Effect of small additives on the combustion of composite solid propellants

ISSN 1990�7931, Russian Journal of Physical Chemistry B, 2009, Vol. 3, No. 6, pp. 926–935. © Pleiades Publishing, Ltd., 2009.Original Russian Text © S.V. Chuiko, F.S. Sokolovskii, 2009, published in Khimicheskaya Fizika, 2009, Vol. 28, No. 11, pp. 49–58.

926

INTRODUCTION

By now, a vast body experimental data on the regu�lating the burning rate of composite solid propellants(CSPs) with small additives of various compounds hasbeen accumulated. Nevertheless, some aspects of themechanism of action of small additives remain insuffi�ciently studied. At the same time, it is obvious that thetheory of CSP combustion cannot successfullydevelop without relying on experimental results;therefore, it is worthwhile to highlight the pointsimportant for constructing theoretical models. In thepresent work, we examine the mechanism of action ofsmall additives and identify the parameters that largelydetermine their efficiency.

We used the experimental design method, anapproach that allowed us to conduct experiments atthe lowest level of mutual correlation of the variables,i.e., to obtain information with the highest degree ofisolation of individual factors and couplings betweenthem.

Statistical models are intended for predicting theburning rate law as a function of the CSP compositionand for exploring the ways of controlling it. Therefore,the variables were only controlled (quantitative) fac�tors. Experimental data were processed using themethods of constructing regression polynomials pro�posed for general analysis of statistical data. Thechoice of the approximation equation and the spacingof the experimental point over the working intervalwere discussed in [1]. One advantage the statisticalmodels offer for the development of combustion the�ory consists in the fact that they represent a general�ized experiment, i.e., contain information on all thesystems studied, thereby being useful for extensivecomparisons of theoretical predictions with experi�ment. Empirical relationships reflected in statistical

models describe correlations between input and out�put parameters, i.e., represent a form of mathematicalmodeling of properties or processes [2]. An analysisbased on statistical models makes it possible to identifysystems with potentially useful properties in order tostudy them later in detail.

1. CONDITIONS AND OBJECTS

We studied CSPs composed of ammonium per�chlorate (AP) of various dispersities, synthetic polyb�utadiene fuel binder (FB), and ASD�1 aluminum (Al).Colloidal metals (CMs), dissolved bis(dicarbollylic)complexes of transition metals (MBDCs), and liquidferrocene plasticizer (FP) served as catalysts. Stron�tium carbonate (SrCO3, SC) and lithium fluoride(LiF) were used as combustion inhibitors. The follow�ing variants of burning rate modification were tested:(1) introduction of ultradispersed (UDAP) andcoarse AP; (2) introduction of combustion catalysts(MBDCs, FP, and CMs); (3) joint introduction of FPand SC. FP and CMs were introduced at the expenseof FB and SC, whereas LiF at the expense of AP. Thesamples were burnt in uncured form in quartz cups8 mm in diameter in a constant�volume bomb undernitrogen atmosphere. The experiment were performedaccording to the Hartley active design [1] and pro�cessed to develop statistical models describing thedependence of the burning rate on the pressure andpropellant composition.

2. COLLOIDAL METALS AS CATALYSTS OF COMBUSTION OF CSPs

We studied metal�free systems composed of AP andFB. The catalysts were CMs with a developed surface,

Effect of Small Additives on the Combustion of Composite Solid Propellants

S. V. Chuiko and F. S. SokolovskiiSemenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119991 Russia

e�mail: [email protected] July 17, 2008

Abstract—The efficiency of controlling the burning rate law of composite systems with small additives ofcombustion catalysts and inhibitors was experimentally studied. The combustion catalysts were colloidal andbis(dicarbollylic) complexes of transition metals and liquid ferrocene plasticizer, whereas strontium carbon�ate and lithium fluoride served as combustion inhibitor. Information on the regularities of action of each ofthe additives tested and of catalyst–inhibitor binary additives on the ballistic characteristics of compositesolid propellants were obtained.

DOI: 10.1134/S1990793109060116

COMBUSTION, EXPLOSION, AND SHOCK WAVES

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 3 No. 6 2009

EFFECT OF SMALL ADDITIVES 927

which were prepared in two�layer electrolytic bath andcoated with a protective oleic acid film.

Chemical and RDX analyses of colloidal metalpowders showed they contained ~80–90% of puremetal and 10–20% coating material. No aging ofmetal samples was detected after a year of storage.

Preliminary experiments were conducted to selectan optimal size of catalyst particles. For this purpose,we used iron powders with a specific surface area of 30to 80 m2/g (as measured by the chromatographicmethod of argon thermal desorption). It was demon�strated that, in this region, the effect of catalyst parti�cle size is very weak, so that powers with a particle sizesmaller than 1 μm are fairly effective, in agreementwith the previous data for aerosol powders; therefore,a further dispersion produces no appreciable changesin the CSP characteristics.

Metal additives were introduced in concentrationsof 1 to 60 wt % into a 80 : 20 wt % mixture. The cata�lysts tested were prepared from iron–copper andiron–chromium alloys, as well as from iron, copper,cobalt, nickel, and zinc. In decreasing catalytic activ�ity, they can be arranged as Fe–Cu, Fe, Cu, Co, andFe–Cr alloy. Additives of 1 wt % nickel or zinc pro�duced no noticeable effect on the burning rate of thesystem.

2.1. Effect of the Specific Surface Area of APon the Efficiency of the Colloidal Iron Catalyst

The specific surface area S0 of AP was varied from2400 to 6500 cm2/g. We studied 80 : 20 wt % AP–FBsystems. All the mixture were doped with 1 wt % cata�lyst in excess of 100%.

An analysis of the slope ϕ of the U(S0) curvesshowed that, in the presence of a catalyst, the effect ofS0 strengthens with increasing pressure faster, but onlyup to 300 atm (according to extrapolation), i.e., ϕc < ϕ0;

therefore, Z ~ , where α < 0 at P < 300 atm and α > 0at P > 300 atm, i.e., ϕc > ϕ0 (Z = Uc/U0 is the catalystefficiency; Uc and U0 are the burning rates of the cata�lyzed and uncatalyzed propellants, respectively). For

example, while U0 ~ , and Uc ~ at 100 atm,

extrapolation yields U0 ~ and Uc ~ at 1000 atm.

Thus, Z ~ and Z ~ at 100 and 1000 atm,respectively. Simply put, while at pressures below300 atm, an increase in S0 leads to a decrease in thecatalyst activity, at higher pressures, one can expect foran increase in the catalytic activity of the additive.

The introduction of a catalyst into the propellantdecreases the pressure exponent in the burning ratelaw. The value of ν increases with S0, tending to 0.6 foruncatalyzed propellants and to 0.5 for catalyzed ones(Fig. 1). In this case, the decrease in the exponent ν isin agreement with [3], since the initial value of ν is

S0α

S00.384 S0

0.25

S00.65 S0

0.95

S00.134– S0

0.3

larger than 0.5. Moreover, the limiting value ν = 0.5 isalso consistent with the expected effect.

2.2. Effect of the Oxidizer�to�Fuel Ratio on the Efficiency of the Colloidal Iron Catalyst

In this series of experiments, the AP (S0 =6500 cm2/g)�to�FB ratio was varied from 80 : 20 to65 : 35 wt %, i.e., for all the mixtures tested, the sto�ichiometric coefficient was α < 1. The mixtures werecatalyzed with 1 wt % iron. The experimental resultsshow that Z = Uc/U0 decreases with increasing pres�sure and increasing oxidizer content Cоx. The slope ofthe Z(P) dependence increased with the fuel contentCf. The maximum catalytic effect, Z = 2.1, wasobtained for a 65 : 35 wt % oxidizer–fuel mixture atP = 30 atm. Note, however, that, in spite of the highvalue of Z, the absolute burning rate always increaseswith α. The burning rate is strongly dependent on theoxidizer content; at 1 wt % and 65 ≤ Cоx ≤ 80 wt %,these dependences read as

.

Thus, the efficiency of colloidal iron depends on thepressure and oxidizer�to�fuel ratio as

where the pressure ranges within 30–100 atm, whereasthe Cоx/Cf ratio ranges from 1.86 to 4.00 (Cf = 1 –Cox),which corresponds to α < 1.

2.3. Influence of Aluminum on the Efficiencyof the Colloidal Iron Catalyst

At the next step, we introduced aluminum powderinto AP (S0 = 6500 cm2/g)–FB mixtures at the

U0 b0P0.68 Cоx

1 Cоx–��⎝ ⎠

⎛ ⎞1.45

and Uc bcP0.52 Cоx

1 Cоx–��⎝ ⎠

⎛ ⎞= =

Z bP 0.16– Cоx

1 Cоx–��⎝ ⎠

⎛ ⎞0.45–

,=

10090807060504030 200 300 400

P, аtm

0.6

0.5

0.4

0.3

0.2

0.1

ϕ

1

2

Fig. 1. Dependence ϕ(P): (1) without and (2) with catalyst.

928


CHUIKO, SOKOLOVSKII

expense of fuel. Colloidal iron was present in a con�centration of 1 wt %. The proportion between oxidizerand fuel in the two systems tested was 70 : 30 and65 : 35 wt %. Aluminum was introduced in concentra�tions of 5 and 10 wt % in the first mixture and of 5, 10,and 15 wt % in the second. Experiments showed thatthe burning rate increases with the aluminum content.The exponent ν for mixtures containing 70 wt % oxi�dizer decreases upon introduction of Al from 0.68 to0.60, being independent of the content of the former.For mixtures with C0 = 65 wt %, ν is virtually insensi�tive to the presence of Al in the concentrations used(ν = 0.69). The value of Z decreases upon Al introduc�tion, especially at low pressures.

2.4. Generalized Curve of Catalytic Activity of Additives

The above experimental results suggest that theefficiency of colloidal iron depends on the pressure,specific surface area of oxidizer, oxidizer�to�ratioratio, and aluminum content. Note that, as theseparameters change, so does the burning rate of theuncatalyzed system U0. The efficiency of action of col�loidal iron (Cc = 1 wt %) as a function of the burningrate of the uncatalyzed system is plotted in the loga�rithmic coordinates in Fig. 2.

As can be seen, with increasing U0, Z decreases.The experimental points fall onto a single curve,which asymptotically tends to 1 as U0 increases. At

U0 > 16 mm/s, Z ~ , whereas Z ~ at U0 <16 mm/s. The point presented in the plot wereobtained at the following governing parameters:20 ≤ P ≤ 500 atm, 2400 ≤ S0(AP) ≤ 6500 cm2/g,2.0 ≤ Cоx/Cf ≤ 4.0 (α < 1), and 5 ≤ CАl ≤ 15 wt %. With

U00.14– U0

0.036–

this parameters, the burning rate of the uncatalyzedformulations range within 5 ≤ U0 ≤ 70 mm/s.

It is interesting to process the data in the (Z 2 – 1)–U0coordinates,1 which show that, at α < 1 and P ≥ 20 atm,the efficiency of action of colloidal iron is related to U0(to an accuracy of ±15%) as (Z 2 – 1)U0 = const (Fig. 3,curve 2).

The general character of this dependence of theefficiency of action of iron�containing additives on theburning rate of the uncatalyzed system is confirmed bythe results we obtained by processing experimentaldata for mixtures of AP with poly(methyl methacry�late) (PMMA) and polystyrene (PS) doped with1 wt % Fe2O3 in the (Z 2 – 1) = f (U0) coordinates(curves 1 and 3 were borrowed from [3]). As seenfrom Fig. 3, all the experimental points at α > 1 andP ≥ 20 atm are closely approximated by the expression(Z 2 – 1)U0 = const, in agreement with the abovedependence. At α < 1 and P < 20 atm and also at α > 1,the experimental data are described by the expression

(Z 2 – 1) = const (Fig. 4).

2.5. Effect of the Catalyst Concentration

To examine the dependence of Z on the burningrate of the uncatalyzed system U0, we studied the influ�ence of the catalyst concentration Cc for the 80 : 20 wt %AP–FB system at pressures from 30 to 100 atm. Theconcentration of colloidal iron was varied from 0.1 to10.0 wt %. It was established that the catalyst contentin the system produces no effect of the character of theZ(U0) dependence—only the absolute value of Z

1 Why this coordinates were chosen is discussed below.

U02

1009080706050403020

U0, mm/s10

987654

3

2

1

Z

Fig. 2. Dependence Z(U0) at 20 ≤ P ≤ 500 atm, 2400 ≤ S0 ≤ 6500 cm2/g, 1.86 ≤ Cоx/Cf ≤ 4.0; 5 ≤ Al ≤ 15 wt % for AP–FB mixturecontaining 1 wt % Fe.



changes, which is described by the dependence Z =

K , where 16 ≤ U0 ≤ 35 mm/s. That theparameter Z only slightly depends on Cc was reportedpreviously. Thus, the catalyst concentration affects the

factor K, which depends on it as K = A0 (A0 is a

constant). The choice of (Z2 – 1) as a variable wasmotivated by the following considerations. Accordingto the Zel’dovich theory [4], the squared burning rate

U0 linearly depends on the heat release rate , i.e.,

U0 ~ (A0 )1/2. Assuming the catalyst additive changesthe heat release rate, the burning rate for the catalyzed

system can be presented as Uc ~ [A0( + Δ)], where Δis the increase in the heat release rate, we can write

whence (Z 2 – 1) ~ Δ/ . If Δ is independent of f (U0),then

(Z 2 – 1) ~ Ai,

if it is, then

(Z 2 – 1) ~ Bi.

As can be seen, in the logarithmic coordinates, the(Z 2 – 1) versus U0 dependence should be linear, as isthe case with processing the experimental data. The

experimentally measured (Z 2 – 1) ~ Bi dependenceshows that the burning rate is the parameter thatlargely determines the efficiency of a catalytic addi�tive, with the value of U0 at which the catalytic effectdisappears depends on the natures of fuel and catalyst.

U00.14– Cc

0.09

Cc0.09

Φ· 0

Φ· 0

Φ· 0

Z2 Uc/U0( ) 1 ΔA0/U02,+= =

U02

U02

U0m

U0m

3. EFFECT OF ULTRADISPERSED AP AND FP AND MBDC CATALYSTS

We examined how effective the introduction ofUDAP (~1 μm�grained) in combination with FP is inweakening the dependence of the burning rate U onthe pressure P. The content of UDAP was variedfrom 30 to 38 wt %, 2700�cm2/g AP fraction from 0to 15 wt %, and D�160 fraction (–160 + 315 μm) from31 to 40 wt %. The catalysts were FP (0.6 to 1.2 wt %),at the expense of FB and MBDC, a compound thatcombines the properties of such known promoters ascarboranes and ferrocenes [5, 6]. These compoundsare π complexes of dicarbollyl ion (the carborane corewithout one boron atom, C2B9H11) with transitionmetals (with partially filled shells) bound by coordina�tion bonds into sandwich structures, similar to fer�rocenes. The catalyst used in the present work,denoted as CF, has the composition Fe–DC–Cs–[(C2B9H11)Fe]Cs. A selection of data is given in Table2, which shows that the introduction of a significantamount of UDAP or FP catalyst forms a system with apressure exponent of ν ≤ 0.35.

4. EFFECT OF THE FERROCENE PLASTICIZER FP CATALYST

The experiments were performed at 22–105 atmwith formulations characterized by the followingparameters:

X1 is the content of the AP fraction with Ssc =8000 cm2/s, 15–35 wt %;


X3 is the content of the AP fraction with d = –160 +315 cm2/s, 15–35 wt %;

10

1

80

0.280706050403020987654

10 U0, mm/s

1

23

Z 2–1

3

Fig. 3. The (Z 2 – 1) versus U0 dependence for AP�basedmixtures at α < 1 and P ≥ 20 atm: (1) PMMA, (2) FB, and(3) PS.

1

80

0.12

42

3

Z 2–1

5

1

3 4 5 6 7 8 910

20U0, mm/s

Fig. 4. The (Z 2 – 1) versus U0 dependence for AP�basedmixtures: (1) PMMA and PS at 100 atm, (2) PMMA at40 atm (α > 1), (3) PMMA at 10 atm (α < 1), (4) PMMAat 10 atm (α > 1), and (5) PS at 10 atm (α < 1).

930


CHUIKO, SOKOLOVSKII

X4 is the content of the FP catalyst, 0–2.5 wt %(introduced at the expense of FB).

The statistical model of the combustion of this pro�pellant, constructed based on 57 experimental points,can be presented as

(1)

The accuracy and mean deviations were 0.985 and0.44 mm/s, respectively. To analyze the model, weused the following definitions and constrains:

(2)

For ∂U/∂P, the statistical model yields

(3)

Combining (1) and (2) gives

(4)

An analysis of expression (4) shows that the effect ofFP is equally determined by the contents of themedium and fine AP fractions.

U mm/s[ ] 3.3 10 3–× X1P 6.78 10 3–× X22–=

+ 0.149X2X4 2.08 10 3–× X2P+

– 8.98 10 3–× X32 0.162X3X4 1.324X4

2– 11.61.+ +

ν P/U( )∂U/∂P, X4 2.5,≤=

X1 X2 X3+ + 65;=

∂U/∂P 3.3X1 2.08X2+( ) 10 3–× .=

U 70 аtm( ) 25.66 0.085X2 0.231X3+( )[–=

+ 6.78X22 8.98X3

2+( ) 10 3–×[ ]

+ X4 0.149X2 0.162X3 1.324X4–+( ).

5. INTRODUCTION OF A COMBUSTION INHIBITOR

The inhibitor was a SC powder with a particle sizeof ~1–2 μm and colloidal CSC with a particle size of~60 Å. These inhibitors were introduced into a systemcomposed of 84 wt % UDAP and 16 wt % FB (poly�urethane). The tests were performed at pressures of 20to 120 atm, temperatures of 20 to 120°С, and inhibitorconcentrations of Cin = 0–5 wt %.

Based on the data obtained, we constructed statis�tical models (not presented in the text), we demon�strated that the maximum inhibiting effect is achievedat ~2 wt % inhibitor. Since the burning rate decreasessubstantially, the pressure exponent ν and temperaturesensitivity coefficient β increases with the CSC con�tent. A comparison of these data with those for cata�lyzed CSP revealed a sharp decrease in the values of∂U/∂P (tenfold) and ∂U/∂T0 (two� to threefold).Under the conditions we used, the values of ν arenearly identical, whereas those of β higher by a factorof 2–3, which can be accounted for by a decreasedburning rate. These results led us to the following con�clusions:

(1) The SC and CSC inhibitors produce no effecton the ∂U/∂T0 derivative, water�soluble the FP cata�lyst increases it substantially. This means that the tem�perature sensitivity coefficient β for the inhibited sys�tems increases due to a decrease in U0.

(2) An analysis of the influence of CSC on the∂U/∂P derivative shows that it decreases with increas�ing Cin (see below, statistical model (5)), a a behaviorthat makes it possible to decrease the exponent ν byintroducing an optimal amount of inhibitor.

(3) A comparison of the SC and CSC inhibitorsrevealed that the inhibition efficiency of the latter issubstantially higher: ∂U/∂P decreases about 1.5�fold,∂U/∂T0 nearly twofold (~25% decrease in β), leadingto a decrease in the combined parameter π = β/(1 – ν)by a factor of ~1.5. At small concentrations of SC(0.1–0.2 wt %) β is observed to decrease.

Thus, for the propellant formulation studied, theperformance of CSC as a regulator of ballistic proper�ties (burning rate and exponent ν) is preferrable. Note,however, that the value of β for the CSC�inhibited sys�

Table 1. Characteristics of colloidal metals

Metal % Pure metal Specific surfacearea, m2/g

Сu 86.4 50

Fe 84.4 80

Ni 61.8 70

Со 75.4 60

Table 2. Effect of combustion catalysts on the characteristics of CSPs containing UDAP

Oxidizer composition, wt % Catalyst, wt % U, mm/sν

UDAP 2700 cm2/g D16 CF FP P = 43 atm P = 74 atm P = 105 atm

38 20.5 10 – 0.55 14.4 18.5 17.3 0.29

38 25.5 5 – 0.50 – 16.4 16.8 0.34

34 19.5 5 – 0.50 13.4 17.3 19.1 0.41

30 33.5 5 1 0.58 16.9 19.3 22.1 0.32

30 33.5 5 – 0.60 11.1 11.9 13.0 0.28



tem is higher than that for the SC�inhibited systemand for the uninhibited (reference) system.

6. JOINT INTRODUCTION OF SC AND FP

Preliminary experiments showed that SC introduc�tion decreases the exponent ν, mainly due to reducingthe burning rate at high pressures. An analysis of vari�ous systems led us to conclude that SC acts via heatabsorption due to its decomposition in the gas phase at~1500°С, a process that decreases the heat flux fromthe gas phase into the condensed phase, therebydecreasing the burning rate. At low pressures, the hightemperature required for SC to decompose is attainedat larger distances from the burning surface than thosecharacteristic of high pressures, a factor that modifiesthe U(P) curve as described above. At the same time,the introduction of FP in significant amounts,required to increase the burning rate of the system,results in an increase in the exponent ν to 0.4–0.5.This occurs mainly due to an increase in the burningrate at high pressures. The FP catalyst is presumablyacts at relatively low temperatures, near or inside thecondensed phase. The joint introduction of SC and FPin the case they act independently (in different zones)offers a promising method for controlling the burningrate and the pressure exponent ν. To determine thecharacteristics of their joint action, we performedexperiments according to an active design at pressuresof 20 to 100 atm with formulations characterized bythe following parameters:



X3 is the content of the FP catalyst, 0.4–1.0 wt %(introduced at the expense of FB);

X4 is the content of the SC inhibitor (introduced atthe expense of the coarse AP fraction);

X5 is the content of the D�160 AP fraction.In all cases, X1 + X2 + X5 = 65 wt %.The experimental data for formulations with a high

FP content (≥2.0 wt %) were excluded from consider�ation. The statistical model based on the remaining 93points can be presented as

(5)

The accuracy of the model, mean deviation, andrelative variance in the burning rate were found to be0.983, 0.42 mm/s, and 2.7%. The ∂U/∂P derivativedepends on the composition as

(6)

U mm/s[ ] 0.664X5– 4.82X4 0.23P 0.025X1X2–+ +=

– 0.169X1X5 7.13 103× X2X3 0.227X2X5+–

– 1.1 10 3–× X3P 0.71X42– 6.72 10 3–× X4P 30.7.–+

∂U/∂P 0.23 1.1 10 3–× X5 6.72 10 3–× X3+–=

– 0.054X4 1.4– 10 3–× P.

As can be seen from (6), at P = const, the value of∂U/∂P decreases with increasing contents of SC andcoarse fraction, but increases with the FP content.Note also that the negative coefficient at X4 is verylarge (Eq. (5)). The efficiency of introduction of thisinhibitor per 1 wt % is 50 times higher than that ofcoarse AP (X5); i.e., SC very effectively decreases boththe burning rate and the derivative ∂U/∂P.

The burning rate can be readily increased by intro�ducing ~35–40 wt % of fine AP. The introduction ofthe medium fraction is not recommended, since itcauses an increase in the pressure exponent ν. Theintroduction of SC is optional, but it weakens thedependence of U on P. The statistical model alsodescribes the effect of FP, the catalyst�plasticizer.According to (6), the derivative ∂U/∂P, increases withthe catalyst content X3. The burning rate (Eq. (5))passes through a maximum at

which yield X3 = 3.78 wt % at 100 atm. Consequently,at FP concentrations above 3.8 wt %, the burning rateU(100 аtm) begins to decrease. The maximum of ν isachieved X3 = 0.6 wt % (P = 100 atm, X2 = X4 = 0, andX5 = 45 wt %) and νmin = 0.145 at U(100 аtm) =44.5 mm/s. This results is consistent the conclusionthat only small concentrations of the catalyst are use�ful in decreasing the pressure exponent ν.

7. JOINT INTRODUCTION OF FPAND LITHIUM FLUORIDE

A lithium fluoride powder with Ssc ~ 2 m2/g wasintroduced (0.2–1.0 wt %) in the same manner as SC.The experimental design was also the same as for con�structing statistical model (5), except that the contentof coarse AP fraction was not varied. Processing theexperimental data, 59 points, gave the following statis�tical model

(7)

The variables wereX1 is the content of the AP fraction with Ssc =

8000 cm2/g, 35–45 wt % (fraction D�160, 20–40 wt %;the rest of a total of 65 wt % falls on the Ssc =2700 cm2/g fraction);

X2 is the content of the FP catalyst, 0.6–1.2 wt %;X3 is the content of the LiF inhibitor, 0.6–1.6 wt %;P = 20–120 atm.The accuracy of the model, mean deviation, and

relative variance in the burning rate were found to be0.974, 0.38 mm/s, and 2.6%.

An analysis of model (7) showed that the use of LiFinstead of strontium carbonate is disadvantageous: to

∂U/∂X3 4.82 1.42X3– 6.72 10 3–× P+ 0,= =

U mm/s[ ] 7.59 9.04X3– 0.2P –=

+ 1.09 10 3–× X12 1.527X2

2 6.04X32 + +

– 0.0746X3P 5.27 10 4–× P2.–

932


CHUIKO, SOKOLOVSKII

obtain low values of ν, it is necessary to introduce largeamounts of FP, LiF, and fine AP. At concentrations ofFP ≤ 1.2 wt % and LiF ~ 0.8 wt %, only eight acceptablecompositions were identified, which however containlarge concentrations of fine AP (35 wt %). As previously,the presence of the medium AP fraction, with Ssc=2700 cm2/g, in the composition is disadvantageous.

Thus, in comparison with SC, lithium fluoride is aless effective “partner” of the FP catalyst. Upon pass�ing from 40 to 100 atm and introducing 1 wt % SC,the derivative ∂U/∂P decreases generally ~1.2 timesmore significantly whereas the burning rate decreases~ 1.3 times less significantly than in the case of lithiumfluoride, yield more favorable values of the exponent ν(Table 4).

Let us consider the structure of the statistical mod�els of systems containing both a catalyst (FP) and aninhibitor. The joint addition of FP with SC or LiF, thedegree of influence of each of the inhibitors is inde�pendent of the content of additives. This results sup�ports the as that these components operate in differentzones of the combustion wave. That the SC inhibitor ismore effective in decreasing the exponent ν unequivo�cally suggests that it operates in the gas phase at a hightemperature (higher than that characteristic of LiF). If

the mechanism of action of the inhibitor is exclusivelythermal (associated with heat absorption by itsdecomposition), substances with a low decompositiontemperature must decrease the burning rate of CSPsalready at low pressures (low effective temperatures ofthe combustion wave) as effectively as they depends onat high pressures. Therefore, one should expect rathera steepening of the U(P) dependence and a decrease inthe burning rate upon introduction of such an addi�tive, especially if it is not too fine (have no time to heatup and decompose at high burning rates). An exampleis ammonium sulfate. Clearly, the notions of the “low”and “high” temperature of the endothermic decom�position of an additive have no sense without takinginto account the structure of the combustion zones:for example, a low�temperature�decomposition addi�tive can become a high�temperature�decompositionadditive upon oxidizer replacement and vice versa.

8. RESULTS AND DISCUSSION

8.1. On Some General Regularities of he Catalysis of Composite Propellants

Studies of the changes in the combustion charac�teristics, structure of the combustion zones and their

Table 3. Calculated burning rateû of CSPs containing FP and SC

AP, wt % Additives U, mm/s

8000 cm2/g 2700 cm2/g D16 FP SC 20* 40* 60* 80* 100* 120*

35 5 25 0.4 0.5 11.5 14.2 16.4 18.0 19.0 19.5

35 10 20 0.6 0.5 11.4 14.3 16.5 18.3 19.4 20.1

35 10 20 0.7 0.5 11.8 14.7 17.0 18.7 19.9 20.5

35 0 30 0.4 0.6 12.1 14.6 16.5 17.9 18.7 19.0

30 0 35 0.4 0.2 11.6 14.5 16.7 18.4 19.6 20.1

30 0 35 0.4 0.3 11.0 13.7 15.9 17.5 18.5 19.0

35 0 30 0.6 0 17.9 21.1 23.8 25.9 27.4 28.3

40 10 15 1.0 0 19.0 22.1 24.7 26.7 28.2 29.1

* The pressure in atm.

Table 4. Calculated combustion characteristics at 70 atm of CSPs containing FP and LiF

AP, wt % FP,wt %

LiF,wt %

U(70 atm),mm/s ν(70 atm)

8000 cm2/g 2700 cm2/g D16

35 15 15 1.4 0.6 17.0 0.34

35 15 15 1.5 0.6 17.4 0.33

35 15 15 1.5 0.7 16.8 0.31

40 10 15 1.5 0.8 16.7 0.28

40 10 15 1.5 0.6 17.8 0.32

45 5 15 1.2 0.6 17.0 0.33

50 0 15 1.3 0.8 16.8 0.28



parameters produced by small additives of certaincompounds can help to gain insights into the mecha�nisms of the fundamental processes involved in com�bustion. Limitations of the available experimentalmethods represent the main obstacle for the realiza�tion of this approach. At the same time, the develop�ment of the theory of the catalysis of composite pro�pellant should rely on experiment. Therefore, it seemsuseful to recapitulate the main regularities that can beused in constructing theoretical models. The aboveanalysis showed that:

(1) There exists no universal mechanism of actionof small additives to composite propellants.

(2) The efficiency of action of the iron�containingcatalyst on the reactions in a oxidizer–fuel systemdecreases with increasing the burning rate of theuncatalyzed system, irrespective of how it wasincreased.

(3) The dependence of the efficiency Z on the cat�

alyst concentration can be presented as Z ~ , with ntypically ranging within 0.10–0.18. In some cases, n =0.2–0.3, which can be attributed to the fact that, whenintroduced in large concentration, some catalysts (forexample, ferrocene oil, etc.) operate as a fuel as well.

(4) The most convincing data on the effect of cata�lyst were obtained in studies performed at theSemenov Institute of Chemical Physics of the RussianAcademy of Sciences. These studies, in which spheri�cal aerosol metal particles were introduced in a num�

ber of composite system, demonstrated that Z ~ (m = 0.04–0.10). None of the systems showed valuesof m ~ 0.5, which might be expected based on predic�tions of heterogeneous catalysis theory. At Z valuesappreciably larger than unity, 1.2–1.8, the effect of thesize of particles of a highly dispersed catalyst turnedout to be relatively weak. Of the interfering factors, itis worthwhile to mention the lumping of catalyst par�ticles, their agglomeration in the course of combus�tion, and accumulation of catalyst on the burning sur�face (under unfavorable conditions). Note, however,that the changeover from powdery to liquid catalystsgives no noticeable effect: only a 10 to 20% change inZ. Thus, this dependence can be considered as auxil�iary, but the fact that the theory predicts a strongdependence of Z on d causes a concern.

(5) Generally, a catalyst acts on all zone of thecombustion wave; therefore, to test theories of purelygas�phase or condensed�phase catalysis, it is necessaryto select special model formulations or to take intoaccount the real situation.

(6) As follows from the experimental data, whenexamining the effect of iron�containing catalysts, it isnecessary to identify catalytically active sites and spe�cies. In the reactive zones of the combustion wave,iron�containing catalyst produce Fe, FeO, Fe2O3, spe�cies that operate in combustion wave zones withproper conditions for redox reactions with cyclic

Ccn

dcm–

regeneration of Fe, Fe2O3, FeO. Moreover, experi�mental results show that, when only Fe and Fе2O3 areformed, the catalyst turns out to be ineffective, sincefor the catalytic process to proceed, it is necessary toreduce Fe2O3 to FeO, i.e., to form FeO. Observationsdetected Fe, FeO, and Fе2O3 in the combustion wavezones. When an iron�containing catalyst was added toNM, no FeO in the flame was observed and, as conse�quence, no catalysis. No catalysis was observed as wellfor potassium perchlorate doped with Fе2O3, which isquite expected since the flame spectrum featured onlyFe atom lines.

8.2. Maximum Catalytic Efficiency

The results of the present work make it possible toestimate the utmost efficiency of catalyzing AP�basedcomposite formulations with colloidal metals. A cata�lyst can act in three ways: (1) make the U(P) depen�dence steeper, thereby increasing ν, (2) make ν smaller(as in the case under consideration), or produce noeffect on ν.

This means that, in the first case, the catalyst effi�ciency Z enhances with increasing U0; in the secondcase, it decreases, whereas remains unchanged in thethird. Generally, all the indicated modes of action ofthe catalyst can be realized for one particular system,since the behavior of the Z(P) dependence changeswith pressure, as in the case of catalyzed AP deflagra�tion. It was demonstrated [3] that, under certainassumptions regarding the mechanism of action of thecatalyst, the introduction of a catalyst makes the pres�sure exponent ν tend to 0.5: if before catalyst introduc�tion, ν0 > 0.5 or ν0 < 0.5, the after ν is brought closer to0.5. That this is only a special case follows from thefact that there are catalysts capable of weakening theU(P) dependence so that ν will be substantially smallerthan 0.5, for example, in the case of double�base pro�pellants. The system studied in the present work (AP–FB) is characterized by ν0 > 0.5 and νc 0.5, inagreement with theoretical predictions. An example ofa strengthening of the U(P) dependence is the AP–FB

system doped with Fe2O3: Z = 0.58 .

An analysis of the data on the catalysis of combus�tion of the AP–FB–D16 (carborane plasticizer) sys�tem (with a high burning rate) by colloidal iron showsthat the efficiency of the catalyst in this case also rap�idly decreases with increasing U0. For example, U0 =45 mm/s, Z = 1.04. At U0 = 100 mm/s, the burningrate rise is expected to be less than 5%; the effect dis�appears completely at U0 ~ 120–140 mm/s (Z ~ 1).Given that the curves in Fig. 5 are of general character(i.e., all the possibilities for increasing U0 except for itsdependence of the initial temperature were used), weacknowledge that, with the ingredients used, it is prac�tically impossible to influence the burning rate at U0 ≥100 mm/s by introducing metal catalysts. Because of aweak Z(Cc) dependence, it is impractical to increase Cc

U00.65

934


CHUIKO, SOKOLOVSKII

On the other hand, for systems with polyacetylenefuel, the same catalyst (1 wt % colloid iron) at thesame initial burning rate U0 = 41 mm/s, yields Z =1.27, a value higher than that for the given system(Z = 1.2) and for the FB–D16 system (Z = 1.04).This example shows that the utmost burning rate U0at which the catalytic effect is still possible isstrongly dependent on the nature of the propellantingredients.

Based on the results of this part of the work, wewould like to emphasize once more that there is no asingle, universal mechanism of action of small addi�tives on the combustion of composite propellants. Letus illustrate this conclusion with the help of Fig. 5.

Let the initial system be an oxidizer–fuel mixture,which is characterized by a classical domelike U(α)dependence. Upon introduction of a small additivethe Z(α) dependence may exhibit three types of behav�ior (Fig. 5): for AP–PMMA and AP–PS mixturesdoped with Fе2O3, the Z(α) dependence correspondsto curve 1 (Bakhman et al.); for AP–butyl–ferrocenemixtures, the Z(α) dependence also corresponds tocurve 1; the behavior of Z for AP–butyl– Fe2O3 mix�tures is represented by curve 2; the behavior of Z forAP–butyl–СuOCr2O3 mixtures is represented bycurve 3 (Egorov et al.); whereas the Z(α) dependencefor AP–FB–Fe system is similar to curve 1.

These examples show (a) that the same additives indifferent systems catalyze different processes and (b)that different additives in the same system affect dif�ferent transformations. The effect of the additive isalso different. In the case represented by curve 1, theburning rates of catalyzed mixtures are always lowerthan the maximum value U for uncatalyzed mixtureattained by varying α; if the behavior represented by

curve 2 is realized, the burning rates of catalyzed mix�tures can substantially exceed the maximum burningrate of the uncatalyzed mixture.

Dependences symbolized by curve 1 are typical ofmixtures in which the interaction between the ingredi�ents is catalyzed. At an optimal composition and thecorresponding conditions of combustion, such mix�tures need not to be catalyzed at all. All possible andthermodynamically most effective processes proceedcompletely and at the maximum rate, with the highestpossible temperature being achieved.

Dependences typified by curve 2 are characteristicof the catalysis of transformations of one of the com�ponents, for example, oxidizer decomposition.

Curve 3 represents situations where a given catalystacts only at high temperatures or in the presence ofcertain reactants, behaving as an inert componentotherwise.

The above analysis suggests that, in the mixturestudied (AP–FB–iron�containing catalyst), the cata�lyst acts on the interaction between the fuel and oxi�dizer, so that the pressure exponent ν decreases, themost important case for practice. The experimen�tally established regularities are interesting in thatrespect that the efficiency of the catalyst decreaseswith increasing initial burning rate of the mixture as

(Z 2 – 1) ≈ const irrespective of how this initialburning rate was achieved, with s = 1 at α < 1 and highpressures and s = 2 at α > 1 and low pressures.

CONCLUSIONS

(1) The experimental results show that there existno a single mechanism of action of small additives onthe combustion of composite systems, and, therefore,no universal theory of this phenomenon can be pro�posed.

(2) The efficiency of colloidal iron�containing cat�alysts acting on the reaction between oxidizer and fueldecreases with increasing initial burning rate of the

mixture as (Z – 1) = const irrespective of the meansby which this initial burning rate was achieved, withs = 1 at α < 1 and high pressures and s = 2 at α > 1 andlow pressures.

(3) A wide variety of possibilities of controlling theburning rate law of composite solid propellants isoffered by the joint introduction of a catalyst andinhibitor into the system, where the catalyst largelydetermines the burning rate whereas the inhibitor gov�erns the pressure exponent.

(4) The strontium carbonate catalyst acts in thegas phase at high temperatures (~1500°С), whichmake it advantageous to use it in combination with

U0s

U0s

1

2

3

1

1 α

Z = Uc/U0

Fig. 5. Various types of Z(α) dependence at constant pres�sure (for details, see the text).



catalysts having relatively low decomposition tem�peratures.

REFERENCES

1. I. G. Zedgenidze, Experimental Design in Studies ofMulticomponent Systems (Nauka, Moscow, 1976) [inRussian].

2. S. V. Chuiko, F. S. Sokolovskii, and G. V. Nechai,Khim. Fiz. 16 (2), 54 (1997).

3. A. F. Belyaev and N. N. Bakhman, Combustion of Het�erogeneous Condensed Systems (Nauka, Moscow, 1967)[in Russian].

4. Ya. B. Zel’dovich, Theory of Combustion of Powders andExplosives (Nauka, Moscow, 1982) [in Russian].

5. R. Grimes, Carboranes (Academic, New York, 1970;Mir, Moscow, 1974).

6. M. F. Hawthorne, Acc. Chem. Res. 1, 281 (1968).

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Effect of small additives on the combustion of composite solid propellants