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Owing to the inevitable loss in communication channels, the distance of entanglement distribution is limited to approximately 100 kilometres on the ground1. Quantum repeaters can circumvent this problem by using quantum memory and entanglement swapping2. As the elementary link of a quantum repeater, the heralded distribution of two-party entanglement between two remote nodes has only been realized with built-in-type quantum memories3-9. These schemes suffer from the trade-off between multiplexing capacity and deterministic properties and hence hinder the development of efficient quantum repeaters. Quantum repeaters based on absorptive quantum memories can overcome such limitations because they separate the quantum memories and the quantum light sources. Here we present an experimental demonstration of heralded entanglement between absorptive quantum memories. We build two nodes separated by 3.5 metres, each containing a polarization-entangled photon-pair source and a solid-state quantum memory with bandwidth up to 1 gigahertz. A joint Bell-state measurement in the middle station heralds the successful distribution of maximally entangled states between the two quantum memories with a fidelity of 80.4 ± 2.2 per cent (±1 standard deviation). The quantum nodes and channels demonstrated here can serve as an elementary link of a quantum repeater. Moreover, the wideband absorptive quantum memories used in the nodes are compatible with deterministic entanglement sources and can simultaneously support multiplexing, which paves the way for the construction of practical solid-state quantum repeaters and high-speed quantum networks.
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The electrochemical properties of vanadium-based materials as cathode materials for aqueous zinc ion batteries are still restricted by low conductivity, sluggish reaction kinetics, and poor structural stability. Herein, the [VO6] octahedron, as the basic unit of vanadium-oxide layer of ammonium vanadates (NH4V4O10, denoted as NVO), is incorporated by F atoms to regulate the coordinated environment of vanadium. Density functional theory (DFT) calculations and experimental results show that both physicochemical and electrochemical properties of NVO are improved by F-doping. The enhanced electronic conductivity accelerates the electron transfer and the expanded interlayer spacing expedites the diffusion kinetics of zinc ions. As a result, the F-doped NVO (F-NVO) electrode shows a high discharge capacity (465 mAh g-1 at 0.1 A g-1), good rate capability (260 mAh g-1 at 5 A g-1), and long-term cycling stability (88% capacity retention over 2000 cycles at 4 A g-1). The reaction kinetics and energy storage mechanism of F-NVO are further validated by in situ and ex situ characterizations.
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Conspectusπ-Conjugated polymers have gained significant interest because of their potential applications in optoelectronics, bioelectronics, and other domains. The controlled synthesis of π-conjugated block polymers optimizes their performance and enables novel properties and functions. However, precise control of the self-assembled architectures of π-conjugated polymers remains a formidable challenge. Inspired by the precise helical architectures of biomacromolecules, the helical polymers and the supramolecular helical assemblies have gained significant attention. Helical polymers with an excess of one-handed helicity can be optically active with a strong tendency toward self-assembly. Incorporating a helical polymer into a π-conjugated polymer can induce asymmetric helical assemblies, leading to novel chiral materials with unique functionalities.To control the self-assembly of architectures, π-conjugated polymers are usually synthesized into block copolymers by incorporating a polymer with self-assembling characteristics. Although various π-conjugated block copolymers have been produced, precise and asymmetric self-assembly is still challenging and has rarely been addressed. Incorporating helical polymers into the π-conjugated polymers can induce a precise and asymmetric self-assembly, which transfers the chirality of the helical polymer block to the π-conjugated polymer, resulting in chiral supramolecular architectures with unique chiroptical properties and functionalities. However, synthesizing hybrid block copolymers containing two distinct polymer blocks is complicated. Some general strategies such as connecting the chain ends of two preformed homopolymers and extending the chain of a prefabricated π-conjugated polymer with a second monomer are time-consuming and require complex synthetic protocols. Therefore, developing novel strategies for the facile synthesis of π-conjugated block copolymers with a predictable molar mass, low dispersity, and tunable composition is of practical importance.Recently, we investigated a controlled synthesis of helical polyisocyanides, helical polyallenes, and helical polycarbenes by developing advanced Pd(II) and Ni(II) catalysts. These helical polymers were successfully incorporated into π-conjugated polymers, including polythiophene, polyfluorene, and poly(phenyleneethynylene), via a one-pot sequential living block polymerization of the two distinct monomers using Pd(II)- or Ni(II)-complexes as catalysts. As a result, a variety of well-defined π-conjugated block copolymers containing helical polymeric blocks were readily synthesized. Although the copolymerized monomers possess different structures and polymerization mechanisms, the one-pot block copolymerization followed a living polymerization mechanism and provided the desired π-conjugated block copolymers in high yields with controlled molar mass, narrow size distribution, and tunable composition.Remarkably, the helical polymeric block induces the π-conjugated block copolymer asymmetric self-assembly into a supramolecular, one-handed helical architecture resulting in distinct optical properties. More interestingly, by utilizing the crystallization of conjugated blocks and one-handed helical blocks, the crystallization-driven and helix-induced precise asymmetric living self-assembly yielded a family of uniform and single-handed helical architectures with controlled dimensions, narrow distribution, and well-defined helicity. The transfer of helical chirality to the supramolecular architectures rendered the achiral π-conjugated blocks with unique chiroptical properties such as the emission of white light over a broad optical spectrum and the circularly polarized luminescence.
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Polyallenes with appropriate pendants can form stable helices and exhibit significant optical activity. These helical polyallenes contain reactive double bonds that allow for further functionalization, making them a class of chiral functional materials with broad application prospects. This review article delves into the intricacies of synthesizing well-defined helical polyallenes through controlled synthetic methodologies, including helix-sense selective living polymerization, regioselective and asymmetric living polymerization, and one-pot block copolymerization of allenes with aryl monomers. The systemically outlined characteristics of the resulting helical polyallenes and related copolymers are summarized include their unique chiroptical properties, stimuli-responsiveness, helix-induced chiral self-assembly, and circularly polarized luminescence (CPL). Additionally, current challenges and future perspectives in the research of controlled synthesis, functionalities, and applications of helical polyallenes are discussed in detail.
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The practical application of aqueous zinc-ion batteries (ZIBs) indeed faces challenges primarily attributed to the inherent side reactions and dendrite growth associated with the Zn anode. In the present work, N-Methylmethanesulfonamide (NMS) is introduced to optimize the transfer, desolvation, and reduction of Zn2+, achieving highly stable and reversible Zn plating/stripping. The NMS molecule can substitute one H2O molecule in the solvation structure of hydrated Zn2+ and be preferentially chemisorbed on the Zn surface to protect Zn anode against corrosion and hydrogen evolution reaction (HER), thereby suppressing byproducts formation. Additionally, a robust N-rich organic and inorganic (ZnS and ZnCO3) hybrid solid electrolyte interphase is in situ generated on Zn anode due to the decomposition of NMS, resulting in enhanced Zn2+ transport kinetics and uniform Zn2+ deposition. Consequently, aqueous cells with the NMS achieve a long lifespan of 2300â h at 1â mA cm-2 and 1â mAh cm-2, high cumulative plated capacity of 3.25â Ah cm-2, and excellent reversibility with an average coulombic efficiency (CE) of 99.7 % over 800 cycles.
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Porous frameworks with controlled pore structure and tunable aperture are greatly demanded. However, precise synthesis of this kind of materials is a formidable challenge. Herein, we report the fabrication of two-dimensional (2D) supramolecular polymer frameworks using a precisely synthesized rod-like helical polyisocyanide as link. Four three-arm star-shaped polyisocyanides with the degree of the polymerization of 10, 20, 30 and 40, and having 2-ureido-4[1H]-pyrimidinone (UPy) terminals were synthesized. 2D-Crystalline polymer frameworks with apertures of 5.3, 10.1, 13.9, and 19.1â nm were respectively obtained through intermolecular hydrogen bonding interaction between the terminal Upy units. The pore aperture is dependent on the length of polyisocyanide backbone. Thus, well-defined supramolecular polymer frameworks with controlled and uniform hexagonal pores were obtained, as proved by small-angle X-ray scattering (synchrotron radiation facility), atomic force microscopy, and Brunauer-Emmett-Teller analyses. The frameworks with uniform large pore aperture were used to purify nanomaterials and immobilize biomacromolecules. For instance, the membranes of the polymer frameworks could size-fractionation of silver nanoparticles into uniform nanoparticles with very low dispersity. The frameworks with large aperture facilitated the inclusion of myoglobin and enhanced the stability and catalytic activity.
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The development of chiral alignment media for measuring anisotropic NMR parameters provides an opportunity to determine the absolute configuration of chiral molecules without the need for derivatization. However, chiral alignment media with a high and robust enantiodiscriminating property for a wide range of chiral molecules are still scarce. In this study, we synthesized cholesterol-end-functionalized helical polyisocyanides from a chiral monomer using a cholesterol-based alkyne-Pd(II) initiator. These stereoregular polyisocyanides form stable and weak anisotropic lyotropic liquid crystals (LLCs) in dichloromethane systems, exhibiting highly optical activities in both single left- and right-handed helices. The preparation process of the media was straightforward, and the aligning property of the LLCs could be controlled by adjusting the concentration and temperature. Using the chiral polyisocyanides, we extracted the residual dipolar coupling for an enantiomeric pair of isopinocampheol (IPC), as well as a number of pharmaceutical molecules, demonstrating excellent enantiodiscriminating properties for a broad range of chiral compounds.
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Designing superb dielectric capacitors is valuable but challenging since achieving simultaneously large energy-storage (ES) density and high efficiency is difficult. Herein, the synergistic effect of grain refining, bandgap widening, and domain engineering is proposed to boost comprehensive ES properties by incorporating CaTiO3 into 0.92NaNbO3 -0.08BiNi0.67 Ta0.33 O3 matrix (as abbreviated NN-BNT-xCT). Apart from grain refining and bandgap widening, multiple local distortions embedded in labyrinthine submicro-domains, as indicated by diffraction-freckle splitting and ½-type superlattices, produce slush-like polar clusters for the NN-BNT-0.2CT ceramic, which should be ascribed to the coexisting P4bm, P21 ma, and Pnma2 phases. Consequently, a high recoverable ES density Wrec of ≈ 7.1 J cm-3 and a high efficiency η of ≈ 90% at 646 kV cm-1 is achieved for the NN-BNT-0.2CT ceramic. Such hierarchically polar structure is favorable to superb comprehensive ES properties, which provide a strategy for developing high-performance dielectric capacitors.
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Vanadyl phosphate (VOPO4 ·2H2 O) has been regarded as one of the most promising cathode materials for aqueous Zn-ion batteries due to its distinct layered structure. However, VOPO4 ·2H2 O has not yet demonstrated the exceptional Zn ion storage performance owing to the structural deterioration during repeated charging/discharging process and poor intrinsic conductivity. In this work, 2D sodium vanadyl phosphate (NaVOPO4 ·0.83H2 O, denoted as NaVOP) is designed as a cathode material for Zn-ion batteries, in which sodium ions are preinserted into the interlayer, replacing part of water. Benefiting from the in situ surface oxidization, improved electronic conductivity, and increased hydrophobicity, the NaVOP electrode exhibits a high discharge capacity of 187 mAh g-1 at 0.1 A g-1 after activation, excellent rate capability and enhanced cycling performance with 85% capacity retention after 1500 cycles at 1 A g-1 . The energy storage mechanism of the NaVOP nanoflakes based on the rapid Zn2+ and H+ intercalation pseudocapacitance are investigated via multiple ex situ characterizations.
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Recently, cyclic polymers have attracted increasing interest due to their unique topologies, properties, and functions compared to the linear analogues. This mini-review focuses on the recent advances in the synthesis and applications of cyclic polymers. First, the main synthetic methods for cyclic polymers, namely ring closure and ring expansion methods, are presented and discussed, followed by a review on the exploration of the properties and applications of synthetic cyclic polymers. Finally, a critical assessment of the preliminary studies exploring the efficient synthesis and potential applications of cyclic polymers are presented, and the remaining challenges in the field as well as ideas for solving these challenges will be discussed.
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In this work, π-conjugated block copolymers consisting of poly(phenyl isocyanide) (PPI) and polyfluorene (PF) segments are facilely prepared by one-pot sequential polymerization of phenyl isocyanide (monomer 1) and 7-bromo-9,9-dioctylfluorene-2-boronic acid pinacol ester (monomer 2). The Pd(II)-terminated PPI is first prepared via polymerizing monomer 1 catalyzed with phenyl alkyne-Pd(II) complex and then utilized to initiate the controlled Suzuki cross-coupling polymerization of monomer 2, yielding various PPI-b-PF copolymers possessing controlled molar mass and narrow dispersity. Owing to the helical conformation of PPI segment and π-conjugated structure of PF segment, PPI-b-PF copolymers present distinctive optical property and fascinating chiral self-assembly behavior. During the self-assembly process, chirality transfer from helical PPI block to the supramolecular aggregates of helical nanofibers occurs to afford optically active helical nanofibers with high optical activity. Furthermore, the self-assembled helical nanofibers exhibit excellent circularly polarized luminescence performance.
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Cianetos , Luminescência , Cianetos/química , Polímeros/química , Conformação Molecular , PolimerizaçãoRESUMO
A pair of enantiomeric photoswitchable PdII catalysts, alkyne-PdII /LR-azo and alkyne-PdII /LS-azo , were prepared via the coordination of alkyne-PdII and azobenzene-modified phosphine ligands LR-azo and LS-azo . Owing to the cis-trans photoisomerization of the azobenzene moiety, alkyne-PdII /LR-azo and alkyne-PdII /LS-azo exhibited different polymerization activities, helix-sense selectivities, and enantioselectivities during the polymerization of isocyanide monomers under irradiation of different wavelength lights. Furthermore, the achiral isocyanide monomer A-1 could be polymerized efficiently using alkyne-PdII /LR-azo under dark condition in a living/controlled manner. Further, it generated single right-handed helical poly-A-1m (LR-azo ), confirmed by the circular dichroism spectra and atomic force microscopy images. However, the polymerization of A-1 almost could not be initiated under 420â nm light in identical conditions of dark condition. Moreover, the photoswitchable catalyst alkyne-PdII /LR-azo exhibited high enantioselectivity for the polymerization of the racemates of L-1 and D-1, respectively. D-1 was polymerized preferentially under dark condition with a D-1/L-1 rate ratio of 70, yielding single right-handed polyisocyanides. Additionally, reversible enantioselectivity was observed under 420â nm light using alkyne-PdII /LR-azo , and the calculated polymerization rate ratio of L-1/D-1 was 57 because of the isomerization of the azobenzene moiety of the catalyst. Furthermore, alkyne-PdII /LS-azo showed opposite enantioselectivity and helix-sense selectivity during the polymerization of the racemates of L-1 and D-1.
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Inspired by biological helices (e.g., DNA), artificial helical polymers have attracted intense attention. However, precise synthesis of one-handed helices from achiral materials remains a formidable challenge. Herein, a series of achiral poly(biphenyl allene)s with controlled molar mass and low dispersity were prepared and induced into one-handed helices using chiral amines and alcohols. The induced one-handed helix was simultaneously memorized, even after the chiral inducer was removed. The switchable induction processes were visible to naked eye; the achiral polymers exhibited blue emission (irradiated at 365â nm), whereas the induced one-handed helices exhibited cyan emission with clear circularly polarized luminescence. The induced helices formed stable gels in various solvents with helicity discrimination ability: the same-handed helix gels were self-healing, whereas the gels of opposite-handed helicity were self-sorted. Moreover, the induced helices could separate enantiomers via enantioselective crystallization with high efficiency and switchable enantioselectivity.
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Developing high performance and environment-friendly fluoropolymers is greatly desired. In this work, we found that 2-diazo-1,1,1-trifluoroethane can be polymerized by air-stable alkyne-palladium(II) catalysts following a living polymerization mechanism, affording a fluoropolymer, poly(trifluoromethyl methylene) in high yield with controlled molar mass and low dispersity. This polymer bears trifluoromethyl on every main chain atom and thus has good resistance to chemical corrosion, high hydrophobicity, and excellent dielectric constant with low dielectric loss. Due to the steric hindrance between the trifluoromethyl pendants, the synthetic poly(trifluoromethyl methylene) can twist into a stable helix. The one-handed preferred helices synthesized using chiral PdII -catalysts exhibit high optical activity and circularly polarized luminescence. Remarkably, such polymer can be completely degraded to (E)-1,1,1,4,4,4-hexafluorobut-2-ene at high temperatures (>280 °C). Additionally, taking advantage of the living chain end, the polymer can be further modified.
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Inspired by the perfect helical structures and the resulting exquisite functions of biomacromolecules, helical polymers have attracted increasing attention in recent years. Polyisocyanide is well known for its distinctive rodlike helical structure and various applications in chiral recognition, enantiomer separation, circularly polarized luminescence, liquid crystallization, and other fields. Although various methods and catalysts for isocyanide polymerization have been reported, the precise synthesis of helical polyisocyanides with controlled molecular weight, low dispersity, and high tacticity remains a formidable challenge. Owing to a limited synthesis strategy, the controlled synthesis of topological polyisocyanides has barely been realized. This Accounts highlights our recent endeavors to explore novel catalysts for the living polymerization of isocyanides. Fortunately, we discovered that alkyne-Pd(II) catalysts could initiate the living polymerization of isocyanides, resulting in helical polyisocyanides with controlled structures, high tacticity, and tunable compositions. These catalysts are applicable to various isocyanide monomers, including alkyl isocyanides, aryl isocyanides, and diisocyanobenzene derivatives. Incorporating chiral bidentate phosphine ligands onto alkyne-Pd(II) complexes formed chiral Pd(II) catalysts, which promoted the asymmetric living polymerization of achiral isocyanide, yielding single left- and right-handed helices with highly optical activities.Using alkyne-Pd(II) catalysts, various topological polyisocyanides have been facilely prepared, including hybrid block copolymers, bottlebrush polymers, core cross-linked star polymers, and organic/inorganic nanoparticles. For instance, various hybrid block polyisocyanides were easily produced by coupling alkyne-Pd(II)-catalyzed living isocyanide polymerization with controlled radical polymerization and ring-opening polymerization (ROP). Combining the ring-opening metathesis polymerization (ROMP) of norbornene with Pd(II)-catalyzed isocyanide polymerization, bottlebrush polyisocyanides and core cross-linked star polymers were easily prepared. Pd(II)-catalyzed living polymerization of poly(lactic acid)s with isocyanide termini resulted in densely grafted bottlebrush polyisocyanides with closely packed side chains. Moreover, the surface-initiated living polymerization of isocyanides produced a family of polyisocyanide-grafted organic/inorganic hybrid nanoparticles using nanoparticles with alkyne-Pd(II) catalysts anchored on the surfaces. Surprisingly, the nanoparticles and star polymers with helical polyisocyanide arms performed exceptionally well in terms of chiral recognition and resolution. Incorporated organocatalysts such as proline and prolinol units onto the pendants of optically active helical polyisocyanides, a family of polymer-based chiral organocatalysts, were generated, which showed significantly improved stereoselectivity for the asymmetric Aldol reaction and Michael addition and can be easily recycled.Using a chiral alkyne-Pd(II) catalyst, single-handed helical polyisocyanides bearing naphthalene and pyrene probes were produced from achiral isocyanide monomers. These polymers showed excellent self-sorting properties as revealed using a fluorescence resonance energy transfer (FRET) investigation and were self-assembled into two-dimensional (2D) smectic nanostructures driven by both helicity and chain length. Incorporating helical poly(phenyl isocyanide) (PPI) onto semiconducting poly(3-hexylthiophene) (P3HT) induced the asymmetric assembly of the resulting P3HT-b-PPI copolymers into single-handed cylindrical micelles with controlled dimensions and tunable photoluminescence.
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Quantum memories at telecom wavelengths are crucial for the construction of large-scale quantum networks based on existing fiber networks. On-demand storage of telecom photonic qubits is an essential request for such networking applications but yet to be demonstrated. Here we demonstrate the storage and on-demand retrieval of telecom photonic qubits using a laser-written waveguide fabricated in an ^{167}Er^{3+}:Y_{2}SiO_{5} crystal. Both ends of the waveguide memory are directly connected with fiber arrays with a fiber-to-fiber efficiency of 51%. Storage fidelity of 98.3(1)% can be obtained for time-bin qubits encoded with single-photon-level coherent pulses, which is far beyond the maximal fidelity that can be achieved with a classical measure and prepared strategy. This device features high reliability and easy scalability, and it can be directly integrated into fiber networks, which could play an essential role in fiber-based quantum networks.
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Photonic polarization qubits are widely used in quantum computation and quantum communication due to the robustness in transmission and the easy qubit manipulation. An integrated quantum memory for polarization qubits is a useful building block for large-scale integrated quantum networks. However, on-demand storing polarization qubits in an integrated quantum memory is a long-standing challenge due to the anisotropic absorption of solids and the polarization-dependent features of microstructures. Here we demonstrate a reliable on-demand quantum memory for polarization qubits, using a depressed-cladding waveguide fabricated in a ^{151}Eu^{3+}:Y_{2}SiO_{5} crystal. The site-2 ^{151}Eu^{3+} ions in Y_{2}SiO_{5} crystal provides a near-uniform absorption for arbitrary polarization states and a new pump sequence is developed to prepare a wideband and enhanced absorption profile. A fidelity of 99.4±0.6% is obtained for the qubit storage process with an input of 0.32 photons per pulse, together with a storage bandwidth of 10 MHz. This reliable integrated quantum memory for polarization qubits reveals the potential for use in the construction of integrated quantum networks.
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The measurement of anisotropic residual dipolar couplings (RDCs) parameters for the structure elucidation of organic molecules relies on suitable alignment media. Employment of self-assembled liquid crystalline systems to create anisotropic alignment can be an effective way to realize aligned samples and acquire RDCs. This Mini-review highlights the recent advances on amino acid-based helical polymers and supramolecular oligomers forming rigid, rod-like structures that aggregate into ordered liquid crystalline phases, including amino acid-based helical polyisocyanides, polyacetylenes, polypeptides, and oligopeptides assembled alignment media. The methodology for the determination of anisotropic liquid crystals is briefly discussed, and a summary of recent research progress in the enantiodifferentiation of helical polymers aligned media is followed. In addition, the self-assembled mechanism of oligopeptides and their RDCs structural analysis are also described.
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Cristais Líquidos , Aminoácidos , Cristais Líquidos/química , Espectroscopia de Ressonância Magnética/métodos , Oligopeptídeos , PolímerosRESUMO
End-functionalization is an effective strategy for constructing functional materials. A method for chain-end functionalization of helical polycarbenes is herein developed that relied on Sonogashira coupling reaction. In this work, a family of helical polycarbenes with controlled molecular mass (Mn ) and low polydispersity (Mw /Mn ) is readily prepared using Pd(II) and the Wei-Phos ligand as initiator. The Pd(II) complex is confirmed to remain at the chain end of polycarbene. Subsequently, a series of terminal alkyne derivatives with interesting functional groups, including the F atom, aldehyde, or anthracene groups, are synthesized. They could be installed at the chain end of polycarbene through Sonogashira coupling reaction catalyzed by the Pd(II) complex at the chain end. Moreover, a couple of hybrid block copolymers are easily obtained by installing terminal alkynes modified by another type of polymer. The structures of the isolated polymers are confirmed by 1 H nuclear magnetic resonance (1 H NMR), 19 F nuclear magnetic resonance (19 F NMR), 31 P nuclear magnetic resonance (31 P NMR), and Fourier transform infrared spectroscopy (FT-IR), respectively. The self-assembly properties of the hybrid block copolymers are also investigated by atomic force spectroscopy analysis. By the hereby developed method, various functional groups can be introduced at the chain end of helical polycarbenes for constructing functional polymer materials, moreover, the transition metal residues at the end of polymer chains can be easily removed.
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Alcinos , Polímeros , Ligantes , Espectroscopia de Ressonância Magnética , Espectroscopia de Infravermelho com Transformada de FourierRESUMO
Helical polymers present some interesting and distinctive properties, and one of the most distinguished applications of them is the chiral recognition and resolution of enantiomers. In this work, star-shaped hybrid helical poly (phenyl isocyanide) (PPI) with polyhedral oligomeric silsesquioxanes (POSS) as the core was designed and synthesized by "grafting to" strategy. The homoarm star-shaped hybrid POSS-(PPI)8 was first obtained by the click reaction between azide-modified POSS (POSS-(N3 )8 ) and alkynyl-modified PPI (PPI-Alkynyl). The hybrid POSS-(PPI)8 was with predominated left-handed helical conformation and exhibited excellent ability in the enantioselective crystallization of racemic compounds. In the meantime, heteroarm star-shaped hybrid (PEG)4 -POSS-(PPI)4 was prepared by the click reaction of POSS-(N3 )8 with PPI-Alkynyl and alkynyl-modified poly (ethylene glycol) (PEG-Alkynyl). The hybrid (PEG)4 -POSS-(PPI)4 was amphiphilic, and it could self-assemble to form spherical micelles in aqueous solutions.