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At least 1,549 records · Page 86

Self-Assembled Bolaamphiphile-Based Organic Nanotubes as Efficient Cu(II) Ion Adsorbents

Self-assembled organic nanotubes (ONTs) have been actively examined for various applications such as chemical separations and catalysis owing to their well-defined tubular nanostructures with distinct chemical environments at the wall and internal/external surfaces. Adsorption of heavy metal ions onto ONTs plays an essential role in many of these applications, but it has rarely been assessed quantitatively. Herein, we investigated interactions between Cu 2+ and single-/quadruple-wall bolaamphiphile-based ONTs having inner carboxyl groups with different inner diameters, COOH-ONT 10nm and COOH-ONT 20nm . We first examined the effects of Cu 2+ on their nanotubular structures using SAXS, STEM, and AFM. COOH-ONT 10nm was stable in aqueous Cu 2+ solution in contrast to COOH-ONT 20nm owing to the presence of polyglycine-II-type hydrogen bonding networks within its wall. Subsequently, we studied the Cu 2+ adsorption behavior of COOH-ONT 10nm by monitoring the concentration of unbound Cu 2+ using linear sweep anodic stripping voltammetry. The Cu 2+ adsorption was quick, attributable to efficient Cu 2+ partitioning through the open ends of the ONT, followed by fast Cu 2+ diffusion in the uniform, relatively large nanochannel. More importantly, the Cu 2+ adsorption capacity and affinity of COOH-ONT 10nm were measured at different pH using the Langmuir adsorption model. The adsorption capacity was similar at the pH range examined, showing the participation of approximately 25% of the inner carboxyl groups in the adsorption. The adsorption affinity increased with pH, indicating the essential role of the deprotonated carboxyl groups in the Cu 2+ adsorption. Most interestingly, the Langmuir adsorption constant was significantly higher than those of previously reported synthetic adsorbents and planar monolayer based on carboxyl binding sites. The high Cu 2+ affinity of the ONT was attributable to the highly dense binding sites on the well-defined nanoscale concave structure of the inner channel. Furthermore, these results provide a valuable guideline to designing self-assembled nanomaterials for efficient chemical separations, detection, and catalysis.

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Efficient Electrosteric Assembly of Nanoparticle Heterodimers and Linear Heteroassemblies

Bottom-up approaches to the synthesis of nanostructures are of particular interest because they offer several advantages over the traditional top-down approaches. In this work, we present a new method to self-assemble nanoparticles into controlled heteroaggregates. The technique relies on carefully balancing attractive electrostatic forces with repulsive steric hindrance that is provided by surface-grafted polyethylene glycol (PEG). Two different-sized gold nanoparticles (GNPs) were used as a model system: 13 nm GNPs were functionalized with PEG-thiol and mercapto dodecanoic acid, while 7 nm GNPs were functionalized with PEG-thiol and (11- Mercaptoundecyl)trimethylammonium bromide. When mixed together, these oppositely charged particles self-assemble into stable colloidal structures (i.e., nanoclusters) whose structure depends strongly on the surface concentration of PEG. Smaller structures are obtained as the PEG surface concentration increases because steric hindrance dominates and prevents uncontrolled aggregation. In particular, under the right conditions, we were able to selectively synthesize heterodimers (which are effectively Janus particles) and linear heteroassemblies. In conclusion, this method is scalable, and it provides a step forward in bottom-up synthesis of nanomaterials.

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Self-Assembled Thermoresponsive Molecular Brushes as Nanoreactors for Asymmetric Aldol Addition in Water

The manipulation and tunability of self-assembled block copolymers through external stimuli presents an attractive strategy to develop smart polymer-based nanoreactors as supports for non-orthogonal tandem catalysis. We report on thermoresponsive core-shell micelles based on poly[norbornene-poly(2-methyl-2-oxazoline-block-2-propyl-2-oxazoline)]-graft-poly[norbornene L-proline] (P[NB-P(MeOx-b-PropOx)]-graft-P[NB-L-proline]) as catalyst supports for L-proline. These molecular brushes exhibit large differences in lower critical solution temperature behavior and nanostructure size in water depending on the chain-lengths and proline connectivity. L-Proline-mediated aldol reactions expose the efficiency by which the molecular brushes self-assemble into micelles. Molecular brushes with an extended backbone show higher activity and selectivity, suggesting better core-shell segregation of the micelles and exclusion of water from the catalytic site. Catalytic efficiencies are not improved above the cloud point temperature, the catalytic be-havior is rather sensitive to conformational changes of the polymer chains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-Assembled Vesicles from Mixed Brush Nanoparticles in Solution

The self-assembly of binary polymer-grafted nanoparticles (NPs) in a selective solvent is investigated using coarse-grained simulations. Simulations are performed using theoretically informed Langevin dynamics (TILD), a particle-based method that employs a particle-to-mesh scheme to efficiently calculate the nonbonded interactions. Here, the particles are densely grafted with two immiscible polymers, A and B, that are permanently bound to the NP either at random grafting sites (random-grafted) or with all the A chains on one hemisphere of the NP and all the B chains on the other hemisphere (Janus-grafted). For NPs with random grafting, the polymers phase-separate on the surface of the NP to form Janus-type structures in dilute solution, even though some of the chains have to stretch around the particle to form the Janus structure. When the solvent quality is sufficiently poor for the solvophobic chains, the binary grafted NPs assemble into various structures, including double-walled vesicles. In particular, vesicles are formed when the solvophilic volume fraction is between 0.2 and 0.3, in a similar range to that required for vesicle formation in diblock copolymers in a selective solvent. For mixed-grafted NPs, there is considerable variation in the structure of each individual NP, but nevertheless, these NPs form ordered vesicles, similar to those formed by Janus-grafted NPs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-Assembly and Post-Fabrication Functionalization of Microphase Separated Thin Films of a Reactive Azlactone-Containing Block Copolymer

We report on the thin film self-assembly and post-fabrication functionalization of cylinder-forming poly(styrene-block-2-vinyl-4,4-dimethylazlactone) (PS-b-PVDMA) block copolymers (BCPs). Thermal annealing of an asymmetric BCP composition, to drive microphase separation in thin films, results in high defect densities and poor long-range order. Using FTIR spectroscopy and ellipsometry, we demonstrate that thermal annealing results in reactions between the azlactone groups and the underlying substrate leading to BCP “pinning”. Further, we demonstrate that solvent annealing circumvents these issues and drives high fidelity microphase separation of the BCP in thin films. The solvent annealing approach also enables control over domain orientation; we show that parallel and perpendicularly oriented cylinders with diameters of 11.7 ± 1.2 nm and a center-to-center distance of 25.2 ± 2.6 nm can be obtained using a BCP with M n = 29.5 kDa and f S = 0.75. The PVDMA segments in these self-assembled thin films remain available for reaction with primary amine-functionalized nucleophiles. X-ray photoelectron spectroscopy (XPS) depth-profiling reveals that reactions between azlactone groups and incoming amines occur primarily in the top few nanometers of the reactive domains. Finally, we demonstrate that the azlactone groups in both parallel and perpendicularly oriented cylindrical thin films can selectively incorporate trimethylaluminum vapor, which can be subsequently converted into Al 2 O 3 nanowires and nanodots with dimensions of 16 and 12 nm, respectively.

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Versatile Synthesis of Amine-Reactive Microgels by Self-Assembly of Azlactone-Containing Block Copolymers

Relations between molecular design, chemical functionality, and stimulus-triggered response are important for a variety of applications of polymeric systems. In this paper, reactive amphiphilic block copolymers (BCPs) of poly(2-vinylpyridine)-block-poly(2-vinyl-4,4-dimethylazlactone) (PVP-b-PVDMA) were synthesized and assembled into microgels capable of incorporating functional amines. The composition of the PVP-b-PVDMA BCPs was varied to control the number of reactive sites in the spherical aggregates created by self-assembly of PVP-b-PVDMA BCPs in a 2-propanol/THF (v:v = 19:1) solvent mixture, which is selective for PVP. PVDMA and PVP segments were selectively cross-linked by 1,4-diaminobutane (DAB) or 1,4-diiodobutane (DIB) to fabricate core- and corona-cross-linked azlactone-containing microgels, respectively. Non-cross-linked aggregates of PVP-b-PVDMA and DIB-cross-linked microgels dissociate when exposed to THF, which is a good solvent for both blocks. However, the DAB-cross-linked BCP microgels swell in THF, suggesting the formation of a stable, three-dimensional network structure. Finally, because of their ability to be reactively modified in ways that allows their stability or disassembly characteristics to be tailored, these azlactone-containing BCP microgels provide an attractive platform for applications in a wide range of fields, including catalysis, imaging, molecule separation, and guest loading for targeted delivery.

36 MATERIALS SCIENCE↗

Defect Annihilation in the Directed Self-Assembly of Block Copolymers in Films with Increasing Thickness.

We investigate directed self-assembly (DSA), with 3x density multiplication, of symmetric polystyrene-block-poly(methyl methacrylate) (L-0 = 28 nm) with increasing film thicknesses and reveal a thickness limit above which the defect annihilation mechanism is different than in thinner films. Block copolymer films of increasing thickness underwent DSA on a macroscopic chemical pattern under optimum geometrical and chemical conditions. Scanning electron microscopy and grazing-incidence small-angle X-ray scattering (GISAXS) were used to characterize the long-range ordering and buried structures as a function of film thickness and thermal annealing time. Rotational GISAXS measurements revealed a critical thickness of similar to 3L(0,) below which defect annihilation is cooperative across the film depth and above which it is faster at the free surface than in the film's interior. In the latter case, defects can persist in the film's interior despite perfect assembly and registration at the free surface of the film.

Chen, Xuanxuan↗

Design and Characterization of Hybrid Multilayer Structures: Layer-by-Layer Growth of Polymer and Graphene Oxide Assemblies and Their Utility in Fuel Cell Applications

We report the layer-by-layer growth of poly- (ethylenimine) (PEI) that has been modified with sulfamate functionalities (S-PEI) using Zr 4+ -complexation interlayer linking chemistry. We have also deposited adlayers of graphene oxide (GO) that have been modified to possess sulfate functionalities (SGO), onto the S-PEI layers. The multilayer assemblies are formed with sulfamate/sulfate and sulfate/sulfate (S-PEI + S-GO) interlayer linking chemistry. In all cases the adlayer thickness is consistent with predictions based on van der Waals volume and/or molecular mechanics calculations. X-ray photoelectron spectroscopy (XPS) is used to characterize the Zr/S stoichiometry in the multilayer assembly. The utility of these hybrid multilayer structures is demonstrated in a Proton Exchange Membrane (PEM) fuel cell, where they are shown to reduce H 2 gas crossover by 15% with only a 12 nm thick layer.

fuel cell↗

Patternable Mesoporous Thin Film Quantum Materials via Block Copolymer Self-Assembly: An Emergent Technology?

Recent developments in quantum materials hold promise for revolutionizing energy and information technologies. The use of soft matter self-assembly, for example, by employing block copolymers (BCPs) as structure directing or templating agents, offers facile pathways toward quantum metamaterials with highly tunable mesostructures via scalable solution processing. Here, we report the preparation of patternable mesoporous niobium carbonitride-type thin film superconductors through spin-coating of a hybrid solution containing an amphiphilic BCP swollen by niobia sol precursors and subsequent thermal processing in combination with photolithography. Spin-coated as-made BCP-niobia hybrid thin films on silicon substrates after optional photolithographic definition are heated in air to produce a porous oxide, and subsequently converted in a multistep process to carbonitrides via treatment with high temperatures in reactive gases including ammonia. Grazing incidence small-angle X-ray scattering suggests the presence of ordered mesostructures in as-made BCP-niobia films without further annealing, consistent with a distorted alternating gyroid morphology that is retained upon thermal treatments. Wide-angle X-ray scattering confirms the synthesis of phase-pure niobium carbonitride nanocrystals with rock-salt lattices within the mesoscale networks. Electrical transport measurements of unpatterned thin films show initial exponential rise in resistivity characteristic of thermal activation in granular systems down to 12.8 K, at which point resistivity drops to zero into a superconducting state. Magnetoresistance measurements determine the superconducting upper critical field to be over 16 T, demonstrating material quality on par with niobium carbonitrides obtained from traditional solid-state synthesis methods. Here. we discuss how such cost-effective and scalable solution-based quantum materials fabrication approaches may be integrated into existing microelectronics processing, promising the emergence of a technology with tremendous academic and industrial potential by combining the capabilities of soft matter self-assembly with quantum materials.

36 MATERIALS SCIENCE↗

Biocompatible Nanocoatings of Fluorinated Polyphosphazenes through Aqueous Assembly

Nonionic fluorinated polyphosphazenes, such as poly[bis(trifluoroethoxy)phosphazene] (PTFEP), display superb biocompatibility, yet their deposition to surfaces has been limited to solution casting from organic solvents or thermal molding. Here in this paper, hydrophobic coatings of fluorinated polyphosphazenes are demonstrated through controlled deposition of ionic fluorinated polyphosphazenes (iFPs) from aqueous solutions using the layer-by-layer (LbL) technique. Specifically, the assemblies included poly[(carboxylatophenoxy)(trifluoroethoxy)phosphazenes] with varied content of fluorine atoms as iFPs (or poly[bis(carboxyphenoxy)phosphazene] (PCPP) as a control nonfluorinated polyphosphazene) and a variety of polycations. Hydrophobic interactions largely contributed to the formation of LbL films of iFPs with polycations, leading to linear growth and extremely low water uptake. Hydrophobicity-enhanced ionic pairing within iFP/BPEI assemblies gave rise to large-amplitude oscillations in surface wettability as a function of capping layer, which were the largest for the most fluorinated iFP, while control PCPP/polycation systems remained hydrophilic regardless of the film top layer. Neutron reflectometry (NR) studies indicated superior layering and persistence of such layering in salt solution for iFP/BPEI films as compared to control PCPP/polycation systems. Hydrophobicity of iFP-capped LbL coatings could be further enhanced by using a highly porous polyester surgical felt rather than planar substrates for film deposition. Importantly, iFP/polycation coatings displayed biocompatibility which was similar to or superior to that of solution-cast coatings of a clinically validated material (PTFEP), as demonstrated by the hemolysis of the whole blood and protein adsorption studies.

36 MATERIALS SCIENCE↗

Enhanced Hybridization and Nanopatterning via Heated Liquid-Phase Infiltration into Self-Assembled Block Copolymer Thin Films

Organic–inorganic hybrids featuring tunable material properties can be readily generated by applying vapor- or liquid-phase infiltration (VPI or LPI) of inorganic materials into organic templates, with resulting properties controlled by type and quantity of infiltrated inorganics. While LPI offers more diverse choices of infiltratable elements, it tends to yield smaller infiltration amount than VPI, but the attempt to address the issue has been rarely reported. Here in this paper, we demonstrate a facile temperature-enhanced LPI method to control and drastically increase the quantity and kinetics of Pt infiltration into self-assembled polystyrene-block-poly(2-vinylpyridine) block copolymer (BCP) thin films. By applying LPI at mildly elevated temperatures (40–80 °C), we showcase controllable optical functionality of hybrid BCP films along with conductive three-dimensional (3D) inorganic nanostructures. Structural analysis reveals enhanced metal loading into the BCP matrix at higher LPI temperatures, suggesting multiple metal ion infiltration per monomer of P2VP. Combining temperature-enhanced LPI with hierarchical multilayer BCP self-assembly, we generate BCP-metal hybrid optical coatings featuring tunable antireflective properties as well as scalable conductive 3D Pt nanomesh structures. Enhanced material infiltration and control by temperature-enhanced LPI not only enables tunability of organic–inorganic hybrid nanostructures and properties but also expands the application of BCPs for generating uniquely functional inorganic nanostructures.

36 MATERIALS SCIENCE↗

Self-Assembled Magnetic Nanoparticle Layers: Structural Control for Reconfigurable Magnetism and Functional Applications

We advance soft X-ray vector ptychographic tomography to map the 3D magnetization field in self-assembled superparamagnetic nanoparticles at a liquid–liquid interface, revealing how layered structures influence magnetic ordering. We observe that monolayers with low coordination numbers exhibit weak magnetic order, with magnetic vortices disrupting spin alignment. In contrast, bilayers and trilayers with higher coordination numbers display long-range magnetic order with strong spin correlations across larger distances and a suppression of magnetic vortices. We further quantify the average distance for vortex–antivortex pairs as 26.0 ± 2.0 nm, while vortex–vortex and antivortex–antivortex pairs exhibit larger separations, averaging 44.9 ± 5.2 and 54.1 ± 7.4 nm, respectively. These experimental results are supported by micromagnetic Monte Carlo simulations. Our findings illustrate how layered structures enhance magnetic order and spin correlation in superparamagnetic nanoparticle assemblies, providing a promising approach for tuning magnetic properties in applications such as data storage, microrobotics, and biomedicine.

Lu, Xingyuan↗

Variable-Temperature Scattering and Spectroscopy Characterizations for Temperature-Dependent Solution Assembly of PffBT4T-Based Conjugated Polymers

The solution structure of conjugated polymers (CPs) from which the films are cast is critical for tailoring the thin-film morphology thus device performance. Here, we used multimodal variable-temperature scattering and spectroscopy tools to fully quantify the solution assembly of poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,3'''-dialkyl-2,2';5',2'';5'',2'''-quaterthiophen-5,5'''-diyl)] (PffBT4T) polymers with varying side-chain lengths at different assembly temperatures. The conformational and aggregation behaviors for PffBT4T-based CPs were found to be very sensitive to both temperature and side chain length using ultraviolet–visible (UV–vis) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, dynamic light scattering (DLS), and small-angle neutron scattering (SANS). We found that with slightly increasing side chain length from 2-octyldodecyl (C8C12) to 2-nonyltridecyl (C9C13), PffBT4T-based CPs show a significant decrease in aggregation-to-dissolved chain transition temperature (10 °C), degree of aggregation, enthalpy change of aggregation, and size of the aggregates in solution. At room temperature, PffBT4T polymer strongly aggregated to form fabric structure with the film thickness of a few nanometers in thickness and hundreds of nanometers in length, as probed by atomic force microscopy (AFM), transmission electronic microscopy (TEM), and dynamic light scattering (DLS). At the elevated temperature above the aggregation-to-dissolved chain transition temperature, PffBT4T is fully dissolved and adopts a semiflexible coil conformation with the persistence length of 3.1 nm for PffBT4T-C8C12 and a slightly increased persistence length of 3.4 nm for PffBT4T-C9C13, according to temperature-dependent SANS measurements. Longer side chains of PffBT4T-C9C13 also lead to less aggregation enthalpy gain compared with PffBT4T-C8C12. This work provides a solution structure manipulating strategy of CPs and thus will inspire the molecular design and processing protocols of CPs toward higher performance electronic devices.

36 MATERIALS SCIENCE↗

Chiral Recognition of Lipid Bilayer Membranes by Supramolecular Assemblies of Peptide Amphiphiles

On the basis of the exclusive existence of homochirality in biomolecules and the well-known phenomenon of chiral recognition, it is obvious that chirality is a crucial factor in biological events. We report here that supramolecular assemblies of peptide amphiphiles interact with lipid bilayer membranes in a stereospecific manner. When negatively charged chiral phospholipid bilayer vesicles were subjected to the assemblies, we found that peptide amphiphiles with l-amino acids show stronger affinity for the liposomes compared to the ones with d-amino acids. To examine their biological functions, we tested the cytotoxicity of nanofibers against mammalian primary cells using human bone marrow mesenchymal stem cells and murine astroglial cells. In this work, we demonstrated that cell viability increased when d-amino acids were incorporated in the structure of peptide amphiphiles, which is consistent with our finding of their weaker interactions with lipid bilayer membranes.

36 MATERIALS SCIENCE↗

Light-Driven Water Splitting by a Covalently Linked Ruthenium-Based Chromophore–Catalyst Assembly

The preparation and characterization of new Ru(II) polypyridyl-based chromophore–catalyst assemblies, [(4,4'-PO 3 H 2 -bpy) 2 Ru(4-Mebpy-4'-epic)Ru(bda)(pic)] 2+ (1, bpy = 2,2'-bipyridine; 4-Mebpy-4'-epic = 4-(4-methylbipyridin-4'-yl-ethyl)-pyridine; bda = 2,2'-bipyridine-6,6'-dicarboxylate; pic = 4-picoline), and [(bpy) 2 Ru(4-Mebpy-4'-epic)Ru(bda)(pic)] 2+ (1') are described, as is the application of 1 in a dye-sensitized photoelectrosynthesis cell (DSPEC) for solar water splitting. Furthermore, on SnO 2 /TiO 2 core–shell electrodes in a DSPEC configuration with a Pt cathode, the chromophore–catalyst assembly undergoes light-driven water oxidation at pH 5.7 in a 0.1 M acetate buffer, 0.5 M in NaClO 4 . We observed photocurrents of ~0.85 mA cm –2 , with illumination by a 100 mW cm –2 white light source, after 30 s under a 0.1 V vs Ag/AgCl applied bias with a faradaic efficiency for O 2 production of 74% measured over a 5 min illumination period.

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Conformational Dynamics of AcrA Govern Multidrug Efflux Pump Assembly

Multidrug efflux pumps of pathogenic, Gram-negative bacteria comprise an innate resistance mechanism and are key contributors to the emerging global pandemic of antibiotic resistance. Several increasingly detailed cryo-electron microscopy maps have been resolved of an entire efflux pump complex, AcrAB–TolC, resulting in atomistic structural models. Using a recent model, we have carried out nearly 40 μs of molecular dynamics simulations to study one of the key components of the protein complex AcrA, the membrane fusion protein that connects the inner-membrane-bound AcrB to the outer-membrane-bound TolC. Here, we determined a three-dimensional potential of mean force (PMF) for AcrA, which displays two main conformational basins representing assembly competent and incompetent states. Corresponding experiments show that stabilizing mutations at an interdomain interface shift the dynamic equilibrium between these states to the incompetent one, disrupting pump assembly and function and resensitizing bacteria to existing antibiotics. The modulation of AcrA dynamics through pharmacological intervention therefore presents a promising route for the development of new antibiotics.

59 BASIC BIOLOGICAL SCIENCES↗

Lanthanide Separations through Helicate Self-Assembly

Skyrocketing demand for rare-earth elements makes their isolation and reuse from electronic waste an increasingly attractive alternative to mining. Typically, the capture of individual lanthanides from mixtures requires the iterative design of complex, macrocyclic ligands, a sometimes successful but often laborious process. Here we show that the self-assembly of rare-earth ions with a ditopic ligand, L d , results in the selective incorporation of smaller lanthanides and gives rise to impressive separation factors. Comparison to a monotopic ligand, L m , shows that the separation performance of ditopic L d critically depends on the presence of two adjacent binding sites. Isothermal titration calorimetry (ITC) experiments show that the selectivity of L d for smaller ions is thermodynamically driven and provide evidence of positive cooperativity among the two binding sites of L d . The simplicity of the separation procedure reported here, requiring only 1 min of sonication in methanol, shows the potential applicability of this approach to real-world separations. Here, by achieving efficient rare-earth separations in small, synthetically facile helicates, this work shows the promise of self-assembly as a mechanism to drive metal separations.

Alcohols↗

Dictating Nanoparticle Assembly via Systems-Level Control of Molecular Multivalency

Nanoparticle assembly can be controlled by multivalent binding interactions between surface ligands, indicating that more precise control over these interactions is important to design complex nanoscale architectures. It has been well-established in natural materials that the arrangement of different molecular species in three dimensions can affect the ability of individual supramolecular units to coordinate their binding, thereby regulating the strength and specificity of their collective molecular interactions. However, in artificial systems, limited examples exist that quantitatively demonstrate how changes in nanoscale geometry can be used to rationally modulate the thermodynamics of individual molecular binding interactions. As a result, the use of nanoscale design features to regulate molecular bonding remains an underutilized design handle to control nanomaterials synthesis. Here in this paper we demonstrate a polymer-coated nanoparticle material where supramolecular bonding and nanoscale structure are used in conjunction to dictate the thermodynamics of their multivalent interactions, resulting in emergent bundling of supramolecular binding groups that would not be expected on the basis of the molecular structures alone. Additionally, we show that these emergent phenomena can controllably alter the superlattice symmetry by using the mesoscale particle arrangement to alter the thermodynamics of the supramolecular bonding behavior. The ability to rationally program molecular multivalency via a systems-level approach therefore provides a major step forward in the assembly of complex artificial structures, with implications for future designs of both nanoparticle- and supramolecular-based materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗