Light-Scattering Instrument for Kinetic Measurements in Aerosols with Changing Particle Size Distributions BY M. D. CARABINE AND A. P. MOORE Department of Chemical Engineering and Chemical Technology Imperial College Prince Consort Road London S.W.7. Receiued 13th December 1972 The construction and use are described of a laser light-scattering instrument for kinetic measure- ments of the particle size distribution in a developing aerosol. In the present stage of development, the time resolution (of the order of seconds) is adequate fur the study of aerosols which are developing by growth and by coagulation. Such an in situ measurement is preferable for particles and for kinetic studies. The systems investigated are of importance in atmospheric pollution namely the formation of solid particles by interaction of ammonia and sulphur dioxide and the hygroscopic growth of sulphuric acid droplets in humid atmospheres.The precision of the data-analyzing procedure is such that it yields modal particle sizes and distribution spread parameters accurate to within 4 and 10 % respectively even with about 5 % random fluctuations in the measurements of the angular distribution of scattered intensity. The size distribution of particles or droplets in an aerosol suspension can be deduced from the variation of intensity of scattered light with either the angle of scattering the polarisation or the wavelength. The method of sizing has the advantage that the particles need not be disturbed by e.g. deposition before electron microscopic examination or by electrification prior to sizing.Minimal iiiterference with the aerosol is essential if it is required to observe the changes of particle-size distribution with time which can often be important in practical cases both in manufacturing of particulate products and in atmospheric pollution.2 Instan-taneous measurement of light intensity is a further feature which makes the technique particularly suitable for monitoring rate processes provided that the input parameters such as scattering angle or wavelength can be varied quickly enough. This paper describes a light-scattering instrument designed for kinetic measure- ments of size distribution in an aerosol with a time resolution in its present initial stage of development which is adequate for the study of aerosols which are developing growth and by coagulation of particles.Our particular interest is in systems in which a vapour from the suspending mediun is being transferred to the condensed phase e.g. a suspension of hygroscopic acid droplets which are growing in a humid atmos- phere or a suspension of solid particles being formed by interaction of gases such as ammonia and hydrogen chloride or ammonia and sulphur dioxide. The size distribution of the aerosol thus formed and its variation with time depend on such processes as condensation coagulation diffusion and sedimentation. In the range of conditions which are relevant to atmospheric pollution significant size change by condensation growth occurs in general'on a time scale of tens of seconds.3* Coagulation in a given aerosol causes time variation in both the number and the size of the particles.The number concentration varies predominantly according to second-order kinetics and at a inoderately high atmospheric concent ra-tion of say lox3m-3 the half-life would be of the order 100 s. 176 M. D. CARABINE AND A. P. MOORE The times involved in changes in size due to Brownian coagulation are illustrated in fig. 1 in which the successive distributions have been computed for intervals of 110 s. particle radiuz/prn FIG.1.-The particle size distribution at time intervals of 110 s resulting from the Brownian coagula-tion of a dispersion initially having a modal radius 0.25 pm and a zeroth-order logarithmic breadth parameter a.= 0.10. In the aerosol referred to above which is produced by interaction of ammonia and sulphur dioxide it has been shown by sampling on filters (with consequent uncertainties) followed by electron microscopy that the particles undergo growth typically from 0.03 pm to 0.2 pm in about lo3 s and then to about 0.5 pm in further 5 x lo3 s. The aggregates in the 0.2-0.5 pm range are formed of primary particles predominantly of size less than 0.1 pm. The proportion of small particles is aug- rncnted when traces of moisture or oxygen are added to the carrier gas. CRITERIA FOR THE CHOICE OF METHOD A tinic interval of about 1-10 s is considered short enough for meaningful size distribution measurements in the systems referred to above and if angular distri- bution of intensity is the chosen method a scan of the angles must be achieved within this time.To obtain sufficient intensity of scattered light from a dilute suspension of sub-micrometre particles a high-intensity light-source such as a continuous laser is required. Besides the high intensity it has the advantages for light scattering of monochromaticity and linear polarisation-and Harris et a!.$ have shown experi- mentally that there is no difference in scattering behaviour between conventional incoherent light sources and coherent laser sources. The scanning-speed requirement rules out the use of several techniques reviewed e.g. by Kerker which have been developed to study essentially time-invariant dispersions using conventional light sources.Thus the "polarisation ratio " method 'would require rotating the plane of polarisation of the beam through 90"at each observation angle ; while the methods using " scattering ratio " or " turbidity spectra " 8. at different wavelengths would necessitate repeated retuning of the laser. Hence the only technique compatible with the required scanning speed and the laser source is one using the angular variation of intensity. Angular scanning intro- duces its own problems which must be carefully considered in the design. The LIGHT-SCATTERING INSTRUMENT optically-effective volume is defined by the geometry of the light-receiver system and the incident beam and contains all the scattering particles which contribute to the measured intensity for a particular angle of scattering 8.Ideally if the detector receives only parallel light the optically effective volume varies simply in direct proportion to sin 8 if the cell containing the aerosol is cylindrical and free from flaws. However in practice a finite solid angle also means that data are recorded for an angular range 8+A8 rather than for the unique angle for which theoretical data are normally computed. Tabibian and Heller lo have shown that in the absence of steep maxima or minima in the intensity against angle curves a solid angle not in excess of steradian is permissible. Problems common to all light-scattering methods include multiple scattering and extinction of the beam. These interfere if the concentration of particles is above a certain limit whose value depends at a given wavelength in a given medium on the refractive index and the size of the scatterers.These two complications are respectively avoided by working at sufficiently low dilutions and by using relative intensities of light scattered at the various angles (see eqn (2) later). The more practical difficulties of inadvertent reflections of the incident and scattered beams are specific to individual scattering cells. The devices used to minimize them in this apparatus are described below. The essence of achieving precision in the size-distribution measurement is to record light intensity for a large number of scattering angles. Before considering the present design we examine the possible arrangements which are compatible with rapid scanning a laser source and a photo-multiplier detector.These alternatives are (a) to use a stationary light source and a single detector which is moved rapidly through a series of angular positions; (b) to use a stationary source and a separate photomultiplier stationed at each angle; and (c) to hold both source and detector static and to deflect the incident beam itself through the series of angles. Alternative (a) has been previously adopted l1 but mechanical movement of the detector must be relatively slow in a low-cost instrument. Alternative (b) is also unsuitable as it demands a number of photomultipliers of known relative sensitivities together with a complex and costly multichannel data-acquisition system. THE INSTRUMENT The present instrument based on alternative (c) achieves the measurement economically with one source one detector and several inexpensive mirrors.The arrangement is shown schematically in fig. 2. The plane mirror at position R rotated by a stepper motor about an axis perpendicular to the scattering plane (the plane of the diagram) reflects the source beam sequentially on to a series of static plane mirrors M at the positions marked. From each of the latter mirrors the beam is directed back to the centre of the scattering system at A and the photomultiplier detects the light scattered by the optically effective volume of aerosol. There is a slight divergence of the beam over the optical path (less than 1 mradian) and to keep it constant for all the beams the stationary mirrors are positioned on an ellipse with the principal foci at A and R.The laser beam and the line PM-A define the hori- zontal scattering plane of the instrument. The scattering angles which range from 8 to 172"have a precision of *0.33" determined by the stepper motor. A helium-neon laser with a 15 mW output at 632.8 nm is used as the light source. The photomultiplier has a "modified S-20 "spectral response yielding a high quantum efficiency at this wavelength compared with other photocathodes. Plane-front-surface mirrors are used throughout and precise adjustment of the stationary ones is M. D. CARABINE AND A. P. MOORE effected by three-point spring mountings. A special light trap has been constructed from black glass-fibre-reinforced resin to minimize back reflections from the trans- mitted light beams.Based on the conventional Rayleigh horn but having a wide curving aperture it traps any light entering within an angular range of 174". In this apparatus it is attached directly to the gas-tight scattering cell opposite to a thin semi-circular glass window which admits the incident beams with negligible distortion. FIG.2.-Schematic plan view of the optical system. The positions x are locations of stationary mirrors M ; R is the rotating mirror ; A is the scattering centre ; L and PM are the laser source and photomultiplier detector. ANGULAR SCANNING CONTROL AND DATA ACQUISITION Initial adjustment of the rotating mirror is made to a start position defined by an infra-red position detector situated under the main baseplate of the instrument.Thereafter the rotating mirror scans through the predetermined stepping pattern. A count of the number of steps taken determines the end of each scan whereupon the mirror is rapidly brought around to the start position and the sequence repeated. The mirror can be advanced in single steps to enable alignment of each stationary mirror and determination of the corresponding scattering angle. A block diagram of the control circuitry which governs the stepper motor is shown in fig. 3. The motor moves through 3.75'. at each step. When a full scan is required to have readings at eight angular stations four steps are necessary between each and for sixteen positions two steps. Provision is made for half scans and for the peripheral mirrors to be used in " odd " as well as "even " numbered positions.The control logic is performed by standard integrated circuit techniques the stepping rate and timing being derived throughout from the mains frequency with basic clock pulses at 100 Hz. The " start " command releases the clock inhibiting gate to enable the motor to step at this rate until the infra-red detector halts it at the LIGHT-SCATTERING INSTRUMENT start position. A delay of 300 ms foliows before the first reading and thereafter after each change of position giving time for internal resets. The time interval between readings of intensity is 200 ms derived like the delay by division of the clock rate. The motor is stepped to a new position each time the required number of readings is satisfied and this can be up to eight at each position.CONTINUOUS 4 SAMPLE 1 SCAhi PQ3GRAtJME FIG.3.-Schematic diagram of the electronic system controlling the angular scanning. "Even-Odd " selects which set of mirrors is to be scanned " 8-16 " selects the number of mirrors to be scanned "Full-Half " selects full (ca. 180 deg.) scan or half (cu. 90 deg.) scan. Selection of " End " inhibits the clock when the current scan is complete. The number of completed scans and angular position are visually displayed on serial counters and the intensity readings are recorded on paper tape for subsequent analysis. ANALYSIS OF DATA The theory of Mie l2 is used to compute the angular intensity functions (i and i2 for perpendicular- and parallel-polarised incident light respectively) for spherical particles of known size and refractive index.For a system of heterodisperse particles the scattered intensity at a particular angle is given for the perpendicular polarised case by Id@= 1h(a7QPb) da (1) M. D. CARABINE AND A. P. MOORE where p(a) is the normalised size-distribution function. The experimentally-deter- mined scattering signals are related to I,(@ as follows l,(O) = c sin 8[s,/so -sh/sb] (2) where the symbols are c a constant proportional to the number concentration; sin 8 factor for the change in observed volume at different angles ; so photomultiplier signal from aerosol at angle 8 ; $4 correction term for background light e.g.stray light scattering from edges of stops etc. ; so sh incident beam intensities at time of measur-ing so s;. For convenience the two-parameter zeroth order logarithmic distribution (ZOLD) of Espenscheid et aZ.13 has been adopted in this work after experimental checks that such a distribution does describe the aerosols under study.14 Typical theoretical curves of intensity against the scattering angle are shown in fig. 4 for spherical particles of refractive index 1.52. Readings at suitably chosen angles discriminate well between the different distributions of sizes in this sub-micro-metre range. The method is inapplicable if the greater part of the distribution is in the Rayleigh scattering regime i.e. with diameter <0.06 pm. A computer programme has been devised to solve the complex probleni of inverting the light scattering data to give the corresponding size distributions.First the theoretical intensities are computed for an assumed distribution (using eqn (1) and producing curves such as those in fig. 4) and the percentage differences for all angles found between these values and the recorded experimental data. The parameters of this "first-guess" distri-bution are then adjusted in successive steps to minimize the sum of squares of these differences according to the method developed by P~well,'~ until a final estimate for the aerosol is reached. In order to evaluate the accuracy of the light-scattering inversion programme theoretical intensity values for a set of eight angles were computed for several chosen -1.5 -0 45 90 135 angle/deg.angle/deg. FIG.4.-Theoretical intensity against scattering angle for fight plane-polarised perpendicular (I,) and parallel (I,) to the scattering plane. Curves (a-f)are for distributions having a modal diameter 0.40 pm and the following ZOLD spread parameters (a)uo = 0.50 ; (b) uo = 0.40; (c) u0 = 0.30 ; (d)oo = 0.25 ; (e)uo = 0.20; (f)uo = 0.10. I82 LIGHT-SCATTERING INSTRUMENT distributions. These were then used as experimental input data on which to perform the routine search analysis. The resulting "best fit " distributions were within 4 % of the modal diameter and 10 % of ao even when the input intensity data were subjected to 4 % random fluctuations. The authors acknowledge generous provision by Courtauld's Educational Trust Fund of equipment and a maintenance bursary and assistance from L.Tyley and T. Hunt in the design of the electronic control system. B .Y. H. Liu and A. C. Verma Anulyt. Chem. 1968,40,843; B. Y.H. Liu V. A. Marple and H. Yazdani Environmehtal Sci. Tech. 1969 3 381. M. D. Carabine Chem. SOC.Reu. 1972,1,411. B. J. Mason Discuss. Faraday SOC.,1960,30,20. L. Coutarel E. Matijevic M. Kerker and Chao-Ming Huang J. ColZoid Interface Sci. 1967 24,338. F. Harris G. Sherman and F. Morse I.E.E.E. Trans. Antenna Propagation AP-15,1967 p. 141. M. Kerker The Scattering of Light and Other Electromagnetic Radiation (Academic Press N.Y. and London 1969). 'M. Kerker E. Matijevic W. Espenscheid W. Farone and S. Kitani J. Colloid Interface Sci.1964 19 213. W. Heller and M. Wallach J.Phys. Chem. 1963 67 2577. W. Heller and M. Wallach J.Phys. Chem. 1964 68,931. lo R.Tabibian and W. Heller J. Colloid Interface Sci. 1958 13 6. J. E. L. Maddock M.Sc. Thesis (Univ. London 1970). G. Mie Ann. Phys. 1908 25 377. l3 W.Espenscheid M. Kerker and E. Matijevic J. Phys. Chem. 1964 68 3093. l4 M. D. Carabine J. E. L. Maddock and A. P. Moore Nature Phys. Sci. 1971 231 18. M. Powell Computer J. 1965 7 303.