Dispersed carbon formation in acetylene self-combustion

627

ACETYLENE SELF-COMBUSTION

Work on ethyl nitrate explosions (Fig. 4, B) is still in progress. The activation energy, E, obtained from the explosion limit at 250 and 268°C is much lower than thermal theory demands. Again there is too much decomposition during the induction period. The decomposition of ethyl nitrite is not sufficiently exothermic to become explosive. Figure 4, H shows the first-order decomposition of 0.50 mm Hg of C2H~ONO at 336°C. The rate constants obtained from experiments at low initial pressure at 280, 336 and 360°C are in very good agreement with the rate expressions of Levy 7 and Steacie and Shaw. s Kinetic runs with half-lives of a few seconds are reproducible and accurate. The observed decrease of k with decreasing pressure (k = 0.25 sec-1 at 10 mm Hg, 0.10 sec-1 at 1 mm Hg) is due to the unimolecular aspect of this decomposition. At much higher pressures the decomposition becomes autocatalytic (Fig. 4, G), probably because of the catalytic effect of the reaction product, acetaldehyde/

Summary A versatile apparatus for the study of gas explosions or fast reactions has been described which consists essentially of fast, sensitive transducers, some circuitry, an oscilloscope and a Land camera. The circuitry permits us to make any ~oy of the transducer pressure range full-scale on the scope. This apparatus was used

to study the rate of admission and of temperature equilibration of various inert gases to a heated vessel. The usefulness of the apparatus in nonexplosive reactions whose half-lives m a y be as short as a few tenths of a second has also been shown. Several explosive reactions were examined, the decomposition of N~H4 and of EtON02 and the NO2-H~ reaction. The detailed course of these explosions differs in m a n y ways from t h a t predicted by the thermal theory. REFERENCES 1. FRANK-KAMENETSKII, D. A.: Diffnsion and Heat Exchange in Chemical Kinetics. Translated from the Russian Edition by N. THON. Princeton University Press, 1955. 2. SEMENOV, N. N.: Some Problems in Chemical Kinetics and Reactivity, Vol. 2. Translated by M. BOUDART. Princeton University Press, 1959. 3. GRAY, P., LEE, J. C., LEACH, H. A., A N D TAYLOR, D. C.: Sixth Symposium (International) on Combustion, Reinhold Publishing Corporation, New York, 1957, p. 255. 4. GILBERT, M.: Combustion and Flame, 2, 137, 149 (1958). 5. ASHMORE, P. G., AND LEVITT, B. P.: Trans. Faraday Soc., 54, 390 (1958). 6. GRAY, P., AND HARPER, M. J. : Trans. Faraday Soc., 55, 581 (1959). 7. LEVY, J. B. : J. Am. Chem. Soc., 78, 1780 (1956). 8. STEACIE, E. W. R., AND SHAW, G. T.: Proc. Roy. Soc. (London), A146, 388 (1934).

65 DISPERSED CARBON FORMATION IN ACETYLENE SELF-COMBUSTION By P. A. T E S N E R

Introduction Acetylene self-combustion results in the formation of hydrogen and dispersed carbon or carbon black. This process has been investigated by many authors, 1-~ but the mechanism of dispersed carbon formation is still not well understood. The present paper is an a t t e m p t to perform a theoretical calculation of the process of dispersed carbon formation in the self-combustion of acetylene, i.e., when flame propagates in acetylene containing no oxygen.

The calculation is based on a model developed by the author TM14 involving two-stage formation of dispersed carbon (nucleation and particle growth). A comparison of the calculated results with the experimental d a t a shows good agreement.

Experimental Procedure Flame propagation in acetylene differs from similar processes in other gaseous substances or their mixtures in that the process yields

628

DETONATIONS AND EXPLOSIONS

not only a gas, but also dispersed solid carbon. decomposition proceeds, the difference between The basic idea of the method applied b y us the diameters of two growing particles remains in the analysis process consists in the fact t h a t constant at all times, and the relative sizes of the structure and size distribution of particles the particles can serve to determine the time of of dispersed carbon formed by acetylene self- their formation. I t is obvious t h a t the largest combustion characterize the totality of the particles were the first to form in a given eleprocesses which occur during the explosion. mentary volume, and conversely, the smallest Therefore, a study of the distribution curves were the last. for the dispersed carbon formed yields data on This representation of the process makes it the mechanism of the processes occurring at easy to determine the number of particles and the combustion front. This is feasible because to construct particle-size distribution curves for the structure of the dispersed products remains any degree of decomposition of the initial unchanged after the termination of the process, acety]ene. Thus, such calculations m a y be due to the high thermal stability of carbon. helpful in constructing curves expressing the Acetylene self-combustion is characterized dependence of the number of particles formed either b y an explosion or b y a combustion, and the thickness of the carbon layer produced depending upon the conditions attending the on the degree of acetylene decomposition. process. The self-combustion of acetylene conLet the particle-size distribution be as tained in a closed volume at pressures above follows: 2 atmos abs is followed b y an explosion which diameter number of particles rapidly develops into a detonation. Heating of dl nl acetylene to a temperature of above 500°C s d2 n2 causes a spontaneous thermal decomposition : of acetylene at even atmospheric pressure. di ni Under certain conditions, therefore, there exists : a possibility of continuous thermal decomposidm n.~ tion of acetylene similar to the stationary combustion of a premixed gas mixture. where di ~ di-1. Then, at the moment when However, the process should follow on essend~-size particles were formed, particles with ditially identical lines in each elementary volume ameters equal to d~ or less were nonexistent, of acetylene both in the case of an explosion while all the other particles had a diameter whicla and in that of continuous steady-state decomwas smaller by dn than the final one. Conseposition. Our conception of this process is as quently, neglecting the size of the nuclei, the follows. distribution of all the particles existing at that The initial act of acetylene decomposition moment (which we call "n-distribution") should accompanied by the formation of hydrogen be: and carbon black consists in the nucleation of diameter number of particles carbon particles. This nucleation, whose mechd n + l d,~ nn+l anism we will not consider here, sets in at some : critical temperature. As soon as the first nuclei are formed they grow rapidly by direct decomdl -- d. ni : position of the acetylene molecules at their surface. With this process and with a further din--d, n,~. rise in temperature new nuclei are formed and The total volume of all of the carbon particles grow. resulting from a complete acetylene decomWe find it plausible to assume that in any position is : elementary volume in which the temperature and composition of the gaseous phase at any i~rn point are identical, all particles grow at the Vm = ~Tr ~ d~ ni. (I) same linear rate. In other words, given the same temperature and composition of the gaseous The total volume of all the particles of "nphase the linear rate of particle growth is inde- distribution" corresponding to a certain interpendent of the particle diameter. Hence, as mediate stage of acetylene decomposition

629

ACETYLENE SELF-COMBUSTION

will be : i~m

yn=~

~

i=n+l

(d~-d,~)~.

(2)

i=m

Thus, the degree of acetylene decomposition corresponding to this particle size distribution will be:

(3)

yjy,~ .

Similarly, the total surface area can be found T A B L E 1. SIZE DISTRIBUTION OF PARTICLES OF ACETYLENE CARBON BLACK ACCORDING TO WATSON 15 Interval Index i

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

T A B L E 2.

Diameter di

50 100 200 300 400 500 600 700 800 900 1000 1250 1500 1750 2000

for each distribution. The total particle surface area for " n - d i s t r i b u t i o n " (Sn) is given by the following e q u a t i o n :

Number of Particles in the Interval (ni)

units

%

7 62 369 1088 1968 2255 1956 1548 954 593 336 303 101 27 9

0.060 0.535 3.187 9.4O7

17.007 19.478 16.888 13.472 8.242 5.122 2.902 2.617 0.873 O. 233 0.077

Sn

=

7r

E i=n+l

(di

-- dn):ni.

(4)

CALCULATIONS

The calculation was performed for Schawinigen acetylene carbon black obtained by continuous thermal acetylene decomposition at atmospheric pressure. Watson 15 carried out t h o r o u g h electron-microscopic m e a s u r e m e n t s of particle sizes of this carbon black. Table 1 gives the results of these m e a s u r e m e n t s for 11,576 particles. Table 2 gives the total volume and the total surface area of the particles, the total n u m b e r of particles and the degree of acetylene decomposition, calculated for distributions from 1 to m. The calculations m a d e use of E q u a t i o n s (1) and (4). The total surface and the total n u m b e r of particles do not represent absolute values based on the t o t a l i t y of the particles measured in the electron-microscopic investigation, b u t values based on one ml of the initial acetylene. These values were obtained by m u l t i p l y i n g the values given by Equations (2) and (4) by the ratio (K = 2.94 × 10 s) of the weight of carbon in 1 milliliter of acetylene to the total weight of the carbon particles measured by the electron micro-

CALCULATION OF THE D E G R E E OF DECOMPOSITION 1 SURFACE AREA AND NUMBER OF PARTICLES FOR D I F F E R E N T DISTRIBUTIONS

No. of Distribution n

Thickness of the Formed Carbon Layer

14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

125 250 375 5O0 550 600 650 700 750 800 850 900 950 975 100

Total Volume of Particles Equation (2) ~8

7.38 8.10 4.58 1.97 3.33 5.45 8.79 1.41 2.26 3.60 5.73 8.92 1.35 1.64 1.99

X X X X X X X X X X X X X X X

107 lOs 10 ° 101° 101° 1010 101° 10 n 1011 1011 1011 1011 1012 1012 1012

Degree of Decomposition Equation (3)

Total Particle Surface Area Equation (4)

%

6m2 ~nl-I

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 82.748 100.0

0.052 0.364 1.67 6.33 9.9 15.5 24.5 39.2 62.7 99.3 152.0 224.0 334.0 373.0 435.0

Total Number of Particles

ml-1

2.64 1.06 4.03 1.29 2.28 4.03 6.85 1.13 1.72 2.38 2.96 3.28 3.39 3.40 3.42

X × X × X X X X X X X X X X X

109 101° 101° 1011 10 u 101I 1011 1012 1012 1012 1012 1012 1012 1012 1012

630

DETONATIONS AND EXPLOSIONS

scope, i.e., to the weight of carbon contained in the carbon particles corresponding to "0-distribution." Results

Figure 1 is a graphic representation of the results of these calculations. The curves of Figure 1 suggest a few interesting conclusions. The curves of the total number of particles show t h a t the formation of new particles occurs mainly at the beginning of the decomposition. Thus, ten per cent of decomposition results in the formation of 1.6 × 1018 particles which is about 50 per cent of all the particles formed. The curve for the thickness of the carbon layer formed has a similar shape, which indicates t h a t the initial stages of decomposition are marked b y a more intensive growth of the carbon layer than the subsequent stages. Conversely, the curves for the total particle-surface area show a practically 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, present some interest. These curves, however, are not kinetic curves, because they represent the dependence of the process parameters, not on time, but on the degree of decomposition. To obtain kinetic relations from 500

~o

// 0 o

2.~ 50 z~ llccompa~ition oi" ocetylene , 7.

0 IgO

FIG. 1. Development of formation of dispersed carbon by self-combustion of acetylene: Curve 1, total number of particles; Curve 2, total surface area of particles; Curve 8, thickness of the carbon layer.

these curves, the time element must be included in some way. To achieve this, the following a t t e m p t was made initially. In order to calculate the early stage of the process, we postulated values for the rate of growth of the carbon surface area in the thermal decomposition of acetylene and for the activation energy of this process at low temperatures (500 ° to 600°C). 1~ I t was also assumed that, due to the adiabatic nature of the process, the temperature of the system is determined b y the amount of heat released by the reaction, which is proportional to the degree of decomposition. However, calculation showed that the rate of surface area growth at a temperature corresponding to the beginning of the explosive decomposition of acetylene was so low t h a t 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 led us to the conclusion t h a t the actual process of growth of the first particles formed in the explosion is 6 to 7 orders faster than at a temperature of 500 ° to 700 ° which corresponds to the low initial degree of acetylene decomposition. There can be only one explanation of such a discrepancy. At the moment of nucleus formation, a growing carbon particle has a considerably higher temperature than that which would correspond to the degree of acetylene decomposition attained at t h a t moment. Inasmuch as the interaction of the acetylene molecules and the nuclei, and their decomposition at 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 because of the high rate of the process, such a supposition seems realistic enough. 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 (3000°K) attained when the decomposition of acetylene is complete. Moreover, it was assumed t h a t the gas layer which is 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 decomposition. In other words, it was assumed that the process under consideration has an activation energy E = 0 and t h a t the reaction rate depends only on the number of collisions of acetylene molecules with the surface. Natu-

ACETYLENE SELF-COMBUSTION

rally, a calculation based on such assumptions yields a maximum decomposition rate and a minimum reaction time. The number of collisions of acetylene molecules with the surface was determined from equations of molecular kinetic theory. Such a calculation produces a correct result for the number of molecular collisions with the surface only at the instant of nucleation. Subsequently, the number of collisions decreases, because the concentration of acetylene drops and the concentration of hydrogen rises in the surface layer as a result of the reaction. I n a steady-state process the growth rate would be determined by the diffusion of acetylene molecules toward the surface. However, we are dealing with an essentially nonsteady-state process, and it is very difficult to estimate the role of diffusional resistance in this case. Therefore, as a first approximation, we neglected diffusion and assumed t h a t 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 the previous ones, should lead to the overestimation of the growth rate. The maximum rate of particle growth obtained in this manner proved to be

631

/t

77me,microsecond,~

FIG. 2. Kinetic curves of the process of formation of dispersed carbon by self-combustion of acetylene: Curve 1, Rate of particles formation; Curve 2, total surface area of the particles; Curve 3, degree of acetylene decomposition.

formation. Of special interest is the particle formation curve which shows a considerable induction period and a sharp peak in the particle formation rate. The time from the moment of formation of the first particles to the beginning of the rapid growth of the formation rate makes up about 2/~sec of the total duration of the process (about 7 #sec). The sharp peak on the curve of the formation of carbon-particle nuclei is due to the rapid rise in the rate of nucleation w = 2.09 X 10-2C e m / s e c , (5) at the beginning of the process and the no less where C = acetylene concentration in vol per rapid drop in this rate which is observed when cent. If the thickness of the carbon layer formed the acetylene concentration is still high. The cause of the rapid rise in the nucleation is ~ (A), the time necessary for its formation rate is not entirely clear. This rise can hardly will be be explained b y the rapid rise in temperature t -sec. (6) because the maximum gradient of the growth 2.09 C X 106 rate corresponds to the initial degrees of decomWith the aid of this equation the curves of position. Figure 1 were converted to kinetic curves The maximum rate of particle formation presented in Figure 2. corresponds to about 10 per cent of acetylene To do this, we determined the growth rate decomposition. This leads to the conclusion from Equation (5), found the thickness of the t h a t nucleation occurs essentially in the temformed carbon layer, ~, graphically, and calcu- perature range from 500 to 800°C. lated the reaction time from Equation (6) for a The drop in the nucleation rate is attributed certain range of variation in the degree of to the competing reaction of particle growth decomposition. Then we found graphically the whose activation energy is close to zero, whereas number of newly formed carbon particles, An, the activation energy of the nucleation process and determined the absolute rate of formation o f ' is of the order of 60 to 70 kcal/mole. new particles or the rate of nucleation (in units The calculation was based on assumptions of cm -3 sec-0, with the known reaction time. that led to the maximum possible rate of the process and hence, the minimum possible Discussion duration of the reaction. The kinetic curves of The graph of Figure 2 represents kinetic Figure 2 give an estimated value of 7 ~see for curves of the process of dispersed carbon the total duration of the explosion. o

632

DETONATIONS AND EXPLOSIONS

To compare this value with direct experimental results, the author used the measurements of the rate of acetylene detonation based on the d a t a of Bone and Frazer. '7 These measurements were carried out at atmospheric pressure. The detonation was produced by means of a detonator placed in the acetylene. The initial flame velocity over a length of 0.5 m was 2,135 m/sec, the length of the incandescent spin head of the detonation front was about 10 cm. Based on these results, the duration of the chemical detonation reaction may be estimated at 0.1 ~ 47.10-6 sec. 2135 - This value is only about 7 times the one found by calculation. Considering that the length of the region of incandescent carbon particles should exceed t h a t of the chemical front of the reaction, because some time is needed for the cooling of the particles, the actual divergence betwe ~n these values is still smaller. This suggests the unexpected conclusion t h a t the extreme assumptions used in the calculations do not lead to a considerable overstatement of the reaction rate and, consequently, are clos2 to the actual values. Indeed, if one assumes that the divergence is due only to diffusion, then, considering the tremendous absolute reaction rate, this slowing-down should be regarded as insignificant. Conversely, if diffusional resistance is assumed to be zero, it must be concluded that the reaction does not involve all of the acetylene molecules t h a t strike the surface, but only one out of every four or five molecules. In other words, the activation energy of the growth process is not zero, but a value of the order of 6000 to 8000 cal/mole. If we assume, however, that the actual process involves diffusional and kinetic resistance (which are more realistic), the conclusion must be drawn t h a t the activation energy of the process does not exceed a few thousand calories per mole, and that diffusional resistance is quite insignificant. Consequently, in the acetylene explosion the growth of carbon particles is, indeed, due to the direct destruction of acetylene molecules that strike the carbon surface, and the reaction involves practically each of these molecules. In this case the heat released in the exo-

thermic decomposition reaction has no time to dissipate, and the growing particle has a considerably higher temperature than the ambient gas during the major part of the reaction. Because of the avalanche-like and highly unstable nature of the process, in spite of its tremendous rate, diffusion decreases its rate only slightly (less than by one order of magnitude). As regards the mechanism of nucleation in the process considered, the following m a y be stated. Because of the short reaction time, nuclei cannot result from polymerization reactions, as has been shown convincingly. 4 Hence, nuclei are the simplest carbon-particle radicals formed from active acetylene molecules. The computed absolute rates of carbonparticle formation make it possible to estimate the activation energy of the nucleation process. The curve of Figure 2 shows t h a t the maximum rate of nucleation is 2.3 × 10 TM m1-1 sec -1. This value makes it possible to estimate the activation energy of the nucleation process at about 60 kcal/mole for a bimolecular 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 discussed in the works cited in references 8 and 9. I t 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 subsequent growth of these nuclei seems to be a purely molecular process. I t 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 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, in which the temperatures of the growing carbon particle and the gas should be identical. Conclusions The growth of carbon particles in acetylene explosions results from the direct decomposition of acetylene molecules at the surface of the growing particle. The activation energy of the process is close to zero, thus practically each

CONDENSATION OF PRODUCTS IN DIBORANE-AIR DETONATIONS

collision of an acetylene molecule with the surface leads to a reaction. The total rate of the chemical reaction at the front of the acetylene explosion is determined by the rate of the reaction of acetylene molecule decomposition at the surface of the carbon particles which, in turn, depends on the rate of nucleation. The temperature of the growing carbon particle from the moment of nucleation and during the maior part of the reaction considerably exceeds the equilibrium adiabatic temperature of the gas corresponding to the degree of decomposition achieved. 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 but slightly inhibited by hydrocarbon diffusion. The carbon-particle nuclei in acetylene explosions obviously represent the simplest carbon particles--radicals formed by a molecular and/or a chain process from the molecules of the initial acetylene.

6.

7.

8.

9.

10. 11. 12.

13.

REFERENCES 1. ALEKSEEV, D.: Proceedings of Shelaputin Institute, Moscow 4, 167 (1915). 2. RIMARSKI,V. W. ANDKONSCHAK,M.: Autogene Metallbearbeitung, 24, 51 (1931). 3. FRANK-KAMENETSKII, :D. A.: Acta Physicochimica, 18, 148 (1943). 4. PORTER, G.: Combustion Research and Reviews, p. 108. Butterworths Scientific Publications, London, 1955. 5. JONES, G. W., KENNEDY, R. E., SPOLAN, J,,

14.

15. 16.

17.

633

AND SCOTT, G. S. : United States Bureau of Mines. Report Invest. No. 4695, 1950. GAYDON, A. G., AND FAIRBAIRN,A. R.: Fifth Symposium (International) on Combustion, p. 324. Reinhold Publishing Corporation, New York, 1955. ROBERTSON, W. W., MAGEE, E. M., FAIN, J., AND MATSEN, F. R.: Fifth Symposium (International) on Combustion, p. 628. Reinhold Publishing Corporation, New York, 1955. WESTBROOK,E. A., HELLWIG, K., AND ANDERSON, R. G. : Fifth Symposium (International) on Combustion, p. 631. Reinhold Publishing Corporation, New York, 1955. STEI-ILING,F. C., FRAZEE, J. D., AND ANDERSON, R. C.: Sixth Symposium (International) on Combustion, p. 247. Reinhold Publishing Corporation, New York, 1957. GREEN, E. F., TAYLOR, R. L., AND PATTERSON, N. L.: J. Phys. Chem., 62, 238, (1958). ATEN, C. F., AND GREEN, E. F.: Discussions Faraday Soc., No. 22, 162, (1956). HOOKER, W. J.: Seventh Symposium (International) on Combustion, p. 949. Butterworth and Company, Ltd., 1959. TESNER, P. A.: VNIIGAZ Proceedings, Gostoptehisdat, Moscow, N 3 (11), 34, 1958. TESNER, P. A.: Seventh Symposium (International) on Combustion, p. 546. Butterworth Scientific Publications London, 1959. WATSON, J. H. : Anal. Chem. 20, 567, (1948). TESNER, P. A.: Eighth Symposium (International) on Combustion, p. 807. The Williams & Wilkins Company, Baltimore, 1962. BONE, W. A., AND FRAZER, R. P. : Proc. Roy. Soc., (London) A230, 363 (1932).

66

CONDENSATION OF PRODUCTS IN DIBORANE-AIR DETONATIONS By F. J. M A R T I N , P. H. K Y D D AND W. G. BROWNE Introduction This study was initiated to assist in the evaluation of high-temperature thermodynamic data for products of the combustion of boron compounds with air. Precise measurements of detonation velocities for diborane-air mixtures have been made. These have bee~ compared with detonation

velocities calculated by hydrodynamic theory with the use of several proposed sets of thermodynamic data for the product gases. The agreement over a wide range of starting compositions between observed and calculated velocities for one set of thermodynamic data lends strong support to this particular set. 1 With the use of the data selected in this way,