Thermal Stability and Decomposition Kinetics of Polysuccinimide

The thermal stability and decomposition kinetics of polysuccinimide (PSI) were investigated using analyzer DTG-60 under high purity nitrogen atmosphere at different heating rates (3, 6, 9, 12 K/min). The thermal decomposition mechanism of PSI was determined by Coats-Redfern method. The kinetic parameters such as activation energy (E), pre-exponential factor (A) and reaction order (n) were calculated by Flynn-Wall-Ozawa and Kissinger methods. The results show that the thermal decomposition of PSI under nitrogen atmosphere mainly occurs in the temperature range of 619.15 693.15 K, the reaction order (n) was 3 4 , the activation energy (E) and pre-exponential factor (A) were obtained to be 106.585 kJ/mol and 4.644 × 10 min, the integral and differential forms of the thermal decomposition mechanism of PSI were found to be   3 4 ln 1        and     1 4 4 1 ln 1 3          , respectively. The results play an important role in understanding the thermodynamic properties of polysuccinimide.


Introduction
Polyaspartic acid (PASP, CAS181828-06-8) has amino and carboxyl groups, which belongs to the biological macromolecule material and is a kind of polymer of amino acids.Since it has the characteristics of good biocompatibility and biodegradability, PASP has been widely used in industrial and medical fields as a new type of green chemicals [1].Polysuccinimide (PSI, CAS6899-03-2) is the intermediate of PASP.The experimental formula and relative molecular mass of its monomer are C 4 H 3 O 2 N and 97.074 g/mol, respectively.The chemical structure of the monomer can be written as: In view of this, PSI is a kind of linear polyimide with high activity and it is easy to open ring changing into poly asparagine with side chains.With the special property, many kinds of derivatives that were used as drug carriers have been prepared [2].
The thermal stability and decomposition kinetics of Polysuccinimide (PSI) were investigated by TG-DTA method.Kinetic parameters such as activation energy (E) and pre-exponential factor (A) were calculated by Flynn-Wall-Ozawa (F-W-O) and Kissinger methods.The kinetic mechanism function of thermal decomposition of PSI was established by Coats-Redfern method.Using TG-DTA method to study the stability of drugs has the advantages of less sample dose, short experimental period and reliable results.These data not only play an active role in understanding the thermodynamic properties of PSI but also provide a theoretical basis for practical application.

Materials and Instruments
Polysuccinimide (the mass fraction was higher than 99.5%) was purchased from Henan Xinlianxin Fertilizer Limited Co. α-Al 2 O 3 (standard material, Shimadu Company in Japan) was used as standard material in the process of thermal analysis.
The TG-DTA analyzer (type DTG-60, Shimadzu Corporation, Japan) was used to determine the TG-DTA curves of the sample.SPN-500-type nitrogen generator (Hewleet-Packard, Beijing Institute of Technology, China) was used to provide a high purity nitrogen atmosphere for the experimental system of thermal analysis.Fourier Transform Infrared Spectrometer (type WQF, Beijing Beifen-Ruili Analytical Instrument (Group) Co, Ltd) was used to analyze PSI.Gel permeation chromatography (type Agilent1100, Agilent Corporation, America) was used to analyze PSI's purity and the number-average molecular weight (M n ) and polydispesity index (M w /M n ).

Experiment Methods
The PSI sample was dried in the vacuum oven at 378.15 K before analysis.The thermogravimetric measurements were carried out at different heating rates (3, 6, 9, 12 K/min) from room temperature to 873.15 K under high purity nitrogen atmosphere (20 ml/min).Mass of each powdered sample was about 4 -5 mg.

FTIR Analysis of PSI
FTIR spectra of PSI were recorded in the wave number range of 4000 -500 cm −1 .The result is shown in Figure 1.From Figure 1, we can know that the carboxyl group of branched chain in the opened ring appears at 1400 cm −1 , the carbon-carbon bond appears at 1165 cm −1 , the coupled carbonyl group appears at 1720 cm −1 and the carbonyl group in the ring obviously appears at 1797 cm −1 .that the number-average molecular weight (M n ) of PSI is 2.7941 × 10 4 g/mol, the polydispersity index of relative molecular mass (M w /M n ) of PSI is 21.644 and Polymerization degree of PSI is obtained to be 287.5.
In general, the thermal decomposition of a solid polymer under inert atmosphere can be summarized as: B solid → C solid + D gas .Polymer is finally decomposed into solid residue (C) and gaseous matter (D).
The kinetic analysis of solid-state sample is usually given by Equation (1) [17]     where d dt  is the rates of conversion;  is the con- version degree that can be defined as which m 0 and m f are the initial and final masses of the sample, respectively; m t is the mass of the sample at time t (or temperature T) of the decomposition process, mg.In Equation ( 1), is the temperature dependent rates constant and is normally assumed to obey the Arrhenius equation: where A is the pre-exponential factor (min −1 ), E is the activation energy (kJ/mol) of the kinetic process, R is the gas constant (8.314J/(mol•K)) and T is the absolute temperature (K).
is approximately constant when the values of α are the same at the different heating rates β i , so it is easy to obtain values of E by plotting lgβ against 1/T at the certain conversion degree α.Moreover, taking into account the heating rates β = dT/dt under non-isothermal condition, d dt  can be de-

Coats-Redfern Method
Coats-Redfern method can be described as Equation (7).[8][9][10]12]: scribed by Equation (3): Equation ( 4) can be obtained by combing Equations ( 1)-( 3), which describes the thermal decomposition kinetics.Based on TGA data, the kinetic parameters can be calculated from Equation ( 4).[18]: where g(α) comes from one of 34 forms of integral formula in the literature which are shown in Table 1 [11].From Equation (7), the values of both E c and A c can be obtained for any selected g(α) and fixed β i (i = 1, 2, 3, 4, even more).The calculating steps in detail are: 1) choose the same α j for each heating rates β i and calculate the corresponding g(α ij ); 2) give the corresponding tempera- ture T ij according to α ij ; 3) describe the sketch of

Kissinger Method
The formula of Kissinger method is given by Equation ( 5) [3][4][5]: versus 1/T i for each fixed β i , and calculate the values of both E c and ln(A c ) according to the slope and intercept of the line, respectively; 4) determine the mechanism function of the thermal decomposition process.Generally, the selected mechanism functions should meet all the conditions, which are: 1) 0 < E c < 400 kJ/mol; 2) where i = 1, 2, 3, 4 (or even more); T pi is the peak temperatures of different DTA curve at different heating rates.By plotting  2 ln i p i T   versus 1/T pi , the activation energy E k and pre-exponential factor A k can be calculated based on its slope (−E k /R) and intercept ln(A k R/E k ), respectively.
   in which ln(A k ) are obtained from Kissinger method.If g(α) meet the requirements mentioned above, g(α) can be regarded as the probable mechanism function for the thermal decomposition process.

Flynn-Wall-Ozawa (F-W-O) Method
F-W-O method can be used directly to calculate the activation energy E. The integral formula of F-W-O method [14][15][16] is showed in Equation ( 6):

Determination of High Temperature Heat-Resistance of PSI
In Equation ( 6), since the value of The activation energy data obtained by above-mentioned methods can be used to evaluate the high temperature heat-resistance of PSI.The relationship between activa-Table 1. 34 types of thermal decomposition mechanism functions.
tion energy and lifetime of polymer can be expressed by Equation ( 8) [19]: where t f is the lifetime of PSI at the temperature of T f , T α is the temperature at the conversion degree α.Combined Equations ( 4) and ( 8), T f can be shown as:

Thermal Decomposition of PSI
TG and DTA curves of PSI sample are shown in Figures 3 and 4. The thermal analysis data are summarized in Table 2.In Figure 3, the thermal decomposition temperature at different heating rates increases with the increasing of  .That indicates the decomposition temperature is affected by the heating rate  .Besides, each TG curve of PSI under nitrogen atmosphere has an obvious mass loss process where percentage of mass loss   increases gradually with the increasing of heating rates and TG curve moves toward to the right.
From Figures 3 and 4, the thermal decomposition of PSI under nitrogen atmosphere mainly occurs in the temperature range of 619.15 to 693.15 K. Mass loss is accompanied by heat absorption, so thermal decomposition process and solid rearrangement reaction may simultaneously happen in this process.The activation energies calculated at different conversion degree using Flynn-Wall-Ozawa method are shown in Table 3 and the relationship between E 0 and conversion degree α are showed in Figure 6.

Plots of
The results show that the correlation coefficients (R 2 ) of FWO method is better, the values of activation energy is between 81.509 and 122.205 kJ/mol and increase with the increasing of conversion degree.From Table 3 and Figure 6, the average value of activation energy E o is 104.202kJ/mol and the pre-exponential factor lgA o is 9.967.
The kinetic parameters calculated by Coats-Redfern method are listed in Table 4.The values of activation energy and exponential factor calculated by Coats-Redfern method compare respectively with the average value of activation energy calculated using FWO method and the value of pre-exponential factor obtained by Kissinger method, the results are listed in Table 5.
The thermal decomposition process of PSI in the temperature stage of 619.15 to 693.15 K is consistent with the sequence number 14 in

High Temperature Heat-Resistance of PSI
Selecting t f = 60 s and α = 15% as the evaluation indexes of the high temperature heat-resistance of the polymer.According to Equation (12), value of T f of PSI in nitrogen atmosphere is 259.27˚C.The result shows that the high temperature heat-resistance of PSI is not very well.

Conclusion
The thermal behavior of polysuccinimide under nonisothermal condition was investigated using TG-DTA method at different heating rates in nitrogen atmosphere.
The results show that the thermal decomposition of PSI under nitrogen atmosphere mainly occurs in the temperature range of 619.15 -693.15K, the reaction order (n) was 3/4, the activation energy (E) and pre-exponential factor (A) were obtained to be 106.585kJ/mol and 4.644 × 10 9 min −1 , the integral and differential forms of the thermal decomposition mechanism of PSI were found to be  

Figure 2 .
Figure 2. The analysis diagram of PSI by gel permeation chromatography.

Figure 3 .
Figure 3.The TG curves of PSI in nitrogen atmosphere.

Figure 4 .
Figure 4.The DTA curves of PSI in nitrogen atmosphere.


against 1/T p of PSI by Kissinger method is shown in Figure 5.The values of activation energy E k and exponential factor ln(A k ) calculated by Kissinger method are 143.874kJ/mol and 23.897 min 1 , respectively.The linear correlation coefficient (R 2 ) is 0.9852.
E c and ln(A c ) meet better with the conditions of both besides, the relative coefficients (R 2 ) are much better.The integral and differential forms of the mechanism function are     .The values of E c and ln(A c ) are obtained to be 108.967kJ/mol and 16.802 min −1 .So the activation energy and pre-exponential factor of thermal decomposition process of PSI can be regarded as 106.585 kJ/mol and 4.644 × 10 9 min −1 (i.e.average values obtained by the Coats-Redfern and FWO methods).The thermal decomposition kinetic equation of PSI can be described as:

Figure 5
Figure 5. Plots of

Figure 6 .
Figure 6.FWO curves of PSI at different conversion.

Table 3 . The activation energy E o and exponential factor lgA o of PSI.
α E o (kJ/mol) lgA o (min −1 )