Diffusion, phase behavior, and gelation in a two-dimensional layer of colloids in osmotic equilibrium with a polymer reservoir.

The addition of enough non-adsorbing polymers to an otherwise stable colloidal suspension gives rise to a variety of phase behaviors and kinetic arrest due to the depletion attraction induced between the colloids by the polymers. We report a study of these phenomena in a two-dimensional layer of colloids. The three-dimensional phenomenology of crystal-fluid coexistence is reproduced, but gelation takes a novel form, in which the strands in the gel structure are locally crystalline. We compare our findings with a previous simulation and theory and find substantial agreement.

Dynamical analysis of bacteria in microscopy movies.

Recent advances in microscopy, computing power and image processing have enabled the analysis of ever larger datasets of movies of microorganisms to study their behaviour. However, techniques for analysing the dynamics of individual cells from such datasets are not yet widely available in the public domain. We recently demonstrated significant phenotypic heterogeneity in the adhesion of Escherichia coli bacteria to glass surfaces using a new method for the high-throughput analysis of video microscopy data. Here, we present an in-depth analysis of this method and its limitations, and make public our algorithms for following the positions and orientations of individual rod-shaped bacteria from time-series of 2D images to reconstruct their trajectories and characterise their dynamics. We demonstrate in detail how to use these algorithms to identify different types of adhesive dynamics within a clonal population of bacteria sedimenting onto a surface. The effects of measurement errors in cell positions and of limited trajectory durations on our results are discussed.

Hook length of the bacterial flagellum is optimized for maximal stability of the flagellar bundle.

Most bacteria swim in liquid environments by rotating one or several flagella. The long external filament of the flagellum is connected to a membrane-embedded basal body by a flexible universal joint, the hook, which allows the transmission of motor torque to the filament. The length of the hook is controlled on a nanometer scale by a sophisticated molecular ruler mechanism. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook-length variants of Salmonella enterica. Measurements of plate-assay motility, single-cell swimming speed, and directional persistence in quasi-2D and population-averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild-type hook length. We conclude that too-short hooks may be too stiff to function as a junction and too-long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook-length control mechanism is therefore a prime example of how bacteria evolved elegant but robust mechanisms to maximize their fitness under specific environmental constraints.

Bacteria as living patchy colloids: Phenotypic heterogeneity in surface adhesion.

Understanding and controlling the surface adhesion of pathogenic bacteria is of urgent biomedical importance. However, many aspects of this process remain unclear (for example, microscopic details of the initial adhesion and possible variations between individual cells). Using a new high-throughput method, we identify and follow many single cells within a clonal population of Escherichia coli near a glass surface. We find strong phenotypic heterogeneities: A fraction of the cells remain in the free (planktonic) state, whereas others adhere with an adhesion strength that itself exhibits phenotypic heterogeneity. We explain our observations using a patchy colloid model; cells bind with localized, adhesive patches, and the strength of adhesion is determined by the number of patches: Nonadherers have no patches, weak adherers bind with a single patch only, and strong adherers bind via a single or multiple patches. We discuss possible implications of our results for controlling bacterial adhesion in biomedical and other applications.

Swimming in a crystal.

We study catalytic Janus particles and Escherichia coli bacteria swimming in a two-dimensional colloidal crystal. The Janus particles orbit individual colloids and hop between colloids stochastically, with a hopping rate that varies inversely with fuel (hydrogen peroxide) concentration. At high fuel concentration, these orbits are stable for 100s of revolutions, and the orbital speed oscillates periodically as a result of hydrodynamic, and possibly also phoretic, interactions between the swimmer and the six neighbouring colloids. Motile E. coli bacteria behave very differently in the same colloidal crystal: their circular orbits on plain glass are rectified into long, straight runs, because the bacteria are unable to turn corners inside the crystal.

Escherichia coli as a model active colloid: A practical introduction.

The flagellated bacterium Escherichia coli is increasingly used experimentally as a self-propelled swimmer. To obtain meaningful, quantitative results that are comparable between different laboratories, reproducible protocols are needed to control, 'tune' and monitor the swimming behaviour of these motile cells. We critically review the knowledge needed to do so, explain methods for characterising the colloidal and motile properties of E. coli cells, and propose a protocol for keeping them swimming at constant speed at finite bulk concentrations. In the process of establishing this protocol, we use motility as a high-throughput probe of aspects of cellular physiology via the coupling between swimming speed and the proton motive force.

Self-assembly of patchy colloidal dumbbells.

We employ Monte Carlo simulations to investigate the self-assembly of patchy colloidal dumbbells interacting via a modified Kern-Frenkel potential by probing the system concentration and dumbbell shape. We consider dumbbells consisting of one attractive sphere with diameter σ1 and one repulsive sphere with diameter σ2 and center-to-center distance d between the spheres. For three different size ratios, we study the self-assembled structures for different separations l = 2d/(σ1 + σ2) between the two spheres. In particular, we focus on structures that can be assembled from the homogeneous fluid, as these might be of interest in experiments. We use cluster order parameters to classify the shape of the formed structures. When the size of the spheres is almost equal, q = σ2/σ1 = 1.035, we find that, upon increasing l, spherical micelles are transformed to elongated micelles and finally to vesicles and bilayers. For size ratio q = 1.25, we observe a continuously tunable transition from spherical to elongated micelles upon increasing the sphere separation. For size ratio q = 0.95, we find bilayers and vesicles, plus faceted polyhedra and liquid droplets. Our results identify key parameters to create colloidal vesicles with attractive dumbbells in experiments.

Self-assembly of "Mickey Mouse" shaped colloids into tube-like structures: experiments and simulations.

The self-assembly of anisotropic patchy particles with a triangular shape was studied by experiments and computer simulations. The colloidal particles were synthesized in a two-step seeded emulsion polymerization process, and consist of a central smooth lobe connected to two rough lobes at an angle of ∼90°, resembling the shape of a "Mickey Mouse" head. Due to the difference in overlap volume, adding an appropriate depletant induces an attractive interaction between the smooth lobes of the colloids only, while the two rough lobes act as steric constraints. The essentially planar geometry of the Mickey Mouse particles is a first geometric deviation of dumbbell shaped patchy particles. This new geometry enables the formation of one-dimensional tube-like structures rather than spherical, essentially zero-dimensional micelles. At sufficiently strong attractions, we indeed find tube-like structures with the sticky lobes at the core and the non-sticky lobes pointing out as steric constraints that limit the growth to one direction, providing the tubes with a well-defined diameter but variable length both in experiments and simulations. In the simulations, we found that the internal structure of the tubular fragments could either be straight or twisted into so-called Bernal spirals.

Equilibrium phases of one-patch colloids with short-range attractions.

Inspired by experimental studies of short-ranged attractive patchy particles, we study with computer simulations the phase behavior and the crystalline structures of one-patch colloids with an interaction range equal to 5% of the particle diameter. In particular, we study the effects of the patch surface coverage fraction, defined as the ratio between the attractive and the total surface of a particle. Using free-energy calculations and thermodynamic integration schemes, we evaluate the equilibrium phase diagrams for particles with patch coverage fractions of 30%, 50% and 60%. For a 60% surface coverage fraction, we observe stable lamellar crystals consisting of stacked bilayers that directly coexist with a low density fluid. Inside the coexistence region, we observe the formation of lamellar structures also in direct NVT simulations, indicating that the barrier of formation is low and experimental realization is feasible. For sufficiently strong interactions, these structures spontaneously assemble from the fluid in simulations, suggesting that they might also easily form in experimental systems. In the Janus case, i.e. at 50% surface coverage fraction, no lamellar structures are formed, and the stable crystals are similar to those that have been found previously for a longer interaction range (i.e. 20% of the particle diameter). At 30% coverage fraction, we identify novel 'open' crystal structures with large unit cells of up to 14 particles that are stable in the strong interaction limit.

Cooperative polymerization of one-patch colloids.

We numerically investigate cooperative polymerization in an off-lattice model based on a pairwise additive potential using particles with a single attractive patch that covers 30% of the colloid surface. Upon cooling, these particles self-assemble into small clusters which, below a density-dependent temperature, spontaneously reorganize into long straight tubes. We evaluate the partition functions of clusters of all sizes to provide an accurate description of the chemical reaction constants governing this process. Our calculations show that, for intermediate sizes, the partition functions retain contributions from two different structures, differing in both energy and entropy. We illustrate the microscopic mechanism behind the complex polymerization process in this system and provide a detailed evaluation of its thermodynamics.

Phase diagram of one-patch colloids forming tubes and lamellae.

We numerically calculate the equilibrium phase diagram of one-patch particles with 30% patch coverage. It has been previously shown that in the fluid phase these particles organize into extremely long tubelike aggregates (G. Munaò et al. Soft Matter 2013, 9, 2652). Here, we demonstrate by means of free-energy calculations that such a disordered tube phase, despite forming spontaneously from the fluid phase below a density-dependent temperature, is always metastable against a lamellar crystal. We also show that a crystal of infinitely long packed tubes is thermodynamically stable, but only at high pressure. The full phase diagram of the model, beside the fluid phase, displays four different stable crystals. A gas-liquid critical point, and hence a liquid phase, is not detected.

Predicting crystals of Janus colloids.

We present a numerical study on the phase diagram for a simple model of Janus colloids, including ordered and disordered structures. Using a range of techniques, we generate a set of crystal structures and investigate their relative stability field in the pressure-temperature and temperature-density planes by means of free-energy calculations and thermodynamic integration schemes. We find that despite the Janus colloids' simple architecture, they form stable crystal structures with complicated bond-topologies on an underlying face-centered-cubic or hexagonal-close-packed lattice. In addition, we find a phase consisting of wrinkled bilayer sheets, competing with both the fluid and the crystal phases. We detect a metastable gas-liquid coexistence which displays a micellization-driven re-entrant behavior.

Bonding assembled colloids without loss of colloidal stability.

A facile method is demonstrated for bonding assembled colloids without loss of colloidal stability by thermal annealing. Examples include both close-packed and non-close-packed structures. The confocal microscopy image shows a cross-section of a 3D labyrinthine structure after it was made permanent. The 3D network is completely preserved after the annealing step.

Band formation in mixtures of oppositely charged colloids driven by an ac electric field.

We present experiments on pattern formation in a Brownian system of oppositely charged colloids driven by an ac electric field. Using confocal laser scanning microscopy we observe complete segregation of the two particle species into bands perpendicular to a field of sufficient strength when the frequency is in a well-defined range. Because of its Brownian nature the system spontaneously returns to the equilibrium mixture after the field is turned off. We show that band formation is linked to the time scale associated with collisions between particles moving in opposite directions.

Electrophoresis of concentrated colloidal dispersions in low-polar solvents.

We present a method to accurately measure the electrophoretic mobility of spherical colloids at high volume fractions in real space using confocal laser scanning microscopy (CLSM) and particle tracking. We show that for polymethylmethacrylate (PMMA) particles in a low-polar, density- and refractive-index-matched mixture of cyclohexylbromide and cis-decahydronaphthalene, the electrophoretic mobility decreases nonlinearly with increasing volume fraction. From the electrophoretic mobilities, we calculate the ζ-potential and the particle charge with and without correcting for volume fraction effects. For both cases, we find a decreasing particle charge as a function of volume fraction. This is in accordance with the fact that the charges originate from chemical equilibria that represent so-called weak association and/or dissociation reactions. Finally, as our methodology also provides data on particle self-diffusion in the presence of an electric field, we also analyze the diffusion at different volume fractions and identify a nonlinear decreasing trend for increasing volume fraction.