GENERAL, DISCUSSION Dr. R. D. Cade (Stanford Res. Inst.) said: In reply to Dr. Mason, we have studied the kinetics of the reaction of ammonia with sulphuric acid droplets suspended in air, both when the droplets consisted of concentrated sulphuric acid and when they consisted of dilute sulphuric acid. The reactions are extremely rapid even at the very low concentrations to be found in the smog-laden atmo- spheres of cities. Our calculations suggest that when the droplets consist of concentrated sulphuric acid, during the initial stages of the reaction about one out of every ten collisions of ammonia molecules with the sulphuric acid surfaces results in reaction. The overall reaction rate is controlled by diffusion within the droplets. On the other hand, when the sulphuric acid is dilute our results suggest that every collision results in reaction and the overall reaction rate is controlled by the rate of diffusion of ammonia in the gas phase.In the latter case the initial reaction is probably that of ammonia with water, and the sulphuric acid subsequently reacts with the ammonium hydroxide thus produced and prevents the reverse reaction from occurring to an appreciable extent. The reactions were so rapid that it was necessary to use a flow system for determining the reaction kinetics. Thus, distance from the point of mixing at which sampling was undertaken was proportional to the reaction time. The sampling was undertaken by passing the entire aerosol through a bed of molecular sieve material (artificial zeolite) which removed the ammonia but permitted the nitrogen and suspended particles to pass through unchanged. The particles were then collected with an elec tr 0s tat ic precipitator and analyzed colorime t r icall y for sulphate and for ammonia.When the droplets consisted of dilute rather than concentrated sulphuric acid, the relative humidity in the aerosol had to be main- tained at such a high level that the molecular sieve material was not effective for removing the ammonia. In this case, crystalline oxalic acid was substituted for the molecular sieve material and was found to be highly satisfactory. In reply to Dr. Elton, results obtained at Stanford Research Institute and else- where suggest that dark (thermal) reactions involving olefins at concentrations existing in smoggy atmospheres do not appear to produce aerosols.For example, the reactions of olefins with ozone at such concentrations produce only gases. However, photochemical reactions involving olefins in air, which, of course, require the presence of substances such as nitrogen dioxide and aldehydes to absorb sunlight, do produce aerosols. Recent experiments at the Institute have indicated that photochemical reactions in the system olefins + air+ NQ2+ SO2 produce highly concentrated aerosols when exposed to sunlight. Such reactions are prob- ably of great importance to the visibility-decreasing properties of smogs of the Los Angeles type. Dr. P. G. Wright (Dundee) said: Tesner 1 concludes from his results that the decomposition of acetylene at the surface of carbon particles is not diffusion- controlled.This is to be expected for even the largest of the particles (radius a ~ l O 3 A) under his conditions (SOOOK, 1 atm). In terms of Fuchs' theory 2 of evaporation and condensation, the retardation due to diffusion may be represented in the steady state (for the non-steady state the retardation is even less) by dividing by the denominator * 1 Tesner, this Discussion. 2 Fuchs, Physik. Z. Sowjet., 1934, 6, 225. * (communicated) : In its usual application (evaporation and condensation) the theory of Fuchs 2 requires that the condensable species 2 shall be rare with respect to the gaseous 1, so that single diffusion and mutual diffusion shall be indistinguishable. In the present application, though there is much acetylene as well as much hydrogen, there is true mutual diffusion because for each C2H2 molecule which decomposes, one gaseous H2 molecule is formed.Consequently, the denominator does not require further correction. 222FIG. 1 .-Linolenic acid particles; magnification 3940 x . FIG. 2.--L,inolenic acid particles; magnification 3940 X . FIG. 3 .-Silver chloride particles coated with linolenic acid; magnification 3940 X . FIG. 4.-Silver chloride particles coated with linolenic acid ; magnification 3940 x . To face p. 2231GENERAL DISCUSSION 223 a here represents the probability that an acetylene molecule decomposes on striking the surface of a carbon particle. 22 is the mean molecular velocity of acetylene (8.1 x 104 cm sec-1 at 800°K). D J ~ is the coefficient of mutual diffusion of acetylene and its decomposition product hydrogen.Its value may be taken to be approxim- ately equal to that of the (measured 1) coefficient of mutual diffusion of oxygen and hydrogen (4-8 cm2 sec-1 at 800°K and 1 atm). Taking A = 2012122 = 1.2 x 10-4 cm = 12a, even if a is as much as 1.0, the value of the correcting denominator is l + - x - X - =1*003. (; l!2 :3) Thus the retardation due to diffusion cannot exceed 0.3 %. Prof. Milton Kerker (Potsdum, N. Y.) said: We would like to report on progress in preparing " coated aerosols " since our paper was communicated. Linolenic acid has been chosen as the coating material both because of the ease with which it can be condensed on silver chloride aerosols and because by exposure to the vapours of osmium tetroxide, it can be fixed for electron microscopic observations.Fig. 1 and 2 are electron micrographs of linolenic acid aerosols. These were prepared by passing silver chloride nuclei from a hot wire through a boiler con- taining linolenic acid at 120" and 125" respectively, and subsequent cooling in an air condenser. The flow rate was 242 ml/min. Collection was effected by thermal precipitation. The particles were exposed to the osmium tetroxide for 3 h and observed in the electron microscope without further treatment. The silver chloride nuclei were sufficiently small so that they gave no visible Tyndall beam prior to entering the boiler, although the emergent linolenic acid aerosol itself was quite turbid. No aerosol was formed under the same conditions in the absence of silver chloride nuclei.Fig. 3 and 4 are electron micrographs of silver chloride aerosols coated with linolenic acid. The silver chloride nuclei were prepared in the generator de- scribed in our paper and then passed through the linolenic acid boiler at 110". The boiler of the silver chloride generator was maintained at 1010" and 1100" respectively, and the flow rate at 356 and 930ml/min respectively. The collec- tion, fixation and electron microscopy were carried out as described above. Fig. 4 is typical of coated aerosols with a thin coating. Although the coating appears somewhat as a blur this is not due to the picture being out of focus, as direct inspection on the microscope screen can easily show. By comparison, uncoated silver chloride particles give a sharp picture.It will probably be necessary to obtain densitometric traces in order to determine the thickness of the coating in such cases. We are still engaged in elucidating the relation between the conditions under which these aerosols are prepared and the type of aerosol particle obtained. We have not yet analyzed any of the light-scattering data. Prof. Milton Kerker (Potsdam, N. Y.) said: It is rather interesting that the refractive index of 1.486 used for dioctyl phthalate corresponds so closely to the value of 14821 used by us for linolenic acid aerosols. We have compared the total Mie scattering coefficients published by Penndorf for rn = 1.486 with our results. We find that the small difference in refractive index results in an average difference of 1.5 % between the two sets of scattering coefficients, and in one case the difference is as great as 5 %.This is a significant difference in view of the fact that the scattering coefficient itself oscillates with size between extrema that differ , 1 Walker and Westenberg, J. Chem. Physics, 1960, 32, 436,224 GENERAL DISCUSSION from the mean by only 20 %. Furthermore? the total scattering coefficient is frequently less sensitive to size and refractive index than the angular scattering functions themselves. This would suggest that it is probably necessary to know the refractive index of the particles to a high degree of precision. As an illustration of the vagaries that may be encountered in scattering by particles larger than the wavelength, we present some scattering data in table 1 for particles corresponding to our concentric sphere model.The refractive indexes are for a silver chloride sphere encased in a spherical shell of linolenic acid, The total size is determined by v = 2nb/i17 where b is the particle radius. The size of the inner sphere is given by a = 2na/I, where a is its radius, We have selected y = 30" (measured from the backward direction) as illustrating an extreme but not an unusual situation. TABLE l.-SCATTF,RING FUNCTION il AT y = 30" m1= 2.105 o x v 38.67 -20 x v 49.64 -40 x v 2203 -60 X v 7-43 -80 x v 1 18.48 -90 X v 26.67 a95 x v 8.01 -98 x v 32.62 a99 x v 26.68 1.00 x v 24- 67 v = 12.0 m2= 1.4821 v = 12.1 v = 12.2 21.48 22.65 26.00 25.60 7.1 1 9.13 55.68 19-96 107.47 105-44 14.1 1 12.04 41.59 55.36 25.09 16.80 21.43 7.63 11.99 -63 m3 = 1.OOO v = 12.3 v = 12.4 27-77 27.21 29.8 1 28.86 8.21 5.04 10.79 17.30 29.83 28.52 17.14 27.78 22.80 13-09 4-50 29.38 a 1 3 29.73 8.84 30.73 A particle for which a = v = 12.2 corresponds to a silver chloride sphere of about 0.8 ,u radius illuminated by blue light. A change of v by 0.1 unit, which is certainly less than the accuracy of any known method of determining the size of such particles, results in an increase of scattering by more than an order of mag- nitude.Furthermore, a coating of linolenic acid whose thickness is 1 % of the particle radius (v = 12.2, a = 0 . 9 9 ~ 12.2) causes a comparable variation in scattering. These computations have been carried out with an IBM 704 digital computer. Our programme encompasses the single sphere corresponding to the Mie theory as a degenerate case. Although the National Bureau of Standards has also programmed this problem for the same computer, we found their programme so slow that the cost of running extensive computations became excessive.From an input of a, v, ml, m2 and m3, our present programme will produce a complete set of scattering data in about 4sec. This includes angular scattering functions at 21 angles of observation. With the availability of Dr. Gucker's angular functions, this could be increased to 181 angles of observation at little or no appreciable increase in running time. The results with our programme agree precisely with those of the National Bureau of Standards for the concentric sphere case and with various values in the literature for the single sphere case as well as with various hand-computed check-points.At the present time we have com- puted the 1500 cases corresponding to v = 0.1 (0-l), 15-0 for a = (0, 0.20, 0.40, 0.60, 0.80, 0.90, 0.95, 0.98, 099)X V . Prof. Milton Kerker (Putsdam, N.Y.) said: Dr. Gucker and Dr. Rowel1 have very successfully eliminated two of the most troublesome perturbations in light- scattering work, polydispersity and secondary scattering, by making their ob- servations upon a single particle. By their very ingenious experimental work they have been able to deal with a perfectly monodisperse and infinitely dilute aerosol. In our laboratory, Dr. MatijeviC, Dr. Ottewill (on leave from Cambridge University) and I have recently been able to make light-scattering observations on another perfectly monodisperse and infinitely dilute aerosol, viz.a spider fibre.FIG. 1 .-Electron micrograph of spider fibre; magnification 6500 x . To face p. 2251GENERAL DISCUSSION 225 This system has the added advantage, that since it can be suspended from a simple frame, the spurious reflections associated with an enclosing cell are also eliminated. This work will be reported in detail elsewhere and we will only summarize our results here. The fibre studied was from a theridiid species, an electron micro- graph of which is shown in fig. 1. The fibre radius was about 112 mp although it was probably not of circular cross-section. The fibre was oriented with its axis perpendicular to the scattering plane and the intensities of the horizontal and vertical components of the scattered radiation were determined at various angles of observation.The ratio of these two intensities, the polarization ratio, was calculated for comparison with the theoretical results. Data was obtained at 436, 546 and 598 mp. We utilized amplitude functions computed by Rayleigh 1 and more recently by Larkin and Churchill 2 to calculate intensity functions, assuming the refractive index was 1.5. From theoretical curves of polarization ratio against radius for various angles of observation, it was possible to evaluate the radius corresponding to the experimentally determined polarization ratios of the spider fibre. The results are given in table 1 and agree very well with the electron microscopically determined value of 112 mp.The quantities in parenthesis are experimental values of the polarization ratio. Agreement was not obtained at angles less than 105", possibly due to the deviation of the cylinder from circularity. Apparently the 90"-scattering is less sensitive to fibre shape than that at other angles. TABLE 1 .-RADIUS OF SPIDER FIBRE CALCULATED FROM POLARIZATION RATIO 436 105 mp (-455) 107 mp (-395) 103 mp (-535) 546 111 (-145) 94 (-100) 1 20 (-235) 598 122 (-150) 109 (-120) 1 29 (-200) Attention should be drawn to a very striking phenomenon associated with scattering by infinite (long) cylinders illuminated at perpendicular incidence. The light is scattered in a disc, of thickness delineated by the incident beam, which is parallel to the scattering plane.The spider fibres were visible only when viewed along the radii of this disc, the scattered light diverging only slightly from parallelness in this plane. This divergence of the scattered light in only one direction is implicit in the theory, the scattered intensity decreasing as llr and not as l/$. Dr. W. Smith (D.S.I.R., Stevenage) said: In connection with Prof. Churchill's paper, I wonder whether he has seen the work of Vermeulen et aZ.,3 who found that their experimental results fitted the equation, wavelength, m p 0 = 900 e = 750 0 = 105' This can be obtained from eqn. (7) of the paper by expanding the hyperbolic functions, and omitting orders higher than the first. Vermeulen was concerned with much larger particles, and it is interesting to see that Prof.Churchill's ex- pression covers such a wide range. For reflection, Calderbank et aZ.4 have found that their experiments fitted where k is a constant depending upon the refractive index ratio. It should be possible to give theoretical support for this expression by obtaining it from 12 of 1 Rayleigh, Sci. Papers 434 (1919), cited by van de HuIst in Light Scattering by Small 2 Larkin and Churchill, J. Opt. SOC. Amer., 1959, 49, 188. 3 Vermeulen, Williams and Langlois, Chem. Eng. Prugr., 1955, 51, 85. 4 Calderbank, Evans and Rennie, in Rottenberg (ed.), Int. Symp. Distillation, 1960 Particles, chap. 15 (John Wiley and Sons, New York, 1957). (The Institution of Chemical Engineers, London). H226 GENERAL DISCUSSION the paper, but when I attempt to get 12 from eqn.(5) and (6) I find that no boundary condition will fit for an infinite depth of liquid-as would be required for the ideal case of reflection. Could Prof. Churchill give the solution for 121 It is noticeable that the solution (eqn. (7)) becomes trivial for the case S = 0, whereas one would expect it to converge to the ordinary solution for the condition where there is no side scatter. Dr. G. A. H. Elton (Brit. Baking Ind. lies. Assoc.) said: In the experiments described by Prof. Churchill, two approximately monodisperse samples of spheres were used, one batch had a mean diameter of 0.814 p, and the other a mean diameter of 1.171 p. I would like to ask Prof. Churchill whether, in his view, the results obtained with particles of this sort of size can be extended with confidence to much larger particles (e.g. diameters of ZOp), and to heterodisperse systems.I ask this question because in scaling down an atmospheric aerosol in the way which Prof. Churchill describes, it would be very convenient to be able to study hetero- disperse systems of larger particles of the types which occur naturally in fogs and clouds, provided that the results which Prof. Churchill found with monodisperse small particle systems can be applied to such cases. Prof. Frank T. Gucker (Indiana University) said: Did not Chandrasekhar derive an equation covering the case of multiple scattering from a semi-infinite atmosphere, and would this solution be of any assistance in treating the problem under discussion ? Prof. S. W. Churchill (University of Michigan) (communicated) : In reply to Dr.Smith the individual solutions of eqn. (5) and (6) are p cosh [y(l, - Z)] + NaS(B + S ) sinh [p(1, - l)] p cosh (pl,) + N q ( B + S ) sinh (pl,) ’ I , = and BNa, sinh [p(l, - l)] p cosh (pl,) + Na,(B + S ) sinh (pZt] I , = (9) For S = 0, corresponding to no absorption or sidewise loss, the following ex- pressions can be obtained by direct solution of eqn. (5) and (6) or by application of L‘Hospital’s rule to eqn. (8) and (9) : 1 + No,B( I, - I ) I , = l+Nas,Bl, ’ N~J3(1, - d) I , = 1 + Na$I, Eqn. (7) does not, as suggested, become trivial for S = 0. L’Hospital’s rule yields Application of which can also be obtained from eqn. (10). Eqn. (12) has the same form as the empirical equation of Vermeulen et al., indicating that their p is equivalent to our NosB.As suggested, an expression of the same form is obtained for finite absorption or sidewise loss by expanding the hyperbolic terms and retaining only the first order terms for small thickness; their p is then equivalent to our Na,(B+ 8. Eqn. (10) and (11) also yield an expression for the reflectivity which has the same form as the empirical equation of Calderbank et al., indicating that their k is equivalent to our l/BZt. The simple two-flux model thus provides theoretical support for both correlations and a physical interpretation of the coefficients.GENERAL DISCUSSION 227 In reply to Dr. Elton, we would expect our findings to be applicable semi- quantitatively to larger particle sizes and heterodisperse systems. In reply to Prof.Gucker, Chandrasekhar 1 derived exact expressions in the form of integral equations for multiple scattering by finite and semi-infinite atmo- spheres but computed numerical values only for isotropic and Rayleigh scattering. We have recently carried out numerical calculations for multiple scattering by a semi-infinite atmosphere for several realistic angular distribution functions,Z but these distributions do not correspond to the values of a used in the experiment reported herein. Dr. €3. J. Mason (ImperiaE College, London) said: I can confirm that the aggregation of ice crystals increases quite rapidly when the air temperature rises above about - 6°C. In measuring the electrification which results when impacting ice crystals rebound from the surface of an ice sphere, we find that the charging falls rapidly when the air temperature rises above -6°C because, at these tem- peratures, the crystals stick and do not bounce off.There is also radar and direct observational evidence that the aggregation of snow crystals to form snowflakes proceeds very rapidly at temperatures near the 0°C but this may be greatly assisted by the presence, in the cloud, of supercooled water droplets which may act as a cement to bind the crystals together. However, there were no supercooled droplets in our experiments nor, I believe, in those of Dr. Hosler. Although it is fashionable to attribute the adhesion between ice crystals to the presence of a liquid film on their surfaces, I find it difficult to conceive of a " liquid " layer many molecules thick at temperatures well below 0°C ; nor do I think it necessary.We have found that when a temperature difference is estab- lished across an ice crystal this is accompanied by a potential gradient, the crystal becoming, in effect, a dipole. The charge separation suddenly increases at tem- peratures above -S"C, the increase occurring mainly in the surface layers. Per- haps the adhesion of ice crystals may be attributed to these electrical forces. Dr. Hosler describes how his crystals aggregate in chain-like fashion and fold under their own weight. I have observed small ice crystals to aggregate in chains in the presence of an electric field and to behave as he describes. I wonder whether, in his apparatus, where ice crystals are striking an insulated tube, quite large electric fields might not be set up and that ice crystal aggregation may occur as a result of the charges induced in them by temperature gradients and external electric fields.I should like to see the adhesion between ice surfaces studied under very clean conditions with the adsorption of impurities eliminated or greatly reduced. Prof. C. L. Hosler (Penn. State University) said: As Dr. Mason suggests, we feel that there were no water droplets present during our experiment. This was one of the first things we looked for when we found our maximum sticking at - 11°C. Observations of individual ice crystals showed no growth over periods of many minutes indicating that no liquid phase was present. I would be interested to see whether Dr.Mason would observe sticking at temperatures lower than -6°C if he had a cloud composed of plates. I believe his experiment was carried out under conditions where only columns were pro- duced. We observed that columns did indeed stick very poorly. but at temper- atures below -10°C our experiment dealt only with plates which seemed stickier than columns. Dr. Mason's point concerning electrical effects and adsorbed impurities is an important one. We made no effort to measure the electric field in the test section and we used the air in the laboratory without special treatment. Just as the role of adsorbed materials greatly affects the activity of nucleating materials, H am sure that they must play an important role in determining the surface 1 Chandrasekhar, Radiative Transfer (Oxford Univ.Press, 1950). 2 Churchill, Chu, Leacock and Chen, DASA report IZQ. 1184 (Ann Arbor, Michigan, 1960).228 GENERAL DISCUSSION characteristics of ice. In spite of extraneous effects that adsorption might produce, however, the experiments showed a very consistent relationship between the number of ice crystals sticking to the aggregate and the temperature and crystal type. Dr. G. A. H. Elton (Brit. Baking Ind. Res. Assoc.) (communicated): The Dis- cussion has been use€ul in crystallizing a number of important physico-chemical questions which must be answered before substantial progress can be made in a number of branches of this subject. It seems to be generally agreed that the Volmer-Weber-Becker-Doring theory of nucleation is not entirely satisfactory as it does not fully describe the early stages of nucleation, nor does it account for the differing effect of positive and negative ions.It is clear that great caution must be exercised in applying thermodynamic treatments to nucleation processes in which the number of molecules involved in an aggregate is very small. The use of bulk properties such as surface tension and contact angle is likely to be par- ticularly hazardous. It is also interesting to note that, as Prof. Ubbelohde pointed out, a cluster of water molecules around a single ion can represent quite a con- centrated solution. For example, a single ion in 55 molecules of water will give a dioplet of radius 7 to 8 A, with an equivalent concentration of approximately 1 N. Turning to mechanisms of growth and shrinkage of droplets, it is established that very small (submicron droplets) in a heterodisperse aerosol change their size mainly by the evaporation-condensation mechanism, but this falls off in rate as the size increases. Coagulation becomes more important with increasing size but is not really significant in tranquil conditions until the radius exceeds about 20p. For droplets of radius of the order of 1 p, electrical double layer effects are important, especially in turbulent conditions. The forces involved are of short range, but can nevertheless be of great importance in determining coalescence efficiencies. The problem of the interaction of electrically neutral droplets containing electrical double layers presents an interesting field for theoretical work, and further experimental results covering, in particular, the effect of droplet size and electro- lyte concentration are necessary. With regard to the collision and coagulation of ice particles, there is also a need for basic physico-chemical work on the question of whether or not a liquid film exists on the surface of ice below 0°C and, if so, how thick this film is.