Thermal degradation process and kinetics of poly(dodecamethyleneisophthalamide)

Received Feb.25, 2003; The financial support provided by Henan Province (China) for outstanding youthful and middle-aged teacher.

Abstract Thermal degradation process and kinetics of poly(dodecamethyleneisophthalamide) (PA12I) in nitrogen have been studied by using thermogravimetry. It was found that the thermal degradation process of PA12I is a one-step reaction in nitrogen. The degradation temperature linearly rises with the increasing of the heating rate. The equilibrium degradation temperatures gained by extrapolation of the temperatures at the max weight-loss rate, at the beginning and at the end of the weight-loss stage of TG curves are 456.6ºC, 439.5ºC and 470.5ºC, respectively. In order to determine the actual reaction mechanism of the decomposition process, it is necessary to ascertain the values of activation energy using kinetic methods, such as Kissinger, Flynn-Wall-Ozawa or Friedman method, then to compare these values with that obtained using Coats-Redfern method. Analysis of experimental results suggested that the actual reaction mechanism is R₁ deceleration type.
Keywords poly(dodecamethyleneisophthalamide), PA12I, degradation process, degradation kinetics

1 INTRODUCTION
The study of the thermal degradation of a polymer is of major interest since it can, in many cases, determine the upper temperature limit of use for a material. Also, considerable attention has been directed towards the exploitation of thermogravimetric data for the determination of kinetic parameters. For this purpose, the thermogravimetric analysis (TGA) is a technique widely used because of its simplicity and the information afforded by a simple thermogram.
    Many of the methods of kinetic analysis are based on the hypothesis that, from a simple thermogravimetric trace, meaningful values may be obtained for parameters such as activation energy and pre-exponential factor. There are many proposed methods to calculate kinetic parameters and these reported values depend not only on experimental conditions but also on mathematical treatment of data. Poly(dodecamethyleneisophthalamide)(PA12I) is a semiaromatic, amorphous and transparent polyamide. In this paper, we studied its thermal degradation process and mechanism of a solid state process.

2 KINETIC METHODS    
All kinetic information can be extracted from dynamic experiments by means of various methods. All kinetic studies assume that the isothermal rate of conversion , da/dt, is a linear function of a temperature-dependent rate constant, k, and a temperature-independent function of the conversion, a, that is:
    (1)
that expresses the rate of conversion , da/dt, at a constant temperature(T) as a function of the reactant concentration loss and rate constant.
   According to Arrhenius equation
(2)
where A, the pre-exponential factor , is assumed to be independent of temperature, E_a is the activation energy, T the absolute temperature, and R the gas constant.
    Combination of Eqs. (1) and (2) gives
     (3)
    In the case of polymer degradation, it is assumed that the rates of conversion is proportional to the concentration of material that has to react,
f(a)=(1-a)ⁿ       (4)
    (5)
    If the sample temperature is changed by a controlled and constant heating rate, b=dT/dt, the variation in the degree of conversion can be analysed as a function of temperature, this temperature being dependent on the time of heating.
(6)
    This is the fundamental expression of analytical methods to calculate kinetic parameters on the basis of TG data. These methods can be distinguished as based on degree of conversion measurement. a, and   based on heating rate b.
    The variation in the degree of conversion can be analysed as a function of temperature, this temperature being dependent on the time of heating. Therefore, the rate of conversion may be written as follows:
       (7)
    A combination of Eqs. (3) and (7) leads to

(8)
integration of this equation from an initial temperature, T₀, corresponding to a degree of conversion a₀，to the inflection temperature, T_p, where a=a_p, gives
   (9)
if T₀ is low, it may be reasonably assumed that a₀=0 and considering that there is no reaction between 0 and T₀^[1]:
(10)
where is the integral function of conversion.
    In the case of polymers, the degradation process follows either a sigmoidal function or a deceleration function. Table 1 shows different expressions of for the different solid state mechanisms^[2-4]. These functions were satisfactorily employed in the only known method for the estimation of reaction mechanisms from dynamic TG curves.

Table 1 Algebraic expressions for g(a) for the most frequently used mechanisms of solid state processes

2.1 Kissinger method^[5]
Kissinger method has been used in the literature to determine the activation energy of solid state reactions from plots of the logarithm of the heating rate versus the inverse of the temperature at the maximum reaction rate in constant heating rate experiments.
    The activation energy can be determined by Kissinger method without a precise knowledge of the reaction mechanism, using the following equation.
     (11)
where b is the heating rate, T_p and a_p are the absolute temperature and weight loss at the maximum weight-loss rate(da/dt)_p ,respectively. A is the pre-exponential factor, and n is the reaction order.
    From a plot of versus and fitting to a straight line, the activation energy E_a can be calculated from the slope.
2.2 Flynn-Wall-Ozawa method^[6-8]
Eq (10) is integrated using the Doyle approximation^[9,10]. The result of the integration after taking logarithms is
(12)
where b, A, E_a and T have the known meanings.
    This is one of the integral methods that can determine the activation energy without a knowledge of reaction order. It is used to determine the activation energy for given values of conversion. The activation energy for different conversion values can be calculated from a log b versus 1000/T plot.
2.3 Friedman method^[11-13]
This method is probably the most general of the derivative techniques and is based on the intercomparsion of the rates of conversion dα/dt for a given degree of conversion a determined using different heating rates b.
    This method utilizes the following logarithmic differential equation derived from Eq . (5)
(13)
    Using this equation, it is possible to obtain values for E_a over a wide range of conversions by plotting ln(da/dt)versus 1/T for a constant a value.
2.4 Coats-Redfern method^[14,15]
Coats-Redfern used an approximation for the resolution of Eq. (10), obtaining
(14)
Activation energy for every degradation process listed in Table 1 can be determined from a plot of versus 1000/T.
3 EXPERIMENTAL
3.1 Material
The material evaluated in this study was PA12I which was synthesized by the following process:
Into a 100ml stainless steel autoclave 3 parts of dodecamethlyene diammonium isophthalate (PA12I salt) and 10 parts of distilled water were added. After purging several times under vacuum nitrogen repeatedly, the reactor was sealed and monomer/water mixture was heated to 220ºC over two hours period wherein the pressure finally reached to 2.3MPa. After the reaction was held at 220ºC for an hour , the pressure was decreased to atmospheric pressure by an open pipe through water seal tube in an hour. Then the vessel was kept at atmospheric pressure for two further hours. The gained polymer has a reduced viscosity of 1.17dl/g, measured in a 0.5g/dl solution in 96% sulfuric acid at 25ºC.
3.2 Apparatus
The thermogravimetric analysis was performed with NETZDCH TG 209 Thermal Analyzer. Samples were in an open platinum sample pan and the experiments conducted in N₂ at a flow rate of 10 mL/min. The temperature was calibrated with indium. Nominal heating rates of 3ºC, 6ºC, 10ºC, 15ºC and25ºC/min were employed and continuous records of sample temperature, sample weight and its first derivative were taken.
3.3 Operating procedure     
The PA12I degradation process is followed by monitoring weight loss according to temperature in a controlled atmosphere (N₂). For these measurements, cylindrical alumina crucibles have been used in which every sample of PA12I has been placed without a previous treatment. Work conditions (gas flow, heating rate and polymer weight) have been separately established in every particular case. The temperature range of the experiments was between 30 and 550ºC in order to completely decompose the polymer and was conducted at a constant heating rate.

4 RESULTS AND DISCUSSION
Fig. 1 shows TG curves corresponding to dynamic experiments carried out at different heating rates: 3 , 6 , 10 , 15and 25ºC/min. We can see from Fig. 1 that these decomposition processes are a single-stage decomposition reaction where the procedural decomposition temperatures can be well defined. The degradation temperature rises with the increasing of the heating rate.

Fig.1 TG curves of PA12I thermal degradation at different heating rates.

The equilibrium degradation temperatures are gained by extrapolation of T₀, T_p and T_f to b=0: ºC, ºC, ºC.
    Using Kissinger method, Eq. (11), the activation energy can be calculated from a plot of versus (Fig. 3). The obtained activation energy is 196.91kJ/mol.

Fig. 4 Polts of log b versus 1000/T with weight loss from 9% to 30% in steps of 3% according to Flynn-Wall-Ozawa method (b=3, 6, 10, 15, 25).

The activation energy can also be determined using the method of Flynn-Wall-Ozawa, Eq. (12), from a linear fitting of lnb versus 1000/T at different conversions(Fig. 4). Owning to the fact that this equation was derived using the Doyle approximation, only conversion values in the low range can be used. For this study, we have used the conversion values: 9, 12, 15, 18, 21, 24, 27 and 30%. Fig. 4 shows that the fitting straight lines are nearly parallel, thus indicating the applicability of this method to our PA12I system in the conversion range studied. This fact suggests that a single reaction mechanism is operative^[16,17]. Activation energies corresponding to the different conversions are listed in Table 2. From these values a mean value of 194.81kJ/mol was found. Table 2 also shows that the activation energy is very close to the value obtained using Kissinger method.

Table 2 Activation energies obtained by using Flynn-Wall-Ozawa method

    Compared to other methods these two methods present the advantage that they do not require previous knowledge of the reaction mechanism for determining the activation energy. Some authors^[2,18] used the activation energies obtained using these two methods to check their thermal degradation mechanism models.

Table 3 Dependence of Activation energy upon fractional weight loss according to Friedman method

    In addition, the activation energy can also be determined using the method of Friedman, Eq. (13), from a linear fitting of ln(da/dt)versus 1000/T for a constant a value. The kinetic parameters obtained by this method have been summarized in Table 3. From these values a mean value of 210.58 kJ/mol is found. And this value is also very close to the value obtained using Kissinger method.

Table 4 Activation energies obtained using the Coats-Redfern method for several solid state processes at a heating rate of 3ºC/min

Table 5 Activation energies obtained using the Coats-Redfern method for several solid state processes at a heating rate of 6ºC/min

Table 6 Activation energies obtained using the Coats-Redfern method for several solid state processes at a heating rate of 10ºC/min

    Using Eq. (14), proposed by Coats and Redfern, the activation energy for every g(a) function listed in Table 1 can be obtained at constant heating rates from fitting of versus 1000/T plots. For this study we have used the same conversion values as those used in the previous methods. Tables 4 - 6 show activation energies, the pre-exponential factors and correlations for conversions in the range 9%-30% at constant heating rate value 3, 6, 10ºC/min, respectively. Analysis of these tables shows that, the activation energies rise with the increasing of the heating rate and at all the heating rate values, the activation energies are in good agreement with those obtained using above mentioned methods correspond to an Rn type mechanism. Also , from these tables it can be seen that the optimum heating rate value is 3ºC/min, at which the activation energy corresponding to a mechanism R₁ is 225.80 kJ/mol, very close to the energies obtained by the above methods. These facts strongly suggest that the solid state thermal degradation mechanism followed by our PA12I system is a deceleration (R_n) type. R₂, R₃and R₁ are equally possible. However an R₁mechanism needs a lower energy to start, and this energy at lower heating rates, where the comparisons are more reliable.

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