Flexible Linkage Research Articles

Flexible Model Predictive Control for Bounded Gait Generation in Humanoid Robots.

With advancements in bipedal locomotion for humanoid robots, a critical challenge lies in generating gaits that are bounded to ensure stable operation in complex environments. Traditional Model Predictive Control (MPC) methods based on Linear Inverted Pendulum (LIP) or Cart-Table (C-T) methods are straightforward and linear but inadequate for robots with flexible joints and linkages. To overcome this limitation, we propose a Flexible MPC (FMPC) framework that incorporates joint dynamics modeling and emphasizes bounded gait control to enable humanoid robots to achieve stable motion in various conditions. The FMPC is based on an enhanced flexible C-T model as the motion model, featuring an elastic layer and an auxiliary second center of mass (CoM) to simulate joint systems. The flexible C-T model's inversion derivation allows it to be effectively transformed into the predictive equation for the FMPC, therefore enriching its flexible dynamic behavior representation. We further use the Zero Moment Point (ZMP) velocity as a control variable and integrate multiple constraints that emphasize CoM constraint, embed explicit bounded constraint, and integrate ZMP constraint, therefore enabling the control of model flexibility and enhancement of stability. Since all the above constraints are shown to be linear in the control variables, a quadratic programming (QP) problem is established that guarantees that the CoM trajectory is bounded. Lastly, simulations validate the effectiveness of the proposed method, emphasizing its capacity to generate bounded CoM/ZMP trajectories across diverse conditions, underscoring its potential to enhance gait control. In addition, the validation of the simulation of real robot motion on the robots CASBOT and Openloong, in turn, demonstrates the effectiveness and robustness of our approach.

Programmable Modular Assembly of Homochiral Ir(III)‐Metallohelices to Reverse Metallodrug Resistance by Inhibiting CDK1

AbstractDrug resistance is a major cause of cancer recurrence and poor prognosis. The innovative design and synthesis of inhibitors to target drug‐resistance‐specific proteins is highly desirable. However, challenges remain in precisely adjusting their conformation and stereochemistry to adapt the chiral regions of target proteins. Herein, using a stepwise programmable modular assembly approach, we precisely engineered two pairs of homochiral dinuclear Ir(III) metallohelices (Λ2S4‐Hbpy and Δ2R4‐Hbpy, Δ2S4‐Hbpy and Λ2R4‐Hbpy) functionalized with flexible dithiourea linkages. The resulting homochiral metallohelices exhibited significant chirality‐dependent photocytotoxicities, and the enhanced structural compatibility of Δ2S4‐Hbpy with the target cyclin‐dependent kinase 1 (CDK1) contributed to its superior photodynamic therapy efficacy, achieving an outstanding photocytotoxicity index (PI) value of 2.3×104. Interestingly, emerging as a critical mediator in the development of oxaliplatin resistance, CDK1 targeting by Δ2S4‐Hbpy achieved enhanced cellular uptake, anticancer activity, and oncosis‐mediated cell death in oxaliplatin‐resistant HCT‐8/L cells. Mechanistic investigations, including proteomic profiling and CDK1 gene silencing, confirmed the pivotal role of chirality‐selective CDK1 targeting in reversing metallodrug resistance. This study introduces a promising platform for constructing and customizing flexible metallohelices with precise conformation and stereochemistry to target drug‐resistance‐specific proteins, offering innovative insights into the designability of metallodrugs to overcome drug resistance.

Fractional order system identification using a joint multi-innovation fractional gradient descent algorithm

This paper proposes a joint multi-innovation fractional gradient descent identification algorithm for fractional order systems. First, the flexibility of fractional calculus is leveraged to design a joint fractional gradient descent algorithm capable of estimating system parameters and unknown orders. The estimated system parameters are used as the initial conditions to identify the unknown order, and the identified order is used as the update conditions for the system parameters. Through the joint iteration of two fractional order gradients, both the identified order and parameters are updated. In addition, multi-innovation theory is applied to extend the joint fractional gradient descent algorithm to a joint multi-innovation fractional gradient descent algorithm, which improves the system identification accuracy. Then, the convergence of the algorithm is theoretically analyzed. Finally, the effectiveness of the algorithm is verified through numerical simulation and an experiment on the identification of an actual flexible linkage system.

Programmable Modular Assembly of Homochiral Ir(III)-Metallohelices to Reverse Metallodrug Resistance by Inhibiting CDK1.

Drug resistance is a major cause of cancer recurrence and poor prognosis. The innovative design and synthesis of inhibitors to target drug-resistance-specific proteins is highly desirable. However, challenges remain in precisely adjusting their conformation and stereochemistry to adapt the chiral regions of target proteins. Herein, using a stepwise programmable modular assembly approach, we precisely engineered two pairs of homochiral dinuclear Ir(III) metallohelices (Λ2S4-Hbpy and Δ2R4-Hbpy, Δ2S4-Hbpy and Λ2R4-Hbpy) functionalized with flexible dithiourea linkages. The resulting homochiral metallohelices exhibited significant chirality-dependent photocytotoxicities, and the enhanced structural compatibility ofΔ2S4-Hbpywith the target cyclin-dependent kinase 1 (CDK1) contributed to its superior photodynamic therapy efficacy, achieving an outstanding photocytotoxicity index (PI) value of 2.3×104. Interestingly, emerging as a critical mediator in the development of oxaliplatin resistance, CDK1 targeting by Δ2S4-Hbpyachieved enhanced cellular uptake, anticancer activity, and oncosis-mediated cell death in oxaliplatin-resistant HCT8/L cells. Mechanistic investigations, including proteomic profiling and CDK1 gene silencing, confirmed the pivotal role of chirality-selective CDK1 targeting in reversing metallodrug resistance. This study introduces a promising platform for constructing and customizing flexible metallohelices with precise conformation and stereochemistry to target drug-resistance-specific proteins, offering innovative insights into the designability of metallodrugs to overcome drug resistance.

Modeling and Active Vibration Control of Flexible Robotic Arm and Its Application in Agricultural Water Conservancy Field

In order to improve the modeling and active vibration control effectiveness of flexible manipulators, this paper combines big data technology to study the modeling and active control of flexible manipulators. In addition, this article decouples the dynamic model of the flexible joint manipulator based on voltage control method, redefines the control input of the system as the voltage of the joint motor, and uses a nonlinear state observer to control the flexible link manipulator. The control strategy proposed in this article is based on a nonlinear state observer, combined with input-output control, to achieve tracking of joint angular displacement in a flexible linkage manipulator. Through experimental research, it can be seen that the big data based modeling and active vibration control research system for flexible robotic arms proposed in this paper can effectively improve the motion control effect of flexible robotic arms.

Bioinspired peptide sensors with tailorable structure for specific and in-situ tracking of Hg2+ biodistribution in living cells upon acute exposure

Metal-biomolecule interactions that are ubiquitous in nature provide fundamental knowledge and rich structural motifs for the development of functional molecules and smart sensors. In this work, inspired by the active sites in metalloproteins, a biomimetic peptide sensor was designed for the selective recognition and activatable sensing of Hg2+ in living biosystems. Tetraphenylethylene (TPE) with typical aggregation-induced emission (AIE) behavior, was introduced as the activatable signal transducer to enable high signal-to-background signaling. The tailorable side chains and flexible peptide linkage were exploited to tune the coordination affinity, selectivity, and fluorescence response toward Hg2+. Benefiting from the rapid response (1 min), high specificity and nanomolar sensitivity, the peptide sensor allows investigating the mechanism of acute toxicity of Hg2+. Capable of penetrating plasma membrane, the peptide sensor revealed the dosage-dependent and dynamic subcellular biodistribution behavior of Hg2+. The finding that Hg2+ preferentially accumulates and rapidly enriches in nucleoli of cells upon short exposure, evidences the adverse effect toward ribosome biogenesis and the resultant genetic deficiencies. These results highlight the peptide sensors as promising tools for not only on-site detection, but also studying the cell biology and toxicology of this metal ion in living biosystems.

Mainchain and sidechain-involving H-bonded asymmetric polyimides containing rigid amide and flexible ether linkages

Hydrogen bonds (H-bonds), usually mainchain amide H-bonds, have been well recognized to play important roles in modulating the properties of polyimides (PIs) by strengthening macromolecular interaction. While the structure-properties relationships of symmetric mainchain amide H-bonded PIs have been extensively researched, the asymmetric H-bonded PIs, particularly those containing rigid-flexible backbone structure, and sidechain-involving H-bonds, have been rarely explored. Herein, starting from designed synthesis of diamine monomers, we present two series of asymmetric PIs containing rigid amide and flexible ether linkages that form mainchain amide-amide and amide-imide H-bonds, lacking or bearing pendent trifluoromethyls (-CF3) that form sidechain-involving amide-CF3 H-bonds. The presence of these three types of H-bonds were revealed by RDF simulation and confirmed by FTIR. Mainchain H-bonded PIs (PI-Ax) show higher Tg than sidechain-involving H-bonded PIs (PI-Tx), while PI-Tx series exhibit higher optical transparency and hydrophobicity, lower dielectric constant (ε′) and better mechanical properties than PI-Ax. The general researches on the PIs’ solubility, WAXD spectra, thermal properties, fluorescence emission and optical transparency, the dihedral angles (φ), fractional free volume (FFV), theoretical gas transport properties, chain geometry optimization and HOMO-LUMO energy gap (ΔE) values have been comprehensively carried out from the aspects of both experiments and theoretical calculation.

Phytosociological Investigations on the Afroalpine Vegetation of the Ruwenzori Mountains (Uganda)

This paper presents the results of a phytosociological study on the Afroalpine vegetation of the Ruwenzori Mountains, one of the most prominent mountain ranges in Africa. This study marks the pioneering comprehensive investigation into the plant communities of this region, which holds significant phytogeographic importance. Through statistical analyses, eight distinct plant communities, three new alliances, two new orders, and one new class were identified within the altitudinal range of 3500 to 4600 m above sea level. These communities are well-defined from both floristic and ecological perspectives. Hierarchical classification was conducted using the quantitative Sørensen (Bray-Curtis) distance measure and the beta flexible linkage method. Furthermore, indicator species for each group were determined by calculating fidelity and constancy (occurrence frequency) within the classified dataset. To assess the validity of the classification results, non-metric multidimensional scaling (NMDS) was carried out. These analyses provide the first phytosociological arrangement of the Afroalpine vegetation of the Ruwenzori Mountains, providing a solid framework and valuable insights into its floristic and ecological characteristics.

Phenylethynyl-Terminated Imide Oligomer-Based Thermoset Resins.

Phenylethynyl-terminated imide (PETI) oligomers are highly valued for their diverse applications in films, moldings, adhesives, and composite material matrices. PETIs can be synthesized at varying molecular weights, enabling the fine-tuning of their properties to meet specific application requirements. Upon thermal curing, these oligomers form super-rigid network structures that enhance solvent resistance, increase glass-transition temperatures, and improve elastic moduli. Their low molecular weights and melt viscosities further facilitate processing, making them particularly suitable for composites and adhesive bonding. This review examines recent advancements in developing ultra-high-temperature PETIs, focusing on their structure-processing-properties relationships. It begins with an overview of the historical background and key physicochemical characteristics of PETIs, followed by a detailed discussion of PETIs synthesized from monomers featuring noncoplanar configurations (including kink and cardo structures), fluorinated groups, flexible linkages, and liquid crystalline mesogenic structures. The review concludes by addressing current challenges in this research field and exploring potential future directions.

Improving the pore properties of porous aromatic frameworks in two aspects via partition strategy

Microporous solids are famous for their high surface area and pore size at the molecular scale, which are crucial for the applications of adsorption, separation and catalysis. An ideal porous solid would simultaneously have a high surface area and nanopores with the desired opening size. However, due to the uncontrollable reaction process of porous organic frameworks (POFs), the acquisition of such a solid is still technically limited. Herein, we reported a simple but platform-wide pore partition strategy to improve the porosity of porous aromatic frameworks (PAFs) in two aspects. This strategy was achieved by introducing a partition unit with flexible linkage to segment the original voids of PAFs into multiple micropore domains. The obtained partitioning PAFs have 130%-217% increments in surface area due to the creation of extra accessible surfaces while the pores are segmented into smaller ones. Notably, the partitioning PAFs showed significantly increased adsorption capacity for CO2 due to their improved surface area. At the same time, the narrowed pore size allowed selective capture of dye molecules by their size differences. Similar to their parent PAFs, the partitioning PAFs retained their high stability in harsh environments. A simple and universal pore partition strategy will be an important step in improving PAF porosity to desired functions.

Linkage Regulation of Back‐To‐Back Connected Dimers as Guest Acceptors Enables Organic Solar Cells with Excellent Efficiency, Stability and Flexibility

AbstractHigh efficiency, stability, and flexibility are key prerequisites for the commercial applications of organic solar cells (OSCs). Herein, three back‐to‐back connected dimers (2Qx‐TT, 2Qx‐C3, 2Qx‐C6) are developed as the guest acceptors for OSCs with improved comprehensive performance. By regulating the linkage from rigid bithiophene to flexible alkyl chain, the back‐to‐back connected dimers display quite different molecular geometry and intermolecular interactions, consequently influencing their packing arrangement, film‐forming process, carrier mobilities, and the device efficiency, stability, and flexibility. By introducing these dimer acceptors as the guest into active layer, these dimers form alloy phases with the host acceptor, promoting film‐forming process and charge dynamics. All ternary devices exhibit improved PCEs of over 18% than the control binary device. Among them, 2Qx‐C3‐based ternary device obtains the best efficiency of as high as 19.03%. Moreover, thanks to the stronger entanglement favored by the dimers with flexible linkage, the PM6:BTP‐eC9:2Qx‐C3‐based device shows outstanding stability and flexibility. The flexible device displays an improved PCE of 16.09% with a crack‐onset strain of 15.0%, showing excellent mechanical robustness close to the all‐polymer devices. This work demonstrates the potential of the back‐to‐back connected dimer acceptors as the guest for highly efficient, stable and flexible OSCs.

Design of bipolar transport D-A discotic liquid crystals based on triphenylene and perylene cores: Effect of the chain length of ester groups

A series of novel discotic liquid-crystalline donor–acceptor dyads (D-A) adjusted by changing the chain length of diester groups on perylene were synthesized based on triphenylene and perylene units which linked by a flexible linkage of 9-nonyloxy-1-amine. The mesomorphism properties and their self-assembly behaviors were studied by differential scanning calorimetry, polarized optical microscopy, one-dimensional wide-angle X-ray diffraction, small angle X-ray scattering and two-dimensional wide-angle X-ray diffraction. Charge carrier mobilities were measured by Time-of-flight device. These discotic liquid crystalline compounds exhibited highly efficient ambipolar charge-transport properties and the charge carrier mobility can reach the order of 10−4 cm2 v−1 s−1 by segregated donor–acceptor columns, providing potential utility of the strategy in organic optoelectronic applications.

Flexible Hydrazone-Linked Metal-Covalent Organic Frameworks with Copper Clusters for Efficient Electrocatalytic Oxygen Evolution Reaction.

Despite the challenges associated with the synthesis of flexible metal-covalent organic frameworks (MCOFs), these offer the unique advantage of maximizing the atomic utilization efficiency. However, the construction of flexible MCOFs with flexible building units or linkages has rarely been reported. In this study, novel flexible MCOFs are constructed using flexible building blocks and copper clusters with hydrazone linkages. The heterometallic frameworks (Cu, Co) are prepared through the hydrazone linkage coordination method and evaluated as catalysts for the oxygen evolution reaction (OER). Owing to the spatial separation and functional cooperation of the heterometallic MCOF catalysts, the as-synthesized MCOFs exhibited outstanding catalytic activities with an overpotential of 268.8mV at 10mAcm-2 for the OER in 1 M KOH, which is superior to those of the reported covalent organic frameworks (COFs)-based OER catalysts. Theoretical calculations further elucidated the synergistic effect of heterometallic active sites within the linkages and frameworks, contributing to the enhanced OER activity. This study thus introduces a novel approach to the fundamental design of flexible MCOF catalysts for the OER, emphasizing their enhanced atomic utilization efficiency.

Thermoplastic polyimide with good comprehensive performance based on carbazole groups and short flexible linkages

AbstractThermoplastic polyimides (TPIs) can meet the requirements of advanced electronic packaging such as flexible copper clad laminate (FCCL) applied under extreme conditions, attributed to their excellent thermal stability, mechanical properties, electrical insulation and chemical resistance. With the increasing demands for electronic devices, such as applications in high‐frequency communication, it is highly desirable to develop high‐performance TPI with good thermoplasticity, thermal stability, mechanical properties and dielectric properties. However, there is a trade‐off between thermoplasticity and other properties. Herein, we introduce an effective strategy to afford TPIs with good performance by copolymerization of a diamine monomer consisted of a coplanar aromatic carbazole group and a short flexible linkage methylene group. On the one hand, short flexible linkages help improve the flexibility of polymer chains and are not too much to enable small‐scale molecular motions below Tg. On the other hand, coplanar aromatic donor groups benefit to strong charge transfer complex (CTC) interaction and π‐π stacking interaction. Based on this strategy, the resultant TPI possesses good thermoplasticity with a proper Tg of 348 °C. Meanwhile, it preserves a low coefficient thermal expansion of 48 ppm K−1, low dielectric constant/dielectric loss factor of 3.27/0.0073 at 10 GHz, and tensile strength of ca. 78 MPa.

Highly conductive and stable anion exchange membranes with dense flexible alkyl ether linkages and 1,2,4,5-tetramethylimidazolium for water electrolysis

Anion exchange membranes (AEMs) are key core materials in water electrolysis, requiring excellent conductivity and chemical durability. In this study, the suspended dense alkyl ether linkages and 1,2,4,5-tetramethylimidazolium ions with high stability are introduced into the polymer structure (PAES-FTMI-x, x = 0.15–0.30) for AEMs. The obtained AEMs with ion exchange capacity of 1.22–1.74 mmol g−1 exhibit high conductivity and dimensional stability. Their hydroxide ionic conductivity and swelling ratio are in the range of 76.28–113.17 mS cm−1 and 9.7%–17.0 % at 80 °C, respectively. The conductivity retention for the representative sample PAES-FTMI-0.25 achieves 90.6 % after soaked in 2 mol L−1 NaOH and 80 °C for 480 h. The assemble water electrolyzer based on PAES-FTMI-0.25 shows 734.97 mA cm−2 of current density at 2 mol L−1 NaOH and 2.0 V of voltage when the temperature is RT. It also has good durable stability at a current density of 500 mA cm−2 for 480 h with only 0.02 V decrease of voltage. This work would provide an effective strategy for the collaborative design and modification of AEMs for alkaline electrolyzed water.

Preparation and characterization of thermo-processable poly(benzimidazole imide)s with soluble and high heat-resistance containing N-phenyl-benzimidazole

In this paper, we present a synthetic strategy for N-phenyl substituted benzimidazole-derived diamines, including 2-(4-(4-aminophenoxy) phenyl)-1-phenyl-1H-benzo[d]imidazole-5-amine (para-diamine) and 2-(3-(4-aminophenoxy) phenyl)-1-phenyl-1H-benzo[d]imidazole-5-amine (meta-diamine). Two distinct series of N-phenyl substituted poly (benzimidazole imide)s (PBIPIs) were synthesized via reaction with different aromatic dianhydrides. The simulation reveals distinct amine reaction activities of two diamine monomers. The obtained PBIPIs exhibit exceptional heat resistance attributed to N-phenyl substituted benzimidazole (BI). The temperature at which weight loss of 5 % (T5%) is in the range of 491–595 °C under N2 environment, while the glass transition temperature is 237–329 °C. The PBIPIs exhibit specific solubility characteristics due to the flexible ether linkage groups' non-coplanarity and bulky pendant benzene groups. The PBIPIs possess tensile strength between 108 and 142 MPa, a tensile modulus of 4.0–5.9 GPa, and an elongation at a break of 4.2–26.4 %, indicating excellent mechanical properties. Additionally, the PBIPI with controlled molecular weight generated from BPADA incorporating 2-(3-(4-aminophenoxy) phenyl)-1-phenyl-1H-benzo[d]imidazole-5-amine (B-BPADA-PA) demonstrates exceptional melt processability. B-BPADA-PA possesses remarkable melt stability since its minimum complex viscosity is only 2100 Pa⋅s at 400 °C, and its melt viscosity ratio is 1.34 at 380 °C.

Effect of Monovalent Cations on the Structure and Dynamics of Multimodal Chromatographic Surfaces.

While multimodal (MM) chromatography is a promising approach for purifying proteins, the lack of a fundamental understanding of how ion-ligand interactions govern selectivity limits its use in the biopharmaceutical industry. This study uses molecular dynamics simulations to study the interactions between simple monovalent cations and two commonly used structurally similar multimodal chromatography ligands, the Capto ligand and Nuvia cPrime, immobilized on the surface. On the Capto ligand surface, ion presence and type play a key role in modulating the formation of phenyl rings and carboxylate clusters. The flexible linkage attaching the Capto ligand to the self-assembled monolayer (SAM) surface allowed multiple ligands to form interactions with the small cations, while large cations interacted less strongly, following the order Li+ > Na+ > K+ > Cs+. Thus, smaller cations resulted in greater ordering on the surface and lower ion diffusivities, while larger cations resulted in less ordering and higher ion diffusivities, following the order Li+ < Na+ < K+ < Cs+. In contrast, due to the rigid attachment of Nuvia cPrime to the SAM surfaces, the cations bound less strongly and had a much smaller effect on ligand clustering or ordering. Additionally, ions in the presence of the Nuvia cPrime surface had generally greater diffusivities than those in the presence of the Capto ligand. Overall, the interaction of cations with the multimodal ligands can lead to unique configurations on the SAM that likely contribute to differential behavior in biological separations.

Rational Design of F-Modified Polyester Electrolytes for Sustainable All-Solid-State Lithium Metal Batteries.

Solid polymer electrolytes (SPEs) are one of the most practical candidates for solid-state batteries owing to their high flexibility and low production cost, but their application is limited by low Li+ conductivity and a narrow electrochemical window. To improve performance, it is necessary to reveal the structure-property relationship of SPEs. Here, 23 fluorinated linear polyesters were prepared by editing the coordination units, flexible linkage segments, and interface passivating groups. Besides the traditionally demonstrated coordinating capability and flexibility of polymer chains, the molecular asymmetry and resulting interchain aggregation are observed critical for Li+ conductivity. By tailoring the molecular asymmetry and coordination ability of polyesters, the Li+ conductivity can be raised by 10 times. Among these polyesters, solvent-free poly(pentanediol adipate) delivers the highest room-temperature Li+ conductivity of 0.59 × 10-4 S cm-1. The chelating coordination of oxalate and Li+ leads to an electron delocalization of alkoxy oxygen, enhancing the antioxidation capability of SPEs. To lower the cost, high-value LiTFSI in SPEs is recycled at 90%, and polyesters can be regenerated at 86%. This work elucidates the structure-property relationship of polyester-based SPEs, displays the design principles of SPEs, and provides a way for the development of sustainable solid-state batteries.

Klasterisasi Data Untuk Sistem Rekomendasi Pemilihan Sekolah Dasar Di Wilayah Surakarta Degan Metode Hierarchy Clustering

The role of parents is very important in determining the school for their children, especially at elementary school level. There are many factors that parents consider when choosing an elementary school, including school quality, distance to school, school fees, content of religious education, school performance and school facilities. The aim of this research is to develop a data clustering concept using Hierarchy Clustering method for an elementary school recommendation system in the city of Surakarta, so that it can help parents in determining the elementary school for their children. In this study, agglomerative clustering with Ward linkage was used, this is because among other linkage methods (Single linkage, ward linkage, flexible linkage and complete linkage), Ward linkage has the highest Silhouette index value, namely 0.666. Cluster optimization in this research was determined by looking at the Silhouette index graph by comparing the Silhouette cluster values 1 to 10 for each linkage method, and obtained the cluster optimization value was 4, so the number of groupings used was 4 clusters. The accuracy of the recommendation system is tested using the Mean Average Error (MAE) statistical calculation, with an MAE value of 0.2, which means the recommendation system is suitable for use.

Nanoparticle Size Influences the Self-Assembly of Gold Nanorods Using Flexible Streptavidin-Biotin Linkages.

The self-assembly of colloidal nanocrystals remains of robust interest due to its potential in creating hierarchical nanomaterials that have advanced function. For gold nanocrystals, junctions between nanoparticles yield large enhancements in local electric fields under resonant illumination, which is suitable for surface-enhanced spectroscopies for molecular sensors. Gold nanorods can provide such plasmonic fields at near-infrared wavelengths of light for longitudinal excitation. Through the use of careful concentration and stoichiometric control, a method is reported herein for selective biotinylation of the ends of gold nanorods for simple, consistent, and high-yielding self-assembly upon addition of the biotin-binding protein streptavidin. This method was applied to four different sized nanorods of similar aspect ratio and analyzed through UV-vis spectroscopy for qualitative confirmation of self-assembly and transmission electron microscopy to determine the degree of self-assembly in end-linked nanorods. The yield of end-linked assemblies approaches 90% for the largest nanorods and approaches 0% for the smallest nanorods. The number of nanorods linked in one chain also increases with an increased nanoparticle size. The results support the notion that the lower ligand density at the ends of the larger nanorods yields preferential substitution reactions at those ends and hence preferential end-to-end assembly, while the smallest nanorods have a relatively uniform ligand density across their surfaces, leading to spatially random substitution reactions.