TI17,0 FitIF CRYJCHEMICALRESEARCH.DEVELOPMENT ,.ENGINEERINGCENTER

M INFRARED SPECTROMETRY OF AEROSOLS0cv,

N

Hugh R. Cadon, U.S. Army Fellow

RESEARCH DIRECTORATE

August 1989

SIl~

', LECC'E-OCT 111989

E'U.S. ARMY

ARMAMENSTlSCNHEICAL COMMAND

Aberdeen Proving Ground, Maryland 21010-U23

89 10 1023 6

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Infrared Spectrometry of Aerosols

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16. SUPPLEMENTARY NOTATION

17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)FIELD GROUP SUB-GROUP •_nAerosol spectrometry ; SF6 -,Spheres-

17 05 01 Optical scattering; CCI 2 f2 Approximations-1 05, 06 1 Methodology J - Water clusters. - Mie Theory:, I

9. ABSTRACT (Continue on reverse if necessary and identify by block number)Aerosol spectrometry denotes a methodology for describing spectral effects of atmosphericconstituents in quantitative, standardized, basic terms. This methodology is based on thepremise that most atmospheric constituents can be described (albeit in some cases veryunconventionally) as specialized kinds of aerosols, some of which exhibit complex changesin spectral behavior between physical phases. Aerosol spectrometry permits an intuitiveunderstanding of the spectral properties of atmospheric constituents and, very importantly,allows insights not found in traditional or purely mathematical treatments. This reportdiscusses liquid and solid particulate aerosols, special cases including Christianseneffects and isosbestics, and the phase-transitional behavior of liquid droplets in vapor.A study of this behavior led to the finding that anomalous (continuum) infrared absorptionin water vapor could be attributed to liquid-like Intermolecular hydrogen bonds in molec-ular complexes (clusters) lony before this observation was made using traditional vapor(continued on reverse) - . . ,

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19. Abstract (continued)

,-spectrometric techniques. In two appendices, IR spectra are given with absorptioncoefficients for gases SF6 and CC1 2 F2 , and extinction by nonabsorbing spheres isconsidered.

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The work described in this report was authorized under Project No.IL1611O1A91A, Independent Laboratory In-House Research (ILIR) and was performedbetween Jouuary 1979 and December 1982.

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CONTENTS

Page

1. INTRODUCTION ..................................................... 7

1.1 Background .................................................. 71.2 Definitions ................................................. 8

2. GENERAL THEORY ................................................... 9

3. PARTICULATE AEROSOLS ............................................. 11

4. VAPORS ........................................................... 13

5. SPECIAL-CASE AEROSOLS ............................................ 15

5.1 The Christiansen Effect ........ ................... ......... 155.2 Isosbestics ................. ................ ................. 16

6. PHASE-TRANSITIONAL AEROSOLS ...................................... 16

6.1 Nonpolar Substances .................... ................. ... 166.2 Polar Substances ........................................... 17

7. WORKSHEET ....................................................... 22

8. CONCL'TIONS ..................................................... 24

LITERATURE CITED ................................................ 25

APPENDIXES

A. MASS EXTINCTION COEFFICIENTS ESTIMATED FUR NONABSORBINGSPHERICAL AEROSOL PARTICLES IN THE GEL , IRIC SCATTERINGREGIME ...... ............... ............................. 29

B. INFRARED ABSORPTION COEFFICIENTS (3-. um) FOR SULFURHEXAFLUORIDE (SF 6 ) AND FREON (CCI 2FV .................. 33

= . I Ii i N

LIST OF FIGURES AND TABLES

FIGURES

I. Extinction Coefficient vs. Particle Diameter for PhosphorusSmoke (Dashed Curve) at x = 10 pm ................................ 14

2. Extinction Coefficient vs. Particle Diameter for Water at= 10 Pm ........................................................ 18

3. Equilibrium Curves for Atmospheric Aerosols of Many Types atStandard Conditions .............................................. 20

4. Worksheet for Aerosol Spectrometry ............................... 23

Table

Classes of Optical Scattering by Aerosols ........................ 10

6

INFRARED SPECTROMETRY OF AEROSOLS

1. INTRODUCTION

1.1 Background.

Traditionally, infrared (IR) spectrometrists have been concerned withobtaining spectra of homogeneous, single-phase samples. Spectra of gases andliquids are run in gas and liquid cells of known lengths with corrections madefor cell window effects, and solids are run, whenever possible, as films orslices of known thickness. Irregular, solid samples are troublesome becausethey must be immersed in media-like mineral oils (mulls) or compressed salts(pellets), and complex interactions occur between the sample particles andthe media, making it very difficult to obtain quantitative spectra. Everyeffort is made to handle samples in such a way that their absorption spectraare not confused by optical scattering effects and vice versa. It is notsurprising, therefore, that the spectrometry of aerosols has always seemedforeboding, that is, something to be avoided. But with the growth in impor-tance of atmospheric optics, especially in the IR, the subject must beaddressed. Traditional spectrometrists, on one hand, deal with atmosphericaerosols in conventional terms (e.g., by considering precipitable vapors ordroplets in an atmosphtric optiCdl path and conceptualizing them as comparableliquid films). On the other hand, applications engineers have developedempirical aerosol wodels that fit certain situations adequately but are notgeneral and have little or no theoretical basis.

The rapid development and general availability of computers in thepast decade have made it possible to use the Mie theory extensively,I permit-ting calculations of aerosol spectral properties that can be verified experi-mentally. The theory works well for spherical or near-spherical particles,and its use for other particle shapes 2 is being investigated. If traditionalspectrometry avoids dealing with aerosols whenever possible, the availabilityof powerful computer models has exactly the opposite '-fect. In recent years,a plethora of theoretical papers has appeared, preser tinj calculations foratmospheric aerosols parametrized in many different .,,ays. Applicationsengineers are left with three apparent courses of at ýun: (1) to learn andadapt traditional spectrometric techniques; (2) tc ,,velop special-case,empirical models because aerosol spectra are easy tý" nbtain but difficult toexplain; and (3) to learrn the Mie theory and it- :i,. clinm fur many specialcases. Understandably, many atmospheric opticist. and systems engineersaccept the secund course of action. This is unfortunate because many classesof derosol optical behavior are beautifully simple. A methodology is what hasbeen missinq between traditional scýectrometry and theoretical models thatpla(Wf~s ill Of>,eI:ts ( f a:rosol spectroretry into a wiairin!i ful arnl intuitivelysa ti ,fyirnj rdimework. This report :)resen ts such a ;;(,th.)do ogyy, which has beernused successfully at this Center for many v.-ars.

As used in this report, aerosol ,,wctrometry denotes a methodologyfor describing spectral effects of atmosi;n'ric cons ituents in quantitative,standarlized, basic terms. An implicit premise in Vbis methodology is thatall atmospheric constituents can be described (alH it iii some cases veryunconventionally) as specialized kinds of aeros(,W o.iome of which exhibit

7

complex changes in spectral behavior between physical phases, especiallybetween the vapor and liquid phases. Aerosol spectrometry gives a clear intu-itive understanding of the classes of spectra for all kinds of atmosphericconstituents and, very importantly, allows insights that would otherwise beimpossible by traditional or purely mathematical treatments. Conversely, manyclasses or cases described for aerosols in this report are immediately recog-nizable as special ones that can be studied by using existing computationalmodels based on the Mie theory. 3 , 4

1.2 Definitions.

Terms used in this report are defined as follows:

a = optical extinction coefficient atwavelength X, m2 /g, or, ifsubscripted by the scatteringcomponent (S) or the absorptioncomponent (A) of the extinctioncoefficient, where a = aA + aS.

C = mass concentration of •articles per unitvolume of aerosol, g/mJ.

D0 = aerosol particle diameter or geometricmean diameter of a distribution, :rn.

f(mx) = correction factor, which depends only onmX.

k,kA, = imaginary part of the complex index ofk kV ,A L' refraction (n - ik)X, unitless, at

k L wavelength x if subscripted; also, for thek vapor, liquid, or solid phase if

s Lirbscripted v, L, or s, respectively; c~reshould be taken not to confuse k), with LL

kL,k L = absorption coefficient of mdat(rialcomprising the aerosol particles, 1,i-1,at wavelength A if subscripted; careshould be taken not to confuse K wit

L = optical path length, m.

A = wavelength, ým.

M = molecular weight, g/g-mole.

8

mN = complex index of refraction, (n ,

uni tl ess.

n,nX, = real part of the complex index of

nX , nX refraction (n - ik)X, unitless, 3tL wavelength X if subscripted; also, for the

ný, vapor, liquid, or solid phase ifS subscripted v, L, or s, respectively.

nq = mass fraction of water vapor clustered

at temperature Ok.

p = actual vapor pressure, mm Hg.

I()= saturaticn vapor pressure, mw H1g.

Q,(Q)x =optical cross-section efficiency factor, atYvelength \ f subscripted, unitless.

r. :aerosol particle (droplet) radius, urn.

- density of the material car:iprising theaerosol particles, g/cm3 .

s saturation ratio or fractional relativehumidity, p/po, unitless.

t - thiicknecs of an equivjlent reu(ipitatedfilm or layer, nm.

T,TX = optical transmittance, at w.,velength Xif subscripted, unitless.

d absolute temperature, K.

2. G[UERAL THEORY

In the visihle region (0.4-0.7 . ,r,'s'n s ext inquishradiation by optical s, ttering and, excri-;" i ar ý-na.-eoue s or pig-fnented materials, particle absorption usiallI i a ot a 1iijnificant contrib-utor to the optical extinction coefficient t. In th S i 11 . iireter,millimeter, and centimeter radar regions, atmospheri,, atrosols extinguishradi0 ie i n Imr,';m t entirely by particle ýhsr,rp* ion. n. , 'iItr r inq, ev,"by re I , , 'I iI t g:j pr it i, 1 t- es -c' th .S Wis ot. f \ _ , i ý ,1 , n" ~' , I-giole at these wavelenoiths. But in the 1P in p l iri the atmosphericwindow region ,ct 7-1 A .m, optical scatt,-i n ' ind i o," io absorptiojn can hotlKcon~rihate heavi y to the overall f•xtiflt i ar; ooser~eo for co!mnon

atmospheric aerosols, water fogs, and dists. f, :n w ye1 ength , the

optical extinction coefficient of an aerosol is the sum of the scattering andabsorption components of the aerosol particles:

(S + IAA (1)

Thus, for most atmospheric aerosols in the visible, aA 0 and

I IS whereas in the radar region, IS - 0 and a, aA But in the IR,

'- aS - a /2. These conditions correspond, respectively, to those of

geometric, Rayleigh-like, and Mie scattering. The classes and conditions aresummarized in the Table, ý,",ere the typical conditions for Mie scattering aregreatly simplified for conve,,ience. Actually, as discussed here and in thereferences, Mie scattering is quite complex.

Table. Classes of Optical Scattering by Aerosols

Class Popular Name Typical Conditions Example

D<< X Rayleigh scattering IS - 0 Water cloiid in theu radar region.S A•

0u Mie scattering oS ý IA Water, fog or dustu cloud in the IR.

•A • S ...

S>'> }Geometric_ .-ca+tering aA o Water cloud ir the

For derosol spectrometry, the Beer-L,;:i is 1 '1er as

ln (i/T ) = C. (2)

where the quantitative vwlue of the optical extt ,, c; i iont 'st ceknown or determined. Often, atmispheric, aero;,-) eo lri u, .ta 11 titer i-ture are reported in uni-,s of reciprocal path Ien. • . d, etc.. eThis has the effect of co 'Oining -x and C in n V , . . ' , iIts

10

the value of the data because the kinds, mixing ratios, and size distributionsof the aerosol species present when the data were taken must be assumedconstant if these data are to b2 used for subsequent predictive purposes. Inaerosol spectrometry, the importance of knowing the optical (mass) extinctioncoefficients of the aerosol constituents is recognized. These data may beuniversally applied if airborne mass concentrations and approximate particlesize distributions can be determined in any real situation. In this way, thefirst important characteristic of the methodology is realized: aerosol spec-trometry is quantitative.

The second and third characteristics of the aerosol spectrometrymethodology are that all atmospheric constituents are described in standard-ized physical units and that a standard set of terms is used for all consti-tuents, even though, in some cases, these units are highly unconventional.(This is especially true for gases.)

In an earlier paper, 5 the authors show that the equivalent thickness(microns) of a homogeneous precipitated film for a gas or aerosol in anoptical path can be expressed as follows:

t = (CL)/p

where the terms are defined in Section 1.2. For a vapor that beh ves likean ideal gas, the mass concentration can be expressed as follows:9

C = (16 Mp)/Ak (ideal gas). (4)

by combining equations 3 and 4, one can readily see that:

t = (16 MpL)/pek (ideal gas). (5)

For example, for saturated water vapor (M = 18) at 20 0C (p = 17.55),each kilometer (L = 1000) of the optical path contains the equivalent of alayer of precipitable water, t = (16)(18)(17.55)(1Or?}/(I.O)(293) = 17,251 Wmthick, or 1.73 precipitable centimeters of water in the traditional use ofthe term if water vapor behaves as an ideal gas.

3. PARTICULATE AEROSOLS

In this section, aerosols of liquid anc solid particles are consid-ered. While the development iý based upon spherical or near-spherical parti-cles, the validity of the Mic theory for particles of other shapes is stillbeing debated.2 In practice, the techniques presented here work very well formany r o ,iiýjn aitriospheri c aerosols.

Many soil-derived dusts 7 and smokes (e.g., sulfuric acid, phosphoric

acid, and thermally generated oil smokes) 5 have particle sizes in the atmo-sphere that are small compared to IR wavelengths (i.e., D. << X). Hlostparticulate aerosols exhibit this behavior at still longer (radar) wavelengths.These are Rayleigh-like conditions (Table) such tLct:

' A ((D )

11

When optical bcattering is negligible, a small particle limit isapproached so that: 8

a X . LX. f(mx) (DL << ) (7)

where

f(mA) = (n2 + k2 )2 +4(n 2 k2 ) (8)+4n- k2) +

and it becomes possible to simulate closely (e.g., a liquid droplet cloud bya liquid film). The film can be treated as a sample absorber in an IR spec-trometer, and its thickness (micrometer) is given directly by equation 3.For most common aerosol materials, f(m,) in equation 8 can be taken as1.0 to a reasonable approximation. For example, for aerosol particulateswhose optical constants extend over ranges as broad as 0 < k < 2 and 0.5 <

n,< 1.5, the range of f(m,) is only -0.5 < f(mj) < 2.^.7 T~Us, afurther approximation is possible for most Terosol materials:

S= kL X/p = 47kx/ -• p (Di << A, for many common aerosols) (9)

and cL may be approximated for equation 2 if only k, and n are known.Reference 8 gives a detailed discussion of these approximations. Also notethat aX is a function of 1/X. Thus, the decrease in a with increasing wave-length for all aerosols is expected and does not necessarily indicate thatcommon aerosols become poorer absorbers at longer wavelengths.

For (spherical) aerosol particles in the Mie or geometric scat-

tering regions (Table), the extinction coefficient is given by:

a = 3(Q)X/2DIJO (10)

where (Q)X is an optic,,l cross-section efficiency factor or multiplier thattypically assumes value:, of 0 < (Q)X < 4 in the Mie region (D. ) and'Q)x A 2 in the geometric region (D0 >> A).

It is very us-2td to plot the extinction coefficient of a givenaerosol material at a given wavelength as a function )f i wide ranc.e (fparticle diameters extending down to the molecular diameters of c(om1onsubstances. Figure I shows an example of data measured for a Ch1 ohorussmoke aerosol at A = 10 Om. Alternatively, the Mie size pardmcter, -D

could be used as the abscissa for similar plots. The dashed curve inFigure 1 extends from the Rayleigh (horizontal se(:tion) throutgn the Vieregion (small maximum typical of absorbing aerosols) and into the geometricregion where it follows the diagonals calculated from equation "'I rspecifi-cally the diagonal for (Q)10 = 2.0]. Thus, Fioure 1 shows the k,,h ri or ofoI0 at A = 10 im for all possible droplet sizes of this jerosol andincludes all three classes of optical scattering suimmarized in thef Tahole.

12

The dashed curve in Figure I becomes horizontal in the Rayleighregime (Dp << X) at some level given by equations 7 and 8 or approximatedby equation 9, where the absorption coefficient and density of the dropletsare the primary factors determining a for these nonscattering absorbingdroplets.

The interactions between particle absorption and optical scatteringare extremely varied for most aerosol materials that are IR absorbers.Superficially, these interactions appear to complicate spectral measurementproblems. In reality, the interactions provide kinds of data not attainableby conventional techniques. Many practical applications are discussed inReferences 5 and 9. Nonabsorbing spherical particles are discussed inAppendix A.

4. VAPORS

In aerosol spectrometry, a vapor is considered a molecular aerosolof the smallest possible particle diameter. This description is highly uncon-ventional but surprisingly useful because it permits, for example, directcomparisons between vapor and aerosol extinctions at a given wavelength. Avapor, observed at any optical wavelength, is the best possible example of aRayleigh scatterer (Dp << X) whose extinction can be assumed due entirelyto absorption attributable to modes of interatomic bonds and molecular rota-tions. The extinction (absorption) coefficients of gases are extremely sensi-tive to the vapor pressure due to pressure-broadening effects. Therefore, itis always necessary to state the partial pressure for which a given ax isreported. 6 * The vapor absorption coefficient increases as partial pressureis reduced, typically reaching some effective maximum < 1 mm Hg.

In IR vapor spectra, the regions of high transparency between absorp-tion bands are often of more interest than the bands. For example, atmosphericgases, including CO2 and H20, define transparent window regions through whichmost electrooptical systems must operate. These wind,-'- vary in transparencyin relationship to partial pressures of the gases and to other complex phenom-ena discussed in Section 6. The band shoulders of ar[nospheric gases, there-fore, ate oftcn more important than the absorption .- aks.

On a plot for a given wavelength (Figure 1), a pure vapor of a non-polar liquid could be represented by a single point. This point would bedirectly above the diameter (molecular) of the vapor molecule on the abscissaand to the right of the vapor absorption coefficient (equations 7 and 8 orapproximated from equation 9) on the ordinate calculated for this wavelength.Furthermore, the concept of the vapor-liquid phase transition can be intro-duced at this point if the vapor is in contact with liquid droplets. (The phas-transition will be discussed in detail in Section 6). Thus, the dashed curvewould be extended to the right as in Figure 1 to represent the liquid phase(droplets). For example, a liquid aerosol of benzene droplets in air could be

*Freon is a registered trademark of E.I. DuPont dr Nemours Company, Wilmington,DE.

13

D <XD# >> X,

102

D< <1

(Q~x10-2"-,)'.

\\4. 0<2.0

1.0

10-4 ,- •i Du

10-4 10- 2 1 102 104

Figure 1. Extinction Coefficient vs. Parti c-If, fiu.i,,,eter fcr PhoýphorusSmoke (Dashed Curve) at x = 10 urn. All three classes ofoptical scattering from the Table are represented. Thesolid diagonals are the geometric 1 i kýits from equation 10.

14

,3nteu by such a smooth curve, because benzene has the same absorptioncoefficient in the vapor phase as in the liquid phase at a given wavelength.

Polar substances are not so cooperative as nonpclar ones. For

example, liquids and vapors of alcohols have different cX .10 In a plot likeFigure 1, the vapor absorption coefficient cannot be shown by a point at theleft-hand end (molecular diameter) of the dashed liquid curve because the vaporhas a smaller absorption coefficient than the liquid does, and its point lieswell below the curve. This behavior invariably indicates intermolecularbonding between molecules in the samples. This circumstance, which will bediscussed in detail in Section 6, is very important.

Appendix B gives IR absorption coefficients for the gases SF6 and* CCI 2F2 •

5. SPECIAL-CASE AEROSOLS

5.1 The Christiansen Effect. 1 1

The well-known Christiansen effect occurs when a suspension of parti-cles in a transparent medium is observed at a wavelength where the refractiveindices of the particles and of the medium are equal, thus producing an opti-cally homogeneous medium with optical bandpass or filter characteristics.Soil-derived, atmospheric dusts and other particulates exhibit the Christianseneffect at IR wavelengths, and their spectra can be simulated by equivalent,

precipitated films of the particulates on optical substrates. 11 Useful

approximation equations apply at the Christiansen wavelengths that are likethose presented in this report for the Rayleigh scattering case. This isbecause the Rayleigh aerosol particles are too small to scatter appreciablyat a given wavelength, whereas the Christiansen aerosol particles at theappropriate wavelengths do not scatter, because their real index matchesthat of the medium (e.g., air), and all extinction arives from absorption asin the case (approximately) for a Rayleigh aerosol.

Thus, Christiansen aerosols are a special ,.ose of a Rayleigh-likeclass in the Table. The thickness of the precipitated, equivalent film ofparticulates is given by equation 3, and the approximations of equations 6, 7,8, and 9 apply. If desired, equation 2 can be writt,.n for the Christiansenpeak as:

ln (I/T') = kL . t (at x Christiansen) (11)

There are other subclasses of Christiansen behavior in aerosols.For example, some kinds of solid particles in liquid droplets or in othersolids can exhibit these effects and might have special applications. Dry,salt particles in air have Ch Tstiansen wavelengths and could affect atmo-spheric transmission spectra. Many kinds of powdered minerals have sharpIR absorption bands and can b 2used to fabricate optical filters onsubstrates like polyethylene. Durable and inexpensive Christiansen filtersmight also be fabricated using such techniques.

15

5.2 Isosbestics. 1 3

Bauman 14 gives an interesting discussion of isosbestics and of"isosbestic points." When only two substances, in equilibrium with each other,are responsible for all absorption in a given wavelength region, at least onepoint must exist in the spectrum where the absorption coefficient will be inde-pendent of the ratio of the concentrations of the two substances. The wave-length at which this occurs is called the isosbestic point or, sometimes, the"isobestic" point. If it can be assumed that the Beer-Lambert Law (equation 2)is applicable, the absence of an isosbestic point is definite proof of thepresence of a third constituent.

Isosbestic points (wave]engths) are found in a great many spectra ofatmospheric constituents. Hodgeslu shows them near 7.5 and 12.5 wm in spectraof continental and maritime aerosols, and he demonstrates that atmosphericextinction coefficients between these wavelengths are surprisingly indepengentof the size distributions used for the condensation nuclei. Carlon et al,show that the extinction coefficients of many common smokes and liquid aero-sols, including water fogs, are almost independent of droplet size distri-bution, and that geometric mean diameters may be used in place of diameterdistributions with very little effect upon the results obtained. Theseinvestigators also show that, at the isosbestic wavelength of 12.5 um whichis found in water and hydrated aerosols like those of Hodges, the aerosol ex-tinc extinction coefficient is completely size-independent from the smallest,possible droplet sizes to droplets as large as about 10 urm, where the geometriclimit begins to take effect, and Q12.5 decreases for larger diameters accord-ing to equation 10 where (Q)12.5 = 2.0. (See Reference 9).

Isosbestics suggest interesting applications that can be studiedmost conveniently by aerosol spectroscopy. For example, if the complexindex of refraction is known for an isosbestic wavelength, it becomes possi-ble to determine remotely the solute concentrations and ratios of chemicalequivalents in the droplets, because at this wavelength in equation 2,ax is constant and quiLe independent of droplet-size distribution where thedroplet-size distribution is, because of thermodynamic considerations,dependent upon the solute concentration of the droplets! Applications existwhere optical extinction at one wavelength could be compared to that at anisosbestic point (wavelength) where the extinction coefficient is a constant.Pure water can be considered the ultimate dilution of solute concentrationfor hydrated atmospheric 3erosols; thus, it is possible to construct a method-ology using isosbestic techniques for infinite combinations of solute concen-trations and wavelengths.13

6. PHASE-TRANSITIONAL AEROSOLS

6.1 Nonpolar Substances.

The concept of the phase transition for the simple evaporation ordroplet growth of liquids like benzene was introduced in Section 4. Benzenewas used as an example of a substance wh)ose vapor and liquid absorption coef-ficients are the same at virtually any wavelength and whose behavior could beshown by a plot like Figure 1, where the vapor absorption coefficient couldbe represented by a point at the left-hand end of the horizontal portion of

16

t.., lashed curve (corresponding ,u tiu... diameter). Investigatorsalso noted that polar substances, including alcohols, 10 cannot be plottedlike benzene because their points for the vapor absorption coefficients liebelow their curves (like the dashed one in Figure 1) for the liquid (droplet)phase.

Only nonpolar substances behave like benzene in this regard. When-ever a vapor point is found (at the molecular diameter as shown in Figure 1)to lie below its liquid curve, this is prima facie evidence that intermolecularbonding exists within the samples and that the intermolecular bonds are active

in the absorption at the wavelength of observation. 1 6 It means that the dif-terence between the vapor and liquid extinction (absorption) coefficients canbe attributed to bonds between adjoining molecules that add their absorption tothe interatomic modes and rotations of individual molecules in the vapor orliquid. It also indicates that intermolecular bonding, and hence absorption,are functions of the phase density of the sampled material. In nonpolarsubstances like benzene, intermolecular bonding appears to be negligibleregardless of phase density, even for density differences as great as thosebetween vapor and liquid samples.

6.2 Polar Substances.

Probably the most significant insights gained by the aerosol spec-troscopy methodology have been those concerning water, especially in thephase transition between the vapor and the liquid. Of all known substances,water exhibits the most pronounced evidence of intermolecular clustering asshown by the ratio of its liquid and vapor absorption coefficients. Thisratio can reach 103 to 104 as shown in Figure 2, where for X = 10 •m, theliquid absorption coefficient is denoted by 110L and the vapor absorptionL

coefficient by 010 , both for normal ambient temperatures. The error barsv

?9,Je vapor point show the range of values obtained by many investigators,8 where the value measured is known to vary ap roximately as the square of

water vapor partial pressure or relative humidity.16

This simple observation concerning the discrepancy between water'sliquid and vapor absorption coefficients, as illustrated in Figure 2, providiedevidence that anomalous IR absorption by water vapor could be due to liquid-like, intermolecular (hydrogen) bonding 3 years before similar evidence wastound by spectroscopists using conventional vapor techniques. 19, In thelatter case, this evidence was found in the temperature dependence of thevapor absorption coefficient in steam at wavelengths near the 7-13 umwindow region where this anomalous continuum absorption of water vapor ismost troublesome. Among vapor spectroscopists, the debate continues to thepresent as to what molecular-aggregate (cluster) species, if any, could

account for the IR continuum absorption of water vapor. 2 1 , 2 2

Meanwhile, the aerosol methodology has been applied since 1965 toapplications and problems associated with atmospheric IR propagation, espe-cially in the 7-13 lim window region, and to the general problem of spectral

17

11I \

clL (- - - -(Q)

4.010-2- 2.0

1.0

10- 4 -WATER

10v = 10Pm

10_6 I D/

10-4 10-2 1 102 104

Figure 2. Extinction Coefficient vs. Particle Diameter for Water atX = 10 om. Liquid droplets are represented by thedashed curve. At the molecular diameter, the liquid

absorption coefficient, a OL, is 103 to 10 ties lar1er

than the vapor absorption coefficient, "IN , for normal

ambient conditions. This simple observation provides primafacie evidence that intermolecular (hydrogen) honding occursin water vapor and liquid and becomes more extensive as thephase density increases through the vapor/liquid-phasetransition.

18

absorption and emission due to clusters ot w~aeC molecules in the vapor phasethat are held together by intermolecular bonds (e.g., hydrogen bonds) or byionic forces. The earliest applications were concerned with the apparentdependence of terrestrial scintillation (heat wave) intensity upon atmos-pheric hum dity, and the effects of such turbulence upon the operation of IRequipment.' 9 This work attributed the modulation to IR absorption by tinywater droplets whose populations were time-varying within the time scale ofnormal atmospheric turbulence. Because the IR modulation was not accompaniedby light scattering in the visible wavelengths, the investigator concludedthat these effects were due to water aerosols of submicron radius that arepresent, or generated, at higher relative humidities (RH). The dependence ofthe modulation intensity (i.e., "droplet" population) upon the square of theRH also was discussed but, in the absence of knowledge then of what are nowcalled water clusters, this humidity dependency was thought to be due to thegrowth of the droplets on soluble condensation nuclei. This led to theparadox that if condensation or combustion nuclei were involved, they wouldbe large enough to scatter visible light. But, reduction in visibility didnot necessarily accompany intense IR absorption and modulation at higher RH.Thus, existence of a then-unaccounted-for water species in the atmosphere wasrequired to explain all observations. However, this did not deter theapplication of these findings. Clear-air-turbulence (CAT) detection aýLad ofaircraft using IR radiometers sensitive to water species was proposed. •3Recently, success in CAT detection using similar equipment has been reported.An extensive compilation IR atmospheric phenomend that could be attributed totiny water, aerosol droplets was published, 2 5 and a model was proposed 2 6 toexplain the IR continuum absorption and other phenomena in terms of fractionsof wdter vapor necessary to be present as liquidlike aerosols to account forthe experimental observations. In the retrospect of more recent developmentsdiscussed below, the phenomena discussed 1 9 , 2 3 , 2 5 , 2 6 can now be considered asexamples of manifestations of molecular aggregates or water clusters that arealways found in the vapor phase.

In a sense, populations of molecular clusters of water monomersindividual molecules) in the atmosphere complete the vast family of atmo-spheric aerosols of all kinds. This concept is illustrated in Figure 3,which is based i~qpart upon work by J. G. Wilson,27 who summarized the work ofC.T.R. Wilson28,S 9 and others. The abscissa shows ".ne radius of all species,r. in micrometers, while the ordinate shows both th,, natural logarithm ofthe ratio of water vapor partial pressure, p, to saturation vapor pressure,po, and the saturation ratio or fractional RH (s) The 100% RH or s = 1.0level is shown as a horizontal line. The growth (with humidity) of allclasses of normal atmospheric, condensation nuclei in the Aitken, combustion(continental), and salt (maritime) size ranges is indicated by dashed curves,and this humidity-dependent growth is completely familiar to all atmosphericphysicists. At saturation humidity or when slight supersaturation exists,these condensation nuclei grow into haze, fog, or cloud-droplet distributionsthat have been extensively modeled. 4 These aerosols absorb IR radiationespecially at longer wavelength, but they announce their presence by the opticdlscattering in the visible wavelengths that always iccompanies them. Nucleiof this kin were first imagined to be involved in the phenomena reported inreference.11

19

2- (7.4)

(4.2)

(2.7)

-ION

o0 - (1.0)

" z / -.-- (100% RH),_ _ o/ / //• •1 I

,, -1- -(0.37) '-i i0(

_ Z .

- . , I ° vC -2 (0.14) 0 I

S( ROPLET SIZE RANGESD 0 0O3SERVED IN FOG-3--0.0) w-z -MEASUREMENTS

W 1 I 0 1Iz

-4-1:0.02ý

10410310210-1 100 6

DROPLET RADIUS (r. )

Figure 3. Equilibrium Curves for Atmospheric Aerosols of Many Types atStandard Conditions. 2 7 The saturation ratio, s, is thefractional RH or ratio of actual-to-saturation vapor pressures,p/pn. The dashed curves represent classes of nuclei that canýjrow to visible or near-visible diameters in typical, atmospherichwnidity conditions. These condensation nuclei include Aitken,combustion (continental), and salt (inaritime) kinds. The peaked,solid curve represents ion hydrates, water ion clusters, or ion-induced neutral water clusters, which are present under normalatmospheric conditions (s < 1.0). These clusters cannot growinto droplets large enough to scatter light except when super-saturations of about 4.2 occur. The dotted curve representshomogeneous clusters like the water dimer, which are not expectedin real atmospheres because of thermodynamic considerations butfor which evidence nevertheless exists.

20

phase-transitional species between the water monomer (vapor) at its molecularradius and liquid water droplets. This class is shown by the peaked, solidcurve labeled ion in Figure 3. These species are ion hydrates or water-ion clusters typically of 10-13 monomers gathered about an ion, and the meanion cluster size (as can be inferred by the slope of the solid curve inFigure 3) depends directly upon the saturation ratio, s. These ion clustershave modes that correspond to IR wavelengths in the continuum absorption, 1 6 , 2 1

and in moist air, it is possible to measure ion concentrations that havetemperature and humidity dependencies similar to those of the IR continuumabsorption. 3 0 , 3 1 The ionic charges have very short lifetimes, but watermonomers clustered about ions also begin immediately to cross-link with oneanother by hydrogen bonding. There is a great deal of recent evidence 3 2 , 3 3

that peaked distributions of ion-induced, neutral water clusters are found inwater vapor in sufficient numbers to explain the IR continuum absorption.Pronounced evidence is seen in IR emission spectra of steam, 3 4 under conditionssuch as those in which vapor spectroscopists first found evidence of intermo-lecular bonding 2 0 and, earlier, Elsasser 3 5 had found an empirical correction towater vapor models to take into account the IR continuum absorption.

In Figure 3, one can see that the peak of the (solid) curve for ionhydrates or ion-induced, neutral water clusters lies near s = 4.2, a supersat-uration far larger than that found in normal moist atmospheres. This meansthat tiny, liquid-like cluster species coexist with larger aerosols in all

atmospheres, and that they are able to produce liquid-like IR absorption with-

out growing large enough to scatter visible light - precisely the conditions

needed to resolve the paradox discussed earlier. The dotted curve in Figure 3

labeled uncharged represents homogeneous clusters like the water dimer that,

because of equilibrium considerations, 2 7 would be expected to grow immediately

into droplets at higher saturation ratios. From the standpoint of aerosol

spectrometry, homogeneous species like the dimer are not likely to be able to

explain the IR continuum absorption. 2 1 , 3 1 , 3 2

Phase-transitional water (cluster) species !,f water lend them-selves readily to the mass units used in aerosol spec(troscopy methodology.Equation 2 is, of course, written for single atmospheric constituents.When more than one constituent is present, equation 2 is written as:

ln (I/TA) = (01 C1 + c2 C2 + ... ) (L) (12)A A

For the case of clusters in water vapor, the monomer concentrationfrom equation 4 can be written C1 = (1 6 )(1 8 )(s)(Po)/Ok z 2 88 (s)(Po)/Okif water vapor is taken to be an ideal gas. The mole or mass fraction ofwater bound in clusters in water vapor, no, is a known function 16 of thesaturation ratio such that n( = Ko(s). Thus, the cluster concentration in

21

equation 12 can be written as C2 = %C 1 = K0 (s)(C1 ), or equation 12 forwater clusters and vapor can be written as:

ln (1/Tx) = 28 8 (s)(Po)/Ok ' (CiX + K (s)"2,) (L)" (13)

That is, the cluster component has an (s)2 deperdence like thatobserved in the IR continuum absorption. A model very similar to the one inequation 13 was given in reference 27, wherein it was shown that in effect,a 2 could be evaluated directly from the optical constants of bulk liquid

vater. This is not surprising because water clusters are the phase-transi-tional species between the vapor and liquid phases. These clusters explain theobservations of Figure 2, where 10 L= 02 in equation 13, and a10 = 1 10L 10 v 10

In other words, the behavior in Figure 2 is due to a mass fraction of= 10- o to 10-3 of water clusters floating in the vapor phase.

These observations are intimately associated with invs igationsof cloud physicists and workers in atmospheric electricity.30,31s 2 Thus,the aerosol spectrometry methodology enables results to be extrapolatedto other disciplines where their association might not even be recognizedusing specialized, traditional, spectroscopic or aerosol modeling techniques.For example, Figure 3 suggRgt• the concept of an IR cloud chamber. Workingwith visible light, Wilson m, ' had to obtain critical supersaturation (peakof solid curve labeled ion near s = 4.2 in Figure 3) to grow droplets that hedetected by optical scattering. If an IR wavelength or monochromator wereused (e.g., near A = 10 um, a study of the prenucleation cluster species inreal atmospheres should be possible.

7. WORKSHEET

A worksheet for aerosol spectrometry is shown in Figure 4. Thisworksheet is not intended to include all possible categories of aerosols andpossible properties such as birefringence. Rather, the sheet is a startingpoint for analyzing a given aerosol and its changes with tim•r:, temperature,humidity, and other parameters. Changes in ki between physical phaseshave been discussed, especially for the case of the vapor/li u!d transitionin water (ice and liquid water also show less pronounced hu- inificantphase-transitional differences). The notations in dashed Loyý, c! the work-sheet are reminders to investigate this area. 'no encounte- increasingdifficulty in applying theory and computational technique as he progressesfrom the top to the bottom of the worksheet. In r:ost cases, empiricalmodels must be used for nonspherical, solid particulates in the tie andRayleigh regions. Additional information is ;provided in the c<?tior ofFigure 4.

22

FACTOIIS DETERIMINING CX IN VISIIILE & III

SAMrLE IDENTIfICATION: ___

X- -~- -- " ' . -,-IGIIL.)V. P.- ______MM) ___ C 'M1- %____PAIITICLE CONSTITTUrNCY' %' ___ _____

CI 1, ASS Lj) A A ý .;-- D ,D COMPAITATLONJrIIASI. RAYLFiI;II Mi IFGI M F It lIT: S C I LM E:

- VArlon R V ;,GAS MODEL

0>.

.01' ES k M01I FCII AllLI'IANISE IEX - GAS 91 (IC'umInl IVl>FN ______ __________

rI~lASIFS?

I-~ 10111 LML CL I10- L 1 __ M1PR

IX WATFI rm;l Ill fX VVAIIlIiI(lVIStIll It" At

1111 IX A(. I1) MI KI M11 PA IE MODUEL

M S I CS

IXI- II SI: IIIIIS/, l~ AAISlot1 11) A

- S~ll IIIRS N I, I l

M S S' I'M'l.A

MO__ I) ___

- FX FTINC 11D15) IN Tx ICI T(WIll; xI IX 4 1 ItPFiS

AEIIIIS;()l cIANG[ S YI dI it I jMt? LIIKsCitii

Figure 4. Workshf-ct for Aerosol Spec trome try. Thi Is phase designationsin bold letters corresipondl to the opt'i ,(-,tter~nq classes alsoimrnarized in the Table: Rayl eig yt, (M',, and Geometric (G).

The physical phases of thý scirplos 1~ hold lettersajnd in shsch~pts. as vipor "V , ~< Iand sollid ~3. Theboundary lines between class/phase !~ correspond to in'portant

Changes affectin,, the extinction c-uefficient, rx, at wavelength,ý. HoriZontil boundary 1 'nes c~orre-spond to phase changes, oftenw~ th, 3t1,,r~d rt r han);t ' r .h(, -(sTpt Iff-ipnt or imagi nary

.7.~~ ~ t r! t(2 T'c c,,) r' re'w s lflo L pn J topajrticle grownh or sizu- reou(,ti'n us ýh.wr ii F 'gyures 1 dind 2.For eXamlpie2 (from Vigurre 2), 1 ,-,iter fo ,',ht begin in class/phase a rea ML on thisvi) wrkhees-, or 4,erý dirc pl et-size reductionwith increased temp;i(ra ture and I wered i nto airca RL , aridfinally evaporote,( to the gas l.IIse and dtirIqo a ma,;jor change inthe absorpti on coefficient wh'i ICj cncr r(,a RV with an atten-

ddnt dri~p i n .0 a s sho wn 'n fi j ur,

v0

8. CONCLUSIONS

The techniques of aerosol spectrometrv are very useful. Thepurpose of this report has been to set forth the methodology by which thesetechniques can be applied to the study of many kinds of atmospheric consti-tuents to yield quantitative, standardized descriptions of spectral behaviorthat are intuitively clear and allow insights that would otherwise be impos-sible by traditional or purely mathematical treatments. Similar descrip-tions and units have been used by other authors 3 6 and are familiar to mostatmospheric physicists. A methodology that places all aspects of aerosolspectrometry in an integrated, intuitively satisfying, framework betweentraditional spectroscopy and theoretical models has been missing. The method-ology presented here permits results to be extrapolated to other disciplinessuch as cloud physics and atmospheric electricity, where the commonality ofinvestigations shared by workers in these fields and atmospheric opticistshas been unrecognized or ignored. New results concerned with molecularcomplexes (clusters) in water vapor show that they are intimately associatedwith electrical properties of the atmosphere, with atmospheric Ik absorptionand Pmission, and with cloud nucleation phenomena. The methodology discussedin this report has been used successfully at this Center for many years andis recommended for consideration and use by app ications-oriented systemsdesigners and atmospheric opticists.

24

LITERATURE CITED

1. G. Mie, Ann. Phys. Vol. 25, p 377 (1908).

2. Acquista, C., "Validity of Modifying Mie Theory to DescribeScattering by Nonspherical Particles," Appl. Opt. Vol. 17, p 3851 (1978).

3. van de Hulst, H.C., Light Scattering by Small Particles, JohnWiley, New York, 1957.

4. Deirmendjian, D., Electromagnetic Scattering on Spherical Poly-dispersions, Elsevier, New York, 1969.

5. Carlon, H.R., Anderson, D.H., Milham, M.F., Tarnove, T.L.,Frickel, R.H., and Sindoni, I., "Infrared Extinction Spectra of Some CommonLiquid Aerosols," Appl. Opt. Vol. 16, p 1598 (1977).

6. Carlon, H.R., "Infrared Absorption Coefficients (3-15 lim) forSulfur Hexafluoride (SF6 ) and Freon (CC1 2 F2 )," Appl. Opt. Vol. 18, p 1474(1979).

7. Carlon, H.R., "Contributions of Particle Absorption to MassExtinction Coefficients (0.55-14 pm) of Soil-Derived Atmospheric Dusts,"Appl. Opt. Vol. 19, p 1165 (1980).

S. Carlon, H.R., "Practical Upper Limits of the Optical ExtinctionCoefficients of Aerosols," Appl. Opt. Vol. 18, p 1372 (1979).

9. Carlon, H.R., Milham, M.E., and Frickel, R.H., "Determination ofAerosol Droplet Size and Concentration from Simple Transmittance Measurements,"Appl. Opp. Vol. 15, p 2454 (1976).

10. Carlon, H.R., "Quantitative Liquid-Phase Infrared Spectra ofSeveral Simple Organic Compounds," Appl. Opt. Vol. 11, p 549 (1972).

11. Carlon, H.R., "The Christiansen Effect in Infrared Spectra ofSoil-Derived Atmospheric Dusts," Appl. Opt. Vol. 18, 2 3610 (1979).

12. Carlon, H.R., "Durable Narrow Abscrpt in Band Infrared FiltersUtilizing Powdered Mineral Materials on Polyethylcr_ Substrates," Appl. Opt.Vol. 1, p 603 (1962).

13. Carlon, H.R., "Isosbestics in Infrared Aerosol Spectra: ProposedApplications for Remote Sensing," Infrared Physics Vol. 21, p 93 (1981).

14. Bauman, R.P., Absorption Spectroscopy, Vol. 1, pp 419-423,John Wiley, New York, 1962.

15. Hodges, J.A., "Aerosol Extinction Contribution of AtmosphericAttenuation in Infrared Wavelengths," Appl. Opt. Vo'. 11, p 2304 (1972).

25

16. Carlon, H.R., "Phase Transition Changes in the MolecularAbsorption Coefficient of Water in the Infrared: Evidence for Clusters,"Appl. Opt. Vol. 17, p 3192 (1978).

17. Bignell, K.J., "The Water-Vapour Infra-red Continuum," Quart.J. Roy. Meteorol. Soc. Vol. 96, p 390 (1970).

18. Roberts, R.E., Selby, J.E.A., and Biberman, L.M., "InfraredContinuum Absorption by Atmospheric Water Vapor in the 8-12 am Window,"Appl. Opt. Vol. 15, p 2085 (1976).

19. Carlon, H.R., "The Apparent Dependence of Terrestrial Scintil-lation Intensity Upon Atmospheric Humidity," Appl. O•t. Vol. 4, p 1089 (1965).

20. Varanasi, P., Chou, S., and Penner, S.S., "Absorption Coeffi-cients for Water Vapor in the 600-1000 cm" 1 Region," J. Quant. Spectrosc.Radiat. Transfer Vol. 8, p 1537 (1968).

21. Carlon, H.R., "Molecular Interpretation of the IR Water VaporContinuum: Comments," Appl. Opt. Vol. 17, p 3193 (1978).

22. Watkins, W.R., White, K.O., Bower, L.R., and Sojka, B.Z.,"Pressure Dependence of the Water Vapor Continuum Absorption in the3.5-4.0-vm Region," Appl. Opt. Vol. 18, p 1149 (1979).

23. Carlon, H.R., "Humidity Effects in the 8-13 am InfraredWindow," Appl. Opt. Vol. 5, p 879 (1966).

24. Kuhn, P.M., Nolt, I.G., Radostitz, J.V., and Stearns, L.P.,"Infrared Passbands for Clear-Air-Turbulence Detection," Optics Letters Vol. 3,p 130 (1978).

25. Carlon, H.R., "Infrared Emission by Fine Water Aerosols andFogs," Appl. Opt. Vol. 1, p 2000 (1970).

26. Carlon, H.R., "Model for Infrared Emission of Water Vapor/Aerosol Mixtures," Appl. Opt. Vol. 10, p 2297 (1971).

27. Wilson, J.G., "The Principles of Cloud Chamber Technique,"Cambridge Monographs on Physics, University Press, Cambridge, England, 1951.

28. Wilson, C.T.R., "Condensation of Water Vapour in the Presenceof Dust-Free Air and Other Gases," Philos. Trans. Vol. 189, p 265 (1897).

29. Wilson, C.T.R., "On the Condensation Nuclei Produced in Gasesby the Action of Rontgen Rays, Uranium Rays, Ultra-Violet Light, and OtherAgents," Philos. Trans Vol. 192, p 403 (1899).

30. Carlon, H.R., "Ion Content of Air Humidified by Boiling Water,"J. Appl. Phys. Vol. 51, p 71 (1980).

31. Carlon, H.P., "Ion Content and Infrared Ahsorption of MoistAtmospheres," ,J. Atmos. Sci. Vol. 36, p 832 (1979).

26

32. Carlon, H.R., "Do Clusters Contribute to the Infrared AbsorptionSpectrum of Water Vapor?" Infrared Phys. Vol. 19, p 549 (1979).

33. Carlon, H.R., and Harden, C.S., "Mass Spectrometry of Ion-Induced Water Clusters: An Explanation of the Infrared Continuum Absorption,"Appl. Opt. Vol. 19, p 1776 (1980).

34. Carlon, H.R., "Variations in Emission Spectra from Warm WaterFogs: Evidence for Clusters in the Vapor Phase," Infrared Phys. Vol. 19, p 49(1979).

35. Elsasser, W.M., "Note on Atmospheric Absorption Caused by theWater Rotational Band," Phys. Rev. Vol. 53, p 768 (1938).

36. Jennings, S.G. , Pinnick, R.G. , and Gil lespic, J.B. , "RelationBetween Absorption Coefficient and Imaginary Index of Atmospheric AerosolConstituents," Appi. Opt. Vol. 18, pp 1368-1371 (1979).

27

Blank

28

I,

APPENDIX A

MASS EXTINCTION COEFFICIENTS ESTIMATEDFOR NONABSORBING SPHERICAL AEROSOL PARTICLES

IN THE GEOMETRIC SCATTERING REGIME

The Beer-Lambert equation for aerosols can be written as:

In (I/TX) = aXCL (A-I)

where

TX = optical transmittance at wavelength A (Jim)

a = mass extinction coefficient (m2 /g)

C = aerosol mass concentration (g/m 3 )

L = optical pathlength (m)

It is straightforward to showI that:

a = 3QX / 2Dpp (A-2)

where the Mie theory 2 gives the value of QA that depends upon the particlediameter D, (vm) compared to the wavelength A, and p is the particle mass

density (g/cm3 ). In the geometric regime (D. >> A), QX----o2.0 as DVincreases. Thus:

aX3/D (DI >> X) (A-3)

The Figure shows values of aX versus D. at the He:Ne laser wave-length (A= 0.63 wm) calculated for spherical droplets of water (dashedcurve 3 ) and several phthalates (dibutyl-, diethyl-, dimethyl-, and dioctyl-solid curves); the latter are commonly used in aerosol chamber testing. 4 Thefigure shows that when D. >> 0.63 pm, the Mie-calculated extinction coef-ficient curves merge into a "tail" whose function is given by equation A-3and whose thickness depends mainly upon the differences in mass densities (p)of the liquids that are represented. The density differences are not obviousbecause of the logarithmic scale used for the ordinate of the Figure. A greatmany liquid and solid substances exist for which, when they are dispersed asspherical particles at wavelengths where their absorption is negligible,remarkably good first approximations of aA can be made using equation A-3.Hence, equation A-3 is a useful one for first calculations involving such

29

10

X = 0.63•im

-1 I/

E -- = If

S1 - I,z I

U-

Siiwiu I0C-, Iz I

10-1

z =

, KEY:_ - DBP, DEP,

/ DMP & DOPII -~- , WATER

1o-2 r 910-2 10-1 1 10 102

DIAMETER, .

FiyUr'c. Mi -Cal cul ated I.xtinction Coeffici ert v, phferical DropletDiameter for the He:Ne Laser Wavelernjth ( 0.63 .:0).The dashed curve is for water droplet., whereas the solidcurves are for droplets of several kOni1, of ,o0thalates(dibutyl , diethyl , dimethyl , and diow-tvl)1

APPENDIX A 30

aerosols when their optical properties are not known at some wavelength X,but Dp >> A . A common example is that of water-fog droplets in the visiblewavelengths. Often, visible-wavelength observations can be combined withinfrared (IR) measurements to yield additional information about an aerosol(e.g., mean particle diameter). 5 Combining equations A-i and A-3 gives:

ln (1/TX) = 3/D• * p CL (DM >> X) (A-4)

and it is straightforward to show that:

ln (1/TA) = w/2 D2 • N • L • 10-6 (Dii >> ) (A-5)

where N is the number of spherical particles per cubic centimeter. EquationA-5 can be extended to some rather practical applications. For example,Middleton 6 estimates meteorological range as that for which a high-contrasttarget is seen with 2% transmittance, that is, TX = 0.02 and ln (I/TX) = 3.912so that equation A-5 can be written as:

N = 2.49 • 106/D2 - L (D• >> A) (A-6)U

As an example, a typical, developing water fog is comprised of drop-lets having mean diameters in the 3-5 Pm range. If an observer could barelysee a high-contrast target at L = 200 m under such conditions, from equation 6,the fog should contain approximately 500-1400 droplets per cubic centimeter.Perhaps a more useful application would be to calculate mean values of DV fromequation 6 using observed ranges (L) and droplet populations (N) measured byindependent means as a water fog aged and dissipated.

APPENDIX A 31

LITERATURE CITED

1. Carlon, H.R., "Practical Upper Limits of the Optical ExtinctionCoefficients of Aerosols," Appl. Opt. Vol. 18, p 1372 (1979).

2. G. Mie, Ann. Phys. Vol. 25, p 377 (1908).

3. Carlon, H.R., Anderson, D.H., Milham, M.E., Tarnove, T.L.,Frickel , R.H. , and Sindoni , I., "Infrared Extinction Spectra of Some CommonLiquid Aerosols," Appl. Opt. Vol. 16, p 1598 (1977).

4. Carlon, H.R., Kimball, D.V., and Wright, R.J., "Laser Monitoringof Mass Concentrations of Monodisperse Test Aerosols," Appl. Opt. Vol. 19,

p 2366 (1980).

5. Carlon, H.R., Milham, M.E., and Frickel, R.H., "Determinationof Aerosol Droplet Size and Concentration from Simple Transmittance Measure-ments," Appl. Opt. Vol. 15, p 2452 (1976).

6. Middleton, W.E.K., Vision Through the Atmosphere, p 105,University of Toronto Press, Canada, 1952.

Af'PENfL X •, 32

APPENDIX B

INFRARED ABSORPTION COEFFICIENTS (3-15 vm)FOR SULFUR HEXAFLUORIDE (SF6 ) AND FREON* (CC1 2 F2 )

B-I. INTRODUCTION

It is well known that Freon"* (CC1 2 F2) and sulfur hexafluoride(SF6 ) are gases with strong absorption in the infrared (IR). For example,they can be used for wavelength calibration of spectrometers or scanningradiometers or in atmospheric tracer studies. Many workers are also awarethat SF6 has a very strong absorption peak that overlaps the CO2 laser lines

near 10.6 0m. The extinction (absorption) of these gases is seldomdiscussed in literature of IR applications. Yet, these data are of poten-tial importance to workers, for example, in the fields of atmospheric oraerosol spectroscopy. The purpose of this report is to present absorptiondata for these gases in mass absorption coefficients that can be, forexample, compared directly to aerosol extinction coefficients and to sug-gest practical applications of these data.

The general expression for the mass concentration C(g/m 3 ) of anideal gas at pressure p(mm Hg) is:

C = 16Mp/Ok (B-I)

where the new, and all subsequent, terms are defined in the glossary of thisappendix. To facilitate direct comparison of the absorntion coefficients ofgases to the extinction coefficients of aerosols, they can both be expressedin mass units at a given wavelength, A, in Beer-Lambert law:

ln (1/TA) = a CLm (B-2)

For aerosols, cL is usually considered to I. a constant at somewavelength. But in reality, ax is a function of other parameters that mustalso be specified. For example, the scattering component of ax is affectedby particle shape, size distribution, and bulk densi'y. For liquid droplets,ax is affected by a solute concentration that, for water-based droplets, is

dependent upon humidity. 1 For gases, a, is a strong function of samplepressure, p, (or of partial pressure, as for gases mixed with atmospheric air).Vapor pressure has no direct counterpart in the condensed aerosol phases.Pressure-broadening of gas absorption bands is well known and widely studied.If desired, investigators can apply corrections for pressure (or temperature)to spectra presented in this report.

*Registered Trade Mark of E.I. Du Pont de Nemours 9 Company, Incorporated,Wilmington, DE.

33

B-2. EXPERIMENTAL PROCEDURE

2 Sulfur hexafluoride spectra were taken at 25 0C by Lagemann and

Jones.2 Sample purity was greater than 98%. Possible contaminants were F2 ,HF, H2 0, and sulfur fluorides, but only traces of SF4 were found. Spectrawere run using a Perkin-Elmer Model 21 spectrometer. A 10-cm long samplecell with KBr windows was used for the measurements reported here. Spectrawere recorded at SF6 pressures of 762, 25.4, and 1.6 mm Hg. The cell wassealed to exclude atmospheric air.

Freon spectra were taken by the author 3 at 25 0C in a 10-cm cellwith NaCl windows. The partial pressure, p, was 4.2 mm Hg in air at I atmtotal pressure. The sample was ae'osol-can propellant identified on itslabel as dichlorodifluoromethane (CC1?F 2 ) and used as a freezing spray with-out added soluues for electronic applications.

Because the value of a is highly dependent upon the pressure ofa gas sample due to pressure-broadening, the values of SF6 herein reportedare For three pressures, including the lowest one given in reference 2(1.6 mm Hg), which yields the maximum values of c for these data. For Freon",only one partial pressure taken in air at 1 atm total pressure was available,and comparative extinction coefficients at different pressures could not becalculated. However, the sample pressure (4.2 mm Hg) was comparable to thelowest SF6 partial pressure used (1.6 mm Hg).

B-3. RESULTS AND DiSCUSSION

Figure B-1 summarizes mt for gas pressures of 762, 25.4, and 1.6 mmHg of SF6 . Figure B[-2 shows ax for CC1 2 F2 at a partial pressure of

p = 4.2 mm Hg. The peak values are 2.4 m2/g at x = 10.64 0m for pure SF6 at

1.6 mm Hg, and 1.2 m2/g at A = 11.8 pm for CC1 2 F2 at 4.2 mm Hg in atmospheric

air.

Taken togoeti .. , these two gases used in conjunction with an isotopicCO2 laser near 10.6 ;i, ,,uld produce intense absorption by SF, on the one

hand (!, = - 2 o/' mm Hg) and relativel/y 0ijh transparency forA

F-eon' ,r ý he t• Ir .03 m2 /g).

The peak absorrotion coefficients reported ihere for Freon' and SF6

are substantially larger than coefficients of acid suokes in this wavelength

region. For example, phosphorus smoke gives a value of - 0.4 m2/g at

S.0 0nm and ;. t ,:, whereas H, SO mists or ', e ii'in ,.l"/gat

4= 8. cm. The value < -A/for typical liquid, water fogs rises from about0.05 to about C).34 /g over the wavelength interval from 7 to 15 j0m.1,3

APP• fD)'' I "I D 34

10

2.4 at 10.64pm

1 I'1.6mm Hg

10-1

E• 25.4mm Hg I

S10-2 _ s Us SIt'

I'I

10-

10_4 - 762mm Hg

SULFUR HEXAFLUORIDE (SF 6 )

250 C

3 4 5 6 7 8 9 10 11 12 13 14 15

X/Jm

Figure B-1. Extinction (Absorption) Coefficients of Sulfur Hexafluoride (SF 6 )

Gas, 3-15 ,jm Wavelengths, 25 'C. Key: %,Dl id curves and trangular

points refer to 762-mm Hg sample pressu-e; short, dashed curves and

square points refer to 25.4-mm Hg sample pressure; long, dashed

curves with circular points refer to 1.b-mm Hg sample pressure.

Samples were run in sealed cell to exclude atmospheric gases.

APPENDIX 6 35

10-2 -

-~ io2

10-3 _

FREON CCi 2 F2

25 0C4.2mm Hg

10-4 -I I I - - I I 1 1

2 4 6 8 10 12 14 16Xpm

Figure b-2. Extinction ',Absorption) Coefficients :nf Freon' (CCI 2 F2 ) Gas,

3-15 nm Waveilengths, Partial Pressurt = 4.2 mm Hy in 1 AtmTotal Atmosphoric Pressure at 25 "'C.

APPENDIX il 36

The integrated absorption coefficients of Freon'T (4.2 2m hg) orSF6 (1.6 mni Hg) over the 8-13 jim IR window were both about 0.1 m /g orslightly less. This is comparable to the absorption coefficient of a waterfog in this window (not including the scattering contribution to the totalextinction coefficient).

Freon' and SF6 are commercially available in gas cylinders thatfacilitate their use in experiments. For example, a known weight of gas canbe introduced into a test chamber simply by weighing the container before andafter dissemination. 4 This is particularly easy if the container is notheavy (e.g., if Freon' is taken from an aerosol can of electronic freeze mist).The volume of a chamber can be determined by introducing a known weight ofgas into it and monitoring the IR transmission at an absorption peak over aknown path. Or the path length (as in a mult'-ass cell) can be approximatedif the volume is known.

For atmospheric studies, extrapolation of the SF6 data suggeststhat this gas could be detected using a C02 -laser transmissometer at a partialPressure as low as about 10-5 mm Hg. This estimate is based upon typicallevels of atmospheric water vapor absorption near A = 10.6 Pm. When aerosolextinction rather than water vapor absorption limits atmospheric transmissionat this wavelength, the detectable partial pressure might be nearer 10- 4 mm Hg.These estimates would, of course, have to be verified by actual observations.

B-4. CONCLUSIONS

The mass dbsorption coefficients for Freon' and SF6 presented inthis report can be used qualitatively (e.g., in the w:veloength calibrationof a spectrometer or scanning radiometer), or semiquantitatively in a varietyof practical applications, some of which are suggested. The absorptioncoefficients are directly comparable to the mass extinction coefficients ofderosols. Such comparison shows that the peak absorption coefficients ofthese gases at lower pressures can be comparable to or greater than those ofstrongly-attenuating aerosols including dcid smokes and water fogs. Butthese gases have rdther low integrated absorption coef' •ients over broadwavelength regions. For example, the integrated abso ,-Jon coefficient overthe 8-13 Pm atmospheric window is 0.1 nm2 /g for both q es at several measuresof pressure related to mercury.

APPENDIX B 37

LITERATURE CITED

1. Carlon, H.R., Anderson, D.H., Milham, M.E., Tarnove, T.L.,Frickel, R.H., and Sindoni, I., Infrared Extinction Spectra of Some CommonLiquid Aerosols," Appl. Opt. Vol. 16, p 1598 (1977).

2. Lagemann, R.T., and Jones, E.A., J. Chem. Phys. Vol. 19, p 534(1951).

3. Carlon, H.R., "Practical Upper Limits of the Optical ExtinctionCoefficients of Aerosols," Appl. Opt. Vol. 18, p 1372 (1979).

4. Carlon, H.R., "CL" Factors for Toxic Agents and Spectral SimulantsDetected by Filter LOPAIR Equipment, CRDL Technical Memorandum 72-1, EdgewoodArsenal, MD, I Dec 1962, AD 472 170.

A# P[,N; ; B 38

GLOSSARY

* optical extinction coefficient (or absorption coefficient for a gas)at wavelength x, m2/g.

C - mass concentration of gas or aerosol, g/m3 .

Lm - optical path length, m.

S- wavelength of observation, um.

M a molecular weight of gas, g.

p a partial pressure or sample pressure of gas, mm Hg.

T - optical transmittance at wavelength x, unitless.

*k a absolute temperature, OK.

APPENDIX B 39