## 3 Results and Discussion
### Degradative Kinetics  
The degradative reaction of the LNR chains can be determined as a second-order reaction with respect to the number of bonds broken during depolymerization [25; 26; 27]. Referring to Equation (2), the intrinsic viscosity obtained can be calculated to the M\({}_{\mathrm{n}}\) values. A chain scission model for random scission of the macromolecule can be derived as in Equation (3):  
\[\frac{1}{\mathrm{M_{n(t)}}}-\frac{1}{\mathrm{M_{n(0)}}}=\frac{\mathrm{kt}}{ \mathrm{M_{0}}} \tag{3}\]  
where M\({}_{\mathrm{n(t)}}\) is the M\({}_{\mathrm{n}}\) of LNR at time = t, M\({}_{\mathrm{n(0)}}\) is the M\({}_{\mathrm{n}}\) of NR at time = 0, M\({}_{\mathrm{0}}\) is the M\({}_{\mathrm{n}}\) of isoprene unit (68 g/mol), and k is the rate constant. As previously discussed, process parameters, i.e., H\({}_{2}\)O\({}_{2}\) concentration, HCOOH concentration, NaNO\({}_{2}\) concentration, and temperature, significantly influence the degradation process. According to the Arrhenius relation, k = A\(\times\)Exp(\(-\)E\({}_{\mathrm{a}}\)/RT) where A, E\({}_{\mathrm{a}}\), R, and T are the pre-exponential factor, activation energy, gas constant, and temperature, respectively. These parameters have been proposed to relate to the kinetic model as a power function. Therefore, Equation (3) can be rewritten as Equation (4):  
\[\frac{\mathrm{M_{0}}}{\mathrm{M_{n(t)}}}-\frac{\mathrm{M_{0}}}{\mathrm{M_{n(0)} }}=\mathrm{A}\times\mathrm{e}^{\frac{-\mathrm{E_{a}}}{\mathrm{kT}}}\left[ \mathrm{H_{2}O_{2}}\right]^{\mathrm{m}}\left[\mathrm{CH_{2}O_{2}}\right]^{ \mathrm{n}}\left[\mathrm{NaNO_{2}}\right]^{\mathrm{o}}\times\mathrm{t} \tag{4}\]  
where [H\({}_{2}\)O\({}_{2}\)], [HCOOH], and [NaNO\({}_{2}\)] are the initial concentration of reagents (mol/L). The exponents of the reactant concentrations m, n, and o are referred to as partial orders of the reaction that must be determined experimentally. The partial order corresponding to each reactant is now calculated by conducting the reaction with varying concentrations of the reactant in question, and the concentrations of the other reactants are kept constant. Figure 8: SEM micrographs (20,000\(\times\)) of the rubber particles after degradation at different reaction times: (**a**) NR, (**b**) 3 h, (**c**) 6 h, and (**d**) 12 h. (The red line is diameter). Generally, the kinetic model, a power function of the process variables, is independent of time. Referring to Figures 4-6, the partial orders can be determined by using a log [(M\({}_{0}\)/M\({}_{n(t)}\) - M\({}_{0}\)/M\({}_{n(0)}\))/t]-log [reactant] plots and the linear regression technique, as shown in Figures 9-11. The corresponding slopes were the partial orders given by m, n, and o, respectively. Condition: H\({}_{2}\)O\({}_{2}\) = 0.4 M, NaNO\({}_{2}\) = 0.02 M, and T = 338 K.  
Figure 10: A log-log plot of [(M\({}_{0}\)/M\({}_{n(0)}\) - M\({}_{0}\)/M\({}_{n(0)}\))/t] versus HCOOH concentration at different reaction times. Figure 9: A log-log plot of [(M\({}_{0}\)/M\({}_{n(0)}\) - M\({}_{0}\)/M\({}_{n(0)}\))/t] versus H\({}_{2}\)O\({}_{2}\) concentration at different reaction times. Figure 11: A log-log plot of [(M\({}_{0}\)/M\({}_{n(0)}\) - M\({}_{0}\)/M\({}_{n(0)}\))/t] versus NaNO\({}_{2}\) concentration at different reaction times. Condition: H\({}_{2}\)O\({}_{2}\) = 0.4 M, pH = 5, and T = 338 K.  
Referring to Figure 7, a plot of In [(M\({}_{0}\)/M\({}_{n(0)}\) - M\({}_{0}\)/M\({}_{n(0)}\))/([0.4]\({}^{1.58}\)[0.1247]\({}^{0.79}\)[0.02]\({}^{-0.65}\times\)t)] versus 1000/T gave a straight line whose slope is equal to \(-1000\)E\({}_{\rm a}\)/R and whose intercept with the \(y\) axis is In A, as shown in Figure 12.  
Figure 12: A natural logarithm plot of [(M\({}_{0}\)/M\({}_{n(t)}\) - M\({}_{0}\)/M\({}_{n(0)}\))/([0.4]\({}^{1.58}\)[0.1247]\({}^{0.79}\)[0.02]\({}^{-0.65}\times\)t)] versus 1000/T at different reaction times.