Thermal decomposition reaction kinetics and storage life prediction of polyacrylate pressure - sensitive adhesive

: The thermal decomposition behavior of polya - crylate pressure - sensitive adhesive ( PSA ) at heating rates of 4, 6, 8, and 10 K · min − 1 was measured by thermogravi - metric analysis ( TGA ) . The kinetic parameters for thermal decomposition reaction of the polyacrylate adhesive were obtained from TG pro ﬁ le by di ﬀ erential method and inte - gral method ( Kissinger, general integral, MacCallum – Tanner, Š atava – Š esták, Agrawal, and Flynn – Wall – Ozawa ) , the results show that the main decomposition stage of the polyacrylate adhesive starts at 301°C and its activation energy is 142.68 kJ · mol − 1 , the pre exponential factor is 10 9.55 , the decomposition mechanism obeys Avrami – Erofeev equation and its decomposition kinetic equation can be expressed as: d α /d T = ( 10 9.55 / β )[( 1 − α ) /2 ][ − ln ( 1 − α )] − 1 exp ( − 1.7161 × 10 4 / T ) . The storage life of PSA at 25°C was pre - dicted to be about 19 years by isoconversional method.


Introduction
Pressure sensitive adhesive (PSA) is a kind of adhesive which is very sensitive to pressure and can be firmly bonded to different kinds of substrates with light finger pressure (1,2).PSA is usually coated on plastic films, fabrics, paper, or metal foils to make PSA tapes, PSA labels, and other products, which have a very wide range of applications (3)(4)(5).In recent years, with the rapid economic development, the demand for PSA and its products in packaging and related industries is increasing day by day.The development of PSA is showing a trend of rapid change, among which polyacrylate PSAs are the most researched and applied (6,7).
Polyacrylate PSA is mainly polymerized from acrylic esters and other vinyl monomers (8).It is a viscoelastic material with both liquid and solid characteristics (9).It has not only liquid fluidity and wettability, but also solid cohesion strength, it is currently the most rapidly developing type of adhesive with the broadest application prospects (10).Polyacrylate PSA has good adhesive properties, simple formulation, non-toxic, harmless, and low cost.It can be made into various pressure sensitive tapes, labels, and protective films, which are widely used in electronic, military, medical, and other fields (11,12).
As a kind of polymer material, the polymer chain segment of polyacrylate PSA is easy to degrade in the long-term use process and finally results in bonding failure, especially at higher temperature (13).If the thermal oxidative stability of polyacrylate PSA is poor, it is easy to lose the pressure sensitivity and this limits their range of application to some extent (14).At present, there are few papers, which focused on the thermal stability of polyacrylate PSA, especially the research on its thermal decomposition kinetics.Therefore, it is necessary to study the thermal properties of polyacrylate PSA.
In this work, a differential method (Kissinger) and five integral methods (General integral, MacCallum-Tanner, Šatava-Šesták, Agrawal, and Flynn-Wall-Ozawa) were employed to study their thermal stability.In addition, the storage life of polyacrylate PSA was predicted by isoconversional method using the thermal decomposition kinetic parameters and thermal decomposition mechanism functions.

Materials and equipment
Polyacrylate PSA were procured from Jiangyin Desay Chemical Trade Co., Ltd, China.
The thermal degradation behavior was observed using thermal gravimetric analysis (STA 449 F3, NETZSCH, Germany).

Measurements
The thermal decomposition behavior of polyacrylate PSA at heating rates of 4, 6, 8, and 10 K•min −1 was measured by thermogravimetric analysis from 50°C to 600°C under nitrogen (50 mL•min −1 ).Amounts of 10 mg of each sample were placed in aluminum oxide crucibles.

Isoconversional kinetics
The principle of the isoconversional method is that when the conversion rate α remains constant, the reaction rate is only a function of temperature, which can be clearly described by Eq. 1 (15).
by which the reaction rate and reaction process can be calculated at any selected temperature T or time t, and the kinetic parameters under isothermal, non-isothermal, adiabatic, and other conditions can be predicted.When α is constant, Eq. 1 can be reduced to Eq. 2 as follows: Therefore, the activation energy E(α) can be calculated without knowing the reaction function (16,17).
Friedman, as the most common differential isoconversional method, proposed to apply the logarithm of the conversion rate dα/dt as a function of the reciprocal temperature at any conversion α (16).
Because f(α) is a constant at any fixed value of α, the logarithm of the conversion rate dα/dt on 1/T keeps a straight line with the slop m = −E/R, and the following equation can be obtained: Therefore, the Friedman method can be used to predict the reaction rate and process under various temperature conditions such as isothermal, non-isothermal, and slow heating (17,18).

Thermal degradation of polyacrylate PSA
In order to truly understand the thermal decomposition behavior of polyacrylate PSA, the TG-DTG curves of the adhesive was obtained at a lower heating rate of 4 K•min −1 , as shown in Figure 1.
TG results state that the main decomposition of the adhesive started at 301°C, ended at 479°C accompanying with a mass loss of 92.2% and a summit peak located at 388°C, and the mass loss rate was about 1.47%.The TG curves of polyacrylate PSA at different heating rates are shown in Figure 2. It can be seen from Figure 2 that with the increase of heating rate, the TG curves of the adhesive gradually moves to a higher temperature, but the deviation is small, that is, the thermal decomposition temperature of the adhesive changes slightly with the increase of heating rate.This may be due to the fact that when the heating rate is slow, there is sufficient time for heat transfer and the thermal energy distribution is relatively balanced.When the heating rate is fast, thermal hysteresis occurs, and the interior of the sample cannot be heated and decomposed in time (19).

Non-isothermal decomposition kinetics of polyacrylate PSA
The peak temperature (T P ) of the adhesive during thermal decomposition can be obtained by differential treatment of the TG curves, as shown in Table 1.
For Eqs. 7 and 8, β is the linear heating rate, T P is the peak temperature, A is the pre-exponential factor, R is the gas constant and equal to 8.314 J•mol −1 •K −1 , E is the apparent activation energy.The kinetic parameters (E and A) for thermal decomposition reaction of polyacrylate PSA were obtained by employing Ozawa (Eq.7) and Kissinger (Eq.8) by using the measured experimental data T P from TG, and the results are listed in Table 2.
It can be seen from Table 2 that the E of thermal decomposition stage of polyacrylate PSA obtained by Flynn-wall-Ozawa and Kissinger method are 138.52 and 135.07 kJ•mol −1 , respectively, and the values of r are 0.9924 and 0.9910, respectively, which shows that the values obtained by the two methods are very close.Therefore, the thermal decomposition kinetic parameters of the adhesive obtained by the two methods are reliable and the results can be used as the reference values for calculating the most probable mechanism function.According to the above analysis, when the heating rate is 4 K•min −1 , the decomposition depth of the main decomposition stage of the adhesive is more than 90%.The thermal decomposition mechanism of the main decomposition stage has a great influence on the service life of the materials in the process of use and storage, so this work mainly studies the most probable mechanism function of the main decomposition stage of the adhesive.
The conversion degrees (a) can be expressed by the mass loss in thermogravimetric analysis.The TG curves at heating rates of 4, 6, 8, and 10 K•min −1 were dealt with mathematic means to obtain the relationship between a and T at different heating rates, as shown in Figure 3.It can be seen from the figure that when the heating rate increases, the temperature required for the thermal  decomposition of the adhesive also increases at the same depth, but the increment is small, which indicates that the thermal decomposition of the adhesive is less affected by the heating rate.
The relationship of activation energy as function of a (Figure 4) was calculated from the original data of T-a at different heating rates (Table 3) by Flynn-Wall-Ozawa method, which showed that the E of the decomposition process changes obviously with the conversion degree increasing from 0 to 1.
To make sure the accuracy of kinetic model function f(a), the range of conversion degrees from 0.325 to 0.775, in which activation energy was approximately constant, was employed to study the reaction mechanism and kinetics.In addition, in order to minimize the influence of different reactions on the calculation of mechanism function, four common single heating rate methods (MacCallum-Tanner, Šatava-Šesták, general integral, and Agrawal (23)(24)(25)(26)) were used to calculate the mechanism functions of the adhesive, see Eqs. 9-12.Substituting the data T-a and 41 mechanism functions (Table A1 in Appendix) in Eqs.9-12, respectively (27), the kinetic parameters and the linear correlation coefficient (r), standard mean square deviation (q), and believable factor (d, where d = (1 − r)q) of the adhesive could be calculated according to the least square method, and the results were shown in Table 4.
According to the discrimination rule of mechanism function (26), 1.The kinetic parameters obtained by integral or differential equations: the apparent activation energy E and pre-exponential factor A should be within the normal range of thermal decomposition reaction, that is, The linear correlation coefficient |r| ≥ 0.98 is calculated by differential method or integral method; 3. The standard deviation of the results calculated by differential or integral method should be less than 0.3; 4. The mechanism function f(a) selected according to the above principles should be consistent with the state of the research object; 5.The kinetic parameters calculated by multiple heating rate method and single heating rate method should be consistent as far as possible.
According to the calculation, the mechanism function no. 17 is most consistent with the principles of "mechanism function discrimination method," that is, the decomposition mechanism of the adhesive in the main stage of thermal decomposition follows Avrami-Erofeev equation, and the calculation results are shown in Table 4.
Therefore, the decomposition mechanism function of the main thermal decomposition stage is: Substituting the average values of E a and log A in Eq. 13 The kinetic equation of the thermal decomposition reaction could be described as follows:

Storage life prediction of polyacrylate PSA
According to the theory in Section 2.3, the non-isothermal TG data obtained by polyacrylic PSA at scanning rates of 4, 6, 8, and 10 K•min −1 can be used to calculate the storage life.In order to ensure the accuracy of the method, the relationship between reaction progress with temperature, reaction rate, and temperature are simulated by Friedman method, and the results are represented in Figures 5 and 6.
In Figures 5 and 6, the solid line is obtained by experimental results and the dashed line is the simulation results.Obviously, simulation results are in agreement with the experimental results at different heating rates, which indicate that the isoconversional method is feasible.
We all know that the storage life of polymer materials is mainly affected by temperature, but in the actual storage process, the temperature rise rate inside the polymer materials is usually relatively slow due to its properties and ambient temperature.Therefore, TG curves (Figure 7) of polyacrylate PSA at slow heating rates (≤1 K•min −1 ) are calculated to obtain more realistic parameters.
Finally, the storage life of polyacrylate PSA at 25°C, 35°C, 45°C, 55°C, and 65°C are predicted as shown in Figure 8. Apparently, the higher the temperature was, the faster the reaction progress was, that is, the shorter the storage life.When 5% of the mass loss is taken as the failure criterion and the storage temperature is 25°C, the storage life of polyacrylate PSA is about 19 years.

Conclusion
The thermal decomposition behavior of polyacrylic PSA was tested by TG analysis under different heating rates.The results showed that the adhesive decomposed fastest at 388°C when the heating rate was 4 K•min −1 , and the mass loss in the main decomposition stage was about  92.2%.The kinetic parameters for thermal decomposition reaction of the adhesive were obtained by differential method and integral method: the activation energy E was 142.68 kJ•mol −1 , the pre-exponential factor A was 10 9.55 , and the thermal decomposition kinetic equation could be expressed as: dα/dT = (10 9.55 /β)[(1 − α)/2][−ln (1 − α)] −1 exp(−1.7161× 10 4 /T).The storage life of PSA at 25°C was predicted to be about 19 years by isoconversional method.
The results are not only beneficial to understand the thermal stability of the adhesive and lay the foundations for practical applications, but also provide research approach for the study of thermal properties and life prediction of other polymer materials.

Figure 3 :Figure 4 :
Figure 3: Thermal decomposition T-a curves of polyacrylate PSA at different heating rates.

Figure 5 :Figure 6 :
Figure 5: Reaction progress of polyacrylate PSA at different heating rates.

Figure 7 :Figure 8 :
Figure 7: TG curves of polyacrylate PSA at different slow heating rates.

Figure A1 :
Figure A1: Infrared spectra of PSA at different thermal degradation stages.

Table 1 :
Peak temperature of polyacrylate PSA at different heating rates

Table 2 :
Values of E and A by using Flynn-Wall-Ozawa and Kissinger method

Table 3 :
Activation energy value calculated by Flynn-Wall-Ozawa method using T-a data

Table 4 :
Kinetic parameters of main stage of polyacrylate PSA thermal decomposition