Morphological control of bundled actin networks subject to fixed-mass depletion.

Depletion interactions are thought to significantly contribute to the organization of intracellular structures in the crowded cytosol. The strength of depletion interactions depends on physical parameters such as the depletant number density and the depletant size ratio. Cells are known to dynamically regulate these two parameters by varying the copy number of proteins of a wide distribution of sizes. However, mammalian cells are also known to keep the total protein mass density remarkably constant, to within 0.5% throughout the cell cycle. We thus ask how the strength of depletion interactions varies when the total depletant mass is held fixed, a.k.a. fixed-mass depletion. We answer this question via scaling arguments, as well as by studying depletion effects on networks of reconstituted semiflexible actin in silico and in vitro. We examine the maximum strength of the depletion interaction potential U∗ as a function of q, the size ratio between the depletant and the matter being depleted. We uncover a scaling relation U∗ ∼ qζ for two cases: fixed volume fraction φ and fixed mass density ρ. For fixed volume fraction, we report ζ < 0. For the fixed mass density case, we report ζ > 0, which suggests that the depletion interaction strength increases as the depletant size ratio is increased. To test this prediction, we prepared our filament networks at fixed mass concentrations with varying sizes of the depletant molecule poly(ethylene glycol) (PEG). We characterize the depletion interaction strength in our simulations via the mesh size. In experiments, we observe two distinct actin network morphologies, which we call weakly bundled and strongly bundled. We identify a mass concentration where different PEG depletant sizes lead to weakly bundled or strongly bundled morphologies. For these conditions, we find that the mesh size and intra-bundle spacing between filaments across the different morphologies do not show significant differences, while the dynamic light scattering relaxation time and storage modulus between the two states do show significant differences. Our results demonstrate the ability to tune actin network morphology and mechanics by controlling depletant size and give insights into depletion interaction mechanisms under the fixed-depletant-mass constraint relevant to living cells.

Highly Responsive Plasmon Modulation in Dopant-Segregated Nanocrystals.

Electron transfer to and from metal oxide nanocrystals (NCs) modulates their infrared localized surface plasmon resonance (LSPR), revealing fundamental aspects of their photophysics and enabling dynamic optical applications. We synthesized and chemically reduced dopant-segregated Sn-doped In2O3 NCs, investigating the influence of radial dopant segregation on LSPR modulation and near-field enhancement (NFE). We found that core-doped NCs show large LSPR shifts and NFE change during chemical titration, enabling broadband modulation in LSPR energy of over 1000 cm-1 and of peak extinction over 300%. Simulations reveal that the evolution of the LSPR spectra during chemical reduction results from raising the surface Fermi level and increasing the donor defect density in the shell region. These results establish dopant segregation as a useful strategy to engineer the dynamic optical modulation in plasmonic semiconductor NC heterostructures going beyond what is possible with conventional plasmonic metals.

Dipolar Ligands Tune Plasmonic Properties of Tin-Doped Indium Oxide Nanocrystals.

Surface functionalization with dipolar molecules is known to tune the electronic band alignment in semiconductor films and colloidal quantum dots. Yet, the influence of surface modification on plasmonic nanocrystals and their properties remains little explored. Here, we functionalize tin-doped indium oxide nanocrystals (ITO NCs) via ligand exchange with a series of cinnamic acids with different electron-withdrawing and -donating dipolar characters. Consistent with previous reports on semiconductors, we find that withdrawing (donating) ligands increase (decrease) the work function caused by an electrostatic potential shift across the molecular layer. Quantitative analyses of the plasmonic extinction spectra reveal that varying the ligand molecular dipole affects the near-surface depletion layer, with an anticorrelated trend between the electron concentration and electronic volume fraction, factors that are positively correlated in as-synthesized NCs. Electronic structure engineering through surface modification provides access to distinctive combinations of plasmonic properties that could enable optoelectronic applications, sensing, and hot electron-driven processes.

Hierarchically Doped Plasmonic Nanocrystal Metamaterials.

Assembling plasmonic nanocrystals in regular superlattices can produce effective optical properties not found in homogeneous materials. However, the range of these metamaterial properties is limited when a single nanocrystal composition is selected for the constituent meta-atoms. Here, we show how continuously varying doping at two length scales, the atomic and nanocrystal scales, enables tuning of both the frequency and bandwidth of the collective plasmon resonance in nanocrystal-based metasurfaces, while these features are inextricably linked in single-component superlattices. Varying the mixing ratio of indium tin oxide nanocrystals with different dopant concentrations, we use large-scale simulations to predict the emergence of a broad infrared spectral region with near-zero permittivity. Experimentally, tunable reflectance and absorption bands are observed, owing to in- and out-of-plane collective resonances. These spectral features and the predicted strong near-field enhancement establish this multiscale doping strategy as a powerful new approach to designing metamaterials for optical applications.

Plasmonic Response of Complex Nanoparticle Assemblies.

Optical properties of nanoparticle assemblies reflect distinctive characteristics of their building blocks and spatial organization, giving rise to emergent phenomena. Integrated experimental and computational studies have established design principles connecting the structure to properties for assembled clusters and superlattices. However, conventional electromagnetic simulations are too computationally expensive to treat more complex assemblies. Here we establish a fast, materials agnostic method to simulate the optical response of large nanoparticle assemblies incorporating both structural and compositional complexity. This many-bodied, mutual polarization method resolves limitations of established approaches, achieving rapid, accurate convergence for configurations including thousands of nanoparticles, with some overlapping. We demonstrate these capabilities by reproducing experimental trends and uncovering far- and near-field mechanisms governing the optical response of plasmonic semiconductor nanocrystal assemblies including structurally complex gel networks and compositionally complex mixed binary superlattices. This broadly applicable framework will facilitate the design of complex, hierarchically structured, and dynamic assemblies for desired optical characteristics.

Modular mixing in plasmonic metal oxide nanocrystal gels with thermoreversible links.

Gelation offers a powerful strategy to assemble plasmonic nanocrystal networks incorporating both the distinctive optical properties of constituent building blocks and customizable collective properties. Beyond what a single-component assembly can offer, the characteristics of nanocrystal networks can be tuned in a broader range when two or more components are intimately combined. Here, we demonstrate mixed nanocrystal gel networks using thermoresponsive metal-terpyridine links that enable rapid gel assembly and disassembly with thermal cycling. Plasmonic indium oxide nanocrystals with different sizes, doping concentrations, and shapes are reliably intermixed in linked gel assemblies, exhibiting collective infrared absorption that reflects the contributions of each component while also deviating systematically from a linear combination of the spectra for single-component gels. We extend a many-bodied, mutual polarization method to simulate the optical response of mixed nanocrystal gels, reproducing the experimental trends with no free parameters and revealing that spectral deviations originate from cross-coupling between nanocrystals with distinct plasmonic properties. Our thermoreversible linking strategy directs the assembly of mixed nanocrystal gels with continuously tunable far- and near-field optical properties that are distinct from those of the building blocks or mixed close-packed structures.

Assembling Inorganic Nanocrystal Gels.

Inorganic nanocrystal gels retain distinct properties of individual nanocrystals while offering tunable, network-structure-dependent characteristics. We review different mechanisms for assembling gels from colloidal nanocrystals including (1) controlled destabilization, (2) direct bridging, (3) depletion, as well as linking mediated by (4) coordination bonding or (5) dynamic covalent bonding, and we highlight how each impacts gel properties. These approaches use nanocrystal surface chemistry or the addition of small molecules to mediate inter-nanocrystal attractions. Each method offers advantages in terms of gel stability, reversibility, or tunability and presents new opportunities for the design of reconfigurable materials and fueled assemblies.

Contact Conductance Governs Metallicity in Conducting Metal Oxide Nanocrystal Films.

Although colloidal nanoparticles hold promise for fabricating electronic components, the properties of nanoparticle-derived materials can be unpredictable. Materials made from metallic nanocrystals exhibit a variety of transport behavior ranging from insulators, with internanocrystal contacts acting as electron transport bottlenecks, to conventional metals, where phonon scattering limits electron mobility. The insulator-metal transition (IMT) in nanocrystal films is thought to be determined by contact conductance. Meanwhile, criteria are lacking to predict the characteristic transport behavior of metallic nanocrystal films beyond this threshold. Using a library of transparent conducting tin-doped indium oxide nanocrystal films with varied electron concentration, size, and contact area, we assess the IMT as it depends on contact conductance and show how contact conductance is also key to predicting the temperature-dependence of conductivity in metallic films. The results establish a phase diagram for electron transport behavior that can guide the creation of metallic conducting materials from nanocrystal building blocks.

Synthetic Control of Intrinsic Defect Formation in Metal Oxide Nanocrystals Using Dissociated Spectator Metal Salts.

Crystallographic defects are essential to the functional properties of semiconductors, controlling everything from conductivity to optical properties and catalytic activity. In nanocrystals, too, defect engineering with extrinsic dopants has been fruitful. Although intrinsic defects like vacancies can be equally useful, synthetic strategies for controlling their generation are comparatively underdeveloped. Here, we show that intrinsic defect concentration can be tuned during the synthesis of colloidal metal oxide nanocrystals by the addition of metal salts. Although not incorporated in the nanocrystals, the metal salts dissociate at high temperatures, promoting the dissociation of carboxylate ligands from metal precursors, leading to the introduction of oxygen vacancies. For example, the concentration of oxygen vacancies can be controlled up to 9% in indium oxide nanocrystals. This method is broadly applicable as we demonstrate by generating intrinsic defects in metal oxide nanocrystals of various morphologies and compositions.

Sculpting the Plasmonic Responses of Nanoparticles by Directed Electron Beam Irradiation.

Spatial confinement of matter in functional nanostructures has propelled these systems to the forefront of nanoscience, both as a playground for exotic physics and quantum phenomena and in multiple applications including plasmonics, optoelectronics, and sensing. In parallel, the emergence of monochromated electron energy loss spectroscopy (EELS) has enabled exploration of local nanoplasmonic functionalities within single nanoparticles and the collective response of nanoparticle assemblies, providing deep insight into associated mechanisms. However, modern synthesis processes for plasmonic nanostructures are often limited in the types of accessible geometry, and materials and are limited to spatial precisions on the order of tens of nm, precluding the direct exploration of critical aspects of the structure-property relationships. Here, the atomic-sized probe of the scanning transmission electron microscope is used to perform precise sculpting and design nanoparticle configurations. Using low-loss EELS, dynamic analyses of the evolution of the plasmonic response are provided. It is shown that within self-assembled systems of nanoparticles, individual nanoparticles can be selectively removed, reshaped, or patterned with nanometer-level resolution, effectively modifying the plasmonic response in both space and energy. This process significantly increases the scope for design possibilities and presents opportunities for unique structure development, which are ultimately the key for nanophotonic design.

Colloidal Nanocrystal Gels from Thermodynamic Principles.

Gels assembled from solvent-dispersed nanocrystals are of interest for functional materials because they promise the opportunity to retain distinctive properties of individual nanocrystals combined with tunable, structure-dependent collective behavior. By incorporating stimuli-responsive components, these materials could also be dynamically reconfigured between structurally distinct states. However, nanocrystal gels have so far been formed mostly through irreversible aggregation, which has limited the realization of these possibilities. Meanwhile, gelation strategies for larger colloidal microparticles have been developed using reversible physical or chemical interactions. These approaches have enabled the experimental navigation of theoretically predicted phase diagrams, helping to establish an understanding of how thermodynamic behavior can guide gel formation in these materials. However, the translation of these principles to the nanoscale poses both practical and fundamental challenges. The molecules guiding assembly can no longer be safely assumed to be vanishingly small compared to the particles nor large compared to the solvent.In this Account, we discuss recent progress toward the assembly of tunable nanocrystal gels using two strategies guided by equilibrium considerations: (1) reversible chemical bonding between functionalized nanocrystals and difunctional linker molecules and (2) nonspecific, polymer-induced depletion attractions. The effective nanocrystal attractions, mediated in both approaches by a secondary molecule, compete against stabilizing repulsions to promote reversible assembly. The structure and properties of the nanocrystal gels are controlled microscopically by the design of the secondary molecule and macroscopically by its concentration. This mode of control is compelling because it largely decouples nanocrystal synthesis and functionalization from the design of interactions that drive assembly. Statistical thermodynamic theory and computer simulation have been applied to simple models that describe the bonding motifs in these assembling systems, furnish predictions for conditions under which gelation is likely to occur, and suggest strategies for tuning and disassembling the gel networks. Insights from these models have guided experimental realizations of reversible gels with optical properties in the infrared range that are sensitive to the gel structure. This process avoids time-consuming and costly trial-and-error experimental investigations to accelerate the development of nanocrystal gel assemblies.These advances highlight the need to better understand interactions between nanocrystals, how interactions give rise to gel structure, and properties that emerge. Such an understanding could suggest new approaches for creating stimuli-responsive and dissipative assembled materials whose properties are tunable on demand through directed reconfiguration of the underlying gel microstructure. It may also make nanocrystal gels amenable to computationally guided design using inverse methods to rapidly optimize experimental parameters for targeted functionalities.

Dynamics of equilibrium-linked colloidal networks.

Colloids that attractively bond to only a few neighbors (e.g., patchy particles) can form equilibrium gels with distinctive dynamic properties that are stable in time. Here, we use a coarse-grained model to explore the dynamics of linked networks of patchy colloids whose average valence is macroscopically, rather than microscopically, constrained. Simulation results for the model show dynamic hallmarks of equilibrium gel formation and establish that the colloid-colloid bond persistence time controls the characteristic slow relaxation of the self-intermediate scattering function. The model features re-entrant network formation without phase separation as a function of linker concentration, centered at the stoichiometric ratio of linker ends to nanoparticle surface bonding sites. Departures from stoichiometry result in linker-starved or linker-saturated networks with reduced connectivity and shorter characteristic relaxation times with lower activation energies. Underlying the re-entrant trends, dynamic properties vary monotonically with the number of effective network bonds per colloid, a quantity that can be predicted using Wertheim's thermodynamic perturbation theory. These behaviors suggest macroscopic in situ strategies for tuning the dynamic response of colloidal networks.

Controlling the Shape Anisotropy of Monoclinic Nb12O29 Nanocrystals Enables Tunable Electrochromic Spectral Range.

Electrochromic smart windows that modulate the solar transmittance in a wide and selective spectral range can optimize building energy efficiency. However, for conventional materials such as bulk transition metal oxides, the electrochromic spectral range is constrained by their crystal structure with limited tunability. Herein, we report a method to control the shape anisotropy of monoclinic Nb12O29 nanocrystals and obtain a tunable electrochromic spectral range. We demonstrate the synthesis of monoclinic Nb12O29 nanorods (NRs), extending one-dimensionally along the b direction, and monoclinic Nb12O29 nanoplatelets (NPLs), extending two-dimensionally along the b and c directions. Upon electrochemical reduction accompanied by Li insertion, the NR films show increasing absorbance mostly in the near infrared region. In contrast, the NPL films show increasing absorbance in the near infrared region first followed by increasing absorbance in both visible and near infrared regions. To elucidate the influence of shape anisotropy, we used density functional theory to construct the lithiated structures of monoclinic Nb12O29 and in these structures we identified the presence of square planar sites and crystallographic shear sites for Li insertion. By calculating the theoretical spectra of the lithiated structures, we demonstrate that the Li insertion into the square planar sites results in absorption in the near infrared region in both NRs and NPLs due to their extension in the b direction, while the subsequent insertion of Li into the crystallographic shear sites leads to absorption in both visible and near infrared regions, which only occurs in NPLs due to their extension in the c direction.

Dynamics of Lithium Insertion in Electrochromic Titanium Dioxide Nanocrystal Ensembles.

Nanocrystalline anatase TiO2 is a robust model anode for Li insertion in batteries. The influence of nanocrystal size on the equilibrium potential and kinetics of Li insertion is investigated with in operando spectroelectrochemistry of thin film electrodes. Distinct visible and infrared responses correlate with Li insertion and electron accumulation, respectively, and these optical signals are used to deconvolute bulk Li insertion from other electrochemical responses, such as double-layer capacitance, pseudocapacitance, and electrolyte leakage. Electrochemical titration and phase-field simulations reveal that a difference in surface energies between anatase and lithiated phases of TiO2 systematically tunes the Li-insertion potentials with the particle size. However, the particle size does not affect the kinetics of Li insertion in ensemble electrodes. Rather, the Li-insertion rates depend on the applied overpotential, electrolyte concentration, and initial state of charge. We conclude that Li diffusivity and phase propagation are not rate limiting during Li insertion in TiO2 nanocrystals. Both of these processes occur rapidly once the transformation between the low-Li anatase and high-Li orthorhombic phases begins in a particle. Instead, discontinuous kinetics of Li accumulation in TiO2 particles prior to the phase transformations limits (dis)charging rates. We demonstrate a practical means to deconvolute the nonequilibrium charging behavior in nanocrystalline electrodes through a combination of colloidal synthesis, phase field simulations, and spectroelectrochemistry.

Understanding the Hydrothermal Formation of NaNbO3: Its Full Reaction Scheme and Kinetics.

Sodium niobate (NaNbO3) attracts attention for its great potential in a variety of applications, for instance, due to its unique optical properties. Still, optimization of its synthetic procedures is hard due to the lack of understanding of the formation mechanism under hydrothermal conditions. Through in situ X-ray diffraction, hydrothermal synthesis of NaNbO3 was observed in real time, enabling the investigation of the reaction kinetics and mechanisms with respect to temperature and NaOH concentration and the resulting effect on the product crystallite size and structure. Several intermediate phases were observed, and the relationship between them, depending on temperature, time, and NaOH concentration, was established. The reaction mechanism involved a gradual change of the local structure of the solid Nb2O5 precursor upon suspending it in NaOH solutions. Heating gave a full transformation of the precursor to HNa7Nb6O19·15H2O, which destabilized before new polyoxoniobates appeared, whose structure depended on the NaOH concentration. Following these polyoxoniobates, Na2Nb2O6·H2O formed, which dehydrated at temperatures ≥285 °C, before converting to the final phase, NaNbO3. The total reaction rate increased with decreasing NaOH concentration and increasing temperature. Two distinctly different growth regimes for NaNbO3 were observed, depending on the observed phase evolution, for temperatures below and above ≈285 °C. Below this temperature, the growth of NaNbO3 was independent of the reaction temperature and the NaOH concentration, while for temperatures ≥285 °C, the temperature-dependent crystallite size showed the characteristics of a typical dissolution-precipitation mechanism.

Wertheim's thermodynamic perturbation theory with double-bond association and its application to colloid-linker mixtures.

We extend Wertheim's thermodynamic perturbation theory to derive the association free energy of a multicomponent mixture for which double bonds can form between any two pairs of the molecules' arbitrary number of bonding sites. This generalization reduces in limiting cases to prior theories that restrict double bonding to at most one pair of sites per molecule. We apply the new theory to an associating mixture of colloidal particles ("colloids") and flexible chain molecules ("linkers"). The linkers have two functional end groups, each of which may bond to one of several sites on the colloids. Due to their flexibility, a significant fraction of linkers can "loop" with both ends bonding to sites on the same colloid instead of bridging sites on different colloids. We use the theory to show that the fraction of linkers in loops depends sensitively on the linker end-to-end distance relative to the colloid bonding-site distance, which suggests strategies for mitigating the loop formation that may otherwise hinder linker-mediated colloidal assembly.

Effects of linker flexibility on phase behavior and structure of linked colloidal gels.

Colloidal nanocrystal gels can be assembled using a difunctional "linker" molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of the gel are controlled macroscopically by the linker concentration and microscopically by the linker's molecular characteristics. Here, we demonstrate using a toy model for a colloid-linker mixture that linker flexibility plays a key role in determining both phase behavior and the structure of the mixture. We fix the linker length and systematically vary its bending stiffness to span the flexible, semiflexible, and rigid regimes. At fixed linker concentration, flexible-linker and rigid-linker mixtures phase separate at low colloid volume fractions, in agreement with predictions of first-order thermodynamic perturbation theory, but the semiflexible-linker mixtures do not. We correlate and attribute this qualitatively different behavior to undesirable "loop" linking motifs that are predicted to be more prevalent for linkers with end-to-end distances commensurate with the locations of chemical bonding sites on the colloids. Linker flexibility also influences the spacing between linked colloids, suggesting strategies to design gels with desired phase behavior, structure, and, by extension, structure-dependent properties.

Enhancing hyperspectral EELS analysis of complex plasmonic nanostructures with pan-sharpening.

Nanoscale hyperspectral techniques-such as electron energy loss spectroscopy (EELS)-are critical to understand the optical response in plasmonic nanostructures, but as systems become increasingly complex, the required sampling density and acquisition times become prohibitive for instrumental and specimen stability. As a result, there has been a recent push for new experimental methodologies that can provide comprehensive information about a complex system, while significantly reducing the duration of the experiment. Here, we present a pan-sharpening approach to hyperspectral EELS analysis, where we acquire two datasets from the same region (one with high spatial resolution and one with high spectral fidelity) and combine them to achieve a single dataset with the beneficial properties of both. This work outlines a straightforward, reproducible pathway to reduced experiment times and higher signal-to-noise ratios, while retaining the relevant physical parameters of the plasmonic response, and is generally applicable to a wide range of spectroscopy modalities.

Gelation of plasmonic metal oxide nanocrystals by polymer-induced depletion attractions.

Gelation of colloidal nanocrystals emerged as a strategy to preserve inherent nanoscale properties in multiscale architectures. However, available gelation methods to directly form self-supported nanocrystal networks struggle to reliably control nanoscale optical phenomena such as photoluminescence and localized surface plasmon resonance (LSPR) across nanocrystal systems due to processing variabilities. Here, we report on an alternative gelation method based on physical internanocrystal interactions: short-range depletion attractions balanced by long-range electrostatic repulsions. The latter are established by removing the native organic ligands that passivate tin-doped indium oxide (ITO) nanocrystals while the former are introduced by mixing with small PEG chains. As we incorporate increasing concentrations of PEG, we observe a reentrant phase behavior featuring two favorable gelation windows; the first arises from bridging effects while the second is attributed to depletion attractions according to phase behavior predicted by our unified theoretical model. Our assembled nanocrystals remain discrete within the gel network, based on X-ray scattering and high-resolution transmission electron microscopy. The infrared optical response of the gels is reflective of both the nanocrystal building blocks and the network architecture, being characteristic of ITO nanocrystals' LSPR with coupling interactions between neighboring nanocrystals.

Dual-Mode Infrared Absorption by Segregating Dopants within Plasmonic Semiconductor Nanocrystals.

When aliovalent dopants are sufficiently segregated to the core or near the surface of semiconductor nanocrystals, charge carriers donated by the dopants are also segregated to the core or near the surface, respectively. In Sn-doped indium oxide nanocrystals, we find that this contrast in free charge carrier concentration creates a core and shell with differing dielectric properties and results in two distinctly observable plasmonic extinction peaks. The trends in this dual-mode optical response with shell growth differ from core/shell nanoparticles composed of traditional plasmonic metals such as Au and Ag. We developed a model employing a core/shell effective medium approximation that can fit the dual-mode spectra and explain the trends in the extinction response. Lastly, we show that dopant segregation can improve sensitivity of plasmon spectra to changes in refractive index of the surrounding environment.