Person:

Perry, Rebecca Wood

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.

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.

Digital holographic microscopy is a fast three-dimensional (3D) imaging tool with many applications in soft matter physics. Recent studies have shown that electromagnetic scattering solutions can be fit to digital holograms to obtain the 3D positions of isolated colloidal spheres with nanometer precision and millisecond temporal resolution. Here we describe the results of new techniques that extend the range of systems that can be studied with fitting. We show that an exact multisphere superposition scattering solution can fit holograms of colloidal clusters containing up to six spheres. We also introduce an approximate and computationally simpler solution, Mie superposition, that is valid for multiple spheres spaced several wavelengths or more from one another. We show that this method can be used to analyze holograms of several spheres on an emulsion droplet, and we give a quantitative criterion for assessing its validity.

The energetics and assembly pathways of small clusters may yield insights into processes occurring at the earliest stages of nucleation. We use a model system consisting of micrometer-sized, spherical colloidal particles to study the structure and dynamics of small clusters, where the number of particles is small (N ≤ 10). The particles interact through a short-range depletion attraction with a depth of a few kBT. We describe two methods to form colloidal clusters, one based on isolating the particles in microwells and another based on directly assembling clusters in the gas phase using optical tweezers. We use the first technique to obtain ensemble-averaged probabilities of cluster structures as a function of N. These experiments show that clusters with symmetries compatible with crystalline order are rarely formed under equilibrium conditions. We use the second technique to study the dynamics of the clusters, and in particular how they transition between free-energy minima. To monitor the clusters we use a fast three-dimensional imaging technique, digital holographic microscopy, that can resolve the positions of each particle in the cluster with 30–45 nm precision on millisecond timescales. The real-space measurements allow us to obtain estimates for the lifetimes of the energy minima and the transition states. It is not yet clear whether the observed dynamics are relevant for small nuclei, which may not have sufficient time to transition between states before other particles or clusters attach to them. However, the measurements do provide some glimpses into how systems containing a small number of particles traverse their free-energy landscape.

We study experimentally what is arguably the simplest yet nontrivial colloidal system: two-dimensional clusters of six spherical particles bound by depletion interactions. These clusters have multiple, degenerate ground states whose equilibrium distribution is determined by entropic factors, principally the symmetry. We observe the equilibrium rearrangements between ground states as well as all of the low-lying excited states. In contrast to the ground states, the excited states have soft modes and low symmetry, and their occupation probabilities depend on the size of the configuration space reached through internal degrees of freedom, as well as a single “sticky parameter” encapsulating the depth and curvature of the potential. Using a geometrical model that accounts for the entropy of the soft modes and the diffusion rates along them, we accurately reproduce the measured rearrangement rates. The success of this model, which requires no fitting parameters or measurements of the potential, shows that the free-energy landscape of colloidal systems and the dynamics it governs can be understood geometrically.