a constant decomposition level are determined. The kinetic activation energy is then determined from a plot of the loga- rithm of the heating rate versus the ...
Thermal Analysis & Rheology
Thermal Analysis Application Brief
Estimation of Polymer Lifetime by TGA Decomposition Kinetics Number TA-125
Summary In many polymer applications the ability to predict product lifetime is valuable because the costs of premature failure in actual end use can be high. For example, federal regulations require the estimation of component lifetime in nuclear reactors, while power companies need to know how long insulation in transformers and transmission lines will last. Thermogravimetric Analysis (TGA) provides a method for accelerating the lifetime testing of polymers so that short term experiments can be used to predict in-use lifetime.
Introduction Wire insulation is a polymer application where the ability to rapidly predict long-term product lifetime is valuable. One test commonly used for estimating wire insulation lifetime is ANSI/ ASTM procedure D-2307. In this procedure, twisted pairs of insulated wire are oven aged (for up to 50 days) at elevated temperatures (up to 240oC) until voltage breakdown occurs. A series of such tests, performed at different oven temperatures, creates a semi-logarithmic plot of lifetime versus the reciprocal of failure temperature. The method assumes first order kinetics and uses extrapolation to estimate the long lifetimes encountered at normal use temperature. The application of first order kinetics to the estimation of polymer lifetimes is particularly fortuitious. Many polymers are known to decompose with first order kinetics. For those that do not, the earliest stages of decomposition can be approximated well with first order kinetics. (1,2,3,4,5). This procedure, while useful, is very time consuming, often taking many months, particularly for highly stable materials. As more and more stable polymeric electrical insulation materials are introduced, the time needed for a full series of tests becomes excessive. It is desirable, if not necessary, therefore, to find a more practical technique. Thermogravimetric Analysis (TGA), which monitors weight changes in a material as temperature changes, offers a viable alternative to oven aging. In the TGA approach, the material is heated at several different rates through its decomposition region. From the resultant thermal curves, the temperatures for
a constant decomposition level are determined. The kinetic activation energy is then determined from a plot of the logarithm of the heating rate versus the reciprocal of the temperature of constant decomposition level. This activation energy may then be used to calculate estimated lifetime at a given temperature or the maximum operating temperature for a given estimated lifetime. This TGA approach requires a minimum of three different heating profiles per material. However, even with the associated calculations, the total time to evaluate a material is less than one day. With an automated TGA such as the TA Instruments Auto TGA 2950, the actual operator time is even lower with overnight evaluation being possible.
Experimental The specific experimental conditions used (such as temperature range and specimen atmosphere) depend upon the material being tested. Experimental design and data reduction are similar for each material, however. In the analysis illustrated here, a high temperature fluoropolymer wire insulation material was examined. The sample size was 40 - 60 mg. Decomposition profiles were obtained while heating at 1, 2, 5, 10 and 20oC/minute in nitrogen between 200 and 500oC. The profile during the first 25% of sample weight loss was used for subsequent calculations.
Results Figure 1 displays the overlaid weight loss curves for the fluoropolymer at several different heating rates. The first step in the data analysis process is the choice of level of decomposition. Typically, a value early in the decomposition profile is desired since the mechanism here is more likely to be that of the actual product failure. On the other hand, taking the value too early on the curve may result in the measurement of some volatilization (e.g. moisture) which is not involved in the failure mechanism. A value of 5% decomposition level (sometimes called conversion) is a commonly chosen value. Other values may be selected to provide correlation with other types of lifetime testing (6).
LOG HEATING RATE vs TEMPERATURE OF CONSTANT CONVERSION
WIRE INSULATION THERMAL STABILITY 0.5% Conversion 1.0% 2.5%
95
90
460
5% size: 60mg atm.: N 2 10% 10°C 5°C 2.0°C 1.0°C
85
80 200
250
300
350
400
450
20% 500
5
Figure 2 shows a series of such lines created from the four curves shown in Figure1 by plotting data at different conversion levels. If the particular specimen decomposition mechanism were the same at all conversion levels, the lines would all have the same slope. This is not the case here. The lines for the low conversion cases are quite different from those of 5% and higher conversion. This justifies our selection of 5% conversion as the best point of constant conversion for the purposes of this test. The next step in the process is the calculation of activation energy (E) from the slope in Figure 2 using the method of Flynn and Wall(7). -R b
[ ] d log β
d (1/T)
Conversion 20 10
5
(1)
2.5
1.0
0.5
1 1.4
Using the selected value of conversion, the temperature (in kelvin) at that conversion level is measured for each thermal curve. A plot of the logarithm of the heating rate versus the corresponding reciprocal temperature at constant conversion is prepared. The plotted data should produce a straight line.
360
2
Temperature (°C) Figure 1
E=
WIRE INSULATION TEMPERATURE (°C) 440 420 400 380
10 HEAT RATE (°C/MIN)
WEIGHT LOSS (%)
100
1000/T (k) Figure 2
1.5
1.6
Where: E = Activation Energy (J/mol) R = Gas Constant (8.314 J/mol K) T = Temperature at Constant Conversion (K) β = Heating Rate (oC/min) b = Constant (0.457) The value of the derivative term (d log β)/[d (1/T)] is the slope of the line in Figure 2. The value for the constant b (given in tabular form in reference 7) varies depending upon the value of E/RT. Thus, an iterative process must be used where E is first estimated, a corresponding value for b is chosen, then a new value for E is calculated. This process is continued until E no longer changes with successive iterations. For the given decomposition reaction for the values of E/RT between 29 and 46, the value for b is within +1% of 0.457, thus this value is chosen for the first iteration. Figure 3 gives values for the activation energy and the corresponding values for E/RT calculated for the five conversion cases shown in Figure 2. Note that all the activation energy values calculated on the first iteration yield E/RT values within the expected range. Thus, no additional iterations are required. The activation energy for the 5% conversion case is quite similar to that for the 1 and 2% cases, giving additional support to the 5% conversion choice.
ACTIVATION ENERGY (wire insulation decomposition) Conversion % 0.5 1.0 2.5 5.0 10 20
Activation Energy (kJ/mol)
E/RT 31 44 44 42 36 36
170 245 246 244 211 212
Toop has postulated a relationship between activation energy and the estimated lifetime of some wire insulation (8). E RTf
+ In
[
E βR
P (Xf)
]
In tf - In
[
E βR
P (Xf)
]
(3)
Equation 2 may be used to create a plot, similar to Figure 4, in which (the logarithm of) estimated lifetime is plotted versus (the reciprocal) of the failure temperature. From a plot of this nature, the dramatic increase in estimated lifetime for a small decrease in temperature can be more easily visualized.
Note: b = 0.457 + 0.004 for 29 < E/RT < 46 Figure 3
In tf =
E/R
Tf =
Kinetic parameters may also be determined by other thermoanalytical techniques. Differential Scanning Calorimetry (DSC) and Pressure DSC may be used to obtain such parameters for use in the estimation of thermal hazard potential of chemicals (9).
(2)
Where:
ESTIMATED LIFETIME tf
= Estimated Time to Failure (min)
E
= Activation Energy (J/mol)
6
Tf
= Failure Temperature (K)
5
1 decade
R
= Gas Constant (8.134 J/mol K)
4
1 yr.
P (Xf)
= A function whose values depend on E at the failure temperature.
3
1 mo.
Tc β
= Temperature for 5% Loss at β (K)
To calculate the estimated time to failure (tf), the value for the temperature (Tc) at the constant conversion point is first selected for a slow heating rate (β). This value, along with the activation energy (E) is used to calculate the quantity E/RT. This value is then used to select a value for log P(Xf ) from the numerical integration table given in Toops paper. The numerical value for P(Xf ) can then be calculated by taking the antilogarithm. Selection of a value for failure (or operation) temperature (Tf) permits the calculation of tf from equation 2 above. Rearrangement of equation 2 yields a form which may be used to calculate the maximum use temperature (Tf) for a given lifetime (tf).
280
Temperature (°C) 300 320 340
360 1 century
1 week 2 1 day 1
= Heating Rate (oC/min)
260
1.9
1.8
1.7 1000/T (k) Figure 4
1.6
1.5
ESTIMATED LIFE
ESTIMATED LIFE (hr.)
TEMPERATURE DEPENDENCE
References
5. IEEE Test Method 323.
1. ASTM Test Method D-2307
6. L. Krizanovsky, et. al., J. Therm. Anal., 13, 571 (1978).
2. IEEE Test Method 101.
7. J. H. Flynn, et. al., Polym. Lett., B4, 323 (1966).
3. IEEE Test Method 259.
8. D. J. Toop, IEEE Trans. Elec. Ins., E1-6, 2 (1971).
4. IEEE Test Method 266.
9. ASTM Test Method E698
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