In volume fluorescence microscopy, refractive index matching is essential to minimize aberrations. There are, however, common imaging scenarios where a refractive index mismatch (RIM) between immersion and a sample medium cannot be avoided. This RIM leads to an axial deformation in the acquired image data. Over the years, different axial scaling factors have been proposed to correct for this deformation. While some reports have suggested a depth-dependent axial deformation, so far none of the scaling theories has accounted for a depth-dependent, non-linear scaling. Here, we derive an analytical theory based on determining the leading constructive interference band in the objective lens pupil under RIM. We then use this to calculate a depth-dependent re-scaling factor as a function of the numerical aperture (NA), the refractive indices n₁ and n₂, and the wavelength λ. We compare our theoretical results with wave-optics calculations and experimental results obtained using a measurement scheme for different values of NA and RIM. As a benchmark, we recorded multiple datasets in different RIM conditions, and corrected these using our depth-dependent axial scaling theory. Finally, we present an online web applet that visualizes the depth-dependent axial re-scaling for specific optical setups. In addition, we provide software that will help microscopists to correctly re-scale the axial dimension in their imaging data when working under RIM.

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Cryogenic electron tomography (cryo-ET) combined with sub-tomogram averaging, allows in-situ visualization and structure determination of macromolecular complexes at sub-nanometre resolution. Cryogenic focused ion beam (cryo-FIB) micromachining is used to prepare a thin lamella-shaped sample out of a frozen-hydrated cell for cryo-ET imaging, but standard cryo-FIB fabrication is blind to the precise location of the structure or proteins of interest. Fluorescence-guided focused ion beam (FIB) milling at target locations requires multiple sample transfers prone to contamination, and relocation and registration accuracy is often insufficient for 3D targeting. Here, we present in-situ fluorescence microscopy-guided FIB fabrication of a frozen-hydrated lamella to address this problem: we built a coincident 3-beam cryogenic correlative microscope by retrofitting a compact cryogenic microcooler, custom positioning stage, and an inverted widefield fluorescence microscope (FM) on an existing focused ion-beam scanning electron microscope (FIB-SEM). We show FM controlled targeting at every milling step in the lamella fabrication process, validated with transmission electron microscope (TEM) tomogram reconstructions of the target regions. The ability to check the lamella during and after the milling process results in a higher success rate in the fabrication process and will increase the throughput of fabrication for lamellae suitable for high-resolution imaging.

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Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.

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The influence of geometry on the local and global packing of particles is important to many fundamental and applied research themes, such as the structure and stability of liquids, crystals and glasses. Here we show by experiments and simulations that a binary mixture of hard-sphere-like nanoparticles crystallizing into a MgZn₂ Laves phase in bulk spontaneously forms icosahedral clusters in slowly drying droplets. Using advanced electron tomography, we are able to obtain the real-space coordinates of all the spheres in the icosahedral clusters of up to about 10,000 particles. The local structure of 70–80% of the particles became similar to that of the MgCu₂ Laves phase. These observations are important for photonic applications. In addition, we observed in simulations that the icosahedral clusters nucleated away from the spherical boundary, which is distinctly different from that of the single species clusters. Our findings open the way for particle-level studies of nucleation and growth of icosahedral clusters, and of binary crystallization.

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Assembling binary mixtures of nanoparticles into crystals, gives rise to collective properties depending on the crystal structure and the individual properties of both species. However, quantitative 3D real-space analysis of binary colloidal crystals with a thickness of more than 10 layers of particles has rarely been performed. Here we demonstrate that an excess of one species in the binary nanoparticle mixture suppresses the formation of icosahedral order in the self-assembly in droplets, allowing the study of bulk-like binary crystal structures with a spherical morphology also called supraparticles. As example of the approach, we show single-particle level analysis of over 50 layers of Laves phase binary crystals of hard-sphere-like nanoparticles using electron tomography. We observe a crystalline lattice composed of a random mixture of the Laves phases. The number ratio of the binary species in the crystal lattice matches that of a perfect Laves crystal. Our methodology can be applied to study the structure of a broad range of binary crystals, giving insights into the structure formation mechanisms and structure-property relations of nanomaterials.

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Multiple samples are required to monitor and optimize the quality and reliability of quantitative measurements of stimulated emission depletion (STED) and confocal microscopes. Here, we present a single sample to calibrate these microscopes, align their laser beams and measure their point spread function (PSF) in 3D. The sample is composed of a refractive index matched colloidal crystal of silica beads with fluorescent and gold cores. The microscopes can be calibrated in three dimensions using the periodicity of the crystal; the alignment of the laser beams can be checked using the reflection of the gold cores; and the PSF can be measured at multiple positions and depths using the fluorescent cores. It is demonstrated how this sample can be used to visualize and improve the quality of STED and confocal microscopy images. The sample is adjustable to meet the requirements of different NA objectives and microscopy techniques and additionally can be used to evaluate refractive index mismatches as a function of depth quantitatively.

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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.

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Self-assembly of nanoparticles (NPs) inside drying emulsion droplets provides a general strategy for hierarchical structuring of matter at different length scales. The local orientation of neighboring crystalline NPs can be crucial to optimize for instance the optical and electronic properties of the self-assembled superstructures. By integrating experiments and computer simulations, we demonstrate that the orientational correlations of cubic NPs inside drying emulsion droplets are significantly determined by their flat faces. We analyze the rich interplay of positional and orientational order as the particle shape changes from a sharp cube to a rounded cube. Sharp cubes strongly align to form simple-cubic superstructures whereas rounded cubes assemble into icosahedral clusters with additionally strong local orientational correlations. This demonstrates that the interplay between packing, confinement and shape can be utilized to develop new materials with novel properties.@en

Confocal microscopy is widely used for three-dimensional (3D) sample reconstructions. Arguably, the most significant challenge in such reconstructions is posed by the resolution along the optical axis being significantly lower than in the lateral directions. In addition, the imaging rate is lower along the optical axis in most confocal architectures, prohibiting reliable 3D reconstruction of dynamic samples. Here, we demonstrate a very simple, cheap, and generic method of multiangle microscopy, allowing high-resolution high-rate confocal slice collection to be carried out with capillary-contained colloidal samples in a wide range of slice orientations. This method, realizable with any common confocal architecture and recently implemented with macroscopic specimens enclosed in rotatable cylindrical capillaries, allows 3D reconstructions of colloidal structures to be verified by direct experiments and provides a solid testing ground for complex reconstruction algorithms. In this paper, we focus on the implementation of this method for dense nonrotatable colloidal samples, contained in complex-shaped capillaries. Additionally, we discuss strategies to minimize potential pitfalls of this method, such as the artificial appearance of chain-like particle structures.

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Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here, we uncover a regime in which solute gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, which scales with interparticle distance as F∼1/r2. Our results show that the dissolution process is diffusion rather than reaction rate limited, and the theoretical model captures the dependence of the interactions on droplet size and solute concentration, using a single fit parameter, l=16±3nm, which corresponds to the length scale of a swollen micelle. Our results shed light on the out-of-equilibrium behavior of particles with surface reactivity.

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We present the synthesis of monodisperse cone-shaped silica colloids and their fluorescent labeling. Rod-like silica colloids prepared by ammonia-catalyzed hydrolysis and condensation of tetraethyl orthosilicate in water droplets containing polyvinylpyrrolidone cross-linked by citrate ions in pentanol were found to transform into cone-shaped particles upon mild etching by NaOH in water. The diameter and length of the resulting particles were determined by those of the initial rod-like silica colloids. The mechanism responsible for the cone-shape involves silica etching taking place with a varying rate along the length of the particle. Our experiments thus also lead to new insights into the variation of the local particle structure and composition. These are found to vary gradually along the length of the rod, as a result of the way the rod grows out of a water droplet that keeps itself attached to the flat end of the bullet-shaped particles. Subtle differences in composition and structure could also be resolved by high-resolution stimulated emission depletion confocal microscopy on fluorescently labeled particles. The incorporation of a fluorescent dye chemically attached to an amine-based silane coupling agent resulted in a distribution of fluorophores mainly on the outside of the rod-shaped particles. In contrast, incorporation of the silane coupling agent alone resulted in a homogeneous distribution. Additionally, we show that etching rods, where a silane coupling agent alone was incorporated and subsequently coupled to a fluorescent dye, resulted in fluorescent silica cones, the orientation of which can be discerned using super-resolution confocal microscopy.

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We describe a facile method to synthesize sterically stabilized monodisperse fluorescent poly(methyl methacrylate) (PMMA) colloids in the polar solvent mixture water/methanol with either a core-shell or a homogeneously cross-linked structure by dispersion polymerization. The particles were sterically stabilized by the polymer poly(vinylpyrrolidone) (PVP). The morphology of the particles was controlled by varying the moment at which the gradual addition of cross-linker and dye was started. The absence of these extra agents at a time when the particle nuclei formed reduced the negative effects on this important process to a minimum and produced a core-shell structure, whereas an essentially homogeneously cross-linked fluorescent polymer colloid structure could be obtained by reducing the starting time of the addition of dye and cross-linker to zero. Three different dyes were chemically incorporated into the polymer network. Such dyes are important for the use of the particles in confocal scanning laser microscopy studies aimed at characterizing concentrated dispersions quantitatively in real space. A series of PMMA particles with different sizes were obtained through the variation of the weight ratio of solvents and the content of cross-linker. Furthermore, the swelling properties of the cross-linked PMMA particles in a good solvent (tetrahydrofuran) were investigated. The particles were stable in polar solvents (water and formamide) but could also successfully be transferred to apolar solvents such as decahydronaphthalene (decalin). The PVP stabilizer also allowed the particles to be permanently bonded in flexible strings by the application of an external electric field.

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