ISSN:0301-5696    

DOI:10.1039/FS97307FX001

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Nucleation Growth Ripening and Coagulation in Aerosol Formation BY W. 3. DUNNING School of Chemistry University of Bristol Bristol BS8 1TS Received 4th December 1972 The atmosphere may be regarded as a carrier gas (the permanent gases) containing water vapour C02and trace substances. The latter comprise gaseous compounds of nitrogen sulphur chlorine carbon and oxygen together with an aerosol of fine particles. The sources of these particles are diverse ; winds lift many from the earth ; smoke from forest fires contributes inorganic ash and carbon compounds; the bursting of bubbles in the sea surface provides salt particles ; some come from volcanic eruptions and meteorites and yet others are of biological origin. Nor must we forget radioactive fallout.Each year domestic and industrial activities introduce hundreds of millions of tons of pollutants gaseous and particulate into the atmosphere. Much of this discharge is invisible but fogs and smokes may often be seen when readily condensible vapours ranging from water vapour and partly burnt fuels to metallic oxides are emitted from cooling towers chimneys and exhausts to undergo cooling by turbulent diffusive mixing with the atmosphere. Fumes from smelting contain volatile metallic salts which condense as fine particles. Sulphuric mist and alkali mist are other undesir- able aerosols. When fired heavy guns often produce smoke composed of water droplets and metallic particles. On the other hand signal smokes serve a useful purpose and the manufacture of carbon black of titanium dioxide and silica involves the production of very fine particles.The knowledge gained by atmospheric scientists is very relevant to the technology of such processes. SIZE DISTRIBUTION OF THE ATMOSPHERIC AEROSOL When the relative humidity is below saturation the particles in the atmosphere may be grouped according to size as follows ; " small ions " (radius rw pm) which consist generally of a singly charged molecule with a cluster of a few neutral molecules ; Aitken particles (5 x pm<r< 10-1pm) ; " large particles " (10-l pm <r< 1 pm) and " giant particles " (1 pm <r <20 pm). For the size range 0.1 pm<r< 10pm Junge found that the size distribution measured at Frankfurt and on the Zugspitze could be expressed by n(r) = Alr4 (1) where n(r)dr is the number of particles with sizes between r and r +dr ; A = 0.054 (ref.(3)) with 4 the volume fraction of the disperse phase. This remarkable law has been confirmed for " country " and " industrial " atmo~pheres.~-~ The size distri- bution for salt particles in marine air deviates from Junge's law.'. Eqn (1) has been found to describe the size distributions in certain artificial aerosol^.^ 7 AEROSOL FORMATION BASIC PROCESSES The following basic processes must be considered prenucleation kinetics nucleation growth ripening and coagulation sedimentation impaction and dispersal. PRENUCLEATION KINETICS In the atmosphere chemical and photo-chemical reactions may take place in the gas phase in water droplets or on the surface of particles and as a result new particles may be nucleated or changes in preformed particles result.'O Hydrogen sulphide and SO are oxidized to form sulphuric acid and sulphates in particular (NH4),S04.The photolysis of NOz gives atomic oxygen which reactswith unsaturated and aromatic hydrocarbons to form aldehydes ketones peroxyacyl nitrates and ozone. Salt particles react with nitrogen oxides and sulphuric acid droplets to give hydrogen chloride nitrates and sulphates. l In industrial processes the mechanism by which supersaturation is generated may be relatively simple for example the admixture of a cool gas or it may involve a complex sequence of elementary reactions as in the production of Ti02. NUCLEATION Condensation may take place on surfaces,12 on insoluble l3 and soluble par- ticle~,~~ on positive and negative ions l5 and even on other molecules in the gas phase.16 In the atmosphere condensation occurs at supersaturations ranging from a few tenths of one per cent to a few tens per cent." Heterogeneous nucleation on "foreign " particles is also common in industrial processes.Attrition may produce particles of the product which then act as centres for further growth. In the absence of foreign nuclei condensation of a vapour make take place by homogeneous nucleation but this requires much larger supersaturations. There are technical processes in which homogeneous nucleation is predominant and the theories of homogeneous nucleation ripening and coagulation are in any case branches of a single comprehensive theory.Chance collisions of single vapour molecules A form dimers A which in turn form trimers A3 and so on. The sequence of reactions may be represented by +A +A . ..A[- +Ai +A,, .. . (i 2) -A -A implying the assumption that only single molecules and not clusters are gained or lost. The rate of formation of the cluster A is given by ht(t)ldt = Pi-14-10) -alw -PrntO)+%+*ni+10) (3) where ni(t) is the concentration of Ai and /Ii and oli are respectively the frequencies of capture and escape from an i-mer. Clusters which are not too small are considered to be very similar to small droplets containing the same number of molecules. There is a critical size of cluster-droplet containing i = K molecules the vapour pressure of which is just equal to the partial pressure pr of the supersaturated vapour and PI = Pa3 exp (2avlllkTrK) (4) where pImis the vapour pressure over a plane liquid surface (r-+a),4 is the surface tension oI1the liquid molecular volume and rK the radius of the critical nucleus W.J. DUNNING Droplets smaller than this tends to evaporate those larger to grow. The steady state rate at which critical nuclei are formed and become free growing is given by J = ZfiKflK (5) where 2 is the Zeldovich l8 factor and classical theory l9 gives Thus J is a very strong function of the supersaturation ratio pr/prm; there is a critical supersaturation ratio below which J is negligibly small. How closely clusters resemble droplets endowed with macroscopic properties is questionable.A "revision " of the theory by Lothe and Pound 2o predicts that the nucleation rate should be higher by a factor of 1017 than that resulting from classical theory. Dunning approached the problem in a different manner and predicted a factor of about lo4 instead of 1017. Further studies by Reiss 22 support the view that the classical expression is effectively valid. REVIEW OF EXPERIMENTAL METHODS AND RESULTS The experimental techniques available for testing the theory are piston cloud chambers diffusion cloud chambers supersonic nozzles and shock tubes. CLOUD CHAMBER EXPERIMENTS Successive expansions of the piston cloud chamber to increasing volumes leads to the appearance of condensation. The results of Wilson 23 and of Powell 24 show a straight line dependence 25 between log (pr/prco)crit and T-s as predicted by classical theory.Lothe and Pound 26 consider that the data of Wilson,23 of Powell 24 and of Volmer and Flood 27 are in agreement with classical theory if 0 = om. In the diffusion cloud chamber,28 vapour and an inert gas lie between the surface of the liquid and a cooler horizontal plate. At a certain height within the gas the upwardly diffusing vapour condenses and drops descend into the pool. The super- saturation at the condensation level may be calculated. Katz and Ostermeier 22 have found remarkably good agreement with classical theory and state that the Lothe- Pound revision does not fit their results at all. NOZZLE EXPERIMENTS When a vapour flowing through a convergent-divergent nozzle reaches super- sonic speeds it expands adiabatically and its temperature falls.At a critical super- saturation condensation occurs and the heat released causes the pressure to increase above the value it would have had in the absence of condensation. Oswatitsch 30 showed how gas dynamics and the kinetics of nucleation and growth may be combined to furnish a detailed description of the pressure changes during the whole course of condensation. Experiments by Wegener and Pouring,31 Stein,32 Barschdorff 33 and Jaeger et al.34show that the experimental nucleation rates for water vapour in air agree roughly with classical theory. Similar agreement has been found for C02 in air,35 for benzene in air 36 and for C2H50Hin air.37 On the other hand measurements on NH3,34CHC13 38 and CC13F 34p 38 agree with the Lothe-Pound revision.For steam 39 (i.e. pure water vapour without a carrier gas) condensation occurs at a rate slower (by a factor of about than classical theory predicts and about 10-1times more slowly than that predicted by Lothe and Pound. Wegener et al.39point out that AEROSOL FORMATION in the steam case all effects which may be due to heterogeneous nuclei can be categoric- ally ruled out. Barschdorff et aL4' have shown that data 41 for the condensation of pure steam is in accord with classical theory modified to include the effect of non-isothermal nucleation. Pure nitrogen shows the same effect.42 SHOCK TUBE EXPERIMENTS In a shock tube (fig.l) a thin diaphragm divides a long tube into two sections. In the " driver " section the gas is at a higher pressure than in the other section. On bursting the diaphragm a shock wave propagates into the low pressure section while an expansion wave passes into the high pressure section. The use of the shock wave P (i) Low a High I FIG.1 .-(i) Shock tube before bursting diaphragm a. Pressure in tube shown above. (ii) Shock tube a short time after bursting diaphragm ; b shock wave c contact surface d limit of expansion wave. Pressure and temperature in tube shown below. for observing relaxation effects and reaction rates is familiar to chemists. Less well known is the technique of Wegener and Lundquist 43 in which the expansion is used to study condensation phenomena.This technique allows a wide range of cooling rates to be investigated in the same experiment 44 and the closed system has advantages. Some preliminary results of such experiments carried out at Yale have been DIRECT INVESTIGATIONS ON CLUSTERS Stein and Wegener 45 have measured the relative intensity of Rayleigh scattered light from a free jet placed in the cavity of an argon laser and found for example in one experiment that there were 10l2 particles ~m-~ and that their average size was about 45A. These figures are in agreement with classical theory. When a supersonic jet of vapour emerges from a nozzle and is collimated by a skimmer and a slit the resulting molecular beam may be examined. Bentley 46 and also Henkes 47 passed the beam into the source of a mass spectrometer and measured the ion currents for the various cluster masses.48* 49 High energy electron diffraction patterns have been obtained from clusters by Anderson and Stein.5o W.J. DUNNING NUCLEATION TIME-LAG When a system suddenly becomes supersaturated clusters must be built up to critical size.51- 52 During this time lag the rate of nucleation J(t) is given approxi- mately by 53 J(t) = J exp (-z/t) (7) where J is the steady-state rate (eqn (5)) and z = K2/pKwhere PK is the frequency of monomer capture by the critical nucleus of size K. In cloud chamber and supersonic nozzle experiments z for water vapour is appreciably less than the " time of observa-tion " during which the supersaturation persists and the steady state approximation is valid.54 When the growth process of the embryos is not simple but say the result of chemical reactions at the surface of the embryos the possibility that the nucleation rate is non-steady must be considered.GROWTH OSTWALD RIPENING AND SMOLUCHOWSKI COAGULATION Fig. 2 illustrates schematically the change in the size distribution n(r) with time. The initial cluster distribution ab relaxes to the steady state distribution cd during the build up period (w 107). The strip ec corresponds to n(r,)dr and to the number of critical nuclei. In the next interval of time these nuclei are born and become free- growing. In the second-next interval the first-born grow and another lot of nuclei are born.In the third-next interval the first-born continue growing the second-born grow and a third batch of nuclei appear and so on until the distribution is that of A. Size r r FIG.2.-Schematic representation of the development with time of the size distribution. As a result of growth the supersaturation decreases with time hence the rate of nucleation is greatest at t-1Oz and decreases to become negligible at the metastable limit ; beyond this limit the continued decrease in the supersaturation is solely the AEROSOL FORMATION result of growth. Clearly the first born are the most numerous class and the largest in size. The foot of the leading edge of the distribution tracing the curve r,, in the (r t) plane shows the growth of the first-born.The number dnuclei being born at any time is related to the height of the ordinate at the trailing edge of the distribution the foot of which initially follows the curve r,. When the supersaturation reaches the metastable limit the height of the trailing edge is negligible (curve E). The supersaturation continues to decrease and in consequence rK continues to increase since r and supersaturation are related by the Gibbs- Thomson relation (eqn (4)); r overtakes the size of the smallest drops and then Ostwald ripening occurs (curves F G). Droplets Iarger than rK continue to grow but those which have become smaller than r begin to evaporate and there is a flux of droplets in the direction r = 0. The distribution now begins to spread out on both sides of r which is itself changing with time.At all times rK must remain smaller than r,,, otherwise the whole precipitate would evaporate contrary to thermodynamic principles. OSTWALD RIPENING The sequence of reactions in eqn (2) and the corresponding rate eqn (3) apply not only to subcritical clusters but also to the drops of condensate so long as the assump- tion remains valid that only single molecules are gained or lost and that reactions between droplets (i.e. coagulation) may be neglected. When we change from discrete distributions niwith integral i to continuous distributions n(r)dr eqn (3) becomes the equation of continuity an(r,t) a[h( r,t)] =O (8) at + ar where i = dr/dt is the rate of growth. Gyarmathy 55 has derived an expression for i,the rate of growth of a droplet from a supersaturated vapour in a carrier gas Here L is the latent heat of condensation per kg A the gas constant per kg of vapour, Pthe total pressure andp the partial pressure of the carrier gas far from the droplet ; D is the diffusion coefficient and I the mean free path the thermal conductivity OJ the medium p the density of the liquid and rK is given by eqn (4).Size distributions during nucleation and growth (e.g. A B C D,E in fig. 2) may be computed from the expressions for i and J and the equation for continuity. When nucleation ceases this source of particles is replaced by a sink for particles near r = 0. Some time after this still assuming that coagulation is absent net growth from the vapour becomes unimportant and the supersaturation changes only very slowly with time; this is the stage of secular ripening.Lifshitz and Slezov 56 obtained an “asymptotic ” solution of the ripening eqns (4) (8) and (9). Wagner 57 extended their results and Dunning 58 further simplified the procedure. If we use Gyarmathy’s eqn (9) for growth (r>rK)and evaporation (Y <rK),the size distribution during secular ripening is of the form Nr t) = dt) h(P1 ’P (10) in which g(t) depends only on the time and h(p) only on the relative size p (p = r/rK) Further s(t>= dto) [I+ (f -fo)l%1-2 (11) W. J. DUNNING 13 where the ripening time constant rR is given by ZR = [I(L2/;CR,T)+(R,TpJPDpI,)I 1.5lR Tp (12) and g(to)and rKO are the values of g(t) and rKat a" start "time to within the period of secular ripening and t>to.The expression for h@) p is o)P = ~[2/(2-p)15 ~XP PP/(~-P)I for (13) = 0 for p22. The total number of particles N(0 t) present during secular ripening varies with time as N(0,t) = N(0 to)[I +(t-tO)/TR]4 (14) where N(0 to)is the number present at the start time. The quasi-stationary size distribution is independent of the original size distri- bution. Its form depends upon the growth-evaporation law. SMOLUCHOWSKI COAGULATION When in addition to the gain and loss of single molecules reactions between all size classes are taken into consideration e.g. the problem becomes more complex. It may be simplified by assuming that Smoluch- owski coagulation occurs for which only the forward reactions in 15 take place.We then have for this process where p (ui u,) is the coefficient of coagulation for particles of volumes ui and L:~and n is the concentration (time dependent) of particles in the volume size class ui. On passing from a discrete to a continuous distribution eqn (16) becomes 59* 6o The left hand side of this equation with 6 = dv/dt corresponds to the terms in eqn (8) and the right hand side to Smoluchowski coagulation. Friedlander and his collabor- ators 60-62 have sought a solution to this equation of the form 44 t)=dt) $(r) (18) in which g(t)is a function only of the time and $ afunction only of q. The dimension- less number y is equal to u/u* where the mean particle volume v* = V(0,t)/N(O,t)and V(0,t) N(0 t) are respectively the total volume and total number of all the particles.Friedlander and Wang 6o have shown that in the case when B is assumed constant an " asymptotic " solution is obtained with g(0 = "(0 t>l"~(O t) (19) and for $(q) analytical expressions 62have been obtained for the lower and upper ends of the distribution. Numerical solutions over the whole distribution have been obtained by Hidy 63 and by Pich Friedlander and Lai.62 These results suggest AEROSOL FORMATION strongly that a quasi-stationary distribution of size is obtained after a prolonged time but a general proof is not available. A size distribution for the hypothetical steady state resulting from coagulation is shown schematically as curve H in fig. 2. CONCLUSION Although with the possible exception of prenucleation kinetics the basic processes are aspects of a single conceptual scheme it is still necessary to treat them as separate stages in the development of an aerosol.In the simplest production systems these processes develop and follow each other in sequence. For example when gases flow into a tube diffusive mixing or chemical reactions generate an increasing supersaturation as the gases move downstream. Further downstream nucleation or growth on foreign nuclei takes place and these are followed by the other processes in overlapping sequence. Should the mixture emerge and mix with the atmosphere a simple first approach would be to suppose that the concentration fields of the components depend only on location and not on time.A steady state is conceived in which a cloud is centred on the source of partly reacted gases and partly condensed products and within it all concentrations and process rates depend only on position. When realistic factors such as turbulence wind convection topography and climate are introduced the complexity of the problem becomes great. Another conceptually simple system would be an analogy with the continuous stirred tank reactor into which reactants enter at a steady rate and the contents are removed at a rate to balance the input. The contents of the tank reach a steady state for which all concentrations rates of reaction nucleation and growth etc. everywhere in the tank become steady and the size distribution becomes This bears a faint resemblance to the atmosphere but again the introduction of realism complicates the problem.C. E. Junge in Adu. Geophys. ed. H. E. Landsberg and J. van Mieghem (Academic Press New York 1958) vol. 4 p. 1. C. E. Junge J. Meteorol. 1955 12 13 ; Tellus 1953 5 1. W. E. Clark and K. T. Whitby J. Atmos. Sci. 1967 24,677. J. Cartwright G. Nagelschmidt and J. W. Skidmore Quart. J. Roy. Met. SOC.,1956 82 82. S. Twomey and G. T. Severynse J. Atmos. Sci. 1963,20 392. S. K. Friedlander and R. E. Pasceri J. Atmos. Sci. 1965 22 571. A. H. Woodcock J. Meteorol. 1953 10 362. D. J. Moore and B. J. Mason Quart. J. Roy. Met. SOC.,1954 80 583. B. Y. Liu also R. Husar and K. T. Whitby see S. K. Friedlander Aerosol Sci. 1970 1 295. lo R. D. Cadle and R. C. Robbins Discuss.Faraday SOC.,1961 30 155. l1 R. D.Cadle in An International Workshop on Nucleation and its Applications ed. C. S. Kiang and V. A. Mohnen (Clark College Atlanta 1972) p. 156 ; P. A. Leighton Photochemistry of Air Pollution (Academic Press N.Y. 1961); M. D. Carabine Chem. SOC.Reo. 1972 1,411. l2 M. Volmer Kinetik der Phusenbildung (Steinkopff Dresden 1939) p. 100. l3 N. H.Fletcher J. Chem. Phys. 1958,29 572; 1959,31 1136. l4 H. Kohler Medd. Met. Hydr. Anst. (Stockholm) 1926 3 No. 8. G. Tohmfor and M. Volmer Ann. Phys. 1938 33 109 ; N. H. Fletcher Physics of Rainclouds (Cambridge London 1962) p. 48. l6 L. B. Allen and J. L. Kassner J. Colloid Inter- Sci. 1969 30 81. N. H. Fletcher loc. cit. ref. (15) p. 32. l8 J. B. Zeldovich J. Exp. Theor.Phys. 1942 12 525 ; Acta Phys. Chem. URSS 1943 18 1. l9 M.Volmer and A. Weber 2.phys. Chem. 1926 A119,277 ; R. Becker and W. Doring Ann. Phys. 1935,24,719 ;R. Becker Theorie der Wiirme (Springer Berlin 1955); F. Kuhrt 2.Phys. 1952 131 205. W. J. DUNNING 2o J. Lothe and G. M. Pound J. Chem. Phys. 1962,36,2080 ; J. Feder K. C. Russell J. Lothe and G. M. Pound Adu. Phys. 1966,15,111; J. Lothe and G. M. Pound J. Chem. Phys. 1968,48 1849 ; J. Lothe and G. M. Pound in Nucleation ed. A. C. Zettlemoyer (Marcel Dekker N.Y. 1969); K. Nishioka G. M. Pound and F. F. Abraham Phys. Rev. A 1970 1 1522. W. J. Dunning in Colloques Internationaux du Centre National de la Recherche Scientifque No. 152 (CNRS Paris 1965) p. 369 ; in Nucleation ed. A. C. Zettlemoyer (Marcel Dekker N.Y.1969). 22 H. Reiss and J. L. Katz J. Chem. Phys. 1967,46,2496 ; H. Reiss J. L. Katz and E. R. Cohen J. Chem. Phys. 1968 48 5553 ; H. Reiss J. Statistical Phys. 1970 2 84; R. Kikuchi J. Statistical Phys. 1969 1 351. 23 C. T. R. Wilson Phil. Mag. 1897 A189 265; 1900 193 289. 24 C. F. Powell Proc. Roy. Soc. A 1928 119 553. 25 W. J. Dunning Disc. Faraday Soc. 1960 30 9 ; P. Wegener and J. Y. Parlange Naturwiss. 1970. 57 525. 26 J. Lothe-and G. M. Pound in Nucleation ed. A. C. Zettlemoyer (Marcel Dekker N.Y. 1969). 27 M. Volmer and H. Flood 2.phys. Chem. 1934 A170,273. 28 A. Langsdorff,Rev. Sci. Instr. 1939,10,91 ; J. P. Franck and H. G. Hertz Z. Phys. 1956,143 559. 29 J. L. Katz and B. J. Ostermeier J. Chem. Phys. 1967 47 478; J.L. Katz J. Chem. Phys. 1970 52 4733 ; loc. cit. ref. (11) (An International Workshop etc.) p. 128. 30 K. Oswatitsch 2.angew. Math. Mechanik 1942 22 1 ; Gasdynamik (Springer Wien 1952) ; P. Wegener and L. M. Mack in Adu. Appl. Mech. ed. Dryden and Karman (Academic Press New York 1958) p. 307 ; P. P. Wegener Non-Equilibrium Flow in Gas Dynamics ed. P. P. Wegener (Marcel Dekker New York 1969) vol. I part I ; P. P. Wegener and J. Y. Parlange loc. cit. ref. (25); W. J. Dunning Discuss.Faraday SOC.,1960 30 9. 31 P. P. Wegener and A. A. Pouring Phys. Fluids 1964 7 352. 32 G. D. Stein Thesis (Yale University 1967). 33 D. Barschdorff loc. cit. ref. (11) (An International Workshop etc.) p. 124. 34 H. L. Jaeger E. J. Willson P. G. Hill and K. C. Russell J.Chem. Phys. 1969 51 5380. 35 K. M. Duff and P. G. Hill in Proceedings of the 1966 Heat Transfer and Fluid Mechanics Institute ed. M. A. Saad and J. A. Miller (Stanford U.P. Stanford 1966) p. 268. 36 B. J. Wu loc. cit. ref. (11) (An International Workshop etc.) p. 121. 37 J. A. Clumpner Thesis (Yale University 1970) ; P. P. Wegener J. A. Clumpner and B. J. C. Wu Phys. Fluids 1972 15 1869. 38 D. B. Dawson E. J. Willson P. G. Hill and K. C. Russell J. Chem. Phys. 1969 51 5389. 39 P. P. Wegener B. J. C. Wu and D. Barschdorff loc. cit. ref. (11) (An International Workshop etc.) p. 120. 40 D. Barschdorff W. J. Dunning B. J. C. Wu and P. P. Wegener Nature (Phys. Sci.) 1972,240 166. 41 A. M. Binnie and J. R. Green Proc. Roy. SOC.A 1943,181,134 ; M. E. Deych V.F. Stepan- chuk and G. A. Saltanov Energetika i Transport 1968 2 34; D. Barschdorff Forschung. Ig.-Wes. 1971,37 146 ; G. Gyarmathy and E. Meyer VDZ-Forschungsheft508 (VDI Verlag Dusseldorf 1965. 42 P. D. Arthur Thesis (Calif. Inst. Technol 1952). 43 P. P. Wegener and G. Lundquist J. Appl. Phys. 1959 22 233 for nucleation studies utilizing the Shock Wave see R. T. V. Kung and S. H. Bauer Proc. 8th Internat. Shock Tube Symp. London July 1971 paper No. 61; J. R. Homer I. R. Hurle and P. J. Swain Nature 1971 229 251. 44 P. P. Wegener and J. Y. Parlange loc. cit. ref. (25). 45 G. D. Stein and P. P. Wegener J. Chem. Phys. 1967,46,3685 ; Twelfth Symposium (Ztzternation- al) on Combustion (Combustion Institute Pittsburgh 1969) p. 1183 ; G. D. Stein LASER und angewandte Strahltechnik No.3 1970; J. A. Clumpner J. Chem. Phys. 1971 55 5042. 46 P. G. Bentley Nature 1961 190 432. 47 W. Henkes 2.Naturforsch 1961 16a 842. 48 R. F. Leckenby E. J. Robbins and P. A. Trevalion Proc. Roy. SOC.A 1964,280,409 ; R. F. Leckenby and E. J. Robbins Proc. Roy. Soc. A 1966 291 389. 49 F. T. Greene and T. A. Milne J. Chem. Phys. 1963,39,3150 ; T. A. Milne and F. T. Green J. Chem. Phys. 1967,47,4095. 50 J. A. Anderson and G. D. Stein loc. cit. ref. (11) (An International Workshop etc.) p. 149. 51 J. Frenkel J. Chem. Phys. 1939 7 200 538. 52 J. C. Fisher J. H. Hollomon and D. Turnbull J. Appl. Phys. 1948 19 775. 53 A. Kantrowitz J. Chem. Phys. 1951 19 1097 ; see also R. Probstein J. Chem. Phys. 1951 16 AEROSOL FORMATION 19 619 ; B.K. Chakraverty Colloques. Intern. Centre Nut. Rech. Sci. No. 152 p. 375 (1965) W. G. Courtney J. Chem. Phys. 1962,36,2009. 54 P. P. Wegener and J. Y. Parlange loc. cit. ref. (25). s5 G. Gyarmathy 2.ungew. Math. Phys. 1963,14,280 ; see also P. P. Wegener J. A. Clumpner and B. J. C. Wu Phys. Fluids 1972,15 1869; J. C. Carstens and J. T. Zung J. Colloid Interf. Sci. 1970,33,299; J. C. Carstens and J. L. Kassner J. Recherch. Atmos. 1968 3,33 ; N. A. Fuchs Evaporation and Droplet Growth (Pergamon London 1957). 56 M. Lifshitz and V. V. Slezov Soviet Phys. J.E.T.P. 1958 35 331 ; see also 0. M. Todesr J. Phys. Chem. URSS 1946,20,630 ; 0.M. Todes and W. W. Kruschev,J. Phys. Chem. URSS 1947 21 301. 57 C. Wagner 2.Elektrochem. 1961 65 581.58 W. J. Dunning in Particle Growth in Suspensions (ed. A. L. Smith) SOC. Chem. Ind. Mono- graph no. 28 (Academic Press London 1973). 59 M. V. Smoluchowski Phys. Z. 1916 17 385; Z. phys. Chern. 1917 92 120. 6o S. K. Friedlander and C. S. Wang J. Colloid Interf. Sci. 1966 22 126. 61 S. K. Friedlander J. Meteorol. 1960 17 375 478 ; J. Meteorol. 1961 18 753. 62 J. Pich C. S. Friedlander and F. S. Lai Aerosol Sci. 1970 1 115. 63 G. M. Hidy J. Colloid Sci. 1965 20 123. 64S. H. Bransom W. J. Dunning and B. Millard Disc. Faruday Soc. 1949 5 83.

ISSN:0301-5696    

DOI:10.1039/FS9730700007

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Kinetic Processes in the Condensation and Evaporation of Aerosols BY E. R. BUCKLE Department of Metallurgy The University Shefield SI 3JD Received 15th December 1972 The stable and metastable states of a vapour are considered in relation to the process of conden-sation. By modelling these states on a gaseous system of growing and evaporating molecular clusters kinetically balanced and by consideration of the requirements of the thermodynamic limit two important properties may be defined ;a number J,dependent on temperature and pressure which is a parameter of the cluster populations and an interfacial free energy 5 which varies with temperature and cluster size but not with pressure. Expressions for J and 5 and for the critical cluster size in metastable states are derived for simple models of cluster reactions.The rates of these reactions are considered for particles in the form of large clusters and coefficients of evaporation and growth obtained which tend to zero with increase in particle size. It is concluded that particles of visible size are not formed by spontaneous condensation under uniform conditions of temperature and pressure. This paper gives further consideration to certain results of a kinetic theory of gaseous c1usters.l The system treated is a homogeneous isothermal assembly of particles formed as a suspension in the vapour by condensation. By a homogeneous assembly is meant one of spacial uniformity in the distribution of particles of the various sizes. The term spontaneous rather than homogeneous is used to describe the process of condensation when this occurs on natural centres and not on impurities or foreign substrates.Application of the cluster theory to the kinetic properties of aerosols will be preceded by some general considerations on the condition of stability of cluster assemblies. This is helpful in clarifying the behaviour of volatile particles in an aerosol under conditions of change. 1. PROPERTIES OF A KINETICALLY BALANCED ASSEMBLY In this section the consequences of the kinetic models are deduced for uniform balanced states representative of stable and metastable equilibrium. The Kelvin equation for the radius of an isolated droplet in supersaturated vapaur represents a system in unstable equilibrium. By contrast the thermodynamic states of a system in which the condensed phase is considered to be the macroscopic equivalent of a cluster in the vapour are stable states in which clusters of all sizes are in equilibrium with single molecules or monomers.We use the results of the previous paper as the starting point for a fuller discussion of the equilibrium issues. In cluster reactions involving one-atom growth or decay A,-,fAl = A, the number densities (m-3) at detailed balance are interrelated by the equilibrium quotients KINETIC PROCESSES IN CONDENSATION AEROSOLS from which 9 c = c! n mi. i=2 This may be formally written as cg = c1 exp ((9-l)J-Sg/kT) (1.3) by defining the functions 0 = Lt cog g+ 9 5 = -kT In (mi/mm); = 0.(1.6) i=2 It will be noted that 5 is size-dependent but J is not. The distributions of (1.3) are kinetically balanced (as distinct from being merely stationary but with a net flow of molecules through the sizes) for all values of J. They should therefore represent characteristic macroscopic states of the vapour of A. Let N1 = Zgc be the total number of A atoms in all states of combination in g>o the system volume V. In order that g may be unrestricted in size we proceed to the thermodynamic limit i.e. we let N1 V- 00 while keeping a finite value for the number density Nl/V = p. The physical significance of J and 5 is arrived at as follows. From (lS) Lt A[,/Ag = 0 (1.7) 94 so from (1.3) Lt A(ln c,)/Ag = J. (1.8 g+ The distribution of c over g therefore ultimately rises falls or levels off according as the value of J is positive negative or zero (fig.1). States with J> 0 do not represent true equilibrium because they violate the requirement of finite density but for J = 0 an equilibrium distribution is possible if 5 tends to positive values with increasing g because the concentrations then tail off (eqn (1.8)). For J<O the fall-off of c is steeper and continuous Ac,/Ag being negative in the limit as g+m. The above results were obtained without specifying any details about the clusters other than the existence of certain limiting properties. It has been found by calculations on simple models for argon and water clusters that except under conditions of high pressure and high temperature to which the theory has not been extended the value of Cg is positive at all g and decreases as the temperature is raised.Assuming that clusters behave as ideal gas molecules the total pressure is and from (1.3) the partial pressures are Pg = Pr expU9 -1)J -5g/w (1.10) where p1 = kT cl. By (1.4) J is determined for a given temperature if c1 is determined. Putting (1.10) into (1.9) and eliminating J by (1.4) we obtain (1.11) E. R. BUCKLE J and c1 are therefore determined by p and T. Reversion of (1.11) would enable cl J and therefore the distribution function c to be computed directly for anyp T. In default of this c1 may be roughly obtained from p = c,kT and the value then refined by employing successive approximations to satisfy (1.1 1).We define Pi = Pg(J = 0) = P1 exp (-CgikT). (1.12) Now by fig. 1 J = 0 is the condition for the greatest value of ps consistent with thermodynamic stability. Also by (1.1) and ( 1.4) J = 0 represents a vapour state in which the cluster concentrations depend only on 5 and become independent of size in the limit g- 00. Therefore pi is the partial pressure of g-clusters in saturated vapour and 5 is the surface free enthalpy per g-cluster. 9 FIG.1.-Terminal B,J= 0;C,J<O. behaviour (diagrammatic) of kinetically balanced cluster distributions. A J> 0 ; Putting J = 0 in (1.4) 0 = l/c," (1.13) giving with (1 .4) PlIPY = exp J* (1.14) py = kT/W,. (1.15) Thus c? is the monomeric concentration in saturated vapour pi is the corresponding partial pressure and (1.14) gives the monomeric saturation ratio.The last two results enable (1.12) to be written as Pi = (kT/wxJ)exp (-CglkT).] (1.16) Finally by combining (1.10) with (1.16) we obtain for the saturation ratio of g-clusters PgIP,"= (p,w,IkT) exp (9-1)J. (1.17) KINETIC PROCESSES IN CONDENSATION AEROSOLS COMPARISON WITH VOLMER THEORY In the Volmer theory 3* the kinetics of nucleus formation is deduced from the rate of a critical size fluctuation in a distribution of clusters supposedly stationary and close to equilibrium. This distribution is expressed by c = c1exp (-W,/kT) (1.18) where W is the reversible isothermal work of formation of a single g-cluster by the process gA1 = A, (1.19) which occurs in g-1 of the steps A1+Ai-1 = Ai.(1.20) W consists of two terms wg= w;+w;. (1.21) Wi is the work of formation of the cluster surface taken as positive. Under condi- tions of T,p favourable to condensation W is negative and is equal to the value of Wg for the process in which the g molecules of the gas A are incorporated into the bulk of the macroscopic liquid phase. Comparison of (1.18) with the stationary distributions (1.3) of the present treat- ment gives We' = [, -Wi = (9-1)JkT with J>O in Volmer's case. In Volmer's formula Wi is taken as proportional to the macroscopic surface tension y regardless of the value of g and -W,"/RTis equated with (g -1) In (PIP"). Equivalent assump- tions are made in the derivation of Kelvin's formula for the critical droplet radius.The first assumption has often been criticized as an oversimplification. Calcula-tions of 5 for the very simple cluster models of the previous paper ' suggest that use of the macroscopic value of the surface tension over-estimates l,, and its use in the theory of condensation consequently under-estimates the numbers of clusters particularly at very small sizes. Volmer's formula for example gives for equilibrium in the vapour cJcf = exp (-yO,/kT) (1.22) where 0 is the surface area. As the temperature is lowered the fractions of small clusters increase (ref. (l) fig. 4) and the error on using (1.22) will therefore be larger. The assumption that -JV,"= (9-1)kTln (pip")is equivalent to writing pip" = exp J in contrast to (1.14).Volmer's approximation is therefore equivalent to p = p, and is appropriate only for stable states of the vapour because in these c falls mono- tonically and steeply with g at low enough temperatures (fig. 1). Eqn (1.17) shows that in a rnetastabze state the concentrations must rise eventually relative to stable concentrations. This was known but disregarded by Volmer in his formulation of W in (1.18). The observability of metastable states is due to time-lag in the evolution of c for sizes exceeding the critical size.' APPROXIMATE FORMULAE Accurate computations of cg and properties of the critical cluster are lengthy but some insight into their roles in the formation of aerosols is obtainable from the present theory with the aid of certain approximations.Both 5 and J are functions of the reciprocal reduced temperature 8 = u'll/kT,where uyl is equal to the depth of the A,-A potential well. E. R. BUCKLE Beginning with cg a property of the g-cluster and not of the whole assembly the results of $8?ref. (1) for mi and w give* when substituted into (1.6) Cg = -kTx In Li[exp (@[Ai -11)-exp (-@[Ai-i=4 { L,[exp (ep -11)-exp el(1+Lie+a;02/2) g 2L,(exp 8-i)(i +L,e +,1",~/2) -kTln -L,[exp (O[A -11)-exp 6]( 1+26) (1.23) where we have put A2 = 1 A3 = 2 for the co-ordination numbers of atoms A in dimers and trimers respectively. The first term in brackets tends to zero faster than the second so that c,>O for large clusters. To the same approximation To determine the critical cluster size g* in a metastable vapour we minimize In c with respect to g by a finite difference procedure.By (1.3) 9-1 AC = 5,-[,-= -kT 9 In (oj/o,) +kT In (coJw,) i=2 i=2 = -kT In (w,/o,). (1.27) The condition for the minimum at which o,= cog+,now gives mu,*= o exp (-J) (1.28) and from (I .4) clmg* = 1. (1.29) The minimum in c lies at g = co when J = 0 and move6 in as J increases. We now obtain g* by solution of (1.28) for &6 + 1.>Ag-and introducing an approximate formula for A,. Since Ag rises slowly from unity at g = 2 to R < 10 say in a macro- scopic cluster we may write Ag,10 = &o+(g-10)A~ (1.30) where the size g = 10 has been arbitrarily taken as the point after which A increases by a fixed amount AA in each growth step.A uniform increment is probably a reasonable approximation at very large sizes. Then (1.28) reduces in a similar way to exp (-[,/ kT) in (1.23) to give J = 6(Am-$,)-In (Lg*/L,). (1.31) Again ignoring the logarithm and substituting (I .30) one finds 9"-10 z= (Aa-Aio-J/O)/AA. (1.32) * Dr. A. A. Pouring has kindly pointed out that eqn (8.5) and (8.8) of ref. (1) should read res- pectively K~ = (ul,g/r~)/(~l,g/rnl)~ ; G(3 8) = 2(exp 8-1)/(1+28). Eqn (8.9) should read G(g> 3 8) = [exp(8[hg -l])-exp (-B[Ag -hg-l -1])]/(1 +xg8+hp2/2). KINETIC PROCESSES IN CONDENSATION AEROSOLS This shows qualitatively how sensitive is the position of the Volmer minimum to the value of J; the smaller is A1 the more rapidly g* decreases when J is increased.The response of a vapour of clusters to changes in pressure is a considerable problem involving extensive calculation. In view of the general hazard of heterogen- eous condensation it has been necessary to devise experiments using rapid adiabatic flow to isolate foreign nuclei. This greatly complicates the theoretical analysis. 2. KINETIC PROCESSES IN UNBALANCED ASSEMBLIES There are special problems in relating the kinetic laws of growth and evaporation of large particles to those of clusters in a condensation aerosol. The results that follow are derived from the general formulae for reaction rates of clusters with g>4. The results for g = 2 3,4 were given previous1y.l UNIMOLECULAR REACTIONS For the process of unimolecular decay or evaporation A = A,-1 +A, (2.1) the rate equation is R~;= ijfgygU,m-3 s-l (2.2) in which the probability of process (2.1) occurring as the result of one of the random re-distributions (is/s) of internal energy in A is given for g>4 by This holds for exp Qexp (x +5,)& where xg+ 5 equals the number of activated internal degrees of freedom of which xg are vibrational.The number of vibrational modes associated with surface atoms is written a,~, which defines a,. Absolute Evaporation Coefficient This coefficient may be defined as the fraction of potential unimolecular evapor- ation events in a cluster that in the absence of any other size-changing process succeed in inducing process (2.1). The coefficient is therefore given by Yguand depends in general on the temperature.Since n = 3 g>4 (2.3) becomes yBu = Pa exp (-nge)/(x -1)(xg -2)tU +&?e+%e2/2)* (2.4) Our present interest is in the approach to macroscopic dimensions (9-co). Then xg = 3g -6-3g and for a spherical particle a,-(36n/g)* and (2.4) becomes qU= (36n/g)*(2/9g2)exp (-;l,O)(l +Age +;12,02/2). (2.5) The lifetime of a g-cluster under these conditions therefore increases with size more rapidly than as gs. Unimolecular Fission This process we represent by A = Ag++Ak7 g>2k>2 E. R. BUCKLE where Akis the fission fragment and Ag-kthe remnant. Let tik be the number of specified vibrational modes lost by A on escape of Ak. Also now that k> 1 let lgk be the number of nearest neighbours of the fragment Ak about to be expelled.The case has previously been given brief considerati~n,~ and is complicated because lgkmay vary for fixed g k on account of the shape of Ak. The decay group of nk vibrations will then involve various combinations of both surface and bulk inter- actions affecting the term agk. A simple case is xg> nk91 when (2.3) gives for the fission probability ygu = (nd3g)"" (2.7) on the rather strong assumption that for such large particles any differences in the relative contributions of surface and bulk interactions do not affect the probabilities of the various critical energy distributions that lead to fission. The result is that the probability of fission will depend only on the random circulation of internal energy and not on the value of Agk or the temperature.It is difficult to assess the size at which this assumption becomes permissible but it appears reasonable to regard the considerations under which (2.3) reduces first to (2.5) and then to (2.7) as establishing that not only is the fission probability greatly reduced but the level of temperature loses its significance as the cluster and its fragment be- come larger. BIMOLECULAR REACTIONS Coalescence The reverse of (2.6)represents bimolecular coalescence. This will be distinguished from coagulation by which is meant the mutual adhesion after collision of particles which do not fuse to form a particle of uniform Ag. It is assumed that coalescence is a property that depends on high volatility and is therefore characteristic of clusters that are embryonic droplets.The concept is somewhat rudimentary in terms of the pres- ent cluster models which are regarded as solid-like,' and a quantitative theory has yet to be worked out. It is evident that those cases of coalescence that are the inverse of slow fission will either have low intrinsic probability or depend upon species in short supply at equilibrium. In view of this and a later conclusion about the time scales for the growth of large particles it is permissible to ignore fission and coalescence as factors contributing to the breakdown of supersaturation. Condensation Coefficient Of frequent use in conventional treatments of the later stages of particle growth is the concept of the condensation coefficient. A theoretical coefficient avsfor the condensation of vapour V on substrate S may be defined as the fraction of molecular collisions on S that in the absence of re-evaporation result in capture.The present theory assumes thermal equilibrium and avs is therefore unaffected by considerations of thermal accommodation. We obtain avsfor the inverse of process (2.1) by dividing the rate Rf by the collision number 2. The rate of A +A = when g> 4 is giving KINETIC P ROCESSES IN CONDENSATION AEROSOLS where n = 3. In this case $ is the surface of the cluster A,. For only the smallest clusters is the numerator on the right of (2.9) appreciably different from unity. Under thermal equilibrium conditions therefore the temperature level loses its influence over avsquite early in the growth of A,.For 9%1 the denominator becomes (Xg/ng)vg or substituting ng = 3 xg = 38 a? = 1/g3. (2.10) Net Condensation Coefficient The experimental quantity analogous to avs is a the net condensation coefficient. This is usually defined in terms of the net condensation flux s-l) from the vapour to the macroscopic surface (g-+oo) and the ideal-gas equations for the separate fluxes to (Fvs)and from (P’) the surface F = a(FVS-FSV) (2.1 1) where Fvs = p/(2nmkT)+ (2.12) Fsv = po/(2nmkT)i. (2.13) Eqn (2.13) follows from (2.12) by the equilibrium requirement of balance of macro- scopic fluxes. The pressures are assumed to be those of monomeric gas so that m = m(A,) = m,,p = pl po = pi in the present context. Fission and coalescence are not considered in the simple derivation of (2.12) and (2.13) and experimentally a is obtained from the measured flux F and the total pressures p and PO.The net condensation coefficient of a cluster in a condensing aerosol is obtained as follows. The net forward rate of the growth step is R;+,-R;+ = Zl,,a,VS-~fg+IY,+l,,, (2.14) it being assumed that the forward and reverse processes on a single cluster occur independently. This requires moderate or low pressures (pS 1 bar). Equating (2.14) to zero at equilibrium the second term on the right becomes Z;:& 3;a,””&+ 1/c;+ 1 9 where the co are saturated concentrations at a temperature equal to that of the This gives for the net flux on the particle condensing vapour and ZT,g = Z,,,/f,f,.Fg = (R,+, 1 -R;+l)lfgOg = Z;:,a?/O,kT)bJ -pug+ llfg) exp (ACg+,lkT)) (2.15) where (13)was used to eliminate c;/ci+ from the evaporation term. Eqn (2.15) applies to net growth or evaporation. Fg is not expressible in a simple form dependent on total pressure and in which a becomes independent of g as 8-m. In this size limit Z:,,/OgkT = 1/(2~m~kT)* (2.16) but the coefficient of p;) is unity only for a J = 0 state when F vanishes at all g. That it should do so is a fundamental requirement of vapour stability. 3. OBSERVATION OF PARTICLE$ IN CONDENSATION AEROSOLS Experiments to determine a in (2.11) involve control over pressure temperature and particle size. The relaxation times of processes affecting pressure and temper- ature must therefore substantially exceed the observation time for visible growth on s.An approximate analysis for low temperatures (fi -p) and supersaturations (0 -Jc 1) E. R. BUCKLE shows that the evolution off depends on (1 +g/2)(g-1) time-dependent terms and involves the g-1 relaxation times z = f,/(R +R:+ 1) of the successive growth stcys A,+A,- = A,. For s+ 1 z = g7/3(2nmlkT)112/01(pl +py exp (ACJkT)). (3.1) Growth of even 1 pm particles would be infinitely slow in the final stages according to (3. l) and the conclusion is that the time scales are against the observation of particles of visible size produced in uniform suspension by spontaneous condensation. This appears to be confirmed experimentally in the type of experiment where spontaneous and uniform condensation is reliably observed.6-8 In such experiments the particles are too small to be distinguished individually.What is observed is a change in pressure or scattering of light resulting from the combined effect of a large nuinber of particles distributed over size. It may be concluded that the coefficient a is with-out experimental or theoretical significance for the condensation of aerosols. The theory of this paper is restricted to situations in which thermal relaxation maintains equipartition in the cluster reactions. In the condensation of substances like water that are sufficiently volatile at ordinary temperatures latent heat is dissi- pated relatively slowly by collisions and an excess of the inert diluent gas B is required by the theory.The aerosol particles will remain volatile for a long time and may re-evaporate if the system is not kept cold. The internal energy of clusters condensing at high temperatures will be affected by the wall temperature and radiative heat transfer may occur homogeneously at low enough pressure. In systems where the high temperature is achieved locally in a flowing gas by exothermic chemical reaction as in the wake of a shock wave or by combustion of fuel gas in a jet both the reaction and the condensation of products nilzjl be facilitated by rapid heat transfer. If the condensing product is involatile a homogeneous particle size distribution will be frozen-in and assuming spontaneous condensation of atoms or molecules the smoke so formed will contain only ultra-fine particles in large numbers.Further growth would depend on properties not con- sidered in this paper such as ionization or field-induced effects capable of promoting the non-random motion and coagulation of such small particles. E. R. Buckle Trans. Furuday Soc. 1969 65 1267. E. R. Buckle and A. A. Pouring unpublished. M. Volmer and A. Weber 2. phys. Cliem. 1926 119,277. M. Volmer Kinetik der Phusenbildung (Theodor Steinkopff Dresden 1939). E. R. Buckle Discuss. Furuduy SOC.,1967 44 287. ' P. P. Wegener and A. A. Pouring Pliys. Fluids 1964 7 352. ' E. R. Buckle and A. A. Pouring Nature 1965 208 367. G. D. Stein and P. P. Wegener J. Chem. Phys. 1967,46 3685. J. B. Homer and I. R. Hurle Proc. Roy. SOC.A 1972 327 61.

ISSN:0301-5696    

DOI:10.1039/FS9730700017

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Chemical Nucleation Theory for Various Humidities and Pollutants BY C. S. KIANGAND D. STAUFFER Physics Department Clark College Atlanta Georgia 30314 U.S.A. Received 28th November 1972 The Flood-Neumann-Doring-Reiss-Doyle theory gives a strong dependence of the nucleation rate on the humidity (for r.h. < 100 %) and shows that under atmospheric condition H2SO4 but not HN03 SO2 or NH3 contributes directly to the aerosol nucleation without pre-existing nuclei. Typically lo9 H2S04 molecules per cm3 are enough to form droplets of aqueous sulphuric acid solutions. One possible mechanism for the formation of atmospheric aerosols is the formation of small droplets consisting of a liquid mixture of water and a pollutant e.g. H2S04. Even around pre-existing nuclei pure water can form droplets that grow to infinite size only if the relative humidity of the atmosphere is greater than 100% ; and a pure pollutant like H,S04 can form large droplets only if its partial gas pressure is greater than the equilibrium vapour pressure over liquid H2S04 i.e.only if its “activity”is greater than one. But droplets consisting of an aqueous solution of the pollutant can grow even for activities smaller than one and humidities smaller than 100% since the partial pressures of both components over a liquid mixture can be much smaller than over the pure materials. If a small mixture droplet is formed out of the gas phase with at least two compon- ents (e.g. H2S04 and H20) then we call this process “chemical nucleation” to distinguish it from other nucleation processes.This paper applies the theory of chemical nucleation to various materials as a function of the relative atmospheric humidity. Our calculations are based on the work of Flood,’ Neumann and Doring,2 re is^,^ and Doyle.4 Our main results and the connection with experiments were reported earlier. REVIEW OF CHEMICAL NUCLEATION THEORY The nucleation process is determined mainly by the free energy AG = A(E-TS-pN) necessary to form a droplet. We write for the formation energy of a droplet consisting of nA water and nB pollutant molecules AG = PA)^ +(AB -P&B +S(~A, ~z&J(x) (1) where the p are the chemical potentials of the two materials (A = H20 B = pollutant e.g. H2S04)if gas and liquid are in equilibrium over a flat mixture surface.The p are the actual chemical potentials in the supersaturated atmosphere ; S is the surface area of the droplet and depends on nA and nB ;y is the concentration-dependent surface tension of the liquid mixture; x = nelh 4-4 (2) is the mol fraction of the pollutant in the droplet. We assume the volume of a droplet 26 C. S. KIANG AND D. STAUFFER to be given by VA??A+ VBnB = 47rr3/3,where Y is the droplet radius and VAand V are the volumes per molecule of pure water and pure pollutant. Thus S = 4nr2. Large mixture droplets can be formed from a gas only if both chemical potentials pAand pBare greater than their values pcAand pcB on the coexistence curve ; that means supersaturation with respect to both vapours is required.In this case the first two terms of the right-hand side of (1) are negative ; the last term is positive and dominates for small droplets. Thus due to the surface tension the droplets have to overcome an energy maximum before they can grow further. For a binary mixture the free energy AG depends on nA and nBand thus can be represented by a surface (“mountain”) in three dimensions. In order to grow the droplets have to overcome the lowest free energy maximum (saddle point). In the growth process most droplets approach this saddle point along the deepest valley leading to this mountain pass.2 This saddle point condition yields two equations = (aG/anA), = O and (aG/dt~B),~0. In the evaluation of these two derivatives the changes of the pc with the mol fraction x (eqn (2)) cancel out because of the Gibbs-Duhem-Margule equation,2-n~d~cA+nBd~cB = 0 (3) (or (1 -x)dpcA/dx = -x dpcB/dx).Then the saddle point condition gives for the composition x* and the droplet radius Y* at the saddle point A& = pA-p,*A = (2yvA/r*)/(l-a*x*) > 0 (44 Apg = ,uB-,u~,*B = (2yvB/r*)/(l +a*(l -x*)) > 0 (4b) or equivalently Ap;/A& = (VA/VB)(1+a*( 1-x*))/(1 -a*x*) (44 r* = 2yvA/((1 -a*x*)Ap;) (44 with = 1.5(1- X 4-VB/VA)(dy/dX)/y. (44 (The star * denotes values at the saddle point.) On insertion of (4) into (l) the a*-corrections cancel out AG* = (47~/3)y*r*~ (5) The equilibrium number of droplets of critical size r* and critical composition x* is proportional to exp (-AG*/RT) ; the factor of proportionality is assumed by Reiss and Doyle to be the total number NA+ NB of gaseous water and pollutant molecules.Under usual atmospheric conditions there exists much less pollutant than water NA 9NB. Droplets at the saddle point grow by incorporation of single molecules such that the composition x remains roughly unchanged (at least for the examples used in this paper). Therefore the growth rate at the saddle point is determined by the pollutant concentrations NB whereas the proportionality factor for the droplet numbers is given by NA for NA$ NB. (Most of the water molecules impinging on the critical size droplets will evaporate again ; only if additional H2S04 molecules have been incorporated into the droplet then also more water molecules can remain with the droplet and keep its composition near x*.) Thus the rate at which new molecules are incorporated into the droplets is given roughly by the product of surface area 47cP2 and pollutant impinging rate PB = NB kT/(2nm~ kT)+ CHEMICAL NUCLEATION THEORY where ing is the mass of a pollutant molecule.The nucleation rate J is the rate at which droplets grow over the saddle point (per cm3 per s) and thus can be approxi- mated as J = 47Cr"2&NA exp (-AG*/kT). (6) The Ap appearing in (4) can easily be evaluated since in the atmosphere the gas densities are very low and therefore application of the ideal gas law gives where PA and Ps are the actual partial pressures of the water and the pollutant whereas PcoA(x) are the equilibrium partial pressures over a large solution and PoDB(x) with composition x (mol fraction).Historically this theory of "chemical nucleation " was developped by Flood who applied it to water+alcohol mixtures. Neumann and Doring introduced the saddle point picture and took into account the possible enrichment of one phase near the droplet surface. (This effect is neglected by us; for the HzO+H2SOo nucleation we found its influence on J to be negligible if calculated as in the theory of ref. (2)). In ref. (1) and ref. (2) the pre-exponential factor for the nucleation rate was simply chosen to be the same as that of pure water which would be too high an estimate for H20+H2SO4nucleation. Reiss derived in detail the pre-exponential factor but used only special limiting cases in the evaluation of the exponential term (e.g.dilute solutions in the liquid droplet). In ref. (1)-(3) the a*-corrections in (4) were neglected. They were introduced by Doyle who applied this theory to H20+H2S0 mixtures at 50 % relative humidity. Bricard et al.' recently evaluated J also for 30 % and 70 % relative humidity. In the next section Doyle's formulae are applied to different materials and humidities in order to give a more complete picture than known to us before. NUMERICAL RESULTS Our figures show the main results from a numerical solution of (4c) and (7) (iteration on an IBM 1130 computer) and the application of (4d) and (6) for the nucleation rate J. The H,0+H2S04 nucleation rate is evaluated at 25"C the H,O +HN03 nucleation at 20°C ; data is taken from ref.(6). Fig. 1 shows some cuts through a free energy surface. Fig. 2 gives some nucleation rates J for chemical nucleation of H,O +H2S04 and H,O +HNOJ mixtures. The " activity " in the figures is simply the actual pollutant partial pressure in units of the pressure of a pure pollutant Torr for H2S04from ref. (4) ; 45 Torr for HNO from ref. (6)). Thus the activity is for the pollutant what the relative humidity is for water. For atmospheric applications it seems to be useful to know the characteristic time z during which the atmospheric content of gaseous pollutant is reduced appreci- ably due to chemical nucleation rates. Fig. 3 gives this time as estimated from z = IVB/x*J-NB/J. Fig. 4 shows the activities necessary to achieve a fixed J = one droplet per cm3/s or a fixed z = one second or ofie month.Critical composition x* and number of mole-cules in a critical size droplet are given by fig. 5. All these results describe homogeneous chemical nucleation without preexisting nuclei. Nucleation of a mixture can also occur as heterogeneous chemical nucleation on pre-existing nuclei * like flat surfaces insoluble particles soluble particles or ions. But also for such heterogeneous nucleation the actual partial pressures of C. S. KIANG AND D. STAUPFER FIG. 1.-Droplet formation energy AG as a function of droplet radius r (HzO+HzS04 at 50 % relative humidity ; activity = 0.005). The numbers on the curves give the mol fraction s of HzS04 in the droplet ; the star indicates the saddle point.r.h. FIG.2.-Nucleation rate J as a function of relative humidity r.h. for H20+ HzS04 (left) and HzO+ HNOJ (right). The numbers on the curves give the activity (= partial pollutant gas pressure in units of Torr for HzSO4 (25‘C) and of 45 Torr for HNOJ (20’0). CHEMICAL NUCLEATION THEORY 1 O6 I 8 -ul 10' I r.h. FIG.3.-Characteristic decay time T-NB/J (cp. fig. 2) as a function of relative humidity r.h. ; the numbers on the curves give the activity. The insert shows the gaseous pollutant concentration NB(t)/NB(t = 0) as a function of time t/T (solid line) and the tangent to this curve at t = 0 (dashed line). Initial activity 0.005 r.h. = SO% 7-lh. x c, .-> .d Y 0 -10 lo3-20% 40% 100 r.h.FIG.4.-Activities and pollutant concentrations N~/crn~ for fixed J or fixed T. The dashed-dotted line is the " zero supersaturation " curve for H20+ HNOJ (lower limit for heterogeneous chemical nucleation). Heterogeneous nucleation on ions or wetted particles with 8 8,radius is indicated by full (H20+ HNO,) and open (H20+ H,SO,) circles. (J = 1 droplet per second and ion or particle for HN03 10-3/sfor H2S04.) C. S. KIANG AND D. STAUFFEK water and pollutant cannot be smaller than those over a flat surface of a liquid mixture in equilibrium with its vapours. This condition (actual partial pressures = equilibrium partial pressures) determines the “ zero supersaturation curve ” of fig. 4. 8C 5c * $ 2c r i 30°/0 60% 900/0 r.h.Fic. 5.-Number of molecules IZ* (left scale) composition x* (centre scale) and radius Y* (right scale) of ” critical ” saddle point droplets for fixed J (left) or fixed activity (right ; as given by the numbers on the curves). Roughly Y* is the minimum radius of wetted particles which can produce heterogeneous chemical nucleation for the given activity and humidity. Nucleation whether heterogeneous or homogeneous does not occur for activities smaller than the activity on the zero supersaturation curve. (For H20+ H2S04 activity = at 20 % relative humidity activity = 10-9-5at 80 % relative humidity.) Heterogeneous chemical nucleation processes may be important for activities between the one on the zero supersaturation curve and the higher ones shown in fig.4for homo- geneous chemical nucleation. Using the same models as in ref. (10) we find for nucleation on ions or on “ dust ” particles of 8 A radius the activities indicated by the circles in fig. 4. (For H20+H2S04 the pre-exponential factor for Jion/Nion is smaller than 1 s-I ; thus Jion/Nion cannot be greater than I s-I for the activities for which nucleation theory is valid(AG* % kT). The same holds for “dust” nucleation.) DISCUSSION This theory shares with others the disadvantage of applying macroscopic concepts to small droplets. Recent indirect evidence indicates that this is a much better approximation than usually assumed ; the results of ref. (1 1) leave little space for a correction factor like lo1’ for the droplet concentrations.But it may be necessary to employ a “ microscopic surface tension ” for the free energy of the droplet. For pure water near O’C this microscopic surface tension was found in ref. (12) to agree with the measured bulk surface tension. However the activities of H2S04or HN03 CHEMICAL NUCLEATION THEORY predicted in our theory might well be wrong by one order of magnitude. (The "zero supersaturation curve " of fig. 4 should be more accurate since no surface tension enters there.) Hydration effects could produce additional complications. For the H20 +H2S04system an additional source of error is the vapour pressure over pure H2S04 taken as Torr (from ref. (4)). If this pressure is actually larger by an order of magnitude then our activities remain roughly unchanged but the partial pressures or concentrations of H2S04 would be increased by a factor 10.s-l to lo3 ~m-~ The nucleation rate is increased from 1 ~m-~ s-' if the volume of a droplet is calculated l4 from the measured density of H20 +H2S04 mixtures and not simply from VAnA+ VBnB = 4zr3/3. Some other corrections were found to be rather unimportant. In the work of Reiss and Doyle the impinging rate is not simply PB but PA/3~(l +tan2 ~)/(PB+PA tan2 4). We found tan 4 = x*/(1 -x*) to be a sufficient approximation ; then this s-I. correction increases J by about one order of magnitude near J = 1 ~m-~ In ref. (12) we used corrections to the classical nucleation theory for the number of droplets with a given size (pure substances) ; instead of number of droplets = N1exp (-AG/ kT),we used number of droplets = qo exp (-AG/kT),where qo near 0°Cfor water is of the order of the particle density at the liquid-gas critical point ~m-~ instead of ATl = monomer concentration = 1017*5 ~m-~).But AG in ref.(12) also contained a logarithmic term giving an additional factor (number of molecules in a for the number of droplets. Thus the three effects discussed in this paragraph roughly cancel each other out of the final results if we may apply our previous experience l2 for "pure " nucleation also to chemical nucleation. Reiss and Doyle also introduced two "Zeldovich " factors for the saddle point ; but the nucleation rate contains the quotient of them which is near 1 (see ref.(4)). For nucleation on ions the product of two other Zeldovich factors for the energy minimum appears in the droplet numbers; it is of order lo-' and was taken into account in fig. 4. We conclude that our results may be inaccurate but should give the correct trends for the dependence on humidities activities ions etc. This could be con- firmed by experiment.l* s Our fig. 4 shows that for different materials the activities are roughly the same; only the transformation from activity to partial pressure or concentration differed by many orders of magnitude for H2S04and HN03. Thus under usual atmospheric conditions on earth where impurities are measured in parts per million or less the high concentration of HN03 necessary for chemical nucleation cannot be reached.Similarly SO2 C2H50H,or NH3 cannot form directly liquid aqueous solution droplets in the atmosphere because of their high pressure whereas H,S04 forms very easily a mixture droplet. The typical partial pressure of the pollutant vapour over a pollutant +water mixture thus indicates directly whether this pollutant can form droplets with water by (homogeneous) chemical nucleation. On the other hand the vapour pressure of NaCl is so small at room temperature Torr from an extrapolation of the results of ref. (13)) that the atmosphere should practically not contain gaseous neutral NaCl molecules. Then again chemical nucleation does not occur. Only for intermediate vapour pressures e.g. near the Torr of H2S04,is this chemical nucleation process of direct importance in the atmosphere.Indirectly both SO2 and NaCl can contribute to aerosol formation by chemical nucleation. As discussed in ref. (4) (15) concentrations of SO2 in the parts per million range are sufficient to produce H20+H2S04aerosols via photoxidation of SO2 to H2S04. And solid NaCl particles in theatmosphere can serve as soluble condensation nuclei for heterogeneous nucleation of pure water ** (for relative C. S. KIANG AND D. STAUFFER humidities > 100 %) or solution droplets (humidities < 100 %). For relative humid- ities less than 100 % and activities less than 1 our chemical nucleation theory describes the only mechanism for the formation of large aerosols from the gas phase. For relative humidities greater than 100 % this chemical nucleation mechanism can be regarded as the initial stage of other aerosol formation processes (e.g.heterogeneous water nucleation on soluble particles 8* '). We hope to discuss this second nucleation process in a later paper.I5 We thank Prof. V. A. Mohnen for drawing our attention to this problem and for encouraging discussions and the National Center for Atmospheric Research Boulder for its hospitality. This investigation is partially supported by NSF Grant GA-33422 Atmospheric Science section and by NIH Grant RR 8006 from the General Research Support Branch Division of General Resources National Institute of Health. ' H. Flood Z. phys. Chem. A 1934 170,286. K. Neumann and W. Doring Z. phys. Chem. A 1940 186,203. H.Ress J. Chem. Phys. 1950 18 840. G. J. Doyle J. Chem. Phys. 1961 35 795. C. S. Kiang D. Stauffer V. A. Mohnen J. Bricard and D. Vigla submitted to Atmospheric Environment. W. R. Forsythe and W. F. Giauque J. Atner. Chem. SOC. 1941,64,48 ; W. F. Giauque E. W. Hornung J. E. Kunzler and T. R. Rubin ibid. 1960,82,62 ; Int. Critical Tables vol. IV (E. W. Washburn et al. ed.) (McGraw Hill Book Company New York and London 1928) Landolt- Bornstein Zahlenwerte und Funktionen vol. I12a (K. Schafer and E. Lax ed.) (Springer Verlag Berlin 1960). Private communication of J. Bricard September 1972. 'B. J. Mason The Physics of Clouds (Ciarendon Press Oxford 1957). K. G. Vohra and P. V. N. Nair J. Arm. Sci. 1971 28 280. Clark College Research Group Phys. Rev. B 1972 6 2780.lo C. S. Kiang Phys. Rev. Letters 1970,24,47 ; K. Binder et a/.,J. Stat. Phys. 1972 6,49 ; and I' Phys. Rev. B 1972,6,2777 ; C. Carlier and H. L. Frisch J. Chem. Phys. 1972 to be published. l2 Clark College Research Group J. Atm. Sci. 1971 28 1222. l3 B. H. Zimm and J. E. Mayer J. Chem. Phys. 1944 12 362. l4 We thank Mr. L. Roland for help on this calculation. 15 D. Stauffer V. A. Mohnen C. S. Kiang to be submitted to J. Aerosol Sc. Notes added in proof 1 The calculation of T in fig. 3 overestimates the time after which the gaseous pollutant is con-sumed since it neglects condensation on already nucleated droplet^.'^ 2 At the third Chemist-Meteorologist Workshop (Ft. Lauderdale Florida Jan. 1973) the name "heteromolecular nucleation " was proposed for what we called here "chemical nucleation." S7-2

ISSN:0301-5696    

DOI:10.1039/FS9730700026

出版商:RSC    

年代:1973

数据来源: RSC

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Evaporation of Fine Atmospheric Particles BY C. N. DAVIES Dept of Chemistry University of Essex Wivenhoe Park Colchester Essex Received 6th December 1972 The decrease in size of aerosol particles due to evaporation is calculated for two situations. In the first the air is saturated with vapour so that evaporation is due to the Kelvin effect and proceeds at the minimal rate ;in the second the air is free from vapour and the rate of evaporation is maximal. The calculations are based upon an interpolation formula covering the transition with decreasing particle size from diffusion control to free molecular flow. 1. INTRODUCTION The rate of evaporation of a pure substance in the form of a spherical particle of radius a when subject to diffusion control in a gas at rest is equal to 4o = -drn/dt = 4naV(n,-n,) (1.1) where n is the concentration of vapour in equilibrium with the surface of the particle n the vapour concentration at a distance from the surface and V the coefficient of diffusion of vapour molecules through the surrounding gas.This equation is valid when the Knudsen number Kn = 2/a (14 1 being the mean free path of the gas molecules is near to zero. Increase of the rate of evaporation due to the particles falling under gravity can be seen from the equation of Frossling to be negligible for radii below 10 pm. If the gas pressure is low or the particle is very small so that Kn is very large the rate of evaporation is 4K = 4na2a(n,-n,)ta (1.3) where Z is the mean velocity of the evaporating molecules and the fraction a is the evaporation coefficient.For intermediate values of Kn the rate of evaporation has been calculated by Fuchs on the assumption that free molecular flow of molecules of vapour as in (1.3) proceeds from the surface of the particle outwards for a distance A and diffusive flow continues from radius a+A to infinity as in eqn (1.1). A is a length near to the mean free path of the molecules of the surrounding gas. Suppose that the concentration of vapour at distance A from the surface is n and that n = 0. The rates of transport across the zones inside and outside radius a+A must be the same hence 4 = 4n(a+A)Vn1 = na2(n,-n,)Za (1-4) which gives after eliminating n C. N. DAVIES In the opinion of Wright,3 his experiments indicate that the thickness of the free molecule region is A = 2V/C (1 4 and from the kinetic theory of gases the coeffiicent of diffusion is given by v = a/3.(1.7) The coefficient of diffusion of the evaporating molecules can therefore be eliminated from eqn (1.5) which becomes 4 = &/(4Kn/3a +1/( 1+2Kn/3)). (1.8) For small values of Kn this reduces to 4 = 40/(1+2Kn(2/a -1)/3) (1.9) which is considered by Fuchs and Sutugin to be accurate for Kn< 1. From eqn (1.1) and (1.2) 4o = &4V/aZa = &4Kn/3u (1.10) so that (1 .8) can be written for large values of Kn as 4 = &/( 1+9a/8Kn2). (1.11) However this equation involves Kn in a manner which Fuchs and Sutugin show to be incompatible with current theory of free molecular flow.The A concept is thus invalid at high values of Kn. They have pointed out that a theoretical solution exists of a mathematically analogous problem which brings the value of 6 to the correct limits as Kn tends to zero and to infinity. They have given an interpolation formula which fits the exact solution closely. This formula results in eqn (1.8) being replaced by the expression 4 = $o/(l +Kn(1.333Kn+0.71)/(Kn+ 1)) (1.12) which reduces to 4 = &o/(l +0.71Kn) for Kn< 1 (1.13) and to 4 = (4K/a)/(1+0.283Kn-I) for Kn9 1. (1.14) Eqn (1.13) is the same as (1.9) when a = 0.97. For other values of 01 the difference between them decreases as Kn decreases and increases as adecreases. At Kn = 0.25 they agree better than 1 % for a = 1 and eqn (1.13) is 18 % low at a = 0.6.At Kn = 0.1 eqn (1.13) predicts a value of 4 low by 8.4 %. Eqn (1.14) is in reasonable agreement with free molecule theory. As far as is known eqn (1.12) is satisfactory for calculating the rate of evaporation of aerosol particles particularly so because for most substances ais probably equal to unity. Hitherto this calculation has been tiresome because of the need for making exploratory determinations of the values of the terms in the denominator of eqn (1.5) or (1.8) as evaporation proceeds and their relative importance changes. This necessity can be avoided when eqn (1.12) is used as explained below. 2. GENERAL FORMULAE FOR THE RATE OF EVAPORATION OF AEROSOL PARTICLES From eqn (1.1) and (1.12) dm/dt = -4naV(1z,-nm)(Kn+ 1)/(1+1.71Kn + 1.333Kn2).(2.1) EVAPORATION OF PARTICLES and the saturation ratio of vapour in equilibrium with the surface of the particle be S = n,/no (2.3) where no is the saturation vapour pressure of the evaporating substance in bulk. Then dY -VndS -n,lno) Y+l dt PA2 y2+ 1.71y+ 1.333’ The saturation ratio S is determined by Kelvin’s equation which for low values of S-1 approximates to S-1 2 2yMIRTap (2.5) where y is the surface tension of the evaporating substance M is its molecular weight R is the gas constant per gram molecule and p is the density of the particle; Tis the absolute temperature assumed to be the same throughout the particle and the surrounding gas. A water droplet evaporating in air cools to the wet bulb tempera- ture which considerably slows down the rate of evaporation; this is on account of the high latent heat of evaporation and high saturation vapour concentration.Substances of lower volatility such as the others shown in table 2 below cool only to a negligible extent which can be calculated by the methods described by Fuch~.~ Two limiting cases arise which correspond to maximal and minimal rates of evaporation. The maximal rate occurs during evaporation into gas which is free from vapour so that n = 0. The minimal rate is for evaporation into gas which is saturated with vapour so that n = no. For evaporation into saturated vapour eqn (2.4) and (2.5) give dY -Vno 2YM Y+l __ -~~ dt p12 RMpA y(y2+ 1.71y+ 1.333) = -DK Y+l y(y2+ 1.71~ +1.333) where the diffusion factor D = Vno/pA2s-’ (2.7) and the Kelvin factor K = 2yM/RTpE.,dimensionless I.Suppose that the particle size initially corresponds to y = yo and reduces to y = y at t = t, then y(y2+1.71y+1.333) dy [It] = -Y+l therefore 0.333(y~-~~)+0.355(y~-y~)+0.623(yo-y,)-0.623 In DK Y+l When the particle is evaporating into vapour-free gas n = 0 and in place of (2.6) eqn (2.4) and (2.5) give Y+l --Y+l D(l +K’Y)y2+1.71~ +1.333’ (2.10) C. N. DAVIES whence [t]? = 1 y(yz+ 1.71y+ 1.333)dy -lYo 9 D yI (Y+ 1)(Y+K) so that yoy2dy 0.377-K D[r]; = s ___ + yI ~+1 1-K 1-K and 1.333-1.71K+Kz 1-K Y +K Owing to the approximation of the Kelvin vapour pressure formula which was used for eqn (2.5) expressions (2.9)and (2.1 I) are only strictly valid for particles which are initially of a sufficiently large size so that In S2 S-I.(2.22) The times tl should not be so long as to allow the particle to diminish to a size beyond which this is no longer true. Table 1 compares values of In S and S-1 for droplets of dibutylphthalate a substance of moderate vapour pressure in air at 20°C; Kelvin's equation gives the exact value of Sas In S = 2yM/RTap. (2.13) It will be seen that the approximation used for formulae (2.9) and (2.1 1) predicts too low a value for S so that the actual size of the droplet after evaporating for a certain time will be smaller than the size calculated by the formulae. The theoretical TABLE1 radius of droplet In S s-1 /m 1.o 0.00787 0.00787 0.5 0.01 59 0.0157 0.1 0.0819 0.0787 0.05 0.1705 0.1574 0.01 1.197 0.787 0.005 3.826 1.574 lifetimes are thus too long.However this is not often of practical importance even for quite small drops because the rate of evaporation increases rapidly as the size diminishes; the error in the calculated lifetime of a drop which was initially greater than about 0.1pm radius is not too great especially wherl it is evaporating into a saturated atm9sphere. 3. LIFETIMES OF AEROSOL PARTICLES The lifetime of a particle is calculated by making y1 = 0 in eqn (2.9)and (2.1 l) yo being the initial value ao/L EVAPORATION OF PARTICLES For particles in a saturated atmosphere this gives the lifetime -L( DK 0.333~:+0.355yg +0.623y0 -0.623 In (yo+ 1)) (3.1) and for particles in a vapour-free atmosphere [filvf = $0.5Yg-( 0.623 -)(Yo-ln YO+^])+ 1-K 1.333-1.71K +K2 1-K (yo-K (3.2) K In E)] where D and K as defined by (2.7) depend on the substance of which the particle is composed and on the gas temperature and pressure.In eqn (2.9) and (3.1) it will be seen that if the time is measured in units of (DK)-' there is a relation between the dimensionless quantity tDK and the dimensionless quantity y which is the radius measured in units of the gas mean free path. For evaporation into vapour free space the situation is more complicated because tD in eqn (2.11) and (3.2) is a function of both the dimensionless particle size y and the dimensionless Kelvin factor K,the latter depending on the nature of the substance of the particle and also on the temperature and pressure of the gas.The progression of y with tD is therefore specific when evaporation takes place into a vapour-free atmosphere. Values of D and K have been calculated for five pure substances and are shown with the basic properties required in table 2; the data are for pure air at one atmos-phere and 20"C,the mean free path being taken as 6 x cm. TABLE 2 substanu Y/dy cm- M p/g cm-3 V/crnZ s-1 sat. v.p./Torr no/g cm-3 vapour mole-cules/cm3 Dls-1 sodium chloride 124 58.5 2.165 0.1 3x 10-25 9.6~10-31 1.21x 10-21 0.0459 diethylhexyl-sebacate 30 426 0.92 0.024 1.49XlO-9 35x10-14 5x10' 234x10-5 0.19 dibutyl-phthalate sulphuricacid 36 55 278 98 1.048 1.84 0.031 0.09 3x 10-5 7.1 X lO.-S 4.6~10-1O 3.8~10-10 1012 2.3~1012 0.38 0.52 0.131 0.04 water 72 18 1.00 0.26 17.54 1.72X 10-5 5.7X 1012 1.24~105 0.0178 Fig.1 shows the decrease in size of aerosol particles with time when evaporating into a saturated atmosphere according to eqn (2.9) and (3.1). The curves are common to all substances and all gases. By dividing the values on the scale of abscissa by DK times in seconds for specific conditions are obtained. In fig. 2 similar curves of particle radius against the dimensionless time Dt in this case are shown for evaporation into vapour-free gas. It turns out that the curve for a particular initial radius is not very sensitive to the value of K and is there-fore only slightly dependent on the specific circumstances.Curves for a = 0.24 pm are shown for K = 0.04 0.13 and 0.19 corresponding to sulphuric acid dibutyl-phthalate and diethylhexylsebacate respectively evaporating into dry air at 20°C and 1 atm. pressure. There is not a lot of difference between these curves. The big differencein absolute time comes about when the dimensionless times are divided by the values of D appropriate to the systems. For example dibutylphthalate evaporates 15 0o0 times more rapidly than does diethylhexylsebacate and this sub-stance in turn goes 2.1 x 1OI6 times faster than sodium chloride. The figures assume a 2 1 in all cases. C. N. DAVIES dimensionless time DKt FIG.1.-Evaporation of particles into vapour-saturated air at 20°C and 1 atm pressure.- eqn (2.9) and (3.1); -- eqn (3.3) evaporation without allowance for free molecular flow. These curves are common to all substances. dimensionless time Dt FIG.2.-Evaporation of particles into vapour-free air at 20°C and 1 atm. pressure. - eqn (2.11) and (3.2) K = 0.1 ;--,eqn (2.11) and (3.2) K = 0.04,0.13and 0.19 ;--,eqn (3.4) evaporation with diffusion control only. EVAPORATION OF PARTICLES From eqn (1.1) and (2.5) the lifetime of a particle in saturated vapour which is subject to diffusion control and the Kelvin effect can be calculated from which is the first term of eqn (2.9); the remaining terms come from the tendency towards control by molecular flow with decreasing radius. Similarly for a particle in vapour-free gas subject only to diffusion control eqn (1.1) gives (3.4) which is the first term of eqn (2.11).In this case the Kelvin and free flow effects come in at about the same radius so that the remaining terms of eqn (2.1I) involve both. The curve of eqn (3.3) for a = 0.3 pm is plotted on fig. 1 showing of course a more rapid evaporation than the curve of eqn (2.9). The exact curve using the correct Kelvin expression instead of expanding the logarithm will lie between the two but very much closer to that of eqn (2.9). A similar curve for diffusion control alone with a = 0.3 pm is plotted on fig. 2 according to eqn (3.4). 4. APPLICATION TO PARTICLES IN THE ATMOSPHERE Saturation vapour concentration with substances such as diethylhexylsebacate or sodium chloride is equivalent to only a low concentration of small particles 1000/cm3 of radius 0.03 pm for the former and 10-'/cm3 of radius 0.0005 pm with the latter.Evaporation of aerosols of such substances therefore invariably takes place into a saturated atmosphere. This might not always be true for substances of moderate vapour pressure such as dibutylphthalate for which a concentration of 1000 particles/cm3 of radius 0.5 pm is equivalent to saturation vapour concentration. Such aerosols generated in the laboratory in containers will be in equilibrium with saturated vapour. In this case evaporation results in the isothermal distillation of the substance from small particles to larger ones and to the walls of the container. The walls of the container usually present a very much greater area than the particles.In the open atmopshere large particles grow at the expense of small ones which therefore require to be con- tinuously generated to maintain a concentration the rate of generation being high for particles of short lifetime. The lifetime of small particles which would otherwise evaporate in minutes is extended if they carry an electric charge. Normally too few charges are available to account for the stabilisation of concentrations of the order of 106/cm3 in this way though the stability of small ions in clean air up to 1000/cm3 is due to the electrical effect. Fine particulate substances in the atmosphere which are present in high anumbe concentration therefore need to be substances of low vapour pressure such s ionicr crystals oxides and a few organic compounds of high molecular weight.The degree of supersaturation necessary for fine atmospheric particles to grow into fog or mist droplets is not attained in the atmosphere. For water vapour in the atmoshpere the absolute maximum value of S is 1.01 and 1,003 is rarely exceeded; particles which are insoluble in water need to be greater than 0.2pm in radius to condense growing water droplets and soluble parfjcles must be greater than 0.06pm radius. Electric charge is of no significance. The life-times of these particles in dry air C. N. DAVIES can be calculated by the equations given above. The possible constituents of con-densation nuclei are limited by the evaporating tendency.N. Frossling Gerlands Beitr. z. Geophys. 1938 52 170. N. Fuchs Phys Z. Sowjetunion 1934 6 (3) 224. P. G. Wright Disc. Faraday SOC.,1960 30 100. N. A. Fuchs and A. G. Sutugin Topics in Current AerosoZ Research Ed. G. M. Hidy and J. R. Brock. (Pergamon Press Oxford 1971). See H&h Dispersed Aerosols chap. 3.2 p. 31. N. A. Fuchs Evaporation and Droplet Growth in Gaseous Media (Pergamon Press Oxford 1959) chap. 1.6 p. 11.

ISSN:0301-5696    

DOI:10.1039/FS9730700034

出版商:RSC    

年代:1973

数据来源: RSC

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GENERAL mscussroiv Dr. E. R. Buckle (University of Shefield) said In introducing his paper Dunning compared the experimental nucleation rates Jexpfor water condensation with those predicted by the so-called "classical "theory Jtheor such that by and large Jexp/Jtheor -lo3. What confidence can be placed on the actual values given for Jexp by the various workers ? Dr. W. J. Dunning (Bristol University) said Prof. J. Clumpner (now at the American University Beirut) has considered all the possible errors (including the so-called "influence coefficients '' of gas dynamics) which may affect the evaluation of Jexp from the Yale nozzle experiments. His conclusions have not yet been published but I understand that for the best work Jexp is known to within a factor of 10 and there is no problem in achieving a factor of lo2.Clearly the precision is adequate to discriminate between theories which predict values of J which differ by factors of 1012- 101 7. Dr. C. S. Kiang (Clark ColZege Atlanta Ga.) said Would Dunning comment on the present state of his eqn (6)? Dr. W. J. Dunning (Bristol University) said In reply to Kiang's question of the present status of my eqn (6) experimenters find it useful to compare their results with classical theory (my eqn (6)) by using a factor rexp to match this theory with their experimental results Jexp = rexp Jclass-In the same way it is useful to compare the rates of nucleation ,Itheor predicted by the different theories Jtheor = rtheor 'Jclass. For example Lothe and Pound's l theory predicts I'L-P-predicts rD -lo4 for water vapour condensation.1017 and my theory The careful work of Wegener Clumpner and Wu on the nucleation and growth of ethanol drops in supersonic flow yielded values of rexp at different stations x along the nozzle (fig. 1). Also illustrated in the figure are the corresponding values of rL and TD; if the classical theory applied rexp would run along the x axis. The value of r, at the onset point is about loi7,the value of rD at this point is about lo5 matching the experimental value of rexp closely. Thus the Lothe-Pound theory predicts nucleation rates which are far too high ; classical theory predicts rates which are rather low In these ethanol experiments the following conditions are favourable.The ethanol was carefully purified the mass-fraction of water vapour in the air was less than The critical nuclei are comparitively large containing 15-20 molecules. The condensation takes place above the triple point so that the nuclei are almost certain to be liquid. In the presence of a carrier gas (eg air) the nuclei and droplets grow under Lothe and Pound J. Chern. Phys. 1962,36,2080. Dunning Adsorption et Croissunce Cristulline (Coll. Int. C.N.R.S. no. 152 Paris) 1965. Wegener Clumpner and Wu Phys. Fluids 1972 15 1869. 42 GENERAL DISCUSSlON isothermal conditions; for pure vapour (e.g. steam) the nuclei and droplets are at a higher temperature than the vapour and nucleation proceeds more slowly. In fig. 2,* the values uniformly calculated of Texpfor ethanol water and benzene are shown plotted against the mass-fraction coo of vapour.For the two latter substances there is more uncertainty about the thermodynamic state of the nuclei and the results for both solid and liquid states are shown; in each case the lower of the pairs is to be preferred for kinetic reasons. Barschdorff Dunning Wu and Wegener have recalculated all experimental results for pure steam and these are all in the range of the hatching at log coo = 0. These results give <lo6 to be compared with l7 = 1 if the classical theory held and with rLP-<rexp lo1' and TD-lo4. 30 10 -20 10 -rL-P -Id" -%x p c rD 10 0 ' I I I I I 0 I 2 x/cm FIG.1.-Nucleation of ethanol in air.Showing the dependence of rexp, FLp rD on x the station after Wegener Clumpner and Wu ref. (3)). Using a shock tube Barschdorff * (unpublished) has investigated the effect of various carrier gases at various mass-fractions on the nucleation rate for water vapour and his results are illustrated in fig. 3; here Jexp/Jtheor = rexp is plotted against coo <lo3. Investigations on other materials have not been so and we find <rexp intensive. Pure nitrogen gives On the other hand experiments on freon and chloroform have given results close to values predicted by the Lothe- Pound theory. * I wish to thank Prof. Wegener and Dr. Barschdofl for allowing me to quote their unpublished results. Dawson Wilson Hill and Russell J. Chem. Phys. 1969 51 5389.GENERAL DISCUSSION U U a **A S 10 -Ah 000 i I no n-tsothermal lo 0.001 0.0 I 0.1 I -5> WO FIG.2.-Nucleation of ethanol water and benzene. rexp as a function of the mass-fraction wo of the substance in air (courtesy of Prof. P. Wegener). A,Ethanol; 0,0 HzO; benzene; 0,., open symbols liquid ; solid symbols crystal. ,O L FIG.3.-Nucleation of H20.reXp as a function of oofor various carrier gases. A Steam; 0, moist air. H20 in argon ; 0,H20in helium ; 0 It must be remembered that " binary "and " hetero-molecular" nucleation theory as discussed by Kiang and Stauffer in this Discussion indicates that impurities in the substance examined would if they were effective always tend to increase the value of rexp-Prof.M. Kerker (Clarkson Coll. Techn. Potsdam) said I wouId ask Dunning what can be said about the form of the size distribution prior to the onset of coagula- GENERAL DISCUSSION tion? We have assumed that the aerosols having a somewhat narrow size distri- bution formed by condensation upon heterogeneous nuclei could be represented by a logarithmic distribution. Dr. W. J. Dunning (Bristol University) said In reply to Kerker the mathematical form of the classical nucleation rate equation seems to be accepted although the values of some of the parameters have been subject to controversy. In a well-defined experiment it is possible to calculate the rates of nucleation and the rates of growth and evaporation of all classes of particles at all stages of the collapse of the super- saturation.Thus the form of the size distribution is ascertainable under such conditions. It is necessary to check by calculation the progress of coagulation since under certain circumstances coagulation may become significant before growth is effectively complete. I have no experience of the Kerker type of aerosol generator and I cannot judge how well defined the thermodynamic variables are. It may be possible to idealize it and calculate the aerosol size distribution to be expected. In this one could assume that Volmer’s theory of heterogeneous nucleation was valid and that an appropriate rate of growth was applicable and at least determine the form of the size distribution thus predicted. Until such studies are made it is not possible to assess whether the logarithmic distribution closely approximates the experimental distribution or not.Dr. E. R. Buckle (Shefield University) (communicated) The size distribution in a spontaneously condensed aerosol will adjust by growth and evaporation towards the stationary form of eqn (1.3) of my paper which resembles Volmer’s distribution (eqn (1.18)). If the conditions change the system will approach a new distribution of similar form. The distribution will be cut off at a size in the region of the critical size in the early stages but eventually will extend to larger sizes as the result of co- agulation. In seeded condensation it may happen that the growing centres are too large at the outset for them to qualify as labile gaseous species and the distributions of my paper would not apply.Prof. C. S. Kiang and Dr. D. Stauffer (Clark College Atlanta Ga.) said Would Dunning give his opinion of the reason why some materials obey classical nucleation theory and some do not. Theoretically the capillarity approximation using the bulk surface tension for small droplets may be inaccurate. Computer simulations of small droplets (“ micro-crystalline calculations ”) do not need such an approximation. Calculations of this type by Burton explain from one model most of the observed deviations from and agreements with the classical nucleation theory. His comparison with classical theory depends on the temperature and the supersaturation which are different for different experiments.(In another preprint Burton proves convincingly the presence of a Lothe-Pound translation-rotation term in such microcrystalline calculations based on vibration frequencies and binding energies of the molecules. This does not yet solve the question whether the capillarity approximation requires too a Lothe-Pound correction since it might already be included in the effective surface tension.) Another (simpler but so far less successful) approach is to make the capillarity approximation to neglect the Lothe-Pound factor but to use a microscopic droplet surface tension different from the measured bulk surface tension. The smaller the J. J. Burton Actu Met. to be published. 0 In this GENERAL DISCUSSION droplet surface tension is compared to the measured bulk surface tension the higher should the nucleation rate be compared with classical theory.We determined this “ microscopic ” surface tension from the two methods,’ (density)/(critical density) and from 1-PVIRT. We found for H20 CH30H and C2H50H good agreement of these microscopic surface tensions with the bulk surface tension. (Experimentally classical nucleation theory works here.) For NH3 C6Hb CHC13 and CFC13 the microscopic surface tensions were much lower than the bulk surface tension (classical nucleation rates are too low here). But unfortunately for hexane heptane octane we also found lower microscopic surface tensions although classical theory works here. Experimentally the possibility cannot be excluded that the water impurities in NH3 lowered the supersaturation necessary for nucleation.2 Our paper on hetero- molecular nucleation indicates that such effects are quite strong for H20 +H2S04.Dr. W. J. Dunning (Bristol University) said In reply to the question of Kiang and Stauffer all possibilities should be considered. With regard to Stauffer’s report on calculations by Burton if we imagine a bulk crystal containing n = km particles to be subdivided into m crystalline nuclei each containing k particles and if E; is the specific surface energy and 0,the surface area of a nucleus the replacement factor qrepwill be 3k-6 1 3n-6 qrep = (&kO-Orn)Ok+ 1 ((bj+qj)-m (fi+&i). j= 1 i= 1 is the surface tension of the bulk crystal ci and yli are the zero-point energies of the ith andjth normal modes of vibration in the nucleus and in the bulk crystal respectively andfi and (bj are their free energies given by 4j = -kT log exp (-hujnj/kT) ni>O with a similar expression for h.The calculation of qrepthus requires a precise evaluation of E; and the frequencies pj of the normal modes in the nucleus and in the bulk crystal. Dr. E. R. Buckle (University of SheBeZd)said The contention in the original paper of Lothe and Pound (ref. (20) of Dunning’s paper) was that the Volmer theory of nucleation is in error in taking no account of the natural chaotic motion of the growing nuclei in the parent phase. I know of no reason for supposing that it was in Volmer’s mind that the embryonic particles were motionless so that it is to be presumed that the particle distribution in his treatment (eqn (1.18) of my paper) was intended to be one of equilibrium involving all thermally accessible energy levels in the various degrees of freedom.In the kinetic formulation of the problem given in ref. (1) of my paper the terms Wi and W of Volmer’s theory are given their molecular interpretations for vapour condensation. The collision terms for the motion of the gaseous clusters appear in the quantity Cs the interfacial free enthalpy. As stated in my paper 5 = WL so that the same terms are contained in 70,of Volmer’s formula. The Brownian motion is therefore taken into the surface tension term and the error in Volmer’s formulation of the reversible work of nucleus formation will reside in the use of a single value of J.Atm. Sci. 1972 28 1222 Appendix B. see J. Chem.Phys. 1972 51 5380 in particular p. 5387. W. J. Dunning in Nucleation ed. A. C. Zettlemoyer (Marcel Dekker New York 1969) p. 35. GENERAL DISCUSSION surface tension for all cluster sizes. As a likely source of error this has long been appreciated and the conclusion is that there is no additional source of error due to the omission of thermal motion terms. It is incorrect to add free enthalpy terms for this motion to Ws as given by Volmer. Dr. W. J. Dunning (Bristol University) said We all recognize the great achieve- ments of Volmer but we should not with hindsight attempt to read intohis work more than is there. For example on p. 97 of his book,' Volmer describes a method due to Gibbs for determining the work of formation of a nucleus of radius r,.One step in this process involves some of the bulk liquid confined in a cylinder by a piston being extruded as a droplet through a small orific in the cylinder wall. The work done in forcing out the droplet is given as This seems to imply that Volmer considered 0,the surface tension to be independent of the radius which it would not be if the Brownian motion is taken into the surface tension term. It seems that both Volmer and Gibbs were tacitly assuming that the droplet stands still on the orifice. In fact the still-attached droplet will be bobbing about on the orifice in Brownian motion and at some stage must be liberated to dance away into the vapour space.The contributions of Kuhrt,2 Lothe and Pound, Dunning and others analyze the consequences of this last stage of liberation. There is a large measure of common agreement but where they differ is in their assessment of the magnitude of the so-called replacement factor. Prof. C. S. Kiang (Clark College Atlanta Ga.) said Dunning mentioned various nucleation processes and their roles in his introductory remarks. From our recent studies we believe that the heteromolecular nucleation (homogeneous or heterogen- eous) process should be included as one of the most important nucleation processes for the fogs and smokes formation in the earth's atmosphere For relative humidity less than 100 % this nucleation process seems to be the only nucleation mechanism with water in the atmosphere.Most of the primary chemical constituents in the atmosphere do not have low vapour pressures and their atmospheric concentrations are measured in p.p.m. or p.p.b. and are not sufficient to allow nucleation in the gas phase. However by chemical reactions or radiation or other energy input secondary products with low volatility can be formed and these reactants may mix with water and undergo heteromolecular nucleation to form new aerosol. For example at room temperature SO2 has vapour pressure around 4atm. In the presence of oxidants (e.g. N02+hv-+NO+0 SO +O-+SO, SO +H,O-+H,SO,) H2S0 can be formed. With only Torr vapour pressure H2S04+ H20 will undergo the heteromolecular nucleation to form aqueous sulphuric acid aerosol. After reacting with NH3 (NH4)2S04 may be formed as stated by Dunning.M. Volmer Kinetik der Phasenbildung (Steinkopff Dresden 1939). F. Kuhrt Z. Physik 1952 131 185 205. J. Lothe and G. M. Pound J. Chem. Phys. 1962 36,2080. W. J. Dunning in Chemistry of the Solid State ed. W. E. Garner (Butterworths 1955) p. 159 ; Adsorption et Croissance Cristalline (Coll. Int. C.N.R.S. Paris 1965) p. 369. see W. J. Dunning Nucleation ed. A. C. Zettlemoyer (Marcel Dekker Inc. New York 1969) pp. 37-47. GENERAL DISCUSSION Dr. E. R. Buckle (Shefield University) said The purpose of my paper is to show that on simple kinetic grounds a particle in a volatile aerosol that is homogeneous and isothermal must grow or evaporate in a way that is dictated by the properties of the whole particulate system.The role of coagulation in particle growth is certainly paramount at low temperatures in very dense clouds of ultra-fine particles although for condensation aerosols the centres of coagulation are particles formed during the previous volatile stage. The properties J that are characteristic of the particle size distribution are found in the growth and evaporation equations of a particle. For instance in eqn (2.15) which gives the net rate of increase of material in a particle the term A(s+l reflects the joint influence of all the particles because its value is related to the size distribution at equilibrium. Now although A(,+ tends to zero for very large clusters the ratio &+l/& is still dependent on J if the processes in the aerosol are occurring naturally.Theoretically therefore the communal effects of the particles are unavoidable. Dr. W. J. Dunning (Bristol University) said Referring to eqn (1)-(5) of Buckle's paper is it possible to assert at this stage of his argument that there is a limiting value of o,as g-' ? If the clusters are bizarre in form how the equilibrium between one such monster and another monster behaves as the monsters increase in size can at present only be conjectured. At the other extreme if the clusters were perfect crystals the equilibrium quotients would oscillate. Dr. E. R. Buckle (Shefield University) said In reply to Dunning if by "monsters " is meant thread-like or branching clusters especially ones without a centre of sym- metry I would expect them to have little chance of formation by homogeneous pro- cesses under the moderate conditions assumed in my paper.They are therefore unlikely to contribute to the formation of stationary states. To prove this it would be necessary to extend the concepts of internal energy fluctuations to include such species. Gaseous ions might interfere in the condensation of heteropolar substances like water to produce elongated structures. For this to have a sensible effect on the condensation process there would have to be very many ions and the gas would be properly regarded as a mixture. Very large clusters are without influence kinetically and I do not visualize the growth of clusters as ever involving the perfect crystalline state. The size at which a pure particle with its inherent structural imperfections is able to assume crystallinity is unknown but it could well be too great for it to have any importance as a rate- determining factor in condensation.Such considerations are important because they bear on a well-known dilemma of " classical " nucleation theory. In the interpretation of condensation by Volmer theory there is always this element of uncertainty about the physical state of the nucleus is it solid or liquid? The uncertainty is embarrassing because macroscopic- ally the surface tension has different values for these states and a decision has to be made as to which to use in the theoretical formula. I doubt whether this difference is really meaningful in nucleation. To overcome this difficulty a theoretical approach is required in which the struc- tures and properties of the condensing particles are related to those of the molecules composing them.As a test of the usefulness of such a theory one would look for its ability to predict the rates of production of the particles and to relate these to measure- able physical properties of the system during condensation. A primitive attempt at such a theory was given in ref. (1) of my paper and Dr. A. A. Pouring and I have been using it in some calculations that should show among other things how sensitive the GENERAL DISCUSSION predictions of the path of condensation are to the molecular details. Whether the comparison of computed and measured values of experimental variables like pressure and temperature will provide a useful check on the adequacy of the cluster models also remains to be seen.Dr. D. Stauffer (Clark College Atlanta Ga.) said Buckle’s eqn (1.9) shows that one can calculate some cluster properties from measured (pressure density temper- ature) relations (equation of state). Fisher’s droplet model gives good agreement with the measured equation of state both near the liquid-gas critical point and at lower temperatures. It also agrees with direct evaluations of cluster concentrations in a two-dimensional m0de1.~ Does Buckle’s approach give an alternative droplet model which also can be tested using the measured equation of state? This would be very valuable as a replacement for the classical nucleation theory.I would also ask what is the relation between his eqn (2.15) and the “ classical ” approach (e.g. eqn (10) of D~nham).~ Dr. E. R. Buckle (Shefield University) said In reply to Kiang and Stauffer I am not optimistic about making comparisons of experimental PV isothermals with theoretical cluster distributions (e.g. my eqn (1.3) and (1.9)) to obtain the properties of the clusters. Except at high pressures for which the cluster models are not intended or at the very high supersaturations which build up in a fast expansion the concentra- tions of clusters fall too rapidly with size. The dependence of the distribution on the external variables should be more apparent experimentally as the system passes through the condensation threshold. During this stage the Volmer minimum in cs and the relaxation hump that follows it move into the region of small cluster sizes and then back out again.The time available for observation is so short that measure- ments with high time-resolution are called for. It seems that the measurements should aim to resolve the sizes also if cluster properties are to be investigated. The results of methods such as bulk scattering of light which give only a mean particle size over a finite time interval would be very difficult to relate to such properties because of the complex form of the relaxing size distribution (the curve of cs against g resembles in shape a PV isotherm of van der Waals at sub-critical temperatures). In the method of Volmer the clusters in an equilibrium store are assumed to grow by molecular collisions and evaporation is ignored.The flux condensation is assumed to be that of eqn (2.12) and is therefore independent of cluster size. Becker and Doering’s modification was to consider also evaporation but again there was no allowance for the possibility that the chance of capture or expulsion of molecules might vary with the size of particle. The theory of my paper shows that the intro- duction of size-dependent accommodation coefficients leads to the conclusion that the net flux on an aerosol particle is dependent on the size distribution and cannot be calculated from the laws for a macroscopic surface. Dr. W. J. Dunning (Bristol Uniuersity) said It seems that the limiting process in Buckle’s eqn (1.5) is not general but ancitipates a Volmer-like model in which the clusters are considered to be compact.Physics 1967 3 255. ’2.Phys. 1970,235 130. Phys. Letters 1972 4QA 345. Phys. Rev.,1972 B6 2777 ; also J. Stat. Phys. 1972 6 49. J. Rec. Atm. 1966 2 331. GENERAL DISCUSSION Dr. E. B. Buckle (University of Shefield) said In a treatment of this kind there is one respect in which the clusters must be regarded as compact. The stepwise processes AgM1 +Al = A, are only amenable to a simple collision theory if the cluster lifetimes are long in comparison with the collision time. High vapour densities are excluded by this and there is therefore some meaning in concepts such as the cluster-gas interface and the surface tension. It is a point of my paper that if clusters are to exist homogeneously at up to indefinitely large sizes the quantity 5 must obey the conditions 5 > 0 AC,/Ag = 0 in the limit as g -+ GO.But this requires w -+ w as g -+ co where a,approaches the constant w from below. These conditions are satisfied if one makes the reasonable assumption that in a growing cluster of iso- tropically bound atoms the nearest-neighbour coordination number k rises to a limit Am. This represents the ordering process that accompanies the differentiation of the condensed phase. With regard to the more diffuse entities only at high vapour densities near the critical point would there be tenuous regions of high local density in significant concentrations. Under such conditions however long-range density fluctuations are already a characteristic of the saturated vapour and the concepts of nucleation theory are no longer useful.Prof. M. Kerker (Clarkson Coll. Techn. Potsdam) said With regard to the paper by Buckle in our experiments on the formation of dibutylphthalate aerosol by cooling a mixture of vapour and NaCl particles (radii ranging from 30 to 100A) we observed that only a small fraction of the particles served as condensation nuc1ei.l Also this number depended strongly upon the rate of cooling ; there were more aerosol particles of smaller average size when the cooling rate was greater. We assumed this was controlled by the rate at which the most effective classes of nuclei could relieve the rapidly increasing supersaturation.Is this observation pertinent to the dynamic processes which Buckle describes in homogeneous nucleation ? Dr. E. R. Buckle (Shefield University) said In reply to Kerker if the particles coagulate while still at temperatures at which they are volatile it confirms that their sizes and individual properties are predetermined by the seed and are not influenced by the kinetic factors that determine size distributions in spontaneously-condensed aerosols. Yet the effect predicted for such an aerosol that the rate of growth of a particle gets slower as its size increases would lead to what Kerker has observed on changing the cooling rate the faster the cooling of the vapour the smaller and more numerous the particles become I believe this is purely coincidental and the effects are characteristic of hetero- geneous nucleation.In experiments on the seeding of water from moist air expanded in the wind tunnel the effectiveness of seed was greatest at low flow rates (i.e. slow cooling) and high humidities. Kerker describes how he makes allowance for the extra time particles have for coagulation if they are moving near the condenser wall. There may also be a connexion between the activity of the NaCl particles as condensa- tion nuclei and their position and speed relative to the wall. The proportion of seed particles that are effective as condensation centres would be expected to be sensitive to the radial velocity and temperature gradients and therefore to the flow speed. Consequently I suspect the reason for what was observed is the non-uniform condi- tions.G. N. Nicholson and M. Kerker J. Colloid Interface Sci. 1973 43 246. E. R. Buckle and A. A. Pouring Nature 1965,208 367. GENERAL DISCUSSION Dr. W. J. Dunning (Bristol University) said With regard to Kiang’s paper how large do the droplets grow before they come to equilibrium with the reduced relative humidity and reduced activity ? The authors have pointed out many possible sources of error and complication. Is the activity of say sulphuric acid derived from the concentration of sulphuric acid in the vapour phase ? Would not this be a composite term including not only H2S04 molecules but other species such as H30HS04? It is assumed that the condition of a nucleus of aqueous sulphuric acid is the same as that of a random sample in the bulk solution.However for bulk solutions some of the sulphuric acid will be dissociated into ions. In nuclei containing say 5 sulphuric acid molecules and perhaps 30 water molecules such dissociation will be inhibited since some of the resultant electrostatic field will stray outside the nucleus where the dielectric constant is low (-1). Further the ions will tend to avoid approaching the surface of the nucleus and to occupy only the middle ; this will affect the entropy of mixing. Such points may need consideration when the theory is developed further. Dr. R. A. Cox (AERE Harwell) said With regard to the heteromolecular nucle- ation of H2S04+H20 vapour mixtures discussed in the paper by Kiang and Stauffer a simple experimental test of the validity of the Flood-Neumann-Doering-Reiss-Doyle theory was suggested by Doyle.His calculations indicated that appreciable nucleation rates would occur at sulphuric acid vapour activities of 10-2-10-3 in air at 50 % relative humidity (RH ;25°C). This corresponded to the equilibrium vapour phase activity above an aqueous solution of H2S04 of composition -75 % wt/wt H2S04. Thus a sulphuric acid solution of this composition should fume in air at 50 % RH. We have measured the concentration of condensation nucleii (CN) in an air-stream passing over concentrated H,S04 solutions of various compositions using a Pollack CN counter. At 72 % wt/wt no CN were detected even at 70 % RH. With 77 % wt/wt H2S04,particles (300-600 ~m-~) were detected at 70 % RH and at 83 % wt/wt the particle counts at 70 % and 5 % RH were 3 x lo5 and lo4 ~m-~ respectively.These experiments are only semi-quantitative since (a) the CN counter does not measure the number of nucleating embryos but only the number of particles which grow to sufficient size to register in the CN counter (225 A). Losses of particles of this size (and smaller) by diffusion to the containing walls will be appreciable. Also (b) equilibrium conditions of H2S04 and H20 vapour were not attained above the liquid surface and the departure from equilibrium cannot be assessed easily. Never-theless these results do indicate that the theoretical predictions are not grossly in error and that heteromolecular nucleation in H2S04+H20 mixtures can occur at an appreciable rate at extremely low partial pressures of H2S04 vapour (i,e.approxi- mately 10-9-10-8 Torr at 50 % RH). Prof. C. S. Kiang and Dr. D. Stauffer (Clark CoZZege Atlanta) said In reply to Dunning 1-6 A is a typical radius of the “critical ” droplets at the saddle point. After this heteromolecular nucleation the droplets grow until the H2S04 gas is (nearly) exhausted which happen for droplet sizes of typically 10-100 A (see ref. (15) for details). The H2S0 activity was determined by thermodynamic relations and specific heat measurements (Giauque et al. ref. (6)) ; the evaluation assumes the presence of only two gaseous species. We do not know the magnitude of the error involved in this approximation. In addition to these dissociation effects which may differ in small J.Chent.Phys. 1961 35 795. GENERAL DISCUSSION droplets from bulk phase dissociation effects one also expects (ref. (2)) an enrichment of one phase near the droplet surface. For small droplets the Gibbs adsorption equation describing this surface enrichment can be seriously wrong in particular if applied to H20+C2H50H heteromolecular nucleation. Computer simulations of small liquid droplets (Monte Carlo molecular dynamics etc.) might eventually answer these questions ; we cannot. In reply to Cox for a 72wt % solution the H2S04 activity is 0.0007 for 77 % it is 0.0044 and for 83 % it is 0.04 according to Giauque et al. (ref. (6)). Dr. D. Stauffer (Clark College Atlanta Ga.) said The vapour pressure of Torr for H,S04 was questioned by Doyle,' who prefers Torr ; which is the better value ? Dr.C. N. Davies (University of Essex) said I agree with Stauffer that there is doubt about the partial pressure of H2S04 above aqueous solutions. It is possible that it could be measured by a technique similar to that described by Frostling.' Droplets as large 8s 2 pm diam. can be kept in suspension with a greatly reduced loss by sedimentation in a cylindrical chamber which is continuously rotated. By holding the atmosphere in the chamber at a constant relative humidity and sampling the aerosol over a long period it might be possible to measure the rate of evaporation of H2S04 as a function of the ambient humidity. Dr. R. G. Picknett (Chem. Defence Est. Porton Down) said I would raise two points about the paper by Davies.The first concerns the evaporation coefficient which must have a value near to unity if the interpolation formula eqn (1.13) is to be applicable. Measurements of this parameter are sparse but a value for water of only 0.04 has been reported and so eqn (1.13) must be employed with caution. Extensive calculations of droplet evaporation have been made by N. L. Cross and myself in which we find that a 70 % difference in droplet lifetime is obtained when evaporation coefficients of 0.04 and 1.0 are used. This is for drops of 5pm radius. My second point concerns the effect of self-cooling on the evaporation rate which Davies correctly states is negligible for the substances other than water in table 2.This effect has also been investigated in the calculations made by N. L. Cross and myself. It is most important for droplet evaporation in vapour-free surroundings and under these conditions it rapidly becomes significant as the vapour pressure increases above 0.1 mbar. If we take a vapour pressure of 1 mbar 10 times as large then a 5pm radius droplet of a typical organic liquid will have the surface temperature depressed by about 0.3"C,i.e. sufficient to cause a material reduction in the rate of evaporation. Dr. C. N. Davies (University of Essex) said In reply to Picknett it is difficult to measure the evaporation coefficient a. Bradley et al.2 gave 0.28 for di-n-butyl phthalate and 0.35 for butyl stearate droplets in air but it was subsequently decided that azl for di-n-butyl phthalate in air hydrogen and fre~n,~ for straight chain hydrocarbons in air,4 and far branched-chain hydrocarbons and a straight-chain fluorocarbon in air.5 For rhombic sulphur it was found that o! = 0.73.6 J.Aerosol Sci. 1970 1 341 ; and 1973 in press. R. S. Bradley M. G. Evans and R. W. Whytlaw Gray Proc. Roy. Suc. A 1946,186,368. J. Birks and R. S. Bradley ibid. 1949 198 226. R. S. Bradley and A. D. Shellard ibid. 1949 198 239. 'R. S. Bradley and G. C. S. Waghorn ibid. 1951 206 65. R. S. Bradley ibid. 1951 205 553. GENERAL DISCUSSION Alty and Mackay concluded that thermal accommodation of water vapour molecules striking a water surface was achieved but that the rate of rc-evaporation of condensing molecules was high at vapour equilibrium so that the rate of evaporation of water molecules from the liquid phase was only 0.034-0.036of the rate of impact from saturated vapour according to kinetic theory.However Jamieson,2 using a dynamic technique found a to be at least 10 times greater than this low value. There has thus been a tendency for a for liquids to increase as experimental techniques improved and recently Jer Ru Maa,3 using a jet tensimeter has obtained results which lead him to conclude that a = 1 for all liquids. Further references are given in table 1.8 of A. G. Amelin’s book Theory of Fog Condensation (Moscow 1972). Picknett’s remarks on evaporation are interesting. For water the tempera- ture of a drop regardless of its size is equal40 that of the ventilated wet bulb thermo- meter.Prof. E.Rosner ( Yale University) said While the evaporation (or condensation) coefficient c1 for the liquids of interest to Davies may indeed be close enough to unity to ensure the utility of eqn (1.12) this assumption would certainly fail for the evapor- ation (or growth) of crystalline aerosols especially when the dominant vapour species do not exist as structural entities in the condensed phase.4 For example low and sharply temperature dependent cc-vaIues have been measured for the individual faces of crystalline solids which (i) dissociate upon sublimation (e.g. AlN(s) Al,O,(s) NH,Cl(s)) or (ii) whose vapours are associated (As(s) and P(s) giving tetramers in the vapour phase). Also of interest in this connection is the fact that for such solids melting is expected to be accompanied by a discontinuous increase (“jump ”) in a (observed for the sublimation of polycrystalline A1203(s) Ga203(s) and 3Al2O3- 2Si02(s)).Since this is probably a general phenomenon holding for phase changes even below the equilibrium transition temperature it is interesting to consider its consequences for the relative evaporation (or grdwth) of aerosols for which the condensed phase may be either crystalline or amorphous. In the usual case for which AHsublim> AH,,,. both high vapour pressure and high a would combine to cause rapid gasification of a liquid aerosol compared to its crystalline counterpart at the same sur- face temperature. For condensational growth from the vapour however these effects would oppose one another causing loss disparity in condensation rates morc than in gasification rates.Finally since compact crystalline aggregates appear to be present (at least as intermediates) during the production of inorganic oxide aerosols in flames we should note that prior to complete sintering such an aggregate (i) would be char- acterized by an effective c1 higher than that corresponding to the surfaces of its crystal- line constituent “ primary ” particles (owing to multiple vapour molecule/solid encounters during escape of condensation from/in the “labyrinth ’7 ; (ii) can lose or gain mass without a corresponding change in the outer dimensions of the aggregate (owing to a change in overall aggregate density p). Dr.C. N. Davies (University of Essex) said Rosner had made some important points. However the association of vapour molecules to form e.g. tetramers will T. Alty and C. A. Mackay ;bid. 1935 149 104. * D. T. Jamieson h’ature 1964 202 583. Jer Ru Maa Ind. Eng. Chem. Fund. 1967 6 504; 1970 8,564; 1970,9 283. This has been reviewed by G. A. Somorjai and J. E. Lester in Progress in Solid State Chemistry H. Reiss ed. (Pergamon Press Oxford 1967) Vol. 4 pp. 1-52. R. P. Burns J. Jason and M. G. Inghram J. Chem. Phys. 1964,40,2739 see also R. P. Burns Ph.D. Dissertation (Dept. Physics Univ. Chicago 1965). GENERAL DISCUSSION reduce the kinetic impact rate by $. so that a corresponding reduction in the rate of vaporization occurs quite apart from any effect due to a.If the vapour is dissociated the impact rates of each type will usually differ so that the values of aneed to adjust themselves accordingly. Prof. M. Kerker (Clarson Coll. Techn. Potsdam) said I would ask Davies how would one transpose this calculation to a heterodisperse aerosol assuming condensa- tion to the wall was minimal and that the process was primarily distillation from smaller to larger particles due to the Kelvin effect? What would the vapour field " seen " by a particular particle be? How would the evaporization rate compare to that for the single particle model? Further questions are (i) how sensitive would the evapor- ation rate be to the evaporation coefficient particularly for small concentration gradients ? (ii) Would one expect that "contamination " might significantly affect evaporation rates? (iii) May one neglect the latent heat effects particularly in an aerosol having a particle concentration of the order of lo6 particles ~m-~ ? Dr.C. N. Davies (University of Essex) said The vapour field " seen " by a particle depends on Kn. When Kn is large the particle " sees " a vacuum roughly up to a distance Kna from its centre. When Kn is very small the concentration gradient outside the particle is such that (4-na" -n*) = a/r where n is the concentration of vapour at radius Y. If the concentration of the aerosol is lo6 particles/cm3 then the volume per particle averages cm3 which is equal to a sphere of radius 62 pm. During quasi-steady evaporation of an isolated particle having a = 0.31 pm the concentration at the surface of a concentric sphere of radius 62 pm would be 99.5 % of the concen- tration at infinity.The evaporation under quasi-steady conditions of such a particle in an aerosol of lo6particles cm3 therefore proceeds at the same rate as it would were the particle isolated. The establishment of quasi-steady conditions requires a time of the order of l/E say s when Kn is large ; for diffusion controlled evaporation the time dependent term is a/ Jnvt. Putting this equal to 0.01 so that the difference between the transient and quasi-steady rates of evaporation is negligible gives t = s. Whatever the value of Kn the time taken to establish quasi-steady conditions is negligible ; the rate of evaporation of a particle in the cloud will be the same as that of an isolated particle.If the coefficient a is very small the rate of evaporation is not controlled by diffusion but by the rate of escape of vapour molecules from the surface even though Kn may be very small. This happens when water droplets are coated with a layer of long chain molecules.1 As a decreases therefore the rate of evaporation becomes less dependent on the concentration gradient and more dependent on a/Kn ; such behaviour is unlikely to occur with drops of organic liquids. Contamination can affect the evaporation of liquid droplets in two ways (i) by lowering the vapour pressure due to the rising concentration of involatile contaminant as evaporation proceeds ; (ii) by forming a film on the surface of aqueous drops which impedes evaporation ; highly specific properties are required in the contaminant for this effect to be large.Suppose the concentration of aerosol is 7.7 x lo-' g/cm3 ; the latent heat of vaporization of DBP is 79 cal/g so that complete evaporation will withdraw from the C. N. Davies Disc. Faraday Soc. 1960 30 144. GENERAL DISCUSSION gas phase 6.1 x cal/cm3. 1 cm3 of air has a heat capacity of 3 x cal/"C. The fall in temperature due to complete evaporation of the disperse phase is thus 3 x 10A4/6.1x lo-' = 4.9"C. Dr. R. G. Picknett (Chem. Defence Est. Porton Down) said Kerker has asked what happens to the evaporation process when a cloud of droplets is present. N. L. Cross and myself have performed calculations for monodisperse aerosols which we hope to publish soon.Provided the mass concentration of aerosol is less than about 1 mg/m3 interaction of the vapour gradients adjacent to neighbouring droplets is negligible and the only effect of the aerosol is to increase the background vapour concentration as the evaporation proceeds thus slowing the process. Prof. M. Kerker (Clarkson Coll. Techn. N. Y.) said We have found our aerosols quite stable to evaporation as pointed out in the discussion on our paper. Since the mass concentration is 1 mg/l. the evaporation must proceed even significantly lower than Cross finds at 1 mg/m. Prof. D. E. Rosner (Yale University) said In quantitative treatments of the evolu- tion of the aerosol size spectrum function n(r x t) under conditions for which the "growth " term d(fn)/ar plays an important role it is common to assume that the individual particle growth rate f is a function of at most the prevailing particle radius r and local environmental variables at position x and time t.For example in the continuum limit (Kn <1) the Maxwell-Smoluchowski equation provides the proportionality fccr-l but it is prudent to recall the assumptions underlying this simple result prior to its formal application to dilute (low volume fraction) aerosols in new situations. In a recent investigation of the vaporization of isolated droplets in the continuum regime conditions leading to the breakdown of the instantaneous focr-l law have been explored with some results of potential significance to aerosol science/technology mentioned here.Briefly for the validity of the f ccr-I law it is not sufficient that droplet and its local environmental conditions undergo negligible fractional changes in the characteristic diffusion time r2/D (where D is the Fick diffusion coefficient for the evaporatingjcondensing vapour). It is also necessary that the velocity of the moving phase boundary be small compared to the character- istic vapour diffusion velocity. This leads to a necessary condition of the form where uV+,is the vapour mass fraction at the droplet surface and coo,, is the vapour mass fraction in the gaseous environment "far " from (i.e. several droplet radii away from) the droplet.2 Ordinarily the density pm of the gaseous environment is much smaller than the density Pdroplet of the droplet itself and the local vapour mass fractions q,, are everywhere much smaller than unity so that this condition for the validity of the quasi-steady approximation (leading to f ccr-') is satisfied.However if one considers a spray of a liquid fuel say at a total pressure level comparable to the D. E. Rosner and W. S. Chang Combustion Sci. Techn. 1973 in press. Under conditions for which the Maxwell-Smoluchowski i' expression is valid the diffusional "driving force "parameter in the absolute value brackets is itself small compared to unity and -i. is linearly proportional to o,,~-Ou,a. However a generalization of the quasi-steady Maxwell-Smoluchowski expression is available for which the i. a r-' dependence is preserved even when the driving force parameter is not small.(See e.g. D. B. Spalding Convective Muss Trunsfer-An Introduction (McGraw-Hill New York 1963)). GENERAL DISCUSSION thermodynamic critical pressure of the fuel then for droplets whose temperature approaches their critical temperature this parameter becomes appreciable and the quasi-steady approximation loses its utility. Interestingly enough this situation is encountered for diesel engine cylinders into which kerosene (pc= 26 atm TCz662 K) is injected as a droplet spray. In such cases a fully transient treatment of the i. function appearing in the aerosol evolution equation is evidently required. D. E. Rosner AZAA J. 1967 5 163.

ISSN:0301-5696    

DOI:10.1039/FS9730700042

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Inorganic Oxide Aerosols of Controlled Submicronic Dimensions H. MOZZANEGA A. THEVENET BY F. JUILLET F. LECOMTE S. J. TEICHNER AND P. VERGNON Institut de Recherches sur la Catalyse (C.N.R.S.) DCpartement de Chimie Physique 69-Villeurbanne France Received 4th December 1972 Metallic oxides aerosols are prepared by decomposition of anhydrous chlorides in the diffusion flame of a hydrogen-oxygen reactor. The flow rate of the chloride vapour the temperature of the flame and the residence time of the reagent in the flame determine the shape (spherical or polyhedral) the dimensions (in the range from 60A to 2000 A) and in some cases the crystalline structure of the particles which in all cases are non-porous. These highly divided oxides exhibit unusual photocatalytic properties which are not encountered with aerosols in the micron range or with porous particles prepared in a conventional way.Titanium dioxide in particular enables the catalytic photo-oxidation (in the u.-v. range) at room temperature of organic and inorganic compounds. Paraffins and olefins are oxidized partially and/or totally whereas ammonia yields N20and NZ,carbon monoxide yields carbon dioxide and hydrogen sulphide yields sulphur dioxide and sulphur. Industrial smokes inject into the atmosphere submicronic particles of metallic oxides which are often in contact with industrial gases containing hydrocarbons ammonia carbon monoxide hydrogen sulphide sulphur dioxide and oxides of nitrogen. Since the natural sedimentation of these aerosols is a slow process their reaction with the above gases in the presence of oxygen and of u.-v.irradiation is of interest in the study of environmental problems. Although the smokes of metallic oxides are usually prepared in the laboratory by electric arc or plasma methods we preferred to generate the submicronic aerosols by the flame reactor method 1* because it permits a good control of the size and the shape of the oxides and also because it is more closely correlated to the industrial " involuntary " generation of particles in the smokes. A special interest was attached to the shape of oxide particles generated in the flame reactor because previous studies have shown that surface properties of anatase aerosols are different for polyhedral or spherical particles.Indeed spherical particles exhibit a statistical abundance of all crystallographic planes whereas polyhedral particles may have some privileged planes developed. Moreover the number of discontinuities at the surface (corners edges and steps) is also greater in the poly- hedral particles and therefore point defects because of poorly coordinated surface ' ions seem to be more abundant in these particles. The size of particles may also control the shape and the defect structure of the surface of particles because when only a small quantity of ions with a normal co-ordination number is present in a particle then only the most stable planes are likely to be de~eloped.~ EXPERIMENTAL The aerosol particles are obtained by decomposition of anhydrous metallic chloride vapour in the hydrogen-oxygen flame of a diffusion multitubular burner.The experimental 57 INORGANIC OXIDE AEROSOLS device has been described in dctail.2* The flow rate of reacting gases the concentration of the chloride in the feed and the temperature of the flame may be varied over a large range. For a given temperature of the flame (obtained by varying the Hz/02ratio) an increase of the concentration of the chloride vapour carried out into the burner by the oxygen feed increases the diameter of particles of the aerosol collected in a electrostatic precipitator. The particles are non-porous and practically monodispersed for each preparation. The photocatalytic properties at room temperature of the aerosols were studied in a differential reactor already described.6 A u.-v.source was used in some cases with a mono- chromator or filters such that the selected wavelength could pass through a silica window and irradiate the aerosol deposited on a porous film in the reactor in the form of a thin layer. The reaction products were analysed by gas chromatography. RESULTS AND DISCUSSION MORPHOLOGY OF AEROSOLS Particles of AI2O3?TiO, SiO, ZrO, Fe203 Crz03 V205,SnO and GeO, were prepared as required from corresponding volatile chlorides (or oxychlorides). The relationship between the concentration of the chloride in the feed and the diameter of particles for each temperature of the flame has been given else~here.~ In the present paper particular attention is attached to the relationship between the shape and the diameter of particles with the surface activity of TiO aerosols prepared in flames whose tempxature is in the range of 1500 to 3000 K.Typical flow rates of gases into the burner for a flame at 3000K are of the order of 8 x mol/s for hydrogen 4x mol/s for oxygen I .2 x mol/s for nitrogen. For a cold flame (e.g. 1500 K) a proportion of the hydrogen is substituted by nitrogen. Titanium tetrachloride vapour flow rate may vary over the range of to 5 x mol/s. The residence time of the particles in the flame which depends on the flow rate of the carrier gas and the cross-sections of the burner tubes may vary between 0.3 x lo- and 15 x lo- s per 1 cm length of the flame. It is assumed that the rate of transformation of the chloride vapour in the flame into the oxide is much higher then the rate of growth of the oxide droplets or particles.Consequently the residence time of “ initial ” molecules of the oxide in an elementary volume of the flame depends on the flow rate of reagents into the burner. On the other hand the concentration of “ initial ” molecules of the oxide or its vapour pres- sure is determined by the concentration of metallic chloride vapour in the carrier (oxygen) gas. An attempt is then made to determine the conditions of the formation in the flame of a particle of the oxide in connection with the concentration of “ initial ” molecules of the oxide and their residence time in the flame. The electron micrograph of fig. la shows a titania aerosol obtained in a cold flame (1700 K) whereas fig.lb shows the aerosol obtained in a hot flame (3000 K). The overall rate of flow of feed gases (H, O, N,) was 1.3 x lo- mol/s for both prepara- tions (residence time 0.05 s/cm) and the flow of titanium tetrachloride was also identical at the low rate of 0.4~ lo-’ mol/s for both aerosols. These results show that for any flame temperature and for a low concentration of reacting species the aerosol particles present have dimensions below 200A and their shape is that of a polyhedral type exhibiting facets. In this range of concentration of TiC14 the influence of the residence time is negligible. When the titanium tetrachloride flow rate is increased almost 100 times (25 to 30 x mol/s) fig. lc (1700 K) and ld(3000 K) show a remarkable difference in the morphology of particles.For the cold flame (lc) the shape of aerosol particles is of the same type as previously shown (la) though their diameter is now increased to FIG. la-Aerosol of titania prepared in a FIG.1h.-Aerosol of titania prepared in a hot cold flame (1700 K). TiCI flow rate 0.4 x flame (3000 K). TiCi flow rate 0.4 x 10-5 mol s-I. Ill01 5-I. Fw. Ice.-Aerosol of titania prepared in a cold FIG. I(/.-Aerosol of titania prepared in a hot flame (1700 K). TiCll flow rate 3Ox flame (3000 K). TiCI flow rate 25 x 10 ' niol s-I. mol s '. ((1) (h) FIG.2-(tr) and (0) Formation of spherical particles of titania from polyhedral particles in a flame of intermediate temperature (2100 K) TiCI flow rate 25 x mol s-l.JUILLET LCCOM TE MOZZANEGA,TEICHNER THEVENET VERGNON 59 360-400A. The variation of the residence time only modifies the size of particles and not their morphology. For the hot flame (Id) the particles now present a perfectly spherical shape of a diameter of the order of 1500 A. It is supposed that this spherical morphology results from the condensation of " initial " molecules of Ti02 into liquid droplets (melting point of Ti02 = 2200 K) which after cooling and quenching give solid particles with the initial shape of droplets. In this latter case the proportion of spherical particles in the aerosol increases when the residence time increases. The question now arises why in the case of a low concentration of titanium tetrachloride and hence of "initial " molecules of Ti02 (fig.lb) the liquid droplets of a smaller diameter are not formed in the hot flame. The polyhedral shape of the particles seems indeed to indicate that condensation of "initial " molecules of Ti02 proceed directly into a solid state in the same manner as a for a cold flame (fig. la) below the melting point of Ti02. Because the flame reactor enables one continuously to vary the temperature of the flame and the residence time in the flame it was possible to set the boundary conditions between the spheres and the polyhedral particles. Fig. 2 shows the micrographs from which the mechanism of the formation of a spherical particle may be deduced. It must also be recalled that spherical particles of diameter smaller than 300& have never been observed for any flame temperat~re,~ which seems to show that the liquid state cannot be formed below some critical diameter of particles.Fig. 2a and 2b seem to indicate moreover that the liquid droplet is not obtained directly from the con- densation of" initial "molecules of TiOz but only by the melting of a group or cluster of small solid polyhedral particles initially condensed. For an intermediate flame temperature (2100K) and a high flow rate of titanium tetrachloride (30x mol/s) a sufficiently high concentration of small (polyhedral) particles is present in the flame to allow the formation of aggregates of particles which at this temperature will just be able to melt-resulting in a spherical cluster. This behaviour should be correlated with two observations (i) the vapour pressure increases when the radius of particles decreases and (ii) the vapour pressure in equilibrium with the condensed phase is smaller for solid than for liquid hence a critical radius of curvature may exist below which only the solid phase is stable.The crystalline structure of titanium dioxide seems also to depend on the dimen- sions and shape of particles. In cold flames for polyhedral particles anatase is principally formed. However for hot flames polyhedric particles may contain up to 30 % of rutile whereas spherical particles contain almost 100 % of anatase. It is therefore not surprising that particles of different morphology and structure exhibit different catalytic properties and also photo-catalytic properties as shown in the next section.PHOTOCATALYTIC OXIDATION IN THE PRESENCE OF SOME OXIDE AEROSOLS It has been already shown that alumina titania or zirconia aerosols (diameter of particles below 300 A)may be reduced on their surface in vacuum at 500°Cgiving non- stoichiometric oxides." * For titania this reduction may be achieved at room temperature in vacuum if the solid is simultaneously irradiated in u.-v. (2000-3600 Moreover titania aerosols exhibit at room temperature photo-catalytic behaviour in the partial and/or total oxidation of hydrocarbon^.^ For this reason a study of their behaviour in the photocatalytic oxidation of inorganic molecules was also undertaken. It must be recalled that the photocatalytic activity e.g. in the oxidation of iso- butane into acetone expressed as a number of micromoles of acetone formed per INORGANIC OXIDE AEROSOLS minute per gram of catalyst spread out on the porous support in the differential reactor is a linear function of the weight of the catalyst up to some critical limit.It has been suggested that this behaviour is related to the surface nature of theprocess and to the need for the u.-v. radiation which is unable to reach the catalyst particles at the bottom of the bed if the thickness of the bed exceeds some critical limit. Further-more all the tests of photocatalytic activity were performed with the mass of the aerosol not exceeding the critical mass. In a typical test of CO oxidation the composition of reacting feed was 12.5 % of 02,25 OJO of CO in 62.5 % of He as a carrier gas with a flow rate of 1 L/h onto 10 to 33 mg of aerosol uniformly deposited on a porous support (fiberglass) in the reactor.Table 1 gives the results of the photocatalytic oxidation of CO at room temperature onto titania aerosols of various surface areas prepared in the flame reactor. TABLE ACTIVITY OF TiOz AEROSOLS 1.-PYOTOCATALYTIC surface area/ m*g-1 morphology total mass in the bed/ mg conversion % activity a pmol COz min-1 tn-2 activity/pmol COz min-1 9-1 temperature o the flame/K st NCt me % rutilc 23.5 32.5 41.O 68.O 70.0 98.0 140.0 spheres spheres spherespoiyhedr. polyhedr. polyhedr. pol yhedr. 20 35 13 19 13 15 10 0.71 2.39 1.51 1.48 1.36 1.73 1.73 72 118 202 135 181 200 350 3.20 3.70 4.90 1.99 2.56 2.04 2.49 3000 3000 2700 1900 1900 1700 1700 a All experiments are performed with a constant intensity of u.-v.beam If the photocatalytic qctivity in micromoles of CO per min and per m2Qmol min-' m-2) is plotted as a function of the surface area (fig. 3) two distinct plots are observed for spheres and polyhedral particles. The activjty per unit surface should be t 6- 5-CI 4--E IC .-f 3-I 0 A b \ 2-I A A I I I I I-I I I I c * 0 50 ! GO I50 S/m2 g-' FIG.3.-Photocatalytic activity for CO oxidation of spherical and polyhedral aerosols. 0,spheres ; A polyhedra JUILLET LECOMTE MOZZANEGA TEICHNER THEVENET VERGNON 61 independent of the extent of the surface if the quality of this surface in catalysis remains constant.This is the case for polyhedral particles whereas for spherical titania the quality of the surface in photocatalysis seems to increase with the specific surface area i.e.,when the particle size decreases. It is difficult to ascribe this behav- iour to a different rutik content (table 1) of aerosols because their surface content is not known. However if the photocatalytic activity depends on surface defect structure (point defects),10 the polyhedral particles have some chance to exhibit the same surface concentration of defects whereas for spherical (melted) particles the organization of the surface may be more difficult to achieve when the dimensions of the particles (for small particles of higher surface area) are close to the crystallo- graphic distances in various planes of the lattice.As previously observed in the photocatalytic oxidation of hydrocarbons,6 titania (anatase) obtained in a conventional manner by hydrolysis of TiCI4 does not exhibit any activity in the oxidation of CO. It must be recalled that this sample is porous and therefore not convenient for a surface photo process. TABLE 2.-PHOTOCATALYTIC ACTIVITY IN THE OXIDATION OF co OF VARIOUS AEROSOLS activity E//imol C@ nature surface area/ml g-1 min-1m-2 70 0.46 37 0.016 220 0 39 0 100 0.017 54 0.03 34 0 13 traces 2 0.45 aThe conditions of irradiation were different from those used for data in table 1 (decreased intensity of u.-v. radiation). Among all the aerosols prepared in the flame reactor titania exhibits the highest photocatalytic activity in the oxidation of CO.Table 2 gives the comparative values of the activity for some aerosols for which the morphological study was not under- taken. The same oxides prepared in a conventional way by precipitation in aqueous media and calcining do not exhibit any measurable photocatalytic activity. In contrast with the photocatalytic oxidation of hydrocarbons where only titania aerosols were active various oxides exhibit some not negligible activity in the CO oxidation. Photo-oxidation of other inorganic substances was mainly studied on polyhedral titania (70 m2 g). A mixture of ammonia (20 %) oxygen (40 %) and helium (40 %) was passed with a flow rate of 1.2 I./h through the differential photoreactor and a conversion of 5 "/o was registered.The reaction products are N (85 %) and N20 (15 %) apart from water. Nitrous oxide is neither photo-oxidized in the same conditions nor can it be used as a source of oxygen in the photo-oxidation of hydrocarbons or CO. Blyholder and coworkers l2 have however observed a phot o-oxidation of CO by nitrous oxide in the presence of ZnO obtained by a conventional method. But this catalyst is also able to oxidize CO with N20 in a thermal process at low temperature. Finally hydrogen sulphide in a mixture of H2S (20 %) O2(30 %) and He (50 %I INORGANIC OXIDE AEROSOLS with a flow rate of 1.2 l./h was photo-oxidized on titania (70 m2/g) with a conversion of 6 %. In the exhaust gases sulphur dioxide and water vapour were identified but sulphur was deposited simultaneously onto the catalyst bed.Experiments to determine the activity of aerosols other than titania in the photo- oxidation of NH3 and H2S are still to be attempted. However it may be already concluded that the state (dimensions morphology) of the oxide particles in industrial smokes is of paramount importance in their surface activity. In conclusion it has been shown that it is not possible to extrapolate and compare data obtained for less divided oxides or for oxides prepared in a conventional way (mainly in aqueous media) so far as their photocatalytic activity is concerned. R. Caillat J. P. Cuer J. Elston F. Juillet R. Pointud M. Prettre and S. J. Teichner Bull.SOC. Cltim. France 1959 152. J. Long and S. J. Teichner Rev. Int. Hautes Temp. Rifract. 1965 2 47. J. Herrmann S. J. Teichner and P. Vergnon J. Catalysis to be published. R. Van Hardeveld and F. Hartog Surface Sci. 1969 15 189. M. Formenti F. Juillet P. Meriaudeau S. J. Teichner and P. Vergnon in Aerosols and Afmos- spheric Chemistry ed. G. M. Hidy (Academic Press N.Y. 1972) p. 45. M. Formenti F. Juillet P. Meriaudeau and S. J. Teichner Chem. Techn. 1971 1 680 and 5th Intern. Congr. Catalysis (Palm Beach 1972). 'B. Arghiropoulos J. Elston P. Hilaire F. Juillet and S. J. Teichner in Reacticity of Solids ed. J. H. de Boer (Elsevier Pub. Company Amsterdam 1961) p. 525. J. Long F. Juillet and S. J. Teichner Rev. Int. Hautes Temp. Rkfract. 1965 2 163. M. Formenti H. Courbon F. Juillet A. Lissatchenko J. R. Martin P. Meriaudeau and S. J. Teichner J. Vac. Sci. Techn. 1972 9 947. lo Ph. Roussel and S. J. Teichner Catalysis Review 1972 6 133. 0. M. Poltorak V. S. Boroninet and A. N. Mitrofanova Proc. 4th Intern. Congr. Catalysis Moscow 1968 ed. J. W. Hightower (Houston 1970) p. 1235. Ken-lchi Tanaka and G. Blyholder J. Chem. SOC.D 1971 14 736.

ISSN:0301-5696    

DOI:10.1039/FS9730700057

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Formation of Ti02Aerosol froin the Combustion Supported Reaction of TiC14and O2 BY A. P. GEORGE AND E. R. PLACE R. D. MURLEY Tioxide International Central Laboratories Portack Lane St ockt on-on-Tees Teeside Receioed 18th December 1972 The formation of particulate TiO has been studied by the addition of small quantities (10-5-10-3 mol fraction) of Ti& vapour to a lean CO +OL+Nz flame with a maximum temperature of about 1400°C. Measurements of TiCI concentration have been made as a function of height (residence time) by u,-v. absorption spectroscopy. The results demonstrate that chemical reaction is essentially complete 50 ms down stream of the CO flame-front at which stage the TiOz particles have reached a diameter of 410 A. Electron microscopic examination of samples of material from the flame shows that particle growth continues for a further 200ms by a flocculation mechanism.This is a major factor determining the final particle size (630 A). Agreement with theoretical flocculation predictions is reasonable both with respect to the development of the mean size and the size distribution. Results of sintering experiments carried out in the flame and of similar measurements carried out in the hot stage of an electron microscope demonstrate that the particles produced in this system exhibit a fusion temperature much below that of the bulk solid (1850°C). The occurrence of sintering in the flame is necessary to account for the form of the TiO particles produced in this system. The high-temperature oxidation of gaseous TiCI4 according to reaction (1) forms the basis of an industrial process for the production of pigmentary TiO TiC14+O,+TiO,(s) +2C1 (AH = -43.4 kcal/mol).(1) The pigmentary properties of the Ti0 are related directly to particle size and size distribution. Consequently it is important to understand the processes that determine these size characteristics. The relevant processes contributing to the final size are nucleation growth by chemical reaction and growth by flocculation. Al-though in principle the theory behind these processes is well understood there is little practical evidence to confirm the behaviour of high-temperature high-concentration small-particle aerosol systems in which chemical reaction is occurring. The present study provides some practical information on these factors which although obtained specifically for the TiCI4 +0 reaction system are relevant to other aerosol systems in similar regimes.The oxidation reaction only occurs at an appreciable rate at temperatures in excess of about 1000°C. Although the reaction is exothermic it does not become self- supporting in the manner of a combustion reaction. In order to establish a system amenable to study it was desirable to avoid the complications inherent in preheating and mixing the reactants. This was achieved by utilizing a lean flat laminar CO+O flame as the source of heat. In this way premixed TiCI4 was reacted with excess O2 in an essentially plug-flow system allowing residence time to be simply related to position.The use of CO as a fuel has the advantages that the flame pro- duces no water or ionization and that the products are relatively inert. Water has a pronounced effect on the reaction and the generation of charged species could affect all stages of the particle formation process. 63 FORMATION OF TiOz AEROSOL EXPERIMENTAL The complete gas delivery and burner system is shown diagramatically in fig. 1 and details of the burner are shown in fig. 2. The burner consists of an hexagonal array of 271 stainless steel hypodermic tubes 0.050" o.d. 0.006" wall thickness the outer three rows 144 in total providing the sheath flame. The upper burner body is cooled by transformer oil circulating from a water-cooled heat exchanger. Flame stability is improved by the provision of a stainless steel gauze 2 cm above the burner mouth.The flame temperature in this system can be controlled independently of the mixture composition by varying the total flowrate. All the measurements described refer to the FIG. 1.-Schematic diagram of burner system 1 2 3 Carbon monoxide oxygen and nitrogen source; 4 5 6 drying tubes; 7 8 9 10 11 12 flowmeters; 13 TiCI4 evaporator; 14 ballotini- packed water condenser ; 15 mixing vessel ; 16 absorption vessel ; 17 burner ; 18 coolant inlet/ outlet ; 19 stabilizing gauze ; 20 vent. FIG.2.-Details of multiorifice buruer. A. P. GEORGE R. D. MURLEY AND E. R. PLACE following flame conditions molar ratio C0/02/N2 = 1/0.95/1.1 ; flow to inner burner = 1 1. min-' ; flow to sheath burner = 3,3 1.min-' ; maximum flame temperature = 1650' K. Additioning of the inner flame gases with TiC14 is achieved using a by-pass system metered fractions of the gases passing through a TiCI4 saturator. The two gas streams then re-unite and flow to the burner via a mixing tube containing ballotini and glw wool plugs where TiCI hydrolysis products formed by reaction with residual water vapour in the gases are removed. The concentration of TiCl4 in the feed gases is determined at the commence- meat and end of an experiment by passing them through an absorption vessel containing tetrachloroethylene for a known period of time. This effects total extraction of TiC14 the concentration of which is subsequently determined colorimetrically in aqueous phase as the peroxo complex.This level of TiC14 is reduced with respect to the flame asa consequenceof losses incurred at the burner face where surface growth of Ti02 takes place irrespective of flame conditions or TiC1 addition level. These losses were determined by mass balance the solids produced in the flame king collected on a glass-fibre filter pad. As a check on completeness of reaction the exhaust gases from these experiments were scrubbed with tetrachloroethylene when no unraacted TiCI4 could be detected. The range of TiCl concentrations expressed as mol fraction of feed gases established using this technique was 4.5 x 10-5-3.3 Particle samples were taken from the flame by direct deposition on to electron microscope grids mounted on a brass holder.Samples were taken by sweeping the grid holder manually through the flame with a sweep time of approximately 1 s the number of passes required to give a particle number concentration sufficient for counting and size analysis varying from 1 to 4 dependent upon flame TiCI4 concentration. The grid mounting and support produces rapid quenching of the sample and this method was found to be superior to a quartz probe technique both in ease of operation and sample reproducibility. Determination of the absorption spectra of TiCI was carried out on the same burner. A deuterium arc lamp and slit collimator were mounted on an optical bench at one side of the burner in diametric opposition to a Hilger and Watt D292 grating monochromator. A constant slit width of 0.8mm was used throughout.The light intensity at the mono- chromator exit slit was measured with an RCA IP 28 multiplying phototube the output from which was displayed on a digital voltmeter. The reference spectrum for TiC14 was obtained on the burner with the flame unignited. The fusion of flame-produced Ti02 partides was examined initially by allowing them to deposit on a fine platinum wire at -9900°C removing a sample for examination and then re-introducing the wire into the flame at -1300"C,after which a further sample was taken. A more quantitative method was later applied in which the particles were deposited directly on palladium grids by brief exposure to a TiC1,-additioned flame after which the grids were placed in the electron microscope hot-stage and heated at a rate of approximately 20°C min-I while maintaining a visual check upon the particles.The temperature range within which the particle clusters underwent a sudden and marked shrinkage was noted. RESULTS AND DISCUSSION A variety of experimental techniques have been applied to the study of this particular reaction system ; those relevant to the present discussion have been detailed above. The discussion centres on the measured particle size distributions of material sampled from the flame a typical example of which is shown in plate 1. All distri- butions were obtained by sizing each particle present on the electron micrograph separately irrespective of its position with respect to other particles. Table 1 shows the change of particle size and standard deviation with residence time.The variation of mean particle size with initial TiCI4 concentration for samples taken at 2cm is shown in fig. 3. The results show clearly that the particles are growing in size as they travel down- stream from the burner and that the final size is related to reactant concentration. s7-3 FORMATION OF TiO AEROSOL TABLEVARIATION OF PARTICLE SIZE PARAMETERS AND GROWTH RATES AT TiCi4MOL FRACTION 2.0x 10-3 sampling position (cm above burner face) 0.5 1.o 1.5 2.0 estimated flame residence time/ms 50 100 160 230 d (geometric weight mean)/pm 0.041 0.055 0.062 0.063 standard deviation 1.372 1.349 1.329 1.354 d (geometric weight mean)/pm calculated -0.061 0.072 0.080 standard deviation -1.340 3..321 1.302 lo-' 5.8~ 7.1 x 10-3 apparent growth rate/(pm s-l) 4x 10-1 1.4~ growth rate/(pm s-l) from Ghoshtagore 4.4~ 3.1 x 7.1x 10-3 4~ 10-4 The main purpose of this work was to understand the processes leading to the initial distribution and the subsequent growth mechanism. The relevant stages to be considered are nucleation growth by chemical reaction and flocculation. X X X X X TiCI4 mol fraction (C,) FIG.3.-Variation of mean particle diameter with initial TiCI4 concentration. NUCLEATION By the use of similar arguments to those proposed by Ulrich,' it can be shown that the critical nucleus size under the experimental conditions which apply here is less than the size of the TiOz molecule. This implies that nucleation does not present a barrier to particle formation which is largely determined by the rate of chemical reaction.Collision processes between small particles is extremely rapid and as shown by the application of simple flocculation theory,' the concentration of particles present rapidly becomes independent of the initial concentration of nuclei. Hence providing that chemical reaction to produce new particles of TiO is rapid compared with the processes of growth by release of TiO at the surface of existing particles and growth by flocculation then nucleation need not be considered further as a factor affecting the final stage of the aerosol produced. We find in accord with Ulrich that assuming instantaneous chemical reaction the particle concentration and size are affected less than 1 % by the initial nucleus size and concentration after times of the order of lod6s.We are concerned here with events occurring at residence times of greater than 50 ms. A. P. GEORGE R. D. MURLEY AND E. R. PLACE The collision rate between small particles can be drastically reduced if they acquire an electric charge. This phenomenon has been shown 2g to occur in the formation of carbon particles but at the maximum temperatures encountered here the measured charge density is much less than that necessary to influence the collision rate of small particles. No particles smaller than 20 A have been observed in any of the samples taken from the smallest residence time position (50 ms). It is concluded that chemical reaction leading to formation of new particles is complete by this stage.CHEMICAL REACTION Evidence from several experimental results suggests that chemical reaction is rapid compared with flocculation. In a one-dimensional system such as the one studied here material deposition is proportional to particle surface area giving a rate of particle growth independent of particle size. This implies an invariant size distribution about an increasing mean diameter. This behaviour is not observed in practice. As shown later the results agree with the predicted behaviour of a floc- culating system. Chemical analysis of the gases present at the highest sampling point (230ms) showed no detectable presence of TiCI4. (The limit of sensitivity of the test gives a minimum value of 97 %for the extent of TiCI4 disappearance at this point.) The disappearance of TiC14 in the early stages of reaction was followed by u.-v.spectro-scopy. The results obtained are given in fig. 4. At a spatial resolution of 2 mm in 25 0 300 350 wavelength /nm FIG. 4.-Absorption Spectra V TiCI4 in 02+NZmixture corrected to flame conditions ; TiC14 additioned flame mol fraction 1.4~ x 2-3 mm above burner face; 0 3-4 mni above burner face ; 014-15 mm above burner face. FORMATION OF TiOz AEROSOL the flame the only position at which the absorption of TiCl could be detected was at a height of 2-3 mm. Even with no allowance for the unknown increase in the absorption coefficient of TiC14 with temperature comparison with the room temper-ature unreacted-TiCl spectrum shows an average degree of reaction of about 70 % integrated over the residence time of 30+ 10 ms.The estimate is even higher than this if reasonable allowance is made for the continuous background absorption prob-ably arising from the presence of TiO particles. Although disappearance of TiC14 cannot be related directly to the formation of TiO it seems likely that this step may well be rate controlling in the reaction. (Ti-C1 bond energy 82 kcal/mol). Values of apparent growth rate at the various sampling stations are given in table 1,assuming no nucleation and complete reaction at the 230 ms sampling point. Ghoshtagore gives the following kine& expression for the growth rate of Ti02 under the conditions appropriate to the concentration conditions used here dr 1.12x lo7 (-S.96 x lo3) dt - T__ exp p(TiC1,) pni s-T The values calculated from this expression are given for comparison in table 1.The predicted values are much slower than those observed experimentally. FLOCCULATIOK The evidence so far presented suggests that neither nucleation nor growth by chemical reaction are dominant factors in determining the final particle size char-acteristics. Consideration of the flocculation process shows that this can account for the essential features of the experimental results. The flocculation process comprises two components the collision process and the behaviour of particles after collision. The first has been widely discussed in the literature e.g. Fuc~s.~ The rate of collision is largely determined by the Brownian motion of particles.Only the presence of strong radial convective flows as for chemical reaction at the surface,6 and the effect of electric charges carried by the particle are likely to cause a marked change in the collision frequency. Chemical reaction can be neglected in this system. Application of electric fields to the aerosol system provides a simple method of estimating the total rate of charge generation by measurement of the saturation c~rrent.~The results of such measurements on this system have shown that at most only half the particles acquire a charge. The presence of charge at this level has a negligible effect on the observed flocculation rates. Equally important as the rate of collisions especially when the particle character-istics are being considered are the processes occurring after collision.A " sticking factor " is commonly employed to describe the fraction of collisions which result in the formation of a floc. However the characteristics of the floc vary widely depending on whether the particles stick and retain their individual identities or at the other extreme fuse completely to form a new " single " particle of larger size as happens with droplet suspensions. To assist in the interpretations of the results use was made of a computer flocculation model which allows predictions to be made of the developing size distribution of an aerosol system starting from any specified initial size distribution. Two classes of particle collision processes can be postulated to account for the observed growth of the individual particles.The first considers collisions between the observed particles and particles too small to be resolved by electron microscopy. If conditions at the first sampling point are considered and the limit of particle size that can be observed is put even as high as lOA then the collision rate of such par- A. P. GEORGE R. D. MURLEY AND E. R. PLACE ticles would be so rapid as to give growth to the final observed size of 630 A in a time of 1 ms. No conditions can be found which would predict steady growth over the observed period of about 180 ms. The second class of collisions concerns only the particles observed on the electron micrographs. If all the particles are considered to be present in the gas phase then the computer predictions for the development of both the mean size and of the size distribution agree closely with the observed particle sizes.With a sticking coefficient of 1.0 the predicted flocculation rate is about 10 "/o too rapid as shown in table 1. The calculation assumes a high degree of fusion between impinging particles since otherwise the collision diameter would increase at a rate much faster than that of the mean mass diameter. Close examination of the electron micrographs of particle samples shows in most cases that there are a number of particles present which appear to show signs of having been formed from two individual particles which have fused together. The particles arrowed in plate 1 have this form.Extrapolation of both theoretical and experimental lo data on the rate of sinter-ing of particles suggests that this phenomenon may allow an appreciable proportion of the particles present to sinter in the time available. Evidence is also available ' showing that particles of very small diameter exhibit properties of the liquid state at temperatures many hundreds of degrees below their bulk melting point. Experi-mental confirmation of this behaviour was found for the present system. Particulate material collected on a platinum probe and then reheated in the flame gases demonstrated a tenfold increase in particle diameter. Direct observation of the fusion process utilizing a hot-stage electron microscope with a sample of particles collected directly on the grid demonstrated a sudden change in structure when the temperature reached -840°C.Plates 2(a) and (b)show the sample before and after heat treatment. Heating effects of the microscope electron beam were shown to be negligible. On the basis of these results it appears plausible that at the temperatures of 1400-1100°Cin the flame rapid fusion of particles takes place. Further confirmation of the behaviour of the aerosol as a flocculating system has been obtained using the concept of the self-preserving size distribution.12 It has been established that given sufficient time the size distribution of a flocculating system expressed in non-dimensional terms should approach an equilibrium form. The properties of the size distribution have been established by Hidy.13 Fig.5 shows the measured size distributions obtained in these experiments compared with the self-preserving distributions. The trend in development of the non-dimensional distribution is similar to that observed by Ulrich and the final form lies close to the self-preserving distribution for high values of Knudsen number the regime which applies to the present particles. Finally results obtained for the variation of particle size at constant residence time with initial reactant concentration given in fig. 3 also demonstrate the appropriate behaviour for a flocculation controlled system. Theory predicts a relationship d = kC& where n can lie between 0.33 for small particles to 0.4 for the simple Smoluchowski equation.The value of tz found experimentally over an eighty-fold range of concentra- tions varies between 0.33 and 0.38 depending on the mean size parameter used. The predicted value of the constant k using small particle theory is 0.93 compared with the experimental value of 0.43. This discrepancy has not yet been resolved. The remaining item is related to the appearance of groups of particles in the samples which were taken. These are clearly observable in certain of the electron microscope pictures and their presence was originally taken as evidence of flocculates FORMATION OF TiO AEROSOL in the gas phase. This factor proved to be the major obstacle in the interpretation of the results but there is now some circumstantial evidence to demonstrate that the groups of particles seen in the samples are an artefact of the method of collection.lo-* Id' I 10 T FIG.5.-Self-preserving size-distribution function x flame residence time 50 ms ; 0 flame residence time 110 ms ; 0flame residence time 180 ms. -theoretical distribution Knudsen number > 10 from Ulrich ; - - - theoretical distribution Knudsen number 0.0 from Hidy. The major points in favour of this argument are (i) the crystal size distribution of the material in the groups is the same within experimental accuracy as the isolated particles; (ii) the apparent degree of flocculation is highest at the earliest sampling time which is contrary to expectation ; (iii) light-scattering measurements l4 on a similar type of system show particle sizes close to that of the single crystals rather than the groups observed on the sampling grids; (iv) flocculation theory cannot explain the apparent amount of flocculation seen on the earliest sample i.e.the maximum flocculation rate is too slow to give the observed result. CONCLUSIONS In the system considered flocculation is the process which essentially determines the particle size distribution. Although the findings refer specifically to this system flocculation will always eventually determine an aerosol-particle size-distribution unless factors such as particle charging reduce the collision rate to a negligible value. However in this system the fusion of particles after collision also plays a major role in that it determines whether the flocculation process leads to groups of small particles or simply larger particles.The fusion behaviour of small particles relevant to high temperature aerosols requires further examination before further conclusions can be made. The authors thank the Directors of Tioxide International for permission to publish this paper. The assistance of Mr. M. J. Westwood with respect to the calculation of theoretical flocculation rates and to Mr. W. Brander who carried out most of the experimental work is gratefully acknowledged. G. D. Ulrich Comb. Sci. Tech. 1971 4,47. E. R. Place F. J. Weinberg 11th Symp. Int. Combustion(The Combustion Institute Pittsburgh 1967) p. 245. J. Lawton and F. J. Weinberg Electrical Aspects of Combustion (Clarendon Press Oxford 1969) p. 247 fF.PLATE 1.-Electron micrograph of sample taken at 1.5 cm above burner face at TiCI4 mol fraction 2.0 x 10-3. [Toface page 70 PLATE2.-Sample of particulate TiOL(a)as taken from the flame ; and (6)after heating to 840’C. A. P. GEORGE R. D. MURLEY AND E. R. PLACE R. N. Ghoshtagore J. Electrochem. Soc. 1970 117 529. N. A. Fuchs The Mechanics ofAerosols (Pergamon Press Oxford 1964) chap. 7 p. 338. P. A. Tesner 7th Symp. Znt. Combustion (Butterworths London 1959) p. 546. ’J. Lawton and F. J. Weinberg Electrical Aspects of Combustion (Clarendon Press Oxford 1969) chap. 5. * M. J. Westwood private communication. W. D. Kingery and M. Berg J. Appl. Phys. 1955 26 1205. N. A. Fuchs A. G. Sutugin Highly Dispersed Aerosols (Ann.Arbor London 1970) p. 85. lo H. V. Anderson J. Amer. Cer. SOC.,1967,50,235. I2 D. L. Swift S. K. Friedlander J. Colloid Sci. 1964 19 621. G. M. Hidy J. Colloid Sci. 1965 20 123. I4 A. R. Jones (Imperial College London) private communication.

ISSN:0301-5696    

DOI:10.1039/FS9730700063

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

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.

ISSN:0301-5696    

DOI:10.1039/FS9730700072

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Condensation and Evaporation of Metallic Aerosols BY E. R.BUCKLE AND K. C. POINTON Department of Metallurgy The University Sheffield S1 3JD Received 22nd January,1973 The heat-pulse cloud chamber has been used to study the condensation of metallic aerosols in the presence of purified argon. Multiplication growth and evaporation of Ca Cd Pb and Zn particles vary with the background temperature in the chamber. The volatile Cd and Zn resemble the alkali halides in that growth occurs readily in suspension when a sufficient vapour pressure is maintained and particles are formed that settle out at appreciable speeds. These particles fall from the cloud independently. With Pb the vapour pressure in the vicinity of the melting point is much lower and nucleation in the vapour at the high temperatures close to its point of generation is followed by the rapid arrest of growth and evaporation as the particles move away into the chamber.This results in the freezing- in of large numbers of minute particles and a smoke is formed in which there is little evidence of further change. When the temperature of the chamber is reduced to room temperature the particles are exceedingly fine and numerous when first condensed but the smoke thins out apparently by agglomeration. Observable motion in the smoke apart from the Brownian motion is dependent on convection in the supporting gas ; the particles move by streaming and do not fall out. The present cloud chamber is modelled on the original design of Buckle and Ubbelohde,' with certain adaptations necessary for its use with metals and for the general improvement of operation.A substantial advantage is obtained by the use of probes which obviate the need to dismantle the chamber for sampling the fall-out and renewing the metal supply. The technique is basically as before and involves the repeated production of aerosols as the temperature of the background is slowly varied. Highly supersaturated vapour is produced by passing current through a coil in a supersaturator probe so as to flash-heat the metal sample above the back- ground temperature. After formation the vapour rapidly cools to form a suspension of droplets or solid particles by condensation. The suspension is viewed telescopically under intense illumination and the behaviour of the particles observed.Other probes are used to sample the fall-out and control the motion of the aerosol. EXPERIMENTAL DESIGN OF CLOUD CHAMBER The chamber is assembled inside a horizontal tube furnace with a Pt-Rh winding. This provides a steady background temperature controllable to 1 K between 400 and 1800 K. The chamber is a muffle of refractory alumina 76 cm long and of 52 mm bore extended at one end via a water-cooled brass head by a Pyrex manipulation section (fig. la 2). The free ends of the extended muffle terminate in brass heads each of which is fitted with a window for viewing the interior of the chamber and two probe carriers. The head mounted on the alumina muffle is also water-cooled. Nine recrystallized alumina crucibles are assembled end-to-end in the muffle dividing tke chamber into a further nine sections and reducing heat loss from the interior.The middle section functions as the generating chamber and com- municates with the heads by means of two Vitreosil pipes passing through axial holes drilled in the floors of the alumina crucibles. Additional holes carry alignment rods and probes. 78 BY E. R. BUCKLE AND K. C. POINTON I' ? f Q (6) FIG. 1.-(a) longitudinal section of cloud chamber ; (6) radial section of generating chamber a supersaturator probe; 6 substrate probe; c exhaust probe; d thermocouple; e chamber window ;f water cooling ; g sample feeder ; h observation window ; i muffle containing crucibles ; j glass section ; k generating chamber ; I viewing pipe ; myprobe recess ; n alignment hole.FIG.2.-Glass manipulation section. 0,supersaturator access turret ; p substrate access turret. CONDENSATION AND EVAPORATION The central crucible is also modified by reducing the bore to match the pipe-section with alumina cement leaving grooves in which the probes are recessed. This construction avoids the formation of turbulent eddies in the aerosols. The central section is observed and illuminated through the pipes which are coated internally with carbon from a sooty flame to reduce their reflectivity. The temperature is probed in the generating section by means of a sheathed Pt/Pt-Rh thermocouple. Gas inlets controlled by needle valves are connected to the end-heads and allow oxygen- and water-free argon to be passed into the chamber from either end after the initial evacuation of air.An exhaust probe extends into the central chamber for local pumping during observations on aerosols. The design of an efficient supersaturating device has involved considerable experiment- ation. A simple design consists of a twin-bore alumina tube carrying leads of 1 mm thick Ni welded to a small heating coil of tungsten. The coil is supplied with current from a Variac. To minimize its effect on the chamber temperature the power dissipated in the coil must be sufficiently low in comparison with the average power input to the furnace windings. At the same time to avoid the shorting of the coil and its subsequent failure it is necessary to protect it from the test metal which otherwise spreads along the coil when molten.A satisfactory design is shown in fig. 3a. The coil is of Mo tightly wound and closely spaced and supported on a former of alumina. It fits into the lower bore of a piece of twin-bore alumina tubing and the upper bore is exposed over the middle 1 cm of its length by grinding to form a slot. The ends of this bore are sealed with alumina cement. The metal sample is held in the slot and the whole assembly attached to the probe after welding the coil to the leads by a tightly fitting sleeve of Pt-Rh. (b) FIG.3.-(a) supersaturator probe; (b) substrate probe (exploded view). q Mo coil; Y Pt-Rh sleeve; s Nitrile rubber gasket ; t insulating compression disc ; u Ni lead ; u thermocouple ; w,coolant gas circuit ; x Pt-Rh connecting sleeve not shown.The substrate probe (fig. 3b) consists of ashort piece of alumina thermocouple sheathing on which a flat surface has been cut. This is connected to a 4-bore capillary probe again with a Pt-Rh sleeve to provide rigid support at high temperatures. A thermocouple in contact with the under surface of the flat gives the temperature of the upper surface with reasonable accuracy. The substrate can be cooled below the chamber temperature by a gas stream conducted via the other two bores of the probe. OPTICAL TECHNIQUE The viewing technique is the same as before.' A large converging lens is used to collect as much light as possible from the diffuse source of a 250-W Hg arc-lamp and to focus it to BY E.B. BUCKLE AND K. C. POINTON form a secondary light source of about 2 ,nun diam on an iris diaphrap. The illuminated aperture is focussed with a converging doublet of short focal length on to ;t second diaphragm consisting of two blades with V-notches enabling the aperture to be narrowed down to give an extremely small tertiary point-source. A final doublet of weak convergence collects the light from this source into a very narrow beam which enters the cloud chamber after passing through a filter to select the 5461 A mercury line. The use of silica windows to isolate the central section was abandoned because of the obscuring effect of metallic condensate strongly illuminated by the incoming light beam. Confinement of clouds to the generating aection was achieved by a new technique of gas flow described below.The advantage to visibility was substantial because the Airy patterns of the cloud particles could be viewed with the telescope directed at a lower angle to the light beam. PROCEDURE To prepare for a condensation run the furnace is set to heat the chamber to a steady temperature about 300 K below the melting point of the metal (table 1). The chamber is evacuated to a pressure between 1 and 10 N m-2 and filled with purified argon to atmospheric pressure. The argon stream is continued during the loading of the supersaturator probe. The slot of the supersaturator is positioned in the manipulation section directly below the vertical turret. Test metal in the form of wire is then fed through the seal in the turret to the heated probe until the slot is full of molten metal.The probe is then pushed into thegener-ating chamber and the gas flow discontinued leaving the whole cloud chamber under a slightly positive pressure. TABLE 1 .-VAPOUR PRESSURES OF THE METALS 4 AT SIGNLFICANTTEMPERATURES (Tf = m.p. Tb = b.p.) metal 0.8 Tt/K TdK ~'(0.8T;)/Nm-2 t Ca 893 1756 7 Zn 554 1180 8x Cd 475 1038 6x Pb 480 2020 3 x lo-' Al 746 2740 3 x lo-" t value for liquid extrapolated from Tf Using the Variac the metal is flash-heated to several 100 K above the background temp- erature until a suspension of condensed particles appears. The particles show a tendency fo move out of the central chamber into the viewing pipes where the temperature is unknown.This is prevented by a slow flow of argon along the pipes. The gas enters at the inlets at each end and is drawn into the central section by the exhaust probe. By careful setting of the needle valves the gas flow may be tuned and the metallic vapour and suspended particles caused to circulate slowly in the central section. Particles can be held almost stationary for periods of up to 30 s depending on the volatility if they occupy positions toward the centre of the rotating cloud. A temperature scanning procedure ' is used to establish the properties of the metallic aerosol that depend on the growth evaporation and physical state of the particles in them. RESULTS Before commencing work on the metals the performance of the apparatus and in particular the new design of supersaturator was tested on gne of the salts studied by Buckle and Ubbelohde.' KI was chosen as a representative salt with a suitable vapour pressure curve and clear-cut cloud phenomena.The critical solidification temperature Tswas reported as 799 K. As the temperature of the cloud chamber was raised from 770 to 800 K marked changes in the behaviour of the KI clouds were seen. Dense clouds of tiny particles CONDENSATION AND EVAPORATION which responded slowly to changes in the supersaturator current gave way at higher temperatures to clouds in which the particles evaporated or grew rapidly as the supply of vapour was varied. The particles in clouds showed twinkling when the background was at 795 K but the effect had vanished when the temperature reached 797 K.T therefore lies between these values as judged from the readings on a thermocouple recessed in the wall of the open-ended generating chamber. The small discrepancy with the value previously reported was not considered to be serious enough to warrant further refinements to the method at this stage and work on the metals was begun after expelling the residual salt under vacuum at high temperature. The correlation T,-0.8 Tf was used as a guide in the search for critical effects in metallic clouds.2* GENERAL OBSERVATIONS ON METALLIC AEROSOLS The work so far has been restricted to telescopic observations. The Airy patterns formed by the particles are similar to those seen with salt aerosols the brightness of the central disc and the number of concentric haloes indicating the relative size.Depending on conditions particles appear thinly in small numbers when the size is large and densely in large numbers when the size is small. Large particles that grow quickly are lost by sedimentation. Such particles may be seen to move independently. When small particles occur in more or less per- sistent streams or " curtains "? and show the eclipsing effect ' as well as Brownian motion within the curtain. The curtains move by streaming in various ways depend- ing on the pattern of convection in the chamber. When the gas flow is suitably tuned the appearance of the curtain in motion is suggestive of the rotation of a stellar nebula. Such conditions of motion are optimum for the observation of single particles in a cloud which is not too dense.The effect known as " twinkling " has not been observed to be a general property of metallic aerosols formed by condensation. With Zn and also with Cd the vast numbers of particles that are formed at temperatures below 0.8 Tf and which may be attributed with confidence to condensation show an indistinct flicker but it has not been possible to detect a sudden onset of this effect. Large twinkling particles are sometimes seen in small numbers during the early stages of formation of a cloud. It is believed that these are ejected along with the vapour as the sample on the super- saturator becomes finally molten. The ejection is not visible with the present design the probe being recessed in the roof but it was clearly observed in the work on salts.Such particles drop out very quickly and may be distinguished from the condensate if turbulence is avoided. A shower of particles has also been observed after tapping the pro be. ZINC At temperatures in the vicinity of 0.8 Tf (table l) large particles are easily grown in large numbers. The aerosol motion is controllable by gas-flow tuning and the lifetimes are substantial (at least 60 s). These particles flicker when seen in isolation. At 500 K the numbers are greater and at 475 K there are small as well as large particles present. The proportion of small particles increases on further cooling and at 390 K stable dense suspensions of minute particles are formed. CADMIUM From 0.8 Tf down to 430 K the aerosols are densely populated with particles that fall out rapidly (in a few seconds).Growth is difficult to induce and the continued BY E. R. BUCKLE AND K. C. POINTON operation of the supersaturator merely produces more particles. At the same time the particles appear to diminish in size by evaporation. Flickering is also observed with this metal. There is no change down to 400 K beyond an increase in number density and a decrease in the size of the particles. With the chamber at room temperature the particles formed by condensation are exceedingly faint but stable. Quantities of larger particles are also formed that possibly originate from unmelted Cd expelled from the probe. These show unusual behaviour in apparently shrinking in size as they fall directly and rapidly towards the floor of the chamber.Similar properties are shown by the particles which fall when the probe is tapped and as the size diminishes so does the speed of descent. There is apparently a connexion between these effects and the presence of residual metallic vapour. If the chamber is flushed with argon and probe particles again dislodged without passing current the effects are not observed. LEAD Aerosols of Pb behave differently from those of Zn and Cd. At 0.8 T' ejected particles appear first then curtains of minute particles formed by condensation. The fine particles are very persistent but do not grow in the vapour. Even above the melting point (601 K) growth is too slow to relieve the supersaturation when the probe is kept hot.Instead the number of particles increases. As the temperature is lowered from 0.8 Tfthe concentration of particles formed in a cloud is increased and the particle size is decreased. The clouds are also less persistent. At room temperature a smoke is formed in which the Airy discs are initially barely visible. The smoke slowly thins out and the particles that remain become brighter indicating growth. Brownian motion continues and there is no loss by sedimentation. The impression is that the process of enlargement is visible at room temperature because of the high density of the initial smoke whereas at higher temperatures the process is still operative but the brightening of the Airy disc cannot be discerned. It is difficult to compare by eye the brightness of the discs when the particles are thinly dispersed.CALCIUM The behaviour of Ca in the chamber also has unique features. A complication is the low vapour density. This leads to the stratification of the particles and inhibits circulation. The same tendency possibly accounts for their persistence at high temperatures when they might be expected to evaporate more readily. The data of table 1 suggest that Ca should behave as a volatile metal like Zn and Cd but sub-stantial growth of the particles could not be induced even at 0.8 Tf. Another problem was reaction of Ca with the alumina of the probe. This inter- fered as the chamber temperature approached T, and when the melting point of Ca was reached (1 116 K) the reaction became self-sustaining and generated curtains of condensate even when the current was off.It is possible that at these high temper- atures A1 is vaporized and condenses along with the Ca. It would be expected (table 1) that pure A1 vapour would condense only to minute particles. DISCUSSION In the work on salts 6* it was established that the cloud lifetimes always tended to decrease as the background temperature was increased. The rise of the temperature through the twinkling threshold T could in many cases be correlated CONDENSATION AND EVAPORATION with a sharp fall in the lifetime. The effect was attributed to the increased evapora- tion of particles which remain liquid throughout the period of observation. It was also observed with salts that when the chamber temperature was much lower than T the clouds formed were persistent and composed of multitudes of minute particles.This may be explained as follows. Assuming that the test material is always heated to the boiling point by the supersaturator the saturation ratio p/p" where po is the vapour pressure at the chamber temperature T can approach very high values whan Tis low (see e.g, table 1). The result is a high concentration of nuclei which have little prospect of growth. From the few results we have obtained so far it would appear that there is an essential difference between the properties of aerosols of metals and salts. If the metal is involatile at the melting point (Pb; table 1) the growth-rate of particles even when liquid is so slow that at high temperatures one merely generates increasing numbers of them without effecting much enlargement.At low temperatures (Pb at room temperature) the number density of particles is much greater so great in fact that even in the first faint smoke agglomeration takes place. It is tentatively pro- posed that it is this that leads to the brightening of the images observed through the telescope. This interpretation will be tested by examination of fall-out. It would be in keeping with microscopical observations on metallic condensate sampled from various other sources such as exploding wires.' Particle aggregation in the fall-out from fine smokes has not been observed with the halides of the metals,'* 6* but it has with oxides,8 which again are often relatively involatile compounds.On theoretical ground^,^ coltision leading to fusion between particles in a volatile aerosol is a rare event in comparison with growth. As defined in this way therefore coagulation should not contribute to the relief of supersaturation by providing a short cut to the aggregation of molecules. It was also argued that under uniform conditions of supersaturation growth should be severely limited. If this conclusion is valid the observed formation of micron-size particles in metallic aerosols is to be attributed to their nucleation and growth under conditions of steep temperature and concentration gradients near the supersaturator. The possibility that they are heterogeneously nucleated on foreign particles already of appreciable size is unlikely if these do not also originate at the supersaturator.We are grateful to the Science Research Council for support including a mainten-ance award to K. C. P. E. R. Buckle and A. R. Ubbelohde Proc. Roy. Suc. A 1960,259 325. 'D. Turnbull and R. E. C& J. Appl. Phys. 1950 21,804. E. R. Buckle Nature 1960 186 875. 0. Kubaschewski E. L1. Evans and C. B. Alcock Metalhrgicaf Thermochemistry (Pergamon Oxford 4th ed. 1967). J. F. Elliott and M. Gleiser Thermochemistry fur Sfeelmaking (Addison-Wesley Reading Mass. 1960) vol. 1. E. R. Buckle and C. N. Hooker Trans.CFaraday Suc. 1962,58 1939. 'E. R. Buckle Condensation and Euworotion ofSofids,ed. E. Rutner et af. (Gordon and Breach New York 1964) p. 537. J. Harvey H. 1. Matthews and H. Wilman Discuss. Faraday SOC.,1960 30 113. E. R. Buckle this Discussion.

ISSN:0301-5696    

DOI:10.1039/FS9730700078

出版商:RSC    

年代:1973

数据来源: RSC