Multi-angle holographic characterization of individual fractal aggregates

Holographic particle characterization uses quantitative analysis of holographic microscopy data to precisely and rapidly measure the diameter and refractive index of individual colloidal spheres in their native media. When this technique is applied to inhomogeneous or aspherical particles, the measured diameter and refractive index represent properties of an effective sphere enclosing each particle. Effective-sphere analysis has been applied successfully to populations of fractal aggregates, yielding an overall fractal dimension for the population as a whole. Here, we demonstrate that holographic characterization also can measure the fractal dimensions of an individual fractal cluster by probing how its effective diameter and refractive index change as it undergoes rotational diffusion. This procedure probes the structure of a cluster from multiple angles and thus constitutes a form of tomography. Here we demonstrate and validate this effective-sphere interpretation of aspherical particles' holograms through experimental studies on aggregates of silica nanoparticles grown under a range of conditions.

Label-free viability assay using in-line holographic video microscopy

Total holographic characterization (THC) is presented here as an efficient, automated, label-free method of accurately identifying cell viability. THC is a single-particle characterization technology that determines the size and index of refraction of individual particles using the Lorenz-Mie theory of light scattering. Although assessment of cell viability is a challenge in many applications, including biologics manufacturing, traditional approaches often include unreliable labeling with dyes and/or time consuming methods of manually counting cells. In this work we measured the viability of Saccharomyces cerevisiae yeast in the presence of various concentrations of isopropanol as a function of time. All THC measurements were performed in the native environment of the sample with no dilution or addition of labels. Holographic measurements were made with an in-line holographic microscope using a 40[Formula: see text] objective lens with plane wave illumination. We compared our results with THC to manual counting of living and dead cells as distinguished with trypan blue dye. Our findings demonstrate that THC can effectively distinguish living and dead yeast cells by the index of refraction of individual cells.

Thermodynamic Signatures of Structural Transitions and Dissociation of Charged Colloidal Clusters: A Parallel Tempering Monte Carlo Study

Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and “beaded-necklace” shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy “beaded-necklace” motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at T=0.20 for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system.

CATCH: Characterizing and Tracking Colloids Holographically Using Deep Neural Networks

In-line holographic microscopy provides an unparalleled wealth of information about the properties of colloidal dispersions. Analyzing one colloidal particle's hologram with the Lorenz-Mie theory of light scattering yields the particle's three-dimensional position with nanometer precision while simultaneously reporting its size and refractive index with part-per-thousand resolution. Analyzing a few thousand holograms in this way provides a comprehensive picture of the particles that make up a dispersion, even for complex multicomponent systems. All of this valuable information comes at the cost of three computationally expensive steps: (1) identifying and localizing features of interest within recorded holograms, (2) estimating each particle's properties based on characteristics of the associated features, and finally (3) optimizing those estimates through pixel-by-pixel fits to a generative model. Here, we demonstrate an end-to-end implementation that is based entirely on machine-learning techniques. Characterizing and Tracking Colloids Holographically (CATCH) with deep convolutional neural networks is fast enough for real-time applications and otherwise outperforms conventional analytical algorithms, particularly for heterogeneous and crowded samples. We demonstrate this system's capabilities with experiments on free-flowing and holographically trapped colloidal spheres.

The role of the medium in the effective-sphere interpretation of holographic particle characterization data

The in-line hologram of a micrometer-scale colloidal sphere can be analyzed with the Lorenz-Mie theory of light scattering to obtain precise measurements of the sphere's diameter and refractive index. The same technique also can be used to characterize porous and irregularly shaped colloidal particles provided that the extracted parameters are interpreted with effective-medium theory to represent the properties of an equivalent effective sphere. Here, we demonstrate that the effective-sphere model consistently accounts for changes in the refractive index of the medium as it fills the pores of porous particles and therefore yields quantitative information about such particles' structure and composition. In addition to the sample-averaged porosity, holographic perfusion porosimetry gauges the polydispersity of the porosity. We demonstrate these capabilities through measurements on mesoporous spheres, fractal protein aggregates and irregular nanoparticle agglomerates, all of which are noteworthy for their industrial significance.

Flexible wide-field high-resolution scanning camera for continuous-wave acoustic holography

We present a system for measuring the amplitude and phase profiles of the pressure field of a harmonic acoustic wave with the goal of reconstructing the volumetric sound field. Unlike optical holograms that cannot be reconstructed exactly because of the inverse problem, acoustic holograms are completely specified in the recording plane. We demonstrate volumetric reconstructions of simple arrangements of objects using the Rayleigh-Sommerfeld diffraction integral and introduce a technique to analyze the dynamic properties of insonated objects.

Real-time particle pollution sensing using machine learning

Particle pollution is a global health challenge that is linked to around three million premature deaths per year. There is therefore great interest in the development of sensors capable of precisely quantifying both the number and type of particles. Here, we demonstrate an approach that leverages machine learning in order to identify particulates directly from their scattering patterns. We show the capability for producing a 2D sample map of spherical particles present on a coverslip, and also demonstrate real-time identification of a range of particles including those from diesel combustion.

Machine-learning techniques for fast and accurate feature localization in holograms of colloidal particles

Holograms of colloidal particles can be analyzed with the Lorenz-Mie theory of light scattering to measure individual particles' three-dimensional positions with nanometer precision while simultaneously estimating their sizes and refractive indexes. Extracting this wealth of information begins by detecting and localizing features of interest within individual holograms. Conventionally approached with heuristic algorithms, this image analysis problem can be solved faster and more generally with machine-learning techniques. We demonstrate that two popular machine-learning algorithms, cascade classifiers and deep convolutional neural networks (CNN), can solve the feature-localization problem orders of magnitude faster than current state-of-the-art techniques. Our CNN implementation localizes holographic features precisely enough to bootstrap more detailed analyses based on the Lorenz-Mie theory of light scattering. The wavelet-based Haar cascade proves to be less precise, but is so computationally efficient that it creates new opportunities for applications that emphasize speed and low cost. We demonstrate its use as a real-time targeting system for holographic optical trapping.

Temperature- and field-induced structural transitions in magnetic colloidal clusters

Magnetic colloidal clusters can form chain, ring, and more compact structures depending on their size. In the present investigation we examine the combined effects of temperature and external magnetic field on these configurations by means of extensive Monte Carlo simulations and a dedicated analysis based on inherent structures. Various thermodynamical, geometric, and magnetic properties are calculated and altogether provide evidence for possibly multiple structural transitions at low external magnetic field. Temperature effects are found to overcome the ordering effect of the external field, the melted stated being associated with low magnetization and a greater compactness. Tentative phase diagrams are proposed for selected sizes.

Dimpled Polyhedral Colloids Formed by Colloidal Crystal Templating

Many approaches to the self-assembly of interesting microstructures rely on particles with engineered shapes. We create dimpled solid particles by molding oil droplets in the interstices of a close-packed colloidal crystal and polymerizing them in situ, resulting in particles containing multiple spherical dimples arranged with various polyhedral symmetries. Monodisperse micrometer-sized droplets of 3-methacryloxypropyltrimethoxysilane (TPM) are mixed with an excess of polystyrene (PS) microspheres (2.58 μm) and allowed to sediment, forming colloidal crystals with TPM droplets inside their interstitial sites. When these crystals are compressed by partial drying, the trapped droplets wet the multiple microspheres surrounding them, forming a three-dimensional capillary bridge with the symmetry of the interstitial spaces, and then mild heating triggers polymerization in situ. Depending on the initial particle volume fraction and extent of drying, a high yield of dimpled particles having different symmetries including tetrahedra and cubes is obtained. The fractional yield of different shapes varies with the size ratio of the TPM droplets and the PS microspheres forming the template lattice. Sedimentation velocity fractionation methods are effective for enrichment of specific symmetries but not complete purification. Our approach for forming polyhedral particles should be readily scalable to larger samples and smaller sized particles if desired.

Bayesian approach to analyzing holograms of colloidal particles

We demonstrate a Bayesian approach to tracking and characterizing colloidal particles from in-line digital holograms. We model the formation of the hologram using Lorenz-Mie theory. We then use a tempered Markov-chain Monte Carlo method to sample the posterior probability distributions of the model parameters: particle position, size, and refractive index. Compared to least-squares fitting, our approach allows us to more easily incorporate prior information about the parameters and to obtain more accurate uncertainties, which are critical for both particle tracking and characterization experiments. Our approach also eliminates the need to supply accurate initial guesses for the parameters, so it requires little tuning.

Tracking E. coli runs and tumbles with scattering solutions and digital holographic microscopy

We use in-line digital holographic microscopy to image freely swimming E. coli. We show that fitting a light scattering model to E. coli holograms can yield quantitative information about the bacterium's body rotation and tumbles, offering a precise way to track fine details of bacterial motility. We are able to extract the cell's three-dimensional (3D) position and orientation and recover behavior such as body angle rotation during runs, tumbles, and pole reversal. Our technique is label-free and capable of frame rates limited only by the camera.

Controlling and tracking of colloidal nanostructures through two-photon fluorescence

Multiphoton absorbing dye-coated trapped spherical bead at the focal plane of femtosecond optical tweezers shows nonlinear optical (NLO) phenomena. One such NLO process of two-photon fluorescence (TPF) has been used for the background-free imaging of a femtosecond laser-trapping event. Due to the high peak powers of femtosecond laser pulses with low average powers, it is possible to not only trap single nanospheres, but encourage optically directed self-assembly. The TPF signatures of trapped particles show evidence of such a directed self-assembly process which, in turn, can provide information about the structural dynamics during the process of cluster formation. We are able to trap and characterize structure and dynamics in 3D until pentamer formation from the decay characteristics of trapping at the focal plane.

Reversible Adsorption Kinetics of Near Surface Dimer Colloids

We investigate the effect of shape on reversible adsorption kinetics using colloidal polystyrene dimers near a solid glass surface as a model system. The interaction between colloid and wall is tuned using electrostatic, depletion, and gravity forces to produce a double-well potential. The dwell time in each of the potential wells is measured from long duration particle trajectories. The height of each monomer relative to the glass surface is measured to a resolution of <20 nm by in-line holographic microscopy. The measured transition probability distributions are used in kinetic equations to describe the flux of particles to and from the surface. The dimers are compared to independent isolated monomers to determine the effects of shape on adsorption equilibria and kinetics. To elucidate these differences, we consider both mass and surface coverage and two definitions of surface coverage. The results show that dimers with single coverage produce slower adsorption, lower surface coverage, and higher mass coverage in comparison to those of monomers, while dimers with double coverage adsorb faster and result in higher surface coverage.

Dynamical properties of two- and three-dimensional colloidal clusters of six particles

Colloidal clusters are important systems for studying self-assembly. Clusters of six colloidal particles attracting each other via short-ranged interactions have been recently studied both theoretically and experimentally. Here we present a computer modelling study of the thermodynamics and dynamics of these clusters using a short-ranged Morse potential in two and three dimensions. We combine energy landscape methods with comprehensive sampling, both of configurations using Markov chain Monte Carlo and also of trajectories using Langevin molecular dynamics propagation. We show that the interaction energies between the particles are probably greater than previously assumed. The rates predicted by transition state theory using harmonic vibrational densities of states are off by four orders of magnitude, since the effects of viscosity are not accounted for. In contrast, sampling short trajectories using an appropriate friction constant and discrete relaxation path sampling produces reasonable agreement with the experimental rates.

Tunable depletion potentials driven by shape variation of surfactant micelles

Depletion interaction potentials between micron-sized colloidal particles are induced by nanometer-scale surfactant micelles composed of hexaethylene glycol monododecyl ether (C_{12}E_{6}), and they are measured by video microscopy. The strength and range of the depletion interaction is revealed to arise from variations in shape anisotropy of the surfactant micelles. This shape anisotropy increases with increasing sample temperature. By fitting the colloidal interaction potentials to theoretical models, we extract micelle length and shape anisotropy as a function of temperature. This work introduces shape anisotropy tuning as a means to control interparticle interactions in colloidal suspensions, and it shows how the interparticle depletion potentials of micron-scale objects can be employed to probe the shape and size of surrounding macromolecules at the nanoscale.

A Detailed Study on the Low-Energy Structures of Charged Colloidal Clusters

The target of this investigation is the systematic characterization of the low-energy structures of charged colloidal clusters that may be important to understand the self-assembling process of biomolecules. The aggregation of charged colloidal particles is governed by the attractive short-ranged Morse potential and the Yukawa repulsive tail to describe the long-range charge effect. A global optimization strategy, based on our own evolutionary algorithm, was adopted to discover the low-energy structures of colloidal clusters composed of up to 20 particles. A detailed analysis of the low-energy structures involving charged particles shows that the appearance of the Bernal spiral as the most stable motif occurs, first, at N = 6, but it is favored for larger clusters (N ≥ 13); for 6 ≤ N ≤ 12, there is a competition between the spiral (which is favored for higher charges) and more spherical-like structures. Finally, we study binary clusters composed by two sets of differently charged colloidal particles. Although a great diversity of low-energy structures is observed (especially for aggregates with one of the components in excess), the global minimum is disputed by three structural motifs depending on the composition of the cluster and, in some cases, on the range of the Morse potential.

Segregation of "isotope" particles within colloidal molecules

Clusters of spherical particles are called "colloidal molecules" because they adopt structures that resemble those of true molecules. In this analogy, the particles are the atoms, the attractive interactions between them are bonds, and the different structures that appear in equilibrium are isomers. We take this analogy a step further by doping colloidal molecules with colloidal "isotopes," particles that have the same size but different bonding energies from the other particles in the system. Our molecules are two-dimensional clusters consisting of polystyrene and silica microspheres held together by depletion interactions. Using a combination of optical microscopy and particle tracking, we examine an ensemble of 4- and 5-particle molecules at different isotope ratios. We find that the isotopes tend to segregate to particular positions in the various isomers. We explain these findings using a statistical mechanical model that accounts for the rotational entropy of the isomers and the different interaction potentials between the different types of particles. The model shows how to optimize the yield of any particular isomer, so as to put the isotopes in desired locations. Our experiments and models show that even in systems of particles with isotropic interactions, the structures of self-assembled molecules can in principle be controlled to a surprisingly high extent.

Holographic Characterization of Protein Aggregates

We demonstrate how holographic video microscopy can be used to detect, count, and characterize individual micrometer-scale protein aggregates as they flow down a microfluidic channel in their native buffer. Holographic characterization directly measures the radius and refractive index of subvisible protein aggregates and offers insights into their morphologies. The measurement proceeds fast enough to build up population averages for time-resolved studies and lends itself to tracking trends in protein aggregation arising from changing environmental factors. Information on individual particle's refractive indexes can be used to differentiate protein aggregates from such contaminants as silicone droplets. These capabilities are demonstrated through measurements on samples of bovine pancreas insulin aggregated through centrifugation and of bovine serum albumin aggregated by complexation with a polyelectrolyte. Differentiation is demonstrated with samples that have been spiked with separately characterized silicone spheres. Holographic characterization measurements are compared with results obtained with microflow imaging and dynamic light scattering.

Self-assembly of colloidal magnetic particles: energy landscapes and structural transitions

The self-assembly of colloidal magnetic particles is of particular interest for the rich variety of structures it produces and the potential for these systems to be reconfigurable.

Structure and dynamics of model colloidal clusters with short-range attractions

We examine the structure and dynamics of small isolated N-particle clusters interacting via short-ranged Morse potentials. "Ideally prepared ensembles" obtained via exact enumeration studies of sticky hard-sphere packings serve as reference states allowing us to identify key statistical-geometrical properties and to quantitatively characterize how nonequilibrium ensembles prepared by thermal quenches at different rates T[over ̇] differ from their equilibrium counterparts. Studies of equilibrium dynamics show nontrivial temperature dependence: nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures. Our results should be useful for extending recent experimental studies of small colloidal clusters to examine both equilibrium relaxation dynamics at fixed T and a variety of nonequilibrium phenomena.

Re-entrant solidification in polymer-colloid mixtures as a consequence of competing entropic and enthalpic attractions

In polymer-colloid mixtures, non-adsorbing polymers dispersed with much larger colloids provide a universal yet specific entropic attraction between the colloids. Such so-called depletion interaction arises from an osmotic-pressure imbalance caused by the polymers and is considered to be independent of temperature. Here we show that, for the most commonly used polymer-colloid depletion systems, the polymer undergoes a crossover from non-adsorbing to adsorbing and that, consequently, the effective colloidal interactions depend on temperature. We also find that a combination of the enthalpic (polymer bridging) and entropic (polymer exclusion) interactions, both attractive, leads to a re-entrant regime where the colloids are dispersed and form solids both on heating and on cooling. We provide a simple model to explain the observed transitions and to fill the theoretical gap at the polymer-adsorption crossover. Our findings open possibilities for colloidal self-assembly, the formation of colloidal crystals and glasses, and the behaviour of temperature-controlled viscoelastic materials.

Exploring energy landscapes: from molecular to mesoscopic systems

We review a comprehensive computational framework to survey the potential energy landscape for systems composed of rigid or partially rigid molecules. Illustrative case studies relevant to a wide range of molecular clusters and soft and condensed matter systems are discussed.

Random-subset fitting of digital holograms for fast three-dimensional particle tracking [invited]

Fitting scattering solutions to time series of digital holograms is a precise way to measure three-dimensional dynamics of microscale objects such as colloidal particles. However, this inverse-problem approach is computationally expensive. We show that the computational time can be reduced by an order of magnitude or more by fitting to a random subset of the pixels in a hologram. We demonstrate our algorithm on experimentally measured holograms of micrometer-scale colloidal particles, and we show that 20-fold increases in speed, relative to fitting full frames, can be attained while introducing errors in the particle positions of 10 nm or less. The method is straightforward to implement and works for any scattering model. It also enables a parallelization strategy wherein random-subset fitting is used to quickly determine initial guesses that are subsequently used to fit full frames in parallel. This approach may prove particularly useful for studying rare events, such as nucleation, that can only be captured with high frame rates over long times.

Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters

We measure all nonzero elements of the three-dimensional diffusion tensor D for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres, for which no analytical calculations of the diffusion tensor exist. We observe anisotropic rotational and translational diffusion arising from the asymmetries of the clusters. In the case of the three-particle triangular cluster, we also detect a small but statistically significant difference in the rotational diffusion about the two in-plane axes. We attribute this difference to weak breaking of threefold rotational symmetry due to a small amount of particle polydispersity. Our experimental measurements agree well with numerical calculations and show how diffusion constants can be measured under conditions relevant to colloidal self-assembly, where theoretical and even numerical prediction is difficult.