Model‐Based Reactor Design to Control Hyperbranched Polymer Architecture

Abstract

L is the linearly incorporated unit, one of whose two B's has reacted, and D is the dendritic unit in which both B's have already reacted. The reaction rate constant, k T is for the reaction between an A group and a B in the T unit, while k L is for the reaction between an A and a B in the L unit. The reactivity of the second B group can be represented by the reactivity ratio, r = k L /k T . The reaction systems in which the magnitude of r can be controlled from zero to infinity have been reported. [6] The DB of an HB polymer without an L unit is unity (DB = 1), and DB = 0 for the linear structure, consisting of L units with a single T unit at the chain end. The HB polymers with DB = 1 can be obtained for r = ∞. On the other hand, however, because of the randomness in the location of T units, various types of HB polymer structure can be formed even with DB = 1, as shown in Figure 2 of ref.[6]. One cannot obtain perfect dendrons even with r = ∞. The expected mean-square radii of gyration for the HB polymers having a specific chain length (degree of polymerization (DP), represented by the symbol, P in this article) are much larger than those for perfect dendrons. [7] In the kinetically controlled polymerization systems, the molecular architecture can be controlled by the residence time distribution of the given polymerization process. An example of the reactor operation to obtain HB polymers with higher DB values is the slow monomer addition method. [5,[8][9][10] In this method, monomers are added very slowly, and the slowly added monomers tend to react with the terminal groups of the HB polymers already formed, resulting in enhancing the DB values. The limiting DB of the large polymer limit, lim DB P→∞ is unchanged during the whole course of polymerization in batch polymerization, irrespective of the magnitude of r. [7] In the case of equal reactivity of both B groups, i.e., with r = 1, the limiting value is 0.5 for batch polymerization. [11][12][13] On the other hand, the value of DB for the ideal slow monomer addition method is A Monte Carlo simulation method, based on the random sampling technique in which a large number of polymers are sampled from the final product, is proposed for the continuous tanks-in-series process. The effect of the sequence of tanks with different sizes is considered for the irreversible step polymerization of AB 2 -type monomer. It is found that the tank sequence starting from a large tank followed by a number of smaller tanks is suitable to produce compact hyperbranched polymers, whose mean-square radii of gyration are much smaller than those formed in batch polymerization. Analytic formulas of the average molecular weights are presented for the tanks-in-series processes, including the post-processes to make the molecular weight distribution narrower by removing residual monomer and by introducing multifunctional core molecules. The present investigation enhances fundamental knowledge that would be useful for the model-based reactor design to control detailed branched architecture of...

Universal Relationships in Hyperbranched Polymer Architecture for Batch and Continuous Step Growth Polymerization of AB2-Type Monomers

“…On the other hand, if one needs looser structure, the core formation should be avoided. The structural control by using the tanks-in-series process was also discussed previously [25].…”

Hyperbranched Polymers Formed Through Self‐Condensing Vinyl Polymerization in a Continuous Stirred‐Tank Reactor (CSTR): 1. Molecular Weight Distribution

“…For the irreversible step polymerization of AB 2 type monomer, which is another method to synthesize the HB polymers, it was found that CSTR leads to much more compact 3D structure with a larger DB for the large‐sized polymers, compared with the corresponding batch polymerization. Although the use of a single CSTR leads to a very broad molecular weight distribution (MWD), it was found that the tanks‐in‐series process with the tank sequence starting from a large tank followed by a number of smaller tanks is suitable to produce compact HB polymers with a sufficient conversion level . The post‐processes to make the MWD narrower were also considered therein.…”

Hyperbranched Polymers Formed Through Self‐Condensing Vinyl Polymerization in a Continuous Stirred‐Tank Reactor (CSTR): 2. Branched Architecture

“…These disadvantages could be mitigated by using a tanks‐in‐series process, with a large first tank followed by a number of small tanks, or ideally, a CSTR followed by a PFR. The post‐processes, such as removal of monomer and the introduction of multifunctional core molecules that react with the unreacted focal point unit, can make the MWD narrower significantly.…”