GENERAL DISCUSSION Prof. M. Kerker (Clarkson Cull. Tech. Potsddm) said The measurement of the extinction cross section of a particle by attenuation measurements of a sample colIected on a glass slide is quite precarious. Among the difficulties are refiection effects due to the glass slide interference effects among the assembled particles and if the collection is somewhat dense multiple scattering effects. Also there is the purely optical problem of eliminating the forward scattered light from the detection system. What precautions did Howard take to assess these? And did he caIculate the refractive index that would correspond to his measured extinction cross-section for comparison with the literature values? Alternatively did he compare calculated values of the extinction cross-section for particles of the size he had with his measured values of the extinction cross-section? Prof.J. B. Howard and Dr. B. L. Wersborg (Depr. Chern. Eng. M.I.T.) said In reply to Kerker attenuation by reflection from the glass slide was adequately elimin- ated by directing the laser beam first at a clean spot adjacent to the particle deposit and then at the deposit. The recorded signal which was the difference between the second and first attenuation signals measured the attenuation by soot particles. Interference among particles was trivial a conclusion based on the fact that attenuation by the different deposits which ranged from less than a monolayer to only a few particle layers was a linear function of deposit depth. Calculations employing the ranges of possible values of the optical coefficients of the particles studied show that scattering is negligible compared with absorption for all values of the diameter/wavelength ratio encountered in the experiment.The optical measurements will be described more fully in a forthcoming publication. The extinction cross-sections cannot be calculated since data on the refractive index of young growing soot particles are not available. However data are available on the refractive index of aged soot and the values give extinction cross sections larger than those measured in this work. According to Dalzell and Satofim,' the complex refractive index of aged acetylene soot for the wavelength in question (6328A) is rn = 1.57-0.44i which gives an extinction cross-section larger by a factor of 28-3.8 than the values found in this study.This difference is qualitatively reasonable since young soot particles contain more hydrogen and have less crystal stucture than aged soot. Dr. C. N. Davies (University of Essex) said I think that aerosols of dibutyl phthalate are too volatile for use in the experiments of Nicolaon and Kerker. Since the aerosols were undiluted the gas phase must have been saturated with the vapour of dibutyl phthalate and eqn (2.9) and (3.1) of my paper are then suitable for calculat- ing rates of evaporation. Coagulation times from 82-327 s are shown in table 5 ; it will be supposed that the temperature of the aerosol in the ageing vessel was 20°C. Calculations of evaporation have been carried out for particles of radii as shown in table 3.' W. H. Dalzell and A. F. Sarofim J. Heat Transfer 1969 91 100. 157 GENERAL DISCUSSION It is evident that during the coagulation period vapour must be distilling isothermally from the smaller particles to the larger ones so that the ascribing of change in size loss of weight in particle radius/ aerosol Pm lifetimels 320 s 160 s DBP in helium DBP in nitrogen 0.235 0.314 940 1210 39 % 27.6 % 19 x 12.8 % distribution to coagulation alone is incorrect. Some of the vapour would also condense on the walls of the vessel which have an area much exceeding that of the aerosol particles; the authors state that they were unable to detect any hold-up on this account but an assessment of the amount of vapour concerned in relation to the accuracy of analysis is lacking.An assessment also of the accuracy of the rather indirect optical measurement of size distribution would be of interest. The mass concentration of aerosol measured by thermal precipitator sampling was 5 % less than the figure obtained with millipore filters. A thermal precipitator can be a very accurate instrument for sampling aerosols but it is possible for vapour to condense in the small cavities of filters due to the Kelvin effect. Prof. M. Kerker (Clarkson Coll. Techn. N. Y.) said In reply to Davies we have checked repeatedly for hold-up of dibutylphthalate in the coagulation chamber and have always found this to be negligible. Some recent results are presented here for three different flow rates.In this case the dibutylphthalate aerosol is in helium at a pressure of 0.50+0.01 atm so that any distillation to the walls would be expected to be more pronounced than for the aerosol in the paper which is for nitrogen at atmos-pheric pressure. The modal radius was 0.25pm. The aerosol was collected on millipore filters (pore 1.2 pm) just prior to entrance into and after exit from the coagulation chamber (volume 2570 ml ; wall area 1800 cm2). Residence time in the chamber varied from 1.28-2.57 min. As is apparent from the table the loss appeared to be about 2 %. The error in weighing the samples is about 1 % so that hold-up in the coagulation chamber is negligible. TABLE 1 .-HOLD-UP OF DIBUTYLPHTHALATE AEROSOL IN THE COAGULATION CHAMBER aerosol conctntration/(nig/l) flow 1.0 I/m flow 1.5 l/m flow 2.0 I/m initial aerosol 1.70 1.62 1.57 coagulated aerosols 1.68 1.59 1.55 One would expect that isothermal distillation from smaller particles to larger ones would occur even more slowly than distillation to the walls both because the wall area is larger than the surface area of the aerosol particles but more especially because these aerosols are quite monodisperse (even those which have coagulated for some time) so that the driving force which is derived from the range of Kelvin vapour pressures is much smaller.Accordingly we do not believe that distillation either to the walls or from particle to particle plays a significant role in the processes occur- ring in the hold-up tube.More direct evidence that the mechanism by which the aerosol ages is coagulation rather than distillation is contained in the two electron micrographs fig. 1 and 2. These depict a linolenic acid aerosol (modal radius a = 0.248 pm) prior to entry into the coagulation chamber and after exit (hold-up time 5.26min). The aerosol was "fixed " prior to collection for electron microscope observation by treatment with OsO,. (The apparent spots in the centre of each particle are due to penetration of the glossy photographic print in the process of obtaining the particle size distri- FIG. 1.-Electron micrograph of linolenic acid aerosol prior to coagulation; see table 2 for size distribution. FIG.2.-Electron micrograph of linolenic acid aerosol after coagulation (5.26 min) ; see table 2 for size distribution.[Tofacepage 158 GENERAL DISCUSSION bution with a Karl Zeiss particle counter.) The size distributions for each of these electron micrographs is given in table 2. It is significant that although the average particle size increases the smallest particles in the population are neither completely scavenged nor reduced to a smaller size as would be expected were the principal mechanism distillation from small to TABLE 2.-PARTICLE SIZE DISTRIBUTION OF INITIAL AND COAGULATED LINOLENIC ACID AEROSOL radius/pminitial (%) 0.18 - 0.21 13.9 0.25 58.1 0.28 23.3 0.32 3.8 0.35 0.6 0.38 - 0.41 - coagulate (%) 0.5 8.3 24.9 19.1 13.8 9.6 5.3 5.4 radius/pminitial (%) 0.44 - 0.47 0.2 0.51 - 0.54 - 0.57 - 0.60 - 0.63 - 0.67 - coagulated (%) 3.7 2.7 3.0 1.o 1.1 0.6 0.9 0.2 large particles rather than coagulation.Also examination of the distribution of sizes in table 2 shows that the frequency of the modal size decreases as would be expected for coagulation and does not shift to a smaller size category of the same frequency as would be expected for the distillation mechanism. 1 IJ 60 80 100 I20 8 FrG. 3.-Polarization ratio against scattering angle for initial aerosol (UM= 0.24pm uo = 0.10 N = 1.2 x 10’ ~m-~) for coagulation times 41 (--) 56 (-. -.) 78 (. . . . .) and 110 (-) s. Davies is surely mistaken when he characterizes the optical measurements as “ rather indirect.” They are most direct since they occur in situ without perturbing the system and can be interpreted in a straightforward method.The sensitivity of the light scattering to the evolution of the particle size distribution in the course of coagulation is illustrated in fig. 3 which represents the curves of polarization ratio GENERAL DISCUSSION against scattering angle for an initial aerosol aM= 0.24 prn c0 = 0.10 N = 1.2x lo7 ~m-~ for coagulation times 41 56 78 and 110s. The separation of these curves indicates that the light scattering canclearly resolve differences of 2-3 SI in coagulation time. Fig. 4 depicts graphically the. resolution in coagulation time attainable for a particular experimental run. In this case the initial particle size distribution was aM= 0.31pm cro = 0.10 N = 5.6 x lo6 ern? The experimental coagulation time was 82s.The figure is a plot of the deviation measure (eqn (5)) against the min FIG.4.-Deviation measure against coagulation time for initial aerosol UM = 0.31 pm uo = 0.10 N = 5.6 x lo6 ~m-~ after 82 s in hold-up tube. The minimum is at 2.50min. calculated coagulation time. The minimum at 2.50 min is certainly well resolved by these light scattering data to within no more than 1-2 s. The resolution becomes less at longer coagulation times when the aerosol becomes polydisperse and it is for that reason that the light scattering can no longer be used to monitor the process beyond about one-third to one-half a life-time. The criterion becomes the depth of the minimum in the curves of the deviation measure against time.Dr. C. N. Davies (Uniuersity of Esses) (communicated) I am grateful to Kerker for the details of his experiments but must admit that 1 am puzzled by the results. His fig. I and 2 which claim to show the coagulation of 0.25 pm radius aerosol of linolenic acid during 326s which may be due to incorrect sampling,' and many circular particles of about the same volume as the chain in the sample of coagulated aerosol. His table 2 shows that some 3 % of the final number of particles has twice the initial radius. T cannot see how so many multiplet particles could have formed ' J. 0.Irwin P. Armitage and C. N. Davies Nature 1949 163 809 ; S. A. Roach The Theory of Ratidotn Climtping (Methuen 1968). GENERAL DISCUSSION by coagulation while airborne.A rough calculation based on the half-life of the aerosol being 250 s indicates that there arc about 20 times too many eightfold multi- plets. The effect of evaporation might therefore have been obscured. Dr. G. H. Walker (Clark College Atlanta Ga.) said The techniques of light beating spectroscopy have been developed to the point where they offer a valuable supplement to the more traditional approaches. Recently Hinds and Reist have applied these techniques successfully to aerosol measurements. Does Kerker think that light beating spectroscopy can be applied profitably to the problems of aerosol growth and coagulation? Prof. M. Kerker (Clarkson Coll. Tech. Potsdani) said The use of in situ light scattering measurements to study dynamical processes of aerosols such ascoagulation appears to have many advantages.Would Brock please comment on the possibility of relaxing some of the present constraints on his method i.e. the restrictions of narrow size distributions and unimodality. On the same subject Some of the people at Clarkson are working on the problem of investigating diffusion battery measure- ments. Brock and his colleagues have done quite a lot on the related light scattering problem. We would be interested to learn about his numerical inversion techniques. Any information would be appreciated. Prof. J. R. Brock (Uniuersity of Texas at Austin) said The problem is that conventional light scattering may be quite inadequate to resolve unimodality versus bimodality for a narrow distribution.In fig. (7.35) of ref. (2) we have shown that if light scattering data corresponding to a bimodal distribution is assumed to be uni- modal one will obtain quite a good fit to the data. Accordingly it is necessary to know a priori whether the system is or is not unimodal. The same applies to the skewness of the distribution. Also we generally find that a unique fit to the data cannot be obtained for 0.1 pm particles when the standard deviation is greater than 20-30 %. For larger particles the conditions are even more stringent. Of course our techniques do not involve absolute intensity measurements which are often difficult to obtain. These might relax matters somewhat. Our numerical inversion technique is experimental and calculated measure-ments (for a two parameter distribution) are compared at each of 19 scattering angles.A deviation measure is obtained by summing the square of the differences between these quantities and plotting contours of equal deviation measures in atwo dimensional domain of the two size distribution parameters. If there is a " well ",the bottom of the " well " is selected as the solution. If the distribution is too broad one will ob-tain open valleys which means there is no unique solution. It is my view that light scattering can be a sensitive tool for particle size study but that it must be based upon observation of single particles such as we have carried out re~ently.~ Then one takes advantage of the high sensitivity of light scattering to particle size. Thus we were able to determine the size and refractive index of single glass fibres to 0.25 % and 0.01 R.1.units respectively. I believe the instrumentation recently developed by the late Prof. Gucker of Indiana University offers a great opportunity in this regard. ' Ao~osolSci. 1972 3 OOO. M. Kerker The Scatteritig of Light and Other Electromagnetic Radiation (Academic Press New York 1969) pp. 359-373. D. D. Cookc and M. Kerker J. Colloid Interface Sci.,1973 42 150. W. A. Farone and M. Kerker J. Opt. Soc. Anier. 1966 56 481. S7-6