Mechanical properties and quantum mechanical simulations of natural rubber composites with cerium complexes under aging conditions

To gain a deeper insight into the thermal-oxidative degradation behavior during vulcanization, the Kissinger and Flynn-Wall-Ozawa methods were used for the analysis as detailed in [15]. These methods were used to calculate the activation energy, which was obtained from careful consideration of the correlation between the maximum peak temperature value and the heating rate, in the course of multiple thermal analyses. By applying these methods, we were able to gain a better understanding of the complex and intricate processes occurring during the thermo-oxidative degradation of vulcanization.

1dαdt=Ae(−E2RT)(1−a)n$${{{\rm{d}}\alpha } \over {dt}} = A{e^{\left( { - {{{E_2}} \over {RT}}} \right)}}{(1 - a)^n}$$

Where: A is the exponential perfector. E_α is the activation energy in kJ·mol⁻¹ and R is the ideal gas constant (8.3145 J/(moloK)); The following equation for Kissinger is calculated differently for both sides of the above equation [16].

2lnβTmax2=lnAREa−EaR1Tmax$$\ln {\beta \over {T_{\max }^2}} = \ln {{AR} \over {{E_{\rm{a}}}}} - {{{E_{\rm{a}}}} \over R}{1 \over {{T_{\max }}}}$$

Where: T_max is the temperature at the maximum rate of thermal oxygen degradation as determined by the DTG curve. lnβ/T²_max was plotted against 1000/T_max according to the Kissinger equation. The activation energy E_α can be found by finding the slope -E/R.

The relationship between lnβ /T²_max and 1000/T_max determined by the Kissinger method was shown in Figure 6, and the resulting Eα was listed in Table 3.

Fig. 6.

The accuracy and reliability of the activation energy of the oxygen thermal decomposition process calculated by Kissinger’s method was indisputably confirmed, as evidenced by the fact that the correlation coefficient of all three linear fits was greater than 0.95. Furthermore, a glance at Table 3 showed that the addition of the antioxidant PAS-Ce or the antioxidant 2246 significantly increased the thermal oxygen decomposition energy of NR. This, in turn, led to an apparent inhibition of its decomposition. It was noteworthy that the activation energy of thermal oxygen decomposition of the combined PAS-Ce/NR system exceeded the activation energy of the combined 2246/NR system.

According to the report, Kissinger’s method was considered a model-free technique for thermal oxygen decomposition processes because it used a different approach without considering the decomposition model [17]. However, an alternative method, the Flynn-Wall-Ozawa (FWO) method, was introduced to improve the reliability of the activation energy calculated by the Kissinger method, which gave different activation energy values for the thermal decomposition of oxygen. The FWO method derived the activation energy for the thermal decomposition of oxygen by determining the characteristic temperature corresponding to different weight loss rates (β ). The activation energy was calculated by comparing β with the logarithm of 1000/T and then with the linear slope obtained by linear fitting. Then, when plotting the activation energy versus weight loss, the range of activation energy values should include the activation energy of the thermal decomposition of oxygen determined by the Kissinger method. It was worth noting that in Figure 7 the correlation coefficient of all fitted lines was greater than 0.96. Thus, the activation energy of the oxygen thermal decomposition process was calculated very reliably for the three NR samples by the FWO method.

Fig. 7.

Figure 8 illustrates the correlation between activation energy (E_α) and conversion rate (α) as determined for three NR composite systems by the FWO method. Each curve had an endpoint corresponding to the initial stage of NR backbone failure. Then, an autocatalytic process took place, which led to a decrease in the value of E_α [18]. Interestingly, the PAS-Ce/NR composite system requires significantly higher E_α values for thermotoxic degradation than the 2246/NR system. In addition, three curves ranging from 10% to 60% were integrated to obtain the average E_α range, and then the area values were divided from 65% to 100%. The resulting values are presented in Table 4. It was worth noting that the E_α values were different for different NR composite systems. The PAS-Ce/NR composite system showed a rapid increase in E_α followed by minimal fluctuations, while the 2246/NR system was characterized by a small but relatively constant increase in E_α.

Fig. 8.

The corresponding E_α values calculated by the Kissinger method fall within the range calculated by the FWO method, so the results were practically reliable and reflect the actual kinetic information.

As a widespread material in various industries, rubber was often exposed to heat and oxygen in the air. Heat stimulated oxidation and oxygen caused thermal degradation. Therefore, thermal-oxidative aging of rubber was the most common and important way of rubber aging. Thermal oxidative aging of rubber tended to lead to autocatalytic oxidation. In particular, the entire reaction process associated with the thermal oxidative aging of NR occurred through the mechanism of autocatalytic free radical oxidation. This process was divided into three distinct stages [19–21]. (1) Chain initiation: Under the influence of heat and light, the unsaturated double bonds between the molecular structure of the rubber material dissociate, leading to the cleavage and breaking of molecular chains and crosslinks, resulting in the formation of the free radical NR·.

(2) Chain growth: The reactive R· rapidly combined with oxygen molecules to form the substituent radical ROO·. ROO· continued to react with the rubber molecular chain, forming new radicals R· and the hydroperoxide ROOH, which under certain conditions decomposed to form the radical RO· and the radical HO·. These reactive radicals continued to react with the rubber molecular chain to form alcohols, water, and the R- R-radical. Thus, the R- formed in the previous aging cycle participates in the next cycle. This generates more free radicals and accelerates the thermal oxidative aging process of the rubber. In summary, the thermal oxidative aging process of rubber was characterized by autocatalytic oxidation.

(3) Chain termination: During the Kautschuk thermal-oxidative aging cycle, free radicals bind to or disproportionate with non-radicals. This completed the chain reaction. As a result, during aging, some rubber particles became hard and brittle as a result of free radical binding, which increased cross-link density [22], while some rubber particles degraded in molecular chains, reducing cross-link density and becoming sticky and soft [23].

Based on the results of the study, it was found that the aging mechanism of NR can be effectively controlled by reducing the concentration of surrogate free radicals in the degradation phase. Interestingly, it was observed that the O-H bond between the PAS-Ce antioxidant and the 2246 antioxidant exhibited significant reactivity and preference towards the agent radical reaction.

This directly contributed to reducing the concentration and reaction rate of the substituent radicals in NR, thus effectively preventing its thermal and oxygen aging [24]. Here, it can be firmly concluded that the energy dissipation in O-H bond dissociation reactions between antioxidants can be distinguished by their levels of effectiveness in protecting NR.

The free energies of the C-H bond of the NR molecule, the O-H bond of the PAS-Ce antioxidant, and the dissociation reaction of the 2246 antioxidant were calculated by quantum mechanical (QM) simulations as shown in Figure 9.

Fig. 9.

After optimizing the desired structural balance, a frequency analysis was performed using the Dmol3 module. This allowed accurate calculations of the zero-point energy at each dissociation point and corrected energy values for the NR configuration. To better understand the effect of temperature on the dissociation reactions, the Gibbs free energy of each dissociation reaction was carefully calculated over the full range of possible operating temperatures of NR, from 200 K to 375 K, at atmospheric pressure. The sum of the electronic energies of the reagent and product radicals calculated for each dissociation reaction at 0 K is given in Table 5. Through these complex calculations and detailed analysis, a deeper understanding of the basic mechanical properties of the dissociation mechanism of NR can be achieved.

A closer reading of the combined data in Table 5 reveals a clear trend: NR has the lowest dissociation energy and the highest activity at position a, which is most susceptible to the damaging effects of oxygen radicals. This important insight suggests that oxidative degradation plays a crucial role in the overall degradation of NR.

For further analysis, Table 6 details the energy corrections of the reactants and products at different temperatures. It is worth noting that no energy correction values for the H-radical at different temperatures are given in this table. These results provide important information for the development of improved methods and techniques aimed at increasing the functionality and durability of NR products. Through a nuanced understanding of the complex molecular mechanisms of NR, new solutions can be achieved to optimize its properties.

The free energies of each dissociation reaction at different temperatures are listed in Figure 10 according to Equation (9).

Fig. 10.

After careful analysis of the molecular structure of the two antioxidants, it was found that the dissociation energies of their O-H bonds are lower than those of the C-H bonds in NR. This important discovery led to the understanding that the two antioxidant molecules dissociate readily from NR chains when exposed to thermal-oxidative aging. In addition, both antioxidant PAS-Ce and antioxidant 2246 are effective in dissociating reactive hydrogen radicals with oxygen during aging, thereby terminating the free radical chain reaction initiated in NR during aging.

In addition, it was found that the free energy required to destroy the g-dot was significantly lower than the free energy required to destroy the h-dot. This finding indicates that the antioxidant PAS-Ce was significantly more effective than the antioxidant 2246 in inhibiting the thermal-oxidative aging of NR. This may be due to the electronic structure, atomic number, and coordination ability of the cerium layer. Cerium, which had an empty 4d orbital and a relatively large atomic radius, has a strong coordination ability and was able to trap more radicals growing along the chain, providing better protection for NR.

In essence, the advanced molecular structures of the two antioxidants and their unique properties played an important role in determining the protective effect of NR against thermal-oxidative aging. These discoveries were important for the development of more effective and durable NR products and paved the way for further developments in materials science.