Raman scattering on single aerosol particles and on flowing aerosols: a review

J AerosolScl, Vol 21, No 4, pp 483 509, 1990 Printed m Great Britain

0021-8502/90 $300+000 © 1990PergamonPressplc

RAMAN SCATTERING ON SINGLE AEROSOL PARTICLES AND ON FLOWING AEROSOLS: A REVIEW G . SCHWEIGER Fachgebiet Thermodynamik, Universit/it Duisburg Postfach 10 15 03, D-4100 Duisburg 1, F.R.G.

(Recezved 21 July 1989, and in final form 20 November 1989) Abstract--The physical prinoples of Raman scattenng are briefly outlined. The different effects on the intensity, shape and frequency of Raman bands, especially for hquids and liquid mixtures, are discussed. The peculiarities of Raman scattering on micrometer sized particles are presented. Methods to calculate Raman scattering on micro particles are referred to briefly. The effect of morphology dependant resonances on Raman scattering on levitated particles is discussed. Finally, the different experimental concepts, Raman scattenng on levitated particles (optically or electrodynamically trapped) on particle chains and flowing aerosols are descnbed.

1. I N T R O D U C T I O N

From a very basic point of view Raman scattering can be considered as the modulation of the scattered light by the nuclei and electron clouds of the scattering molecules. As a consequence, the Raman lines in the spectrum of the scattered light contain information on the properties that rule the motion of the nuclei and electrons in a molecule, like orientation and distance of the nuclei, symmetry properties of the molecules, effects of temperature and pressure on the molecule, etc. It is the art of the theoretist to understand and describe these molecular properties and their effects on the scattered light quantitatively, and it depends on the state of the art of experimental techniques and on the skills and innovative talent of the experimentalist to detect and record the faintest details of the Raman spectra. Since the invention of the laser a powerful light source is available for Raman spectroscopy, and not only the experimental techniques but also the theoretical understanding in this field has made dramatic progress. Most of the information which can be extracted from the Raman spectrum is also available in the infrared absorption or the emission spectrum. There are, however, two very important differences as will be outlined in more detail in the next chapter: the frequencies of spectral lines in the absorption or emission spectra are properties of the molecule. In Raman scattering the frequency difference (and not the frequency) between the incident radiation and the Raman line is a molecular property. Consequently the frequency (or wavelength) range covered by the Raman spectrum depends not only on the properties of the scattering molecule but also on the frequency (wavelength) of incident radiation. The second very important peculiarity in Raman scattering is that, although an energy transfer between the field of incident radiation and the scattering molecule takes place (this causes the frequency shift between incident and scattered radiation), the incident photon is not absorbed as in infrared or fluorescence spectroscopy. The disturbances of the molecules due to Raman scattering are, therefore, much smaller than those for fluorescence or infrared absorption. Raman scattering is in consequence much less sensitive to the environment of the molecules (effects of collision with other molecules, etc.) than, for example, fluorescence. Before the Raman process is described in more detail, one main disadvantage of this techmque should also be mentioned. Raman scattering is, apart from some nonlinear variants (coherent antistokes Raman scattering, resonance Raman scattering, etc.) which will not be considered here, a very weak effect. The scattering cross section, which is the total scattered light flux divided by the incident light flux density, is in the order of 10-27 cm 2 for light scattered elastically on molecules, whereas the corresponding Raman scattering cross section is in the order of 10-3o cm 2. The excitation cross section for fluorescence depends 483

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G Sc HWEItoER

strongly on material and excitation wavelength, but is usually many orders of magmtude larger than the scattering cross section for Raylelgh scattering. Most of the information which can be extracted from Raman scattering on bulk material is also of interest in aerosol research. Examples are. Identification of the chemical composition of the sample, determination of ~ts temperature or its state, etc. Some of the aspects of Raman scattering are especially crmcal in mlcropartlcle analysis, like sample heating or signal to noise problems due to the very small mass of the sample. But one peculiarity can only be observed by Raman scattering on sphercial or spheroidal aerosol particles. The Raman spectrum of such particles shows additional peaks not present in the bulk spectrum. These peaks are caused by morphology dependant resonances, an effect which will be discussed later in this article. An important aspect of Raman scattering ~s ~ts potential for in situ analysis of aerosols or individual aerosol particles. Most of section 4 wdl be devoted to this application. Some of the aspects of Raman scattering on micropart~cles, especially instrumentation related aspects, were recently discussed by Schrader (1986) 2 BASIC THEORY OF RAMAN SCATTERING

Classical treatment of light scattering There are a number of excellent textbooks treating the Raman effect in great detail, so we restrict ourselves to a presentation of the basic relations (see for e.g. Herzberg, 1945, 1950; Anderson, 1971, 1973; BrandmiiUer and Moser, 1962). In the classical interpretation of the Raman effect (and we will follow this concept due to its simplicity whenever possible) the Coulomb forces of the electric field of radiation induces a dipole moment in a molecule exposed to this radiation. In general the induced dipole moment/~ and the electrical vector/: of this radiation is not parallel. The quantitative relation between the dipole moment and the electric field is given by

~=4rreoS E.

(1)*

The polarizability tensor & represents the response of a specific molecule to the external electrical field/~. The polarizability tensor is a material property, which in general depends on the intermolecular distance and on the motion of the electron cloud. The nuclei carry out thermal motions. These rotational and vibrational thermal motions change the internuclear distances which may cause changes in polarizability. There are other sources affecting the polarizability, electronic motions, intermolecular collisions, photon interaction, etc., which will be excluded from our consideration, although they can give reason for the appearance of frequency shifted lines in the scattering spectrum. In the following we will assume that the wavelength of the incident light is much larger than the molecular dimensions which is in most cases a reasonable assumption for visible light. The electric field of the incident wave can, therefore, be considered to be independent of the coordinate of the electrons and nuclei of the scattering molecule. Furthermore, we assume that the frequency of the incident light is far enough away from any eigenfrequency of the system to neglect resonance effects. Only small displacements from the equilibrium position of the nuclei are caused under this condition (in the following we will consider only the motion of nuclei and neglect electron motions). The effect of the field of the incident wave on polarizability is, therefore, reasonably well described by a Taylor expansion around the equilibrium position. The first tensor element of polarizability truncated at the first order reads.

*The factor 4n eohas to be used m this equation to be consistent with the dimension and magmtude of the polanzabdlty calculated from measurements m electrostatic units or m the GauB system, the dimension of ct = L 3

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485

The triple xr, YK, ZK represents the displacement of the K-nucleus from its equilibrium position. This displacement is a more or less complicated function of time. It is well known from classical dynamics that the motion of N centers of mass coupled by elastic forces can be represented as the superposition of harmonic oscillations in 3 N - 6 distinct directions ( 3 N - 5 directions for linear molecules). These directions are called the normal coordinates ~ / o f the system. Expressing the polarizability tensor in the normal coordinate one gets: o

-/~xx

\

The electric field/~ of equation (1) oscillates with the frequency vo of the incident wave and has in cartesian coordinates the three components: Ex = E o ex cos 2~ vo t;

Ey = E o ey cos 2n vo t;

Ez = E0 ez cos 27tVot.

(4)

Eo is the amplitude of the incident wave and ~ is a unit vector in the direction of the electrical field. Equations (3) and (4) introduced into equation (1) give the following expression for the x-component of the dipole: o e~ + ~txy 0 ey + %, o ez] cos2nvot Px = 4n 8o E o [~x~

+4ne°E°~ 1_\0¢,)o e~+ ~--~ )oe+, O / ~"~ \-~i ]o ] x ~o ~ [cos 2re(re + v~)t + cos 2~ (% - vl) t].

(5)

This equation shows that the incident wave induces a dipole moment which oscillates with the same frequency as the incident wave but also with the sum and difference frequencies Vo_ v~. The amplitude of the oscillation which has the same frequency as the incident wave is proportional to the equilibrium polarizability and the amplitude of the incident wave. The amplitudes of the frequency-shifted components are again proportional to the amplitude of the incident wave, but proportional to the derivative of the polarizability with respect to the direction of the normal coordinates. From classical electrodynamics it is known that an oscillating dipole emits electromagnetic radiation with the same frequency as the oscillation frequency of the dipole. From equation (5) it follows, therefore, that the scattering molecule radiates with the same frequency as the incident radiation, this is the elastically scattered light, but also with the frequencies vo + v,. This part of the scattered light is called Raman scattered light. The Raman effect is, as shown before, an inelastic scattering process, where the interaction of the incident field with the internal motion of the scattering molecule causes an energy transfer between the incident light field and the molecule, which results in the scattering of frequency shifted photons. In contrast to infrared radiation no permanent dipole moment is necessary for elastic or Raman scattering. The light flux d~b radiated into the space angle dt~ can also be calculated by using classical electrodynamics, giving [see Jackson (1975) or Corney (1977)]: d~

1 [- k 2 q 2

where Zo is the freespace impedance, Z0 = ~ , #o and 8o are the magnetic and electric field constants, respectively, k = 2#v/c is the magnitude of the wave vector, c the propagation velocity of the wave and fo is a unit vector into the direction of observation. By introducing the radiant flux density D = 1 /8 o iE o [2 into equation (6) we get: 2X/Uo p =_ 1 dq~ = k4l[fo x (~ox t~o ] 12,/~o = 4rr 8o E o = ~te D df~

(7)

486

G SCHWEIGER

where/50 is a normalized dipole moment: it has the same dimension as ~. For a hnear oscillator we can finally wrlte' l d4~ 12 D dr2 = k41p° sin 2 0,

(8)

where 0 is the angle between fo and /~o. This is the well-known characteristic dipole radiation. Its intensity is proportional to the fourth power of the frequency and proportional to the radiant flux density of the incident radiation. Its angular variation is given by sin 2 0. An examination of the state of polarization of the dipole radiation would show that the electrical field vector is always parallel to the direction of oscillation of the dipole, in other words, the dipole radlanon is completely polarized. The right hand side of equation (8) has the dimension of an area and is called the (molecular) dlfferennal scattering cross section. If the polarizability is rotationally symmetric, the total scattered intensity can be calculated easily. From equation (5) it follows that the dipole moment is gwen by:

~=4rCeo~Eo~[~cos2rCVot+~(~,)o~°COS2rt(Vo+V,)t 1.

(9)

For linearly polarized light the direction of ~ is fixed in space, and equation (8) can be applied to calculate the total scattered radiation per incident power density. For this purpose equation (8) has to be integrated over the space angle dD, which yields the factor 8n/3, The total scattered light per incident power density per molecule [which is also called total (molecular) scattering cross section a] is, therefore,

If the polarizability is not a scalar quantity, as for non-spherical molecules, this equation still holds qualitatively. It can be transformed into the correct equation if the scalar quantities are replaced by the appropriate components of the scattering tensor. The essence of the classical treatment of light scattering is given by equation (10). The classical treatment predicts the appearance of frequency shifted lines in the scattering spectrum correctly. The magnitude of frequency shift is also in agreement with experimental findings. Finally, Raman lines will only be generated if the derivatives of the polarizability tensor do not disappear. The classical treatment of the Raman process does not predict the intensities of the Raman lines correctly.

Intensities of Raman lines and the quantum mechanical concept Equation (10) was derived for one individual molecule. In a practical scattering situation a great number of molecules participate in the process. If interference effects cancel each other out, or if the scattering process is incoherent (as for the linear Raman effect), the total intensity scattered by N molecules is simply the product ~br = NtrD. From equation (10) it follows that the intensity raUo between a Stokes line (the Raman line shifted to lower frequencies) and the corresponding anti-Stokes line (the line shifted to higher frequencies) does not depend on temperature. This is in contradiction to experimental observations. Only a quantum mechanical treatment of Raman scattering predicts the intensities of Raman lines correctly. A detailed quantum mechanical treatment of Rayleigh and Raman scattering was given for the first time by Placzek (1934). In the quantum mechanical picture of emission or absorption of radiation the total intensity emitted from N molecules, due to the interaction with a radiation field of energy density p(vo), is given by:

qbn,,(v')=hv' Wn,np(vo)Nn..

(11)

The photon energy emitted per transition between the energy levels E,~E,, is hv', the probability for the transition per molecule per unit energy density and unit time is W.,, and

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487

n. is the fraction of molecules in the energy level En. The energy of the emitted (scattered) photon is related to the energy difference of the energy levels participating in the process by (h = Planck's constant): (12)

hv' = hv o + (E. - E=).

The energy of the emitted (scattered) photon hv' can be larger or smaller than the energy hvo of the incident photon. This depends on the sign of the difference E , - E=. A figurative representation of the Raman scattering process closely following the quantum mechanical picture of the process is shown in Fig. 1. A photon of the incident radiation is annihilated (virtually absorbed). Its energy pushes the molecule to a state indicated by a dashed line in Fig. 1. By definition this state is not an eigenfunction of the system, because we exclude absorption processes. The frequency of the incident radiation was assumed to be far from any absorption frequency. The molecule can, therefore, not really dwell in the energy levels marked by the dashed lines in Fig. 1. It avoids this uncomfortable situation by creation of a photon which brings the system back to an eigenstate. If this state is identical to the initial state the created photon has the same energy, and therefore the same frequency, as the incident annihilated photon. This is called elastic scattering of radiation. However, the creation of a photon can leave the system in an energy eigenstate above or below the initial state. In this case the created (inelastically scattered) photon has an energy lower or higher than the annihilated incident photon. The frequency of the created photon can be smaller ('Stokes' Raman scattering) or higher ('anti-Stokes' Raman scattering) than the frequency of the incident photon. If the creation of the photon is connected with a change of rotational energy, the corresponding Raman line is called rotational Raman line and, correspondingly, vibrational Raman lines are inter-related with changes in vibrational states. The scope of the quantum mechanical treatment is the calculation of the probability W~,.. A comparison of equation (11) with equation (10) shows that after replacing the radiation energy density p(v)=D(vo)/C that the transition probability can be written as: 16~2 W"m= 3h (ko+__lkn,nl)SGn,,(Vo).

(13)

The quantum mechanical calculation of Gm shows that in effect intermediate levels are involved in Raman transitions as shown in Fig. 1. Only if at least one transition from the initial to the intermediate state and from this to the final state occurs is Raman scattering

E ROTATIONAL RAHAN EFFEC_T _

/

I1-' IIANTI- I I / I II I ISTOKES-IY I

!t !f

VIBRATIONAL RAHAN EFFECT rSTOKES LINE ~ANTI-STOKES LINE

J;

J:o

V=l

i=it

= V=O J--=o

Fig. 1 Plctoral representation of the trans~tlon path in Raman scattering.

488

G SCHWEIGER

possible (allowed by the selection rules). This condition is known as the third common level rule, see e.g. Plaszek (! 934). For a harmonic oscillator--a good approximation for many molecules--the vibrational selection rule is strictly A V= + 1. For unharmonic oscillations 'over-tones' appear in the Raman spectrum due to the transitions AV= +2, + 3, A detailed discussion of selection rules for rotational transitions can be found in the textbooks cited above. In most cases A J = 0 , + 1, + 2 applies For linear molecules one can often assume that the total angular momentum is perpendicular to the 'molecular axis (A = 0), in this case AJ = 0, + 2 holds. The rotational bands are designated O, P, Q, R and S branches, if the rotational quantum number change is AJ = - 2, - 1, 0, + I, + 2, respectively The involvement of a thlrd common level in the transition matrix has not to be mlsmterpreted by considering the Raman transition as a real two-step process, first, a photon is absorbed and then re-emitted with a different energy. This is incorrect, because the probabilities for absorption or emission are proportional to the square of the transmon amplitudes in contrast to Raman scattering, where the transition matrix is built by products of transition amplitudes between different pairs of energy levels As a consequence, the transition probabilities and the selection rules for Raman scattering are quite different from those for absorption, fluorescence or infrared radiation. Finally, because Raman scattermg is a scattering process and not an absorption-emission process, it is much less sensitwe to the local environment of the scattering molecule (quenching effects can cause severe difficulties in fluorescence spectroscopy, for example). We go back to equation (11) and replace I4I,,. by equation (13), and assume that the occupation number n, can be described properly by Boltzmann statistics. From equation (11) it therefore follows that:

,.,.(v') O(Vo)

8re (k,)4 Gn,,,N 3

yne - E"/k r ~,g,e

-E'/kT

"

(14)

!

The quantity g. is the degeneracy of the level n. This equation shows that the intensity of a specific Raman line depends on temperature. The measurement of Raman line intensities offers the opportunity for local temperature measurement, by a technique very successfully applied in gas dynamics and combustion research (Ledermann and Sachs, 1984).

Summary of basic properties of Raman spectra (a) Frequency shift. In the foregoing paragraphs the relation between the Raman spectrum and the vibrational and rotational energy levels was outlined. One of the main fields of application of the Raman effect is indeed the revelation of molecular structures. Together with infrared spectroscopy Raman spectroscopy plays a crucial role in the determination of molecular structures. The other classical domain of Raman spectroscopy is the identification of molecules, in other words the analysis of the chemical composition of an unknown sample. Similar to the infrared spectrum the Raman spectrum represents a 'fingerprint' of the scattering molecule. The Raman spectra of a great number of chemical substances can be found in the literature. Several textbooks are available which contain collections of Raman spectra; examples are Schrader and Meier (1974, 1975, 1976), Brame and Graselli (1976, 1977), Graselli et al. (1981), Freeman (1974), Ross (1972) and Dolish et al. (1974). Raman spectra comprise of relatively few lines if the molecules are composed of only a few atoms (simple molecules), an example is shown in Fig. 2. The spectra become more and more complicated the larger the molecules are. In Fig. 3 the Raman spectra of diethylsebacate and dibutylphtalate are shown. The identification of the different chemical components in an unknown sample is certainly only possible as long as the characteristic lines of these components can be identified in the spectrum. This aspect of Raman scattering has been used very successfully in the last 15 years for the determination of the composition of gaseous me&a, even in such hostile environments as combustion processes. Lederman and Sacks (1984) recently gave a survey of the applications of Raman scattering to the flow field and combustion research.

Review of Raman scattering on single aerosol particles and on flowing aerosols

489

Nz

A

C02 ~

200

i lolt 2'Ioo

2ooo

~'oo

~ooo

RAMAN SHIFT (Eft11)

~-

Fig. 2. Raman spectrum of mr containing CO 2 and acetone vapor showing the most prominent lines.

(a)

50-

40-

DES

~_ 30o'I

,.=, 20I--

10O-

J i

17

18

19

WAVENUMBER (I03cm -I)

(b) ~

5o4O-

DBP

3o-

10O-

I 17

'

'

'

'

I

'

'

'

'

18

I

19

WAVENUMBER (103cn~1) Fig. 3. Raman spectrum of (a) DES (diethylsebacate) and (b) DBP (dibutylphtalate).

The application of this technique for the identification of molecular composition in gases at elevated densities, in liquids or solids is not as straightforward as for gases at moderate densities. The reason is the increasing importance of intermolecular forces, which effect the line shift, band shapes, or both. In effect, the Raman spectrum can be used to investigate

490

G SCHWEIGER

intermolecular forces as outlined by Srivastrava and Zaidi (1979). Due to these intermolecular forces a frequency shift is usually observed if the pressure is increased. Examples can be found in the article of Sherman and Wilkinson (1980). However, this effect is often small. An increase in pressure from 1 to 20 kbar shifts the frequency of the fundamental Raman band of diamond approximately by five wave numbers. Zerda et al. (1987) have recently investigated the density and temperature effect on the C - H v3 and C - O v3 stretching modes of liquid methanol. They found that in the density range from p =0.842 g cm -3 to p =0.886 g c m -3 the peak frequency shifts by approximately 5 cm-1 wave numbers. Zakin et al. (1986) made similar measurements on aqueous solutions of pyridine, which showed line shifts in the order of 10 c m - 1, depending on the vibrational mode m the pressure range from 0 to 30 kbar. Obviously the frequency shift depends strongly on the chemical substances under investigation. Not only pressure, but also phase changes can affect the Raman spectrum. The frequency shift observed in phase changes depends on the vibrational mode causing the Raman line and is usually accompamed by intensity changes. Green et al. (1985) recently measured the intensities and frequency shifts for chlorocyclopropane. The most prominent lines in the gas phase are: 3031 cm -1, 1204cm -1 and 880 cm -1. The corresponding lines in the liquid phase are 3018 cm-1, 1203 cm -~ and 874 cm- 1, and in the solid phase 3013 c m - 1, 1199 c m - 1 and 868 c m - 1. Line shifts due to phase changes can be found in the book by Ross (1972). (b) Intensities. The intensities of Raman lines depend on the number of molecules of a specific chemical component in the scattering volume and on temperature, as shown by equations (11) and (14). This relation holds for most gases at moderate pressure and has found wide-spread application in fluid dynamics and combustion research for the local determination of gas composition and temperature (as mentioned before). Examples of the dependence of Raman line intensities m gaseous samples are given in Figs 2, 4 and 5, and for a liquid mixture in Fig. 6. These measurements were carried out with the apparatus described in section 4. Deviations of equation (14) are found in liquid and solid samples. Two reasons for this can be identified, as pointed out by Schr6tter and K16ckner (1979). Due to the close neighbourhood of the surrounding molecules the local electromagnetic field is different to the external incident field. In equation (14) the local energy flux density D o has to be inserted, which can usually be expressed as a function of the refractive index of the medium and the energy flux density of the incident radiation.

16 1412-

g,

10-

8+ >I,-Z LIJ I,-Z

64.-

Z 'r

2-

e'e.

0

o

2

~

/,

8

~o

VOLUHE f.ONEENTRATION(%) " - - ~

Fig 4 Dependenceof the Raman mtensRyof acetone on the volume concentration m air

Review of Raman scattering on single aerosol particles and on flowing aerosols

(a) I

10

~

75

2sO19350

19400 WAVENUMBER (c.TI)

(b)

Z w I--

2"

z

1OC

O"

J

19350

WAVENUMBER( c ~

Fig 5. Rotational Raman band of C O 2 (a) at room temperature and (b) at T = 102°C.

___

z

DBP25%

16

I~

WAVENUMBER (on"I)

I

16

=

Fig. 6. Part of the Raman spectrum of a mlxture of DES and DBP at two different mixing ratios.

491

492

G SCHWEIGER

If the refractive index depends on concentration (composition) of the sample, the local field and, therefore, the intensities of the Raman lines also depend on concentration. The other source of a deviation of the line intensity from equation (14) is due to intermolecular forces. This effect depends on the chemical components in the sample. The effect is usually weak for nonpolar liquids. A quantitative prediction of this effect is difficult because it depends on the distribution and type of molecular neighbours, on the interaction strength between dissimilar neighbours and on the electronic properties (transition frequencies). Complexes are often formed especially in aqueous solution, which--in addition to the intensity change--also affect the band shape and line frequencies. The solvent effect is usually different for different Raman lines of the same solute. A number of research groups have investigated this effect. Fin] et al. (1968) have investigated the solvent effect for a number of hydrocarbons. The effect on the 459 cm- 1 mode of tetrachloride reproduced from this work is shown m Fig. 7. The solvent effect on the intensity of various Raman lines of carbon disulfide is displayed m Fig. 8. These measurements were made by Kroto and Teixeira-Dias (1972). Similar measurements for a variety of solute solvent combinations were made by Bahnick and Person (1968), Babich and Kondilenko (1968), Wall and Hornig (1967), Venkateswarlu and Jagatheesan (1963, 1964), Sidorov et al. (1965) and Rea (1960). (c) Bandwzdth and bandshape. Intermolecular forces often not only affect intensitiesband intensities can be enhanced or reduced due to the presence of other chemmal components--but also bandwidth. This can be seen from Fig. 9 which shows the linewidth of SO 2 dissolved in different liquids. Obviously the reduction of linewidth observed by Ouillon and Le Duff(1973) depends on the solvent. Similar observations were made for the linewldth of isopropanol in aqueous solution by Tanabe (1984). There are several mechanisms that can affect frequency, bandwidth and intensities by intermolecular forces, namely resonant transfer of vibrational energy and intermolecular coupling such as Fermi resonances, vibration-rotation interactions or coUisional displacement. The contrlbutzon of these effects increases with density, as already mentioned in connection with the effect on line shift. Zerda et al. (1987) have also investigated the density effect on the hnewidth of the C-O and C - H mode of liquid methanol. Not only intermolecular forces affect the intensity, shape and width of Raman bands, but also temperature. The intensity of the Raman lines depends [as we can see from equation (11)

T

1,/,*'

CC[4' 4'5° cm'l o

1,01

v c,~c~ &, ~HsBr

l

1,4

t'l CHICN & (CH~zCO V CHCtl

O C#~CH~

0,8

OCHBr)

0, 0

20

40

60

80

100

CCI~(%)

Fig. 7 Scattenngcoefficientsvs volumeconcentrationin vanous solvents. Reproduced from Fm~ et al. (1968).

Review of Raman scattering on single aerosol particles and on flowing aerosols

493

0,2S

c32s% 0.20

0.15100-000

2f0-11~0

0,10

o,os~ 02*0-000

Vol % CSzin ~Hlo Fig. 8 Plot of the intensities (relatwe to the 100-000 band) of vanous CS2 bands as a function of concentration in cyclopentane (from Kroto and Teixeira-Dias, 1972).

~

CS2

I

c ct,+.

v

CzHsOH

30-

<3

20

CoH6

~vl/2 (v~)

(cm-~)

Fig 9. Comparison of the width of the vI and v3 Raman line of SO 2 m different hqmds at room temperature (from Oufllon and Le Duff, 1973)

and (14)] on the occupation numbers and, therefore, on temperature. This can be clearly seen in Fig. 5; although the rotational band is recorded with such a high resolution that the individual rotational lines are resolved, the change of bandshape and width with temperature is obvious. The rotational structure of the Raman band of liquids cannot usually be resolved, but they can be affected by temperature. Zerda et al. (1987) have measured the temperature effect on the linewidth and peak frequency for liquid methanol and Walrafen et al. (1986) measured the shape of the O - H mode of water at different temperatures. The quantitative evaluation of Raman spectra is usually quite straightforward for gases, but can be complicated for liquids. For application of this technique to aerosol analysis this does not seem to be a disadvantage, because the different effects can be determined by Raman scattering on bulk materials.

494

G SCHWEIGER 3 THEORY OF RAMAN SCATTERING ON M I C R O P A R T I C L E S

Qualitatwe description

It is well known that the shape and size effect of particles in the field of electromagnetic radiation does not depend on the absolute dimensions of the particles, but on the ratio x = r~d/2, d is the particle diameter and x is called the size- or Mie-parameter. In the context of this paper we define microparticles as those having a Mie-parameter in the range of approximately 0.01
Fig. lO(a) Quahtauvepictureof the transm~ttexifieldm the ¢quatonalplane ofa mlcrospherc drawn by using the laws of geometricaloptics

Fig. lO(b). Qualitauve p~cture of the radlauon ermtted by a dipole located in the oquatonal plane of a mlcrosphere

Review of Raman scattering on single aerosol particles and on flowing aerosols

495

Certainly, the laws of geometrical optics cannot be applied in the size range under consideration. Nevertheless, the situation shown in Fig. 10, where geometrical optics are used, qualitatively reflects the real field distribution, as a comparison with Fig. 11 shows. The method of multipole expansion was used to calculate the local energy flux density of the transmitted field shown in Fig. 1l(a). To calculate the projection effect shown in Fig. 1l(b) a number of dipoles, all oscillating with the same amplitude, were uniformly distributed in the equatorial plane. Then the contribution of each dipole to a specific scattering direction was calculated. Figure l l(b) shows the results for back-scattering. It can be seen that the contribution of different dipoles to the back direction is quite different depending on the position. The emission of those dipoles being located in the high amplitude regime in Fig. 11(b) is focused predominantly into the back direction, in contrast to the radiation emitted from other positions. We see that the qualitative result found by simple arguments from geometric optics is confirmed by the eminating field by exact calculations. The angular distribution of Raman scattered light is a result of the superposition of the focusing effect and the projection effect. With this kept in mind, the interpretation of Fig. 12 is quite straightforward. Figure 12 shows the contribution of different regions of the equatorial plane to the Raman scattering into three different directions. In Fig. 12 (a) the projection effect does not enhance the region of the main maximum of the transmitted field, but that of the smaller second maximum. This explains the appearance of two areas from the region where light is emitted, preferentially in the forward direction (scattering angle 0-- 0°). Using similar arguments, the relatively complicated situation reproduced in Fig. 12(b) can be understood. Figure 12(c) shows that a relatively small region contributes predominantly to back-scattering. This becomes clear because for back-scattering the region where the transmitted field has its maximum (due to the focusing effect) coincides with the region from

a)

b)

Fig. ll(a) Transmitted field in the equatorial plane of a microsphere, Mie-parameter x=lO. Oa)Relative contribution of dipoles uniformly distributed in the equatonal plan to the emission in the negative z-direction (back scattering). All dipole moments oscillate with the same amplitude.

496

G SCHWEIGER

o) )ncldent beom scoffered beom

b)

c)

Fsg 12 Relatwecontributionof &fferentreg0onsin the equatorial plane to Raman scatteringinto (a) forwarddirection,scatteringangle 0 = 0, (b) by 90°, 0 = 90 and (c) into the backward&rectlon,0 = 180, Mie-parameterx = 10 (vertical scales not identical) where the outgoing radiation is emitted predominantly in the backward direction (scattering angle 0 = 180 °) caused by the projection effect. The results of the theoretical analysis of Raman scattering on microparticles reproduced in Figs 11 and 12 were calculated by Rambau and Schweiger (1988). The fact that different areas contribute very differently to scattered ra&ation can be helpful in reducing the computing time needed for a numerical calculation of Raman scattering. Quantitative description

The problem of a quantitative prediction of Raman scattering on microparticles was first attacked by Kerker et al. (1978). They applied the method of multipole expansion to calculate the incident and transmitted fields, and the Raman field reside the scattering particle and outside of it. The algorithm was first published by Chew, McNulty and Kerker (1976). A short time after that the method was extended to concentric spheres of different optical properties by Chew, Kerker and McNulty (1976). The first numerical results were published by Kerker et al. (1978) for incoherent scattering, and by Chew et al, (1978) for coherent scattering. Kerker and Druger (1979) extended the calculations to higher size parameters. Finally, the method was applied to non-spherical scatterers. Chew et al. (t980) investigated scattering on cylinders and Wang et a l. (1980) scattering on dielectric spheroids. A summary of the method of multipole expansion to calculate the radiation scattered inelastically on dielectric spheres was given by McNulty et al. (1980). In principal the contribution of each individual molecular dipole has to be calculated, a certainly hopeless task. In practice, the Raman intensity is calculated by considering only a

Reviewof Ramanscatteringon singleaerosolparticlesand on flowingaerosols

497

representative number of dipoles distributed randomly in the particle. The number of dipoles necessary for a correct prediction increases quickly with particle size. Calculations for spherical particles of size parameter 0t= 20 carded out ori a HP1000/900A computer at our institute consumed a total of approximately 100 h computing time. (The angular distribution of Raman scattering in one scattering plane was calculated at steps of 3°, the contributions of 2 x 104 dipoles were included in the calculation.) The development of a fast algorithm to calculate the Raman scattering in a more acceptable time is urgently needed. One possible concept which is presently investigated by Rambau and Schweiger (1988) is that only those regions contributing preferentially to scattering are calculated with a dense dipole distribution, whereas other regions are only taken into account with a low dipole density, or by global considerations. Multiple expansion is not the only method available to calculate the interaction of electromagnetic radiation with microparticles. Barber and Massoudi (1982) recently gave a review of some alternative methods. Purcell and Pennypacker (1973) described a method in which an arbitrarily shaped particle is divided into a number of identical elements arranged in a cubic lattice. Spherical dipole oscillators are placed into the subunits. The polarizabilities of these dipoles are related to the bulk dielectric constant. Each dipole is exposed to the incident radiation and the radiation of all other dipoles. The total scattered field at an external point is then the sum of the dipole fields. This method was used by Singham and Salzmann (1986) for the evaluation of the scattering matrix of an arbitrarily shaped particle. A reformulation of this concept was recently given by Singham and Bohren (1987), which permits physical interpretation of observables and provides a rational basis for making computations more efficient. Although, to the author's knowledge none of these.methods has been applied to calculate Raman scattered light up to now, there seem to be no principal obstacles to adapt one or the other of these methods to Raman scattering.

Morphology-dependant resonance effects One peculiarity of the scattering process on microparticles has attracted considerable interest, especially in recent years. This is the appearance of so-called structural or morphology dependent resonances (MDR). At specific size parameters the elastically, or inelastically, scattered light shows a sharp increase in magnitude. The physical reason for this resonance effect is that the microparticle can be considered as an optical cavity. If the incident light wave coincides with an eigenmode the incident wave is coupled effectively to this eigenmode. The amplitude of this eigenmode is considerably enhanced compared to non-resonant excitation and the radiation of this eigenmode contributes preferentially to the scattering process. Mathematically the resonances are caused because at specific (but complex) arguments the denominator of one of the expansion coefficients becomes zero. The expansion coefficient has a pole. As this is only the case for complex arguments one speaks of virtual eigenmodes. For real frequencies the denominator cannot become exactly zero, however it becomes small enough for the corresponding expansion coefficient to increase drastically. The denominator has an infinite number of zeros, but most of these resonances are either so broad or so narrow that their contribution is negligible. Some, however, are observable, and to distinguish between the various poles for a given coefficient an additional index has to be used. The present understanding of resonance phenomena in the interaction between light and microparticles was recently reviewed by Hill and Benner (1988). Although most of the theoretical and experimental work on structural resonances was done on elastic scattering, most of these results also hold true for inelastic scattering. The reason is that the denominator for the expansion coefficients of the transmitted field, the elastically scattered and the Raman field, are all the same. 'Double' resonances are also possible. A double resonance is a resonance in the transmitted field and simultaneously in the Raman field, Schweiger (1990a). If a resonance of the transmitted field is excited by an appropriate wavelength, a resonance in the Raman spectrum is very probably present simultaneously,

498

G SCHWEIGER

because the Raman spectrum usually covers a certain wavelength range so that one or several Raman frequencies fulfil the resonance condition. Owen et al. (1982) discussed the excitation of resonances for elastic, fluorescence and Raman scattering on m]cropartzcles and glass fibers with diameters in the micrometer range. Examples of resonance peaks observed in the fluorescence spectrum em]tted from a 6/zm diameter fiber, a dye-coated fiber (d=9.8/lm) and in the Raman spectrum of a 10.1 #m glass fiber are shown. The excitation of resonances sensitivity depends on the size parameter. The determinauon of the size parameter at which resonances are observed is, therefore, a very accurate method to determine the size of individual particles. Hill et al. (1985) have demonstrated this for elastically scattered light, and Tzeng et al. (1984) used the morphology dependent peaks m fluorescence light to accurately determine the szze of evaporating micropartlcles. The excitation of input or output resonances causes peaks in the Raman spectrum of microparticles not present in bulk material, see Fig. 15. The mterpretation of Raman spectrum of spherical or spheroidal particles is complicated by these MDR peaks. Careful provisions have to be made to not misinterpret resonance as 'true' Raman lines,

4. A P P L I C A T I O N OF RAMAN S C A T T E R I N G M i c r o R a m a n spectroscopy

The basic idea to analyze the molecular composition of microparticles is verified in micro Raman spectroscopy by focusing a laser beam to the particle of interest, which is deposited on an appropriate substrate. The scattered light is collected by a high quality, high aperture objective, e.g. a microscope objective and imaged onto the entrance slit of a monochromator. The application of this concept to analyse microparticles was first reported by Rosasco et al. (1974, 1975) from the National Bureau of Standards in Washington D.C. The idea that analysis of fgram samples should be possible has been discussed by Hirschfeld (1973). The experimental set-up used by Rosasco et al. (1975) is sketched in Fig. 13. One early recognized problem of this technique is particle heating. As the particle remains in the laser beam during the whole period of recording the Raman spectrum, very small absorption coefficients can cause severe particle heating. The concept to eliminate or reduce this problem is the use of a material that acts as an effective heat sink and to reduce the laser power to the lowest acceptable level.

~90° mlrllmum dewahonprtsm ~beom sphffer microscope OCulor

~

m~croscopeobjechvefor /beam f~usl~ and samplev,~wt~ ) elhl~oldolcollechonmirror

Fig 13 The experimentalset-up for mlcro-Ramanspectroscopyused by Rosasco,Etz and Casatt (1975)

Reviewof Raman scattering on single aerosol particles and on flowingaerosols

499

(NH4

so4 v3 III

v1

v~ Ill

v2 I 1

1000

WAVENUMBER Icn~11 Fig. 14. Raman Microprobe spectra of sulfate speciesin liqmd and sohd micropartlcles. Top figure: spectrum of microdroplet (~ 30/~m diameter); center figure: spectrum of an ~ 8 ~ particle of crystalline ammonium sulfate; and bottom figure: spectrum of an ~ 5/~m particle of anhydrite (from Etz et al., 1979).

In a series of publications the potential of this technique was demonstrated and improved by the NBS group (Rosasco and Etz, 1977; Etz et al., 1978; Blaha et al., 1978; Cunningham et al., 1979; Blaha et al., 1979). An overview given by Etz (1979) shows the potential of this technique for analysis of organic (pyrene, phenanthrene) and inorganic [(NH4)2, SO4, CaSO4] solid particles as well as of liquid particles (H2SO4). An example is shown in Fig. 14. Approximately simultaneously with the work at NBS in Washington a slightly different experimental technique for similar applications was developed by Delhaye and Dhamelincourt (1975) at the University of Lille, France. In this technique the photomultiplier was replaced by an image intensifier and a solid state camera. By scanning the laser beam and by use of the camera a larger area of the sample could be analyzed. This technique may be well suited for the analysis of samples on filters. Both techniques were described in detail by Rosasco (1980), and examples of the application of the micro Raman techniques in a variety of different fields are given in this article. The time required to record a Raman spectrum can be appreciably reduced by a multichannel detector. Delhaye et al. (1982) showed that the time required to record part of the Raman spectrum of aspirin could be reduced by a factor of 150 by replacing the PM by a detector array. Comparison between these two recording techniques was also made by Steinbach et al. (1982). They reported a reduction of the required recording time by a factor of 20. The concept of micro Raman spectroscopy (Raman Microprobe) led to the development of a powerful technique for the non-destructive analysis of very minute samples. In a number of investigations the usefulness of this technique to investigate the composition of aerosol particles was demonstrated, see for e.g. Blaha et al. (1978), Cunningham et al. (1979) or Blaha et al. (1979). The technique proved to be so successful that commercial instruments are now on the market. Micro Raman spectroscopy is not an in situ technique, aerosol particles have to be collected by an appropriate probe before they can be analyzed. As a consequence all well known problems connected with extraction of a sample by a mechanical probe

500

G

SCHWE1GFR

(probe-aerosol interaction, evaporation, condensation, reactions after extraction of the particles from the aerosol system) remain.

Raman spectroscopy of single particles This section deals with the analysis of single aerosol particles which are not deposited on any substrate, but remain totally surrounded by the carrier gas. Three techniques are presently in use: optical trapping, electrodynamical trapping and generation of a chain of nearly identical particles moving through the test region. In the first two methods (trapping of single particles) the scattering process is observed on a single individual particle. The most severe limitation of this technique is particle heating by absorption of the laser beam. In the case of electrodynamic trapping the particles have to be charged. In the third technique the particle moves through the laser beam. It stays there only for fractions of a second, depending on its velocity; particle heating is, in this case, of minor importance, but the droplets have to be generated with a very high reproducibility. (a) Optically levitated particles. A very suitable concept for Raman scattering experiments on single isolated microparticles is their trapping by light pressure. This technique was pioneered by Ashkin (1970) and Ashkin and Dziedzic (1971, 1975). A quantitative description of this phenomenon was given by Roosen (1979) and Jin Seung Kim and Sang Soo Lee (1982, 1983). By this method a microparticle is suspended freely in a focused vertical laser beam. The particle takes a stable position in the beam at the location where the radiation pressure in the divergent beam is balanced by the gravitational force. The radial stability, perpendicular to the beam axis, of this light pressure trap is provided by the radial gradient in the laser light flux, which results in a force pushing the particle towards the beam axis. Particles in the size range from 1 to 40 #m can be handled easily by this technique. Thurn and Kiefer (1984a) recorded the Raman spectra of glass spheres in the size range of 30 #m stably suspended by this light pressure trapping technique. These spectra showed a characteristic regular ripple structure superimposed on the spectrum recorded on bulk material. In a subsequent publication these ripples were interpreted as structural resonances m the Raman field (Thurn and Kiefer, 1984b). The appearance of resonance peaks depends on the shape of the scattering particles. Minute deviation from a spherical (or spheroidal) shape can reduce or suppress the resonance peaks in the spectrum. These resonances are, therefore, better observed on liquid particles, which have shapes very close to ideal spheres, Thurn and Kiefer (1985). Schweiger (1990b) observed peaks in the Raman spectrum of dibutyl phthalate particles using the technique of optical levitation. An example is shown in Fig. 15. These peaks can be interpreted as input resonances (resonances in the transmitted field). The size of the slowly evaporating DBP particles matches, from time to time, exactly the resonance conditions for the transmitted field. This causes an increase in the amplitude of the electromagnetic radiatmn within the particle, and the scattered Raman intensity increases too. The evaporation process, however, causes a continuous size change and the increase of the transmitted field is only transient The technique of trapping a particle by radiation pressure was also applied by Lettieri and Preston (1985), to record the Raman spectrum of 10-35/~m droplets of dioctyl phthalate. Spectra were recorded at different times on droplets growing by condensation. In addition to the Raman spectra white light scattering was also recorded in the same frequency range as the Raman spectra. Both measurements showed resonance peaks having a frequency shift if the particle size changed. The Raman spectra showed more resonance peaks than the white light spectrum in the same frequency region. (b) Electrodynamically levitated particles. An alternative, and very usefiJl, technique to suspend micropartictes freely is dectrodynamic levitation (EDL). Since the first applications of the idea to suspend microdroplets by electrical forces were done by Millikan in his famous experiments, the most important progress was decoupling of the vertical electrostatic force to compensate gravity from those electrical forces that stabilize the particle horizontally. This horizontal stabilization is achieved by generation of an inhomogeneous a.c. electrical

Reviewof Raman scatteringon singleaerosol particles and on flowingaerosols

l

1800

~

lZ.OO >-

501

m~crop~ce i

1000

I I /butkmoferlol.

Vl Z

600 2(~I

i

160( 120(

.E v

800

Z w m

L_

tOO

18~

2c]00

3000

31'00

RAMAN SHIFT (cm -I)

3200

Fig. 15. The upper figureshows part of the Raman spectrum recorded from a slowlyevaporating DBP particle.~~ 15/an. Alsodisplayedis the samepart of the spectrumrecordedfromscatteringon bulk material. The lower trace showsthe differencebetweenthe particle and bulk spectrum. field between the top and an annular electrode, and between the annular electrode, and the bottom electrode. A d.c. voltage between the top and bottom electrode causes a vertical electrical field. The Coulombic forces acting on the charged particle of this field compensate the gravitational force. The electrodes are shaped in such way that the applied time varying voltages cause an electric field the strength of which has a minimum in the center of the equipment. It is sometimes called electrodynamical balance, because the d.c. voltage applied between the top and bottom electrode, which pulls the particle into the center of the device, is proportional to the weight of the particle. The most popular version of EDL apparatus uses hyperbolically shaped bottom and top, electrodes while the center electrode is a torus with a hyperbolic cross section. This configuration was proposed by Wuerker et al. (1959). Straubel (1955) has demonstrated the trapping of charged particles in the field generated between a ring, or parallel wire, and the surroundings. Paul and Raether (1953) proposed a linear version of the EDL and discussed its performance. They also tested apparatus consisting of four rod-like electrodes. Their main interest was the investigation of the performance of electrically charged filters. Some variants of this concept were developed. Arnold and Folan (1987) have constructed a device they call 'Spherical Void Electrodynamic Levitator' by shaping the top and bottom electrode in the form of a spherical cap. The central electrode is built in such a way that a spherical void is formed by the three electrodes. The electrodynamic trap, especially the hyperbolic type, became increasingly popular for light scattering experiments. Elastic light scattering experiments using this device were performed, for example, by Ray et al. (1988), Richardsbn, Hightower and Pigg (1986) and

502

G. SCHWEIGER

Richardson et al. (1986). A detailed description of the EDL and further examples of apphcation can be found in the article of Arnold (1988). The techmque was also used for fluorescence studies. Further information on this application are given by Campillo and Lm (1988) Recently the EDL techmque was also applied to Raman scattering. Hang Fung and Tang (1989a) report the Raman spectra of electrodynamlcally suspended ammonium sulfate and sodium nitrate solution droplets. They were able to distinguish between dry sodium mtrate and the same particle after transformation into a solution droplet by the difference in frequency shift for sohd sodium nitrate (Av = 1066 cm- ~) and the free ion m solution (Av = 1050 cm- 1). In addition, the Raman spectrum of the liquid droplet shows features which are probably caused by structural resonances. In the same paper the Raman spectrum of a particle composed of a mixture of NaNO 3 and (NH4)2SO 4 is shown. Measurements were also made on ammonion bisulfate droplets by the same author, Fung N. H. and Tang, I. N. (1988) and very recently Tang and Fung (1989) analysed the composition of particles containing sulfates and nitrate by Raman scattering. (c) Particle chams. In thin technique a commercial vibrating orifice generator was modified to produce a chain of nearly identical droplets, Tzeng et al. (1984). The droplets travel through the scattering volume with a typical velocity of a few meters per second. A number of different experiments was performed by this technique including Raman experiments. Stimulated Raman scattering from individual water and ethanol droplets was observed by Snow et al. (1985). An example of this measurements is reproduced in Fig. 16. It shows the stimulated Raman spectrum of H20 and D20 together with those from bulk materials. Due to the nonhnear nature of stimulated Raman scattering the Raman lines only appear at the morphology dependent resonance frequencies. The effect of these resonances on the line shape of stimulated Raman scattering was demonstrated by Qian and Chang (1986a). Finally, the appearance of multi-order Stokes lines in the stimulated Raman spectrum could be shown by Qian and Chang (1986b) by observation of the spectrum of the second-harmonic output (0.532/~m) from a Q-switched Nd-doped YAG-laser scattered on CC14 droplets QI H20

~tk

s .o "AtLLd.. ._,tOUUULL, bl

----

020

RAHAN SHIFT

(cm-1)

Fig. 16. The cw-spontaneousRaman scattenngfrom bulk H 2 0 and D 2 0 m a cuvctt¢ Is shown m the upper trace. The lower spectrum is due to stimulated Raman scattering on microdroplcts ( from

Snow et al., 1985)

Review of Raman scattering on single aerosol particles and on flowing aerosols

503

Not only could stimulated Raman scattering be observed on microparticles, but also other nonlinear effects. Gustafson and Byer (1984) observed coherent anti-Stokes Raman scattering on 60 #m diameter glass spheres filled with deuterium gas. One could consider these experiments as CARS experiments on a layered mieroparticle. Qian et al. (1985) observed coherent Raman mixing and coherent anti-Stokes Raman scattering from micrometer-sized droplets of ethanol and of water. Whereas the spectral lines from coherent Raman mixing and stimulated Raman scattering were observed only at the morphology dependent resonance frequencies, the CARS spectra showed no morphology dependent peaks. Calculation of the angular variation of CARS intensities from benzene droplets in the Mie-size range were performed by Cooney and Cross (1982). The observation of nonlinear effects, despite the very small droplet volume, is possible mainly because the droplet acts as an optical resonator and a wave, especially under resonance conditions, and can travel many times through (or along the surface of) the droplet before it leaves the droplet. Recently Eickmanns et al. (1987) have reviewed the use of nonlinear optical emissions, e.g. lasing and stimulated Raman scattering (SRS), to provide a nearly instantaneous in situ, non-intrusive technique for obtaining chemical and morphological information on a single droplet moving freely in air. The authors were able to record stimulated Raman spectra on aqueous solutions of K N O 3 and (NH4)zSO4. The Raman resonances were observed at frequencies within the Raman band and at morphology dependent resonances (MDR). The separation of MDR's were, therefore, used to determine the droplet size, which was found to be 2a-~ 90 #m. The relation between the amplitude of the observed stimulated Raman peaks and the concentration is relatively complex, because it depends on the concentration and a convolution of the Raman band profile and the feed-back of the MDR's. Raman spectroscopy of flowing aerosols

Micro Raman spectroscopy has been proven to be a very powerful method for analysis of micro-sized particles. However, to be applied to aerosol analysis the particles have to be collected and removed from the aerosol system by an appropriate device. This technique can, therefore, not be considered as an in situ method in aerosol research. Single particle trapping or generation of particle chains was the method preferentially chosen to study basic phenomena associated with the interaction of light and microparticles. Raman scattering on flowing aerosols was the concept used by Schweiger (1987) to investigate the potential of Raman scattering as an in situ method to study transport processes between particle and gas phase in aerosols. Benner et al. (1979) have already recorded part of the Raman spectra of COMPUTER

COUNTER \

ANPLIF~R IL OISCRININATOR/

CONTROLER PHOTOHULTIPLIER HOUSIN6

Fig. 17. Expcnmental set-up for Raman scattering on flowing aerosols used by Schwelger (1987).

504

G SCHWEIGER ~~ROSOL

ABSORBERA ~.~GENERATOR 1 (itl v~a,la.E ill /Z. ",4iD.-..--.,.~..~lP"~r%~ I"-'1

if/ 'l 1

MIRROR~, ~~MI~R TOBLOWER Fig 18 Aerosolgeneration and light path for the measurement of the angular dependent Raman scattenng on flowingaerosols(detail of Fig. 17).

(NH4)2SO 4 aerosol particles by blowing an aerosol containing these particles through the scattering volume of a multipass cell. An Ar-ion laser was used together with a single monochromator and a SCT vidicon. However, the spectrum was spoilt by a high fluorescence background. The experimental set-up used by Schweiger (1987) is shown in Fig. 17. Details of the aerosol generating system and the optical system to collect the Raman scattered light are given in Fig. 18. One of the problems associated with quantitative analysis of molecular composition is the effect of boundary conditions. The effect of particle size and shape was discussed in section 3. One approach to circumvent this effect proposed by Schweiger (1987) is to factorize the scattered intensity into a composition dependent part, which we designate by R(2o, 2i, ci) and a size dependent part P(n, 20, 2i, eo, x). The composition dependent factor R depends on the wavelength 20 of the incident wave, on 2, the wavelength of the Raman scattered light and the molecular composition c,. The size factor P is not only a function of the Mie-parameter x, but also depends on me wavelength of Raman scattering 2, the index of refraction n and scattering geometry (scattering and aperture angle). The composition dependent part R is identical with the bulk Raman spectrum. The average number of photons (ns) scattered per unit sample time can, therefore, be expressed as follows:

(n~(:.)>

--=C'Tr(2)R(2 Io P= l'lo

o, 2,, c,)P(n, 2,, ~o, t)o, x)

(15a)

p(n, 2,, eo, x)x3f(x)dx d~.

(15b)

x = 0

The power density of the incident beam is given by I., T~(2) is the wavelength dependent transmission of the experimental set-up, and ~o is a unit vector, which defines the scattering geometry (the angle between incident beam and the optical axis of the objective which collects the scattered light).The quantity p is the morphology dependent part of the differential scattering cross section, f(x) is the particle size frequency function and f~o is the aperture angle of the scattered light defined by the objective lens and its distance from the scattering volume. The size factor P can be considered to be independent from the molecular composition as long as the effect of molecular composition on the refractive index n is small. The dependence of R on composition can be determined from Raman scattering on bulk

Review of Raman scattering on single aerosol particles and on flowing aerosols

505

material. For a quantitative determination of the molecular composition of the aerosol particles the size factor P must be known in the wavelength interval 2o _<2 _ 2i (or at the specific wavelength) where the Raman spectrum is actually recorded. This factor can be calculated in principal as outlined in section 3. The calculation is complicated and time consuming. In some cases it may be easier to determine this function experimentally by Raman scattering on aerosol particles with a known index of refraction and known size parameter x. Once P has been measured for a range of refractive indices and size parameters, the calculation of P using the experimental results should not be too complicated. Obviously the particle size frequency function f(x) has to be known (determined for example by elastic scattering). If the wavelength interval of the Raman lines recorded is small, and if the refractive indices of the different chemical components are nearly the same, the size factor P can be considered to be constant for a given particle size distribution. Under these conditions the molecular composition of the aerosol particles can be determined without knowing P. This was demonstrated by Schweiger (1987) by scattering experiments on particles containing DES (diethyl sebacate) and DBP (dibutylphtalate) at different mixing ratios. Figure 19 shows examples of Raman spectra recorded from scattering on aerosols with different chemical particle composition. A comparison between the particle composition determined by Raman scattering and the actual concentration adjusted by appropriate mixing of the DES:DBP solution fed to the aerosol generator is shown in Fig. 20 [ Figs 17 to 20 are quoted from Schweiger (1987)]. The Raman spectra recorded on flowing aerosols not only contain information on the molecular composition but also on the number concentration, size distribution and even on the degree of homogeneity (degree of mixedness) of the particles, as was recently shown by Schweiger (1990b). The second normalized moment of the scattered light can be written as: (P)

2 = 14 --

a2

(16a)

(N)

fxfn[x3p(n,&,g, eo,x)]Zf(x)dxd az ="

p2

(16b)

The second moment can be easily determined by calculating the normalized factorial moment of the photocounts. Such a measurement can be used to determine either the number ( N ) of particles traversing the scattering volume in the mean during the sample time or, if ( N ) is known, to determine the second moment of the size distribution t7z. In contrast to the analysis of elastically scattered light the mean particle number ( N ) , or the calculated moments of the size distribution, are substance specific. One can determine, for example, the number concentration of those particles containing a specific chemical component. 1.0

o

/

~9 i3 1"I i,1 il DES.DBP MIXING RATIO

Fig. 19. Companson of the DBP concentration determined by Raman spectroscopy w,th the adjusted concentration in the hqmd from which the aerosol is generated.

506

G SCHWEIGER .lm

J SO

J 16300

16400

OBP 25%

~SO0

WAVENUMBER(crn"1)

16600

=-

Fig. 20. Raman spectra for differentDBP DES mixturesrecorded from the aerosol

5. C O N C L U S I O N f Raman spectroscopy appears to be a technique enabling analysis of aerosol particles with a great potential as yet widely uninvestigated. However, a number of difficulties and complications can already be identified. A problem inherent in the use of Raman spectroscopy for a quantitative determination, independent of its application to particles or bulk material, is the effect of intermolecular forces on the intensity, shape and frequency of the Raman bands. Although a number of investigations were carried out in the past, the only conclusion which can definitely be drawn is that in some liquid mixtures these effects are important and in others, especially non-polar solutions, the intermolecular effects are small. This may pose a severe limitation on the application of Raman spectroscopy to the analysis of mixtures of unknown composition. If only the concentrations are unknown, but not the chemical components, these effects can be studied on bulk material and then the results can help to interpret the intensity measurements correctly. On the other hand, the intermolecular effects, which often depend on the state of aggregation may be helpful to discriminate between Raman scattering from the vapor phase and from the liquid or solid state of the same chemical component. This may be important in evaporating or nucleating aerosols. Raman scattering on aerosols shows some peculiarities unknown in Raman scattering on bulk material, such as size effects on intensity, angular variation of the scattered intensity and resonance effects. Resonance peaks may be confused with ordinary Raman lines. However, resonance effects have not been observed up to now in scattering experiments on flowing aerosols because the particle size varies from particle to particle, and usually many particles contribute to the Raman signal. In addition, from theoretical consideration as well as from experimental evidence one would expect that structural resonances can be identified relatively easily, due to their quasi periodic character. Another complication only present in Raman scattering on particles is probably more inconvenient than the possible resonance effects. This is the dependence of the intensity of scattered light on the particle size. This may cause problems even if only relative concentrations have to be determined, because the size effect on intensity depends on the wavelength. In general, a quantitative evaluation of the Raman spectra is only possible if the size effect as a function of the wavelength and if the particle size is known.

Review of Raman scattering on single aerosol particles and on flowing aerosols

507

It is only a matter of speculation how important size effects may be if scattering experiments are carried out on flowing aerosols having a broad size distribution. The effect of the aperture angle on the size dependence of the scattered intensity is also unknown. One would expect some kind of smoothing so that the size dependence is reduced if the aperture angle is increased. The experimental techniques, especially for Raman scattering on flowing aerosols, which is the method of choice if particle heating might be critical, are far from being very sophisticated. The experiments made up to now were 90 ° scattering experiments. Theoretical analysis shows that backward scattering would probably give better signal to noise ratios. Furthermore, no experiments are known where Raman scattering from the vapor phase could be separated from Raman scattering on the particle phase, although several concepts seem to be promising for this purpose. As a final remark, to the author's judgement, it has to be pointed out that Raman scattering for aerosol analyses offers a whole bunch of possible applications, but many obstacles to its successful use are also visible. At present it is unknown whether the opportunities will surpass the obstacles, or vice versa.

REFERENCES Anderson, A. (Editor) (1971) The Raman Effect, Vol. 1 Princzples. Marcel Dekker, New York. Anderson, A. (Editor) (1973) The Raman Effect, Vol. 2 Applicatwns Marcel Dekker, New York. Arnold, S. and Folan, L. M. (1987) A Spherical void electrodynamic levitator. Rev. Scwnt. Instrum. 5g, 1732-1735. Arnold, S. (1988) Spectroscopy of single levitated micron sized particles. In Optical Effects Associated with Small Particles (Edited by Barber, P. W. and Chang, R. K.), pp. 65-131. World Scientific, Singapore. Ashkm, A. (1970) Acceleration and trapping of particles by radiation pressure. Phys. Rev. Lett. 24, 156-159. Ashkin, A. and Dziedzlc, J M. (1971) Optical levitation by radlaUon pressure. Appl. Phys. Lett. 19, 283-285. Ashkm, A. and Dziedzic, J. M. (1975) Optical levitation of hqmd drops by radiation pressure Science 187, 1073-1075 Babich, I. L. and Kondilenko, I. I. (1968) On the concentration dependence of Raman line intensities. Opt. Spectrosc 726-729 Bahmck, D. A. and Person, W. B. (1968) Raman intensity stu&es on CC14 m various systems. J. chem. Phys 48, 1251-1261. Barber, P. W. and Massoudl, H. (1982) Recent advances in hght scattering calculations for nonspherical particles. Aerosol Sci Technol. 1, 303-315. Bonnet, R. E., Dornhaus, R., Long, M. B and Chang, R. K. (1979) Inelastic hght scattenng from a distnbution of microparticles. In Microbeam Analysts (Edited by Newbury, D. E.), pp. 191-194 San Francisco Press, San Francisco. Blaha, J. J., Rosasco, G. J. and Etz, E. S. (1978) Raman microprobe characterization of residual carbonaceous matenal associated with urban airborne particulates. Appl Spectrosc -~2°292-297 Blaha, J. J., Etz, E. S. and Cunningham, W. C. (1979) Molecular analysis of macroscopic samples with a Raman Microprobe: Applications to particle characterization. Scanning Electron Microscopy. I. Sem. Inc. AMF O'Hare, pp. 93-101. Brame, G. E. and Graselli, J. G. (Editor) (1976, 1977) Infrared and Raman Spectroscopy, Part A, B, C. Marcel Dckker, New York. Brandmiiller, J. and Moser, H. (1962) Einfiihrung in die Raman-spektroskople, Dr. Dietrich Steinkopf. Campfllo, A. J. and Lm, H. B. (1988) Absorption and fluorescence spectroscopy of aerosols. In Optical Effects Associated with Small Particles (E&ted by Barber, P. W. and Chang, R K.), pp. 141-199 World Soentiflc, Singapore. Chew, H., McNulty, P. J. and Kerker, M. (1976) Model for Raman and fluorescent scattering by molecules embedded m small particles. Phys. Rev. AI3, 316-404 Chew, H., Kerker, M. and McNuity, P. J. (1976) Raman and fluorescent scattering by molecules embedded m concentric spheres J. Opt. Soc. Am. 66, 440-444. Chew, H., Sculley, M., Kerker, M., McNulty, P. J. and Cooke, D. D. (1978) Raman and fluorescent scattering by molecules embedded m small particles" results for coherent optical processes. J Opt. Soc. Am 68, 1686-1689. Chew, H., Cooke, D. D. and Kerker, M. (1980) Raman and fluorescent scattenng by molecules embedded m dielectric cylinders. Appl. Opt. 19, 44-52. Cooney, J and Gross, A. (1982) Coherent Anti-Stokes Raman scattenng by droplets m the Mle size range Opt. Lett. 7, 218-220. Corney, A. (1977) Atomic and Laser Spectroscopy. Clarendon Press, Oxford. Cunnmgham, W. C., Etz, E. S. and Zoller, W. H. (1979) Raman microprobe characterization of South Pole aerosol. In Microbeam Analysis (Edited by Newbury, D. E.), pp. 148-154 San Fconcisco Press, San Francisco. Delhaye, M. and Dhamehncourt, P (1975) Raman microprobe and microscope with laser excltatmn. J Raman Spectrosc. 3, 33-43. Deihaye, M., Bridoux, M., Dhamehncourt, P., Barbillat, J., Da Sdva, E. and Roussel, B (1982) A new generation of laser Raman microspectrometers: mlcromars. In M~crobeam Analysts (edited by Heinrlch, K. F. J.), pp. 275-278. San Francisco Press, San Francisco.

508

G SCHWEIGER

Dohsh, F. R, Fately, W G and Bentley, F F (1974) Characteristic Raman Frequencies of Orgamc Compounds J Wiley and Sons, New York Elckmans, J H, Qlan, S X. and Chang, R V. (1987) Detection of water droplet size and anion species by nonlinear optical scattering Part Charact 4, 85-89 Etz, E S, Rosasco, G J and Blaha, J J. (1978) Observation of the Raman effect from small, single particles its use m the chemical identification of airborne particulates In Environmental Pollutants, Detectmn and Measurement (Edited by Torlbara, T Y, Coleman, J R, Daneke, B. E. and Feldman, I.), pp 413-456 Plenum Press, New York Etz, E S (1979) Raman Microprobe analysis' pnnclples and applications Scanning Electron Microscopy I Sem Inc AMF O'Hare, pp. 67-92 Finl, G , Mirone, P and Patella, P (1968) Solvent effects on Raman band intensities J Molec Spectros~ 28, 144-160 Freeman, S K 0974) Applications of Laser Raman Spectroscopy. J. Wiley and Sons, New York Fung, K H and Tang, I. N (1988) Raman spectra of singly suspended supersaturated amonmm bisulfate droplets Chem phys Lett 147, 509-513 Fung, K H and Tang, I. N (1989a) Composition analysis of suspended aerosol particles by Raman spectroscopy sulfates and nitrates J Colloid Interface Scl 130, 219-224 Graselll, J G , Snavely, M K and Bulkin, B J (1981) Chemical Appl,catmns of Raman Spectroscopy. J Wiley and Sons, New York Green, P M , Wurrey, C and Kaslnsky, V. F (1985) Vibrational spectra of chlorocyclopropane J Raman Spectrosc. 16, 177-184 Gustafson, E K and Byer. R L (1984) Coherent anti-Stokes Raman scattering from small volumes Opt Lett 9, 220-222 Hang Fung, K and Tang, I. N. (1988) Raman scattenng from single solution droplets Appl. Opt 27, 206-208 Herzberg, G (1945) Molecular Spectra and Molecular Structure Vol II, Infrared and Raman Spectra of Polyatomw Molecules Van Nostrand Reinhold Corp., New York Herzberg, G (1950) Molecular Spectra and Molecular Structure Vol I, Spectra of Dlatomlc Molecules. Van Nostrand Reinhold Corp, New York Hill, S C, Rushforth, C K, Benner, R E and Conwetl, P. R (1985) Sizing dielectric spheres and cyhnders by aligning measured and computed resonance locations' algorithm for multiple orders. Appl. Opt. 24, 2380-2390. Hill, S. C and Benner, R. E (1988) Morphology-dependent resonances. In Optical Effects Associated with Small Particles (E&ted by Barber, P. W. and Chang, R. K.). World Scientific, Singapore. Hlrschfeld, T. (1973) Raman microprobe' wbratlonal spectroscopy m femtogram range. J Opt Soc Am. 63, 476 Jackson, J. D (1975) Classical Electrodynam~cs. L Wiley and Sons, New York Jm Seung Klm and Sang See Lee (1982) Radiation pressure on a dielectric sphere in a Gaussmn laser beam. Opt Acta 29, 801-806 Jln Seung Kim and Sang See Lee (1983) Scattenng of laser beams and the optical potential well for a homogeneous sphere J Opt Soc Am 73, 303-312 Kerker, M, McNulty, P J, Sculley, M, Chew, H., Cooke, D. D (1978) Raman and fluorescent scattering by molecules embedded in small particles, numencal results for incoherent optical processes J Opt Soc Am 68, 1676-1685 Kerker, M and Druger, S D (1979) Raman and fluorescent scattering by molecules embedded m spheres w~th radii up to several mulUples of the wavelength. Appl. Opt. 18, 1172-1179. Kroto, H W. and Teixelra-Dlas, J J. C. (1972) The effects of mtermolecular interacuons in the Raman spectrum of liquid CS 2 Spectrochlm. Acta 28A, 1497-1502 Lederman, S and Sacks, S (1984) Laser &agnostics for flowfieids, combustion and MHD applications. AIAA J 22, 161-173 Lettierl, T. R and Preston, R E. (1985) Observatmn of sharp resonances in the spontaneous Raman spectrum era single optically levitated microdroplet. Opt. Commun. 54, 349-352 McNulty, P J., Chew, H W and Kerker, M (1980) Inelastic hght scattering In Aerosol Mlcrophysics I, Particle lnteractmn (Edited by Marlow, W H.) Oudlon, R and Le Duff, Y (1973) Etudes des rales de diffusion Raman du dioxyde de soufre dissous dans des hquides Adv. Raman Spectrosc. 1, 428-435 Owen, J F., Barber, P. W and Chang, R K. (1982a) Morphology dependent Raman spectra from mlcroparticles. In Mlcrobeam Analyses (Edited by Hemrich, K. F J.), pp. 255-260. San Francisco Press, San Francisco Owen, J F, Chang, R K and Barber, P W (1982b) Morphology-dependent resonances m Raman scattering, fluorescence emlssmn and elastic scattenng from mlcroparticles. Aerosol Sc~. Technol 1,293-302 Paul, W and Raether, M (1953) Das elektrische massenfilter. Z. Phys. 140, 262-273 Placzek, G (1934) Raylelgh-Streuung und Raman-effekt In Handbuch der Radmlogle, Vol. VI, Part 11 (Edited by Marx, E ) Purcell, E M and Pennypacker, C R. (1973) Scattering and absorption of hght by nonsphencai &electnc grains Astrophys. J 186, 705-714 Qlan, Shi-Xiong, Snow, J. B. and Chang, R. K (1985) Coherent Raman mixing and coherent anti-stokes Raman scattering from individual micrometer-size droplets. Opt Lett. 10, 499-501 Qian, Shl-Xiong and Chang, R K. (1986a) Phase-modulauon-broadened line shapes from micrometer-size CS2 droplets Opt Lett 11, 371-373 Qian. Shl-Xlong and Chang, R K (1986b) Multmrder Stokes emission from micrometer-size droplets Phys Rev Lett. 56, 926-929 Rambau, R and Schweiger, G. (1988) Numencal results on Raman scattenng by spherical aerosol particles Proc European Aerosol Conf., Lund, Sweden, August 30-September 2 Ray, A K., Lee, J and Tflley, H. L. (1988) Direct measurements of evaporation rates of single droplets at large Knudsen numbers. Lanomu~r 4, 631-637 Rea, D. G (1960) Effects of solvent on Raman band intensities. J. Molec. Spectrosc 4, 507-517

Rewew of Raman scattering on single aerosol particles and on flowing aerosols

509

Richardson, C. B., Hlghtower, R. L. and Pigg, L. (1986) Optical measurement of the evaporation of sulfuric acid droplets. Appl. Opt. 25, 1226-1229. Richardson, C. B., Lm, H. B., McGraw, R. and Tang, I. N. (1986) Growth rate measurements for single suspended droplets using the optical resonance method. Aerosol. Sci. Technol. 5, 103-112. Roosen, G (1979) La L~vitation optique de spheres. Can. J. Phys. 57, 1260-1279. Rosasco, G. J., Etz, E. S. and Casatt, W. A. (1974) Investigation of the Raman spectra of individual micrometer-sized particles. I V Intern. Conf. on Raman Spectroscopy, Brunswick, Maine. Rosasco, G. J., Etz, E. S. and Casatt, W. A. (1975) The analysis of discrete fine particles by Raman spectroscopy. Appl. Spectrosc 29, 396-404. Rosasco, G. J. and Etz, E S. (1977) The Raman microprobe: a new analytical tool. Res./Dev. 28, 20-35. Rosasco, G. J (1980) Raman microprobe spectroscopy. In Advances of Infrared and Raman Spectroscopy, Vol. 7 (Edited by Clark, R J. H. and Hester, R. E.), pp. 223-282. Heyden, London. Ross, S. D. (1972) lnoroamc lnfiared and Raman Spectra. McGraw-Hill. Schrader, B. (1986) Micro Raman, fluorescence and scattering spectroscopy of single particles. In Physical and Chemical Characterization of Individual Airborne Particles (Edited by Sporny, K. R.). Ellis Horwood Last, Chlchester, U K. Schrader, B. and Meter, W. (1974, 1975, 1976) Raman/lnfrarot-Atlas organischer Verbindungen. Bd 1, 2, 3, Verlag Chemic. Schr6tter, H. W. and Kl6ckner, H. W. (1979) Raman scattering cross sections in gases and liquids. In Raman Spectroscopy of Gases and Liquids (Edited by Weber, A.). Springer-Verlag, New York. Schweiger, G. (1987) ln-s~tu determination of the molecular composition of aerosol particles in a monodlsperse model aerosol. Part. Charact. 4, 67-73. Schwelger, G. (1990a) Observation of input and output structural resonances m the Raman spectrum of a single spherodal dielectric mlcroparticle. Optzcs. Lett. (to be published). Schweiger, G. (1990b) Observation of morphology dependent resonances caused by the input field in the Raman spectrum of microparticles. J. Raman Spectros. (to be published). Schwelger, G. (1990c) Raman scattering on moving microparticles: calculation and measurement of the first and second moments. Aerosol Sci Technol. (to be pubhshed). Sherman, W. F. and Wilkinson, G. R. (1980) Raman and infrared studies of crystals at variable pressure and temperature. In Advances in Infrared and Raman Spectroscopy, VoL 6 (Edited by Clark, R. J. H. and Hester, R. E.) Sldorov, N K, Bratanova, L. F. and Stalmakhova, L. S. (1965) Principal parameters of the Raman lines of the monohalogenobenzenes and their variation with temperature and solvent. Opt. Spectrosc. RI9, 206-212. Smgham, S. B. and Bohren, C. F. (1987) Light scattering by an arbitrary particle" a physical reformation of the coupled dipole method. Opt. Lett. 12, 10-12. Singham, S. B. and Salzmann, G. C. (1986) Evaluation of the scattering matnx of an arbitrary particle using the coupled dipole approximation. J. chem. Phys. 84, 2658-2667. Snow, J B., Qmn, Shi-Xiong and Chang, R. K. (1985) Stimulated Raman scattenng from individual water and ethanol droplets at morphology-dependent resonances. Opt. Lett. 10, 37-39. Snvastrava, R. P. and Zmdi, H. R. (1979) Intermolecular forces revealed by Raman scattering. In Raman Spectroscopy of Gases and L~qmds (Edited by Weber, A.). Springer-Verlag, New York. Sieinbach, W. R., Lohrstorfer, C. F. and Etz, E. S (1982) Analytical applications of a multiplex detector laser Raman microprobe. In Mzcrobeam Analysis (Edited by Heinnch, K. F. 3.). San Francisco Press, San Francisco. Straubel, H. (1955) Zum (~ltr6pfchenversuch von Millikan. Naturwiss. 42, 506-507. Tanabe, K (1984) ConcentraUon dependence of Raman hnewidth of isopropanol in aqueous solution. J. Raman Spectrosc. 15, 248-251 Tang, I. N and Fung, K. H. (1989) Characterization of inorganic salt particles by Raman spectroscopy. J. Aerosol. Scz. 20, 609. Thurn, R. and Kiefer, W (1984a) Raman-microsamphng techmque applying lewtation by radiation pressure. Appl. Spectrosc. 30, 78-83. Thurn, R. and Kiefer, W. (1984b) Observations of structural resonances in the Raman spectra of optically levitated dielectric mlcrospheres. J Raman Spectrosc. 15, 411-413. Thurn, R. and Klefer, W. (1985) Structural resonances observed in the Raman spectra of optically levitated liquid droplets. Appl Opt. 24, 1515-1519. Tzeng, H. M., Wall, K. F., Long, M. B. and Chang, R. K. (1984) Evaporation and condensation rates of hqmd droplets deduced from structure resonances in fluorescence spectra. Opt. Lett 9,273-275. Venkateswarlu, K. and Jagathcesan, S. (1963) Temperature dependence of the intensities of Raman lines of xylenes in solutions. Acta Phys. Austrmca 19/2, 105-110. Venkateswarlu, K. and Jagatheesan, S. (1964) Solvent effect on Raman hnes" xylenes and cresols Acta Phys Austriaca 19, 212-216. Wall, T. T and Hornlg, D F. (1967) Raman spectra of water in concentrated ionic solutions. J. chem. Phys. 47, 784-792. Walrafen, G. E., Fisher, M. R., Hokmabadi, M. S. and Yang, W. H. (1986) Temperature dependence of the low- and high-frequency Raman scattenng from hquid water. J. chem. Phys. 85, 6970-6982. Wang, D. S., Kerker, M. and Chew, H. W. (1980) Raman and fluorescent scattering by molecules embedded m dielectric spheroids. Appl. Opt 19, 2315-2328 Wuerker, R. F., Shelton, H. and Lang Mmr, R. V (1959) Electrodynamlc containment ofcharged particles J. appl Phys. 30, 342-349. Zakm, M R, Grubb, S G., King, Jr., H. E. and Herschbach, D. R. (1986) High pressure study of assocmted medm: Raman scattering of pyndine complexes in aqueous solution. J. chem. Phys. 84, 1080-1088. Zerda, T W., Thomas, H. D., Bradley, M. and Jonas, J. (1987) High pressure isotropic bandwidths and frequency shifts of the C-H and C-O modes of liqmd methanol. J. chem. Phys. 86, 3219-3224.