HTPOTHESIS FOR PROPELLANT BGRNINQ
863
AX HYPOTHESIS FOR PROPELLAKT BURXING‘ ROBERT E . WILFOiYG,* STANFORD S. P E S S E R , 3 A K D FARRIXGTOS DASIELS
Department of Chemistry, Cnztersaty of Wzsconsan, Madason, M’asconszn Received January 9 , 1950
When nitrocellulose “burns” the surface undergoes violent decomposition and evolves large quantities of hot gases vhich can be used for propulsion purposes. As the surface molecules are decomposed and ejected, fresh layers of molecules are exposed successively deeper and deeper in the propellant. The rate of regression, or “peeling-off ’’ of one molecular layer after another, has been measured directly and found to be of the order of 2 cm./sec. at a pressure of 1500 lb./in.z A small bomb nas developed (2) for the rapid determination of the linear burning rate of experimental propellants under pressure, making use of fuse vires and timing circuits. The linear rate of burning depends greatly on the pressure of the gases surrounding the propellant and to a small extent on the initial temperature of the propellant. The purpose of this investigation was to try to explain the mechanism and predict the behavior of propellant burning in the simplest possible way from general concepts of chemical kinetics. Most of the experiments were carried out with double-base powder containing 54 per cent nitrocellulose (13.25 per cent nitrogen), 43 per cent nitroglycerin, and 3 per cent s-diethyldiphenylurea. The laboratory facts and many field observations are in accord with the following simple but obviously incomplete hypothesis. The rate-determining step in the burning of the propellant is the decomposition of the molecules a t the surface. It is an unimolecular reaction which involves merely the endothermic breaking of the oxygen-nitrogen bond in the nitrate group of nitrocellulose or nitroglycerin. The fragments of SO2 and organic radicals] similar to (CHO), are thrown out from the surface and then react in the gas phase. The heat from this exothermic gas reaction is transferred to the propellant by diffusion, convection, and radiation, raising the temperature of the surface molecules to a temperature in the neighborhood of 1000°C. Nitrocellulose and nitroglycerin contain the folloiving structural unit:
0
-C-
I H-C-0-X -C-
7
I
l This paper is based on work carried out a t the C‘niversity of Wisconsin under Contract OESlsr-762 with the Office of Scientific Research and Development and described in part in OSRD Reports 6559 and 3206. A portion of this material was presented a t the Symposium on Kinetics of Propellants which was held under the auspices of the Division of Physical and Inorganic Chemistry a t the 112thMeeting of the American Chemical Society,NewYork City, September 15, 194i. * Present address: E. I. du Pont de Nemours and Company, Waynesboro, Virginia.
864
R. E. WILFONG,
S. S. PENNER, AND F. DANIELS
Of the various bonds in this unit the weakest is the 0--N bond. Less energy is required to break the 0-K bond than the other bonds, C-H, C-C, C-0, and Y=O, and the rate of breaking these 0-N bonds, which are a t the surface, can be estimated a t a given temperature with the simple formulas of chemical kinetics and making use of independent constants. The effect of pressure on the rate of burning of a propellant is very large and cannot be calculated a priori on the hypothesis proposed here. The simple assumption is made that the heat transferred back to the freshly exposed surface is constant at constant pressure, thus giving conditions for a unimolecular stage of the reaction a t an elevated but constant temperature. A steady state is reached in which the heat transferred from the exothermic gas reaction is equal to the endothermic heat of the bond breaking. Qualitatively it can be seen that if the exothermic reaction between the fragments in the gaseous envelope surrounding the propellant is bimolecular in nature, it will increase in rate with an increase in pressure. Moreover, the envelope of burning gases will be driven closer to the surface of the propellant. An increase in the rate of the gaseous reaction increases the rate a t which heat is evolved and transferred back to the surface. A higher pressure then gives a higher temperature, which in turn gives a faster reaction a t the surface and the faster reaction gives a greater rise in pressure in a closed space and so on,-leading to an explosion. However, this explosion is not a detonation in which all molecules decompose instantly throughout the mass; the decomposition is still confined to the surface molecules. With the help of empirically determined constants determined from measurements of the burning rate of the propellant, 0. I(.Rice ( 5 ) has developed a broader theory which gives the effect of pressure on the burning rate. Boys and Corner (1) have developed a theory emphasizing the importance of the exothermic gas reaction as the rate-determining step in the steady state, whereas the hypothesis offered here emphasizes the importance of the endothermic unimolecular surface reaction as the rate-determining step. Both are different views of the same phenomenon. The Rice theory is broad enough to include both views, and it can give quantitative calculations making use of constants which are determined empirically from experiments on the burning rates. Experimental measurements and general observations will now be cited in support of the simplified hypothesis proposed here. THE UNIMOLECULAR SURFACE REACTION
The rate-determining step is the isothermal unimolecular rupture of the oxygennitrogen bonds at the surface. The general equation for a unimolecular reaction is
where k is the specific reaction rate, R, T , N , and h are the gas constant, absolute temperature, Avogadro’s number, and Planck’s constant, respectively, and A&,t 3 Present address: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.
HYPOTHESIS FOR PROPELLAKT BURNING
865
and AHsct are the ent.ropy and heat of activation. ASaetmay be regarded as essentially zero for the breaking of a bond, and a t 1000°C. the formula' becomes: k = 3 x 1013e-AHdRT (2)
A lower limit for the activation energy is the energy required to break the weakest bond in the molecule, i.e., the heat of dissociation of the 0-S bond. This bond strength has been given various values but is probably not far from 45,000 cal.jmole. Inasmuch as the fragments of the rupture involve free radicals which require very small activation energy for recombination, the activation energy for rupture is probably not much greater than the heat of reaction as given by the bond strength. Experiments with nitrocellulose at elevated temperatures gave 46,iOO cal.; mole, as described in a later section. R'ith this value for the activation energy, equation 2 gives at 1000°C. 1; = 5.5
x
105
(3)
where k is expressed in reciprocal seconds. The significance of k and the frequency factor can be interpreted in terms of the mechanical picture of the surface reaction. The specific rate constant k is defined by the equat'ion
where n is the number of potentially reactable molecules, i.e., the number of 0-N bonds at the surface of the propellant, and dnldt is the rate In seconds of the number being broken. A minimum value of the number of 0-S bonds at the surface can be calculated from the density and the chemical composition. A cube of the propellant, 1 cm. on an edge, weighs 1.63 g. I t contains 54 per cent by weight of nitrocellulose (13.25 per cent of which is nitrogen) and 43 per cent of nitroglycerin (18.5 per cent of which is nitrogen). There is then 0.246 g. of nitrogen or 1.07 x loz2atoms of nitrogen per milliliter. Each atom of nitrogen provides one oxygen-nitrogen bond, giving 1.07 X loz2bonds per milliliter. When the 1 em. cube of propellant burns, the linear rate of regression involves burning inward from one surface which contains (1.07 X 1022)2'3 or 4.8 x 1014 oxygen-nitrogen bonds per square centimeter, provided the surface is perfectly smooth. Rough surfaces and cracks will, of course, increase this surface. A minimum rate of burning in seconds at a constant surface temperature of 1000°C. then is given by equations 3 and 4: dn - ;it = kn = (5.5 X 10') X 4.8 X
=
2.6 X lozosee.-'
(5)
where n is the number of 0-S bonds per square centimeter. The value of n remains constant, because when a surface molecule is decomposed with expulsion of its fragments another molecule just below it is exposed. Accordingly the rate remains constant as long as the steady state is maintained, with a constant gas
' This formula and its application
have been discussed in general terms by Daniels (3).
866
R . E. WILFOXG, 9. S. PENNER, AKD F. DANIELS
pressure and constant surface temperature. The reaction is then apparently of zero order, since the concentration of reactants remains constant. in cross section This rate of breaking 0-N bonds along a propellant 1 can be translated into a linear burning rate by dividing by the number of bonds per centimeter of length, 1.07 X loz2.Thus equation 5 , expressed in number of bonds broken per second, becomes equation 6 when expressed in centimeters per second.
if the surface is assumed to be molecularly flat. The experimentally determined rate of burning is much faster than this-about 2 cm. per second a t a pressure of 1500 1b.,h2 The effective surface area is certainly much greater than the ideal, molecularly flat surface calculated by taking the two-thirds power of the volume. Boiling or bubbling of a liquid at the surface could well increase the number of molecules in the surface by a factor of 100 and bring the burning rate up to the experimentally observed value; and there is evidence also for cracks in the surface which expose an additional number of 0--S bonds. In fact, the “effective’’ surface may even extend out a short distance from the geometrical surface as particles of the propellant are shot forth into the gas space. The burning surface was suddenly quenched by blowing out a rupture disc in the bomb, and the propellant surface and suitable controls were then allowed to stand in dye solution, the solution was evacuated, and the vacuum was broken. The dyes methyl violet, gentian violet, and basic fuchsin were found to be suitable for diffusion into minute cracks in colloidal nitrocellulose or double-base powder. They penetrated as a dense layer 0.0125-0.017 cm. thick in the surface which had been burnt, as revealed by microscopic examination of their sections. The penetration of the surface caused by the arrested burning is due to cracks, and if these cracks were present a t the time of burning, it can be estimated that they could expose 2 x IO4 0-Ti’ bonds along the cracks per square centimeter (8). I t is possible, of course, that the cracks may have been produced by the rapid cooling of the surface as well as by the quick heating. If part of these surfaces of cracks is added to the flat surface the calculated burning rate can be made to increase over 100-fold and to check with the observed burning rate. ACTIVATION
ENERGY OF NITROCELLULOSE~
The activation energy was calculated from measurements on the rate of decomposition of nitrocellulose at different temperatures in the neighborhood of 16OoC.,using the apparatus shown in figure 1. About 2.0 g. of nitrocellulose containing 13.4 per cent nitrogen was deposited from acetone solution onto glass pearls in a glass vessel. The small spheres gave rapid heat exchange with a flowing stream of nitrogen and assured isothermal conditions even during the exothermic reaction. The uniform film of nitrocellulose, after drying, was of the order of loo0 molecules in thickness. The glass 8 More details are given in part of a Ph. D. thesis presented by S. S. Penner a t the Universitv of Wisconsin in 1946.
HYPOTHESIS FOR PROPELLAXT BURXING
867
inlet coil and the reaction chamber Tvere immersed in the thermostat, and purified nitrogen from a tank was passed through, but measurements of the decomposition were not made until the two thermometers gave the same reading. The exit nitrogen, which contained the products of the decomposition of nitrocellulose, vias passed through a pair of absorption towers containing sodium hydroxide. Several outlets permitted collection of successive samples. An excess of acidified 0.02 9 potassium permanganate was then added in k n o w quantity and allowed to stand for 15 min., after which an excess of potassium iodide was added and the solution was tirated xith sodium thiosulfate. The volume of potassium permanganate used up (Le,, the difference in volume of thiosulfate solution for successive samples) is a measure of the amount of nitrogen dioxide and organic reducing material liberated, which in turn is a measure of the amount of nitrocellulose decomposed. The reaction is apparently of zero order, because there is a T-ery large number of potentially decomposable molecules at the surface and because irhen n niolecule at the surface decomposes ts place is taken by another one just under it.
FIG.1. Apparatus for measuring t h e r a t e of decomposition of nitrocellulose
For the calculation of the activation energy the number of milliliters of sodium thiosulfate required per unit of time in the titration may be used as a measure of the decomposition rate, dc,’dt, at a given temperature. Sample data are given in table 1. Sinety milliliters of 0.2 S sodium hydroxide was used for absorption and 15 ml. of 1:s sulfuric acid and 10 ml. of potassium permanganate (equivalent to 13.98 ml. of sodium thiosulfate) were added. These data are plotted in a log dc,!dt us. 1 / T graph in figure 2 , where it is seen that a straight line is obtained with a slope \rhich multiplied by -2.303 R gives an activation energy of 47,400 cal.,/mole. It is gratifying to note that the last measurement ( S o . 5 ) v a s obtained after the nitrocellulose had been heated to higher temperatures and brought back to loIver temperature. The fact that this point falls on the line shom that the reacting system is reproducible and that it has not changed with time and temperature. The upper dotted line gives a qualitative insight into some of the complications involved in the gaseous products which are evollred. Air was used instead of nitrogen in these experiments, and the larger amounts of potassium permanganate reduced at the higher temperatures can probably be explained on the as-
868
R. E . WILFONQ, S. S. PENNER, AND F. D.4NIELS
sumption that the oxygen oxidized some of the organic material a t the higher temperatures and thus prevented the reduction of some nitrogen dioxide. The larger amount of nitrogen dioxide remaining in the gases leads to a larger difference in the titration with sodium thiosulfate. Three sets of determinations were made, giving 46,000, 46,700, and 47,400 cal./mole for the energy of activation. The average value is 46,700. In attempting to study the primary step in the decomposition of nitrocellulose or double-base powder a t an elevated temperature it is essential to sweep out the TABLE 1 Rate of decomposition of nitrocellulose Temperature in "C. . . . . . . , , . . . . .
..I I
Back-titration, Na*S*03in milliliters , . , . . . . . . , . . . . . . . , . . . . dc/dt in terms of milliliters of Na2S203 per h o u r . ,. , , . , . . . . ,
,
130.5
140.0
149.5
13.55
12.95
10.85
7.40
11.75
0.40'
2.00
6.20
13.10
4.40
FIG.2. Determination of the activation energy for the decomposition of nitrocellulose
products of decomposition as fast as they are formed. When such propellants stand for long periods of time at room temperature, enough nitrogen dioxide accumulates to give definite color and odor. In fact, a test for nitrogen dioxide with special paper is a standard test for the instability of an old propellant, and stabilizers such as diphenylamine are introduced which combine directly with nitrogen dioxide. At elevated temperatures however, the nitrogen dioxide undergoes chemical reaction with the residual organic matter. This reaction leads to the production of nitric oxide and nitrogen and a variety of partially oxidized
HYPOTHESIS FOR PROPELLANT BCRNING
869
organic materials which have been the object of considerable study in several laboratories. At the higher temperatures which prevail in normal propellant burning a t high pressures the nitric oxide and the organic material react further to give chiefly nitrogen, Tvater, and carbon dioxide (and carbon monoxide if there is insufficient oxygen). Only under these conditions is the full heat of the propellant burning realized and only then can the high surface temperature be maintained. When the reduction of the nitrogen dioxide to nitrogen is not complete the burning will be abnormally slow, as in “fizz burning” at low pressures in the laboratory or in intermittent “chuffing” in field tests. Although nitrogen dioxide is readily observed in the slow decomposition of nitrocellulose at room temperature and a t 16OoC.,attempts to find it in the products of high-temperature “burning” were unsuccessful. At the higher temperature it probably decomposes or reacts ITith the organic material before it can be isolated by quick chilling. I t is unimportant from a practical standpoint whether nitrogen dioxide is formed in the first step and later reduced to nitric oxide and nitrogen in the gaseous reactions vhich follow the initial unimolecular decomposition, but since the 0--S bond is the weakest bond it seems likely that the primary step, a t high temperatures as well as a t low temperatures, is the breaking of this bond and the initial production of nitrogen dioxide. Experiments were carried out with the addition of materials designed to explore the possibility of chain reactions. Lead tetraethyl and iron pentacarbonyl incorporated in the propellant had only a slight effect in reducing the burning rate, indicating the absence of long chains in the propellant or the gaseous reactions. Inert materials like carbon dioxide and magnesium oxide reduced the burning rate by increasing the heat capacity and lowering the temperature. The decomposition of nitrocellulose becomes complicated and abnormal if the products of decomposition are not removed from the surface. The nitrocellulose decomposition vessel was prepared as it was in the experiments shown in figure 1, but before taking the measurements it was allowed tostand a t 160°C. for several days without sweeping any gas through the vessel. The log dc/dT us. 1/T line was not straight and it changed slope markedly with successive heating and cooling, giving lower activation energies. Some of the activation energies given in the literature (6,7) agree with the value (46,700) obtained in t,his investigation and others are considerably lorer. Complications due to the accumulation of intermediate products of the decomposition may have been involved. When the propellant burns under field conditions the decomposition products are quickly swept away from the surface by the large volume of gases evolved, thus meeting the requirements for the hypothesis proposed here. SURFACE TEYPER.iTURE . I S D EFFECT OF IXITIAL TEMPERATURE
The hypothesis offered here suggests that the extreme surface layer is a t a high temperature. Experimental evidence of such a high temperature was sought by incorporating temperature-indicating substances in the propellant, burning the propellant in a bomb, and quenching by the rupture of a thin metal disc \\-hen the pressure reached I500 lb./in.? The standard double-base powder mas mixed with acetone, and extruded after introducing finely divided copper powder.
870
R . E . TVILFONQ, 8. 6 . PENNER, AND F. DANIELS
A study of microphotographs showed that although some larger cubical particles remained unmelted, all copper particles smaller than 0.0004 cm. which were in the surface were melted into spheres. This fact showed that the particles had attained a temperature of a t least 1083"C., which is the melting point of copper. The smallest sphere had a diameter of 0.00025 mm. In other experiments finely powdered alkaline earth carbonates were incorporated in the propellant, and after arrested burning the surface was treated with phenolphthalein. A red color is produced if the carbonate has decomposed thermally to leave the oxide. Experiments showed over one-fourth of the particles of calcium carbonate had been decomposed, whereas practically none of the barium carbonate particles had been decomposed. These experiments support the view TABLE 2 Specific reaction rates of unimolecular reactions TEYPEPA.
35,000
TUPE
40,WO
45,000
50,wO
7 x 106 1.07
5 x 104 1.08
4 x lo* 4 x 10' 1.09 1.11
x 107
k
2
1.05
2 x 10' 1.05
2
kma -. . . . . . . . . . . . . . . . . . . . . . . . . . . ki?w
1.06
3.0 X 10' 1.07
k..................................
1.0 x 10 1.04
2 x 107 1.04
4 x 10' 1.05
7 x 10' 1.05
8 x 108 1.03
2 x 108 1.03
4
kirw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -
x 10'
kirw
k
x
1.04
107
8 x 106 1.04
that the extreme surface temperature was hot enough to dissociate calcium carbonate. A surface temperature above 1000°C. can be calculated theoretically by dividing the heat of reaction by the heat capacity. Moreover the heat conductivity of the double-base powder is low, less than that of fire brick and one-tenth that of paraffin wax. The outermost molecular layer peels off the propellant surface in about one-millionth of a second, so that it has little chance to conduct the heat returned from the hot gases back into the cool interior. The heat from the envelope of burning gases then is used chiefly in raising the temperature of the outermost molecular layers. There is another argument for a high surface temperature. Two criteria must be met in the propellant burning at 1500 l b , / h 2 : the burning rate is about 2 linear centimeters per second and it increases about 0.5 per cent per degree rise in initial temperature. I t will be shown in table 2 that those two criteria can be met only if the surface temperature is high.
HYPOTHESIS FOR PROPELLANT BCRNIXG
8il
-1high initial temperature, T , , \vi11 lead to a high surface temperature, T,, for burning. If one sample of a given propellant has an initial temperature 1.O"c. higher than a second one, and both are subjected t o the same amount of heat from the burning gases, the first one will have a higher surface temperature than the second and will burn faster. I t will not be 1.O"C. higher, but in the neighborhood of 1000°C. it will be about 0.4"C. higher, because the heat capacities of both increase at higher temperatures as new modes of vibration are brought into play. The heat capacity cannot be measured at these high temperatures irhere the material has only a transitory existence. It is estimated by analogy ivith specific heat data for hydrocarbons (4) that the heat capacity will increase from 62.8 cal.deg.-' mole-' a t room temperature t o 164 cal.deg.-' mole-' a t 1000°C. I n table 2 values of ?i are calculated irith the formula =
3
x
1013e-bXettlRT
for various activation energies and temperatures and the effect of inital temperatures is indicated by ___ lZTi + 10
k,;
or
ky,+4 T,
The term kT8+d,lkT8should have values of about 1.05 to be in agreement with the 0.5 per cent increase in rate per degree rise in temperature. These values occur only above 1000"A. or 1373°K. for activation energies between 45,000 and 50,000 cal./mole. Values of li of about 5 X 10' are required to give linear burning rates of 2 em. per second, as shoivn in equations 3 and 6, if the burning surface is molecularly flat. As pointed out before, this large value of k can be obtained only a t unreasonably high temperatures and it is necessary to allow for a rougher surface. An effective surface factor of 100 seems reasonable and in agreement with evidence from the penetration of dyes. Combining this surface factor xith a calculated value of li of about 5 X lo5,a numerical value of 5 X 10' is obtained which gives a rate of burning of 2 em. per second. Table 2 shows that this yalue is i obtained at a surface temperature of about 1000°C. when the activation of ? energy is between 45,000 and 50,000 cal./mole. This correction for effective surface area is unsatisfactory, but it permits an hypothesis of burning based on simple concepts of kinetics. The surface temperature, like the surface factor, is somewhat indefinite and may be interpreted to be the effective temperature of the outer surface of the propellant and to include even a small gas layer adjacent to the propellant. Further investigations should be carried out to ascertain more definitely the true temperature of the outside layer of molecules during the microsecond in which the molecules are decomposing a t very high temperature, in the neighborhood of 1000°C. Ordinary temperature-measuring devices do not easily record the temperature of a thin outer layer of molecules, on account of the conduction of heat by the instrument itself. Studies of the rate of burning of propellants in a very rapid stream of hot inert gas Trould be helpful.
872
J. H. FRAZER AND B. L. HICKS SUMMARY
1. An hypothesis is offered for the burning of propellants in which it is assumed that the rate-determining step is the breaking of the 0-N bonds a t the extreme surface of the propellant. I t is assumed that the effective surface temperature is of the order of 1000°C.,maintained in a steady state by the heat coming back from an envelope of gases which are undergoing violent exothermic action. These gases include nitrogen oxides and organic fragments. 2. Experimental evidence is offered for the high surface temperature and for an activation energy of 46,700 cal./mole. 3. Applying the simple formula for a unimolecular bond-breaking process, calculations are made for the linear burning rate and for the influence of the initial temperature of the propellant. REFERENCES (1) BOYS,S. F.,A N D CORNER, J . : Confidential report. B.L.,J R . , HCGGETT, C., DANIELS, F., A N D WILFONG,R . E . : Anal. Chem. (2) CRAWFORD, 19, 630 (1947). (3) DAXIELS, F . : Ind. Eng. Chem. 36, 501-10 (1943). G.S.,A N D HUFFMAN, H . M.:Free Energies of Some Organic Compounds, p. 68. (4) PARKS, The Chemical Catalog Company, Inc., New York (1932). ROBERT:J. Phys. & Colloid Chem. 64, 885 (1950). (5) RICE,0.K . A N D GINELL, (6) ROBERTSON, R . , A N D NAPPER,S. S.: J. Chem. SOC.91, 764 (1907). S . : Physik. 2. Sowjetunion 1, 610 (1932). (7) ROGISSKY, (8) WILFONG, R.E.: Ph. D. Thesis, University of Wisconsin, 1944, pp. 13 and 49.
THERMAL THEORY OF IGNITION OF SOLID PROPELLANTS' J. H. FRAZER
AKD
B. L. HICKS
Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland Received J a n u a r y 9 , 1950
1
The ignition processes in a solid propellant are closely connected with the flow of heat in the propellant. I t should therefore be possible to describe some aspects of ignition in terms of a purely thermal model in which rate of reaction is a function only of the temperature. A number of calculations have been made during the past two years of temperature as a function of position and time for a simple thermal model of ignition for which the external heating rate conforms approximately to the course of heating by the igniter of the propellant in a rocket. In this preliminary note only the more important results of the calculations will be discussed. The data presented are not final. 1 Presented a t the Symposium on Kinetics of Propellants which was held under the auspices of the Division of Physical and Inorganic Chemistry a t the 112th Meeting of the American Chemical Society, New York City, September 15,1947.
