Bridging the Gap: 3D Real-Space Characterization of Colloidal Assemblies via FIB-SEM Tomography

Insight in the structure of nanoparticle assemblies up to a single particle level is key to understand the collective properties of these assemblies, which critically depend on the individual particle positions and orientations. However, the characterization of large, micron sized assemblies containing small, 10-500 nanometer, sized colloids is highly challenging and cannot easily be done with the conventional light, electron or X-ray microscopy techniques. Here, we demonstrate that focused ion beam-scanning electron microscopy (FIB-SEM) tomography in combination with image processing enables quantitative real-space studies of ordered and disordered particle assemblies too large for conventional transmission electron tomography, containing particles too small for confocal microscopy. First, we demonstrate the high resolution structural analysis of spherical nanoparticle assemblies, containing small anisotropic gold nanoparticles. Herein, FIB-SEM tomography allows the characterization of assembly dimensions which are inaccessible to conventional transmission electron microscopy. Next, we show that FIB-SEM tomography is capable of characterizing much larger ordered and disordered assemblies containing silica colloids with a diameter close to the resolution limit of confocal microscopes. We determined both the position and the orientation of each individual (nano)particle in the assemblies by using recently developed particle tracking routines. Such high precision structural information is essential in the understanding and design of the collective properties of new nanoparticle based materials and processes.Comment: 17 pages, 4 figures, Supplemental Information at articles webpage: https://doi.org/10.1039/C8NR09753

Silica-Coated Gold Nanorod Supraparticles: A Tunable Platform for Surface Enhanced Raman Spectroscopy

Plasmonic nanoparticle assemblies are promising functional materials for surface-enhanced Raman spectroscopy (SERS). Gold nanorod (AuNR) assemblies are of particular interest due to the large, shape-induced local field enhancement and the tunable surface plasmon resonance of the AuNRs. Designing the optimal assembly structure for SERS, however, is challenging and requires a delicate balance between the interparticle distance, porosity, and wetting of the assembly. Here, a new type of functional assemblies–called supraparticles–fabricated through the solvent-evaporation driven assembly of silica-coated gold nanorods into spherical ensembles, in which the plasmonic coupling and the mass transport is tuned through the thickness and porosity of the silica shells are introduced. Etching of the AuNRs allowed fine-tuning of the plasmonic response to the laser excitation wavelength. Using a correlative SERS-electron microscopy approach, it is shown that all supraparticles successfully amplified the Raman signal of the crystal violet probe molecules, and that the Raman signal strongly increased when decreasing the silica shell thickness from 35 to 3 nm, provided that the supraparticles have a sufficiently high porosity. The supraparticles introduced in this study present a novel class of materials for sensing, and open up a wide parameter space to optimize their performance

Inferentialism as an alternative to socioconstructivism in mathematics education

The purpose of this article is to draw the attention of mathematics education researchers to a relatively new semantic theory called inferentialism, as developed by the philosopher Robert Brandom. Inferentialism is a semantic theory which explains concept formation in terms of the inferences individuals make in the context of an intersubjective practice of acknowledging, attributing, and challenging one another’s commitments. The article argues that inferentialism can help to overcome certain problems that have plagued the various forms of constructivism, and socioconstructivism in particular. Despite the range of socioconstructivist positions on offer, there is reason to think that versions of these problems will continue to haunt socioconstructivism. The problems are that socioconstructivists (i) have not come to a satisfactory resolution of the social-individual dichotomy, (ii) are still threatened by relativism, and (iii) have been vague in their characterization of what construction is. We first present these problems; then we introduce inferentialism, and finally we show how inferentialism can help to overcome the problems. We argue that inferentialism (i) contains a powerful conception of norms that can overcome the social-individual dichotomy, (ii) draws attention to the reality that constrains our inferences, and (iii) develops a clearer conception of learning in terms of the mastering of webs of reasons. Inferentialism therefore represents a powerful alternative theoretical framework to socioconstructivism