Surface tension measurement and calculation of model biomolecular condensates.

The surface tension of liquid-like protein-rich biomolecular condensates is an emerging physical principle governing the mesoscopic interior organisation of biological cells. In this study, we present a method to evaluate the surface tension of model biomolecular condensates, through straighforward sessile drop measurements of capillary lengths and condensate densities. Our approach bypasses the need for characterizing condensate viscosities, which was required in previously reported techniques. We demonstrate this method using model condensates comprising two mutants of the intrinsically disordered protein Ddx4N. Notably, we uncover a detrimental impact of increased protein net charge on the surface tension of Ddx4N condensates. Furthermore, we explore the application of Scheutjens-Fleer theory, calculating condensate surface tensions through a self-consistent mean-field framework using Flory-Huggins interaction parameters. This relatively simple theory provides semi-quantitative accuracy in predicting Ddx4N condensate surface tensions and enables the evaluation of molecular organisation at condensate surfaces. Our findings shed light on the molecular details of fluid-fluid interfaces in biomolecular condensates.

Measuring many-body distribution functions in fluids using test-particle insertion.

We derive a hierarchy of equations, which allow a general n-body distribution function to be measured by test-particle insertion of between 1 and n particles. We apply it to measure the pair and three-body distribution functions in a simple fluid using snapshots from Monte Carlo simulations in the grand canonical ensemble. The resulting distribution functions obtained from insertion methods are compared with the conventional distance-histogram method: the insertion approach is shown to overcome the drawbacks of the histogram method, offering enhanced structural resolution and a more straightforward normalization. At high particle densities, the insertion method starts breaking down, which can be delayed by utilizing the underlying hierarchical structure of the insertion method. Our method will be especially useful in characterizing the structure of inhomogeneous fluids and investigating closure approximations in liquid state theory.

Phage liquid crystalline droplets form occlusive sheaths that encapsulate and protect infectious rod-shaped bacteria.

The opportunistic pathogen Pseudomonas aeruginosa is a major cause of antibiotic-tolerant infections in humans. P. aeruginosa evades antibiotics in bacterial biofilms by up-regulating expression of a symbiotic filamentous inoviral prophage, Pf4. We investigated the mechanism of phage-mediated antibiotic tolerance using biochemical reconstitution combined with structural biology and high-resolution cellular imaging. We resolved electron cryomicroscopy atomic structures of Pf4 with and without its linear single-stranded DNA genome, and studied Pf4 assembly into liquid crystalline droplets using optical microscopy and electron cryotomography. By biochemically replicating conditions necessary for antibiotic protection, we found that phage liquid crystalline droplets form phase-separated occlusive compartments around rod-shaped bacteria leading to increased bacterial survival. Encapsulation by these compartments was observed even when inanimate colloidal rods were used to mimic rod-shaped bacteria, suggesting that shape and size complementarity profoundly influences the process. Filamentous inoviruses are pervasive across prokaryotes, and in particular, several Gram-negative bacterial pathogens including Neisseria meningitidis, Vibrio cholerae, and Salmonella enterica harbor these prophages. We propose that biophysical occlusion mediated by secreted filamentous molecules such as Pf4 may be a general strategy of bacterial survival in harsh environments.

Topology of Orientational Defects in Confined Smectic Liquid Crystals.

We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in pointlike units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.

Stabilisation of hollow colloidal TiO2 particles by partial coating with evenly distributed lobes.

Photo-catalytically active crystalline TiO2 has attracted special attention due to its relevance for renewable energy and is typically obtained by the calcination of amorphous TiO2. However, stabilising hollow colloidal TiO2 particles against aggregation during calcination without compromising their photocatalytic activity poses two conflicting demands: to be stable their surface needs to be coated, while efficient photocatalysis requires an exposed TiO2 surface. Here, this incompatibility is resolved by partially coating TiO2 shells with evenly distributed 3-trimethoxysilyl propyl methacrylate (TPM) lobes. These lobes act both as steric barriers and surface charge enhancers that efficiently stabilise the TiO2 shells against aggregation during calcination. The morphology of the TPM lobes and their coverage, and the associated particle stability during the calcination-induced TiO2 crystallization, can be controlled by the pH and the contact angle between TPM and TiO2. The crystal structure and the grain size of the coated TiO2 shells are controlled by varying the calcination temperature, which allows tuning their photocatalytic activity. Finally, the durable photocatalytic activity over many usage cycles of the coated TiO2 compared to uncoated shells is demonstrated in a simple way by measuring the photo-degradation of a fluorescent dye. Our approach offers a general strategy for stabilising colloidal materials, without compromising access to their active surfaces.

Characterization of MIPS in a suspension of repulsive active Brownian particles through dynamical features.

We study a two-dimensional system composed by Active Brownian Particles (ABPs), focusing on the onset of Motility Induced Phase Separation (MIPS), by means of molecular dynamics simulations. For a pure hard-disk system with no translational diffusion, the phase diagram would be completely determined by their density and Péclet number. In our model, two additional effects are present: translational noise and the overlap of particles; we study the effects of both in the phase space. As we show, the second effect can be mitigated if we use, instead of the standard Weeks-Chandler-Andersen potential, a stiffer potential: the pseudo-hard sphere potential. Moreover, in determining the boundary of our phase space, we explore different approaches to detect MIPS and conclude that observing dynamical features, via the non-Gaussian parameter, is more efficient than observing structural ones, such as through the local density distribution function. We also demonstrate that the Vogel-Fulcher equation successfully reproduces the decay of the diffusion as a function of density, with the exception of very high densities. Thus, in this regard, the ABP system behaves similar to a fragile glass.

Dislocation-controlled formation and kinetics of grain boundary loops in two-dimensional crystals.

The formation and kinetics of grain boundaries are closely related to the topological constraints imposed on their complex dislocation structure. Loop-shaped grain boundaries are unique structures to establish such a link because their overall topological "charge" is zero due to their null net Burgers vector. Here, we observe that a local rotational deformation of a 2D colloidal crystal with an optical vortex results in a grain boundary loop only if the product of its radius and misorientation exceeds a critical value. Above this value, the deformation is plastic and the grain boundary loop spontaneously shrinks at a rate that solely depends on this product, while otherwise, the deformation is elastically restored. We show that this elastic-to-plastic crossover is a direct consequence of the unique dislocation structure of grain boundary loops. At the critical value, the loop is structurally equivalent to the so-called "flower defect" and the shrinkage rate diverges. Our results thus reveal a general limit on the formation of grain boundary loops in 2D crystals and elucidate the central role of defects in both the onset of plasticity and the kinetics of grain boundaries.

Model-Free Measurement of the Pair Potential in Colloidal Fluids Using Optical Microscopy.

We report a straightforward, model-free approach for measuring pair potentials from particle-coordinate data, based on enforcing consistency between the pair distribution function measured separately by the distance-histogram and test-particle insertion routes. We demonstrate the method's accuracy and versatility in simulations of simple fluids, before applying it to an experimental system composed of superparamagnetic colloidal particles. The method will enable experimental investigations into many-body interactions and allow for effective coarse graining of interactions from simulations.

Interrupted Motility Induced Phase Separation in Aligning Active Colloids.

Switching on high activity in a relatively dense system of active Janus colloids, we observe fast clustering, followed by cluster aggregation towards full phase separation. The phase separation process is however interrupted when large enough clusters start breaking apart. Following the cluster size distribution as a function of time, we identify three successive dynamical regimes. Tracking both the particle positions and orientations, we characterize the structural ordering and alignment in the growing clusters and thereby unveil the mechanisms at play in these regimes. In particular, we identify how alignment between the neighboring particles is responsible for the interruption of the full phase separation. Our large scale quantification of the phase separation kinetics in active colloids points towards the new physics observed when both alignment and short-range repulsions are present.

Dynamics of individual Brownian rods in a microchannel flow.

We study the orientational dynamics of heavy silica microrods flowing through a microfluidic channel. Comparing experiments and Brownian dynamics simulations we identify different particle orbits, in particular in-plane tumbling behavior, which cannot be explained by classical Jeffery theory, and we relate this behavior to the rotational diffusion of the rods. By constructing the full, three-dimensional, orientation distribution, we describe the rod trajectories and quantify the persistence of Jeffery orbits using temporal correlation functions of the Jeffery constant. We find that our colloidal rods lose memory of their initial configuration in about a second, corresponding to half a Jeffery period.

Geometry-induced capillary emptying.

When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary cross-sectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counterintuitive behavior. This opens the possibility of creating very sensitive microfluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping.

Bulk synthesis of silver-head colloidal rodlike micromotors.

Colloidal particles with asymmetric catalytic activities are emerging micro/nanomotors that harvest chemical energy for propulsion in fluids. It is of general interest to produce such particles with high performance, in large quantity and at low cost. In this paper, we present a facile bulk method to synthesize silver-head colloidal silica rods. These particles self-propel towards their active sites by reacting with hydrogen peroxide, and the velocity is tuned via the fuel concentration. We show that these motors are highly efficient; compared to the currently available chemical-phoretic micro/nanomotors they show similar performance of self-propulsion at fuel concentrations that are two orders of magnitude smaller.

A new family of urea-based low molecular-weight organogelators for environmental remediation: the influence of structure.

Gelation processes grant access to a wealth of soft materials with tailorable properties, in applications as diverse as environmental remediation, biomedicine and electronics. Several classes of self-assembling gelators have been studied and employ non-covalent bonds to direct assembly, but recently attention has come to focus on how the overall shape of the gelator molecule impacts its gelation. Here we study a new sub-family of low molecular weight organogelators and explore how steric rearrangement influences their gelation. The gels produced are characterised with X-ray diffraction and small-angle neutron scattering (SANS) to probe their ex situ and in situ gelation mechanisms. The best examples were then tested for environmental remediation applications, gelling petrol and oils in the presence of water and salts.

Communication: Contact values of pair distribution functions in colloidal hard disks by test-particle insertion.

We apply Henderson's method for measuring the cavity distribution function y(r) [J. Henderson, Mol. Phys. 48, 389 (1983)] to obtain the pair distribution function at contact, g(σ+). In contrast to the conventional distance-histogram method, no approximate extrapolation to contact is required. The resulting equation of state from experiments and simulations of hard disks agrees well with the scaled particle theory prediction up to high fluid packing fractions. We also provide the first experimental measurement of y(r) inside the hard core, which will allow for a more complete comparison with theory. The method's flexibility is further illustrated by measuring the partial pair distribution functions of binary hard-disk mixtures in simulation. The equation for the contact values can be used to derive familiar results from statistical geometry.

Two-Dimensional Melting of Colloidal Hard Spheres.

We study the melting of quasi-two-dimensional colloidal hard spheres by considering a tilted monolayer of particles in sedimentation-diffusion equilibrium. In particular, we measure the equation of state from the density profiles and use time-dependent and height-resolved correlation functions to identify the liquid, hexatic, and crystal phases. We find that the liquid-hexatic transition is first order and that the hexatic-crystal transition is continuous. Furthermore, we directly measure the width of the liquid-hexatic coexistence gap from the fluctuations of the corresponding interface, and thereby experimentally establish the full phase behavior of hard disks.

Structural disorder, filament growth and self-poisoning in short rods confined onto a flat wall.

Confocal microscopy was used to directly observe the structural coarsening of the first layer of short colloidal rods sedimented onto a flat wall. Based on an image analysis algorithm we devised, quantitative information on the location, orientation and length of each particle can be extracted with high precision. At high density the system undergoes structural arrest, and becomes trapped in a disordered state of randomly arranged filaments that are composed of side-by-side aligned rods. The frustration of structural order is signalled by a new peak that emerges in the radial distribution function. Configuration analysis shows that the peak is primarily due to pairs of particles that are arranged in a "T" shape, a configuration that is compatible with neither crystallization nor filament growth. Our results point to a self-poisoning mechanism for the frustration of structural order, and highlight the importance of particle shape in controlling colloidal assembly thus materials properties.

Equilibrium Grain Boundary Segregation and Clustering of Impurities in Colloidal Polycrystalline Monolayers.

We investigate the segregation of impurities to grain boundaries in colloidal polycrystalline monolayers using video microscopy. A model colloidal alloy is prepared by embedding large spherical impurities in a polycrystalline monolayer of small host colloidal hard spheres, which stops grain growth at a finite grain size. The size ratio between the impurities and the host particles determines whether they behave as interstitial or substitutional impurities in the bulk crystal, akin to those in real alloys. We find that the partitioning of impurities between the grains and the grain boundaries is in very good agreement with the Langmuir-McLean adsorption model for equilibrium grain boundary segregation. This enables the direct measurement of the free energy of adsorption for the two types of impurities. Near saturation, we characterize the spatial distribution of the adsorbed impurities and find that it strongly depends on their interstitial or substitutional nature. This is because the relative importance of clustering and mixing due to nonadditivity is determined by geometrical constraints imposed by the crystalline host lattice.

On the Gaussian approximation in colloidal hard sphere fluids.

We study the behaviour of the self-intermediate scattering function and self-van Hove correlation function for quasi-two-dimensional colloidal hard sphere fluids at a range of area fractions. We compute these functions first directly from the particle coordinates and secondly from the mean squared displacement via the Gaussian approximation. This allows us to test the validity of this approximation over a range of length and time scales, where we find that the Gaussian approximation holds if the hydrodynamic limits are appropriately probed. Surprisingly, only small deviations from Gaussian behaviour are seen at intermediate times, even for dense fluids. We next consider these deviations from Gaussian behaviour firstly via the non-Gaussian parameter and secondly by considering the relaxation times of the intermediate scattering function. From these measurements we develop a scaling relation in order to directly determine the combinations of wavevectors and times at which the non-Gaussian behavior is seen. This allows for the clear identification of the hydrodynamic regimes and thus provides new insight into the crossover between long- and short-time self-diffusion.

Thermal Analog of Gimbal Lock in a Colloidal Ferromagnetic Janus Rod.

We report an entropy-driven orientational hopping transition in a magnetically confined colloidal Janus rod. In a magnetic field, the sedimented rod randomly hops between horizontal and vertical states: the latter state comes at a substantial gravitational cost at no reduction of magnetic potential energy. The probability distribution over the angles of the rod shows that the presence of an external magnetic field leads to the emergence of a metastable vertical state separated from the ground state by an effective barrier. This barrier does not come from the potential energy but rather from the vast gain in phase space available to the rod as it approaches the vertical state. The loss of rotational degree of freedom that gives rise to this effect is a statistical mechanical analogue of the phenomenon of gimbal lock from classical mechanics.

Self-assembly and crystallisation of indented colloids at a planar wall.

We report experimental and simulation studies of the structure of a monolayer of indented ("lock and key") colloids, on a planar surface. On adding a non-absorbing polymer with prescribed radius and volume fraction, depletion interactions are induced between the colloids, with controlled range and strength. For spherical particles, this leads to crystallisation, but the indented colloids crystallise less easily than spheres, in both simulation and experiment. Nevertheless, simulations show that indented colloids do form plastic (rotator) crystals. We discuss the conditions under which this occurs, and the possibilities of lower-symmetry crystal states. We also comment on the kinetic accessibility of these states.