Direct visualization of bottlebrush polymer conformations in the solid state.

Although the behavior of single chains is integral to the foundation of polymer science, a clear and convincing image of single chains in the solid state has still not been captured. For bottlebrush polymers, understanding their conformation in bulk materials is especially important because their extended backbones may explain their self-assembly and mechanical properties that have been attractive for many applications. Here, single-bottlebrush chains are visualized using single-molecule localization microscopy to study their conformations in a polymer melt composed of linear polymers. By observing bottlebrush polymers with different side chain lengths and grafting densities, we observe the relationship between molecular architecture and conformation. We show that bottlebrushes are significantly more rigid in the solid state than previously measured in solution, and the scaling relationships between persistence length and side chain length deviate from those predicted by theory and simulation. We discuss these discrepancies using mechanisms inspired by polymer-grafted nanoparticles, a conceptually similar system. Our work provides a platform for visualizing single-polymer chains in an environment made up entirely of other polymers, which could answer a number of open questions in polymer science.

Geometry-Directed Self-Assembly of Polymeric Molecular Frameworks.

Despite the significant advances in creating assembled structures from polymers, engineering the assembly of polymeric materials into framework structures remains an outstanding challenge. In this work, we present a facile strategy to construct polymeric molecular frameworks through the assembly of T-shape polymer-rod-sphere amphiphiles in the bulk state. Various frameworks are yielded as a result of delicate interplays among three components of the T-shape amphiphiles. The internal structure of frameworks was revealed by combining experimental investigations and computational simulations. The frameworks display good solution-processability, thermal stability, and uniform pore-forming capability, which endow the resultant frameworks with great potential in scalable fabrications.

Discovery of Structural Complexity through Self-Assembly of Molecules Containing Rodlike Components.

Hierarchical structures are important for transferring and amplifying molecular functions to macroscopic properties of materials. In this regard, rodlike molecules have emerged as one of the most promising molecular building blocks to construct functional materials. Although the self-assembly of conventional molecules containing rodlike components generally results in nematic or layered smectic phases, due to the preferred parallel arrangements of rodlike components, extensive efforts have revealed that rational molecular design provides a versatile platform to engineer rich self-assembled structures. Herein, first successes achieved in polyphilic liquid crystals and rod-coil block systems are summarized. Special attention is paid to recent progress in the conjugation of rodlike building blocks with other molecular building blocks through the molecular Lego approach. Rod-based giant surfactants, sphere-rod conjugates, and dendritic rodlike molecules are covered. Future perspectives of the self-assembly of molecules containing rodlike components are also provided.

Pattern Synthesis of Linear Antenna Array Using Improved Differential Evolution Algorithm with SPS Framework.

In this paper, an improved differential evolution (DE) algorithm with the successful-parent-selecting (SPS) framework, named SPS-JADE, is applied to the pattern synthesis of linear antenna arrays. Here, the pattern synthesis of the linear antenna arrays is viewed as an optimization problem with excitation amplitudes being the optimization variables and attaining sidelobe suppression and null depth being the optimization objectives. For this optimization problem, an improved DE algorithm named JADE is introduced, and the SPS framework is used to solve the stagnation problem of the DE algorithm, which further improves the DE algorithm's performance. Finally, the combined SPS-JADE algorithm is verified in simulation experiments of the pattern synthesis of an antenna array, and the results are compared with those obtained by other state-of-the-art random optimization algorithms. The results demonstrate that the proposed SPS-JADE algorithm is superior to other algorithms in the pattern synthesis performance with a lower sidelobe level and a more satisfactory null depth under the constraint of beamwidth requirement.

Spherical Supramolecular Structures Constructed via Chemically Symmetric Perylene Bisimides: Beyond Columnar Assembly.

Like other discotic molecules, self-assembled supramolecular structures of perylene bisimides (PBIs) are commonly limited to columnar or lamellar structures due to their distinct π-conjugated scaffolds and unique rectangular shape of perylene cores. The discovery of PBIs with supramolecular structures beyond layers and columns may expand the scope of PBI-based materials. A series of unconventional spherical packing phases in PBIs, including A15 phase, σ phase, dodecagonal quasicrystalline (DQC) phase, and body-centered cubic (BCC) phase, is reported. A strategy involving functionalization of perylene core with several polyhedral oligomeric silsesquioxane (POSS) cages achieved spherical assemblies of PBIs, instead of columnar assemblies, due to the significantly increased steric hindrance at the periphery. This strategy may also be employed for the discovery of unconventional spherical assemblies in other related discotic molecules by the introduction of similar bulky functional groups at their periphery. An unusual inverse phase transition sequence from a BCC phase to a σ phase was observed by increasing annealing temperature.

Magnifying the Structural Components of Biomembranes: A Prototype for the Study of the Self-Assembly of Giant Lipids.

How biomembranes are self-organized to perform their functions remains a pivotal issue in biological and chemical science. Understanding the self-assembly principles of lipid-like molecules hence becomes crucial. Herein, we report the mesostructural evolution of amphiphilic sphere-rod conjugates (giant lipids), and study the roles of geometric parameters (head-tail ratio and cross-sectional area) during this course. As a prototype system, giant lipids resemble natural lipidic molecules by capturing their essential features. The self-assembly behavior of two categories of giant lipids (I-shape and T-shape, a total of 8 molecules) is demonstrated. A rich variety of mesostructures is constructed in solution state and their molecular packing models are rationally understood. Giant lipids recast the phase behavior of natural lipids to a certain degree and the abundant self-assembled morphologies reveal distinct physiochemical behaviors when geometric parameters deviate from natural analogues.

Breaking Parallel Orientation of Rods via a Dendritic Architecture toward Diverse Supramolecular Structures.

Self-assembled nanostructures of rod-like molecules are commonly limited to nematic or layered smectic structures dominated by the parallel arrangement of the rod-like components. Distinct self-assembly behavior of four categories of dendritic rods constructed by placing a tri(hydroxy) group at the apex of dendritic oligo-fluorenes is observed. Designed hydrogen bonding and dendritic architecture break the parallel arrangement of the rods, resulting in molecules with specific (fan-like or cone-like) shapes. While the fan-shaped molecules tend to form hexagonal packing cylindrical phases, the cone-shaped molecules could form spherical motifs to pack into various ordered structures, including the Frank-Kasper A15 phase and dodecagonal quasicrystal. This study provides a model system to engineer diverse supramolecular structures by rod-like molecules and sheds new light into the mechanisms of the formation of unconventional spherical packing structures in soft matter.

Topologically Directed Assemblies of Semiconducting Sphere-Rod Conjugates.

Spontaneous organizations of designed elements with explicit shape and symmetry are essential for developing useful structures and materials. We report the topologically directed assemblies of four categories (a total of 24) of sphere-rod conjugates, composed of a sphere-like fullerene (C60) derivative and a rod-like oligofluorene(s) (OF), both of which are promising organic semiconductor materials. Although the packing of either spheres or rods has been well-studied, conjugates having both shapes substantially enrich resultant assembled structures. Mandated by their shapes and topologies, directed assemblies of these conjugates result not only in diverse unconventional semiconducting supramolecular lattices with controlled domain sizes but also in tunable charge transport properties of the resulting structures. These results demonstrate the importance of persistent molecular topology on hierarchically assembled structures and their final properties.

Efficacy of epidural steroid injection in the treatment of sciatica secondary to lumbar disc herniation: a systematic review and meta-analysis.

Epidural steroid injection for the treatment of sciatica caused by disc herniation is increasingly used worldwide, but its effectiveness remains controversial. The review aiming to analyze the efficacy of epidural steroid injection on sciatica caused by lumbar disc herniation. Randomized controlled trials (RCTs) investigating the use of epidural steroid injections in the management of sciatica induced by lumbar disc herniation were collected from PubMed and other databases from January, 2008 to December, 2023, with epidural steroid injection in the test group and epidural local anesthetic and/or placebo in the control group. Pain relief rate, assessed by numerical rating scale (NRS) and visual analogue scale (VAS) scores, and function recovery, evaluated by Roland Morris Disability Questionnaire (RMDQ) and Oswestry Disability Index (ODI) scores, were recorded and compared. Meta-analysis was performed by Review Manager. In comparison to the control group, epidural steroid injections have been shown to be effective for providing short- (within 3 months) [MD = 0.44, 95%CI (0.20, 0.68), p = 0.0003] and medium-term (within 6 months) [MD = 0.66, 95%CI (0.09,1.22), p = 0.02] pain relief for sciatica caused by lumbar disc herniation, while its long-term pain-relief effect were limited. However, the administration of epidural steroid injections did not lead to a significant improvement on sciatic nerve function in short- [MD = 0.79, 95%CI = (0.39, 1.98), p = 0.19] and long-term [MD = 0.47, 95% CI = (-0.86, 1.80), p = 0.49] assessed by IOD. Furthermore, the analysis revealed that administering epidural steroid injections resulted in a reduction in opioid usage among patients with lumbar disc herniation [MD = -14.45, 95% CI = (-24.61, -4.29), p = 0.005]. The incidence of epidural steroid injection was low. Epidural steroid injection has demonstrated notable efficacy in relieving sciatica caused by lumbar disc herniation in short to medium-term. Therefore, it is recommended as a viable treatment option for individuals suffering from sciatica.

Sequence-Isomerism-Controlled Macromolecular Self-Assembly in Dendritic Rod-Like Molecules.

Although in Nature sequence control is widely adopted to tune the structure and functions of biomacromolecules, it remains challenging and largely unexplored in synthetic macromolecular systems due to the difficulties in a precision synthesis, which impedes the understanding of the structure-property relationship in macromolecular sequence isomerism. Herein, we report the sequence-controlled macromolecular self-assembly enabled by a pair of rationally designed isomeric dendritic rod-like molecules. With an identical chemical formula and molecular topology, the molecular solid angle of the dendron isomers was determined by the sequence of the rod building blocks tethered with side chains of different lengths. As a result, entirely different supramolecular motifs of discs and spheres were generated, which were further packed into a hexagonally packed cylinder phase and a dodecagonal quasicrystalline sphere phase, respectively. Given the efficient synthesis and modular structural variations, it is believed that the sequence-isomerism-controlled self-assembly in dendritic rod-like molecules might provide a unique avenue toward rich nanostructures in synthetic macromolecules.

Self-Assembly of Poly(Janus particle)s into Unimolecular and Oligomeric Spherical Micelles.

Using shape-persistent Janus particles to construct poly(Janus particle)s and studying their self-assembly behaviors are of great interest, but remain largely unexplored. In this work, we reported a type of amphiphiles constructed by the ring-opening metathesis polymerization of nonspherical molecular Janus particles (APOSS-BPOSS), called poly(Janus particle)s (poly(APOSS-BPOSS)n, n = 12, 17, 22, and 35, and Mn = 35-100 kg/mol). Unlike traditional bottlebrush polymers consisting of flexible side chains, these poly(Janus particles) consist of rigid hydrophilic and hydrophobic polyhedral oligomeric silsesquioxane (POSS) cages as side chains. Interestingly, instead of maintaining an expected extended chain conformation, they could also collapse and then self-assemble to form unconventional unimolecular or oligomeric spherical micelles in solutions with a feature size smaller than 7 nm. More importantly, unlike traditional amphiphilic polymer brushes that could form unimolecular micelles at a relatively high degree of polymerization by self-assembly, these poly(Janus particles)s could accomplish self-assembly at a quite low degree of polymerization because of their unique chemical structure and molecular topology. The formation of unimolecular and oligomeric micelles was also further confirmed by dissipative particle dynamics simulations. This study of introducing the POSS-based poly(Janus particle)s as a class of shape amphiphiles will provide a model system for generating unimolecular and oligomeric micellar nanostructures through solution self-assembly.

Crowding-Induced Unconventional Phase Behaviors in Dendritic Rodlike Molecules via Side-Chain Engineering.

Dendritic molecules with a fanlike or conelike conformation are common molecular building blocks to construct supramolecular columnar or spherical phases. Although it is well-accepted that the preferred molecular conformation of dendritic molecules dictates their packing schemes, manipulation of this crucial parameter usually requires significant changes in molecular structures and tedious synthetic efforts. Herein, we report a simple yet highly efficient strategy to tune the molecular conformation of dendritic rodlike molecules by adjusting the length of alkyl side chains tethered to the rods. Strikingly, tiny chemical structure differences can largely change the "crowding" near the branching point to induce the "fanlike to conelike" conformational transitions and thus result in the formation of diverse supramolecular structures, including the columnar phase, double gyroid phase, and the unconventional Frank-Kasper σ and A15 phases. Our study provides a practical platform for further investigation of unconventional structure formation and phase transitions in soft matter.

Screw dislocation-induced pyramidal crystallization of dendron-like macromolecules featuring asymmetric geometry.

We report herein that dendron-shaped macromolecules AB n crystallize into well-ordered pyramid-like structures from mixed solvents, instead of spherical motifs with curved structures, as found in the bulk. The design of the asymmetric molecular architecture and the choice of mixed solvents are applied as strategies to manipulate the crystallization process. In mixed solvents, the solvent selection for the Janus macromolecule and the existence of dominant crystalline clusters contribute to the formation of flat nanosheets. Whereas during solvent evaporation, the bulkiness of the asymmetric macromolecules easily creates defects within 2D nanosheets which lead to their spiral growth through screw dislocation. The size of the nanosheets and the growth into 2D nanosheets or 3D pyramidal structures can be regulated by the solvent ratio and solvent compositions. Moreover, macromolecules of higher asymmetry generate polycrystals of lower orderliness, probably due to higher localized stress.

Supramolecular Self-Assembly of Perylene Bisimide-Based Rigid Giant Tetrahedra.

Recently, ordered structures constructed from rigid three-dimensional (3D) shaped polyhedra have been drawing general interest, with the tetrahedron being the simplest one but showing complicated assembly behaviors. Rigid tetrahedron building blocks have been shown to form quasicrystalline and crystalline phases with high packing fractions by both simulation and experiments. Nevertheless, the study of 3D tetrahedral building blocks is limited, especially in the field of supramolecular self-assembly. Here, we present an experimental study of rigid giant tetrahedral molecules constructed by attaching four bulky polyhedral oligomeric silsesquioxane (POSS) cages to a tetrahedral perylene bisimide (PBI) scaffold. Self-assembly of these giant tetrahedra is mediated by π-π interaction between the tetrahedral PBI-based scaffolds and their overall tetrahedral symmetry. A monolithic nearly centimeter-sized hexagonal supramolecular structure was observed in the giant tetrahedron with short flexible linkers between PBI and POSS cages, while a micrometer-sized crystalline helical structure formed in that with completely rigid aromatic linkers. Their significant difference in electrical conductivity could be explained by two completely different packing models of the giant tetrahedra.

Continuous Curvature Change into Controllable and Responsive Onion-like Vesicles by Rigid Sphere-Rod Amphiphiles.

We observe the formation of highly controllable and responsive onion-like vesicles by using rigid sphere-rod amphiphilic hybrid macromolecules, composed of charged, hydrophilic Keggin-type clusters (spheres) and hydrophobic rod-like oligofluorenes (OFs). Unlike the commonly used approach, which mainly relies on chain bending of flexible molecules to satisfy different curvatures in onion-like vesicles, the rigid hybrids form flexible interdigitations by tuning the angles between OFs, leading to the formation of bilayers with different sizes. The self-assembled vesicles possess complete onion-like structures from most inner to outer layers, and their size (layer number) can be accurately manipulated by different solution conditions including solvent polarity, ionic strength, temperature, and hybrid concentration, with fixed interbilayer distance under all conditions. Moreover, the vesicle size (layer number) shows excellent reversibility to the change of temperature. The charged feature of spheres, rod length, and overall hybrid architecture shows significant effects on the formation of such onion-like vesicles.

Transition Kinetics of Self-Assembled Supramolecular Dodecagonal Quasicrystal and Frank-Kasper σ Phases in ABn Dendron-Like Giant Molecules.

A series of noncrystalline ABn dendron-like giant molecules DPOSS-MPOSSn (n = 2-6, DPOSS: hydrophilic polyhedral oligomeric silsesquioxane (POSS) cage; MPOSS: hydrophobic POSS cage) were synthesized. These samples present a thermodynamically stable phase formation sequence from the hexagonal cylinder phase (plane group of P6mm), to the Frank-Kasper (F-K) A15 phase (space group of Pm3̅n), and further to the F-K σ phase (space group of P42/mnm), with increasing the number of MPOSS in a single molecule (n, from 2 to 6). Moreover, for DPOSS-MPOSS5 and DPOSS-MPOSS6, an intriguing dodecagonal quasicrystal (DQC) structure has been identified and revealed as a kinetic favorable metastable phase at lower temperatures, while the thermodynamically stable phase is the σ phase. The detailed investigation of the transition kinetics between the DQC and σ phase in these samples makes it possible to identify how the self-assembly directs the phase transition in terms of molecular and supramolecular aspects.

Identification of a Frank-Kasper Z phase from shape amphiphile self-assembly.

Frank-Kasper phases, a family of ordered structures formed from particles with spherical motifs, are found in a host of materials, such as metal alloys, inorganic colloids and various types of soft matter. All the experimentally observed Frank-Kasper phases can be constructed from the basic units of three fundamental structures called the A15, C15 and Z phases. The Z phase, typically observed in metal alloys, is associated with a relatively large volume ratio between its constituents, and this constraint inhibits its formation in most self-assembled single-component soft-matter systems. We have assembled a series of nanosized shape amphiphiles that comprise a triphenylene core and six polyhedral oligomeric silsesquioxane cages grafted onto it through linkers to give a variety of unconventional structures, which include the Z phase. This structure was obtained through fine tuning of the linker lengths between the core and the peripheral polyhedral oligomeric silsesquioxane cages, and exhibits a relatively large volume asymmetry between its constituent polyhedral particle motifs.

Hierarchical Self-Organization of AB n Dendron-like Molecules into a Supramolecular Lattice Sequence.

To understand the hierarchical self-organization behaviors of soft materials as well as their dependence on molecular geometry, a series of AB n dendron-like molecules based on polyhedral oligomeric silsesquioxane (POSS) nanoparticles were designed and synthesized. The apex of these molecules is a hydrophilic POSS cage with 14 hydroxyl groups (denoted DPOSS). At its periphery, there are different numbers (n = 1-8) of hydrophobic POSS cages with seven isobutyl groups (denoted BPOSS), connected to the apical DPOSS via flexible dendron type linker(s). By varying the BPOSS number from one to seven, a supramolecular lattice formation sequence ranging from lamella (DPOSS-BPOSS), double gyroid (space group of Ia3̅d, DPOSS-BPOSS2), hexagonal cylinder (plane group of P6mm, DPOSS-BPOSS3), Frank-Kasper A15 (space group of Pm3̅n, DPOSS-BPOSS4, DPOSS-BPOSS5, and DPOSS-BPOSS6), to Frank-Kasper sigma (space group of P42/mnm, DPOSS-BPOSS7) phases can be observed. The nanostructure formations in this series of AB n dendron-like molecules are mainly directed by the molecular geometric shapes. Furthermore, within each spherical motif, the spherical core consists hydrophilic DPOSS cages with flexible linkages, while the hydrophobic BPOSS cages form the relative rigid shell, and contact with neighbors to provide decreased interfaces among the spherical motifs for constructing final polyhedral motifs in these Frank-Kasper lattices. This study provides the design principle of molecules with specific geometric shapes and functional groups to achieve anticipated structures and macroscopic properties.