**1. Introduction**

Polyimides (PI) are an essential class of polymers with a set of valuable properties. In addition to heat, thermal, radiation, and chemical resistance, good film-forming properties, high mechanical strength, and excellent insulating properties, polyimides demonstrate good biocompatibility in vitro and in vivo, as well as low toxicity [1–3]. Multicomponent copolymers, in which PI blocks are combined with blocks of biocompatible aliphatic polymers, have great potential for the development of materials for tissue engineering.

Although atom transfer radical polymerization (ATRP) has been successfully used to synthesize many types of copolymers, it remains a challenge to synthesize copolymers of different architectures using monomers that polymerize through fundamentally different mechanisms, such as ATRP and ring opening polymerization (ROP). To solve this problem, one can use initiators containing two types of functional groups capable of initiating each of these processes in parallel and independently [4,5]. Second approach is introduction of a functional group that initiates the polymerization of the second monomer at the stage of initiation or termination of the first monomer polymerization (post-modification) [6].

Thus, in [7], graft copolymers with poly(2-hydroxyethyl methacrylate) (PHEMA) backbone and block copolymer side chains containing blocks of poly(ε-caprolactone) PCL

**Citation:** Kashina, A.V.; Meleshko, T.K.; Bogorad, N.N.; Lavrentyev, V.K.; Yakimansky, A.V. Molecular Brushes with a Polyimide Backbone and Poly(ε-Caprolactone) Side Chains by the Combination of ATRP, ROP, and CuAAC. *Polymers* **2021**, *13*, 3312. https://doi.org/10.3390/ polym13193312

Academic Editor: Edina Rusen

Received: 27 August 2021 Accepted: 22 September 2021 Published: 28 September 2021

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and poly(butyl acrylate) (PBA) were synthesized. Copolymers of PCL with poly(octadecyl methacrylate) (POMA) and poly(N,N-dimethylamino-2-ethyl methacrylate) (PDMAEMA) PCL-*b*-PODMA-*b*-PDMAEMA or PCL-*b*-(PODMA-*co*-PDMAEMA) were obtained in [5], in which the PODMA block had a "pseudo-brush" structure due to long aliphatic tails. Another example of a successful combination of the different methods of controlled polymerization is the synthesis of a three-armed star-shaped polymer with arms of different structures, for which different methods were used [4]. Thus, the PCL arm was obtained using ROP, the polystyrene (PS) arm was obtained by the NMP, and the poly(tert-butyl acrylate) (PTBA) was obtained by the ATRP.

The ROP is effectively combined with other CRP methods in the synthesis of various copolymers. Thus, in [8], the authors describe the preparation of triblock copolymers with a central PCL block and peripheral PDMAEMA blocks using a combination of ROP with RAFT. Synthesized by ROP PCL with hydroxyl end groups was functionalized using 4-cyanopentanoic acid dithionaphthalenoate (CPADN) and used as a macro-RAFT agent for polymerization of DMAEMA to obtain the targeted triblock copolymers. An efficient method for the synthesis of linear di- and triblock copolymers with PCL blocks with narrow molecular weight distribution is to carry out ROP on mono- or difunctional polymer initiators. ROP of CL on the corresponding polymer initiators with hydroxyl chain ends provides copolymers in which PCL blocks are covalently attached to a block of polydimethylsiloxane [9], polyisobutylene [10], and poly(ethylene oxide) [11].

Grafting of polyester chains with narrow molecular weight distribution, in particular, PCL for the production of molecular brushes is also of great interest. The method of click chemistry is often used to graft PCL chains [12,13]. For example, in [12], the surface modification of the nanodispersed cellulose systems by grafting PCL chains using clickchemistry is described. However, to obtain molecular brushes with polyester side chains, ROP is easier to perform [14]. Therefore, numerous articles are devoted to the synthesis of molecular brushes with homopolymer PCL side chains or block copolymer side chains with a PCL block [12,13]. Carrying out polymerization of CL on multifunctional polymer initiators with varying numbers and positions of initiating groups leads to the production of PCL blocks with narrow molecular weight distribution, which are usually grafted to the carbochain backbone. To our knowledge, there are no data on the introduction of PCL blocks into the side chains of molecular brushes with a polyarylene backbone.

At the same time, works on combining aromatic PIs with aliphatic polyesters, in particular with PCL, have been going on for more than two decades. With simple mixing of homopolymer PI and PCL, for example, through a common solvent, phase separation of polymers is observed at the macroscopic level [15]. A more uniform phase system of PI and PCL is obtained by synthesizing chemically bonded PI and PCL blocks [15–20]. Until recently, the covalent bonding of these polymers was carried out either by stepwise polycondensation, leading to the production of linear alternative segmented (or multisegmented) block copolymers [18,19], or by cross-linking between PI and PCL chains in a polymer mixture or between PI and PCL layers in a multilayer coating [16,17,20]. A valuable feature of such copolymers is microphase separation [17], which gives them new interesting, for example, membrane properties. Thus, based on multisegmented linear block copolymers containing segments of polyurethanimide and PCL, effective diffusion membranes have been developed for the separation of binary mixtures of organic liquids [17]. However, the preparation of such segmented block copolymers is very laborious. Another method for combining PI and PCL by preparing block copolymers with sequentially attached PI and PCL blocks was proposed in [21]. In [22] the synthesis of linear block copolyimide with PCL and PI blocks based on 3,3'-dioxybenzidine was proposed using ROP of CL on a difunctional polyimide initiator. The obtained copolyimide was intended to improve the dispersion of carbon nanotubes in low-boiling organic solvents.

It should be noted that the introduction of PCL blocks into multiblock copolymers is of considerable interest from the point of view of further applications of these copolymers, since PCL blocks are capable of undergoing alkaline [23] and plasma [24] etching and biodegradation. The synthesis of new initiators and ROP of monomers and macromonomers containing functional groups on such initiators is a promising strategy for the preparation of macromolecules of complex architecture. In recent years, due to the development of the ROP method, it has been successfully used to obtain copolymers of different chemical structures and architecture.

Earlier, our research group reported the synthesis of triblock copolymers based on polyimide with external blocks of poly(ε-caprolactone) (PCL) [25], as well as grafted pentablock copolymers of linear-brush topology with external PCL and PMMA blocks and an internal brush-type block PI-*g*-PMMA [26]. This work is devoted to the development of methods for the synthesis of previously undescribed molecular brushes with a PI backbone and PCL side chains. To obtain such copolymers, a combination of various synthesis methods was used, including polycondensation, ATRP, ROP, and Cu (I) catalyzed azidealkyne Huisgen cycloaddition (CuAAC) [27].
