Topological polymer chemistry for designing multicyclic macromolecular architectures

Abstract

The geometrical conception and current synthetic challenges of topological polymer chemistry have been reviewed. On the basis of the systematic classification and isomeric properties of polymer chain topologies, a variety of novel multicyclic macromolecular constructions have now been rationally designed and subsequently realized by intriguing synthetic protocols. In particular, cyclic and multicyclic polymer products are effectively produced by an electrostatic polymer self-assembly of telechelic precursors that contain cyclic ammonium salt groups accompanying polyfunctional carboxylate counteranions and the subsequent covalent conversion through the ring-opening or through the ring-emitting reaction of the cyclic ammonium salt groups by carboxylate counteranions (Electrostatic Self-assembly and Covalent Fixation (ESA-CF) process). Furthermore, the ESA-CF process, in conjunction with effective linking/cleaving chemistry (including the metathesis condensation (clip) and alkyne-azide addition (click) reactions), has been demonstrated as a new synthetic protocol for unprecedented multicyclic macromolecular topologies.

Introduction

In the macroscopic world, we often observe that the form of objects directs their functions and properties.^{1, 2} Remarkable developments in nanoscience and nanotechnology now allow the fabrication of extremely small objects with precisely defined structures.^{3, 4, 5} In the field of synthetic polymer chemistry, the form of macromolecules has long been restricted to a linear or a randomly branched topology. However, in the last decade, a variety of precisely controlled topologies that include cyclic and multicyclic forms in addition to branched ones have been realized by the introduction of intriguing synthetic techniques based on living polymerization as well as self-assembly protocols.^{6, 7, 8, 9, 10}

In this review, recent progress in topological polymer chemistry^{11, 12, 13, 14} is discussed (with particular emphasis on cyclic and multicyclic polymers) to provide new perspectives for polymer science and polymer materials engineering.

Geometrical classification and isomeric properties of cyclic and multicyclic polymer construction

A rational classification of distinctive polymer topologies provides a basis for understanding their mutual structural relationships, and this classification shoud eventually provide their practical synthetic pathways. We have formulated a systematic classification procedure for nonlinear (particularly cyclic and multicyclic) polymer architectures composed of sufficiently long and flexible segment components,¹⁴ which relies on graphical presentation by the constitutional isomerism of alkanes (C_nH_2n+2) and mono- and polycycloalkanes (C_nH_2n, C_nH_2n−2, and so on). In this procedure, the total number of termini (chain ends) and junctions (branch points) as well as the total number of branches at each junction and the connectivity of each junction are taken as invariant (constant) geometric parameters. Euclidian geometric properties such as the distance between two adjacent junctions or the distance between the junction and terminus are taken as variant parameters, conformation with the flexible nature of the randomly coiled polymer segments. Furthermore, topological constructions with five or more branches at one junction are allowed, while relevant hydrocarbon isomers with the corresponding molecular formula are absent.

Thus, a series of branched polymer topologies are hierarchically classified by alkane molecules with a generic molecular formula of C_nH_2n+2, namely, a line construction by propane (C₃H₈), a linear and a three- or a four-armed star construction by butane (C₄H₁₀) or by pentane (C₅H₁₂) isomers, respectively, and two new constructions of an H-shaped and a five-armed star architecture by the relevant hexane isomers (C₆H₁₄).

Likewise, a series of ‘ring with branches’ constructions are classified by the graph representation of the monocycloalkane molecules of the C_nH_2n form, namely, a simple ring construction by cyclopropane (C₃H₆), as well as a tadpole, and a simple ring structures defined by the two isomers of C₄H₈. The two new constructions are produced by the corresponding cyclopentane isomers (C₅H₁₀), which are distinguished from each other by their junction and branch structures (that is, one has two outward branches at one common junction in the ring unit, while the other has two outward branches located at two separate junctions in the ring unit).

A series of internally and externally linked double and triple cyclic polymer constructions are classified by reference to the bicyclo- and tricycloalkane isomers, respectively. Thus, the three basic dicyclic constructions that are free of outward branches are produced from bicycloalkanes of C_nH_2n−2, corresponding to θ-shaped, 8-shaped and manacle-shaped forms produced by bicyclo[1,1,0]butane, spiro[2,2]pentane, and bi(cyclopropane), respectively (Scheme 1). Furthermore, the 15 tricyclic constructions free of outward branches are produced from tricycloalkanes of the C_nH_2n−4 form, including the two spiro, the three bridged and the four fused forms as well as the six others that have hybrid forms consisting of single and dicyclic topologies (Scheme 1).

During the hierarchical classification of the cyclic and multicyclic polymer constructions, the topological relationships of some sets with distinctive constructions have been revealed by elucidating their isomerism.^{11, 12, 13, 14, 15} The isomerism, derived from the Greek words ‘isos’ (equal) and ‘meros’ (part), is a key concept of chemistry that dates back to Berzelius.¹⁶ A set of isomers possesses the same chemical constitution (and the same molar mass) but different properties. The subsequent discovery of constitutional (structural) isomerism by Kekulé¹⁷ has further extended rational understanding of both the static and dynamic structures of organic substances with carbon skeletons. The constitutional (structural) isomers refer to a set of compounds with distinctive connectivity of their atoms or atomic groups. In contrast, the stereoisomers refer to isomers that have indistinguishable connectivity but that are distinctive from each other in terms of the Euclidean geometric rigidity of the molecules, such as the restriction of bond angles, bond bending and bond rotation.

Remarkably, a pair of polymeric isomers is produced from an identical set of telechelic (end-reactive) polymer precursors and end-linking reagents. As a prototypical example, a pair of manacle- and θ-shaped polymers that possesses identical termini, junction numbers and branch numbers at each junction is produced by the combination of three units of a bifunctional polymer precursor and two units of a trifunctional end-linking reagent (Scheme 2). These isomers are formed from the least common combination of the functionalities of the polymer precursor and the end-linking components. Moreover, another topological isomer with a pretzel form is produced when the two polymeric ring units entwine (Scheme 2).

In practice, we have successfully synthesized the particular pair of θ- and manacle-shaped polymers by an electrostatic self-assembly and covalent fixation (ESA-CF) process (described in a later section) by using an assembly that uses bifunctional linear polymer precursors with cyclic ammonium salt groups carrying trifunctional carboxylates or trifunctional star-shaped polymer precursors carrying bifunctional carboxylates.^{18, 19, 20} This synthesis was the first example of deliberately produced polymeric topological isomers or, more precisely, topologically distinct polymeric constitutional isomers. These polymeric topological isomers, as well as a pair of linear and ring polymers, were separated by reversed phase chromatography under critical and near-critical interaction conditions.^{18, 19, 20, 21, 22}

The chemical assignment of the polymeric topological isomers with either θ or manacle construction has subsequently been performed by using polymers containing a cleavable olefinic group in a backbone segment (Scheme 3a).²³ Thus, a pair of θ- and manacle-shaped polymeric isomers with a metathesis-cleavable olefinic unit at the specified position were synthesized by the ESA-CF process by using a linear precursor with an inner olefinic group at the center position. By size-exclusion chromatography analysis of the products, the subsequent metathesis cleavage of the olefinic group at the specific position of the two isomer frameworks show that the θ-shaped isomer transforms into a two-tailed tadpole product with a similar three-dimensional size, whereas the manacle-isomer transforms into two units of a tadpole product with a significantly reduced three-dimensional size (Scheme 3a).

A pair of isomeric 8-shaped polymers with a metathesis-cleavable olefinic unit at the focal position was synthesized through the ESA-CF process using a tetracarboxylate containing a trans-3-hexenyl group as a counteranion (Scheme 3b).²⁴ The subsequent metathesis cleavage of the olefinic group converted the dicyclic 8-shaped construction into either of two simple loops with one or two prepolymer units. Any fractions containing polymeric [2]catenane products were undetectable, implying that the two prepolymer segments were not effectively entangled, even they were placed spatially close to each other in this system.

To produce polymer catenanes through the entanglement of the two polymer segments, a modified ESA-CF process was applied, and programmed self-assembly occurred through the cooperative electrostatic and hydrogen-bonding interaction of the polymer precursors (Scheme 3c).²⁵ Thus, a cyclic polymer precursor with a hydrogen-bonded isophthaloylbenzylic amide group and a dicarboxylate counteranion containing the hydrogen-bonding unit was first prepared through the ESA-CF process. Another telechelic polymer precursor that contained an isophthaloylbenzylic amide group at the center position and cyclic ammonium salt groups was subsequently prepared and subjected to polymer cyclization by the ESA-CF protocol in the presence of the preformed cyclic polymer with a hydrogen-bonding unit (Scheme 3c). A polymeric [2]catenane comprising the two different cyclic polymer components was isolated with a yield as high as 7%, and this product was unequivocally characterized by matrix-assisted laser desorption/ionisation-time of flight mass spectroscopy.

Current synthetic challenges for cyclic polymers

A variety of novel cyclic and multicyclic macromolecular constructions have now been rationally designed and subsequently synthesized by intriguing protocols either by the end-linking of telechelic precursors^{26, 27} or by the ring-expansion polymerization process.^{28, 29, 30}

End-linking of telechelic precursors

A direct end-to-end-linking reaction of an α-ω-bifunctional linear polymer precursor with a bifunctional coupling reagent is a straightforward method to prepare ring polymers.⁸ In practice, however, this bimolecular process has rarely been applied to produce high purity ring polymers in high yields. The rare use of the process has two main causes: first, the asymmetric telechelics formed as the product of the first step is prone to react again with the coupling reagent to form a symmetric telechelics, which cannot undergo cyclization: second, a high dilution condition is required to complete the intramolecular cyclization process and avoid concurrent intermolecular chain extension by using the strictly stoichiometric balance of the large polymer and the small coupling compound. However, this dilution inevitably causes serious suppression of the reaction rate obeyed by the second-order kinetics. Accordingly, to isolate the ring polymer product, a fractionation procedure is required to remove the linear side products that have the same chain length (Scheme 4).³¹

An alternative unimolecular polymer cyclization process has been introduced that uses α-ω-heterobifunctional polymer precursors, which are obtainable through living polymerization techniques. In particular, a highly efficient alkyne-azide addition reaction (a click process) has been demonstrated to be a remarkably improved polymer cyclization process in which a ring poly(styrene) was effectively synthesized with a heterotelechelic polystyrene precursor that contains an alkyne and an azide group at each end (Scheme 4). This precursor is obtainable by the atom transfer radical polymerization protocol.³² This click cyclization has also been used to prepare a ring poly(N-isopropyl acrylamide) to examine the effects of topology on its phase transition properties.^{33, 34, 35}

We have developed an effective unimolecular polymer cyclization process with symmetric olefinic-telechelics, which are conveniently obtainable through the direct end-capping reaction of a variety of living polymers.³⁶ The quantitative conversion of the atom transfer radical polymerization-terminal bromoalkyl group into allyl groups was achieved with allyltributylstannane (Keck allylation) for polyacrylates^{37, 38} and with allyltrimethylsilane/TiCl₄ for polystyrene.³⁹ These allyl-telechelics were then subjected to a metathesis clip reaction under dilution to effectively produce both cyclic homopolymers and block copolymers, including an amphiphilic poly(butyl acrylate)-b-PEO and polystyrene-b-PEO.^{37, 38, 39} Remarkably, a micelle formed from the obtained cyclic amphiphile exhibited significantly enhanced thermal stability in comparison with that of its linear counterpart.⁴⁰ This finding is regarded as the first example of an amplified topology effect by a synthetic cyclic polymer upon self-assembly (Scheme 4).^{11, 12, 13}

Ring-expansion polymerization

A ring-expansion polymerization proceeds through the repetitive insertion of a monomer into a cyclic initiator. Therefore, the dilution condition is not a prerequisite, in contrast to the end-linking process that uses telechelic precursors. However, the reactive propagating unit is inherently included in the backbone segment, and it is not readily removed by retaining the ring polymer structure.^{41, 42}

To circumvent this problem, a ring-expansion polymerization has been combined with the end-linking technique.⁴³ Thus, as a typical example, a cyclic stannous dialkoxide has been used as an initiator for the ring-opening polymerization of ɛ-caprolactone. By taking advantage of the living nature of this process, a few units of a photo-cross-linkable acrylate functionalized ɛ-caprolactone derivative have subsequently been introduced, followed by the intramolecular photo-cross-linking of the acrylic groups under dilution. The removal of the stannous dialkoxide initiator fragment by hydrolysis produces a stable ring polymer product, while the precise cross-linking chemical structures are inherently obscure. A ring-shaped nano-object (directly observable by atomic force microscopy) is constructed by this process through the subsequent grafting reaction onto the polymer backbone.⁴⁴

For the one-step synthesis of ring polymers free of initiator residues, a novel ring-opening metathesis polymerization catalyst with a specifically designed cyclic ligand has been developed.⁴⁵ This catalyst polymerizes cycloalkenes like a cyclooctene, and also promotes the end-biting chain transfer reaction to regenerate the catalyst species and reinitiates the polymerization. In this process, the chain transfer occurs randomly during the propagation; consequently the chain length distribution (molecular weight distribution) of the polymer products cannot be controlled. A ring-shaped nano-object is produced by this ring-expansion process by using either a bulky dendronized monomer or post-grafting reactions.^{46, 47}

More recently, ring polyesters and polylactams with narrow size distributions have become obtainable with an N-heterocyclic carbene initiator.⁴⁸ In this process, the end-biting chain transfer is assumed to eliminate the initiator species after the complete conversion of the monomers by the zwitterionic ring-opening polymerization.

ESA-CF for cyclic polymer topologies

As the previous sections have briefly shown, we have developed an ESA-CF technique for the design of nonlinear polymer architectures (Scheme 5).^{11, 12, 13, 18} In the ESA-CF process, a variety of linear and star telechelic precursors of poly(tetrahydrofuran (THF)), poly(ethylene oxide), poly(styrene) and poly(dimethylsiloxane) have been used as key polymer precursors. These precursors have moderately strained cyclic ammonium salt groups that are typically five membered, accompanying appropriately nucleophilic counteranions such as carboxylates. Small (low-molecular weight and water soluble) and large (polymeric and water insoluble) carboxylates can be used in this ESA-CF process, as shown previously in Scheme 3.⁴⁹ The corresponding electrostatic polymer complexes are formed in high yields by the simple precipitation of a telechelic precursor with cationic end-groups into an aqueous solution containing small carboxylate salts. They can also be formed by the coprecipitation of an equimolar mixture of cationic and anionic polymer precursors. The cations and anions always balance the charges, even under dilution, and the selective nucleophilic ring-opening reaction occurs at an elevated temperature, to convert the ionic interaction into a permanent covalent linkage (Scheme 5).

This ESA-CF protocol has been applied successfully for the efficient synthesis of various ring polymers, which have optional specific functional groups at the designated positions of the ring polymer structures (kyklo-telechelics and cyclic macromonomers) for the construction of further complex polymer topologies, including a variety of ‘ring with branches’ polymers (that is, a simple tadpole, as well as twin-tail and two-tail tadpole forms).^{11, 12, 13}

An alternative covalent conversion process has also been developed by using a telechelic precursor with unstrained cyclic ammonium salt end groups (Scheme 6).^{50, 51} Thus, telechelics with six membered, N-phenylpiperidinium salt groups carrying either monofunctional benzoate or bifunctional biphenyldicarboxylate counteranions can be prepared. Upon subsequent heating, the carboxylate counteranion undergoes selective nucleophilic attack at the exo-position of the cyclic ammonium salt group to cause the elimination of the N-phenylpiperidine units from the polymer chain ends. Consequently, by the ESA-CF procedure, ring polymers containing simple ester linking groups are effectively obtainable through the ring-emitting covalent conversion under dilution (Scheme 6). This result contrasts with the impractical bimolecular process for ring polymer synthesis by a conventional esterification reaction under dilution involving a polymeric diol and a dicarboxylic acid.⁵²

Multicyclic polymer constructions by the ESA-CF process in conjunction with effective covalent linking chemistries

The multicyclic polymer constructions shown in Scheme 1 include three subgroups (that is, spiro, bridged and fused forms). The dicyclic constructions correspond to 8-shaped, manacle-shaped (or two-way paddle shaped) and θ-shaped forms.^{11, 12, 13, 14} The ESA-CF process, which can be conducted in conjunction with an effective linking chemistry by the intramolecular metathesis condensation of olefinic groups (clip) and by the alkyne-azide addition (click) reactions, has now been demonstrated to be a powerful synthetic protocol for the construction of multicyclic polymer topologies.^{11, 12, 13}

Spiro-multicyclic constructions

Among a series of spiro-multicyclic constructions, (Scheme 7) a dicyclic 8-shaped polymer was directly obtainable with the ESA-CF process, but it could also be produced by conjunction with the metathesis (clip) process (Scheme 8). First, an 8-shaped polymer was produced with a self-assembly containing two linear telechelic precursor units carrying one tetracarboxylate counteranion unit.¹⁸ The alternative metathesis condensation (clip process) could be applied by using either a ring prepolymer with an allyloxy group, a twin-tailed tadpole polymer precursor with two allyloxy groups at the tail-end positions or a ring polymer precursor with two allyloxy groups at opposite positions (Scheme 8).⁵³

Two spiro-tricyclic polymer forms with either a trefoil or a tandem tricyclic topology were also produced by the ESA-CF process. The first form was produced by a self-assembly consisting of three linear telechelic precursor units carrying a hexafunctional carboxylate counteranion,¹⁸ and the second form was produced by the click linking of two cyclic prepolymers with two alkyne groups at the opposite positions of the ring unit and another with an azide group, both of which are obtainable by the ESA-CF technique (Scheme 8).⁵⁴

Likewise, a tandem spiro-tetracyclic polymer construction was produced by the click coupling between an 8-shaped dicyclic prepolymer with two alkyne groups at the opposite positions of the two ring unit and another single cyclic precursor with an azide group (Scheme 8).⁵⁴ Tandem spiro-multicyclic polymers with multiple ring units were also produced by the click self-polycondensation of a cyclic precursor with alkyne and azide groups at opposite positions of the ring unit, which is obtainable by the ESA-CF technique (Scheme 8).⁵⁴

Bridged-multicyclic constructions

Among a series of bridged-multicyclic constructions (Scheme 9), a dicyclic manacle-shaped polymer was obtainable in conjunction with a θ-shaped polymeric isomer through the ESA-CF with an assembly composed of three linear bifunctional precursor units carrying two trifunctional carboxylate counteranion units (Scheme 10), as described in the previous section.^{18, 19} The ESA-CF procedure was also applicable to an assembly composed of two star-shaped trifunctional precursor units carrying three bifunctional carboxylate counteranion units (Scheme 10).²⁰ Alternatively, a pair of dicyclic polymeric topological isomers with θ and manacle constructions were formed through the metathesis clip process using an H-shaped precursor with allyloxy end groups at each chain end (Scheme 10).²¹

The selective construction of a dicyclic, manacle-shaped polymer topology was achieved through the click coupling of a bifunctional linear telechelic precursor containing azide groups with a cyclic polymer precursor bearing an alkyne group obtainable through the ESA-CF protocol (Scheme 10).⁵⁴

Likewise, a bridged-tricyclic three-way paddle-shaped polymer was obtained by the relevant click coupling reaction between a star-shaped trifunctional precursor containing azide groups with a cyclic polymer precursor bearing an alkyne group (Scheme 10).⁵⁴ Bridged-multicyclic polymers consisting of cyclic and linear or branched polymer units were also produced by the click polycondensation of a cyclic precursor containing two alkyne groups at the opposite positions of the ring unit from the respective linear/branched telechelic precursors with azide groups (Scheme 10).⁵⁴ These topologically unique polymers are considered to be topological block copolymers that include alternate cyclic and linear (or branched) segments.

Fused-multicyclic constructions

In contrast to their spiro and bridged counterparts, the class of fused multicyclic polymer topologies (Scheme 11) is considered to be particularly intriguing in the context of programmed polymer folding. This folding is recognized to be crucial in diverse events in biopolymer systems, such as DNA packaging and the three-dimensional structure formation of proteins, as well as the remarkable stability and activity revealed by some cyclic proteins (cyclotides).⁵⁵ Moreover, the topologically significant polymer constructions that include a doubly fused tricyclic α-graph, a triply fused tetracyclic K_3,3 graph and a triply fused tetracyclic prisman graph remain an ongoing synthetic challenge to extend the current frontier of polymer chemistry (Scheme 1).^{11, 12, 13, 14}

A fused-dicyclic θ-shaped polymer was obtained selectively through the ESA-CF process with a self-assembly containing a three-armed, star telechelic precursor carrying a tricarboxylate counteranion (Scheme 12).⁵⁶ Alternatively, as described in the preceding section, the θ-shaped polymer could be formed along with a manacle-shaped polymeric isomer, either through ESA-CF or the metathesis clip process using the relevant polymer precursors (Scheme 10).

A doubly fused tricyclic polymer with a δ-graph construction was produced from an 8-shaped kyklo-telechelic precursor with two allyl groups at opposite positions, which was prepared by the ESA-CF protocol.⁵⁷ In this process, a prescribed self-assembly consisting of two units of a linear precursor with cyclic ammonium salt groups and an allyl group at the center position was used, accompanying a tetracarboxylate counteranion. The subsequent metathesis clip process could fold the two polymer ring units together (Scheme 12).⁵⁷

The ESA-CF process, in conjunction with a tandem alkyne-azide click and an olefin metathesis clip reaction, has now been developed as an effective means for the production of programmed folding forms by synthetic polymers, such as a doubly fused tricyclic γ-graph and a triply fused tetracyclic unfolded tetrahedron graph construction (Scheme 12).⁵⁸

A summary of the synthetic procedure and characterization of the γ-graph polymer is described as a typical example.⁵⁸ Thus, a cyclic poly(THF) precursor with an allyloxy and alkyne group was first synthesized by the ESA-CF protocol. A linear poly(THF) with azide end groups was prepared by simply terminating a living polymerization of THF with tetrabutylammonium azide. The subsequent click reaction was performed in the presence of copper sulfate and sodium ascorbate by using these complementary polymer precursors to produce a bridged-dicyclic (manacle) polymer precursor with two allyloxy groups at the opposite positions of the ring units. Finally, an intramolecular olefin metathesis reaction (clip) of the bridged-dicyclic polymer precursor was conducted under dilution (0.2 g l⁻¹) by the repeated addition of a Grubbs’ catalyst first generation into the reaction solution.

¹H-nuclear magnetic resonance was used to monitor the chemical transformation to produce the γ-graph polymer from the polymer precursors. As shown in Figure 1, the signal of the ethynyl protons at 2.53 p.p.m. in the cyclic polymer precursor and the signal of the azidomethylene protons at 3.30 p.p.m. in the linear polymer precursor were replaced by a triazole proton signal at 7.65 p.p.m., confirming the effective click reaction producing a manacle-shaped precursor. The signals for the allyloxy units at 5.26–5.44 and 5.99–6.12 p.p.m. can be seen to remain intact during the click process. After the metathesis (clip) reaction, the signals of the allyloxy units are completely replaced by those of the inner olefinic units at 6.07–6.12 (cis) and 5.90–5.95 (trans) p.p.m., which is indicative of effective γ-graph polymer production even under applied dilution.

Figure 1

¹H-nuclear magnetic resonance spectra of a γ-graph polymer and its precursors. Reprinted with permission from Sugai et al.⁵⁸ Copyright (2011) American Chemical Society.

Moreover, matrix-assisted laser desorption/ionisation-time of flight mass spectral analysis unequivocally substantiated the production of the γ-graph polymer. In the series of precursor and the product spectra shown in Figure 2, a uniform series of peaks with an interval of 72 mass units was observed for all samples, corresponding to the repeating THF units; moreover, each peak exactly matched the molar mass calculated from the chemical structures of the products. Thus, for the manacle-shaped polymer precursor, the peak at m/z=7926.4, which is assumed to be the adduct with Na⁺, corresponds to the expected chemical structure with the expected degree of polymerization, DP_n, of 85; (C₄H₈O) × 85+C₁₀₄H₁₂₈N₁₀O₁₆, plus Na⁺ equals 7926.332. For the γ-graph polymer, the peak at m/z=7898.3, which is assumed to be the adduct with Na⁺, corresponds to the expected chemical structure with a DP_n of 85; (C₄H₈O) × 85+C₁₀₂H₁₂₄N₁₀O₁₆, plus Na⁺ equals 7898.278. As the γ-graph polymer is produced from a manacle-shaped precursor by the elimination of an ethylene molecule, their molecular weights differ by 28 mass units. This result was confirmed by the comparison of the two mass spectra shown in Figure 2.

Figure 2

Matrix-assisted laser desorption/ionisation-time of flight mass spectra of a γ-graph polymer and its precursors. Reprinted with permission from Sugai et al.⁵⁸ Copyright (2011) American Chemical Society.

Concluding remarks and future perspectives

Numerous future opportunities are anticipated with ongoing progress in topological polymer chemistry. The new concept of topological isomerism has now been introduced for the hierarchical classification of nonlinear and multicyclic polymer constructions. A pair of topological isomers that occur uniquely in flexible nonlinear polymer architectures has indeed been synthesized by the ESA-CF process with newly designed telechelic polymer precursors that contain cyclic ammonium salt groups. Further synthetic challenges should include topologically significant polymers, such as tricyclic α- and β-graph constructions, as well as a tetracyclic K_3,3 construction by using specifically designed telechelic precursors with appropriate Cayley-tree constructions. These syntheses will extend the current frontier of synthetic polymer chemistry.¹⁴ In addition, topological polymer chemistry now offers unique opportunities for the exploration of any topological effects in polymer materials because a variety of topologically defined polymers have now become systematically available.¹⁴ With theoretical and simulation progress, we expect to achieve unique topological control over static and dynamic properties that rely on conjectures of topological geometry, particularly but not limited to those intuitively envisaged from common Euclidian geometry.

Single and multicyclic polymer topologies (ring family tree).

Polymeric topological isomers.

Chemical processes of polymeric topological isomers. A full color version of this scheme is available at Polymer Journal online.

Ring polymer synthesis by the end-linking of telechelic polymers.

Electrostatic polymer self-assembly and covalent fixation.

Ring-opening and ring-emitting processes for covalent conversion.

Spiro-multicyclic constructions.

Synthesis of spiro-multicyclic polymers. A full color version of this scheme is available at Polymer Journal online.

Bridged-multicyclic constructions.

Synthesis of bridged-multicyclic polymers. A full color version of this scheme is available at Polymer Journal online.

Fused-multicyclic constructions.

Synthesis of fused-multicyclic polymers.