Electron microscopy is often required to correlate the size and shape of plasmonic nanoparticles with their optical properties. Eliminating the need for electron microscopy is one crucial step toward in situ sensing applications, especially for complicated sample conditions such as during irreversible chemical reactions or when particles are embedded in a matrix. Here, we show that a machine learning decision tree can accurately predict gold nanorod dimensions over a wide range of sizes. The model is trained by using similar to 450 nanorod geometries and corresponding scattering spectra obtained from finite-difference time-domain simulations. We test the model using a set of experimental spectra and sizes obtained from correlated scanning electron microscopy images, resulting in predictions of the dimensions of gold nanorods within similar to 10% of their true values (root-mean-squared percentage error) over a large range of sizes. Analysis of the decision tree structure reveals that a relationship with resonance energy and line width of the localized surface plasmon resonance is sufficient to predict nanorod dimensions, notably outperforming more complicated models. Our findings illustrate the advantages of using machine learning models to infer single particle structural features from their optical spectra.

Noble metal nanoparticles host surface plasmon resonances that confine electromagnetic waves below the diffraction limit of light, making them effective building blocks for near-field optical antennas. Efficient prediction and design of nanoantenna systems are facilitated by improved understanding of their optical properties. Here, we utilize an intuitive coupled-dipole model for fan-shaped gold nanorod trimers together with experiments to investigate the role of near- and far-field effects upon optical dichroism using both linear and trochoidal polarizations with cartwheeling field motion matching the geometry of the trimers. Our coupled-dipole model predicts the linear and trochoidal dichroism that we observe in experiments, and we demonstrate that trochoidal intensity modulation can be tuned and reversed by varying the geometric parameters of the gold nanorod trimers. Simple analytical models, coupled with easily understood visualizations, provide a useful framework for predictive nanoantenna design applications.

Understanding nanoscale protein conformational changes at solid-liquid interfaces is critical for predicting how proteins will impact the performance of biomaterials in vivo. Crowding is an important contributor to conformational stability. Here we apply single-molecule high resolution imaging with photobleaching to directly measure dye-conjugated fibronectin's unfolding in varying conditions of crowding with human serum albumin on aminosilanized glass. Using this approach, we identify serum albumin's crowding mechanism. We find that fibronectin achieves larger degrees of unfolding when not crowded by coadsorbed serum albumin. Serum albumin does not as effectively constrict fibronectin's conformation if it is sequentially, rather than simultaneously, introduced, suggesting that serum albumin's crowding mechanism is dependent on its ability to sterically block fibronectin's unfolding during the process of adsorption. Because fibronectin's conformation is dependent on interfacial macromolecular crowding under in vitro conditions, it is important to consider the role of in vivo crowding on protein activity.

General methods to achieve better physical insight about nanoparticle aggregation and assembly are needed because of the potential role of aggregation in a wide range of materials, environmental, and biological outcomes. Scanning electron microscopy (SEM) is fast and affordable compared to transmission electron microscopy, but SEM micrographs lack contrast and resolution due to lower beam energy, topographic contrast, edge effects, and charging. We present a new segmentation algorithm called SEMseg that is robust to the challenges inherent in SEM micrograph analysis and demonstrate its utility for analyzing gold (Au) nanorod aggregates. SEMseg not only supports nanoparticle size analysis for dispersed nanoparticles, but also discriminates between nanoparticles within an aggregate. We compare our algorithm to those incorporated into the commonly used software ImageJ and demonstrate improved segmentation of aggregate structures. New physical insight about aggregation is demonstrated by the introduction of an order parameter describing side-by-side structure in nanoparticle aggregates. We also present the segmentation and fitting algorithms included in SEMseg within a user-friendly graphical user interface. The resulting code is provided with an open-source interface to provide quantitative image processing tools for researchers to characterize both dispersed nanoparticles and nanoparticle assemblies in SEM micrographs with high throughput.

Plasmonic metal nanoparticles exhibit large dipole moments upon photoexcitation and have the potential to induce electronic transitions in nearby materials, but fast internal relaxation has to date limited the spatial range and efficiency of plasmonic mediated processes. In this work, we use photo-electrochemistry to synthesize hybrid nanoantennas comprised of plasmonic nanoparticles with photoconductive polymer coatings. We demonstrate that the formation of the conductive polymer is selective to the nanoparticles and that polymerization is enhanced by photoexcitation. In situ spectroscopy and simulations support a mechanism in which up to 50% efficiency of nonradiative energy transfer is achieved. These hybrid nanoantennas combine the unmatched light-harvesting properties of a plasmonic antenna with the similarly unmatched device processability of a polymer shell.

Plasmonic nanostructures offer promising applications as nanocatalysts, but optimizing their structure-function relationship using optical superlocalization techniques is hindered by the formation of distorted point spread functions (PSFs). Previously reported localization bias for remotely excited Alexa-647 adsorbed to Ag nanowires is investigated here for its potential to provide useful information about surface interactions. Two main classes of abnormal PSFs are examined: single-lobed PSFs, in which the localization bias arises from various emitter positions around the nanowire, and bilobed PSFs arising from emitters near the top edge of the nanowire. The amount of localization bias for these two populations diverges for ground truth widths less than 300 nm and suggests the latter adsorption and resulting orientation arise more frequently under experimental conditions than is predicted by simulation. Nanowires with widths in the range of 200 to 300 nm are found to have the greatest potential for distinguishing between single-lobed and bilobed PSFs in experiment. Finally, we present a fitting method for abnormal PSFs using a basis of Hermite-Gaussian functions and show that orientation information is encoded in bilobed PSFs.

Developing a mechanistic understanding of protein dynamics and conformational changes at polymer interfaces is critical for a range of processes including industrial protein separations. Salting out is one example of a procedure that is ubiquitous in protein separations yet is optimized empirically because there is no mechanistic description of the underlying interactions that would allow predictive modeling. Here, we investigate peak narrowing in a model transferrin-nylon system under salting out conditions using a combination of single-molecule tracking and ensemble separations. Distinct surface transport modes and protein conformational changes at the negatively charged nylon interface are quantified as a function of salt concentration. Single-molecule kinetics relate macroscale improvements in chromatographic peak broadening with microscale distributions of surface interaction mechanisms such as continuous-time random walks and simple adsorption-desorption. Monte Carlo simulations underpinned by the stochastic theory of chromatography are performed using kinetic data extracted from single-molecule observations. Simulations agree with experiment, revealing a decrease in peak broadening as the salt concentration increases. The results suggest that chemical modifications to membranes that decrease the probability of surface random walks could reduce peak broadening in full-scale protein separations. More broadly, this work represents a proof of concept for combining single-molecule experiments and a mechanistic theory to improve costly and time-consuming empirical methods of optimization.

Plasmon-coupled circular dichroism has emerged as a promising approach for ultrasensitive detection of biomolecular conformations through coupling between molecular chirality and surface plasmons. Chiral nanoparticle assemblies without chiral molecules present also have large optical activities. We apply single-particle circular differential scattering spectroscopy coupled with electron imaging and simulations to identify both structural chirality of plasmonic aggregates and plasmon-coupled circular dichroism induced by chiral proteins. We establish that both chiral aggregates and just a few proteins in interparticle gaps of achiral assemblies are responsible for the ensemble signal, but single nanoparticles do not contribute. We furthermore find that the protein plays two roles: It transfers chirality to both chiral and achiral plasmonic substrates, and it is also responsible for the chiral three-dimensional assembly of nanorods. Understanding these underlying factors paves the way toward sensing the chirality of single biomolecules.

Electrogenerated chemiluminescence (ECL) is a promising technique for low concentration molecular detection. To improve the detection limit, plasmonic nanoparticles have been proposed as signal boosting antennas to amplify ECL. Previous ensemble studies have hinted that spectral overlap between the nanoparticle antenna and the ECL emitter may play a role in signal enhancement. Ensemble spectroscopy, however, cannot resolve heterogeneities arising from colloidal nanoparticle size and shape distributions, leading to an incomplete picture of the impact of spectral overlap. Here, we isolate the effect of nanoparticle-emitter spectral overlap for a model ECL system, coreaction of tris(2,2'-bipyridyl)dichlororuthenium(ii) hexahydrate and tripropylamine, at the single-particle level while minimizing other factors influencing ECL intensities. We found a 10-fold enhancement of ECL among 952 gold nanoparticles. This signal enhancement is attributed exclusively to spectral overlap between the nanoparticle and the emitter. Our study provides new mechanistic insight into plasmonic enhancement of ECL, creating opportunities for low concentration ECL sensing.

After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the structure-function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.

We report a study of the shape-dependent spectral response of the gold nanoparticle surface plasmon resonance at various electron densities to provide mechanistic insight into the role of capacitive charging, a topic of some debate. We demonstrate a morphology-dependent spectral response for gold nanoparticles due to capacitive charging using single-particle spectroscopy in an inert electrochemical environment. A decrease in plasmon energy and increase in spectral width for gold nanospheres and nanorods was observed as the electron density was tuned through a potential window of -0.3 to 0.1 V. The combined observations could not be explained by existing theories. A new quantum theory for charging based on the random phase approximation was developed. Additionally, the redox reaction of gold oxide formation was probed using single-particle plasmon voltammetry to reproduce the reduction peak from the bulk cyclic voltammetry. These results deepen our understanding of the relationship between optical and electronic properties in plasmonic nanoparticles and provide insight toward their potential applications in directed electrocatalysis.

After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the, structure function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which we use to propose the Bethe-ansatz-type expressions for the eigenvalues of the transfer matrix. At most two of the boundary parameters are set to be arbitrary and the bulk anisotropy parameter has values eta = i pi/2, i pi/4, .... We also provide numerical evidence for the completeness of the Bethe-ansatz-type solutions derived, using the s = 1 case as an example.