Polymeric Toroidal Self‐Assemblies: Diverse Formation ...

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Review

Polymeric Toroidal Self-Assemblies: Diverse Formation Mechanisms and Functions

Pengfei Xu, Liang Gao, Chunhua Cai,* Jiaping Lin,* Liquan Wang, and Xiaohui Tian

In recent years, toroidal nanostructures have become an appealing topic in nanoscience owing to their unique structure and promising applications. Among them, polymeric toroidal self-assemblies have attracted considerable attention because of their manipulability and diversity. Despite the substan-tial advances in the area of polymeric nanotoroids, the universal formation principles and functions of these toroids have not been sufficiently sum-marized. This article aims to review recent advances in the formation and function of polymeric nanotoroids. The significant role of theoretical simula-tions in revealing the formation mechanism and inherent structure of toroidal assemblies is emphasized. Additionally, a perspective on the challenges of this research field is addressed.

DOI: 10.1002/adfm.202106036

P. Xu, L. Gao, C. Cai, J. Lin, L. Wang, X. TianShanghai Key Laboratory of Advanced Polymeric MaterialsKey Laboratory for Ultrafine Materials of Ministry of EducationFrontiers Science Center for Materiobiology and Dynamic ChemistrySchool of Materials Science and EngineeringEast China University of Science and TechnologyShanghai 200237, ChinaE-mail: [email protected]; [email protected]

poly(acrylic acid)-b-poly(methyl acrylate)-b-polystyrene (PAA-b-PMA-b-PS) triblock copolymers can self-assemble into toroidal micelles in a way similar to multivalent counterion-induced DNA condensation.[23] In a dioxane/water mixture solution, poly(4-vinylpyridine)-b-polystyrene-b-poly(4-vinylpyridine) (P4VP-b-PS-b-P4VP) triblock copolymers can self-assemble into toroidal micelles when a shear flow is applied.[24] These impressive works inspire research on the fabrication of toroidal nanostructures in assembly systems.

Apart from the direct assembly route, toroids can also be formed via indirect ways, for example, through morphology

transitions of assemblies and disassembly of hierarchical struc-tures.[32–37] In terms of topological structure, toroids can be viewed as ring-shaped cylinders or hollow spheres/vesicles. It has been revealed that spheres, cylinders, vesicles, and disks can transform into toroidal nanostructures under certain conditions. For example, Lin et al. demonstrated that rod-like micelles self-assembled from poly(γ-benzyl-L-glutamate)-graft-poly(ethylene glycol) (PBLG-g-PEG) copolymers can close into toroids via end-to-end coalescence when the solvent quality is altered.[34] Recently, the disassembly of hierarchical structures has become a promising way to produce toroids.[35–37] Compared with simple assemblies, hierarchical structures possess a higher structural hierarchy. The structural feature permits them to disintegrate into individual nanoobjects that are building blocks of these hierarchical structures.[36] In particular, hierarchical structures with a ring-shaped structure motif can yield nanotoroids via the disassembly route. However, these strategies have not been well documented.

Experimental understanding of the formation mechanism of toroidal assemblies usually suffers from difficulties caused by limited experimental techniques. In some ways, theoretical simulations can overcome the limitations inherent in experi-ments because they provide more straightforward and detailed information than experimental observations. To date, various simulation methods, such as molecular dynamics (MD), Brownian dynamics (BD), dissipative particle dynamics (DPD), and self-consistent field theory (SCFT), have been employed as powerful tools to unveil the assembly mechanism.[38–41] Theo-retical simulations can provide detailed mechanism informa-tion on toroid formation. Moreover, the simulation results can chart the course for the related experimental studies. Combining experiments and simulations in the investigation of toroidal assemblies can boost mechanism research in this emerging domain.

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.202106036.

1. Introduction

Toroidal (donut-shaped or ring-shaped) nanostructures are frequently observed in nature.[1,2] The well-known example is the DNA toroidal bundles observed in most bacterial phages and vertebrate sperm cells.[2] Such DNA toroids have poten-tial use in delivery systems for gene therapy. Another example is toroidal protein-conducting channels encountered in cell membranes, which play a key role in the biological processes of cells.[3,4] Moreover, toroidal nanostructures are also found in protofilament structures and peroxiredoxin proteins.[5,6] These examples have inspired numerous efforts to mimic the unique toroidal structure, leading to a better understanding of nature and the creation of advanced nanomaterials.[7–9]

Various strategies have been developed to prepare toroidal nanostructures.[10–28] Among them, polymer self-assembly has drawn considerable attention due to its manipulability and diversity.[29–31] Earlier works usually described the direct self-assembly of polymers to produce nanotoroids mixed with other morphologies. Recently, much effort has been devoted to pre-paring pure toroidal assemblies by controlling assembly con-ditions. For instance, in the presence of diamine molecules,

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Due to their unique geometry and properties, toroidal nano-structures have exhibited intriguing performances and prom-ising applications in numerous fields. For example, toroids are of paramount importance in DNA compaction and storage in chromosomes.[2,42] The inherently hollow nature of nanotoroids provides the possibility to fabricate nanoporous materials, which are of critical importance in catalysis, separations, and many other applications.[43–45] Moreover, nanotoroids show shape-dependent plasmon resonance and promise in photody-namic therapy and cancer therapy.[46,48]

In this review, we summarize the state-of-the-art research and achievements in the formation and function of toroidal assemblies. The main body of the article is divided into three parts. The first discusses the advances in the formation routes of toroidal assemblies. The formation routes are classified into three categories according to the structural hierarchy of building blocks: the direct self-assembly of polymers, the morphological transformation of assemblies, and the disas-sembly of hierarchical structures (Figure 1). In particular, the role of theoretical simulations in disclosing the mechanisms is emphasized. In the second part, we review the functions of nanotoroids. Finally, the challenges and development directions of toroidal assemblies are discussed.

2. Self-Assembly of Polymers into Toroidal NanostructuresThe direct self-assembly of polymers is the most straightfor-ward strategy for generating toroidal nanostructures. Polymers, including synthetic polymers and natural biopolymers, are fea-sible molecular building blocks for constructing toroids. This section discusses the toroids formed through the self-assembly of synthetic polymers and biopolymers.

2.1. Self-Assembly of Synthetic Polymers into Toroidal Nanostructures

With the development of polymer chemistry, copolymers with various topologies, including block, graft, brush-like, and gradient copolymers, have been synthesized. It has been dem-onstrated that these synthetic copolymers can self-assemble into nanotoroids in a selective solvent. In the following, studies regarding the self-assembly of synthetic polymers into exclusive toroids are featured.

As an example, Chang et al. prepared toroidal micelles from polyisoprene-block-poly(2-vinylpyridine) (PI-b-P2VP) block copo-lymer in a THF/ethanol solvent mixture.[49] When ethanol is added to the THF solution of the copolymers, the copolymers self-assemble into aggregates with a core of PI blocks and a corona of P2VP blocks. As shown in Figure 2a, the AFM image reveals that exclusively toroidal micelles with uniform size are obtained. The diameter (Dtoroid) and width (dtoroid) of the toroids are ≈97 and 27 nm, respectively. Additionally, Presa-Soto et al. found that toroids can be obtained through self-assembly of block copolymers containing a crystallizable core-forming block and a coil block, poly-[bis(trifluoroethoxy)phosphazene]-b-poly(styrene) (PTFEP-b-PS), in THF.[50] The formed toroidal micelles have a Dtoroid of ≈190 nm and a dtoroid of ≈60 nm (Figure 2b).

Apart from block copolymers, copolymers with other topolo-gies have been used to produce toroids through solution self-assembly.[51–56] For example, Herrera-Alonso et al. reported that the macromolecular brush poly(glycidyl methacrylate)-graft-poly(ethylene glycol)/poly(d,l-lactide) can self-assemble into toroids in THF/water solution.[53] Schubert et al. observed toroidal micelles assembled from gradient copolymers poly(2-methyl-2-oxazoline)-stat-poly(2-phenyl-2-oxazoline) in eth-anol/water solutions.[54] Toroidal micelles were also reported to be obtained through the cooperative self-assembly of the

Figure 1. Schematic representation of the routes to construct toroidal assemblies. The dashed line arrows indicate the self-assembly of polymers into non-toroidal assemblies and hierarchical structures.



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copolymers with homopolymers.[55,56] For example, Lin et al. investigated the coassembly behavior of poly(acrylic acid)-g-poly(γ-benzyl-l-glutamate) (PAA-g-PBLG) graft copolymers and PBLG homopolymers in THF/water solution.[55] It was found that the aggregate morphology of mixture systems is dependent on the weight fraction of the PBLG homopolymer (fhomo). At lower fhomo values, rod-like micelles are formed, while toroidal micelles appear at higher fhomo values. The toroids with a Dtoroid of ≈500 nm and a dtoroid of ≈200 nm are formed when the fhomo is 0.3 (Figure 2c). The above works indicate that toroid is an attainable morphology from the self-assembly of copolymers with various topologies in solution.

After an in-depth understanding of the abovementioned toroid formation mechanisms was obtained, it was found that various morphology transformations are sometimes involved in the toroid formation process. For example, it was found that in the formation process of toroids, spherical micelles are initially formed and then transform into disks, eventually perforating into toroids.[88] Nevertheless, in general, the details within

morphology evolution are difficult to observe experimentally. Through a stepwise self-assembly approach and theoretical simulation, researchers have thoroughly examined these trans-formation behaviors, and we will discuss their transformation mechanisms in detail in Section 3.

In addition to solution self-assembly, toroidal nanostructures can also be produced through evaporation-induced self-assembly of polymers.[57–66] Generally, the formation of toroids is induced by nucleation at defect sites or impurities during the evaporation of the solution. For example, Fujiki et al. reported that poly(9,9-di-n-decylfluorene) (PF10) self-assembled into toroids on mica surfaces when the chloroform solvent saturated with water was evaporated (Figure 3a).[65] As exhibited in Figure 3b, AFM obser-vations reveal that isolated toroids have a Dtoroid within a narrow distribution of ≈170 nm and a dtoroid of ≈20 nm. Trace water in chloroform solution is crucial for toroid formation. When a dehy-drated chloroform solution of PF10 was subjected to the same conditions, irregular assemblies were predominantly observed. The results reveal that the water microdroplets generated in the chloroform evaporation process can serve as dynamic templates for macromolecule accumulation, leading to toroid formation.

Feringa et al. demonstrated that poly(n-hexyl isocyanate) (PHIC) can self-assemble into long-range ordered toroids on mica when the solvent is evaporated (Figure 3c).[66] The AFM observations reveal a wide range of spatially aligned toroids with a dtoroid of ≈150 nm and a Dtoroid ranging from 0.5 to 1.0 µm (Figure 3d). It was shown that the pattern possesses a high degree of long-range order with a periodic spacing of ≈2–6 µm. Note that the order degree is sensitive to the evapo-ration rate, and faster evaporation leads to a qualitatively less even periodicity, that is, a lower degree of spatial order. The work shows an easy route to yield ordered pattern surfaces with toroidal morphologies.

2.2. Self-Assembly of Biopolymers into Toroidal Nanostructures

Apart from synthetic polymers, biological polymers can serve as building blocks for constructing toroidal nanostructures. It is well known that DNA, a typical biopolymer, can self-assemble into toroids in some viruses and sperm cells.[67] To date, con-siderable effort has been devoted to the study of DNA toroids. Research regarding the self-assembly of biopolymers into toroidal nanostructures is discussed below.

DNA toroid formation, also termed toroidal DNA condensa-tion, has been reproduced and widely studied in vitro. Hud et al. found that intramolecular condensation of DNA into a toroid is a nucleation-growth phenomenon.[68–70] The first step in toroid formation is the spontaneous formation of a nucleation loop, which results from random thermal fluctuations in DNA confor-mation. This loop can then serve as the nucleation site on which the remaining parts of the DNA chain condense to form a pro-totoroid (Figure 4a,b). Finally, the toroid is formed through the convolution of more DNA chains around the prototoroid. Uni-form toroids are observed from 3 kb DNA samples upon con-densation by hexammine cobalt(III) in the presence of 2.5 mM NaCl, where the 3 kb DNA is linear 2961-base-pair plasmid DNA (Figure 4c). Cryo-TEM of DNA toroids provides details regarding the fine structure of DNA organization within toroids.[2] The

Figure 2. a) Molecular structure of the PI-b-P2VP block copolymer and AFM image of the PI-b-P2VP toroidal micelles obtained in THF/ethanol (20/80, v/v) solution. The inset shows the definition of the diameter (Dtoroid) and width (dtoroid) of a toroid. Reproduced with permission.[49] Copyright 2009, Wiley-VCH. b) Molecular structure of the PTFEP-b-PS block copolymer and TEM image of the toroidal micelles from PTFEP-b-PS in THF. Reproduced with permission.[50] Copyright 2016, Wiley-VCH. c) Molecular structure of PAA-g-PBLG graft copolymer and PBLG homopolymer, and TEM image of the toroids self-assembled from PAA-g-PBLG/PBLG mixtures (fhomo = 0.30) in THF/water solution. Reproduced with permission.[55] Copyright 2013, American Chemical Society.



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top-view toroids exhibit circular striations that support the spool-like winding of DNA (Figure 4c). The edge-view images of the toroids further reveal alternating regions of defective and ideal hexagonal packing of DNA. Additionally, the effect of ionic strength on 3 kb DNA condensation was investigated. As shown in Figure 4d, when 2.5 mM MgCl2 was applied, toroids with a larger width were observed. Hud et al. established that the toroid diameter is dependent on the nucleation loop related to the per-sistence length of DNA. In contrast, the toroid width was deter-

mined by the winding kinetics versus thermodynamic limits (regulated by solution conditions). Generally, the persistence length (chain rigidity) of DNA remains almost constant with the change of solution conditions, which results in the uniformity of the nucleation loop.[2] Therefore, this unique loop-and-wind route can achieve the formation of uniform toroids.

In addition to experimental studies, a theoretical model of DNA condensation has been developed. Bloomfield summarized DNA condensation experiments and found that the size of DNA

Figure 3. a) Schematic illustration of the formation of toroids via evaporation-induced self-assembly. b) AFM images of PF10 toroidal nanostructures on mica obtained from evaporation of a solution in water-saturated chloroform. Reproduced with permission.[65] Copyright 2008, Royal Society of Chemistry. c) Schematic illustration of the formation of ordered toroidal morphology on a surface. d) AFM image of the sample prepared by evapora-tion of a toluene solution containing end-functionalized PHIC on mica. Reproduced with permission.[66] Copyright 2010, Royal Society of Chemistry.

Figure 4. a) A model for the process of toroid nucleation and growth (loop-and-wind process). The green circle on the prototoroid illustrates the size of the nucleation loop. b) TEM image of the nucleation loop in the formation process of DNA toroids. Reproduced with permission.[68] Copyright 2000, American Chemical Society. c,d) TEM images of toroids produced by the condensation of DNA with hexammine cobalt(III) chloride in the presence of various ionic strengths: c) 2.5 mM NaCl and d) 2.5 mM MgCl2. Reproduced with permission.[69] Copyright 2003, Springer Nature.



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toroids is independent of their molecular length within the range of 400–40 000 base pairs.[71] He developed a successive association equilibrium theory to explain this finding. Multiple free energy contributions from mixing, bending, hydration, and other nearest-neighbor interactions are considered in this model. He found that the size and distribution of condensed DNA are determined kinet-ically rather than thermodynamically. The condensation process is related to the rigidity and the localized helix structure of DNA.

Apart from the theoretical study, simulations can provide straightforward and detailed information on the DNA conden-sation mechanism.[72–75] Molecular dynamics simulations have been employed to gain a thorough knowledge of semiflexible biopolymer condensation principles. Barbi et al. developed an analytical model and simulated the condensation behavior of DNA with self-interactions.[72] This theoretical simulation can evaluate the various contributions to the free energy: the bending energy, the surface tension, the bulk attractive force, and the chain entropy. Based on the simulations, the critical condensation force for DNA condensation was calculated. Mar-itan et al. performed Monte Carlo simulations to investigate the effect of the stiffness, the DNA length, and the strength of the long-range interactions on the competition between toroidal

and rod-like structures, two possible ground states for DNA condensation.[73] By varying the DNA stiffness and length, three kinds of morphologies, including uncondensed chains, rod-like, and toroidal aggregates, can be observed in the simulations. Based on the results of the DNA condensation simulation, a phase diagram in the space of stiffness k versus length L was constructed. It is shown that the toroid states are more favorable than the rod-like counterparts above a certain stiffness. Interest-ingly, the boundary line between the rod-like and toroid states has an L1/3 dependence on the chain length L and is regardless of long-range interaction strengths. The simulations are con-sistent with some experimental features of DNA condensation.

Research advances in DNA toroids have inspired studies on toroids from other biopolymers, such as polypeptides and xanthan.[76–79] Lin et al. recently reported that PBLG homopoly-mers can self-assemble into uniform toroids through a loop-and-wind route resembling the toroidal condensation of DNA chains.[76] The aggregates were prepared by adding water to the PBLG solution (THF/DMF, v/v, 3/7). The formation mechanism of PBLG toroids was examined by monitoring the morphology evolution of the assemblies under various water additions. As shown in Figure 5a, when 4.7 vol% water

Figure 5. a–c) SEM images of the aggregates self-assembled from PBLG3744 homopolymers at various water contents: a) 4.7 vol%, b) 4.9 vol%, and c) 6.0 vol%. The insets show schemes of the corresponding aggregates. d) Simulation snapshots of the formation of the homopolymer toroid at various simulation times. Reproduced with permission.[76] Copyright 2020, Wiley-VCH. e,f) AFM images of xanthan compacted with chitosan under different conditions: e) room temperature and f) 70 °C after complexation at room temperature. g) AFM image of intermediates from xanthan-polycation com-plexes. Reproduced with permission.[79] Copyright 2004, Wiley-VCH.



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was added to the PBLG3744 solution (the subscript represents the polymerization degree), fibrils several microns in length were observed. With increasing water content, a part of the fibril preferentially curves into a loop (Figure 5b). Then, the remainder of the fibrous structure winds around the circle to form a toroid. As a result, toroids with uniform size are obtained (Figure 5c).

To gain a deep understanding of the formation mechanism of the PBLG toroids, BD simulations of the self-assembly behaviors were performed. The homopolymer PBLG3744 used in the experiments is coarse-grained to R50 (the subscript is the number of R beads). The P bead is joined to each R bead to rep-resent the pendant group of the PBLG backbone. The R-R and P-P pairwise interactions, which are described by the attractive potential, are associated with the hydrophobic nature of PBLG backbones and the π-π interaction between phenyl groups. Their interaction strengths are denoted by the parameters εRR and εPP. Under certain conditions (εRR = εPP = 5.0ε, where ε is the energy unit in the simulation), R50 homopolymers self-assemble into toroidal structures. As shown in Figure 5d, in the initial stage, a number of R50 homopolymers are randomly dis-persed in the simulation box. As the simulation time increases, fibrous aggregates are obtained. One end of the fibrous aggre-gate curves into an initial loop with time. Finally, the remaining parts of the fibers wind around the initial loop, leading to a toroid. These simulation results are in agreement with the experimental observations. Moreover, they found that the ini-tial loop size determines the dimension of the formed toroids. The toroid diameter is associated with polymer flexibility and self-attraction interactions and is less dependent on the length polydispersity of the fibrils. These features show some similari-ties with DNA condensation.

Xanthan, a type of semiflexible biopolymer, can also self-assemble into toroids through the winding mechanism.[78,79] For example, Stokke et al. reported that polysaccharide xan-than compacted with chitosan yields a mixture of toroidal and metastable structures at room temperature (Figure 5e).[79] The fraction of toroids increases with increasing temperature. Fur-thermore, the width of toroids increases while the diameter is almost constant (Figure 5f). These results indicate that the metastable states are driven toward the more stable form of a toroid as the temperature is increased. Figure 5g shows the intermediates in the formation of toroids from xanthan–polyca-tion complexes. This work provides experimental insight into the construction of biopolymer toroids.

The formation of toroids from biopolymers such as DNA has been studied in experiments and theoretical simulations. Gen-eral rules for the building and manipulation of DNA toroids have been suggested. The obtained results can provide valu-able guidance for preparing toroids from polymers other than biopolymers. For example, Kramarenko et al. studied the con-formation behavior of semiflexible dipolar polymer chains via MD simulations.[80] By adjusting the rigidity of the chains and the strength of electrostatic interactions, toroids can be formed by dipolar chains in a process that resembles DNA condensa-tion. This work indicates that the formation principles of DNA toroids could be applied to systems other than biopolymers. This is a potential future direction to explore within the research field of toroids.

3. Transformation of Assemblies into Toroidal Nanostructures

Amphiphilic copolymers can self-assemble into a diverse range of supramolecular aggregates, such as spheres, cylinders, disks, and vesicles, in selective solvents. From the viewpoint of topological structures, toroids can be viewed as ring-shaped cylinders or hollow disks/vesicles. Indeed, it has been demon-strated that under certain conditions, copolymers can first form assemblies (e.g., spheres, cylinders, disks, and vesicles) and then transform into toroids to minimize the free energy of the system. According to the evolution process, the transformation manner can be divided into three categories. One is the perfo-ration of circular/spherical assemblies (e.g., disk-like micelles, spherical micelles, and vesicles); the second is the end-to-end coalescence of cylindrical assemblies; and the third is the assembly of spherical assemblies. In this section, the recent advances in the formation of toroids through three pathways are reviewed.

3.1. Perforation of Assemblies

The perforation deformation of structures with circular/spherical shapes, such as disks, vesicles, and spheres, can result in toroid formation. There have been a few reports on the evolution process that involved both experiment and theo-retical simulations. In general, the toroids formed through the perforation pathway possess a relatively uniform size due to the unique morphology evolution process. In the following, the research concerning this unique route is discussed.

3.1.1. Perforation of Micelles and Vesicles

Work on toroids transformed from disk-like micelles and ves-icles has been reported by Pochan’s group and Jiang’s group. Pochan et al. intensively investigated the morphology trans-formation of assemblies mediated by multivalent organic counterions.[81–84] As an example, toroidal micelles were obtained by the self-assembly of PAA-b-PMA-b-PS triblock copolymer via interaction with organic diamines 2,2’-(eth-ylenedioxy)diethylamine (EDDA) in mixed THF/water solution.[84] A schematic representation of the formation of toroidal micelles is shown in Figure 6a. Upon the addi-tion of water, the PAA-b-PMA-b-PS/EDDA mixture initially self-assembles into disk-like micelles. Subsequently, these disk-like micelles transform into toroidal micelles through the perforation pathway. In Figure 6b, the development of toroidal micelles is presented, and some intermediate struc-tures that form during disk perforation are demonstrated. Small disks are only perforated once through the center in the evolution process, thus forming small toroids. Larger disks perforate at different areas simultaneously, resulting in the formation of the structure with several holes through the micelles. Pochan et al. proposed that the local chain adjustment of core-forming PMA-b-PS chains with high mobility responding to solvent condition changes is critical for perforating disks into toroids.



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In addition, the formation of toroids can be achieved through the perforation of vesicles.[85,86] For example, Jiang et al. demon-strated that the cylinder-sphere-vesicle-toroid transition process can result in the toroidal micelles of P4VP-b-PS-b-P4VP block copolymers.[85] In the experiment, a stirring was applied to the P4VP-b-PS-b-P4VP solution (Diox/H2O, w/w, 75/25). They found that the shear flow is crucial for toroid formation. In Figure 6c, the morphology evolution at different annealing times under a high stirring rate (2000 rpm) was demonstrated. Long cylin-ders formed at an annealing time of 5 min. The cylinders short-ened and broke into spheres over time. As the annealing time further increased, the spheres evolved into vesicles and even-tually perforated into toroids. An illustration of toroid forma-tion via the cylinder-sphere-vesicle-toroid process is shown in Figure 6d. They suggested that the high stirring energy can be absorbed by the micelles, driving the unique morphology evolu-

tion. Interestingly, Jiang et al. also found that when the solu-tions are annealed at a lower stirring rate (200 rpm), toroids can be produced by the straightforward end-to-end coalescence of cylindrical micelles (discussed in Section 3.2).

The studies mentioned above have demonstrated the feasi-bility and rationality of the perforation pathway to form toroids. It was recently suggested that when enhancing the rearrange-ment ability of core-forming blocks to quickly respond to sol-vent condition changes, uniform toroids can be produced via the perforation pathway.[49,50,56,87] In this case, the evolution of morphologies is rarely captured. To some extent, direct self-assembly of polymers into toroids in solution has been considered (as discussed in Section 2.1). For instance, Chang et al. reported that PI-b-P2VP block copolymers can self-assemble into toroidal micelles of uniform size in a THF/ethanol mixture.[49] It is believed that the toroids form through

Figure 6. a) Schematic representation of the perforation of PAA-b-PMA-b-PS/EDDA disk-like micelles into toroidal micelles. b) TEM images of the intermediate structures and toroids during the perforation of the disk-like micelles. Reproduced with permission.[84] Copyright 2008, Royal Society of Chemistry. c) Morphology evolution of P4VP-b-PS-b-P4VP micelles trapped at different annealing times at a high stirring rate (2000 rpm). d) Schematic representation of toroid formation via the cylinder-sphere-vesicle-toroid process. Reproduced with permission.[85] Copyright 2009, American Chemical Society.



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the perforation pathway, that is, the copolymers assemble into spherical micelles, grow into disks, and eventually perforate into toroids. In the evolution process, the low glass transition temperature of the core-forming PI block allows the initial micelles to reorganize readily in response to environmental changes and enables toroid formation.

Theoretical simulations have been employed to examine the perforation behavior to capture the essential features of the perforation pathway and profoundly reveal the formation mechanism of toroids.[88,89,114] For example, Schmid et al. used mesoscopic field-based simulation to study the assembled struc-ture of amphiphilic block copolymers after quenching from the homogeneous state and investigated the evolution process from disks or vesicles to toroids.[88] The system contains amphiphilic diblock copolymers with solvophobic blocks A and solvophilic blocks B dissolved in solvent S. The final self-assembled struc-tures are determined by the copolymer concentration (φp) and the Flory-Huggins parameters χAB, χAS, and χBS. Typical hollow structures, including toroids and cage micelles, can be observed for such a system. Figure 7a shows the morphological evolution process from sphere to disk and then perforate into a toroid. With decreasing φp from 0.20 to 0.18, a perforation process can be observed for the transformation from vesicles to toroids or cage micelles (Figure 7b). The initial micelles first grow into semivesi-cles, then several holes appear in the shells, and eventually, the perforated vesicles develop into toroidal micelles. They found that the perforation process is related to the dynamic stability of micelles. The number of micellar nuclei (i.e., hole number)

depends on the initial size of spherical micelles or small vesicles. For example, when φp is close to the critical micelle concentra-tion, the dynamic stability of large vesicles increases, and the initial number of micellar nuclei decreases. Thus, at the lower φp (close to the critical micelle concentration), the vesicles cannot be disturbed by the environment; they perforate late and finally transform into a large cage micelle (Figure 7c).

Note that the size distribution of toroids formed via the per-foration of disk micelles is more uniform than that of vesicles. This trend could be attributed to the contribution of the bending energy. In a simplified theoretical model, the bending energy of a single toroid with radius R is proportional to k/R (k is the bending rigidity); thus, if all toroids have a uniform diameter R, the total energy for a fixed number of rings is minimal. In contrast, the bending energy of a vesicle is 4πk, which is inde-pendent of the vesicle size. Thus, the total bending energy is only related to the number of vesicles, not their size distribution. The uniformization of the size distribution for the formed toroids is difficult to achieve due to the perforation of the vesicles. Overall, the nucleation-growth process is an efficient method to prepare toroidal structures from initial disks or vesicles.

Due to the limitations of experimental techniques and the complexity of the toroid formation process, an understanding of the formation kinetics is still lacking. It can be seen from the preceding discussions that theoretical simulation is an effective methodology to gain detailed and straightforward information on the toroid formation kinetics. This may be an important topic in the future.

Figure 7. a) Evolution process from sphere to disk and then toroid (φp = 0.20). b) Evolution process from vesicle to toroid (φp = 0.18). c) Evolution process from vesicle to cage micelles (φp = 0.17). Times t are given in units of T = 104τ0. Reproduced with permission.[88] Copyright 2008, American Physical Society.



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3.1.2. In-to-Out Switch of Micelles

As discussed above, spherical micelles can initially transform into vesicles and then perforate into toroids (see Section 3.1.1). Throughout the whole evolution process, the compositions of the core and corona remain almost unchanged. It was recently suggested that toroid formation can be achieved through the in-to-out switch of spherical micelles. This morphology evolution is associated with the inversion of the core and corona of micelles, which is induced by enhanced solubility of core-forming chains or lowered solubility of corona-forming chains.[90–93]

Zhang et al. reported the sphere-to-toroid transi-tion of a pH-sensitive ABC triblock copolymer poly(N,N-dimethylacry lamide) -block -polystyrene-block -poly [N -(4-vinylbenzyl)-N,N-dibutylamine] (PDMA-b-PS-b-PVBA) assembly system through the in-to-out switch strategy of the core-forming C block (PVBA) in solution (Figure 8a).[91] The ABC triblock copolymer self-assembles into spherical micelles with a core-shell-corona structure (Figure 8b). The core consists of the pH-sensitive C block (PVBA), the shell is formed with the solvophobic B block (PS), and the corona is composed of the solvophilic A block (PDMA). Note that the core-forming PVBA blocks can be ionized and solubilized in an acidic aqueous solution. Thus, when the system was acidified by hydrochlo-ride in the ethanol/water mixture, an in-to-out switch of the ionized core-forming PVBA block due to the pH sensitivity of the PVBA block occurred, which resulted in the transformation from spherical micelles to toroidal micelles (Figure 8c).

Additionally, Qiu et al. reported the morphological evolution of PS-b-P2VP spherical micelles on a substrate.[92] The transfor-mation is induced by annealing the spherical micelles in selec-tive solvents. This process involves the formation of spherical micelles with a P2VP core and a PS corona in toluene and subsequent structural inversion on the substrate triggered by solvent annealing (Figure 8d,e). When ethanol vapor, a good solvent for the P2VP block but poor for the PS block, is used in the annealing experiment, the P2VP core tends to be dissolved

out, while the PS corona is gradually frozen. This core-corona inversion on the substrate leads to the emergence of toroids (Figure 8f). Qiu et al. proposed that the restriction of the sub-strate on the core-corona inversion of spherical micelles plays an important role in the formation of toroidal morphology.

As discussed above, toroids can be produced from a series of nanostructures with circular/spherical shapes (i.e., disks, vesi-cles, and spheres) through the perforation pathway and in-to-out switch. In principle, the uniformity of the obtained toroids is related to the size distribution of morphological precursors. To obtain uniform toroids, one focus should be on the manip-ulability of various morphological precursors. However, it is considerably arduous to strictly regulate the formation of ini-tial assemblies and subsequent perforation in a self-assembly process. The stepwise self-assembly method, which contains several assembly processes, has recently attracted consider-able interest because each of the assembly processes can be separately manipulated and preprogrammed, enabling better control of the aggregate morphologies.[94,95] This self-assembly strategy may be employed to produce uniform toroids by indi-vidually manipulating the morphological precursor size and the perforating process. For example, a series of uniform vesi-cles have been obtained in various systems.[96–99] Using these uniform vesicles as precursors in the following step, that is, altering the solution condition, toroids with uniform size may be obtained through the perforation process.

3.2. End-to-End Coalescence of Cylindrical Assemblies

The end-to-end coalescence of cylindrical assemblies is a fea-sible route to generate toroidal nanostructures since toroids can be viewed as ring-shaped cylinders from a topological per-spective. For the cylindrical micelles formed in solution, the semispherical endcaps usually bear higher free energy than the cylinder body due to their higher curvatures.[84] When the surrounding environments become poor for the micelles, the

Figure 8. a) Schematic illustration of the sphere-to-toroid transition of an ABC triblock copolymer through the in-to-out switch of the pH-sensitive core-forming C block. b,c) TEM image of (b) the spherical aggregates of the PDMA-b-PS-b-PVBA copolymer and c) the sample after acidification in the ethanol/water mixture. Reproduced with permission.[91] Copyright 2014, Royal Society of Chemistry. d) Schematic illustration of the transition of PS-b-P2VP spherical micelles into toroidal micelles upon annealing in ethanol on a surface. The blue chains and green chains represent PS and P2VP segments, respectively. e,f) AFM images of (e) the PS-b-P2VP spherical micelles and f) the sample after annealing in ethanol vapor on a silicon wafer. Reproduced with permission.[92] Copyright 2019, American Chemical Society.



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cylindrical micelles bear higher interfacial energy and demand morphological evolution. One way to reduce the higher energy is to proceed with the one-dimensional growth of cylindrical micelles through fusion with other cylindrical endcaps.[100] Another way is to form toroids through end-to-end coalescence. For the end-to-end coalescence of cylinders into toroids, three energy contributions are involved: the bending energy of cylin-ders, the interfacial energy between cylinders and solvent (i.e., self-attraction energy of cylinders), and the extra end-capping energy of cylinders. According to the rigidity of micelles, cyl-inders can be classified into rod-like and worm-like forms, and they show different toroid formation manners. Rod-like micelles with high bending energy can form toroids driven by internal interactions, while worm-like micelles with lower bending energy can transform into toroids driven by the elimi-nation of end-capping energy. In this subsection, we discuss the research regarding the formation of toroids in these two manners.

3.2.1. Driven by Internal Interaction of Rod-Like Micelles

Rod-like micelles usually refer to the rigid cylindrical micelles with higher bending energy.[34] When the solvent becomes poor for the micelles, the interfacial energy between the micelle core and shell is expected to increase. In response, the rod-like micelles tend to transform into collapsed nanostructures to alleviate the higher interfacial energy. Due to the rigidity and anisotropic nature of rod-like micelles, toroids are obtained instead of collapsed spheres.[23,79,84] Note that the contribution

of the bending energy to thermodynamic equilibrium is an important feature of the end-to-end coalescence of rod-like micelles.[104]

The driving force of the bending of the cylinder is relevant to the interfacial energy, which results in toroid formation. For instance, Lin et al. reported the formation of uniform toroids via end-to-end coalescence of rod-like micelles assembled from PBLG-g-PEG graft copolymers. Such a process is also referred to as supramolecular cyclization in their studies.[34] The rod-like micelles were prepared by adding water into the graft copolymer solution, followed by dialyzing the solution against water. In the micellar core, the rigid PBLG backbones align and are oriented along the axial direction of the rods. A cer-tain amount of THF was added to the rod-like micelle solution to trigger transformation. As shown in Figure 9a, as the THF content in the micelle solution increases, the rod-like micelles gradually bend, and the two ends of the rods finally merge to form toroids. Circular dichroism experiments show that with increasing THF content, the band of pendant phenyl groups of core-forming PBLG becomes more prominent, suggesting that the pendant group packing is more constricted (Figure 9b). This internal constriction is related to the unfavorable interfa-cial energy between the micelle core and the corona. The rod-like micelles tend to bend to lower the high interfacial energy. The micelle bending is governed by the tension of the core-corona interface, that is, related to the degree of constriction of pendant phenyl groups. Additionally, rod-like micelles pos-sess extra end-capping energy due to the inadequate coverage of PEG chains.[101,102] When the two rod ends curve to approach each other, they merge to form a toroid.

Figure 9. a) Morphological transformation of PBLG-g-PEG rod-like micelles into uniform toroidal micelles with increasing THF content. b) Circular dichroism spectra of PBLG-g-PEG aggregates in the morphology transformation as a function of added THF content. c) Energy change as a function of the simulation time in the morphology evolution. Reproduced with permission.[34] Copyright 2017, Wiley-VCH.



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Similarly, rod-to-toroid morphology transitions were also observed for asymmetric macromolecular double-brushes of pol-yacrylate-graft-poly(6-(4-butyl-4’-oxyazobenzene) hexyl acrylate)/poly(ethylene oxide) systems.[103] It was found that the macromo-lecular double-brushes self-assemble into spindle-like micelles in THF/H2O and gradually curve into toroids through end-to-end closure upon irradiation with UV light. Photoinduced toroid formation is ascribed to the trans-to-cis isomerization of azoben-zene molecular brushes, which is relevant to the interfacial energy change between spindle-like micelles and solvent.

Lin et al. performed BD simulations to reveal the toroid for-mation mechanism (Figure 9c). The simulation results repro-duce the morphology evolution observed in the experiments. Additionally, energy variations in the self-assembly process were calculated by theoretical simulations. In the formation of rod-like micelles, the total potential energy (Etotal) decreased until it reached an equilibrium state. Upon the addition of THF, the interfacial energy (Einter) was increased. The rod-like micelles tended to bend into curved rods to reduce the interface between the micelle core and shell. This curving process led to an increase in the bending energy (Eangle). Additionally, the inadequate coverage of PEG chains on the rod-like micelle ends could give rise to higher end-cap energy (Eend) at both micelle ends. Eventually, the interplay of the three parts of energy (i.e., Einter, Eangle, and Eend) of the micelles results in a lower Etotal, and toroids are formed. The simulation results thoroughly reveal the related mechanism from different perspectives.

Recently, Gao et al. established a theoretical model to reveal the cyclization conditions of rod-like micelles.[104] Rod-like micelles

are self-assembled from rod-coil graft copolymers, which consist of a rigid backbone with pendant groups and two flexible side chains (Figure 10a). The rigid backbones take parallel packing in the cores, while the micellar ends cannot be entirely covered by side chains, leading to partially exposed ends with high energy. The interaction strength εPP between the pendant groups was increased to simulate the increase of interfacial energy between the micelle core and corona in the experiments, which induces the bending and end-to-end coalescence of rod-like micelles into toroidal micelles. The proposed model assumes that the end-capping energy remains unchanged before the end-to-end coales-cence; that is, the end-cap energy is eliminated only when the two end-caps approach each other. The variation in the bending energy (ΔEbend) mainly comes from the variations in the bending angle potential of copolymer backbones, while the variation in the interfacial energy (ΔEinter) mainly comes from the variations in the self-attraction energy between pendant groups. The expres-sion of the radius of curvature (R) as a function of the interaction strength between pendant groups (εPP) and the backbone rigidity (k) was derived. The theoretical predictions by this model are con-sistent with the BD simulation results and can also well describe the experimental observations of the PBLG-g-PEG copolymer micelles in THF/DMF/water solution. In the experiments, the radius R gradually decreases as the THF content increases (inter-facial energy increases). When the THF content is above 50.0 vol%, end-to-end coalescence occurs, and toroids are obtained. In the simulations, the radius R gradually decreases as the εPP increases. The theoretical predictions are qualitatively consistent with the simulation and experimental results (Figure 10b).

Figure 10. a) Schematic illustration of the supramolecular cyclization of rod-like micelles. b) Dependence of the curvature radius R on εPP and the dependence of R on the THF content. c) The aspect ratio L/D of cylinders and the fraction of toroids for the graft copolymers with various weight-average molecular weight Mw of PBLG. Reproduced with permission.[104] Copyright 2020, Royal Society of Chemistry.



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Due to the geometric features of the toroid, the toroid diam-eter should be larger than the cylinder diameter. The geometric condition for supramolecular cyclization (aspect ratio, L/D > π) is obtained. As shown in Figure 10c, with increasing mole-cular weight of PBLG, the L/D of the rod-like micelles gradu-ally increases, and the fraction of formed toroids significantly increases as the L/D > π. This work delineates the cyclization mechanism of rod-like micelles from a theoretical standpoint. To date, there are a number of experimental works and a few theoretical simulations regarding the rod-to-toroid transfor-mation. However, in-depth theoretical studies of supramolec-ular cyclization are limited. More attention is needed in this research direction.

Very recently, Zhu et al. reported the formation of Moebius strips (featuring both toroidal and chiral structures) via self-

assembly of chiral block copolymer polystyrene-block-poly(d-lactide acid) (PS-b-PDLA) in THF/water mixed solvents.[105] As shown in Figure 11a, the toroids with a Dtoroid of ≈1.14 µm and a dtoroid of ≈240 nm are observed. The magnified SEM and TEM images show that part of the toroids possesses 180° twisted topology (M-twisted). They also examined the formation process of these interesting toroidal nanostructures. When 23.0 vol% water was added to the THF solution of PS-b-PDLA, spindle-like micelles (SLMs) were formed. The SLMs possessed high rigidity due to the crystallinity of core-forming PDLA blocks. After 10 min of stabilization, the SLMs spontaneously trans-formed into toroids through end-to-end coalescence, which is similar to the formation of PBLG-g-PEG toroids reported by Lin et al.[34] The difference is that the coalescence from SLMs to toroids included a 180° twist in the toroid structure.

Figure 11. a) SEM and TEM images of the PS-b-PDLA toroidal micelles. b) Schematic representation of the probable modes for the closing of spindle-like micelles into toroidal micelles. Reproduced with permission.[105] Copyright 2019, Nature Publishing Group.



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As shown in Figure 11b, for face-to-face bonding (end-to-end coalescence), there are four modes for efficient coalescing: end A rotates 90° clockwise (right-handed) and end B rotates 90° counterclockwise (left-handed) (abbreviated as A-R90°&B-L90°, A-R90°&B-R90°, A-L90°&B-L90°, and A-L90°&B-R90°). If the SLMs coalesce through the A-R90°&BL90° or A-L90°&B-R90° mode, no twists along the toroid can be obtained. Coalescing through the A-R90°&B-R90° mode induces a 180° P-twist along with the toroid, whereas coalescing through the A-L90°&B-L90° mode causes a 180° M-twist. Generally, four modes of SLM coa-lescing occur equiprobably. However, the experimental results reveal that the possibility of forming M-twisted Moebius strips is ≈fourfold higher than that of forming P-twisted structures. This distinctive phenomenon is termed symmetry breaking.[106] The authors proposed that relaxation of the internal stress within the SLMs related to oriented stretching of PS chains drives symmetric breaking during the coalescence of SLMs into toroids.

Apart from the Moebius strip, another type of chiral nano-toroid has been reported in polymer systems. Very recently, Lin et al. reported that a binary system containing a polypeptide

homopolymer and its block copolymer can self-assemble into chiral toroids combining toroidal and helical morphologies.[76] Helical nanotoroids were prepared by adding water (a selective solvent for PEG blocks) to PBLG-b-PEG/PBLG solution (THF/DMF, v/v, 3/7). As shown in Figure 12a–c, microscopy obser-vations reveal that uniform toroids with right-handed helical surface patterns are obtained. In the formation process of the helical toroids, the PBLG homopolymers form toroidal tem-plates, and the PBLG-b-PEG copolymers self-assemble into helical patterns on the toroid. Additionally, the chirality of the toroid can be regulated by the chirality of the polypeptide block copolymers. When the PBLG blocks were replaced with poly(γ-benzyl-d-glutamate) (PBDG, which has opposite chirality to PBLG), helical toroids with left-handed chirality were obtained (Figure 12d).

Chiral toroids are of significant fundamental interest due to their specific structural features.[106,107] In the end-to-end coa-lescence of rod-like micelles, the introduction of a chiral block seems to facilitate the formation of chiral toroids, such as in the case of the PS-b-PDLA copolymer system, in which the PDLA is a chiral block. However, this methodology is still emerging, and

Figure 12. a) SEM image, b) TEM image, and c) AFM images of helical toroids self-assembled from the PBLG-b-PEG/PBLG system. The insets in (a), (b), and (c) show a scheme of helical nanotoroids, a representative magnified image, and the AFM height profile along the white line, respectively. d) SEM image of helical toroids self-assembled from the PBDG-b-PEG/PBLG system. The inset shows a schematic of the helical nanotoroids. Reproduced with permission.[76] Copyright 2020, Wiley-VCH.



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the mechanism of chiral transfer from molecules to assemblies is not clear. Increasing attention needs to be given to the forma-tion conditions and mechanisms of chiral toroids. Theoretical simulations can provide valuable and detailed information on the formation of chiral toroids. For example, with the assistance of simulations, more in-depth insight into the formation mech-anism of helical toroids has been gained for the PBLG-b-PEG/PBLG system.[76] It was shown that the block copolymers self-assemble on the homopolymer toroids in a twisted manner and result in the formation of helical surface patterns. The combi-nation of experiments and simulations presents an effective research method for chiral structure formation.

3.2.2. Driven by the Elimination of the End-Capping Energy of Worm-Like Micelles

As discussed above, when rod-like micelles with high bending energy transform into toroids, the devotion of bending energy mainly compensates for the interfacial energy change. Worm-like micelles with high flexibility usually possess lower bending energy. Thus, in the transformation of worm-like micelles into toroids, the extra end-capping energy plays a prominently impor-tant role. The worm-like micelles can transform into toroids via intramicellar end-to-end coalescence or proceed with one-dimensional growth through fusion with other cylinder endcaps to eliminate extra end-capping energy. Note that the probability of forming closed toroids is much lower than that of creating longer, open cylinders. In this case, intermediate structures such as threefold junctions (Y-like junctions) can be formed through the coalescence of one cylinder endcap with another cylinder middle. The second junction formed further along the cylinder produces a loop, that is, a lasso-like structure. Indeed, in most assembly systems, toroids transformed from worm-like micelles are usually accompanied by these intermediate structures.

As an example, Pochan et al. reported that toroidal micelles can be produced by the morphology transformation of worm-like micelles of PAA-b-PMA-b-PS/EDDA in mixed THF/water solvent.[23,84] For the formed toroids, hydrophobic PS and PMA are packaged within the core domain, and hydrophilic PAA and oppositely charged EDDA comprise the micelle corona (Figure 13a). In the THF/water mixed solvent, the PS-PMA chains are highly swollen by THF, which provides PS-PMA with chain mobility and the overall micelle with flexibility. The negatively charged corona-forming PAA block combines with a positively charged diamine EDDA, which produces a self-attraction of worm-like micelles. Self-attraction drives worm-like micelles to transform into toroids to alleviate energetically unfavorable endcaps. Moreover, some intermediate structures, including lasso-shaped and Y-shaped micelles, are trapped during the formation of toroids (Figures 13b), which strongly supports the mechanism that the toroids are formed through the end-to-end coalescence of worm-like micelles.

As another example, Jiang et al. intensively investigated toroidal micelles self-assembled from P4VP-b-PS-b-P4VP triblock copolymer in dioxane/water mixtures.[85,86] In the experiments, a stirring is applied in the copolymer solution (Diox/H2O, v/v, 75/25). The formation process of toroids was revealed clearly by monitoring the morphology evolution. Figure 13c–e shows the

morphology evolution of P4VP-b-PS-b-P4VP micelles at different annealing times under a low stirring rate. At an annealing time of 5 min, long worm-like micelles were obtained (Figure 13c). With increasing annealing time, the cylinders became short and then coalesced into toroids in an end-to-end coalescence manner (Figure 13d,e). Jiang et al. proposed that the stirring energy can be absorbed by worm-like micelles as a driving force, resulting in an internal energy increase of the aggregates. Worm-like micelles transform into toroids via end-to-end coalescence to alleviate the free energy of the system. Note that some branched cylinders are occasionally observed, resulting in complex mor-phologies forming in an end-to-end fashion. These results are analogous with Pochan’s findings, which reveal that the toroids developed through the end-to-end coalescence of worm-like micelles always coexist with the intermediates.

Following the above pioneering works, toroid formation via end-to-end coalescence of worm-like micelles was also dem-onstrated in other copolymer systems.[53,108–111] For instance, Kim et al. prepared toroidal micelles from worm-like micelles of dendritic poly(ethylene glycol)-block-polystyrene copolymer (9(PEG7)-b-PS) in solution.[111] It was found that due to the imperfect cover of the cylinder ends by short PEG chains, the formed worm-like micelles possess high end-capping energy, which facilitates the end-to-end coalescence of cylinders, resulting in toroid formation.

Apart from the above experimental observations, theoretical simulations have been employed to examine the toroidal for-mation mechanism because they can offer straightforward and detailed microscopic information on the dynamic formation process.[112–116] Liang et al. studied the dynamic formation pro-cesses of toroids from amphiphilic triblock copolymers using DPD simulation.[112] In Figure 13f, a typical toroid formation process is presented. The copolymers initially self-assemble into spherical and cylindrical micelles. Subsequently, the spher-ical micelles coalesce with the neighboring cylindrical micelle and produce a “Y-like” junction. With increasing simulation time, a toroidal structure with end caps is formed through the intracoalescence of the free end cap with the cylinder body. Finally, a closed toroid is obtained when the remaining parts merge with the toroid. The dynamic observation of a toroid formation is in accordance with the experimental observations reported by Pochan et al. and Jiang et al.

The coalescence of worm-like micelles is a common method-ology for the preparation of toroids. Considerable efforts have been devoted to investigations of this strategy. However, this intramicellar end-to-end coalescence process (i.e., toroid forma-tion) is always accompanied by intermicellar connections because coalescence tends to eliminate the energetically unfavorable end-caps of worm-like micelles. This tendency leads to the formation of some intermediates and toroids with a wide distribution. Thus, increasing attention should be focused on the manipulation of the intramicellar coalescence process. It has been reported that the introduction of rigid blocks can facilitate the intramicellar coa-lescence process.[117–120] For example, Liu et al. reported that the formation of nanotoroids with uniform size was achieved by the end-to-end coalescence of worm-like micelles of PS/C60 nanohy-brid block copolymers in chloroform.[118] They proposed that the strong interaction of solvophobic C60 molecules can increase the rigidity of worm-like micelles, which facilitates toroid formation



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and stabilizes the formed structures. As a result, relatively uni-form toroids can be obtained.

3.3. Assembly of Spherical Assemblies

As discussed above, the toroid can be obtained through the transformation of various assemblies. As the toroids evolve, the

aggregation number of polymer chains in the formed toroids is usually close to that of the initial micelles. In other words, only intramicellar evolution occurs in the process. It was recently suggested that spontaneous self-assembly of spherical micelles (i.e., intermicellar evolution) can also form toroids that are larger than the initial spheres. Generally, to create a toroid through intermicellar evolution, the core of the spherical micelles should possess a certain degree of exposure (i.e., possessing surface

Figure 13. a) TEM image of the toroidal micelles from the PAA-b-PMA-b-PS and EDDA systems. Inset is a cartoon schematic of the toroidal micelle with cross-section showing hydrophobic PS (red), PMA (brown) core, and hydrophilic PAA (yellow) corona with closely associated EDDA (blue). Reproduced with permission.[23] Copyright 2004, Science. b) TEM image of the intermediate structures trapped during sample preparation. Intermedi-ates are marked with red arrows. Reproduced with permission.[84] Copyright 2008, Royal Society of Chemistry. c–e) Morphological evolution of P4VP-b-PS-b-P4VP micelles trapped at different annealing times under a low stirring rate (200 rpm): c) 5 min, d) 12 h, and e) 24 h. The insets are cartoon schematics of the corresponding aggregates. Reproduced with permission.[85] Copyright 2009, American Chemical Society. f) Sequential snapshots of the formation of toroids from amphiphilic triblock copolymers in dilute solution by theoretical simulation. Reproduced with permission.[112] Copyright 2008, American Chemical Society.



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defects).[121] This prerequisite can be satisfied by increasing the volume fraction of the core-forming chains or lowering the volume fraction of the corona-forming chains. The assembly of spherical micelles into toroids is expected to reduce the surface area of the core and thus increase the density of the corona-forming chains, which reduces the free energy of the system. In the followings, the research regarding this route is reviewed.

Li et al. investigated the coassembly behaviors of PS-b-PEO block copolymers and CoW12-cored supramolecular star polymer (SSP) modified with PS arms in a methanol/dioxane mixture (Figure 14a).[122] With increasing content of CoW12-cored SSP, a series of spherical and toroidal micelles are formed. In such aggregates, the CoW12-cored SSP and PS blocks form the core, while the PEO blocks compose the corona. The assembly behavior of the spheres was examined by both coarse-grained MD simulations and experimental techniques. Figure 14b–d shows sequential snapshots at various simulation times. Spher-ical micelles are first formed from the binary system of PS-b-PEO and CoW12-cored SSP, and then these spheres tend to aggregate with each other to form a toroidal structure driven by the electrostatic interaction of SSP. During this process, the

fusion of micellar cores in the adjacent spherical micelles takes place, accompanied by the rearrangement of the PEO corona, eventually resulting in toroid formation. The formation pro-cess predicted by simulations is verified by catching the inter-mediate structures during the development of toroids in the experiments (Figure 14e–g). Thus, experimental observations and theoretical simulations strongly support that the toroid for-mation mechanism is the assembly of spherical micelles. This work indicates the advantage of combining experiments and simulations in disclosing the toroidal formation mechanism of a multicomponent system.

As discussed in Section 2.2, upon evaporating the polymer solution on a substrate, toroidal morphology can be obtained by spontaneous self-assembly of block polymers. Recent studies have revealed that the assembly of spherical micelles can be induced and lead to the formation of toroids via evaporation of the spherical micelle solution on a substrate.[123–125] Zhang et al. showed that evaporating the PS-b-PAA spherical micelle solu-tion can induce the spheres to assemble into nanotoroids.[124] The underlying mechanism is explained as a hole-nucleation and hole-growth process caused by dewetting. As the solvent

Figure 14. a) Structure of the PS-b-PEO block copolymer and CoW12-cored SSP. b–d) Sequential snapshots of the formation of toroidal micelles at various simulation times: b) 14 ns, c) 15 ns, and d) 72.4 ns. The blue chains, yellow chains, and red particles denote the PEO segments, PS segments, and CoW12 clusters, respectively. e–g) AFM images of intermediate states during the formation of toroids from spherical micelles. Reproduced with permission.[122] Copyright 2015, American Chemical Society.



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is evaporated, holes open up and grow in the film formed by micelle solution, and they can serve as nucleation sites to accu-mulate the micelles around their rim, resulting in the forma-tion of toroids. In addition to the dewetting effect, the mechan-ical strain fields presented during the evaporation process can also drive toroidal morphology formation.[126,127] For instance, He et al. observed the toroidal structure of polystyrene-b-poly(methyl-methacrylate) (PS-b-PMMA) block copolymer during rapid evaporation of 1,1,2,2-tetrachloroethane (Tetra-CE) solvent, in which Tetra-CE is a good solvent for both blocks but a preferential affinity for the PMMA block.[126] They found that the copolymers initially form spherical micelles in the solution. Under fast solvent evaporation, the mechanical strain fields present in the evaporation process drive the spheres closer and merge into a toroid.

As mentioned above, the obtained toroids in most cases of the assembly of spherical assemblies are not monodisperse due to the uncontrolled aggregation and the polydispersity of spherical micelles. Recently, it has been shown that the intro-duction of a monodisperse circular template is an efficient method for fabricating monodisperse nanorings. Chen et al. reported the formation of core-shell nanorings by introducing circular plasmid DNA into a solution of PEG-b-P4VP spher-ical micelles.[128] Due to the attraction between the oppositely charged DNA and P4VP core of the mielles, the micelles organ-ized on the circular plasmid DNA forming a cyclic beads-on-a-string structure. With the further fusion of the cores of the neighboring micelles along the string, a nanoring was formed. In this system, each nanoring contains one circular DNA chain, therefore the obtained nanorings are monodisperse, and the size of the nanoring can be manipulated by the size of the cir-cular DNA template.

The assembly of spherical micelles is a convenient method-ology for the preparation of toroidal nanostructures. However, in most studies, spherical micelles transform into cylinders instead of toroids to decrease the surface curvature. Although the introduction of a circular template and evaporation-induced method provides some solutions to the problem, more attempts are still required to reveal the conditions and underlying mech-anism of this strategy. With a continuously deepening under-standing of the mechanism, an assembly methodology of spherical micelles with general applicability can be developed. Additionally, the characteristics of the initial spheres play a key role in the resulting morphology. The final structure can be tuned by various spherical structures. For example, Chen et al. demonstrated that the Janus spherical micelles of PEO-b-PAA and poly(2-vinyl naphthalene)-block-poly(acrylic acid) can assemble into tubular and 2D sheet-like superstructures.[129] It is anticipated that by delicately modifying the surface charac-teristics of spherical micelles (e.g., patchy spherical micelles), novel toroidal structures can be produced. This can be a focus of future work on spherical micelle assembly.

4. Disassembly of Hierarchical Assemblies into Toroidal NanostructuresWith the development of supramolecular chemistry, a variety of hierarchical nanostructures can be obtained through various

self-assembly strategies. It is known that hierarchical struc-tures can disintegrate into individual nano-objects, which are building blocks of hierarchical nanostructures.[36,37] This pro-cess is known as disassembly, which is a reverse process of assembly. For example, Yabu et al. and Zhu et al. reported that hierarchical microparticles can disassemble into individual nano-objects with various shapes, such as spheres, cylinders, disks, cups, and bowls, depending on the morphology and internal structure of the original microparticles.[130–132] In par-ticular, hierarchical structures comprised of a toroid-shaped motif can yield toroids via the disassembly route. In this sub-section, recent advances regarding toroid formation through the disassembly route are summarized.

4.1. Disassembly of Toroid-Containing Hierarchical Nanostructures

Recent advances in the development of self-assembly strate-gies allow the construction of hierarchical nanostructures with diverse shapes and internal morphologies. Exceptionally, 3D confined assembly of copolymers (self-assembled in a three-dimensionally constrained tiny space, e.g., emulsion drop-lets) is applied as a facile and robust approach for preparing nanostructures with tunable internal morphologies.[35,133] For example, a variety of novel microparticles with tunable internal structures, including onion-like, pupa-like, bud-like, stacked, and other complex particles, have been produced by the 3D confined assembly of copolymers in emulsion droplets.[35,133] These hierarchical nanostructures can be subsequently disinte-grated into micelle-like nanostructures by selectively dissolving one domain while the other remains unchanged (known as the confined assembly-disassembly method). In particular, individual toroids can be obtained through the disassembly of nanostructures with a ring-shaped internal structure (e.g., pupa-like microparticles).

A schematic illustration of the 3D confined assembly-disas-sembly method for preparing toroids is shown in Figure 15a. Typically, the organic solution of copolymers is first emulsified into droplets with an aqueous surfactant. After removing the organic solvent, the copolymers gradually concentrate inside the droplets and self-assemble into microparticles with a ring-shaped internal structure. These hierarchical nanostructures can disassemble into individual toroids by selectively dissolving one domain.

Zhu et al. demonstrated the formation of toroids from PS-b-P4VP and a 3-n-pentadecyphenol (PDP) system (where PDP with a phenol group can form hydrogen bonds with P4VP) via the 3D confined assembly/disassembly method.[134] Microparti-cles with various shapes and internal structures can be formed depending on the fine regulation of PDP content. When the molar ratio of PDP to PVP units was 0.6, elliptic microparticles with stacked toroids inside were obtained (Figure 15b). Within the microparticles, the PS block composed the dispersed phase (ring-shaped cylinder), while the P4VP(PDP) complex formed the continuous phase. These elliptic microparticles can be sub-sequently disassembled into individual nanotoroids by cleaving the PDP with a selective solvent (breaking the hydrogen bonding) (Figure 15c). In the disassembly process, nanocups,



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nanodisks, and twisted aggregates can also be produced by the disassembly of microparticles depending on the content of PDP. Additionally, they employed the 3D confined assembly/disassembly strategy to ABC triblock copolymer PS-b-PI-b-P2VP (PDP).[135] A number of nano-objects, including nanotoroids, were obtained in the study.

In addition, the confined assembly/disassembly method was employed to produce Janus nanorings that have distinguishing compositions on each side of the toroids. For example, Gröschel et al. reported the synthesis of Janus nanorings from microparticles with stacked toroids inside ABC triblock copol-ymers via the confined assembly/crosslinking/disassembly method.[35] In this method, polystyrene-block-polybutadiene-block-poly(methylmethacrylate) (PS-b-PB-b-PMMA) triblock copolymers concentrate inside the emulsion droplets and self-assemble into microparticles consisting of a 2D concentric arrangement of nanorings (Figure 15d). Three microphases can be clearly distinguished by examining the inner morphology: the PMMA lamellae and PS lamellae stack alternately, while the PB strings are located in-between. Then, cross-linking the PB microphase and subsequently dissolving the PMMA and PS microphases by THF allow the formation of Janus nanorings

possessing two separated polymer brushes of PS and PMMA on the top and bottom (Figure 15e). Additionally, they found that the yield of Janus nanorings is related to the volume frac-tion of PB blocks; that is, decreasing the PB volume results in the formation of Janus spheres and rods, while increasing the PB volume leads to Janus nanorings and Janus disks.

Recently, the synthesis of toroids with multiple chemical functionalities on their surfaces was achieved by the con-fined assembly/disassembly method. Monteiro et al. reported the formation and disassembly of stacked toroidal nano-rattles with multiple surface chemical functionalities in water.[136] First, spherical particles of a thermoresponsive poly(Nisopropylacrylamide)-block-polystyrene (PNIPAM-b-PS) block copolymer were synthesized in situ by aqueous-phase emulsion polymerization using functional MacroCTAs (i.e., R-PNIPAM) as seed particles, sodium dodecyl sulfate as a sur-factant, and 2,2-azobisisobutyronitrile as an initiator. Multifunc-tional chemical groups (e.g., thiolactone, dopamine, pyridyl disulfide, biotin, and alkyne) could be introduced through the R-group on MacroCTAs. After removal of the unpolymerized sty-rene and cooling temperature below the lower critical solution temperature of the PNIPAM block, chemically multifunctional

Figure 15. a) Schematic illustration of the 3D confined assembly/disassembly method for preparing toroids. b,d,f) TEM images of hierarchical micro-particles self-assembled from copolymers under 3D confinement. c,e,g) TEM images of toroids obtained by disassembling the corresponding hierar-chical microparticles. Reproduced with permission.[134] Copyright 2013, Wiley-VCH. Reproduced with permission.[35] Copyright 2019, American Chemical Society. Reproduced with permission.[136] Copyright 2017, American Chemical Society.



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stacked toroid nanorattles are formed in water due to the restric-tion of the 3D confined sphere (Figure 15f). It was revealed that the nanorattles consist of a shell of stacked toroidal micelles and a core of smaller stacked toroidal micelles. Through the addition of toluene, hierarchical structures can be released into individual toroids with multifunctional chemical groups (Figure 15g). Mon-teiro et al. found that these functional toroids show high cou-pling efficiencies with biological molecules and probes, allowing their applications in the biological detection field.

The above works demonstrate that confined assembly fol-lowed by disassembly is a feasible and robust strategy for the fabrication of toroids. However, the obtained toroids are usually not uniform due to the inhomogeneity of the morphology and internal structure of microparticles. To realize the controllable size and uniformity of toroids, the microparticle morphology, including the overall shape and internal structure, should be more precisely and elegantly manipulated under confinement conditions. For example, since the overall shape of microparti-cles is usually related to the feature of confined space, replacing droplet confinement with columnar confinement may result in the formation of nanostructures with a uniform overall shape. To date, theoretical simulations have predicted a number of hierarchical structures formed under 3D confinement. Among them, hierarchical structures comprised of ring-shaped building blocks such as stacked disk-like structures can serve as prom-ising candidates for disassembly.[39,40] In addition, a series of impressive toroidal structures (e.g., Janus nanorings and toroids with surface functionalities) have been created through confined assembly followed by a disassembly strategy. These structures can serve as platforms to fabricate asymmetric hybrid nanoma-terials or selectively couple with functional groups. One focus of future work in this domain is to enrich the variety of toroidal nanostructures and find more practical applications.

4.2. Disassembly of Helical Nanostructure

Helical nanostructures, a form of hierarchical nanostructures, have been constructed from a variety of building blocks. From the viewpoint of topological structure, the helical structures can be viewed as the end-to-end connection of spirally-opened toroids. It is known that under certain conditions, helical struc-tures can disassemble into discrete toroidal nanostructures. Alteration of external conditions (e.g., temperature, solvent, and pH) is usually required to overcome the energy barriers of the unfavorable disassembly process.[137–139]

Lee et al. reported that heat stress as an energy source can induce toroidal nanostructures to undergo helical growth and random disassembly.[137,138] The aromatic macrocycle adopts a folded conformation and can self-assemble into uniform toroids in THF/H2O solvent (Figures 16a,d). When the micelle solution was annealed at 50 °C for 20 min and then cooled back to 25 °C, the toroids transformed into spirally open toroids (active toroids) and then autonomously assembled into helical structures through the end-to-end connection (Figures 16c,e). Note that with increasing annealing time, the helical struc-ture autonomously shortens in length with irregular disas-sembly and finally disintegrates into intact toroids after 9 days (Figures 16c,f).

To deepen the insights into the evolution process, theo-retical simulations based on a coarse-grained model were performed. The formation of toroids was simulated by mole-cular dynamics, providing molecular packing information of the toroid (Figure 16b). The wedge-shaped molecules with a dimeric aromatic core in the eclipsed state are aligned roughly perpendicular to the plane of the toroid, and the hydrophobic cores of the toroid are surrounded by oligoether chains. The dynamic equilibrium between static toroids (closed toroids) and active toroids (spirally open toroids) was also investigated by simulations. Figure 16g shows a plot of the average helix length against time. Both experimental and simulation results show that the length of helical assemblies first increases and then gradually decreases with increasing time. The assembly/disas-sembly behaviors coexist in the dynamic process. In the ini-tial stage, the toroids are mostly active. As the incubation time increases, the active toroids gradually relax into static toroids, resulting in a decreased assembly rate. When the assembly rate is lower than the disassembly rate, the length of the helical assemblies starts to fall, and the assemblies finally disintegrate into static toroids.

Moreover, the energy variation of the assembly and dis-assembly of toroids upon energy input was calculated. The energy of the formed helical structure can be calculated by EN = E0 – 2ΔE(N-1)/N, where N is the toroid number in a helical structure, E0 is the energy of the closed toroid, and ΔE is the energy difference between two closed toroids and a helical toroid dimer. The energy of an infinitely long chain is thereby Einfinite ≈ E0 – 2ΔE. The energy of the open toroid is higher than that of the closed toroid in the molecular slipped packing mode. As shown in Figure 16h, the individual static toroids possess the global minimum in the energy landscape. Upon heating, the eclipsed packing of the dimers in the static toroids transforms into slipped packing of active toroids and causes a dramatic energy increase. To lower the free energy, the active toroids nucleate and grow to form helical assemblies. As thermal energy is consumed over time, the helical structures gradually disassemble into static toroids with global minimum energy. Meanwhile, the slipped packing of the dimers relaxes into eclipsed packing. These theoretical simulation results are in good agreement with experimental observations.

The works mentioned above demonstrate that hierarchical helical nanostructures can disassemble into individual toroids upon introducing external energy. This concept may inspire researchers to fabricate toroids through the disassembly of other hierarchical nanostructures. For example, Cai et al. reported that superhelical structures can be obtained through the coassembly of PBLG-b-PEG block copolymers and PBLG homopolymers.[140] By regulating the self-assembly temperature and initial solvent nature, distinctive hierarchical morpholo-gies, that is, abacus-like structures, can be formed.[141] With the assistance of simulations, it was found that the homopolymers form a rod-like template, and the block copolymers assemble on the bundle, forming a toroidal shell.[140] It is anticipated that the distinctive abacus-like structures can also disassemble into discrete toroids by selectively dissolving the rod-like tem-plate. Expanding the research scope of the disassembly strategy to other systems for fabricating toroids could be one focus of future work.



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Figure 16. a) Molecular structure of the aromatic macrocycle and schematic representation of the toroidal assembly with an eclipsed conformation. b) Calculated static toroidal structure from MD simulation. c) Schematic representation of the assembly of active toroids (green) and disassembly into static toroids (blue). d) TEM image of toroids formed by aromatic macrocycles in THF/H2O solvent. e,f) TEM images of the aggregates formed by the molecule in aqueous solution at various times after heat treatment: e) 4 days and f) 9 days. g) Time-dependent average helix lengths and fitted curve from Monte Carlo simulations (dotted curve). h) Energy variation representing assembly and disassembly of toroids upon energy input. Reproduced with permission.[137] Copyright 2019, Nature Publishing Group.



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5. Functions of Toroidal Nanostructures

Owing to the unique and elegant structures of annular shapes with an internal cavity, toroidal nanostructures exhibit intriguing functions and promising applications. It has been reported that nanotoroids have potential in the fields of photodynamic therapy and cancer therapy because they have the lowest mononuclear phagocyte system uptake and highest tumor accumulation compared to nanospheres and nanoplates of the same size.[46–48] Polymeric toroidal assemblies are expected to possess tremendous prospec-tive applications due to their distinctive diversity and better organization. To date, increasing attempts have been made

to develop the functions of toroidal assemblies. In this sec-tion, the progress on the functions of toroidal assemblies is summarized.

5.1. Nanoreactors for the Synthesis of Inorganic Nanoparticles

The inherent internal cavity of toroids allows them to serve as nanoreactors for the synthesis of inorganic nanoparticles.[142–146] The size of the interior cavity of toroids determines the size of the formed nanoparticles. Thus, the toroidal nanoreactor can offer straightforward size control of nanoparticles through subtle manipulation of the cavity dimension.

Figure 17. a) Schematic representation of the synthetic peptide nanotoroid as a nanoreactor to nucleate AuNP growth within the internal cavity. b,c) Scanning force micrograph images of (b) the nanotoroids with AuNPs inside the cavities and c) AuNPs after removal of the nanotoroids. Repro-duced with permission.[142] Copyright 2004, American Chemical Society. d,e) AFM images of metal nanoparticles obtained from the photoinitiated reduction of metal ions bound to toroidal plasmid DNA: d) nickel and e) cobalt nanoparticles. Reproduced with permission.[145] Copyright 2009, American Chemical Society.



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Matsui et al. reported that toroids self-assembled from synthetic peptides and organic Au salts can be employed as nanoreactors to synthesize Au nanoparticles (AuNPs) inside cavities.[142] A schematic representation of the nanotoroid function as a nanoreactor to synthesize AuNPs is shown in Figure 17a. Through the reduction of Au ions trapped in the cavities, AuNPs were grown inside the cavities of nanotoroids (Figure 17b). The resulting nanoparticles can be subsequently extracted by destroying the nanotoroids via prolonged UV irra-diation. As shown in Figure 17c, AuNPs with a diameter of ≈12 nm are obtained after removing the toroidal nanoreactors. The AuNP size is uniform due to the narrow size distribution of the cavity dimension of the nanotoroid templates formed by synthetic peptides. Similarly, Drain et al. reported that nickel or cobalt inorganic nanoparticles can be produced by using toroidal plasmid DNA as the nanoreactor.[145] Incubation of low concentrations of nickel or cobalt salts with plasmid DNA leads to the formation of toroids. Then, upon exposing the sample to UV light, photooxidation and degradation of the DNA mold occur, which leads to the reduction of the metal ions and the formation of the metal nanoparticles. As shown in Figure 17d,e, nickel and cobalt nanoparticles with a diameter of 40–60 nm were obtained. Moreover, it was found that the size of nanopar-ticles can be manipulated by the diameter of the toroidal DNA. When a smaller circular DNA is employed as the nanoreactor, metal nanoparticles with a smaller diameter can form.

5.2. Building Blocks for Nanoporous Superstructures

Nanoporous superstructures are critically important in catal-ysis, separations, purification, and many other applications.[147] A variety of approaches, such as breath figure fabrication, tem-plating of mesoporous silica, metal-organic framework forma-tion, covalent organic framework formation, and the creation of organic cage solids, have been developed to prepare porous materials.[148] Given the inherently hollow nature, toroids can serve as supermolecular building blocks to fabricate porous superstructures.

Recently, Manners et al. demonstrated that toroidal micelles can hierarchically assemble into multidimensional nano-porous superstructures through the modulation of intertoroid interactions.[45] The toroidal micelles were prepared by self-assembly of the PI-b-P2VP block copolymer in a THF/ethanol mixture. Various kinds of block copolymers were introduced to modulate the interactions between PI-b-P2VP toroids. When hydroxyl-functionalized poly(ferrocenyldimethylsilane)-block-poly(methylvinylsiloxane) (PFS-b-PMVS(OH)2) block copolymers were introduced to coassemble with the toroids, the toroids aggregated into 3D nanoporous superstructures upon drying on a substrate. Manners et al. proposed that PFS-b-PMVS(OH)2 provides hydrogen bonding groups on the corona of toroids (i.e., hydroxyl), which drives 3D associations through synergistic hydrogen bonding interactions. As shown in Figure 18a, sponge-like nanoporous structures with a pore size of ≈85 nm are formed. Transmission electron microtomog-raphy analysis reveals that the sponge-like structure possesses a continuous nanoporous framework with uniform pores (Figure 18b).

In addition, Guerin et al. reported that 3D multi-tori meso-structures can be obtained from PFS-b-PI and PFS-b-PS block copolymers in mixed solvents through a multistep assembly process.[149] Both copolymers first self-assemble into amorphous micrometer-large vesicles. Then, the PFS-b-PS copolymer con-fined in these mesosized vesicles crystallizes and forms elon-gated micelles. Due to space constraints, elongated micelles are forced to grow concentrically along the equatorial plane of the drupelet-shaped particles, leading to toroid formation (Figure 18c). This behavior induces the transformation from a large vesicular mesostructure to 3D multi-tori structures. As shown in Figure 18d,e, spherical hollow mesostructures com-prising a network of toroids are obtained. The pores in the 3D multi-tori structures have a relatively narrow size distribution, with a diameter of ≈1.0 µm and a width of ≈300 nm.

As discussed above, the nanoporous superstructures have a narrow distribution of pore size. In principle, the pore size can be tuned by changing the toroid diameter. These features permit them to be applied in the storage or separation of var-ious guests (such as proteins or viruses). Additionally, the func-tions of such nanoporous superstructures can be modulated by the elaborate design of toroid chemistry. For example, core- or shell-cross-linking chemistry can be applied to “lock-in” the assemblies, allowing them to be applied widely. However, this novel strategy for constructing nanoporous superstructures is just emerging, and more effort should be focused on exploring the varied structures and functions.

5.3. Fabrication of Composite Nanostructures

Toroids can be employed as templates for fabricating functional composite nanostructures.[150–152,156–158] To achieve this goal, the surface or corona of the toroidal assemblies is required to possess some groups/sites to selectively associate with func-tional components. Generally, corona chemistry and DNA ori-gami techniques are applied to offer groups/sites for forming advanced composite nanostructures.

As discussed in Sections 2 and 3, core-shell toroids can be obtained by the self-assembly of various copolymers, and a copolymer composed of a PVP block is representative among them. The formed toroids have a hydrophobic core and a hydro-philic corona containing the PVP block. Due to the compl-exation ability of the PVP block, the toroids can offer versatile templates for the fabrication of composite nanostructures. For instance, Chang et al. and Qiu et al. respectively reported that toroidal micelles composed of P2VP coronas can be used as a template to grow AuNPs on toroid surfaces, resulting in the for-mation of organic-inorganic hybrid toroids.[49,56]

Additionally, hollow composite toroids can be obtained after the removal of the polymer core. For example, Yang et al. reported that the core-shell toroidal templates of P4VP-b-PS-b-P4VP block copolymers allow the formation of a series of composite nanotoroids by associating with inorganic nano-particles.[150] The obtained toroids contain PS cores and com-posite shells composed of P4VP blocks and functional inor-ganic components. After the PS cores are removed, hollow composite toroids are derived (Figure 19a). Figure 19b shows that hollow ZnO/PVP composite toroids are produced after



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removal of the template. Similarly, SiO2/PVP composite toroids can also be obtained by associating various components and removing the PS core. Hollow toroids have shown the ability to encapsulate large guest molecules in the intratoroidal nano-space. For example, Kim et al. reported that the rim interiors of hollow toroids can efficiently encapsulate fullerenes and fer-rocene derivatives.[153] The composite toroids exhibit distinct photoelectric properties arising from the encapsulated inor-ganic nanoparticles. It is anticipated that an increasing number of functions of the composite toroids can be developed. For instance, apart from chemical and biological applications, com-posite toroids can exhibit intriguing magnetic properties.[154,155]

In addition to corona chemistry, the DNA origami tech-nique has recently been applied to introduce functional sites for forming advanced organic-inorganic hybrid nanostructures owing to its outstanding designability and manipulability. For instance, Liu et al. demonstrated that hybrid nanotoroids are fabricated through an ordered combination of AuNPs on the surface of the toroids formed by DNA origami.[158] The arrange-ment of AuNPs on the origami toroid surfaces can be varied by manipulating preprogrammed binding sites. As shown in Figure 19c,d, toroids with an inner diameter of 120 nm are obtained. The AuNPs on the toroid surfaces arrange in a left-handed or right-handed fashion. Interestingly, the circular dichroism spectra revealed that the left-handed hybrid nano-toroids exhibit characteristic peak-to-dip line shapes in the vis-ible spectral range, whereas their right-handed counterparts display corresponding mirrored spectra. This result can permit them to be applied in photoelectric and magnetic fields. It has been reported that the incorporation of AuNPs into a polymeric domain can modify the refractive index of composite struc-tures, resulting in modulation of the optical properties. The for-mation of a percolating network structure of AuNPs can further enhance the electrical properties of the composite material.[159] Nanotoroids with AuNPs arranged on surfaces are expected to exhibit intriguing photoelectric properties, and increasing efforts may be focused on their applications.

As discussed above, toroidal assemblies have numerous intriguing functions. However, research on toroid functionali-zation is still not comprehensive. One of the major obstacles is that it is difficult to precisely and efficiently tune the toroid size. Investigations on the regulation of toroid size are worth pursuing due to the fundamental interest of the structure and the benefit for the development of toroid functions. The theo-retical prediction of the properties of polymers and the formed nanostructures is an important developing direction in the field of theoretical simulation.[160] These simulation methods can be extended to predict the functional performance of toroidal assemblies. It can help to understand the structure-property relationship of toroidal structures and reveal the contribution of the toroidal geometry to their unique properties.

6. Challenges and Directions of Development

Recent research progress on the formation and function of toroidal assemblies has been reviewed. A variety of distinctive routes were explored to obtain toroids. The knowledge gained from toroid formation can help understand many biological

processes, such as toroidal condensation of DNA. Additionally, toroids have shown unique functions assigned to their shape, which fascinates science and technology on account of their potential applications. Due to the research values, increasing efforts have been devoted to the studies of toroidal assemblies. However, investigations on toroidal assemblies are insufficient, and some issues still need to be addressed.

6.1. Diversity of Toroidal Nanostructures

Despite increasing developments in toroidal nanostruc-tures, the concept of toroids is still limited in individual ring-shaped morphology. Recently, the exploration of noncircular toroids (i.e., polygonal toroids) and interlocked toroids has emerged.[161–166] For example, Li et al. reported that polygonal micelles with shapes resembling quadrilaterals and triangles were observed from an ABC triblock copolymer containing an insoluble liquid crystalline block.[161,162] Qiu et al. reported the formation of rectangular platelet micelles based on an approach that involves seeded growth of crystallizable polymer blends of block copolymers and homopolymers. The platelet micelles can subsequently disassemble into rectangular toroids.[163] The core-forming liquid crystalline or crystalline block usually pre-fers to adopt an ordered arrangement in the assemblies, facili-tating the formation of polygonal toroids. Studies on these polygonal toroids can enrich the morphology of assemblies and help deepen our understanding of the formation mechanism of toroids. Very recently, it has been reported that the fabrica-tion of interlocked toroids has been achieved.[164–166] Liu et al. found that DNA origami toroids hierarchically self-assembled into interlocked structures containing two, three, or four toroids through an AuNP-templated approach.[165] These exotic nanostructures promote further study of the toroid formation mechanism. Additionally, they empower broad applications in nanorobotics and nanomachines, which greatly encourage researchers to devote more effort to studying them. It can be anticipated that the development of novel toroidal nanostruc-tures could be a frontier in the domain.

6.2. Theoretical Simulations of Toroidal Nanostructures

It is necessary to achieve a full understanding of the formation mechanism, including the kinetic process of toroid formation, to precisely control the size distribution of toroids and even fur-ther utilize the intermediate structure (e.g., curved micelles) to construct complex hierarchical nanostructures. Self-assembly is a complicated and instantaneous physicochemical process, and it is difficult to disclose the toroidal formation principles by depending exclusively on the experiments. Theoretical simu-lations provide straightforward and detailed microscopic infor-mation on the dynamic formation process, which is expected to help elucidate the mechanism. For example, He et al. reported that toroidal structures can be obtained through the perforation pathway using an SCFT method.[88] This finding reveals a for-mation mechanism of toroids and guides related experimental studies on the unique evolution pathway. The theoretical sim-ulation is supposed to address more critical issues in future



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studies. However, in the simulations, the precise correla-tion between the experimental conditions and the simulation parameters still remains challenging. The proper mapping of the experiments into simulation models is an important topic in the future.

In addition, studies on toroid formation can motivate the progress of simulation methods. The formation of toroidal assemblies takes place across a wide range of spatial scales from nanometers to microns and timescales from picoseconds to hours. For example, the self-assembly of the polymer (e.g., DNA) into toroids takes place at the molecular level and can be finished in seconds, while the morphology transformation of assemblies into toroids takes place at the nanoscale and can be extended to hours or days. Thus, developing multiscale simula-tion approaches is necessary for gaining deeper insights into the formation rules of toroidal assemblies.

6.3. Manipulatable Fabrication of Toroidal Nanostructures

The tunable size and uniformity of toroidal nanostructures are still challenging. Investigations on these structural fea-tures are beneficial for the comprehensive understanding of toroid formation and are directly associated with their perfor-mances in practical applications. Thus, it is necessary to find a feasible and effective method to prepare toroids with uniform and tunable sizes. The assembly of biopolymers such as DNA can form uniform nanotoroids through the winding route. The toroid dimension is associated with polymer flexibility and self-attraction interactions and is less reliant on the polydis-persity of winding objects.[2] Mimicking the formation route of biopolymer toroids is an important direction of development. For example, Chen et al. reported that colloidal gold nanowires or carbon nanotubes can be wound into toroids through the

Figure 18. a) AFM image and b) transmission electron microtomography images of a 3D nanoporous superstructure formed through 3D association of toroidal micelles. Reproduced with permission.[45] Copyright 2018, American Chemical Society. c) Schematic representation of the formation of 3D multi-tori mesostructures. d,e) SEM images of spherical hollow mesostructures consisting of a network of toroids. Reproduced with permission.[149] Copyright 2020, Science.



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contraction of their polymer shells.[167,168] In the two-component system, the polymer shell can reply to changes in solvent and produce a self-attraction interaction, driving the long nanowire or nanotubes to wind into toroids. The toroid size is relatively uniform and can be regulated by the rigidity of winding objects and the contraction of the polymer shells. These works shed light on the exploration of the winding route to form toroids in other systems.

Additionally, improving the yield of toroidal nanostruc-tures remains a significant challenge. To date, the formation of toroidal assemblies is usually operated in a dilute solution (<0.5 wt%). The yield is still far from sufficient for extensive uses. Polymerization-induced self-assembly (PISA) may be a feasible means to address this issue because assemblies can be produced at high concentrations (up to 30 wt%).[169] It has been reported that PISA has been employed for producing various assemblies, such as spherical micelles, worm-like micelles, and vesicles.[170] These assemblies with high concentrations can be used to produce toroids through the transformation route, improving the scalability of toroidal assemblies. It can be anticipated that the scalable production of nanotoroids via PISA could be a developing frontier in the future.

6.4. Applications of Toroidal Nanostructures

The practical application of toroidal structures is a significant research focus. To date, there have been few studies on the

properties of toroids. Nevertheless, the potential application of toroids in a variety of fields has emerged. For example, in biological fields, Bradley et al. demonstrated that toroids pos-sess selective cellular uptake in various cell lines, which has applications in cellular separations, as selective cell tags, or in site-specific liver disease therapies.[171] Additionally, it is known that the surface patterns of assemblies have a significant effect on their biological performance.[172] The construction of surface nanostructures on toroidal assemblies (e.g., helical toroids[76]) is expected to confer intriguing biorelated properties.

In the field of photoelectronics, toroidal structures assem-bled from building blocks of light-responsive groups or organic-inorganic hybrids can exhibit unique optical properties.[173,174] For example, Maji et al. found that the vesicles and toroids of metal-organic molecules show efficient funneling of excitation energy and hence may be used as a light-harvesting antenna.[173] In brief, the applications of toroids in these fields are emerging. In addition to their biological and photoelectric uses, they could have broader applications in numerous fields.

7. Conclusion

In this review, we present a summary of the recent advances in the formation of toroidal assemblies. There are three major routes of toroid formation: the self-assembly of polymers, transformation of assemblies, and disassembly of hierarchical assemblies. The corresponding formation mechanisms are

Figure 19. a) Schematic representation of template synthesis of hollow composite nanotoroids. The gray area represents the PVP corona shell, the black grid area represents the PS core, and the black solid area represents the composite shell. b) TEM image of ZnO/polymer composite toroids after removal of the template. Reproduced with permission.[150] Copyright 2007, Wiley-VCH. c,d) TEM images of the c) left-handed and d) right-handed hybrid nanotoroids. The insets are illustrations and magnified images of the corresponding assemblies. Reproduced with permission.[158] Copyright 2016, American Chemical Society.



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presented, with close attention paid to the viewpoint of theo-retical simulations. Toroidal assemblies can exhibit intriguing functions due to the unique structure of an annular shape with an internal cavity. These advances may offer guidance and motivate future studies in this area. However, there are many challenges ahead, such as the lack of controllable fabrication and diverse morphology. Additionally, despite achievements in revealing the formation mechanism of toroidal assemblies, pro-found theoretical studies on understanding the formation rules are limited. We are convinced that toroidal assemblies can be continuously developed and eventually applied in the future.

AcknowledgementsP.X. and L.G. contributed equally to this work. This work was supported by the National Natural Science Foundation of China (52073095, 51621002, 51833003, and 21975073) and the project of Shanghai municipality (20ZR1471300).

Conflict of InterestThe authors declare no conflict of interest.

Keywordshierarchical nanostructures, polymer self-assembly, theoretical simulations, toroids

Received: June 22, 2021Revised: August 3, 2021

Published online:

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Pengfei Xu received his Bachelor’s Degree from East China University of Science and Technology (ECUST) in 2014. He is currently a doctoral candidate in Materials Science and Engineering at ECUST under the supervision of Prof. Jiaping Lin, undertaking the self-assembly of polypeptide-based copolymers.



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Liang Gao received his Bachelor’s Degree (2013) and Ph.D. (2019) under the supervision of Prof. Jiaping Lin in Materials Science and Engineering from ECUST. Now, he is working as a postdoctoral researcher in ECUST. His research is focused on the theoretical simulation of polymer systems, and the hierarchical self-assembly of copolymers.

Chunhua Cai received his Ph.D. degree in 2010 under the supervision of Prof. Jiaping Lin from ECUST. Since then, he has been worked in the School of Materials Science and Technology of ECUST. He was promoted to full professor in 2019. In 2016–2017, he worked as a visiting researcher scholar at Stephen Z. D. Cheng’s group at the University of Akron in the United States. His research mainly focuses on polymer self-assembly.

Jiaping Lin received his bachelor and master degrees from Shanghai Jiao Tong University, and Ph.D. from ECUST (1993). After that, he obtained a postdoctoral fellowship from Japan Society for the Promotion of Science (JSPS), a Lise-Meitner fellowship of Fonds zur Förderung der wis-senschaftlichen Forschung (FWF), and worked as a postdoctoral researcher in the Tokyo Institute of Technology and University of Linz in Austria, respectively. He has been in ECUST ever since returning home from abroad in 1997. He became a full professor in 1999. His current research interests include copolymer self-assembly, liquid crystalline polymers, and biomaterials.

Liquan Wang received his Ph.D. degree under the supervision of Prof. Jiaping Lin in Materials Science and Engineering from ECUST in 2011. Now he is working in the School of Materials Science and Technology of ECUST. In 2016–2017, he worked as a visiting researcher scholar at California Institute of Technology. His research interest centers on the theoretical calculation and computer simulation of complex polymer systems.



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Xiaohui Tian received his bachelor’s and master’s degrees from Nanjing University in 1985 and 1988 and has been a faculty member since then. He received his Ph.D. degree from the Mendeleev University of Chemical Technology, Russia, in 1995. He has been at ECUST since 1999, and has been a full professor since 2006. His research interests are metal coordination polymers and optical properties of organic molecules.


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