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S. EL G O L L I and G. M A D E L A I N E Centre d'Etudes Nucldaires, Foutenay-aux-Roses, Dept. of Technical Service Protectinn Jbr Atmospheric Safety Research

and P. Y. T U R P I N and J. B R I C A R D University of Pai4s VI, Laboratoire de Physique des Adrosols, 11 Quai Saint-Bernard, 75005 Paris France

(Received 15 January, 1975)

Abstract. After recalling briefly the optical properties of aerosols, we describe the principle and the working conditions of photoelectric apparatus for aerosol measurements. Two size distribution analyzers are presented: the first one is based on a classical detection principle, the minimum detectable radius being 0.2/zm, and the maximum concentration 3 × 104 particles cm-3; the second one is based on a photon counting technique, with which particles of radius between 0.03 and 0.2/tm can be measured at maximum number concentration of 2 × 108 particles cm -3. We describe then two Condensation Nuclei Counters (CNC) with continuous flux; in these types of apparatus, the vapor of a liquid is condensed on Aitken nuclei using a Peltier effect device. They are thereby rendered visible and counted using a classical photoelectric method. One apparatus works under normal conditions of pressure and temperature, while the other one works under stratospheric conditions, i.e., at low pressure and temperature. The concentration range is still between 10 and l0 s nuclei crn -8 and the minimum concentration is 0.1 particle cm -~ in the case of the stratospheric counter. The four devices work oll individual particles; their characteristics are compared to those of commercially available apparatus and their advantages discussed. 1. Introduction The counters a n d particle analyzers b a s e d on light scattering by individual particles enable the d e t e r m i n a t i o n o f the c o n c e n t r a t i o n a n d size d i s t r i b u t i o n o f u n k n o w n aerosols. Thus, these counters are particularly useful when studying a n d controlling our a t m o s p h e r i c environment. In o r d e r to o b t a i n reliable measurements, it is imp o r t a n t to k n o w the response o f the a p p a r a t u s as a f u n c t i o n o f the dimensions a n d the refractive index o f the particles; in the case o f irregular particles, one has to k n o w also the effect o f their shape. I n the ideal case o f a t r a n s p a r e n t (or w e a k l y a b s o r b i n g ) h o m o g e n e o u s spherical a n d isotropic particle, the response m a y be calculated using the results o f electromagnetic t h e o r y (1). It is possible t o d a y to find c o m m e r c i a l particle analyzers (Bausch a n d L o m b C o m p a n y - Rochester, R o y c o Instruments, M e n l o P a r k ) a n d c o n d e n s a t i o n nuclei counters ( G e n e r a l Electric) for w h i c h characteristics a n d limits have a l r e a d y been discussed in the literature. W e shall describe in this p a p e r two particle analyzers a n d two C N C ' s with b r o a d e r possibilities c o m p a r e d to the previously m e n t i o n e d a p p a r a t u s , to characterize atWater, Air, and Soil Pollution 5 (1975) 11-38. All Rights Reserved Copyright @ 1975 by D. Reidel Publishing Company, Dordrecht-Holland

12

S.ELGOLLIETAL.

mospheric aerosols between about 10 ~ and several/zm, for number concentration as high as 106 cm -3 and as low as 0.1 cm -3.

2. Theoretical Review: Scattering of Light A light beam is always partly scattered and absorbed when passing through a cloud of particles suspended in a gas or a colloidal solution. In both cases, even when there are no particles, the molecules of the gas or of the liquid scatter and absorb the luminous radiation, the absorption occurring only in well defined spectral regions depending on the chemical composition of the molecules. It works the same way for an aerosol (or a hydrosol) the size of which is comparable with the wavelength of the incident light; the scattered radiation is preponderant and the absorption can often be neglected if the wavelength of the incident light with regard to the chemical nature of the particles is well chosen. The basis of the theory of light scattering by particles has been established by Mie [1] and was particularly well developed by Van de Hulst [2] and Kerker [37]. We shall only recall the main results concerning ideal spherical, homogeneous, isotropic and completely transparent particles (real refractive index). Then we shall determine in what way these results may be modified for absorbing and spherical particles (complex refractive index of the form n=no-ik) and for particles of any index and shape. 2.1. SCATTERING BY A SPHERICAL, HOMOGENEOUS AND TRANSPARENT PARTICLE (REFRACTIVE INDEX no) LIT BY A PLANTWAVE

2.1.1. Mie Theory and Scattering Diagrams To calculate theoretically the light scattered by an isolated particle in suspension in a homogeneous, isotropic and transparent medium, Mie solved the Maxwell equations for a plane monochromatic wave falling on the 'drop', the latter behaving then as a resonator. The incident wave induces forced oscillations of the electrical charges of the resonator, which are synchronous with the applied field and which induce electric and magnetic secondary fields inside and outside the sphere. The composition of the fields allows calculation of the scattered intensity I outside the particle as a function of four parameters : the direction of observation with respect to that of the incident wave, the refractive index n o of the particle, the wavelength 3~ of the light used, and the diameter d of the particle. The last two parameters (2 and d) only act through the fundamental ratio:

IId

perimeter of the particle

2

wavelength

Thus the 'normalized' scattered intensity whose expression is: I=

flux scattered per unit of solid angle incident flux on the geometrical surface of the particle

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can be expressed by: I = Iof(c~ ~, n, 0),

where I 0 is the intensity of the incident light. It can be shown that even if the incident wave is not polarized, the scattered wave always is more or less polarized, and I in the direction 0 can be written as : I (c~,, n, 0) = ~

1

{ii (c~,, n, 0) + iz (~r, n, 0)}

1/2//~ 2 is a factor of normalization; i x is the scattered c o m p o n e n t in the observation plane; and i 2 is the c o m p o n e n t scattered perpendicularly to the observation plane which is defined by the direction of the incident light and the direction of observation. Their expressions are respectively:

1)

il =

~n = ].

m (m +

i2 =

~n = ].

2m + l (am% + bmli=) m ( m + 1)

am and bm are functions of c~r and no only: physically they represent respectively the m-electric and magnetic components of the field. H,, and % are functions depending on 0 only, the calculations of which requires the Legendre functions. We can thus calculate the luminous intensity scattered in a given 0 direction by spherical and transparent particles of any index and diameter. As an example Figures 1 to 3 show the scattering diagrams (variations of I as a

/ m

.

\

f A,

I, I1 I.

/I;3 t _j x._g

\ /

Fig. 1. Light scattering diagram for ct<0.3; variations of the normalized scattered intensity I as a function of the scattering angle 0.

14

S. EL G O L L I ET A L .

function of 0) for a given particle of index no and diameter d. We can see that the shape of the diagram depends essentially on e,. When ~ is very small: (at < 0.3) we have Rayleigh scattering (Figure 1): x = i, + i~ = A ~

(]

+ cos ~ o)

with 1

2

and the diagram is symmetric with respect to the particle (3). I being the normalized intensity, the real intensity will be proportional to d 6 and 2 -4. When ~, is close to I, the Mie Theory mentioned above must be applied. The diagram changes and the quantity of light scattered forwards increases, at the expense of the light scattered backwards and laterally (Figure 2 drawn from [4]).

Incident light

!°

¢

K I

2700

90 °

1800 Fig. 2. Light scattering diagram for a = 1.2 and n = 1.33. For 1 < er < 30, the Mie theory can also be applied. As c~rincreases secondary lobes

appear, the number of which, between 0 ° and 180 °, is approximately equal to e, (Figure 3 drawn from [5]). Moreover the angular spread of the front lobes decreases

RECENTADVANCESIN PHOTOELECTRICAEROSOLMEASUREMENTS

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when ar increases, and merges for large particles with the diffraction theory studied in classical optics; the biggest part of the energy scattered is located in the main forward lobe.

lO

102

101

.

60

.

.

.

.

.

120

10 ~

180

Fig. 3. Variations ,of the normalized scattered intensity I and of its components il and i2 as a function of the scattering angle 0 for c¢= 10 and n = 1.44.

For a t > 3 0 , the angular aperture of the front lobe where 847oo of the scattered energy is located, is given approximately by the formula:

y

35 (in degrees) = d '

with d i n / ~ m .

In this field of large particles the Mie theory can be replaced by classical optics and the scattered flux caa~ be calculated in a given direction by applying the diffraction, reflexion and refraction laws (theory of Wiener [6], [7]). Then one can demonstrate that the total flux scattered in all directions by a transparent ' d r o p ' . . . (if d~> 2) is equal to twice the flux intercepted by its geometrical outline (it can also be said that the 'extinction coefficient' ~b/q~o* is equal to 2). N u m e r o u s authors gave tables of value of the functions i 1 and i 2 [5], [8], [9], and [I0], but in rather restricted limits of the index n o and er* ~bis the total flux scattered in 4Hsr, and ~b0the flux caught by the geometrical cross section of the drop.

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S.ELGOLLIETAL.

AS far as we are concerned we have computed i 1 and i2 using the Penndorf's method [5], in the following cases: 0.1 1 10 50

< c~, <
1 10 50 250

with a 0.1 step w i t h a 1 step with a 5 step w i t h a 10 step

for all values of 0 such as: 0<0<

180°

with

1°step

and for the following indexes: no = 1.33 (water), 1.4, 1.6

(latex)

and

1.8.

We have calculated from our results the flux scattered by aerosol particles into the apertures of our measuring devices. Indeed, in our experiments, each particle is no longer lit by a plane wave but by a beam with a non-negligible aperture and we measure the flux scattered by each of them into the aperture of a photometer, in order to get their size distribution. 2.1.2. Calculation of the Flux Scattered by the Particles Let us suppose that the drops are lit by a beam with an aperture u and that we measure the flux scattered into the objective of a photometer of aperture u. If we call B the brightness of the source (in fact B is the lighting of the input diaphragm D of the illumination system (see Figure 4a)) the elementary illumination dE produced in O by a beam seen from O under a solid angle dr2 will be (11): dE = B dr2

I':dLu

(a)

A

p

~l~ x

~z

1o

(b)

/

SJo, (c)

Figs. 4a-c. Oy axis of the condensor; Ox axis of the microscope.

LJ N

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let us put dr2 = sinc~ dc~ d e dE -- B sine de d e . The intensity scattered by a drop of radius r located in O, in the direction OP making an angle ~' with the axis Oy of the illumination system is (see Figure 4b):

dl = dEIIr2f (~r, n o, 0) = Bflr2f(~r, n o, 0) sine

de de

0 represents the angle of OP with the prolongation of any incident beam such as AO, and f (er, no, 0) the scattering function of the drop in the 0 direction. If we integrate this expression over the condenser aperture we get the total intensity scattered along OP, that is to say along the c( direction: U/2 21I

/(e')=Hr2B

f f f(c%no, O) sinc~dc~d¢. 0

(1)

0

The figure has cylindrical symmetry about the Oy axis (axis of the illumination system), so we can choose the point P in the plane yOz, and operating on unit vectors carried by OA and OP, we can write: cos 0 = cos a cos a' + sin e sin ~' cos ¢ which permits us to calculate 0 as a function of c~, e', and ¢ and then I(~') by the relation (1). In order to calculate the flux ¢ scattered into the aperture of the measuring photometer, let us first suppose that the axis of the photometer is perpendicular to the illumination system one (directed along Ox in Figure 4c). If we call el the angle of OP with Ox, the elementary flux caught by the photometer in an elementary solid angle d£21 will be: dq5 = I (c() dr21

(2)

with dr21 = sin cq de 1 d¢1. The total flux received by the photometer will be equal to: v/2 2n ¢=

f 0

f I(~')sincq dcq 6¢1,

(3)

0

U/2 being the

half aperture of the photometer. In the particular case of the scattering close to 90 °, we can demonstrate, using again the unit vector in the direction OP, that the relation between e', cq and ¢1 is: cos c~' = sin ~1 sin ¢1-

(4)

In the general case, the axis Ox of the photometer makes any angle 7 ( 5 90 °) with the illumination system one (Oy), and relation (4) is no longer valid.

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S.EL GOLLI ET AL.

Let (O, x, y, z) be the initial rectangular trihedral taken as reference (Figures 5 and 6) and (O, x, Yl, z) be the trihedral obtained for any orientation of the photometer axis and the illumination system one. The new system of axes may be considered as deduced from the old one by a rotation of an angle y of Oy around Oz in the plan

xOy.

I¢/1

",P/y

171'I j > z I

oy1 y, Fig. 5. Coordination systems (see text).

z i d'l

i \.¥

\yM R

Fig. 6. Coordination systems (see text).

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RECENT ADVANCES IN PHOTOELECTRIC AEROSOL MEASUREMENTS

In these conditions, relation (4) has to be replaced by the next one: cos e] = cos c~' cos ? + cos cq sin 7

(5)

(one can find in reference [12] the detail of the calculation). As cos c( = s i n el s:in~bl (from Equation (4)), we have a new relation a m o n g c~, cq and q51: cos e~ = sin ~bj sin el cos 7 + cos el sin y, (6) a relation valid whatever the rotation y of the second system compared to the first one. We must notice that the inclination ]3 of the Ox and Oy axes is related to Y by fl = II / 2 - y. 10

16

~

16:

no= 1,8 no= 1,6

13=90 °

no=1.4

~ n o =

1.33

/

I dI Fig. 7.

~0°

I=01

2rrR k I

102

Variations of tile normalized scattered flux as a function of the dimension parameter ~r, for U / 2 = 30 °, u / 2 = 10 °, fl = 90 °.

20

S. EL GOLLI ET AL.

C o m b i n i n g the relations (3) a n d (6) allowed us to calculate the flux scattered for values o f ? equal to 45 °, 40 ° a n d 0 ° ( c o r r e s p o n d i n g respectively to angles 13 o f 45 °, 50 ° a n d 90°), for indexes n = 1.33, 1.4, 1.6, 1.8.

2.1.3. Results and Comparisons W e have calculated these integrals on apertures c o r r e s p o n d i n g to o u r experimental conditions (see below) i.e. U = 60 ° a n d u = 20 ° ; we a p p l i e d the S i m p s o n m e t h o d which is m u c h m o r e precise t h a n the t r a p e z o i d m e t h o d or the M o n t e - C a r l o m e t h o d [13]. Figures 7 a n d 8 represent the theoretical curves o b t a i n e d f r o m the n o r m a l i z e d scattered flux q~/q~o(i.e. referred to the unit surface o f each particle) as a function o f the f u n d a m e n t a l p a r a m e t e r c~,, the index n o being a p a r a m e t e r . 10

o

16'

= 1,8 p=45 °

16 2

= !,6 =1,44 =1,33

~r _2nR ld'

1'oo

1'o~

1~o2

Fig. 8. Variations of the normalized scattered flux as a function of the dimension parameter C~r, for U/2 = 30°, u/2 = 10°, fl = 45 °.

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These curves can be compared to those obtained by Hodkinson and Greenfield [14] and call for the following remarks: The normalized scattered flux is a rapidly increasing function of the dimension, for particles of parameter er < l, corresponding to an approximate diameter d = 0.15 ~tm, in the visible spectrum. In fact this range corresponds to the superior limit of the Rayleigh range in which the real flux scattered is proportional to d 6 and explains the difficulties encountered by the constructors of particle counters to decrease the minimum diameter detectable by their devices. The first maximum of these curves takes place for ~r values between 1.5 and 3 whatever the axis orientation and the particles index; it practically corresponds to the lower limit of the lVlie range, between the validity range of the 'molecular' scattering on one hand and the classical geometric optical range on the other hand. If the angle between the two axes is close to 90 ° (Figure 7), the normalized scattered flux depends much on the refraction index of the particle. Besides, the real scattered flux is proportional to the surface of the particle only for values of e > 100 ( d ~- 15/~m) which is the lower limit of the validity range of classical optics (~bocd2). For an angle close to 45 °, the variations of the response as a function of the index are very strongly decreased especially for er > 10 (d-~l.5/~m). Moreover, starting from this value we are in the range of geometrical optics (real flux scattered proportional to the surface) which constitutes a real improvement compared with the preceding case. 2.2.

S C A T T E R I N G BY A S P H E R I C A L , H O M O G E N E O U S A N D A B S O R B I N G P A R T I C L E (INDEX OF THE F O R M rt -----no (1 - -

ik)

We shall limit ourselves to the case where the particle is weakly absorbing (k < 1). In the Rayleigh scattering case (~,<0.3), calculations show that the scattering diagram is nearly the same for non absorbing particles having the same real index (on the contrary when k--+ 0% for instance for a metallic particle, the backward scattering is nine times more important than the forward one). As for the scattered flux, the Hodkinson and Greenfield [14] and Quenzel calculations [15J show that as long as ~ is less than 1, the responses of the devices working in different optical conditions remain very close to those corresponding to transparent particles with the same index. For larger dimensions (~r>0.6), the scattering diagrams, computed according to the Mie theory, on the one hand, and to the diffraction and reflexion laws on the exterior surface, on the other hand, coincide starting from [16]: 2.5 c~ -~ 5 In - - (for a carbon particle with an index n - 2 - i , it corresponds to a diameter close to

1/~m). As a matter of fact, the light transmitted through the particle after a certain number

22

s. ELGOLLIEr AL.

of internal refractions and reflections is considerably decreased because the particle is absorbing. The scattering diagram is then similar to the diffraction diagram produced by an opaque screen having the same size as the particle and to the diagram of external reflection by the particle; this similarity is all the more valid if the more absorbing the particle is (see Figure 9 from [17]).

ld'-

kNormalized

104 .

scattered

intensity

, ... ~""

~L

~ . it

1()2

; •

4

V"q ' t

103 0

,

30

"

,

60

;'~',

90

'

," "

120

"~

15,0

~

180 8 in

,

0

30

_

-

60

,..

['xt'l'."

90

"~ 120

150

18'(~

degrees

Fig. 9. Variations of the normalized scattered intensity as a function of the scattering angle 0 for a = 10, n - 1.75, k = 0.05, and c~= 20, n -- 1.75, k 0.05. (1) Mie theory. (2) Light scattering and reflexion; (3) Reflexion only. For scattered flux it can be shown [14] [15] that important deviations from the ideal case of transparent particles can happen, these deviations being different according to the optical conditions of measurements and to the size of the particles: by measuring carbon particles (n~-2-i) with an apparatus calibrated with latex particles (n = 1.6), we can make a mistake of a factor of 2 on their size determination. 2.3. CASE OF A PARTICLEHAVINGANY INDEX AND SHAPE In the preceding paragraph, we have studied the behavior of particles assuming that they have a spherical shape, for which, though difficult, the calculations can be made. In the case of a particle having any shape the problem is particularly complex. It is impossible to solve Maxwell equations in the case of a resonator in which there is no element of geometric symmetry. Aerosols being in suspension in a gaseous medium (or in a liquid in the case of hydrosol), are oriented randomly with respect to the direction of the incident light. Their scattering diagram will be seen by a fixed observer under different angles 0 (also quite at random) and the information drawn from them will only give average indications. Besides, the scattering diagram is very much influenced by the particle shape factor, especially when they are larger than 1/zm. In this case most apparatus being calibrated using spherical particles (often latex ones) the results obtained on any aerosol by photo-electric method can only give indications 'equivalent in signal to spherical particles'. If we want to have a better idea of the size distribution, it is more advisable to use methods of impaction and microscopic analysis which is always possible (but more fastidious) in the considered dimensional range.

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3. Apparatus for Photoelectric Measurements From what precedes we can see that if we illuminate particles under given conditions and if we measure the flux scattered by each one of them in a photometer with a known aperture, we can deduce their distribution in size and their concentration in number by applying the scattering laws. The general principle of these (procedures) follows: we define with a light source and a diaphragm system a uniformly lighted field through which the particles to be analyzed pass. The light scattered by the particles into the aperture of the photometer is measured by a photodetector, the photometer axis making with the lighting system an angle different from one apparatus to another. A measurement off the axis presents the advantage of avoiding most of the parasitic light coming either directly from the source or from the parasitic reflections in the chamber (especially if light traps are used). Finally the use of large optical apertures enhances considerably the useful scattered flux. 3.1. PHOTOMETERFOR THE MEASUREMENTOF LARGEPARTICLES(r> 0.15 #m) Figure 10 shows the scheme of an apparatus we have built in our laboratory which permits the measurement of the size distribution of particles of radius larger than 0.15/~m. A source S illuminates uniformly a diaphragm D placed behind a collecting lens which forms the image of S on the first lens of a condenser symbolized by L. The condenser forms the image of D on i in the field of the measuring photometer. Is. the photometer the objective m forms on i the image of a diaphragm d, behind which a lens I forms', the image of the entrance-pupil of m on the photocathode of a photomultiplier.

Fig. 10. Opticalsetup of a photometer: (1) source S; (2) field diaphragm D; (3) condensor; (4) field of measurement; (5) photometer objective m; (6) field diaphragm d; (7) photomultiplier.

24

S. EL GOLLI ET AL.

In these conditions, the field of measurement has the form of a parallelepiped defined in the space by the images of the diaphragms D and d, and lit uniformly as the diaphragm D is lit uniformly. The air stream with suspended aerosol particles is directed perpendicular to the plane of Figure 10. As a particle crosses the field, the light scattered into the aperture of the photometer around a mean direction of 50 ° is measured by a photomultiplier. The output is a current pulse for each particle measured. The pulses at the output of the phototube are detected during their rise-time by an operational amplifier with variable gain, then sent to a 'crest-detector' circuit. The pulses sampled are then fed to the direct input of a 400 channel amplitude analyzer, the analog numerical convertor of which transforms the amplitude of the signal to be analyzed into a periodic sequence of pulses. The number of pulses is proportional to this amplitude and represents the address of the channel where this signal must be counted. One can thus obtain the curve: •A/" = f (A), where X is the number of particles stored in each channel and A the signal amplitude. After calibration of the apparatus with homogeneous and spherical particles of known index, one can deduce from the curve J V ' = f ( A ) the size distribution of droplets AN/AR=g(R), AN being the number of droplets of a radius between R and R + AR. With this apparatus one can study the size distribution of volatile aerosols and make measurements with very rapid sampling flow rates. This permits avoiding false readings from the diffusion of small particles and also from viscous action of the walls on large particles. Our setup avoids most of the drawbacks met when using certain commercial apparatus as done and analyzed by Jaenicke [18], i.e. the 'cross sensitivity' and the loss by coincidence. 3.1.1. Cross Sensitivity Cross sensitivity is expressed by the fact that all the particles of a given diameter do not always give the same signal and therefore are counted in the analysis in different channels. The main reasons are the following ones: In a great number of counters the measuring volume is illuminated by a filament lamp. To get an intense illumination one forms the image of this filament in the field but as a consequence the latter is no longer uniformly lit: the quantity of light scattered by the particle depends on the spot where it passes through the volume. In our apparatus the light source is an arc lamp (high pressured mercury vapor) having a strong brilliancy. Taking into account the shape of the lighting diagram of this lamp, the disposition of the diaphragm D and its size, the latter is uniformly lighted. This was proven by picking up the image i with an ocular to form a new and very much enlarged image on a screen; this image is uniformly lit. The sensitivity of the detector photocathode is not always uniform and the re-

-

RECENT ADVANCES IN PHOTOELECTRIC AEROSOL MEASUREMENTS

25

sponse can change depending on the point where the light scattered into the photometer by each particle arrives. In our device we form the image of the entrance pupil of the photometer on the photocathode, and not the image of the particle in the field. In these conditions, the light arrives on a large area of the photo-cathode, which permits integrating the possible variations, and this area remains the same whatever the position of the particle in the field. - A particle can be partly hidden by the field diaphragm and thus give a weaker signal than expected, that is to say behave like a smaller particle. Bricard et aI. [19] have calculated the corrections to be made to the distribution of particles so as to take into account this effect which depends on the sizes of the field, of the particles and also of their concentration; the correction is sensitive only to large particles. Finally Pinnick and Hofman [20] have studied the effects of the statistical distribution of photoelectrons in the detector on the enlargement of the response of the device for a monodisperse aerosol. This enlargement can be stressed by the fact that all the particles do not have exactly the same length of passage in the illuminated volume. As we pointed out before, the brilliancy of our light source is very high and for particles having a radius larger than 0.15 ktm, the luminous information associated with each of them is large enough to be integrated and detected as 'a current pulse' (by contrast to the voltage pulses obtained from separate photoelectrons, as we shall see below in another type of apparatus). The relative statistical errors are thus very weak and we have checked that the mean amplitude of the pulses obtained for a given class of particles is nearly independent of the time during which they cross the ilIuminated field. -

3.1.2. Losses by Coincidence

Since we want to measure the size distribution, we must work on individual particles, or in other words, the measurement has a meaning only if we can avoid the registration of several particles present at the same time in the field as one large particle [21]. Let us consider an aerosol flux of an average concentration of _Nparticles per cubic centimeter. If we call V the volume of the field, the average number of particles rfi inside the field is ~ := ??V. The problem is to calculate the probability of getting more than one particle at the same time in the field. The drops come in the field in a perfectly random way; insofar as Poisson's law is valid, the probability of finding k drops in the field at the same time is: P (k) = f~k. __ k~ e

-Nv

P ( k ) = (?¢V) k - k!

26

S. EL G O L L I ET A L .

I f one puts r~ = PTV= 0.1, Poisson's law gives: l-P(0)-P(2) P(1)

0.0951

- 0.0499

i=z P ( 1 ) -

0.0517

or

9.51~

or

4.95~

or

5.17~.

One can see that if we respect this condition on the product 37V, the probability for two or more particles to coincide in the field will only be 5.17~. In our apparatus the volume V is adjustable by changing the sizes of D and d, which is particularly interesting when one wants to make measurements on aerosols of a high concentration in number.

Fig. 11. Amplitude spectrum of the voltage impulsions obtained at the anode of the photomultiplier.

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The different diapb_ragms used ~ a v e been Obtained b y photoengraving on nickel and blackening by oxidation; the maximum number concentration admissible in the apparatus is 3 x 104 particles cm -3, which is sufficient to measure industrial dusty atmospheres in the field of sizes larger than 0.15 pm. Increasing the sizes of D and d, the minimum concentration is 0.3 particles cm -3 if one considers that a counting rate of one particle s- 1 is sufficient. As we pointed out before it is necessary to calibrate the apparatus with calibrated particles. Moreover tl~is method enables checking the excellent resolution of the setup as shown on Figure 11. It represents the amplitude spectrum of the voltage pulses furnished at the anode of the photomultiplier, as obtained from the pulverisations of mixtures of calibrated and monodisperse latex particles solutions of diameters 0.3 #m, 0.5/~m, 0.7 pm, 1.09 ~um and 1.9 pro. 3.2. PHOTON DETECTION PHOTOMETER FOR SMALL PARTICLES @2> 0.03 tim)

In order to improve the characteristics of the above apparatus as far as dimensions are concerned, we have worked out a new device which allows the detection of particles of radius equal to 0.03 #m [22]. 3.2.1. Description The optical scheme of this last counter is identical to the one previously described but the axis of the lighting and of the scattered light collection devices now make an angle of 90 °, which permits us to better avoid the parasitic light (Figure 12). The principle of detection is very different though. Previously one measured the amplitude of a voltage pulse which corresponded to the flux scattered by each particle crossing the photometer field, this flux is now measured by counting a discontinuous

J 1

m

Fig. 12. Schemeof the photometer: (1) mirror; (2) source S; (3) collecting lens; (4) field diaphragm D; (5) filter; (6) condensor L'; (7) observation field i; (8) objective m; (9) field diaphragm d; (10) relay lens l; (11) photomultiplier.

28

S. EL GOLLI ET AL.

sequence of photons. As a matter of fact (Figure 13), the scattered flux ~b decreases very fast with the diameter d of the particle below 0.2/tm: in our spectral conditions of lighting, one is at the limit of the Rayleigh range, where we have shown that ~b is proportional to r 6 : ~b is then sufficiently weak to create at the photo-cathode of the detector, separated photoelectrons, each one of them being obtained from a scattered photon. Each pulse obtained at the anode is the result of the amplification of these separated photoelectrons, and the measurement consists in counting the number of

J lo °

101

10 2

10 3

d rla m-I I

I

i

I

I

0,1

0,2

0,3

0,4

0,5

Fig. 13. Variation of the light scattered flux by a particle as a function of the diameter of the particle. pulses per unit of time, the time during which the particle crosses the field. Figure 14 shows the shape of the signal obtained at the detector anode for particles of 0.23/~m and 0.188 #m in diameters. For this analysis to be valid, the elementary pulses can not overlap, that is to say that the time-constant of the anodic circuit should be the shortest possible. That is why we have supplied the charge circuit with a fast preamplifier, the output of which is connected to an amplifier-former-digital counting device. The half-width of each pulse at the output of the preamplifier is of the order of 10 ns. To make sure that we do detect separated photoelectrons we have made some preliminary experiments, connecting a fast amplifier amplitude selector and a counting scale at the output of the preamplifier. With this setup, one can establish the differential

RECENT ADVANCES IN PHOTOELECTRIC AEROSOL MEASUREMENTS

Fig. 14. Signal obtained at the anode of the photonic size analyzer.

29

30

S. EL GOLLI ET AL.

spectrum of the voltage pulses delivered by the phototube, corresponding to the number Hi of pulses, the height of which is between A~+IAAi and A i - ½ A A i (AA i being the width of the analyzing channel, i.e., here AA~ = 1 V). Our hypothesis being verified, the spectrum obtained is a 'lone photoelectron spectrum', the characteristics of which are well known [21]. Under these conditions, the probability for one voltage pulse to correspond to two or more simultaneous photoelectrons being very low, one can assert that the average number H of pulses detected per unit of time when a particle crosses the field is directly proportional to the number ~ of incident photons on the photocathode during the same time; therefore it is proportional to the flux scattered by this particle. 3.2.2. Measurement and Treatment of the Informations We have just seen that the signal corresponding to each particle is made of a sequence of pulses, the amplitude spectrum of which is that of a lone photoelectron. In other respects, a parasitic signal exists that we shall call a background noise, made of two components: the background noise proper to the tube: radiation of thermal origin (at the photocathode level essentially), radiation by field effect, ionization of residual gases, etc. One can reduce it by selecting a low quantum background noise tube, and by cooling the photocathode and the first dynodes with liquid N 2. the background noise due to the molecular scattering of the air contained in the photometer field and in which the particle is suspended. One can note though that the illuminated volume contains a sufficient number of air molecules that the molecular scattering remains constant with time, the number of molecules leaving the field being equal on an average to the number of molecules entering the field. The total noise is made of pulses which also belong to the spectrum range of a lone photoelectron and one can point out that the background noise exists whether there is a particle in the field or not. In order to decrease that component one can reduce the dimensions of the lighted volume, but one decreases at the same time the probability of finding a particle in the field. The anodic signal corresponding to the interesting events cannot be easily separated from the background noise: the noise and the signal pulses amplitude spectrum being identical, all the methods of amplitude selection are inefficient. That is why we have been lead to create a logic of presence optimization of a particle in the field (which will not be described here) so that the systematic starting of measurements by pulses of the background noise has been avoided. This logic allows defining a standard time of measure which serves to count the number of pulses per unit of time attached to the signal of each particle during the time it crosses the field. In order to register the information associated to the cloud of particles to be analyzed, one uses a multi-channel selector of which only the core-memory, the address register and the arithmetic register are employed. The number counted during a measurement is introduced in the address-register to designate the number of the channel which is then incremented by one unit with the arithmetic register. At the -

-

RECENT ADVANCES IN PHOTOELECTRIC AEROSOL MEASUREMENTS

31

end of an experimen~L one obtains directly a curve representing the number of events as a function of the number of pulses created by each one of them, which afterwards enable one to obtain the size distribution. In order to get the size distribution from the experimental histogram, it is then necessary to apply a treatment of the type used for the analysis of multidimensional data to these results. The photon radiation in the case of a very weak flux (23) and the conversion photonphotoelectron at the photocathode both have a random character. It follows that a particle of diameter dk does not give rise to a definite signal which depends on the category k to which it belongs, but only to a random number of elementary pulses. This number follows a Poisson distribution around a certain mean value ek depending on the class k of the particle. It is therefore normal to consider that if we divide the sought size distribution into m classes, the experimental histogram obtained is a linear combination oir m Poisson curves with mean values ek (k = 1,..., m): the coefficients of this linear combination must then represent the weight of each class of particles in the whole size distribution. The most adequate statistical analysis to solve the problem is the linear regression we used at first. The results, although giving an excellent precision in the reconstruction of the experimental spectrum, were sometimes quite incompatible with the physical phenomena we had to explain. That is why later on we developed a very special method we call the 'restrained regression' [24] (which requires techniques of quadratic programming which we shall not explain here): the 'explanation' of the experimental spectrum is this time compatible with the physical facts and the precision is nearly always as good as in the case of the classical linear regression. 3.2.3. Performances and Results The lower limit of detection is reached when a particle gives a signal of the same order of magnitude (in terms of an average of number of photons) as the one due to the molecular scattering of the air contained in the field of measurement. The radius of the lower limit is now 0.03/~m, which corresponds to an improvement of the signal sensitivity by a factor close to 3000 in comparison with the 'classical' apparatus previously described. The maximum concentration permitted is also a function of the dimensions of the diaphragms D and d of Figure 12; it can reach 2.5 x 10 6 particles cm-3, which corresponds to the limit of rapid coagulation of the particles (of the order of a minute). As an example, Figure 15 shows some results for measurements of atmospheric aerosols obtained [2511for the curve 15a in an almost pure atmosphere (Puy de D6me, France, altitude 1465 m) and for the curve 15b in an urban polluted atmosphere (in Paris at the University of Paris VI). One can compare in the first case the concentrations found, with the condensation nuclei counter (650 particles cm - 3), the principle of which will be stud./ed below, with the classical (for R > 0 . 2 pro) and photon analyzers (for R < 0 . 2 prn) (total: 410 particles cm-3). This comparison shows that in natural non-polluted atmospheres, the number of detectable particles of radius less

32

S, EL GOLLI ET AL.

dN dR

J--

1

:

b

lo

lo I

10 0

10-2

I 1 0 -1

\o

I 10 o

~ 101

R [lam] >

Fig. 15. Size distribution of atmospheric aerosols. Variation of the particle concentration as a function of their radii: 15a) Puy de D6me summit, France; 15b) Paris, University of Paris VI, France.

than 0.03 pm is low. Moreover, the curves present a maximum close to 0.05 ym, and for larger radius the size distribution is continuous and decreases following a law of the type dN/dr=c~r-p, with/~ close to 4. These results are in good agreement with those obtained by Junge [26] and Renoux and Tymen [27]. In the case of an aerosol coming from the sea (measurements made at the Center of Nuclear Studies at La Hague in Normandy, France), we have obtained similar distributions but with notably higher concentrations. Curve 15b does not present any more the maximum characteristic of pure atmosphere, which corresponds, if it exists, to a radius smaller than the limit of detection of the analyzer (r = 0.03 ym). The distribution is still continuous and of the form dN/dr = c
RECENTADVANCESIN PHOTOELECTRICAEROSOLMEASUREMENTS

33

One can think that the displacement of the maximum towards low radius and the considerable increase,, of concentration could be due to the photolysis of gaseous impurities which is very important in very polluted urban atmospheres. 3.3. CONDENSATIONNUCLEI COUNTERWITH CONTINUOUSFLUX According to the results of the nucleation theory, it is almost impossible to find, in normal conditions, particles with a diameter less than about 10 A. The device we describe now enables measuring the concentration of an aerosol of a size larger than 10 -.3 #m, by a photoelectric method. It is quite obvious that such small particles, also called 'Aitken nuclei', [28, 29] cannot be detected directly by the luminous flux they scatter. To 'see them' we make them flow through a supersaturated water vapor (for instance). With enough supersaturation each Aitken nucleus produces a droplet. The droplets formed are then large enough to be counted. The necessary supersaturation can be obtained by lowering, with an adiabatic expansion, the temperature of the gaseous medium containing the aerosol previously saturated with vapor. In the present device, the lowering of temperature is obtained by a continuous circulation in a refrigerated pipe [30] [31]. 3.3.1. Condensation Nuclei Counter Working Under Normal Pressure The condensation (Figure 16) and dragging device of the droplets requires a saturator (a case with the inside walls lined with a spongy cloth soaked with the liquid (butylic Alcool) whose vapor will be condensed) followed by a calibrated spray nozzle cooled with a Peltier effect module and an aspirator device with a constant flow [39]. The flow speed of the droplets in the observation field is uniform and adjustable in the whole field of measurement.

Todraggingdevice

~Observat ion chamber Field of Measurement~ ] ~ /Light trap

0ptic19~tta~am"~'~'-~'-"- - ~ . . _ ~ ~ - ~ lnterchangeablecalibrailed nozzle-

C°nverge_~ n t ~ Aerosolinlet ~ - - - - ~ S . o ° g i o u . ma,eria,

I]~

~q~. Peltier effect cooler module

(! ][~---~ll ~'~"Watercirculation ~ ~ H o t face .u

idi.er

Fig. 16, Condensingand dragging devices of the droplets of a CNC with continuous flux,

34

S. EL GOLLI ET AL.

The optical setup used has been inspired by the size analyzer optical set-up previously described [30]. The droplets formed on the condensation nuclei move perpendicularly with respect to the plane defined by the optical axis of the condenser and the photometer. Knowing the flow speed, the section of the field perpendicular to it and the number of pulses counted per unit of time at the output of the photomultiplier, one can deduce the concentration in number of particles N. In this apparatus the coincidence probability reaches 3% for a number concentration of 8.8 x 105 particles cm-3 and is only 5% for 1.3 x 106 particles cm-3 ; the minimum concentration detectable is about 10 particles cm -3. The pulses can be processed in two ways: either the apparatus works as a counter and each pulse is transmitted to a counting scaler with printer output, or the apparatus works as a size analyzer and the pulse is sent to an amplitude analyzer (multichannel selector) which permits getting the size distribution of droplets of diameter larger than 0.3 pro. In this case one uses the fact that the luminous flux in our working conditions (a photometer collecting the scattered light at 45 ° forwards) is almost independent of the refractive index of the particles, a fact which enables the direct calibration of the apparatus with calibrated particles. In our experimental conditions the fraction of droplets of diameters larger than 2/~m formed by condensation did not exceed 10% for a concentration of nuclei close to 103 particles cm -3. The maximum diameter measurable decreases when the concentration increases and remains under 1 /~m when we go beyond 70 x 103 particles cm -3. These diameters can be considered as negligible in comparison to the field dimension which allows us to neglect the corrections coming from the limitation of the field by diaphragms D and at. In the previous conditions, a comparison made with an Aitken counter showed us that our apparatus indicated three times more nuclei than it was possible to visualize in the reticulated glass plate of the Aitken counter. 3.3.2. Condensation Nuclei Counters Working at Reduced Pressure With the aim of studying stratospheric aerosol we attempted to adapt the former apparatus to the nuclei counting under reduced pressure working conditions (around 60 Tort). The optical set up is about the same as the previous one, except for magnifying the illumination system and the photometer, each of them being now equal to 1. The sizes of the D and d diaphragms have to be adjusted to be able to measure the very low stratospheric nuclei concentration, with sufficient accuracy: the minimum concentration is now 0.1 nuclei cm -3, for a counting rate of 0.5 pulse s -1. Some studies made with condensation nuclei counters (where the supersaturation was achieved by a sudden adiabatic expansion) have shown an important decrease of the counting rate when the surrounding pressure decreases [32], [33], and [34]. These counting defects cannot be assigned either to the evaporation or to losses by diffusion towards the walls or to particle coagulation. We resumed these experiments working principally on a 200 1 capacity vessel con-

R E C E N T ADVANCES IN P H O T O E L E C T R I C AEROSOL MEASUREMENTS

35

nected to a pumping device which enabled it to be put under reduced pressure [35]. We have thus checked with a cooling counter previously described, that the counting losses increase progressively when the pressure decreases and become equal to 100~ for a mercury pressure of 100 mm. By carrying out the size analysis of the droplets obtained with a multichannel selector we realized that the signals delivered by the photomultiplier decreased in amplitude when the pressure decreased and that for a pressure close to 100 Torr they could be confilsed with the background noise. It works as if, under low pressure, droplets are unable to develop themselves sufficiently and the amount of scattered light is too weak to be detected. We have resumed experiments of counting rates variations as a function of the supersaturation, i.e., as a function of the temperature differences A T between the blast-pipe and the saturator, and for different pressure [36] for a vapor of n-butylalcohol. Figure 17 presents the results obtained for two values of the pressure: 760 Torr and 60 Torr. These curves call for the following remarks: - When A T increases, the number of particles counted for a given aerosol increases rapidly, up to a first discontinuity for A T 1 (points A). The counting rate then increases

A T = Tsaturato r

_ Tnozzle

• 10 s t

104 o

105 + "104 o

760mmHg

60 mm Hg

~T [%] .

_

~

f

16

p

21

36

Fig. 17. Variation of counting rates as a function of dT= (T saturator - T nozzle).

36

S. EL GOLLI ET AL.

less rapidly up to a second discontinuity A T 2 (points B), where the phenomenon of homogeneous condensation of the vapor appears which produces a fast new increase. - The AT1 value for which the first discontinuity appears increases as the pressure decreases from ATI=16°__ I°C at atmospheric pressure (and for an atmospheric aerosol) to AT1 = 2 1 ° + I°C at 60 Torr. - The A T 2 value of the second discontinuity is equal to A T 2 = 3 6 ° + 1 ° C and is independent of the pressure. According to the nucleation theory, in the case of butylalcohol, the supersaturation needed for the rapid expansion of the homogeneous condensation must be larger than 470~; it corresponds in our experimental conditions to a A T of 36°, which agrees well with the previous results. The AB part shows that condensation does occur on all the particles and that they are all detected. However, the AB part is slightly ascending. Two explanations could be given: (a) the size analysis of condensation drops shows that they are not monodisperse. The average size of the particles increasing with the supersaturation, therefore with the value of AT, the existence of an electronic threshold of detection, beyond which a particle is counted, could partly explain the increase of the counting rate. (b) the homogeneous condensation of the vapor can also contribute, for a A T less than 36 °C. The hypothesis of a homogeneous condensation starting on this side of point B is supported by the comparison of parts AB and BC of the curves obtained, on the one hand, at 760 Tort, and on the other, at 60 Torr: for the two portions of the curves, the slopes are larger in the second Case than in the first one. In any case, one notices that the counting losses mentioned above in the case of measurements at reduced pressure can be explained only if the working point chosen is close to the first discontinuity (point A). That is why we have chosen to warm up the saturator so that it can always work in the neighborhood of the second discontinuity (point B); that is to say, at a A T value less than but as close as possible of A T z =36°C. By repeating the experiments at pressures varying between 760 Tort and 60 Torr, one has been able to present Table I where we give experimental and 'theoretical' counting values, i.e., corrected for the pressure in the classical way, and warming of the saturator. One can see that this artifice enables eliminating the counting losses at reduced pressure (P. Delattre [38]). -

TABLE I Experimental and theoretical counting values !o T o r t

760

560

360

260

160

60

760

87000

53000

27000

15000

4500

800

5000

C o m p u t e d concentration

-

69000

41000

30000

18000

5200

5200

Losses ~

-

17

31

50

73

100

-

63000

40000

30000

18000

5000

5000

Measured concentration

Measured concentration by heating

87000

RECE NT ADVANCES IN PHOTOELECTRIC AEROSOL MEASUREMENTS

37

4. Conclusion After having briefly stated the m a i n optical properties of aerosols, we have shown the w o r k i n g principle o f f o u r sets o f a p p a r a t u s which can, using photoelectric methods, o b t a i n the m a i n characteristics o f aerosols, i.e. the size d i s t r i b u t i o n a n d the average concentration. These m e t h o d s enable the study o f the whole d i m e n s i o n range f r o m 10 . 3 / ~ m up to several tens of/~m; besides, they have been conceived so t h a t one can m a k e in all cases direct in situ m e a s u r e m e n t s on individual particles whatever the c o n c e n t r a t i o n , in o r d e r to get the absolute counting, a n d this, up to concentrations close to 2 x 10 6 particles c m - 3 (fast c o a g u l a t i o n limit of the particles). The m e a s u r e m e n t s m a d e with the l a b o r a t o r y p r o t o t y p e s on a t m o s p h e r i c aerosols have shown the validity a n d the self-consistency of the results obtained. Their setting o n an industrial scale should p e r m i t i m p r o v i n g c o n s i d e r a b l y the answers to the p r o b lems o f the detection o f very thin particles a n d the c o n t r o l o f dusted atmospheres.

References [i] [2] [3] [4]

Mie, G.: 1908, Ann Physik 25, 377. Van de Hulst, H. C.: 1957, Light Scattering by Small Particles, Wiley and Sons, New-York. Cabannes, J. : 1929, La Diffusion Moldculaire de la Lumidre, P.U.F., Paris. Green, H. L. and Lane, W. R.: 1969, Particulate Clouds, Dusts, Smokes and Mists, Spon, Londres, p. 110. [5] Penndorf, R. : 1963, Research on Aerosol Scattering in the Infrared, Wilmington. [6] Wiener, C. : 1907, Die Helligheit des klaren Himmels, Ablandl. Kaiserl. Leopold Karo Deutch. Akad. Naturf. 73, 1. [7] Bricard, J. : 1957, Handbuch tier Physik, 44, Springer, Berlin, 329. [8] Gumprecht, R. O. : 1952, J. Opt. Soc. Amer. 42, 226. [9] Lowan, A. N. : 1948, Appl. Math. 4, Washington. [10] Pangonis, W. J., Heller, W., and Jacobson, A. : 1957, Tables of Light Scattering Functions for Spherical Particles, D6troit, Wayne State Univ. Press. [11 ] Bricard, J., Duquesne, M., and Turpin, P. Y. : 1966, Ddtection Photonique de la LumiOre Diffusde par les Adrosols Ultrafins, C. R. Acad. Sciences t. 263, 1380. Turpin, P. Y. : 1970, Informations adrauliques et Thermiques 27, 14. 112] E1 Golli, S., Bricard, J., Turpin, P. Y., and Treiner, C. : 1974, Aerosol Sci. 5, 1. [13] El Golli, S. : 1971, Thermique Adraulique 5, 515. [14] Hodkinson, J. R. and Greenfield, J. R.: 1965, Appl. Opt. 4, 11, 1463. [15] Quenzel, H.: 1969, Appl. Opt. 8, 1, 165. [16] Hodkinson, J. R. : 1963, Staub 23, 374. [17] Hodkinson, J. R. : 1966, 'The Optical Measurements of Aerosols', in Aerosol Science, Acad. Press. [18] Jaenicke, R.: 1972, Aerosol Sci. 3, 2, 95. Liu, B., Berglund, R., and Agarval, J. : 1974, Environ. 8, 717. [19] Bricard, J.. Deloncle, M., and Israel, G.: 1959, Ann. Geoph. 15, 415. Deloncle, M. : 1963, Th6se d'Etat, Paris. [20] Pinnick, R. G. and Hofman, D. J.: 1973, AppL Opt. 12, 11, 2593. [21] Turpin, P. Y.. 1967~ Rev. Opt. 46, 6, 309. [22] Turpin, P. Y. : 1972, Th~se d'Etat, Paris. [23] Glauber, M. : 1965, Optical Coherence andPhoton Statistics, Dunod, Paris. [24] Cazes, P. and Turpin, P. Y.: 1971, Revue de Statist. Appliqudes, XIX, 4, 23. [25] Bricard, J., Cazes, P., Reiss, P., and Turpin, P. Y. : 1972,'Contribution ~ l'6tu de de l'a6rosol atmosph~rique dans le domaine submicronique ~ l'aide de m6thodes photo61ectriques', C.R.A.S. Paris, 275, 263.

38

[26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

[37] [38] [39]

S. EL GOLLI ET AL.

Junge, C. : 1963, Air Chemistry and Radioactivity, Acad. Press. Renoux, A. and Tymen, G. : 1973, Chemosphere 2, 49. Aitken, J. : 'A Portable Nucleus Counter', Proe. Roy. Soe. Edinburgh XVI. Pollak, L. W. and Metnieks, R. : 1959, 'Instruction for use of Photoelectric Condensation Nuclei Counters', Geophysical Bulletin 16, Dublin. Reiss, P. : 1972, Th6se de Sp6cialit6, Paris. Bricard, J., Madelaine, G., Reiss, P., and Turpin, P. Y. : 1972, Compteur de Noyaux de Condensation/t Flux Continu', C. R. Acad. Sci. Paris 275, p. 837. Pollak, L. W. and Metnieks, A. L.: 1960, Geophys. Pure Appl. 47, 123. Pollak, L. W. and Metnieks, A. L.: 1961, Geophys. Pure Appl. 50, 7. Junge, C. E., Chagnon, L. W., and Manson, T. E.: 1961, Metals 18, 81. Bricard, J., Delattre, P., Lebeaupain, G., and Madelaine, G. : '174, 'Comptage de Noyaux de Condensation h Pression R6duite', C. R. Aead. Sci. Paris, 278, 191. Bricard, J., Delattre, P., and Madelaine, G. : 1974, 'Counting of Condensation Nuclei at low Pressures - Application to Photolysis of Gazeous Impurities in the Stratosphere', CIAP Publication CIAP. Kerker, M. : 1969, The Scattering of Light, Academic Press, New York and London. Delattre, P. : 1974, Th6se Dr Ingenieur, Paris. Reiss, P. : 1973, ThOse de sp6cialit6, Paris.