OF MUNITIONS AND EXPLOSIVES IN ROMANIA
2. PBX CHARACTERISATION 1. PBX composition
2.4. Kinetic parameters of PBX's and its compounds
Simultaneous thermal analysis (DSC and TG) were employed to investigate the thermal decomposition in non-isothermal conditions of PBX's mixtures.
The measurements were carried out using a Rheometric Scientific®STA 1500 equipment. The samples (sizes ranges between 1.6 mg to 2.6 mg) were carefully loaded into open alumina crucibles and a dry nitrogen purge flows of 50 ml.min-1 at 0.1 MPa absolute pressure was used in all measurements.
Non-isothermal kinetic analysis was used to estimate Arrhenius parameters of PBX's and components. The results are discussed on a comparative basis taking into account the dependencies of the activation energy upon the degree of conversion.
Thermal decomposition of the individual components
Each component was firstly studied alone providing a comparative basis for comparative purposes in the viz., of regarding the subsequent study on their mixtures. Figure 1 shows the DSC curves of the different individual components of PBX's materials.
1 Standard deviation.
Figure 1. Typical DSC curves of individual compounds for an heating rate of 10 K.min-1.
The obtained thermogram for RDX is in agreement with previous studies4. The endothermic peak in Figure 1 corresponding to the melting process starts at 497±1 K (HR of 10 K.min
-1
).
From the TG curves was observed that the mass loss occurs in the temperature range 496 K to 524 K. The TG curves obtained for HTPB shows the presence of two stages. IPDI and DOS DSC curves show an endothermic peak ascribable to the evaporation.
Thermal decomposition of PBX's based on RDX
Figures 2 and 3 present typical thermoanalytical curves for the tested PBX's. Differences in the rates of the global exothermic decomposition process are observed when the composition of the binder change. The mass loss increases as HTPB, HTPB/DOS and HTPB/DOS/IPDI are added to RDX. In the same way the exothermic peaks appear more and more abrupt and the correspondent peak temperatures shifted to lowers temperatures.
Figure 2. Typical TG curves for PBX based on RDX at an heating rate of 10 K.min-1.
300 350 400 450 500 550 600 650
Temperature (K) Weightloss(%) RDX/HTPB
RDX/HTPB/DOS/IPDI
RDX
RDX/HTPB/DOS 50%
300 350 400 450 500 550 600 650 700 750 800 850
Temperature (K)
HeatFlux
HTPB
IPDI RDX
DOS 10mW ExoEnd
300 350 400 450 500 550 600 650
Temperature (K)
HeatFlux
1-RDX 2-RDX/HTPB 3-RDX/HTPB/DOS 4-RDX/HTPB/DOS/IPDI
20mW ExoEnd
1 2 3 4
Figure 3. Typical DSC curves for PBX based on RDX at a heating rate of 10 K.min-1.
No relevant departures from RDX alone are encountered in the temperature at which the mass loss begins. Table 4 shows the extrapolated onset temperature (Ton) and peak temperature (Tp).
Table 4. Extrapolated onset temperature and peak temperature for PBX, based on RDX, and RDX.
Material Studied E (K.min-1)
Tp2
(K)
Ton range (K) RDX
5 10 15
507.63 517.69 524.64
488.43 – 488.56 496.64 – 497.95 499.87 – 500.38 RDX/HTPB
5 10 15
506.87 516.79 521.73
487.57 – 487.88 495.18 – 497.02 502.87 – 504.02 RDX/HTPB/DOS
5 10 15
506.20 512.78 517.83
487.76 – 490.56 491.44 – 492.47 505.08 – 505.19 RDX/HTPB/DOS/IPDI
5 10 15
495.90 500.03 500.80
480.05 – 489.78 491.50 – 496.37 495.75 – 496.56
The kinetic analysis of the RDX based mixtures were based on the TG curves. TG curves were normalised to establish a degree of conversion, D, ranging from 0 to 1. Friedman method5 was applied to estimate the activation energy at different levels of D
The theory supporting the kinetic analysis is based in the Arrhenius expression, D
D kT f dt
d (3)
2 Average of peak temperature for each heating rate.
Where, ¸
¹
¨ ·
©§ RT exp E A T
k ,
D is the degree of conversion, E the activation energy, A the pre-exponential factor, T the absolute temperature, R the gas constant, t the time and f(D) the conversion model function6. Applying logarithms to Eq. (3) we get,
> @
RT A E
dt ln
ln d ¸
¹
¨ ·
©
§ D D
f (4)
Eq.(4) permits to estimate the value of E without any assumption other than the rate of the process being described by the Arrhenius law.
With the purpose to obtain a simple kinetic model function, f(D) able to describe the process, the kinetic equations were transformed to a generalized kinetic equation at infinite temperature7,8. Due of its flexibility and reduced number of kinetic exponents the empirical function h(D) of Sestak-Berggren model, SB (M,N)9,10 was selected to reproduced f(D).
h(D) = DM (1 – D)N (5)
The kinetic exponents M and N in the SB (M,N) model are evaluated according to the relationship9
>
D D@
T
D¸
¹
¨ ·
©
§ ln A Nln 1 d
ln d P (6)
Where
M M
1 N P M
D D
(7)
A plot of ln (dD/dT) against ln [DP (1–D)] gives us a slope corresponding to the kinetic exponent N and the value of A is obtained from the axis intersection value.
The invariance of E with D is a prerequisite considering the applicability of Eq.(4). Figure 4 shows the evaluation of E as a function of D for the mixtures RDX/HTPB and RDX/HTPB/DOS. The observed pattern for the RDX/HTPB/DOS reactive system is a clear indication that the process is too much complex to be tractable within the framework of kinetic analysis, based on the available thermoanalytical data. Worst results (not shown in Fig.
4) were obtained for the RDX/HTPB/DOS/IPDI mixture.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 D
100 150 200 250 300 350 400 450
E(kJmol-1)
RDX/HTPB RDX/HTPB/DOS
Figure 4. Activation energy as a function of the degree of conversion calculated from the Friedman method for PBX's based on RDX.
Concerning to RDX/HTPB the thermal decomposition suggests that it would be reasonable to proceed with the kinetic analysis following Friedman method. Tab. 5 shows the mean value
of E calculated from those values of E satisfying the criterion of a deviation from the mean value within the interval of r10%.
The kinetic model function h(D) able to describe the thermal decomposition of RDX/HPTB get M=0.9 and N=0.8.
Table 5. Kinetic parameters of the materials studied.
Material D range
Temperature range3
(K)
E (kJmol-1)
A4 (s-1) RDX 0.14 – 0.84 495.90 – 523.84 200.25 r 35 4.51 x1018 DOS 0.08 – 0.27
0.47 – 0.90
505.73 – 536.48 552.16 – 572.52
60.56 r 1
86.70 r 1 IPDI 0.05 – 0.90 408.61 – 473.82 59.98 r 1 3.42 x104 HTPB– 1st Stage 0.33 – 0.62 649.04 – 676.70 77.62 r 6 HTPB– 2nd Stage 0.04 – 0.90 708.53 – 758.72 262.56 r 7
RDX/HTPB 0.17 – 0.89 492.54 – 512.69 170.02 r 3 5.72 x1015 RDX/HTPB/DOS 0.11 – 0.34 490.23 – 503.95 158.95 r 5 RDX/HTPB/DOS/IPDI 0.2 – 16 471.40 – 486.78 117.17 r 15
3 Average temperature at different heating rates E for the same degree of conversion D.
4 The values here presented are an average of all measurements performed.
5 Standard deviation.
6 This range of D corresponds to 10 percent of total mass loss during decomposition process.
3. COOKOFF MODELLING OF PBX CYLINDER CHARGE