# Polymerization of Isobutylene in a Rotating Packed Bed Reactor: Experimental and Modeling Studies
## 3 Results
### Effect of N and Estimation of P  
The effect of the rotating speed \(N\) on the \(M_{n}\) of PIB is displayed in Figure 6a. It is observed that \(M_{n}\) increases remarkably from 1400 to 2550 g\(\cdot\)mol\({}^{-1}\) with increasing \(N\) from 600 to 1600 rpm, and then reaches a plateau when \(N\) is larger than 1600 rpm. The simulated \(M_{n}\) fits well with the experimental data. These results indicated that the polymerization of PIB could be intensified by enhancing the mixture in RPB, and the \(M_{n}\) could be tuned by regulating rotating speed. Moreover, both the micromixing rate and coalescence-redispersion frequency of the liquid droplets could be enhanced by increasing \(N\)[28; 38]. The percentage of droplet number participating in coalescence-redispersion process is denoted by the coalescence probability \(P\); it can be calculated with the analogous flow chart as shown in Figure 4 and listed in Table 3. It is observed that \(P\) increases with increasing \(N\) from 600 rpm to 1600 rpm. Ln\(P\) is linearly related to ln\(N\) when \(N\) is less than 1600 rpm, as shown in Figure 6b. The relationship between \(N\) and \(P\) is deduced as Equations (18) and (19), which is consistent with a previous report [17]. Moreover, exo-olefin terminal content in HRPIB is calculated as about 85 mol% and insensitive to \begin{table}
\begin{tabular}{c c c} \hline \hline \(T\)/\(K\) & \(M_{n}\)/(g\(\cdot\)mol\({}^{-1}\)) & \(k_{p}\)/(10\({}^{4}\) L\(\cdot\)mol\({}^{-1}\cdot\)s\({}^{-1}\)) \\ \hline
267 & 4890 & 15.0 \\
274 & 3880 & 12.0 \\
279 & 3420 & 10.6 \\
283 & 2550 & 10.1 \\
290 & 2220 & 8.5 \\ \hline \hline \end{tabular} \({}^{1}Q_{M}=33.7\) L\(\cdot\)h\({}^{-1}\), \(Q_{l}=6.24\) L\(\cdot\)h\({}^{-1}\), [M]\({}_{k}=2.00\) mol\(\cdot\)L\({}^{-1}\), [I]\({}_{k}=0.22\) mol\(\cdot\)L\({}^{-1}\), \(N=1600\) rpm.  
\end{table} 
Table 2: The calculated values of \(k_{p}\) based on \(T\) and experimental \(M_{n}\). Figure 5: Calculation flow chart for the kinetic parameters. \(N\), so \(M_{n}\) of HRPIB can be tuned by adjusting \(N\) from 0 to 1600 rpm without affecting exo-olefin terminal content. \[P=1.12\ \times\ 10^{-6}\cdot N^{1.58},\ (N\ \leq\ 1600\ \mathrm{rpm}) \tag{18}\]  
\[P=0.15,\ (N\ >\ 1600\ \mathrm{rpm}) \tag{19}\]  
Effect of \([M]_{0}/[I]_{0}\) on the \(M_{n}\) of PIB is displayed in Figure 7, where \([M]_{0}/[I]_{0}\) is the initial concentration ratio of the monomer and initiating system in RPB. It is observed that \(M_{n}\) decreases with decreasing \([M]_{0}/[I]_{0}\) no matter whether \([M]_{0}/[I]_{0}\) is changed through decreasing \([M]_{t}\), decreasing \(Q_{M}\), increasing \([I]_{t}\) or increasing \(Q_{I}\). The simulated \(M_{n}\) fits well with the experimental \(M_{n}\). The decrease in \([M]_{0}/[I]_{0}\) would reduce the relative quantity of monomers and improve the relative quantity of active centers, resulting in the decrease in \(M_{n}\). It is worth noting that the effect of \([M]_{0}/[I]_{0}\) on the \(M_{n}\) in Figure 7a,c is more remarkable than that in Figure 7b,d, which indicates that \(M_{n}\) is more sensitive to changes in the monomer parameters. It can be concluded that \(M_{n}\) of PIB can be tuned by altering \([M]_{t}\), \([I]_{t}\), \(Q_{M}\) and \(Q_{I}\), and a low \([M]_{0}/[I]_{0}\) is necessary to obtain low molecular weights of PIB. However, a low \([M]_{0}/[I]_{0}\) is detrimental to the content of exo-olefin terminals in PIB [6], since a decrease in exo-olefin terminal content from 92 to 78 mol\(\%\) is observed with decreasing \([M]_{0}/[I]_{0}\) from 135 to 30. Therefore, a suitable \([M]_{0}/[I]_{0}\) should be chosen considering the demands of both the molecular weight and exo-olefin terminal content. In this paper, optimal \([M]_{0}/[I]_{0}\) was found to be 49, where HRPIB with \(M_{n}\) of 2550 g\(\cdot\)mol\({}^{-1}\) and exo-olefin terminal content of 85 mol\(\%\) could be obtained.