanda100µm-pinholebetween
extractedfromtheslopeofsuchlines.
thelenses. Thebeamdiameterinfrontofthecavityisabout
The ability to measure precisely minimal differences in
1mm,withenergyofabout50µJ.Theintensityofthebeam
ring down times between an empty cavity (τ ) and a cav-
emergingfromtheCRDcellismeasuredwithaphotomulti- o
ity filled with aerosols (τ) provides a good estimate of the
plier(HamamatsuH6780-02). Thephotomultipliersignalis
maximumsensitivity. Todeterminetheminimumdetectable
fedintoadigitalstorageoscilloscope(LeCroy,model9361,
extinctioncoefficientweusethefollowingdefinitionforthe
300MHz), which is triggered simultaneously with the laser
detectionlimit(Brownetal.,2002):
pulse. The digitized data is transferred and stored in a per-
sonalcomputerusingaLabVIEWprogram. L 1τ
Determininganaccuratedecaytimeiscriticalforprecise αmin = C×d τm2in (10)
measurements of the extinction coefficient of the aerosols. o
Transverse modes inside the cavity lead to non-exponential where 1τ .is the standard deviation of the decay time for
min
decay which leads to inaccurate determination of the decay 400shotswhichwasobtainedforacavityfilledwithonlydry
time. Two effects of transverse modes are commonly ob- nitrogen. Intheexperimentspresentedhere,τ =16µs(τ is
o o,
servedincavityringdownspectroscopy(Schereretal.,1996, the decay time for cavity filled only with dry nitrogen) and
1997). Thefirstmodulatesthedecayasaresultofmultiple 1τ is about 0.02µs for an average of a 400 laser shots
min
Atmos. Chem. Phys.,7,1523–1536,2007 www.atmos-chem-phys.net/7/1523/2007/
σ ×
σ ×
α
σ ×
σ ×
A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy 1527
1.5x10-5 5
n= 1.606 + i0.038
250 nm
n= 1.597 + i 0.005
400 nm
n= 1.598 + i 0.00
-1cm) 1.2x10-5 σ =1.865×10-8 cm2 σex =1.167×10-8 cm2 670500 nnmm (Q)ex 4 PolyStyrene Spheres (PSS)
Extinction coefficient, (αex 369...000xxx111000---666 ex σex = 3.441×10-9 cm2 Extinction efficiency 123
σ = 3.471×10-10 cm2
ex
0.0 0
0 400 800 1200 160 0 1 2 3 4 5 6 7 8 9 10
1 Concentration [p/cc] Size parameter (x )
4
2 Figure 3.
Fig.3. Theextinctioncoefficient(αext)measuredasafunctionof5 FFiigg.u4r.eT 4h.e extinctionefficiency(Qext)asafunctionofsizeparam-
particle number density of ammonium sulphate at different sizes eter (x) of polystyrene spheres (PSS). The solid curves represent
(250, 400, 600 and 750nm). The number density was controlled theMiefit:n=1.606+i0.038wasobtainedbyfitalltheexperimental
usingadilutionapparatus. Theextinctioncrosssection(σext)was datapoints,whilen=1.597+i0.005wasobtainedbyfitonlyasubset
extractedfromalinearfitforeachsizeandisindicatedontopof ofsizesstartingfrom350nm(theexcludedsizesareenclosedbythe
eachline. dottedcircle). Thegreencurve(n=1.598+i0.00)isfromPetterson
etal.(2004).
operatingat10Hz. Thisresultsinaminimumdetectableex-
tinction coefficient of 3.77×10−9cm−1. It should be noted
that this sensitivity is calculated for a cavity filled with a repeatedmeasurementsofthesameparticlesizebutfordif-
homogenous distribution of nitrogen; however, in the case ferentconcentrations)(Pressetal.,1992,1992,Eq.15.5.5).
of measuring particles such as aerosols, the fluctuation of The algorithm does not require an initial guess for the real
aerosol concentration inside the cavity would lead to larger and imaginary parts of the refractive index. Rather it scans
fluctuations in decay time and in turn to lower sensitivity. through all possible physical values of the indices and pro-
A statistical treatment needs to be performed in the case of gressivelyincreasestheresolutionofthesearchuntilitfinds

aerosols. Since such a treatment is not in the scope of this the absolute minimum in the merit function within the de-
article, we refer the reader to the detailed treatment by Pet- siredprecision.
terssonetal.(2004),whofoundthatthecontributionoffluc- For mixtures of two components, the measured extinc-
tuationsinaerosolconcentrationinsidethecavitytothetotal tion efficiency of the mixture is compared with the extinc-
sensitivityisverysmallleadingtosensitivityofthesameor- tion efficiency calculated using the mixing rules outlined in
derastheinstrumentlimit. Sect. 1, namely, (1) molar refraction and absorption; (2)
the volume-weighted linear mixing rule; (3) the Maxwell-
2.3 Retrievalandmixingrulemethods
Garnettrule;and(4)anextendedeffectivemediumapproxi-
mation(EEMA)similartothedynamiceffectivemediumap-
Theretrievalalgorithmforsinglecomponentparticlescom-
proximation (Eq. 15 Sihvola and Sharma, 1999), where the
pares the measured extinction efficiency as a function of
effective refractive indices estimated using the mixing rules
size parameter with the extinction efficiency calculated us-
are input to the Mie scattering subroutine for homogeneous
ing the Mie scattering subroutine for homogeneous spheres
spheres by Bohren and Huffman (1983, Appendix A). The
byBohrenandHuffman(1983,AppendixA),whilesimulta-
measured extinction efficiency for the mixture is also com-
neouslyvaryingtherealandimaginaryrefractiveindicesof
pared with the extinction efficiency calculated using (5) the
theparticles.Itfindsthesetofrefractiveindicesbyminimiz-
coreplusshellmodel,wheretherefractiveindicesofthein-
ingthe“meritfunction”(similartoavariance)χ2/N2,where
dividual components comprising the mixture are input to a
χ2is
layeredsphereMiescatteringsubroutine(BohrenandHuff-
N (Q −Q )2 man, 1983, Appendix B; coded in Matlab by C. Maetzler,
χ2 = extmeasured extcalculated i (11)
ε2 2004).Themeritfunctionformixturesisdefinedinthesame
Xi=1 i fashionasforsinglecomponentparticles,andthemixingrule
N isthenumberofparticlesizes, andε istheestimateder- ormodelwiththesmallestmeritfunctionisdeemedthebest
ror in the measurement (taken as the standard deviation of match.
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1528 A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy
5 scattering subroutine described above for two different size
n = 1.518 + i 0.002 ranges, one using all the sizes we measured, and the other
n = 1.520 + i 0.0
usingasubsetofsizesstartingfrom350nm. Threedifferent
n = 1.530 + i 0.0
)x4 (NH4)2SO4 fitting curves are shown in Fig. 4 in addition to the exper-
e imental data obtained for the ten different PSS sizes. The
Q
cy ( 3 black curve is obtained by a Mie fit for all measured parti-
n clessizes,yieldinganindexofrefractionofn=1.606+i0.038
e
ci withmeritfunction(χ2/N2)valueof0.91. Theredcurveis
fi
ef 2 obtainedforasubsetofsizesstartingfrom350nm(exclud-
on ingthefirstfourpointswithinbythedottedcircle),yielding
cti anindexofrefractionofn=1.597+i0.005withχ2/N2=0.06,
n
xti 1 substantially lower than the χ2/N2 obtained using all sizes.
E
Thegreencurveisobtainedbyusingn=1.598+i0,avaluere-
portedbyPetterssonetal.(2004)fortherefractiveindexof
0
0 1 2 3 4 5 6 7 8 9 10 PSS. Our results are in close agreement with the refractive
Size parameter (x ) index given by Pettersson et al. (2004) for PSS. However,
1 by using a subset in which the small sizes are excluded we
2 FFiigg.u5r.eT 5h.e extinctionefficiency(Qext)asafunctionofsizeparam- clearlyimproveourfittingbyminimizingthemeritfunction.
eter(x)ofammoniumsulphate.ThesolidcurvesrepresentMiefit:. Note that n=1.600+i0.000 (not shown) also provided a low
n=1.518+i0.002 was derived from using all the experimental data merit value (0.10), so that we cannot rule out an imaginary
points, while n=1.520+i0.00 was obtained by fit a subset starting refractive index of zero as a possibility for the PSS spheres
from4350nm.(Theexcludedsizesareenclosedbythedottedcircle.) we measured within the precision of our retrieval scheme.
Thegreencurve(n=1.530+i0.00)isfromPettersonetal.(2004). It is difficult to determine low imaginary refractive indices
with better precision from retrieval schemes in general (see
BohrenandClothiaux,2006,pp.163–165).
3 Resultsanddiscussion
Theextinctionefficiencyofammoniumsulphateasafunc-
tionofsizeparameterforparticlessizesbetween250nmand
3.1 Extinctioncrosssectionmeasurements
850nmisshowninFig.5.SimilartoPSS,wefirstfitthedata
forallsizesandthenforonlyasubsetofsizesstartingfrom
In addition to the extinction coefficient, the particle extinc-
350nm. For all the sizes, we obtain n=1.518+i0.002 and
tioncrosssection(σ )canbedeterminedbymeasuringα
ext ext
χ2/N2=2.49 (black curve). For the subset of sizes, we ob-
fordifferentparticleconcentrations(N),andusingtherela-
tionshipα =σ ×N. Theextinctioncoefficientasafunc- tainn=1.52+0iandχ2/N2=0.14(greencurve).Theredcurve
ext ext
is obtained with a refractive index of n=1.53+i0.0, which is
tionoftheparticleconcentrationofammoniumsulphatefor
reported to be the index of refraction of the AS (Pettersson
four different sizes (250nm, 400nm, 600nm, and 750nm),
et al., 2004). The refractive index of salt aerosols (such as
and the corresponding σ determined for each size are
ext
AS)stronglydependsontherelativehumidityandthecrys-
shown in Fig. 3. It is seen that the extinction increases lin-
talstructure. Inourexperiments,therelativehumidityisbe-
earlywithparticleconcentration,asexpected.
low3%(dryaerosols). Therefore,theindexofrefractionob-
3.2 Polystyrene spheres and ammonium sulphate tained from our measurement should be compared to other
(NH ) SO studies in which the index of refraction was determined in
4 2 4
dryconditions. TheindexofrefractionofdryAScrystalsre-
To test the performance of the new CRD system, we mea- portedforthreecoordinateaxes(orthorhombiccrystalstruc-
sured the optical properties of polystyrene spheres (PSS) ture) are n =1.520, n =1.523, and n =1.533, respectively
α β γ
andammoniumsulphate(AS),bothwithwell-knownindices (Lide, 1997). Our retrieved index of n=1.52+i0.0 is consis-
of refraction (Lack et al., 2006; Pettersson et al., 2004). tent with that for the third axis, but slightly lower than the
We measured the extinction efficiency of 10 different sizes othertwoaxes.
ofcommerciallyavailablePSS(Dukescientificcorporation, For both ammonium sulphate and PSS, excluding the
USA). The extinction efficiency (Q ) of these particles as smallestparticlesslightlyimprovesthefit. Apossiblereason
ext
afunctionofthesizeparameter(bluesquares)isdepictedin for this behavior could be the presence of larger multiply-
Fig. 4. The standard deviation of the extinction efficiency chargedparticlesthatwouldhavethesamemobilityassingly
(1Q )iscalculatedbymeasuringtheextinctionefficiency chargedparticles. IntheCRDspectrometer,thesemultiply-
ext
ofthesamesizeatdifferentconcentrations. Theconcentra- charged particles contribute strongly to the decay time and
tionoftheparticlesrangesfrom150to2500particlescm−3. result in higher extinction efficiency. The multiple charge
To retrieve the index of refraction and to get best fit of Mie effect could be reduced by using very dilute solution in the
theorywiththeexperimentaldataforQ ,weusedtheMie atomizer that shifts the mean diameter in the distribution to
ext
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A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy 1529
4
smallersizeswhichreducesthenumberofmultiplycharged
4.5
largeparticles.
4.0
3.3 Sodium chloride (NaCl), glutaric acid and their mix-
3.5
tures
)e
Q
y (3.0
Aerosols in atmosphere are more complex than laboratory- nc
generated pure aerosols. Typically they are composed of cie2.5
mixturesoforganicandinorganicmoleculesthatcanbear- on effi2.0
ranged in different ways, such as homogeneous mixtures ncti Glutaric acid
or as coated particles. Urban and pollution aerosols con- xti1.5 Mie: n = 1.410 + i 0.000
E Sodium Chloride (NaCl)
tainbothorganicandinorganiccomponents(Murphyetal.,
1.0 Mie: n = 1.546 +i0.003
2006),whiledustorseasaltparticlesareoftencoatedbycon- NaCl : glutaric acid 1:1
densedorganicandinorganic(Falkovichetal.,2004; Maria 0.5 Mie: n = 1.483 + i0.010
NaCl : glutaric acid 2:1
et al., 2004; Posfai et al., 1998; Russell et al., 2002; Terva-
Mie: n = 1.507 + i0.017
hattu et al., 2002). Therefore, exploring the optical proper- 0.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
tiesofmixedparticlesisimportantforexploringtheoptical Size parameter (x)
5
propertiesofatmosphericaerosols. Todoso,westudiedthe
optical properties of mixed NaCl and GA particles, which6 FFiigg.u6r.eE 6x.t inctionefficiency(Qext)asafunctionofsizeparameter
arecommoncomponentsofseasaltparticles. Firstwemea- (x)obtainedforsodiumchloride,glutaricacid,andthemixturesof
sured the optical properties of pure NaCl solution and GA NaClandglutaricacidwithmolarratios1:1and2:1respectively.
aerosols. Then we measured the optical properties of mix- The solid curves are the result of the Mie fit to the experimental
turesofthesetwocomponentspreparedwithaknownmolar points.
ratio(1:1,2:1). Weassumethattheaerosolsgeneratedfrom
these solutions are homogenous and that the molar ratio of
However,oftenitisimpossibletoverifythevalidityofthese
thesolutionismaintainedintheaerosol,becausebothcom-
calculations. Usingoursystem,itispossibletogeneratepar-
poundsdissolveverywellinwater. Thisassumptionislater
ticles of known compositions and structures and to retrieve
verifiedbycalculationsoftherefractiveindex.
theirrefractiveindex,whichcanbecomparedtocalculations
The extinction efficiency as a function of size parameter
by different mixing rules. We employ a variety of mixing
forparticlesofNaCl,GA,andparticlesgeneratedfrommix-
rulestocalculatethecomplexindexofrefractionformixed
tures with molar ratios of NaCl and GA of 1:1 and 2:1, re-
aerosolandcomparethecalculatedindexwiththeindexre-
spectively, are shown in Fig. 6. The standard deviation of
trievedfromourmeasurements.
the measurements is also shown. The solid lines represent
We start with two non-absorbing components, NaCl and
Mie fitting curves obtained using the same refractive index
GA. The refractive indices retrieved for pure NaCl and GA
retrievalalgorithmdescribedinSect.2.3.
aerosols are used as input for calculating the refractive in-
Asummaryoftheretrievalresultsforthemixedparticles
dicesofthemixturesbythedifferentmixingrulesandmod-
are given in Table 1. In these experiments, we used very
dilute solutions (20–50mg L−1) for the small particle sizes els. Inallcases,NaClistreatedasthematrixandGAasthe
inclusion. Two delicate points are noted regarding the im-
(100–300nm). Thisclearly improvesthefitforallsizes, as
plementation of the mixing rules. First, mixing rules (2–4)
is evident from the small differences in the merit functions
requirethevolumefractionoftheinclusion.Whenwecalcu-
(χ2/N2) between the retrievals for all the sizes and for the
latethisvolumefractioninamannersimilartothatdonein
subsetsizesstartingfrom350nm. Forexample,theretrieval
climatemodels(usingthemassfractionanddensityofeach
forpureGAaerosolsusingallsizesyieldsn=1.41+i0.0,with
substance), the volume fraction comes out too high. So in-
χ2/N2=0.10,whiletheretrievalforpureGAusingthesubset
stead,wecalculatethevolumefractionusingthevolumesof
ofsizesyieldsn=1.41+i0.0,withχ2/N2=0.13.
the solutions of NaCl and GA used to create each mixture.
Second, rule (1) (molar refraction/absorption) requires the
3.4 Calculationsusingmixingrules
totalmolarvolumeofthemixture,definedasthetotalmolec-
ular weight divided by the total density, the latter of which
As stated in Sect. 1, optical properties of aerosols in the at-
is both difficult to measure and difficult to estimate if not
mosphereareoftencalculatedusingvariousmixingrulesand
dealingwithtabulatedsolutionsofelectrolytesinwater(e.g.,
models. Theunderlyingassumptionforthesemixingrulesis
Tang,1997).Consequently,wemakeasimilarassumptionto
that it is possible to calculate the complex refractive index
Jacobson(2002)insuchcircumstancesandcalculatethetotal
of complex particles through the knowledge of the proper-
ties (density, molecular weight, refractive index) of the in- molarvolumeas: Vtot=χNaCl(cid:16)MρNNaaCCll(cid:17)+χGA(cid:16)MρGGAA(cid:17),where
dividualconstituents, andthewayinwhichtheyaremixed. χ is the molar ratio (not to be confused with the similar
i
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1530 A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy
Table1. RefractiveindexretrievalsusingMietheoryforsodiumchloride,glutaricacid,andmixturesofthetwowithmolarratios1:1and
2:1,respectively.Theretrievalwasperformedinonecaseusingalltheexperimentalsizesandintheothercaseusingasubsetofsizesstarting
from350nm.Thebestfitwasdeterminedbyobtainingthesmallestmeritfunction(χ2/N2).
Retrievalusingallsizes Retrievalusingsubsetofsizes(from350nm)
Sample Refractiveindex χ2/N2 Refractiveindex χ2/N2
NaCl 1.546+i0.003 0.04 1.544+i0.000 0.09
Glutaricacid 1.410+i0.000 0.10 1.410+i0.000 0.13
1:1NaCl:Glutaricacid 1.483+i0.010 0.06 1.480+i0.004 0.08
2:1NaCl:Glutaricacid 1.507+i0.017 0.01 1.507+i0.019 0.02

molarvolumeisnotaccurateenoughforthesemixtures. The
5
n = 1.477 + i0.00 core plus shell model also produces a higher merit function
n = 1.483 + i0.01
thanmixingrules(2–4), asmightbeexpectedfromthefact
Q)e 4 thattheNaClandGAarehomogeneouslymixedinsolution,
y ( notlayered.
c
en 3 Therefractiveindicesobtainedbyusingmixingrules(2–
ci
effi 4) are very close to those retrieved from the experimen-
n 2 tal data for both mixtures. For example, the linear mixing
o
cti rule for all the sizes of the 1:1 mixture produce a refrac-
n
Exti 1 tive index of n=1.477+i0.0, while retrieved refractive index
isn=1.483+i0.01. Acomparisonbetweentheextinctioneffi-
ciencyasafunctionofthesizeparameterofthesetworefrac-
0
tiveindicesandtheresidualbetweenthecurvesareshownin
0 1 2 3 4 5 6 7 8 9 10
Size parameter (x) Fig. 7. The curves are very close; differences in the curves
appear at larger size parameters than were measured. We
0.2
couldprobablyimprovethefitbymeasuringlargersizes,but
Residual -000...011 tahtmesoiszpehsewree.chosearemorerelevanttoactualparticlesinthe
-0.2
1
3.5 Rhodamine 590, ammonium sulphate, and their mix-
Fig. 7. Comparison between the refractive index obtained using
tures
linear mixing rule for the 1:1 mixture of NaCl and glutaric acid
(n=1.477+i0.0) and the refractive index retrieved from measure-
We used Rhodamine 590 (Rh-590) which has peak absorp-
mentsofthesamemixtureusingMietheory(n=1.483+i0.01). The
curvesareverysimilarforsmallsizeparameters,whiledifferences tioninthevisiblearound530nmasamodelforstronglyab-
areobservedforhighersizeparameters.Notethedifferentscalefor sorbingaerosols. Inaddition,wemeasuretheopticalproper-
theresiduals. tiesofaerosolscomposedofmixturesofRhodamine590and
ammoniumsulphateinfourdifferentmolarratios1:10,1:50,
1:100, and 1:500. Generating these aerosol mixtures is not
variable in the merit function), M is the molecular weight, as easy as the mixtures of NaCl and GA, since Rh-590 has
i
andρ isthedensity(astabulatedforthesubstance’snatural averylowsolubilityinwater(0.1–1%),whichcouldpoten-
i
state). tiallyaffectthehomogeneityoftheaerosolsduringtheatom-
Results of these calculations for 1:1 and 2:1 mixtures of izing process. To minimize this effect, we dissolve the Rh-
NaClandGAaregiveninTables2and3. Thecalculations 590ina10%methanol/watersolution. Becausemethanolis
are done for all the sizes and for the subset starting from a fairly optically neutral substance (with real index close to
350nmasindicatedinthetables.Mixingrules(2–4)resultin thatofwater–betweenthatofammoniumsulphateandRh-
goodagreementwiththemeasurements. Thesmallestmerit 590 – and zero imaginary index), the possibility of a slight
functionvalue(0.14)isobtainedwiththelinearmixingrule, amount of methanol remaining in the aerosol is not likely
althoughtheMaxwell-GarnettandEEMAalsoprovidesmall to have altered the total extinction coefficient of the mixed
meritfunctionvaluesandmayalsobeappropriateforusein aerosolsbyameasurableamount.

models. Themolarrefraction/absorptionruledoesnotdoas Toretrievethecomplexrefractiveindex,weusedthesub-
well, perhaps because our method for calculating the total routinedescribedinSect.2.3forallthemeasuredsizesand
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A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy 1531
Table2.TheindexofrefractionofthemixtureofNaClandglutaricacidwithmolarratio1:1obtainedbyusingdifferentmixingrules.
NaCl:Glutaricacid1:1(retrievedrefractiveindex1.483+i0.010andχ2/N2=0.06)
Allexperimentalsizes Subsetfrom350nm
Mixingrule EffectiveRefractiveindex χ2/N2 EffectiveRefractiveindex χ2/N2
Molarrefraction/absorption 1.439+i0.000 2.65 1.439+i0.000 4.88
Linear 1.477+i0.000 0.14 1.477+i0.000 0.14
Maxwell-Garnett 1.477+i0.000 0.15 1.477+i0.000 0.15
EEMA,dincl §=0.01µm 1.475+i0.000 0.18 1.475+i0.000 0.21
EEMA,dincl=0.02µm 1.477+i0.000 0.18 1.475+i0.000 0.21
EEMA,dincl=0.1µm 1.476+i0.001 0.15 1.476+i0.001 0.16
§EEMA=extendedeffectivemediumapproximation;dinclisthediameteroftheinclusionsassumedintheEEMA.
*Therearenoeffectiverefractiveindicesinthecoreplusshellmodel.Separaterefractiveindicesofthecoreandshellmaterialareused.
Table3.TheindexofrefractionofthemixtureofNaClandglutaricacidwithmolarratio2:1obtainedbyusingdifferentmixingrules.
NaCl:Glutaricacid2:1(retrievedrefractiveindex1.507+i0.017andχ2/N2=0.01)
Allexperimentalsizes Subsetfrom350nm
Mixingrule EffectiveRefractiveindex χ2/N2 EffectiveRefractiveindex χ2/N2
Molarrefraction/absorption 1.457+i0.000 2.80 1.457+i0.000 6.94
Linear 1.499+i0.000 0.14 1.499+i0.000 0.23
Maxwell-Garnett 1.499+i0.000 0.15 1.499+i0.000 0.25
EEMA,dincl=0.01µm 1.498+i0.000 0.17 1.498+i0.000 0.29
EEMA,dincl=0.02µm 1.498+i0.000 0.17 1.498+i0.000 0.29
EEMA,dincl=0.1µm 1.499+i0.000 0.14 1.499+i0.000 0.24
for a subset of sizes staring from 350nm. The extinction set of sizes from 350nm (solid curves) is shown in Fig. 8b.
efficiency as a function of the size parameter for Rh-590, Thefitinthesmallsizesregion(100–350nm)isasgoodas
(NH ) SO , and the different mixtures of the two are pre- the fit in Fig. 8a, but in the region of larger sizes it is bet-
4 2 4
sented in Fig. 8a. The solid lines represent the refractive ter. TheretrievalshowninFig.8bleadstoadrasticchange
index retrieval using Mie theory with all of the measured inthecomplexrefractiveindexforthe1:10mixtureratio,in
sizes.Theinsetdetailsthedifferentaerosolcompositionsand whichweobtainedn=1.203+i0.728intheretrievalusingall
the resulting complex refractive indices retrieved for each thesizesandn=1.405+i0.486intheretrievalusingthesubset
aerosol sample. As expected, as the fraction of absorbing ofsizes. Likewise,themeritfunctionfor1:10mixtureusing
material in the mixture decreases, the imaginary part of the thesubsetofsizesismuchlower(χ2/N2=0.07)thanthatus-
refractive index decreases, and the real part of the complex ingallsizes(χ2/N2=0.3)(Table4). Fortheothermixtures,
refractiveindexincreases. thedifferencesbetweenthetworetrievalsarenotasdrastic,
Note that the retrieved refractive index for pure Rh-590 as can be seen in the inset patterns in Figs. 8a and b and in
(n=1.00+i1.026)hasaverylowrealpart(closetothatofair) Table4,althoughthemeritfunctionusingthesubsetofsizes
and a high imaginary part. This can be expected from the is again generally lower than using all sizes. This could be
fact that the wavelength of measurement is extremely close explained by the presence of large, multiply charged parti-
tothewavelengthofpeakabsorptionofRh-590(530nm),so cles.
that we are essentially measuring at a frequency just below
the resonance frequency. From the model of a dispersing 3.6 Calculationsusingmixingrules
mediumattributedtoH.A.Lorentz(BornandWolf, 1999),
weexpectacorrespondingpeakintheimaginarypartofthe As in Sect. 3.4, we next employ a variety of mixing rules
indexandavaluealittlehigherthan1.0intherealpartofthe to calculate the complex index of refraction for the mixed
index. (ComparewiththesolidcurveinFig.3ofBulatovet aerosols and compare it with the index retrieved from our
al.,2006). measurements in Sect. 3.3. The refractive indices retrieved
Theextinctionefficiencyofthesameaerosols,butwiththe for pure ammonium sulphate (n=1.52+i0.00) and pure Rh-
refractive index retrieval algorithm applied only to the sub- 590 (n=1.00+i1.026) are used as input for calculating the
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1532 A.AboRiziqetal.: OpticalpropertiesofabsorbingaerosolsbyCRDspectroscopy
Table4. TherefractiveindicesofRhodamine-590(Rh-590)andmixturesofRh-590andammoniumsulphatewithmolarratios1:10,1:50,
1:100,and1:500,respectivelyobtainedusingtheretrievalalgorithmdescribedinSect.2.3tofitMietheorywiththeexperimentaldata.The
fitswereperformedfortwodifferentsizeranges. Thefirstisforalltheexperimentalsizesandthesecondusingasubsetsizesstartingfrom
350nm.Thebestfitwasdeterminedbyobtainingthesmallestmeritfunction(χ2/N2).
Retrievalusingallsizes Retrievalusingsubsetofsizes(from350nm)
Sample Refractiveindex χ2/N2 Refractiveindex χ2/N2
Rh-590 1.1+i1.16 0.53 1.0+i1.03 0.06
1:10Rh-590:(NH4)2SO4 1.203+i0.728 0.30 1.405+i0.486 0.07
1:50Rh-590:(NH4)2SO4 1.491+i0.462 0.02 1.503+i0.420 0.02
1:100Rh-590:(NH4)2SO4 1.514+i0.291 0.10 1.517+i0.236 0.02
1:500Rh-590:(NH4)2SO4 1.537+i0.132 0.18 1.526+i0.103 0.14
4 4
nction efficiency (Q)e 23 nnR(N h==H- 1154..9)1520 2S+ O+ i 14i0.1.06 nction efficiency (Q)e 23 nRn(N h==H- 1154..9)0520 2S+ O+ i 14i0.0.03
Exti n10 =: 1 1 (.N20H34 +)2 iS0O.742 8: Rh-590 Exti 1n0 =: 11 .(4N0H5 4+) 2i0S.O4846 : Rh-590
1 50:1 (NH4)2SO4 : Rh-590 1 50:1 (NH4)2SO4 : Rh-590
n = 1.491+ i0.462 n = 1.503 + i0.42
100:1 (NH4)2SO4 : Rh-590 100:1 (NH4)2SO4 : Rh-590
n = 1.514 + i0.291 n = 1.517 + i0.236
500:1 (NH4)2SO4 : Rh-590 500:1 (NH4)2SO4 : Rh-590
n = 1.537 + i0.132 n = 1.526 + 0.103
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
4 Size parameter (x ) 1 Size parameter (x )
5 Figure 8a 2 Figure 8b.
Fig.8a. Extinctionefficiency(Qext)asafunctionofsizeparame- Fig.8b. Extinctionefficiency(Qext)asafunctionofthesizepa-
ter(x)obtainedforammoniumsulphate,Rhodamine590(Rh-590), rameter(x)obtainedforammoniumsulphate,Rhodamine590(Rh-
and mixtures of the two with molar ratios 10:1, 50:1, 100:1, and 590),andmixturesofthetwowithmolarratios10:1,50:1,100:1,
500:1, respectively. The standard deviation of the extinction effi- and500:1,respectively.Thestandarddeviationoftheextinctionef-
ciencyforalloftheexperimentaldataisalsopresented. Thesolid ficiencyforalloftheexperimentaldataisalsopresented.Thesolid
linesrepresenttheMietheoryfitforthecorrespondingaerosolsam- linesrepresenttheMietheoryfitforthecorrespondingaerosolsam-
plesusingallexperimentalsizes. ple. ThesolidlinesrepresenttheMietheoryfitforthecorrespond-
ing aerosol samples using a subset of experimental sizes starting
from350nm.
refractive indices of the mixtures by the different mixing
rulesandmodels.Inallcases,ASistreatedasthematrixand
Rh-590astheinclusion. AsinthecaseoftheNaCl/GAmix- thetable. Calculationsperformedonthesubsetofsizesgive
tures,thevolumefractionoftheinclusioniscalculatedusing aconsiderablysmallmeritfunctioncomparingtothecalcu-
thevolumesofthesolutionsofASandRh-590usedtocreate lations performed on all sizes, up to an order of magnitude
the mixture. Unlike the case of the NaCl/GA mixtures, we smaller. Inaddition,althoughtheASandRh590arehomo-
havelessinformationregardingthepropermolecularweight geneouslymixedinsolutioninafashionsimilartothemix-
anddensityofRh-590(insolidorliquidphase),sowedonot turesofNaClandGA,themixingruleprovidingthesmall-
includethemolarrefraction/absorptionmixingrulehere. estmeritfunctionistheextendedeffectivemediumapprox-
Resultsofthecalculationsusingdifferentmixingrulesfor imation assuming inclusions of radius d =0.01µm. This
incl
the 1:10, 1:50, and 1:100 mixture sample are given in Ta- indicates that accounting for absorption in a mixture is bet-
bles5,6,and7. Thecalculationsareperformedforallsizes ter achieved with a higher order mixing rule (higher order
andforasubsetofsizesstartingfrom350nmasindicatedin in inclusion size) than with a lower or zeroith order mixing
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