4L
Selected plastics and elastomers c a n be used in rockets. Extremes of physical and chemical needs eliminate others. These are the rules governing selection and a few actively being considered
r7
b I
Chemical Princi T,,
SUCCESSFUL FIRING of a solid rocket motor for a controlled duration culminates a series of accomplishments. These are emphasized by considering the costly and violent failures which they prevent. ‘There must be no ignition delay, and the ignited propellant must not blow u p nor throw sudden shock loads on the vehicle structure or t h e payload. Regular burning depends upon preventing both the exposure of excess areas to the flame front and resonant burning. T o forestall grave accidents, it is necessary to prevent every single faulty operation or negligence, in a long series of preparatory steps. I t follows that all the tasks from formulation to firing must be executed with nothing less than complete success. A knowledge of all underlying chemical principles of solid propellants is essential.
Thermochemistry
Criteria of Performance. The best single criterion of the propulsive capability of a rocket is probablv the boost velocity, ub:
where u is effective exhaust velocity of product gases; M,, mass of unburned propellant; and Mi,Tmass of inert parts, including payload. This equation was derived for ideal conditions, neglecting the effect of gravity and air drag and assuming a start from rest. For evaIuating propellants, intensive properties of the propellant should be separated from the terms characteristic of the rocket dimensions, incrt parts, and other extensive properties. Equation 1 becomes
754
INDUSTRIAL AND ENGINEERING CHEMISTRY
I
ELI MISHUCK and
L. T.
CARLETON
Aerojet-General Corp., Azusa, Calif.
Propellants Manufacture and use of solid propellants is regulated by definite chemical principles-thermochemistry, rheology, polymerization, mechanical properties, aging, and combustion where I, is specific impulse of propellant ( v / g ) ; V,, the volume of propellant; p , its density; g, gravitational acceleration; and B = V,,/Mi. I n some cases B is independent of propellant properties; in others it may depend on p and I,. I n any case, Equation 2 rates rocket motors in terms of the intensive propellant properties, I, and p . For present-day systems, values of I. from 200 to 300 lbf.-sec.-lbm.-l are of interest, with the propellant accounting for 50 to 95% of the total weight of the rocket. I, depends on th.ermochemica1 factors, and p on other physicochemical factors. At the high propellant mass fractions often employed, Z, becomes more important. In practice, propellants giving good values of U b have been developed usually by systematically improving I, while at the same time keeping the density relatively unchanged. T h e connection between the exhaust velocity or specific impulse and the thermochemical nature of the propellant material is shown directly by an additional equation. Isentropic expansion of a heated gas at pressure PI, through a converging-diverging nozzle to the environmental pressure, p 2 , gives u =
gl, =
Here J is the mechanical equivalent of heat; the average molecular specific heat; M , the average molecular weight of exhaust gas; and R, the gas constant. Because of compensating effects, Ia becomes virtually proportional to for common exhaust gases. To calculate Z, for propellants, this simple form cannot be used, but must be replaced by expressions which take account of shifts of equilibria among the exhaust gases during expansion. The chamber temperature, T,, is determined by equating Q (heat of reaction of the propellant at ambient temperature, To) to the heat required to raise the temperature of the product gases from To to To. In formulating new propellants, specific impulses are predicted by solving the equation for v and the heat-balance equation, using known or estimated values of Q, Cp’s, M, and k . The actual specific impulse measured in rocket motors is
cp,
d m
usually 9501, (or more) of that predicted when these values are accurately known. Gas decomposition must be considered for high-performance propellants giving high chamber temperatures. The watergas reaction, which takes place to some extent even at moderate chamber temperature, does not greatly influence performance because it produces a negligible heat of reaction and no net change in molecular weight. However, several product gasese.g., Hz,02-decompose appreciably above 3000’ K., with the consumption of large amounts of heat. The effect of these decompositions is to make a portion of Q in the heat balance unavailable for heating.
Elements Suitable for Propellants. The requirement of low M restricts the choice of solid-propellant components to those containing elements of low atomic weight. Moreover, low-atomic-Wright elements frequently yield greater heat in a particular reaction than d o higher members of the same atomic group. I n another sense, the need for a large Q requires large differences in heats of formation between reactants and products. Formulation. Fortunately, many reactants which satisfy these criteria of performance contain carbon, hydrogen, oxygen, and nitrogen. Since these elements are the basis of organic chemistry and also of polymer chemistry, they provide many other qualities essential to the successful processing and use of solid propellants. T h e modern solid propellant is typically a continuous-binder fuel enclosing particles of oxidizer and other solids. Additional components may include plasticizers, catalysts, antioxidants, and other additives. Some examples of satisfactory binders are polyesters cured by cross linking for rigid propellants, and various types of rubbers used for elastomeric propellants. T h e requirement of maximum performance creates a special problem in
composite propellants. Although solid propellants are normally somewhat fuelrich, the allowable excess fuel is limited by requirements of high heat of reaction, and complete conversion into product gases. T h e properties of some important oxidizers and the amounts needed for the complete oxidation of a typical fuel with the assumed structure CzH40 and density 1.O gram per ml. are : Melting Density, Oxidizer G. M1.-1 NHaNOj KC104 NH4C104
1.73 2.52 1.95
Temp., O
C.
Amount t o Burn CLH4O Wt. 70V01.7~
170 -600 d(~22O)
90 78 84
84
61 73
Special efforts are needed to attain high loadings without sacrificing fluidity in mixing or even creating discontinuities in the binder. Commonly two or more oxidizer grinds are employed to decrease voids. Many other factors must be considered in the selection of a n oxidizer for a particular application, including hygroscopicity, occurrence of polymorphic phase transitions, solubility in binders, and thermal stability.
Rheology of Uncured Propellant Suspensions Rheological properties are important in the mixing and processing of uncured propellant suspensions and in their eventual forming into solid grains. Problems encountered depend on the kind of propellant considered : polymerizable, castable-e.g., polysulfide/NH4C104; nonpolymerizable, castable, gel-type (cast double base) ; and vulcanizable, noncastable (rubber/ NHjNOs). Polymerizable, castable systems are favored for large, present-day, solidVOL. 52, NO. 9
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SEPTEMBER 1960
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Figure 1. Consistency curves of typical uncured composite propellants, illustrating
-I Y
i
A. Thixotropic breakdown
Ew
B. Yield stress C. Dilatancy (in portion)
m
LL 0
lower
w
t
C Y
SHEARINGSTRESS,
F: OYNE
CM-~
propellant grains. Mixing is easier than for noncastable systems, lighter equipment is required, and processing operations generally are simpler. Moreover, case-bonded designs require cast-in-case propellants. Castable, polymerizable propellants offer a greater versatility in the selection of polymerizable monomers as compared to the limited number of polymers suitable for castable gels. Curing temperatures are lower. However, in either case, the requirement for castability imposes many restrictions on selection of components. T h e processing of large volumes of castable propellant requires understanding and control of basic rheological behavior. Settling of suspended solids before curing must be negligible. O n the other hand, the casting must be sufficiently fluid to allow the escape of trapped bubbles, and to assume the shape of the container. The mixing and casting and the transfer of fluids generally require a knowledge of possible variations of viscosity with shearing stress-Le., whether or not Newtonian behavior is maintained. I t is necessary to know how the viscosity of a homogeneous liquid is modified by high loading with suspended solids. Interfacial conditions are critical. All of these effects must be formulated quantitatively and correlated with practical experience. Sedimentation. T h e sedimentation of solids is relatively well understood, for nonflocculated nonagglomerated systems. For example, Steinour (70) adapted Stokes' law to suspensions containing finite concentrations of solids by introducing correction terms for particle size, shape, and concentration. This modification has been applied successfully to a variety of slurries besides solid propellants. Fluidity of a Simplified Model System. T h e viscosity of propellant slurries is a problem of much greater complexity. A Couette-type rotational viscosimeter was developed specifically for these investigations, and has proved
756
generally useful. The viscosimeter determines a consistency curve, relating the rate of shear to the shearing stress Fluidities (reciprocal viscosities) are instantaneous slopes of the curve. Sweeny and Geckler (73) initiated this study by investigating a simplified model, consisting of concentrated suspensions of glass spheres in nonreactive liquids of the same density. Although the media were Newtonian fluids, even these simple slurries followed complex, non-Newtonian behavior. The authors succeeded in relating viscosity quantitatively to solids loading for beads of single size. Sweeny ( 7 7 ) further explored the effect of bead size and size distribution. Fluidity of Uncured Propellants. T h e greater complexity of actual propellants results from many additional factors. Solids of many different shapes, sizes, and chemical compositions are present. Sedimentation, interfacial effects, flocculation-deflocculation effects, chemical reactions, polymerizations, and solubilities must also be considered, and innumerable interactions are possible. I t has not been possible to develop a comprehensive theory which takes account of all these factors, and it is still necessary to rely on systematic empirical observations and good engineering judgment. Using the rotational viscosimeter, Sweeny (12) studied the rheological effects of crystalline inorganic oxidizers in Aeroplex propellants containing uncured polyester-styrene binder. Binders of this class in the presence of a n inhib-
INDUSTRIAL AND ENGINEERING CHEMISTRY
itor are simple, unchanging Newtonian liquids Oxidizer is customarily added in a blend of two or more grinds. to give a maximum loading of solids having a broad, complex distribution of particle sizes with diameters ranging from 1 to 200 microns. A typical consistency curve for a complete propellant formulation (Figure 1,A) shows clearly the non-Kewtonian behavior introduced by the presence of 7570 of oxidizer, T h e area enclosed by the ascending and descending curves, extended to some standard rate of shear, is defined as the extent of thixotropic breakdown and forms a useful parameter for correlation. Increasing the oxidizer content of this propellant by 3% sharply increases viscosity and extent of thixotropic breakdown. A high oxidizer content may also give a finite yield stress, which must be overcome before the mixture will shear. Yield stress appears as a positive intercept on the stress axis for the descending curve, (Figure l$). On the other hand, a large fraction of very finely-ground oxidizer may produce dilatancy at low rates of shear, marked by a downward concavity (Figure 1,C). Interfacial effects substantially influence rheological behavior, and surface-active agents--e.g., sodium lauryl sulfate-provide an indispensable means of controlling castability. Moisture control is also very important in view of the hydrophilic character of the oxidizer particles. Plant experience showed that even small amounts of moisture made many propellant formulations uncastable. T h e opposing effects of water and of a surface-active agent on the thixotropic breakdown of Aeroplex propellants are illustrated in table below. I n a chemically different propellant system, 0.27, of the same surface-active agent reduced by nearly 307, the amount of liquid fuel needed to form a castable mix with oxidizer. Additions of water and surface-active agents to fluid binder alone usually produce no changes. A theory of surface activity in propellant suspensions remains to be worked out, but it must certainly take into account many factors, including solubility, wetting, de-wetting, agglomeration, and chemical interactions. Moreover, the activity of most surface-active agents is not confined to regulating castability, but also influences the subThixotropic Breakdown,
Propellant A
B
Additive, % 0 0.08 HzO 0 0.02 agent 0.05 agent 0.15 agent
Initial Fluidity, Poise-' 0.0060 0.0006 0.0057 0.0160 0.0085 0.0014
Dyne C m . 7 S e c . -1
130 3950 590 100
100 0
Castability V e r y good
No
... ... ... ...
P L A S T I C S A N D ELASTOMERS I N R O C K E T S
These are the criteria for selecting binder ingredients and the method of cure Bulk-polymerized castable propellants should have low viscosity for castability but without sedimentation of solids, no split-out products
b b b b b
have ample pot life have low exotherm heats have sufficient reaciivity for complete low-temperature cure exhibit low shrinkage for case bonding exhibit late getation for case binding
sequent behavior of a propellant in curing and in mechanical tests on cured specimens.
Polymerization of Castable Propellants Requirements for Curing. After the selected constituents of the propellant have been mixed and cast, the individual grains are formed by bulk polymerization and/or curing. T h e necessary dimensional stability is imparted by polycrystallinity (as in a plastisol) or by chemical cross linking. Double-base and plastisol propellants will not be considered here. I n adopting a curing process for bulk-polymerized castable propellants, the following criteria must be satisfied : low viscosity for castability, but without sedimentation of solids; no split-out products; ample pot life; low exotherm heats; sufficient reactivity for a complete low-temperature cure; low shrinkage for case bonding; and late gelation for case bonding. These criteria have dictated the selection of binder ingredients and the methods of curing used at present, which compromise many conff icting demands. For example, with only low viscosity required, a good fuel binder would consist of styrene and methyl acrylate, or a mixture of low molecular weight comonomers for polycondensation, such as fi-phenylene diisocyanate and ethylene glycol. Polyesterification reactions are ruled out because they split out water. However, comonomers of low molecular weight, although very fluid, are intrinsically subject to high exothermal heat, A T , and high shrinkage, AV, on polymerization. Under adiabatic conditions, the maximum temperature rise on polymerizing methyl acrylate loaded with 75y0 inorganic oxidizer is about 200' C. T h e generation of such high temperatures is clearly undesirable. T h e net shrinkage of the same system is about 5%: too high for case-bonded applications A number of methods are generally employed for reducing A T and AV, including the use of monomers with
large inert residues ; long-chain prepolymers; high volume loadings of solid ingredients ; solids with hi& heat capacity, and control of polymerization conditions through the proper choice of catalyst and temperature. Although any or all of these methods may be utilized, the most practical approach invariably includes the selection of monomers with a minimum number of reacting groups per unit volume-e.g. long-chain prepolymers and monomers with large inert residues-because both A T and A V are roughly proportional to this number. By careful selection, fluidity may still be kept within a manageable range. Representative propellant binders include unsaturated polyesters cross-linked with styrene or other vinyl monomers, as well as cross-linked, long-chain polysulfides, and polyurethanes formed by the condensation of long-chain diols, diisocyanates, and polyfunctional crosslinking agents. T h e curing of any one type is influenced by many factors, including a number which are peculiar to itself, as the following example illustrates. Polymerization Kinetics, PolyesterStyrene Binders. Unsaturated polyesters mixed with styrene for cross linking exemplify a castable binder used in numerous free-standing (cartridgetype) grains of small and medium size. T h e polyester acts as a diluent for the shrinkage and exotherm effects which are almost entirely due to the styrene. Adequate pot life may be assured by adding inhibitor, which postpones the onset of polymerization, and the subsequent polymerization reaction is controlled by adding catalyst and accelerator. Temperature stages from 70' to 180' F. are utilized to complete the curing, to control exotherm gradients, and to minimize stresses. Another characteristic of this system is the rapid growth to a three-dimensional structure, so that gelation occurs a t any early stage of the polymerization. Detailed laboratory measurements were performed on the kinetics of the bulk polymerization of polyester-styrene binders. Most additives used in pro-
pellants were shown to affect the reaction to some extent, the ammonium perchlorate oxidizer being a n effective polymerization accelerator. Rates of polymerization were measured with specially designed dilatometers, and supplementary measurements of gel time were made with a pellet-dropping apparatus described by Billheimer and Parrette (7). At 24.8' C., binders containing peroxide catalyst and accelerator polymerized according to a zero-order mechanism for approximately one half of the reaction (Figure 2). T h e polymerization of styrene alone was first-order under the same conditions and was much slower. T h e initial zero-order behavior of the binder and the acceleration of polymerization after 5070 reaction were explained by Trommsdorf (74) as decreases in the rate of chain termination. Because gelation occurred near the end of the induction period, the gel time accurately measures the induction period. Minor changes in the chemical nature of the polyester and in the ratio of polyester to styrene altered the numerical parameters of the curves without affecting the basic pattern. T h e rate of polymerization was increased by simultaneously increasing the concentrations of catalyst and accelerator. Furthermore, certain inhibitors increased gel time in proportion to their content, without influencing the subsequent polymerization rate. Mathematically, the effect of a n inhibitor in increasing gel time to G from B, for inhibitor-free binder, may be expressed as a product of positive and negative powers of per cent concentrations of inhibitor ( I ) , catalyst (C), and accelerator ( A ) with the temperature dependence given by an Arrhenius expression. For one binder system containing 5oy0styrene,
G
- B(hr.)
= G
- 0.4 =
T h e agreement with experiment is very close. From measurements a t 24.6' to 40.8' C., the activation energy for the polymerization rate was calculated to be 15,000 cal. mole.-l Significantly, many ingredients which serve other functions in propellants are also effective accelerators, retarders, or inhibitors. A standard surface-active agent (casting aid) exhibited both inhibiting and retarding effects. O n e standard ballistic additive retarded and another inhibited the polymerization. However, the most pronounced effect on the propellant was due to the presence of the perchlorate oxidizer. Curing Kinetics for PolyesterStyrene Propellants. Propellants formulated with perchlorates and the VOL. 52, NO. 9
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SEPTEMBER 1960
757
n
8-
7-
PROPELLANT
6-
/
5-
/
1
4-
/
800
0
1600
functional condensation polymers and is a n important advantage, because only the shrinkage and exothermal heating which occur after gelation create lockedin stresses. Following the explanation of Flory (4),gelation is determined by the value of a branching coefficient, a , defined as the probability that any polymer chain will end in a branch unit rather than in a n unbranched terminal unit. For trifunctional branching, when Q = l/2 there is a n even chance that the structure will extend infinitely; this condition corresponds to the gel point. T h e coefficient is simply related to extent of reaction, p :
2400
(8).
TIME, MIN
Figure 2.
Typical curing curves at 24.8" C. The reciprocal of unreacted fraction of fuel binder i s plotted against time fuel binder described previously followed a curing mechanism different from that of the binders (Figure 2). T h e polymerization in the propellant w a s evidently first order. Typically, the gel time and polymerization rate were, respectively, '/le and 4 times those of its binder. Accelerator had little effect on the polymerization characteristics of the propellant. However, oxidizer in high concentrations behaved like a strong accelerator, presumably by adsorbing the catalyst and subsequently decomposing it into free radicals. Additional experiments demonstrated that the curing rate of the propellant was directly proportional to the surface area of the oxidizer. Increasing the catalyst concentration decreased the gel time: and increased the polymerization rate in proportion to the one-fourth root of the catalyst concentration. Inhibitor could be used to regulate the gel time of the propellant as well as of the binder, the time being nearly proportional to the inhibitor content. Polycondensation Polymer Binders and Propellants. Certain disadvantages of the systems discussed have led to adoption of binders cured by polycondensation reactions (without split-out products). Polyurethanes prepared from long-chain diols and diisocyanates, in combination with triisocyanates and triols, are representative. Condensation polymerizations difler in several ways from the free-radicalinitiated polymerizations discussed previously. A different reaction order is observed. There is no induction period (consumption of inhibitor), but a continuous, gradual thickening of the reaction mixture. Because gelation occurs relatively late in the reaction, pot life is determined by viscosity limitations. Gelation a t a relatively high extent of polymerization is characteristic of poly-
758
INDUSTRIAL
nature of the propellant? especially since one propellant may give both types of curves under different conditions of temperature or other factors. The work-torupture, determined by the area under the curve, indicates the toughness of the propellant, and appears to be an important characteristic property. Measurements over a range of temperatures are significant in defining safe conditions of storage and operation. Tensile properties of bonded systems, such as the propellant-to-metal or propellant-to-linerto-metal strength, provide additional useful information. It is also desirable to determine stress-strain curves at high rates of straining, because the resulting curves differ substantially from those obtained at moderate rates. A general viscoelastic correlation between maximum stress, or strain at maximum stress, rate of strain? and temperature !vas developed by Smith
where p,, and p , are the extents of reaction of monomers terminating in A and B functional groups, respectively, and p is the ratio of the A groups belonging to branch groups to the total number of A groups in the mixture. Under most practical conditions, Equation 5 gives Q! = high values of p a t gelation-e.g., p 2 , p = 0.717 for equimolar amounts of a triol and a diacid. When these characteristics of polycondensation reactions are combined with the advantages of using large molecules of prepolymers initially, to minimize shrinkage and exothermal heating, all the criteria for a satisfactory cure of case-bonded propellants are satisfied. Obviously, a careful selection of chemical types is necessary to give the proper viscosity and reactivity. However, by judicious compromises between many requirements, the successful curing of large propellant masses is assured.
M e c ha niea1 Pro perties The design and the intended use of rocket motors dictate the mechanical properties required of propellants. Two general types of rocket motors must be considered. The first type has casebonded, internal-burning grains that are cast and cured in the case. Case bonding provides a high ratio of propellant mass to total rocket-motor mass and also eliminates some costly and difficult processing operations. The internal-burning configuration gives a reasonable duration of burning and also permits the use of a lightweight chamber wall, because the wall is insulated by a layer of propellant until burnout. The second type includes motors of small or medium size containing free-standing grains, formed either by casting or by extrusion. Propellants suitable for case-bonded grains need the most careful characterization, because the most difficult problems arise in these applications (9). Time-Dependent Tensile Behavior. Typical stress-strain tensile curves for propellant show that stress may either reach a maximum long before breakage, or increase steadily to the breaking point. The maximum sometimes corresponds roughly with visually observed irreversible separation of binder and oxidizer. The second type of behavior is considered more desirable. There is no simple correlation between the type of curve and the chemical
AND ENGINEERING CHEMISTRY
Relations at Equilibrium. In theory, the relation between tensile stress and elongation at equilibrium correlates directly with molecular structure. Measurements of stress relaxation at constant strain are performed with the object of approaching this equilibrium condition, although ideal conditions are often not realized with actual binder and propellant compositions. When an unfilled rubber is extended for a small, fixed amount, the stress decays with time to a constant value. According to Flory (4),the equilibrium retractive force, T , is
r=2(.-$) were T is absolute temperature; v c / V ~ , moles of effective chains between cross links per unit volume (or cross-link density); and a , relative elongation ratio. Corrections may be applied for chain entanglement, and for the presence of noninteracting diluent-e.g., plasticizer. Plots of stress against time for actual binders exhibit more or less wcll-defined plateaus, followed by a further decay of stress. Nevertheless, cross-link densities calculated from stresses at the plateaus agree satisfactorily with values calculated from measurements of swelling in solvents, and are useful for comparative purposes. Stress-relaxation curves for propellants loaded with 60 to SOY0 of solids typically show slight indications of equilibrium, if any. It is usually necessary to select stresses measured at a set, arbitrary time after the initial stretching. Calculations of cross linking from these measurements are quite useful measures or cure or aging. They also show: strikingly, how an oxidizer reinforces the network structure of the binder. Thus, Table I compares cross-link densities for the same binder loadcd with from 0 to 7OY0oxidizer, calculated on two assumptions: the binder does not wet the filler, and the binder wets (is effectively bonded to) the filler (Guth-Gold and Eilers equations). Cross-link densities from the first assumption rise steadily with loading from less than the theoretical value to 7 times as much. Cross-link densities from the second assumption are not only selfconsistent, but also agree fairly well at all loading levels with values from swelling measurements, which are independent of oxidizer effects. When the strain becomes large enough in a stress relaxation test, the propellant ruptures. The highest strain at which rupture never occurs is now considered one of the most meaningful parameters for characterizing propellant for large grains. Creep a n d Recovery. Measurements of creep under constant stress are per-
PLASTICS A N D ELASTOMERS IN ROCKETS Table 1.
Oxidizer Loading, Wt. yo 0 20 40 60 70 a
r = r o(1
Best Propellant Cross-Link Densities Are Calculated from Stress Relaxation When Binder-Filler Bonds Are Assumed Cross-Link Density in Binder (MEC CC.-1) X 1V Calculated from Stress Relaxation Filler assumed Guth-Gold Eilers Theoretical inert equationa equationb 19.5 19.5 19.5 19.5 19.5
+ 2.5 V F +
stress for loaded binder;
14.5 12.9 12.7 7.2 9.2
14.5 21.5 33.6 58.2 129.0
14.1
VF*)
70,stress
(Ref. 6).
7 = TO (1
for binder alone;
formed to indicate the deformation of grains subject to prolonged loading. Modern elastomeric propellants can show complete recovery after straining by large percentages. A specimen retracts to its original dimensions in a period of time that depends on time and extent of strain. However, its modulus may be substantially reduced (as would be predicted from stress relaxation behavior). This reduction is interpreted to mean that such propellants originally have a network structure which is far more complex than the minimum structure needed to ensure recovery. This network may consist of chain entanglements, branching, and cross links in the binder, and reinforcement by the oxidizer. Portions of the network are steadily being broken under strain, but for a very long time enough network remains to ensure complete dimensional recovery. Beyond a certain percentage of strain, of course, the deformation is irreversible. A useful correlation of the temperature dependence of the creep of solid propellants was provided by Blatz ( 2 ) .
Aging The aging of a solid propellant is the sum of the changes it undergoes in the interval of weeks, months, or years between curing and firing in a rocket chamber. Propellants may be stored under controlled, constant, environmental conditions, or, more likely, with little control, under rather wide extremes of temperature. Mechanisms of Aging. The outward manifestations of aging are changes in the physical and mechanical properties discussed in other sections. These outward changes are symptomatic of physicochemical changes on the molecular scale, and as far as possible, the latter must be identified and measured in order to apply the proper means of prevention, and to establish acceptance limits. Possible types of molecular-scale changes include depolymerizations or scissions of binder chains, decompositions, crystallization of binder, phase changes, effect ascribable to oxidizer, and various changes associated with minor components of the propellant. The degradation of binder chains leads to a loss in the ability of the propellant to withstand the normal stresses expected during handling and firing. It is usually evidenced by an increase in the soluble fraction extractable from the binder, and a decrease in the cross linking, as measured by stress-relaxation or swelling methods. Degradations may result from oxidation, reduction, or hydrolysis reactions, depending upon the types of functional
VP,
14.5 14.0 12.7 7.4 6.8
+ 1 1‘25 - 1.2
2rP VF
calculated from swelling 10.8 12.4 7.6 8.4 11.5
)’ (Ref. 3).
7
is
volume fraction of filler.
groups composing the polymeric chain. Polymers prepared from vinyl monomers may depolymerize by a free-radical chain mechanism. Two or more of these reactions may occur simultaneously, especially since the repeating unit of a polymer may be a large, complex arrangement of subgroups. Small amounts of contaminating water are almost always available for hydrolysis reactions, while oxidations may result from atmospheric air and from the inorganic oxidizer. Interchange reactions are thought to be especially important in stress relaxation, leading to a redistribution of bonds in which the number opposing the applied stress is diminished. Decomposition reactions in the binder, which yield smaller, volatile chemical fragments as products, may cause porosity in the propellant, as evidenced by low density and rapid burning. These reactions are conveniently studied by measurements of gas evolution on heating. The lengthy history of nitrocellulose propellants produced many manometric test methods for determining the quantities of gas evolved and simple indicator paper tests for detecting gaseous products. Many of these same methods and their modifications are used for testing the more recently developed composite propellants. However, there is considerable need for new tests which are specifically applicable to composite propellants. Crystallization of propellant binder at low temperatures or under stress is to be avoided because it reduces the elongation of the propellant. I t is considered an aging phenomenon because it normally occurs over a relatively long period of storage. As with small-molecule compounds, the rate is highest slightly below the melting temperature. Oxidizer is responsible for a number of aging effects in propellant. Oxidizer dissolves appreciably in some binders. This may affect not only the polymerization processes, but also the subsequent aging behavior of cured propellant. The oxidizer may undergo abrupt volume changes by passing through phase-transition temperatures during storage. For example, NH4NO8 undergoes four polymorphic transitions in the range from -13’ to +125O C., including a transition at 32.5’ C., creating an expansion of 3%. The repeated cycling of certain propellants containing NHdNO, through one of these temperatures may create voids. Certain oxidizers are hygroscopic, requiring protection from moist air during storage. Aging effects are not entirely due to the binder and oxidizer. Residual curing catalysts may degrade the binder during
storage. The free-radical degradation of rubbers by peroxides is well known, and catalysts for polycondensations may also catalyze degradation. Plasticizer migration is a problem in some formulations. Ballistic additives may also take part in decomposition reactions. Protection Against Aging. Aging effects are best controlled by precautionary planning at the stage of formulation. This planning involves not only the careful selection of available propellant ingredients, but the synthesis of new and improved materials as well. The formulation should avoid chemically incompatible materials. The polymeric binder should have intrinsically good thermal and chemical stability; weak bonds should be avoided, and the presence of protective groups, such as those with high resonance energy, is often desirable. Structures tending to crystallize should also be avoided. If separate plasticizers are used, they should have strong affinities for the binder-Le., low activity; however, “internal” plasticizers bonded to the binder structure are more desirable. Curing catalysts should be added in minimum amounts, and curing reactions which do not require chemical catalysts or high temperatures are to be preferred. Oxidizers likewise should be inert during storage. Obviously, these requirements conflict at many points with requirements for performance, pot life, castability, efficiency of curing, ballistic properties, and other types of behavior, so that the formulations actually used are by no means ideal, but are only the best possible compromises. Chemical substances are added to many propellants to prevent aging. For example, a stabilizer such as ethyl centralite (diethyl-diphenylurea) is added to doublebase propellant to react with any NO3 evolved and thus prevent autocatalytic decomposition. Antioxidants similar to those used in the rubber industry are added to the binders of many composite propellants.
Combustion Combustion of the propellant grain converts potential, thermochemical energy into kinetic energy to propel the rocket. A controlled combustion under predetermined conditions marks the successful application of all the foregoing principles. T h e rate of energy conversion in a rocket motor is a product of two factorsthe energy converted per unit weight and the weight burned per unit time. T h e first quantity is thermochemical. T h e second quantity, &, equals the product of the burning area, A , linear burning rate, r , and density, p : & = Arp (7) Linear B u r n i n g Rate. T h e linear burning rate, r , whose direction is always normal to the burning surface, is one of the most important ballistic properties. Broadly speaking, the burning rates of composite propellants are determined mainly by the oxidizer employed, b u t are also influenced by other compositional factors. They are essentially independent of the mechanical properties. Thus, uncured propellant VOL. 52, NO. 9
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759
slurries (contained in soda straws) burn at approximately the same rate as cured strands of the same propcllant. Variations of r with pressure and propellant temperature strongly affect rocket performance, and the regulation of these variations has been carefully studied. Over limited ranges at least, the variation with pressure, p, follows a n empirically determined law r = cpn
(8)
in which c and n are constant a t any fixed temperature. Thus plots of log r against log p are normally straight lines. These lines shift upward with increasing temperature, usually without changing slope n. T h e effect of temperature on chamber pressure is a useful quantity, expressed by the temperature sensitivity, T K , as follows :
T h e subscript K indicates that the ratio of burning area to throat area in the rocket is held constant. I t is usually desirable that burning rates should change as little as possible with either pressure or temperatureLe., both nand T K should have minimum values. If n is too high, a momentary increase in the pressure can produce a dangerous, accelerating build-up of pressure, while a high T~ means the chamber must be overdesigned to accommodate large pressure variations. Among propellants in actual use at present, typical values of n and r K are 0.5 and 0.2" F.-I, respectively . Erosive Burning. T h e simplified picture of burning developed here neglects several complicating fators. O n e is grain erosion by high-velocity gases flowing parallel to the burning surface. Within a longitudinal burning volume, erosion is obviously most severe nearest the nozzle, where the mean gas velocity is highest, and is negligible a t the fore end. To a first approximation, the observed burning rate, r ' , is related to 7 , the zero-velocity burning rate a t the same static pressure, by rJ _ - 1 klzl (10)
+
in which u is the space-mean linear gas velocity and k is a constant characteristic of the propellant. Typically, the term klu equals several tenths. I n a detailed analysis, Lenoir and Robillard ( 6 ) replaced klu with a complex function of several parameters of heat transfer and gas flow. Except for being inversely proportional to burning rate, this function is virtually independent of compositional factors. T h e Lenoir-Robillard expression agrees closely with experiment. Therefore, once a general type of propellant has been selected for a certain application, the control of ero-
760
sive burning becomes a problem in rocket geometry, independent of chemical effects. Unstable Burning. During the firing of certain rocket motors, periodic pressure fluctuations may reach large enough amplitudes to rupture the motor. This instability is called resonance (sometimes sonance). I t is characteristic of certain configurations-Le., relatively long interior channels-and of certain compositions. Resonance is ascribed to self-excited acoustical processes within the gases in the burning cavity. Several explanations have been proposed (7). Resonance burning may usually be prevented by simple mechanical expedients or by changes in the chemical formulation. As examples of the former, grain configurations may be altered by perforating the grain in various ways o r by mounting longitudinal "resonance rods" in the burning cavity. Theories of Burning Composite Propellants. T h e proposed mechanisms of combustion of composite solid propellants were recently summarized by Schultz, Green, and Penner (7), who stressed the incompleteness of present knowledge. Summerfield's diffusion flame model and more-complex theories based on different geometrical models were discussed. All are characterized by being purely physical and geometrical and independent of chemical factors. I n contrast, the two-temperature theory of Schultz and Dekker is based on matching experimental observations of individual pyrolysis rates of specific oxidizers and binders to their average surface temperatures in the propellant. T h e steady-state burning rate of the propellant is equated to the (equal) linear pyrolysis rates of the oxidizer and binder, formulated in Arrhenius rate expressions, as follows : r = BO exp[ --Eos/R Tosl (11) = BF e x p [ - E ~ s / R T ~ s l I n general, Bo # BF and Eo, z E*,; hence surface temperatures are also different-Le., To, may either be higher than T,, (as for ;\;H&lOi) or lower (for NHdNO3). At 1000 p.s.i.g., burning rates of NHlNOI propellants correspond to oxidizer-surface temperatures of 562O to 615' K. and binder-surface temperatures of 610' to 1020' K. A model of burning NH4N03 propellant was developed from two-temperature pyrolysis rates and known heats of reaction. This model postulates the following: Solid oxidizer melts a t the surface and decomposes endothermically by sublimation to NH3 and " 0 3 , which recombine in a n intermediate flame zone at about 1250" K . Concurrently, the fuel is gasified at lower temperatures by the heat supplied from this zone. In a n outer zone, the oxidizer and fuel streams mix by diffusion and react at the propellant flame tem-
INDUSTRIAL AND ENGINEERING CHEMISTRY
perature (2000' to 2500O K . ) . T h e pyrolyses are maintained by heat transfer back from the intermediate zone. This model helps explain the operation of burning-rate accelerators. Addition to NH4NOa of several per cent of (NH4)2Cr2O7 does not change the curve of linear pyrolysis rate us. temperature, and hence does not catalyze decompositions in a condensed phase, but rather accelerates the gas-phase reactions. I t thereby increases the heating of the surface and shifts the burning rate to higher values. Regulation of Burning Rates. For a n established propellant formulation, burning rates may be adjusted to some extent by changing the oxidizer-particlesize distribution and by incorporating small amounts of ballistic additives. T h e type of regulation desired may be shifting the entire burning-ratei/pressure curve u p or down; flattening the curve, and perhaps creating a plateau; or lowering the temperature sensitivity. Variations in oxidizer particle size may accomplish the first two kinds of change, while chemical additives are effective for all three. T h e chemical nature of the binder also exerts some influence.
Acknowledgment Important contributions to the preparation of this article were made by R. D. Geckler, A. 0 . Dekker, R . L. Lou, K. W. Bills, K. H. Sweeny, and J. P. Kispersky.
Literature Cited (1) Billheimer, 3 . S., Parrette, R. L., Anal. Chern. 28, 272-3 (1956). ( 2 ) Blatz, P. J., IND.ENG.CHEM.48, 727-9 (1956). (3) Eilers: H., Kolloid-Z. 97, 313-21 (1941). (4) Flory, P. J., "Principles of Polymer Chemistry," Cornell, New York, 1353. ( 5 ) Guth, E., Gold, O., J . Apfiiied Phys. 16, 20-3 (1945). (6) Lenoir, J. M., Robillard, G., 6th Intern. Symposium on Combustion, Reinhold, New York, 1957. (7) Schultz. R. D., Green, L., Jr., Penner, S. S., Combustion and Propulsion Panel Colloquium, 3rd AGARD, Palermo, 1958. (8) Smith, T. L., California Institute of Technology Jet Propulsion Laboratory, Memo. 20-178, 1959. (9) Smith, T. L., IKD. ENG.CHEM.52, 776 (1960). (10) Steinour, H. H., Did., 36, 618-24 (1944). (11) Sweeny. K. H., Division of Petroleum Chemistry, 135th Meeting, ACS, Boston, Mass.. April 1959. (12) Sweeny, K. H., private communication. (13) Sweeny, K. H., Geckler, R. D., J . Apfilied Phys. 25, 1135-44 (1954). (14) Trommsdorf, E., BIOS Rept. 363, 1940. RECEIVED for review October 28, 1959 ACCEPTED May 23, 1960 Division of Paint, Plastics, and Printing Ink Chemistry, Symposium on Plastics and Elastomers for Use in Rockets, 136th Meeting, ACS, Boston, Mass., April 1959.
