# Polymerization of Isobutylene in a Rotating Packed Bed Reactor: Experimental and Modeling Studies
## 1 Introduction  
Polyisobutylene (PIB), the product of isobutylene (IB) polymerization, is an important organic polymer with excellent low gas permeability and high chemical stability, and it can be applied in many fields, such as oil additives, adhesive agents, sealants, paint and lubricants [1]. According to molecular weight, the PIB can be classified as low molecular weight PIB (\(M_{n}\)! 5000 g-mol\({}^{-1}\)), medium molecular weight PIB (40,000 g-mol\({}^{-1}\)! \(M_{n}\)! 100,000 g-mol\({}^{-1}\)) and high molecular weight PIB (\(M_{n}\)! 100,000 g-mol\({}^{-1}\)) [2]. Low molecular weight polyisobutylene with external olefin terminal group accounts for about 75\(\%\) of the polyethylene market due to its substantial use as a precursor for the preparation of less dispersive agents [2]. In the last fifteen years, the three major methods for synthesizing highly reactive polyisobutylene (HRPIB) have been proposed in several articles: (i) using an active cation polymerization technique [3, 4], (ii) using the Lewis acid complex as a catalyst [3, 4] and (iii) using a solvent with weak coordination countra-ions to link metal complexes [5, 6]. It has been reported that HRPIB with low molecular weights can be directly synthetized by cationic polymerization of IB with initiating systems of H\({}_{2}\)O/AlCl\({}_{3}\)/dialklyl ether and H\({}_{2}\)O/FeCl\({}_{3}\)/dialkyl ether [1, 7], which is quite promising for the synthesis of HRPIB. In the process of synthesizing HRPIB by the cationic polymerization of IB, one of the most important and difficult problems is the selection of reactors. The difficulty lies in that the rate constants of propagation in the cationic polymerization of alkenes are similar for most systems with \(k_{p}\) = 10\({}^{\delta\pm 1}\) L-mol\({}^{-1}\)-s\({}^{-1}\)[8, 9], which means that the cationicpolymerization of IB is featured with an extremely fast intrinsic reaction rate. The apparent reaction rate would be significantly affected by micromixing [10; 11; 12; 13; 14]. The extremely rapid polymerization needs reactors that can provide uniform mixing with high efficiency because the properties of the products are greatly affected by the mixing process. Poor and slow mixing of monomers and initiating agents results in inferior products [13; 15; 16]. More specifically, a principle for the selection of ideal cationic polymerization reactors is proposed as \(t_{m}\leq t_{1/2}\) by [PERSON] et al. [17], where \(t_{m}\) is micromixing characteristic time for the species to reach a maximum mixed state at the molecule level and \(t_{1/2}\) is reactive characteristic time. The \(t_{1/2}\) of the cationic polymerization with \(k_{p}\) of \(10^{5\pm 1}\) L\(\cdot\)mol\({}^{-1}\cdot\)s\({}^{-1}\) is estimated in the range of 0.01 to 0.1 ms, while the \(t_{m}\) of a typical stirred tank reactor is estimated in the region of 5 to 50 ms [18]. Therefore, traditional stirred tanks are not ideal reactors for the polymerization of IB. As an apparatus for achieving high gravity conditions on the earth, a rotating packed bed (RPB) reactor mainly consists of a packed rotator and a fixed casing. The high gravity environment is produced by the centrifugal force created by the fast-spinning packed rotator. In RPB, the fluids going through the packing are split into very fine droplets, threads and thin films by the strong shear force, providing a sizeable and fast phase contact area, and resulting in a significant intensification of mixing and mass transfer between the fluid elements [19; 20; 21]. The rate of the mass transfer between gas and liquid in RPB is one to three orders of magnitude larger than that in a conventional packed bed reactor [22; 23; 24; 25; 26; 27]. Notably, the value of \(t_{m}\) in RPB is estimated as 0.01 to 0.1 ms [28], which corresponds to the \(t_{1/2}\) of the cationic polymerization.