DISPERSED CARBQN FBRNTATION IN ACETYLENE SELF-CQI%IBUSTION BY P. A. TESNER All-Union Institute of Natural Gas (Vniigaz), Moscow Received 29th July, 1960 Acetylene self-combustion results in the formation of hydrogen and dispersed carbon or carbon black. This process has been investigated by many authors;X-12 however, the mechanism of dispersed carbon formation is not understood well enough. The present paper is an attempt to perform a theoretical calculation of the process of dispersed carbon formation in self-combustion of acetylene, i.e. when flame propagates in acetylene contain- ing no oxygen. The calculation is based on representations developed by the author 1 3 ~ 1 4 involving two-stage formation of dispersed carbon (nucleation and particle growth). A comparison of the calculated results with the experimental data shows good agreement.GENERAL Flame propagation in acetylene differs from similar processes in other gaseous substances or their mixtures in that the process yields not only a gas, but also dis- persed solid carbon. The basic idea of the method applied by us for process analysis consists in the fact that the structure and size distribution of particles of dispersed carbon formed in acetylene self-combustion characterize the totality of the processes which took place in the explosion. Therefore, a study of distribution curves for the dispersed carbon formed enables one to obtain data on the mechanism of the processes taking place at the combustion front. This is feasible because the structure of the dispersed product formed remains unchanged after the termination of the process, due to the high thermal stability of carbon.Acetylene self-combustion is characterized either by explosion or by combustion features, depending on the conditions attending this process. The self-combustion of acetylene contained in a closed volume under a pressure of over 2 atm is followed by an explosion which rapidly develops into a detonation. The heating of acetylene to a temperature 8 of above 500°C causes a spontaneous thermal decomposition of acetylene at atmospheric pressure as well. Thereafter under certain conditions there exists a possibility of the continuous thermal decomposition of acetylene similar to the stationary combustion of a pre-mixed gas mixture. However, the process should progress on essentially identical lines in each ele- mentary volume of acetylene both in the case of explosion and of continuous steady-state decomposition.Our conception of this process is as follows. The initial act of acetylene decomposition accompanied by the formation of hydrogen and carbon black consists in the nucleation of carbon particles. The nucleation, the mechanism of which we do not consider here, starts after some critical temperature is attained. As soon as the first nuclei are formed they grow rapidly by direct decomposition of the acetylene molecules on their surface. Along with this process and with a further rise in temperature, new nuclei are formed and grow, and so on. We find it plausible to assume that in any elementary volume where the tem- perature and composition of the gaseous phase at any point are identical, all particles grow at the same linear rate.In other words, given the same temperature and composition of the gaseous phase, the linear rate of particle growth is inde- 170I?. A. TESNER 171 pendent of the particle diameter. Hence, as decomposition proceeds, the differ- ence between the diameters of two growing particles remains constant at all times, and the relative sizes of the particles can serve to determine the time of their formation. It is obvious that the largest particles were the first to form in a given elementary volume, and vice-versa, the smallest were the last. This representation of the process permits easy determination of the number of particles and the construction of particle-size distribution curves for any degree of decomposition of the acetylene.Thus, such calculation may be helpful in con- structing curves expressing the dependence of the number of particles €Formed and the thickness of the carbon layer produced on the degree of acetylene decomposition. Let the particle size distribution be as follows : diameter number of particles dl n1 d2 n2 rii ni dm nm where di > di-1. Then, at the moment when dn-sized particles were formed, particles having diameters equal to dn or less were non-existent, while all the other particles had a diameter which was smaller by d, than the ultimate one. Consequently, the distribution of all the particles existing at that moment (hereafter it will be referred to as the " n-distribution ") should be : diameter number of particles The total volume of all the carbon particles resulting from a complete acetylene decomposition is i=m Vm = in: d?ni.i = 1 The total volume of all the particles of the n-distribution corresponding to a certain intermediate stage of acetylene decomposition will be i=m Vn = (di-dJ3ni. i = n + 1 Thus, the percentage degree of acetylene decomposition corresponding to this particle size distribution will be VJ VJOS. (3) The total surface area can be found for each distribution similarly to the total volume. The total particle surface area for the n-distribution (S,) is expressed by the following equation : CALCULATIONS The calculation has been performed for Schawinigen acetylene carbon black which is obtained as a result of continuous thermal acetylene decomposition at172 DISPERSED CARBON FORMATION atmospheric pressure.Watson 15 carried out thorough electron-microscopic measurements of particle sizes of this carbon black. Table 1 gives the results of these measurements covering 1 1,576 particles. TABLE 1 .-SIZE DISTRIBUTION OF PARTICLES OF ACETYLENE CARBON BLACK ACCORDING TO WATSON lS interval diameter number of particles in the interval (nj) index, di i A' units % 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 50 108 200 300 400 500 600 700 800 900 1000 1250 1500 1750 2008 7 62 3 69 1088 1968 2255 1956 1548 954 593 336 303 101 27 9 0060 0.535 3.187 9407 17.007 19.478 16.888 13.472 8.242 5-122 2.902 2.617 0.873 0.23 3 0.077 Table 2 shows the results of calculating the total volume and the total surface area of the particles, the total number of particles and the degree of acetylene decomposition for distributions from 1 to rn.The calculation made use of eqn. TABLE 2.-cALCULATEON OF THE DEGREE OF DECOMPOSITION, SURFACE AREA AND NUMBER OF PARTICLES FOR DIFFERENT DISTRIBUTIONS thickness no. of dis- of the tribution. formed n 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 carbon layer, A 125 250 375 500 550 600 650 700 750 300 850 900 950 975 100 total volume of particles eqn . (21, A3 8.10 X 108 1.97 X 1010 3-33 x 1010 5.45 x 1010 8.79 X 1010 1-41 X 1011 2.26 X 1011 3.60 X 1011 5.73 x 1011 8-92 X 1011 1.35 X 1012 1.64 X 1012 1.99 x 1012 7-38 x 107 4-58 x 109 degree of decompo- sition eqn. (3), % 0.00371 0.04070 0.2301 0.9934 1.676 2.743 4.419 7.087 11-369 18.133 28.826 44.834 67.955 82.748 1000 total particle surface area eqn.(41, cm2 ml-1 0052 0.364 1.67 6.33 9.9 15.5 24.5 39.2 627 99.3 152.0 224.0 3340 373.0 435.0 total number of par- ticles, m1-1 2.64 X 109 1.06 x 1010 4.03 x 3010 1-29 X 1011 2.28 x 1011 4.03 x 1011 6.85 x 1011 1.13 x 1012 1 . 7 2 ~ 1012 2.96 x 1012 3.28 x 1012 3.39 x 1012 3.40 X 1012 3-42 x 1012 238 x 1012 (1)-(4). The total surface and the total number of particles are not absolute values referring to the totality of particles measured in the electron-microscopic investigation, but values related to 1 ml of the initial acetylene. These values were obtained by multiplying the values given by eqn. (2), (4) times the ratio (K = 2 . 9 4 ~ 108) of the weight of carbon in 1 ml acetylene to the total weight of the carbon particles measured by means of an electron microscope, i.e.to the weight of carbon contained in the carbon particles corresponding to the 0-distribution. Fig. 1 is a graphical representation of the results and suggests a few interesting conclusions. The curves of the total nvmlxr of particles show that the formationI?. A . TESNER 173 of new particles takes place only at the beginning of the decomposition. Thus, 10 % decomposition results in the formation of 1 . 6 ~ 1012 particles which is about 50 % of all the particles formed. Of a similar shape is the curve for the thickness of the carbon layer formed, indicating that the initial stages of decomposition are attended by a more intensive growth of the carbon layer than in the subsequent stages.Conversely, the curves for the total particle surface area show a prac- tically linear dependence of the surface area on the degree of decomposition. Thus, the curves obtained provide an idea of the process of dispersed carbon formation and therefore is of interest. These curves, however, are not kinetic curves, since they represent the dependence of the process parameters, not on time, 0 25 5 0 75 I 0 0 decomposition of acetylene, % FIG. 1 .-Development of formation of dispersed carbon by self-combustion of acetylene. Curves 1, total number of particles ; 2, total surface area of particles ; 3, thickness of the carbon layer. but on the degree of decomposition. To obtain kinetic regularities from these curves, the time element should be added to them in some way or another.To achieve this, the following attempt was made initially. In order to cal- culate the early stage of the process we used the direct measurement data on the rate of growth of the carbon surface area in thermal decomposition of acetylene and assumed the activation energy of this process at low temperatures (50I)-60O9C).16 It was also assumed that, because of the adiabatic nature of the process, the system temperature is determined by the amount of heat released in the reaction, which is proportional to the degree of decomposition. However, this calculation showed that the rate of surface area growth at a temperature corresponding to the bzginning of the explosive decomposition of acetylene was so low that the formation of the first particles would require a few hours, and not fractions of a second as is actually the case.This unexpected result has led us to the conclusion that the actual process of the growth of the particles which were the first to form in the explosion is 6 to 7 orders faster than that process at a temperature of 500-700" which corresponds174 D IS 1’ ER SED C A R B 0 N F 0 R MAT 10 N to the low initial degree of acetylene decomposition. There can be only one explanation of such a discrepancy. At the moment of nuclei formation a growing carbon particle has a considerably higher temperature than would correspond to the degree of acetylene decomposition attained at that moment. Inasmuch as the interaction between the acetylene molecules and the nuclei, and their decom- position on the surface of the growing particle, result in the release of a large amount of heat which has no time to be transferred to the gas owing to the high rate of the process, such a supposition seems reasonable.Therefore, it was assumed as a first approximation that the particle temperature, starting from the moment of nucleation, is equal to the maximum temperature of the process (about 3000°K) developing when the decomposition of acetylene is complete. In addition, it was assumed that the gas layer which is the closest to the surface has a temperature equal to the surface temperature and that each collision of a hydrocarbon molecule with the surface leads to an elementary act of decomposition. In other words, it was assumed that the process under con- sideration has an activation energy E = 0 and that the reaction rate depends only on the number of collisions of acetylene molecules with the surface.Naturally, a calculation based on such assumptions yields a maximum possible decomposi- tion rate and a minimum reaction time. The number of collisions of acetylene molecules with the surface was determined from the equations of the kinetic theory. d I 2 3 4 5 6 time, microseconds FIG. 2.-Kinetic curves of the process of formation of dispersed carbon by self-combustion of acetylene. Curves 1, rate of particles formation ; 2, total surface area of the particles ; 3, degree of acetylene decomposition. Such a calculation produces a correct result for the number of collisions of the molecules with the surface only at the first moment of nucleation. Subsequently, the number of collisions decreases, because the concentration of acetylene falls off and the concentration of hydrogen grows in the surface layer as a result of the reaction.In a steady-state process the growth rate would be determined by the diffusion of acetylene molecules towards the surface. However, we are dealing with an essentially non-steady-state process, and it is very difficult to estim- ate the role of diffusion in slowing-down the process. Therefore, as a first ap- proximation, we also ignored diffusion and assumed that the concentration of acetylene near the surface of the particle and throughout the volume was the same during the whole period of particle growth. This assumption, as well as theP. A .TESNER 175 previous ones, should lead to an over-estimation of the growth rate. The maximum rate of particle growth obtained in this manner proved to be w = 2.09 x lO-'C cm/sec, (5) where C is the acetylene concentration in vol. %. formation will be If the thickness of the carbon layer formed is 6 (A), the time necessary for its t = S/249C x 106 sec. (6) Using this equation the curves of fig, 1 were converted to the kinetic curves given in fig. 2. To do this, we determined the growth rate from eqn. (3, then obtained graphically the thickness of the formed carbon layer, 6, and finally calculated the reaction time from eqn. (6) for a certain range of variation in the degree of decom- position. Then we found graphically the number of newly-formed carbon particles, An, and determined the absolute rate of formation of new particles or the rate of nucleation (in units of cm-3 sec-1) using the known reaction time.DISCUSSION The graph of fig, 2 represents kinetic curves of the process of dispersed carbon formation. Of special interest is that the particle formation curve shows a con- siderable induction period and a sharp peak in the particle formation rate. Of the total duration of the process (about 7 psec), the time from the moment of formation of the first particles to the beginning of the rapid growth of the formation rate is about 2psec. The sharp peak on the curve of the formation of carbon particle nuclei is due to the rapid rise in the rate oi nucleation at the beginning of the process and the similar rapid fall-off in this rate which is observed when the acetylene concentration is still high.The cause of the rapid rise in the nucleation rate is not entirely clear. Tbis rise can hardly be explained by the rapid rise in temperature because the maximum gradient of the growth rate corresponds to the initial degrees of decomposition. The maximum rate of particle formation corresponds to about 10 % of the degree of acetylene decomposition. This leads to the conclusion that nucleation takes place essentially in the temperature range from 500 to SOOOC, As far as the drop in the nucleation rate is concerned, it is attributed to the competing reaction of particle growth, whose activation energy is close to zero, whereas the activation energy of the nucleation process is 60 to 70 kcal/mole.As was indicated above, the calculation was based on assumptions that led to the maximum possible rate of the process and hence the minimum possible duration of the reaction. The kinetic curves of fig. 2 permit an &timation of the total duration of the explosion of 7pec. It would be of interest to compare this value with direct experimental results. For this purpose we used the measure- ments of the rate of acetylene detonation based on the data of Bonn and Framr.17 These measurements were carried out at atmospheric pressure. The detonation was produced by means of a detonator placed in acetylene. The initial flame velocity over a length of 0.5 m was 2135 m/sec, the length of the incandescent head of the detonation front being about 10 cm. Based on these results, the dura- tion of the chemical reaction in detonation may be estimated as 0.1/2135~47 x sec.This value is only about 7 times the one found by calculation. Since the length of the region of incandescent carbon particles should exceed that of the chemical front of the reaction, because some time is needed for the cooling of the particles, the actual divergence between these values is still smaller. This suggests the unexpected conclusion that the extreme assumptions used in the calculation176 DISPERSED CARBON FORMATION have not led to a considerable overstatement of the reaction rate and, consequently, are close to the actual values. Indeed, if one assumes that the divergence is due only to slowing-down by diffusion, then, considering the tremendous absolute reaction rate, this slowing- down should be regarded as insignificant.Conversely, if slowing-down by diffusion is assumed to be zero, it should be concluded that the reaction does not involve each of the acetylene molecules hitting the surface, but only one of every four or five molecules. In other words, the activation energy of the growth process is not zero, but 6000 to 8000 cal/mole. If we assume, however, that the actual process involves slowing-down both by diffusion and kinetic processes (which is more realistic), the conclusion must be drawn that the activation energy of the process does not exceed a few thousand calories per mole, and slowing-down by diffusion is quite insignificant. Conse- quently, in acetylene explosion, the growth of carbon particles is, indeed, due to the direct destruction of acetylene molecules hitting the carbon surface, and the reaction involves practically each of the colliding molecules.In this case the heat released in the exothermic decomposition reaction has 110 time to dissipate, and the growing particle has a considerably higher temperature than the ambient gas during the major part of the reaction. Owing to the aval- anche-like and highly unstable nature of the process, in spite of its tremendous rate, the slowing-down by diffusion decreases its rate but only slightly (less than by one order of magnitude). As regards the mechanism of nucleation in the process considered, the following may be stated. Because of the short reaction time, nuclei cannot result from polymerization reactions, as was shown convincingly by Porter.4 Hence, nuclei are simply carbon particles-radicals formed from active acetylene molecules.The computed absolute rates of carbon particle formation allow an estimation to be made of the activation energy of the nucleation process. The curve of fig. 2 shows that the maximum rate of nucleation is 2.3 x 1012 ml-1 sec-1. This value makes it possible to estimate the activation energy of the nucleation process as about 60 kcal/mole for a birnolecular process and 70 kcal/mole for a monomolecular process. The high values of the activation energy of nucleation in molecular reactions suggest that the chain mechanism of nucleation is more probable. The problem of the possible chain mechanism is treated in ref. (8) and (9). It should be emphasized that the formation of carbon radicals is needed only to obtain nuclei of carbon particles, regardless of the mechanism of this formation. The further growth of these nuclei proceeds as a purely molecular process. It should also be noted that the considerable excess of the temperature of the growing carbon particle over the temperature of the ambient gas is characteristic only of the explosion decomposition of acetylene.Of course, no such effect exists in the formation of carbon black from other hydrocarbons and from dilute mixtures of acetylene, where the temperatures of the growing carbon particle and the gas should be identical. CONCLUSIONS (1) The growth of carbon particles in acetylene explosion results from the direct decomposition of acetylene molecules on the surface of the growing particle.The activation energy of the process is close to zero ; thus practically each collision of an acetylene molecule with the surface leads to reaction. (2) The total rate of the chemical reaction at the front of the acetylene ex- plosion is determined by the rate of the reaction of acetylene molecule decomposition on the surface of the carbon particles which, in turn, depends on the rate of nucleation. (3) The temperature of the growing carbon particle from the moment of nucle- ation and during the major part of the reaction considerably exceeds the equilibriumP. A . TESNER 177 adiabatic temperature of the gas corresponding to the degree of decomposition achieved. (4) Because of the avalanche-like nature of the process the rate of particle growth is determined by the rate of the chemical decomposition reaction and is only slightly inhibited by the rate of hydrocarbon diffusion. (5) The nuclei of carbon particles in acetylene explosion represent the simplest carbon particles-radicals formed by a molecular and/or a chain process from the molecules of acetylene. 1 Alekseev, Proc. Shelaputia Inst., Moscow, 1915, 4, 167. 2 Rimarski and Konschak, Autogene Metallbearbeitung, 1931,24, 51. 3 Frank-Kamenetzky, Acta physicochim., 1943,18, 148. 4 Porter, Combustioi~ Research and Reviews (Butterworths Sci. Publ., London, 19551, 5 Jones, Kennedy, Spolan and Scott, Bur. Mines. Report, no. 4695, 1950. 6Gaydon and Fairbairn, 5th Symp. Combustion (Reinh. Publ. Corp., N.Y., 19551, 7 Robertson, Magee, Fain and Matsen, 5th Symp. Combustion (Reinh. Publ. Corp., 8 Westbrook, Hellwig and Anderson, 5th Symp. Combustion (Reinh. Publ. Corp., 9 Stehling, Frazee and Anderson, Gth Symp. Combustion (Reinh. Publ. Corp., N.Y., p. 108. p. 324. N.Y., 1955), p. 628. N.Y., 1955), p. 631. 1957), p. 247. 10 Green, Taylor and Patterson, J. Physic. Chem., 1958, 62, 238. 11 Aten and Green, Faraday Soc. Discussions, 1956,22, 162. 12 Hooker, 7th Symp. Combustion (Buttenvorths Sci. Publ., London, 1958). 13 Tesner, Viziigaz Proc. Gostoptehisdat., Moscow, 1958, N3 (1 1), p. 34. 14 Tesner, 7th Symp. Combustion (Butterworths Sci. Publ., London, 1958), p. 576. 15 Watson, Anal. Chem., 1948, 20, 567. 16 Tesner, 8th Symp. Combustion, (1960). 17 Bone and Frazer, Proc. Roy. Soc. A , 1932,23Q, 363.