HAROLD E. MARSH, Jr. Jet Propulsion Laboratory California Institute of Technology, Pasadena, Calif.
Formulations and Quality Control in Network concepts and a generalized correlation of mechanical properties are useful in systematizing solid-propellant formulation development and improving reproducibility
IN
1953, when development of a new family of elastomeric composites based on polyurethane resin binders was started much of the work on formulations was strictly empirical. Since then, however, a wealth of theoretical background material has been growing (3, 4, 6 , 7). This paper summarizes theoretical tools now used to solve engineering problems-i.e, resin parameters for formulation design and quality control, and a general correlation of mechanical properties. The conclusions reached are: there is a correlation of propellant elongation with polymer network parameters, while tensile capacity becomes a useful formulation family characteristic. Several pairs of parameters such as R,pT,Mr,pe,af are superior to the weight recipe for specifying propellant formulations. Polyurethane Propellants
The present competitive position of solid propellants was generated in the middle 1940’s when elastomeric composite propellants were introduced. For the first time, lightweight hardware was made possible by using case-bonded propellant to protect motor chambers from the high combustion temperature. The
importance of propellant mechanical properties for this arrangement is described in another paper in this issue by Smith (5). Fully cured propellant grain must have sufficient elongation to withstand the strains of temperature cycling and the impact of igniter blasts. Composite solid propellants consist of two major components, a crystalline inorganic oxidizing agent and a polymerizable liquid rubber. The rubber serves both as binder and fuel. Normally, the stoichiometry of combustion is such that the system is highly filled with the solid oxidizer. Solid and soluble additives are employed for various purposes; typical composite solid-propellant additives include ballistic modifiers, surfaceactive agents, plasticizers, and polymerization catalysts. I n this article, composition of polyurethane rubber in the highly filled system is under study, not effects of solids loading and additives. Three basic building blocks are used for the polyurethane-rubber fuel-binder : diisocyanates, low-molecular weight triols, and long-chain diols-linear organic compounds terminated on each end by hydroxyl groups with molecular weights of from 1000 to 2000. 4
20
I/ R
R
’Figure 1. An increase in sensitivity o f the degree of branching to stoichiometry i s obtained at low cross-linking agent concentrations for a systejn containing all polyfunctionals
768
INDUSTRIAL
AND ENGINEERING
CHEMISTRY
le
The principal chemical reaction that brings about the synthesis of crosslinked polymers from these polyfunctional resin-binder ingredients is :
+ R’-0-H
R-N=C=O
+
I
isocyanate
+ alcohol
/
H O urethane
-+
Formulation Parameters
A variety of parameters important in describing a three-dimensional network are available, and others which have particular significance can be devised. When the reaction has proceeded to the point where a, is reached, theoretically, gelation starts and continues rapidly, and the relative amounts of sol and gel are theoretically related to how much a exceeds I/z. Obviously the mechanical properties would be expected to be related to this parameter. The expression derived by Flory ( 7, Z), in terms of this polyurethane system, is : a =
07
OB
OB
09
09
4
07
14
12
I/R
10
05
06
1
I
I 16
’
R-N-C-0-R
12
14
le
I ,B
20
R
Figure 2. The effect of small concentrations of monofunctional component-8 mole of difunctional ingredient-on the degree of branching i s indicated
7 0
PLASTICS A N D ELASTOMERS IN ROCKETS The other parameter which would be expected to have a major effect on mechanical properties is M,, which measures the average chain length between branch units. Perhaps M e of the gel fraction only would be more significant, but this has not been investigated yet. 2 weight of rain
M e = -3 mole of triol
(2)
Deviation from Theory The formulation parameters described above and their relationships represent a simplified and perfect system in much the same way as the gas law. Deviations from this model are brought about by side reactions, different reaction rates, impurities, and other unknown factors. Two of these factors are readily recognized; the effect of one of them has been incorporated in the parametric relationships, as will be iIlustrated below. A consistent finding of most investigators is that maximum or minimum values of a number of properties are not found when isocyanate and hydroxyl groups are in stoichiometric proportions, but rather when isocyanate is in excess of about 591, -R = 1.05. The data of this study also show this effect. The reasons for the need of excm isocyanate are only speculative at this time, and no way has been found to account for them in the relationships presented. The other deviation has to do with monofunctional impurities found in the large-molecular weight diols. A number of these commercial diols contain a small, measurable amount of monofunctional material naturally present as a result of side reactions in their manufacture. As many as 8% of the molecules in a 2000-molecular weight material can be monofunctional. It is appropriate at this time to introduce some new terms which are related as follows : p4
+
PD
f
(3)
1
PM
Employing Flory's statistical technique used in the development of Equation 1 with the new terms listed above, a new
gel-a, = I-without any triol, the more typical system would require pT = 0.265 to reach an aI = 0.9. I t is interesting also to see how far a polymerization reaction must go on before any gelation can occur at all, theoretically. If we let a = cy, = l/2, expressions for the extent of reaction at incipient gelation are obtained:
relationship is derived which accounts for the monofunctional impurity.
Some important characteristics of the resin-binder systems under study are illustrated by graphical relationships of the various parameters described above. The value of degree of branching most significant to propellant properties is the one reached when polymerization is complete, when either f N c o or f a = reaches unity, as cy,
cyf
-.!!&-
R 1.0 - R ~ when D =p TE when D R 2 1.0
=
1
(5) These expressions, plotted in Figure 3, illustrate that the basic urethane-forming reaction must approach completion in many cases in order for gelation to begin. What little bit of reaction remains, of the order of lo%, has the job of building the body of infinite network which gives the binder its properties. Figures 2 and 3 account only for the monofunctional impurity deviation, but not for the observed deviation regarding the need for excess isocyanate, and, as will be seen from the data below, this latter deviation brings with it an enhancement of the gelation characteristics. The concentration of branching units as an index of propellant mechanical properties is more effectively described on a weight basis (M,) rather than on an equivalents basis ( p T ) because of the variation in molecular weight of longchain diols. M , is calculated from the other parameters by the use of chemical analysis data, where E, is the equivalent weight of the diisocyanatc, E D , the equivalent weight of the long chain diol, and E, the equivalent weight of triol:
(6)
The final or ultimate degree of branching, a,, is illustrated in Figures 1 and 2. The system in Figure 1 contains all polyfunctional components, no monofunctional; p D is equal to (1 - pT) as in Equation 1. Theoretically gel formation would be impossible outside of the triangular area. Assuming that the relative concentrations of sol and gel in a fully cured formulation are related to the value of a,, the diagram in Figure 1 illustrates the reason for a common experience with polymers and propellants of this kind. I n general, the lower the concentration of cross-linking agent, the more sensitive the formulations are to the stoichiometric balance of isocyanate and hydroxyl. In Figure 2, the effect of the monofunctional impurity-amounting to 8% of the molecules in the diol-is indicated by the displacement of the apex of the parameter triangle from pT = 0. Some definite concentration of triol-in this case pT = 0.0385-is required to compensate for an equivalent monofunctional concentration when isocyanate and hydroxyl are in stoichiometric balance. The effect of monofunctional impurity on the capacity of the polymer to reach higher states of gelation is even more pronounced. Whereas a stoichiometric mixture free of monofunctional impurity should be able to reach 1 0 0 ~ theoretical o
(9)
This parameter is displayed for two different molecular weights of long chain diol in Figures 4 and 5. Lower molecular weight diols characteristically often have lower monofunctional impurity content. In this respect, a molecular weight
10I
OB
06
d'04
0
0 1
020
18
1s
14
I/#
12
10
12
I*
I4
I8
20
R
Figure 3. A high extent of reaction is required for gelation to begin in low cross-linker formulations containing 8 mole % of monofunctional
i
40
I8
14
16
I
IVff
15
14
18
24
R
Figure 4. The average distance between branch sites is shown for a 2000-molecular weight diol, 8 mole of monofunctiona I
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VOL. 52, NO. 9
SEPTEMBER 1960
769
IO
Figure 5 . The average distance between branch sites i s indicated for a compound obtained from a 1000-molecular weightdiol,4 mole% of monofunctional
0 8
06
O*
02
02 0
18
I*
16
I 2
IO
i2
14
16
I/ R
of 1000 is better than 2000. However, as can be seen in Figures 4 and 5, a polymer with M , = 16,000 can be made from a 2000-molecular weight diol almost as easily as one with an M , = 8000 from a 1000-molecular weight diol. If it is assumed that better elastomeric properties are to be found with higher M,s as long as fairly high degrees of gelation can be had at the same time, the con-
I
+ NOT
I10
18
20
R
CURED
I
I
1.05 '/R
IO
I
I
1.05
1.10
R
Figure 6. The sensitivity of elongation varies with stoichiometry at low crosslinker concentrations--pT = 0.255; traverse D in Figure 7
clusion can be drawn that diols with higher molecular weights and lower monofunctionality should be sought. And, of course, for the castable, composite propellant business, they should be fluid. Relationship between Properties and Parameters
I t would be ideal to map fairly extensive regions of these resin parameters and lay down contours of important propellant properties. However, the only propellant property receiving full attention in the current work is elongation. and the data are limited. Thus, a few traverses and inferences drawn from a number of varied formulations will serve to illustrate the general character of dependence of elongation on formulation parameters. Figure 6 shows how elongation varies with R when pT is held constant, as shown by traverse line D in Figure 7. Figure 8 shows a vertical traverse E where pT is varied at constant R. Elongation appears to be very sensitive to these parameters. In Figure 9, this sensitivity is shown to give a narrow band of useful formulations. Of all of the many propellant formulations made of the diisocyanate small-triol-2000-molecular weight diol system, those inside the band exhibited elongations in the useful range. All formulations inside the inner boundary had elongations too low to be of interest, and all those outside the outer boundary were obviously undercured, having both low elongation and low tensile strength.
I/R I/I?
R
Figure 7. Parameter traverses shown in Figures 6 and 8 were obtained with a variety of formulations
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INDUSTRIAL AND ENGINEERING CHEMISTRY
There are a number of comments to be made about the relationship of tensile properties to resin parameters (Figure 9). A V-shaped arrangement of tensileproperty contours is to be expected in accordance with an interrelationship of M , and CY^. The steepness of the elongation gradient, or the narrowness of the band, is unexpected for an elastomeric system; however, this system is very highly filled. A study of solids loading as an additional parameter would be extremely interesting. The appearance of the minimum at about 5y0 excess isocyanate is typical of experience in the field with both tensile and storage properties. This last observation, accompanied by the fact that propellants with very good properties have been made that theorctically should not gel a t allsee where the band crosses the gelation limit in Figure 9-indicates that a certain portion of urethane hydrogens react to provide additional branch sites. However, the location of the good-cure-poorcure boundary for higher values of p3. departs from the theoretical gelation limit of CY = 0.5. This line would be a closer approximation of cr = 0.6 (Figure 2). This deviation is in rhe same order
*
TRIOL
on
TOTOTAL 0.4 OH RATIO, 0.6
p,
0.8 o
Figure 8. The sensitivity of elongation depends on the cross-linker con= 1.0 traverse € in centration-R Figure 7
R
Figure 9. A narrow band of useful propellant formulations i s obtained from qualitative correlations wlth parameter relationships
P L A S T I C S A N D E L A S T O M E R S IN R O C K E T S as that found by Flory with a system consisting of diol, diacid, and triacid ( 7 , 2). Flory submits the theory that this deviation is due to the occurrence of some intramolecular reaction. A desirable objective of future work with the application of network theory to composite polyurethane propellants would be the incorporation of the two side effects suggested above; the reaction of some isocyanate groups with urethane hydrogen or some other part of the growing polymer to form extra branch sites, and the formation of closed loops by intramolecular reaction. If a rigorous treatment as in the case of the monofunctional reactant appears impossible, an empirical approach should be tried. Although knowledge of important resin parameters and the dependence of propellant properties on them is far from the state where formulations can be calculated to give specific properties with confidence, considerable benefit has been obtained by their use. Probably the most interesting use of resin parameters is for systematic guide lines in new formulation exploration. The quality control of standard propellant formulations has been a very difficult problem. Most of this difficulty arises from the fact that the molecular weight of many diols can vary by as much as 10% and monofunctionality by about 30%. A weight recipe is hopelessly inadequate for specifying propellant formulations with certain properties because of this variation in analysis and the sensitivity of elongation to composition. A propellant binder formulation can be completely described-except for catalyst and other additives-by any two of the following parameters: R, p T , M,, pa, and 01,. These are not all of the possible parameters; however, others are not considered in this paper. Enough work has
been done to indicate that any of the capacity. Two such improvements are following pairs are superior to the weight evident in the two upper curves in recipe: R and p T , R and M , , and CY,Figure 10. and M,. For general use, R and M , seems to be preferable. Nomenclature e Tensile Capacity
One characteristic which seems to be common to all elastomeric composite propellants is that if tensile strength is high, elongation is low and vice versa. Polyurethane propellants are particularly useful in studying this characteristic because it is easy to formulate a wide spectrum of these properties. For a given binder system containing a fixed amount and size distribution of solids and tested under constant conditions, there is a definite mathematical relationship of this interchange. It is hyperbolic in form:
(S - &)e = K where S is the tensile strength at maximum load, e the fraction elongation at maximum load, So a constant, and K a constant. Thus, SO and K describe a whole family of propellant formulations. The name tensile capacity has been given to this family property. If tensile data are plotted as S v s . l / e , one straight line will represent a whole family (Figure 10). This family characteristic holds for the entire diisocyanate small-triol-2000 molecular weight diol system of formulations (bottom curve, Figure 10) in which the various parameters described above have been varied over wide ranges. The plotting of tensile data in this manner is of enormous value in formulation studies. Once a family has been established, including the statistical scatter of data, the existence of a n improved family is readily seen even from the data of just one test batch by the positive deviation of tensile
= the fraction elongation at maxi-
mum load equivalent weight of the longchain diol EX = equivalent weight of the diisocyanate = equivalent weight of triol ET K = tensile capacity slope constant Mo = average molecular weight between triols or branch sites = FNCO or $OH = fraction of NCO P or OH reacted, simply called extent of reaction = p,, NCO or pa, O H = the fraction of 9, NCO or OH reacted at incipient gelation, CY, R = ratio of equivalents of isocyanate to hydroxyl in starting mixture S = the tensile strength at maximum load so = tensile capacity intercept constant CY = the “probability that any given one of the functional groups of a branch unit (triol) leads, via a sequence of bifunctional units, to another branch, rather than to a terminal group” (7, 2 ) , simply called degree of branching = critical value of cy at which gela“C tion-formation of infinite netCY= = 1/2 works-begins. when the branch unit is trifunctional = the value of CY reached when all fff of one or both of the reactants have been used up. I n a system of stoichiometric proportions containing all poly= 1 functional components, = fraction of OH equivalents from P triol in starting mixture = fraction of OH from diol PD = fraction of OH from monool PM = fraction of OH from triol, PT formerly p
E,,
=
“,
2.4
Figure 10. Propellant families are distinguished by tensile capacity correlations
20
literature Cited (1) Alfrey, T., Jr., “Mechanical Behavior of High Polymers,” Interscience, New York, 1948. (2) Flor P. J., J . Am. Chem. Soc. 6 3 , 3083 fi941) (3) Landel, R. F., J . Colloid Sci. 12, 308 (1957’1. (4)’ Moacanin, J., J . Appl. Polymer Sci. 1, 272 (1959). ( 5 ) Smith, T. L., IND. ENC. CHEM.52, 456 (1960). (6) Smith, T. L., J. Polymer Sci. 20, 89 (1956). (7) Zbid., 32, 99 (1958).
RECEIVED for review October 28, 1959 ACCEPTED May 31, 1960
RECIPROCAL OF RELATIVE ELONGATION
Division of Paint, Plastics, and Printing Ink Chemistry, 136th Meeting, ACS, Atlantic City, N. J., September 1956. This research was carried out under Contract No. DA-04-495-0rd 18, sponsored by the Department of the Army, Ordnance Corps, and released for publication. VOL. 52, NO. 9
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