GENERAL DISCUSSION Dr. E. R. Buckle (Shefield University) (communicated) Would Teichner clarify his argument for the conclusion that there is a lower limit to the size at which particles can exist in liquid form? I am confused by the use of the terms " residence time " and " flow rate ". Is it the mass flow rate (rnol/s) of TiCI and not the flow speed that is substantially different for the cases contrasted in fig. la b and fig. lc d of his paper? The flow speed (cm/s) is specified by giving the residence time (0.05 s/cm) only for fig. la,b although it is said that residence times in general varied from 0.003-0.15 s/cm. The point is important because the concentration of vapour as well as the temperature and residence time affects the sizes of particles in a condensa-tion aerosol and it may also affect their morphology.The larger size in fig. Ic is understandable if the mass flow rate is greater while the residence time remains substantially the same since a higher concentration of vapour tends to encourage growth. However this also depends on the temperature and the growth of the nuclei in the flame at 3000 K was clearly faster still (fig. Id). The different shapes may relate to the quenching process. The cooling rates of particles from these high temperatures are controlled by radiation and therefore the size of a particle can be decisive in determining its final crystal form. While it is doubtful if the distinction of particles as liquid or solid can have any meaning when the diameter is only 10 nm say it is reasonable to suppose that the sub-micron particles studied here will be capable of melting and therefore of freezing.In view of the high melting point of Ti02 the condensate at 1700 K cannot begin as liquid so the nucleus grows in the vapour as a solid particle. These particles are probably monocrystals. At 3000 K the nuclei grow into droplets but at low vapour concentrations their size will be limited. Small molten particles stand a better chance than large ones of crystallizing from a single nucleus if growth is controlled by heat transfer. The large liquid particles formed at higher vapour concentrations will not cool so rapidly because of their smaller surface-to-volume ratio. There is therefore a greater likelihood that they will crystallize around many centres and polycrystalline particles tend to take on a spherical outline.Spherical particles of doubly-refracting metallic halides that were condensed from the vapour at temperatures above the melting point showed extinction of plane-polarized light in zones resembling those in the particles of fig. 2b here. The halide particles condensed as droplets and I wonder whether the particle of fig. 26 might have been formed in the same way. How accurately was the flame temperature known in this case? Prof. S. J. Teichner (University of Lyon France) (communicated) In reply to Buckle the residence time is calculated from the inverse of the flow speed and is ex- pressed in s/cm length of the flame. In fig. la b and lc d the mass flow rate is given in molTiCl,/s.According to the value of the mass flow rate of TiCI, two cases should be considered. (i) For a low mass flow rate of TiCI (0.4 x mol s-') only polyhedric particles are formed for any flame temperature (below or above the melting point of TiO,) and for any residence time in the flame used. (ii) For a high mass flow rate of TiC1 (20-3Ox mol s-l) the temperature of the flame and the residence time directly influence the shape of particles. (a) For a low flame-temperature (below the melting point of TiO,) only polyhedric E. R.Buckle and C.N. Hooker Trans. Furuday Soc. 1962 58 1939. 72 GENERAL DISCUSSION particles are formed. Their diameter increases with both (i) increasing TiCI mass flow rate and (ii) increasing residence time at constant TiC14 flow rate.For instance (fig. Ic) the residence time is of 0.12 s cm-I and the particle diameter is 300-400A. When for the same mass flow rate (and the same temperature) the residence time is decreased to 0.003 s crn-l the diameter of particles decreases to lo0 A. (b) For a high flame-temperature (above the melting point of TiO,) and for a large mass flow rate of TiC14 (25 x mol s-l) (value equivalent to the mass flow rate of particles in fig. lc) and for a residence time of 0.15 s cm-' (a value also equiva- lent to that of particles of fig. Ic) spherical particles are obtained (fig. Id). This shows that in order to obtain spherical particles two conditions must be fulfilled (i) the temperature of the flame should be above that of the melting point of the oxide (ii) the mass flow rate or to be more exact the concentration of the species in the flame should be above some critical value for a given residence time.Concerning the comment on the origin of the sphericity of particles which would be correlated with the presence of many nuclei it has been observed (i) that for spherical particles X-ray (line-broadening) diffraction gives evidence of the presence of a monocrystalline solid and not of a polycrystalline solid which then tends to take a spherical outline ; (ii) polyhedric particles on the other hand of dimensions (700 A) well above that of spheres (300A) can also be prepared provided the conditions previously described are fulfilled. Dr. B. Waldie (Heriot-Watt University) said George Murley and Place have presented electron micrographs of particles and data on weight mean particle sizes obtained from electron micrographs.Would they indicate how the shapes of particles were taken into account in obtaining size data from micrographs. The micrograph in plate I does not appear to be shadowed but unless shadowing were used then size data in only two dimensions could be obtained. The variations in intensity of the images in plate I suggest that there could be considerable variation in particle dimen- sions in the direction of viewing. This problem of particle shape was encountered in some previous measurements of rates of coagulation in combustion generated oxide aerosols.'-There simple electron micrographs gave circular images which one was tempted to assume represented spherical particles.In fact shadowing showed the particles to be non-spherical and shape correction factors were obtained from the lengths and shapes of the shadows. The particle sizes were generally larger than those in the present paper because the residence times were about an order of magnitude greater. Teichner has enquired about the possibility of using scanning electron microscopy. This technique was used in the previous study,'. and for agglomerates around 1 pm it tended to confirm the shape factors deduced from shadowed micrographs. A scanning electron micrograph was obtained in which constituent particles down to about 0.1 pm could be distinguished on the outside of agglomerates of around 1 pm size. Subsequent improvements in the resolution of scanning electron micro- scopes could perhaps enable shape data to be obtained for the upper part of the particle size range reported in the paper of George et al.Prof. S. J. Teichner (University of Lyon France) said In reply to Waldie the technique of replica examination is also a convenient way of determining the shape of B. Waldie Ph.D. Thesis (University of Newcastle upon Tyne 1968). B. Waldie and I. Fells Experimental and Theoretical Studies of Gaseous Suspensionsof Thermionic Emittifig Particles for use as MHD Working Fluids in Electricity from MHD Vol. I1 Grit. Atomic Energy Agency Vienna 1968) p. 1161. GENERAL DISCUSSION particles. For spherical particles of titania aerosol (fig. Id of my paper) of a diameter of 1500A a perfectly spherical shape was observed.For polyhedric particles (fig. la b c) for which there is no doubt of the absence of spherical shape the most convenient way of determining their mean diameter d is from the surface area S measured by the gas adsorption method (d = 6/pS where p is the density of the material). The particles of course should not be porous. Their diameter thus determined does not change very much for different geometric forms. Dr. D. Stauffer (Clark College Atlanta Ga) said If one wants to produce mono- disperse aerosols in the size range below 100A is TiO a practical choice? Prof. S. J. Teichner (University of Lyon France) said In reply to Stauffer titanium dioxide aerosols have been studied in our laboratory for many years in connection with their increasing density or sintering properties,l catalytic properties,2 electrical properties and defect structure and photo-catalytic proper tie^.^ Titania may be also prepared as particles of 50 A diam.only (320 m2/g). However obtain- ment of such a highly divided state does not seem to be restricted to titania. Prelim-inary results concerning silica and alumina give evidence for formation of particles of IOOA diam. Probably other aerosols (ZrO, Sn02 Fe,O, FeO V205,Cr,O,) could also be obtained as particles in this diameter range. Mr. E. R. Place (Tioxide Int. Ltd. Billingham)said We have previously shown by shadowing micrograph samples that the particles are spheroidal. Shape is taken into account during the sizing technique in which particles are characterized by the diameter of a sphere of equivalent volume.The particles are assumed to be prolate spheroids with their axis in the plane of the micrograph. Dr. W. J. Dunning (Bristol University) said With regard to the paper by Place under usual conditions of crystal growth low-index planes require two-dimensional nucleation or emergent screw dislocations to bring about their growth. High-index planes do not require these and hence normally grow much more rapidly; thus corners are filled in and the crystal becomes a polyhedron bounded by low-index planes. If under your conditions the supersaturation of TiO is so high that nucleation does not present a barrier to particle formation then two-dimensional nucleation or dislocations are not necessary for the growth of low-index faces.Low-index faces then grow as rapidly as high-index faces and the crystal is no longer polyhedral but spherical. There seems to be a large proportion of spherical particles and of particles with rounded surfaces in his Plate 1. The proportion of round particles should be higher the shorter the residence time. For longer residence times the supersaturation may fall to a level where surface nucleation becomes a barrier to growth and then the proportion of polyhedral crystals should be high. Was such an effect observed? P. Vergnon M. Astier D. Beruto G. Brula and S. J. Teichner Rev. Int. Hautes Tempir. Rifract. 1972,9,27 ; P. Vergnon M. Astier and S. J. Teichner Sintering and Related Phenomena (Plenum Pub].Corp. (N.Y. London) 1973 6 p. 301.) J. Long and S. J. Teichner Bull. SOC. Chim. 1965 2625; M. Th. Vainchtock P. Vergnon F. Juillet and S. J. Teichner Bull. SOC. Chim. 1970 8-9 2806 2812. J. M. Herrmann P. Vergnon and S. J. Teichner Bull. SOC.Chim. 1972,9,271 ; P. Meriaudeau M. Che P. C. Gravelle and S. J. Teichner Bull. Soc. Chim. 1971 1 13 ; P. C. Gravelle F. Juillet P. Meriaudeau and S. J. Teichner Disc. Faruday Sac. 1971 52 140. M. Formenti F. Juillet P. Meriaudeau and S. J. Teichner Chem. Tech. 1971 1 680. GENERAL DISCUSSION The slower rates of growth found by Ghoshtagore may be due to adsorption of impurities on the crystal face or lower supersaturation. Mr. E. R. Place (Tioxide Int. Ltd. Billingham) said In reply to Dunning we find that particles on the whole tend to be more crystalline at shorter residence times.We discount nucleation as an important process for the range of residence times for which we have samples. Nevertheless the change in particle characteristics is puzzling since for flames where the maximum temperature is higher than the bulk melting point crystalline particles are first formed which do not assume a spherical droplet shape until a later stage. Prof. M. Kerker (Clarkson Coll. Techn. Potsdam) said This is a comment on Dunning's question as to whether there is X-ray evidence for polycrystallinity. We always obtained spherical particles of NaCl AgCl and V205 when these aerosols were formed by cooling of the hot vapours. Some crude X-ray and electron diffrac- tion measurements of the NaCl showed no evidence of crystallinity.If the NaCl particles collected by thermal precipitation upon an electron microscope grid were permitted to set for some time in the laboratory prior to electron microscopic observa- tion particularly upon a humid day they changed from spheres to polyhedra including cubes which did give sharp X-ray patterns. We assumed that this change occurred by resolution into a surface layer of water and diffusion to a crystallizing centre. Dr. S. C. Graham (Shell Res. Ltd. Chester) said Place states that his experimental value of n in the equation d = kC,"varies between 0.33 and 0.38 depending on the size parameter used. To the extent that the Ti02 particles are spherical and that coagulation is the only process occurring I would consider the only appropriate size parameter to be the mean particle volume or equivalently the diameter of a particle with the mean volume.This and no other size parameter is directly related to the total particle number density independently of the particle size distribution and the rate of change of the number of particles is equal to the particle collision rate. In fig. 3 his experimental points do give a near-linear plot with a slope n of 0.33 yet as he points out free molecule theory requires a slope of 6/5 x 1/3 = 0.4 and the particles are certainly too small for Smoluchowski's equation (which requires a slope 1/3) to be valid. The cause of the anomalously low values of n may be that the sticking efficiency on collision decreases as the particle size increases.Ignoring van der Waals forces his value of 0.43/0.93 = 1/2.16 for the ratio of observed to predicted value of k corresponds to an experimental collision rate lower than that calculated from the theory by a factor of ten (2.16 3 which implies an overall sticking efficiency significantly less than unity. It is interesting to note that in our paper on lead aerosols the reverse situation exists in that the observed rate exceeds the theoretical value by a factor of about 4.5. Mr. E. R. Place (Tioxide Int. Ltd. Billingham) said In reply to Graham in the expression used to relate diameter with reactant concentration d = kC& the mean value of d used to characterize the size distribution is complex.I agree that the diameter of the particle with the mean volume is the correct average value which relates to particle concentration. However the size dependence of the flocculation rate constant is incorporated in this expression. In the kinetic regime a mean volume diameter and a mean cross-sectional area diameter (relating to the collision cross section are involved) i.e. 76 GENERAL DISCUSSION C = sticking coeficient xo = initial reactant mass concentration d = mean linear diameter and a = mean volume diameter. Under the experimental conditions Knudsen numbers are in the range 3-30 suggesting that particles will be flocculating to some extent in the transition region between kinetic and continuum conditions. Re-examination of the predicted relationships gives d = 0.62 from kinetic and d = 0.72 C,0.33from simple continuum theory.The experimental results lie between these limits with the flocculation rate about 25 % lower than that predicted by kinetic theory. The different relationships obtained using the different mean diameters are thought to reflect the errors in the sizing technique. Higher order means will be increasingly sensitive to small counting errors at the large diameter tail of the distri- bution. In reply to Kerker X-ray line broadening measurements give a crystal size which corresponds approximately to those measured from electron microscopy. Prof. C. S. Kiang (Clark College Atlanta Ca.) said Does Place have any information on the experimental measurements of the bulk surface tension for TiOz ? Mr.E. R. Place (Tioxide Int. Ltd. Billingham) said In reply to Kiang no-a crude theoretical estimate giving a value of 1500 erg/cm2 can be found in Problemy Mettalurgii Titana (Moscow 1967) p. 63-79 by S. G. Moinov and V. A. Reznichenko. Dr. E. R. Buckle (Shefield University) (communicated) In the paper by George et al. the authors discount the nucleation process as rate-determining on the grounds that the nucleus would have to be of sub-molecular size. Would the authors explain how they arrive at this conclusion as it underIies their explanation of the experimental resuIts as dependent on floccuIation or fusion of particles? It is easy to show by Volmer’s theory that the volume of a nucleus is given by v* = 2W*/W“ (1) where W* is the reversible isotherma1 work of nucleus formation and W”is the revers- ible work per unit volume for the phase change in bulk.The value of w”is set by the experimental conditions but W* depends on the rate of nucleation J. J has to be specified before W* can be calculated. The rate of nucleation may be written as J = Kexp(-W*/kT),m-3 s-I where the value of Kdepends on the choice of kinetic model. Then if V is the sample volume the nucleation frequency is r = JV S-1 and W* = kTln(VK/I). The “experimental value ” of I therefore affects v* and an unrealistic result for u* could reflect a wrong choice for I. Mr. E. R. Place (Tioxide Int. Ltd. Billirigham) said In reply to Buckle we have considered primarily the development of the size distribution from the 50 ms residence time position the earliest point at which we have experimental results on particle size by all possible mechanisms.We conclude that growth by chemical reaction is not GENERAL DISCUSSION taking place both because no TiC14 is present and because the change in size distri- bution to the next sampling point is in the opposite sense to that required by a surface growth mechanism. We can include in growth the accretion at the surface of either gas phase TiOz or any nucleus precursor material. If nucleation is slow (large nuclei) then growth at the particle surface already present should be rapid in com- parison. We do not observe this. Rapid nucleation (small nuclei) would imply a high concentration of small particles which are not seen on the size distribution.Jf they are sufficiently small not to be resolved then they must be removed extremely rapidly by flocculation. The variation in particle diameter over an eighty-fold change in reactant concentration implies an approximately constant number concentration of particles at the final sampling point. It seems unlikely that a nucleation-controlled system would give this result. We conclude therefore that nucleation is not occurring in the region of measure- ment to any significant extent. As a consequence of this we suggest that nucleation occurs earlier in the system. It is under these conditions of very rapid nucleation with a large driving force due to fast chemical reaction that we estimate that the nucleus size could be submolecular. Although I agree with the relations derived by Buckle surely it is the stable nucleus size which physically determines the nucleation rate and not vice versa. Dr. E. R. Buckle (Shefield University) (communicated) With reference to the last point raised by Place my meaning was that his count of nuclei must be correct before he can derive from theory the properties of the nucleus including its size.