Pair-distribution function of active Brownian spheres in three spatial dimensions: simulation results and analytical representation.

The pair-distribution function, which provides information about correlations in a system of interacting particles, is one of the key objects of theoretical soft matter physics. In particular, it allows for microscopic insights into the phase behavior of active particles. While this function is by now well studied for two-dimensional active matter systems, the more complex and more realistic case of three-dimensional systems is not well understood by now. In this work, we analyze the full pair-distribution function of spherical active Brownian particles interacting via a Weeks-Chandler-Andersen potential in three spatial dimensions using Brownian dynamics simulations. Besides extracting the structure of the pair-distribution function from the simulations, we obtain an analytical representation for this function, parametrized by activity and concentration, which takes into account the symmetries of a homogeneous stationary state. Our results are useful as input to quantitative models of active Brownian particles and advance our understanding of the microstructure in dense active fluids.

Electrostatic interactions control the adsorption of extracellular vesicles onto supported lipid bilayers.

Communication between cells located in different parts of an organism is often mediated by membrane-enveloped nanoparticles, such as extracellular vesicles (EVs). EV binding and cell uptake mechanisms depend on the heterogeneous composition of the EV membrane. From a colloidal perspective, the EV membrane interacts with other biological interfaces via both specific and non-specific interactions, where the latter include long-ranged electrostatic and van der Waals forces, and short-ranged repulsive "steric-hydration" forces. While electrostatic forces are generally exploited in most EV immobilization protocols, the roles played by various colloidal forces in controlling EV adsorption on surfaces have not yet been thoroughly addressed. In the present work, we study the adsorption of EVs onto supported lipid bilayers (SLBs) carrying different surface charge densities using a combination of quartz crystal microbalance with dissipation monitoring (QCM-D) and confocal laser scanning microscopy (CLSM). We demonstrate that EV adsorption onto lipid membranes can be controlled by varying the strength of electrostatic forces and we theoretically describe the observed phenomena within the framework of nonlinear Poisson-Boltzmann theory. Our modelling results confirm the experimental observations and highlight the crucial role played by attractive electrostatics in EV adsorption onto lipid membranes. They furthermore show that simplified theories developed for model lipid systems can be successfully applied to the study of their biological analogues and provide new fundamental insights into EV-membrane interactions with potential use in developing novel EV separation and immobilization strategies.

Collective guiding of acoustically propelled nano- and microparticles.

One of the most important potential applications of motile nano- and microdevices is targeted drug delivery. To realize this, biocompatible particles that can be guided collectively towards a target inside a patient's body are required. Acoustically propelled nano- and microparticles constitute a promising candidate for such biocompatible, artificial motile particles. The main remaining obstacle to targeted drug delivery by motile nano- and microdevices is to also achieve a reliable and biocompatible method for guiding them collectively to their target. Here, we propose such a method. As we confirm by computer simulations, it allows for the remote guiding of large numbers of acoustically propelled particles to a prescribed target by combining a space- and time-dependent acoustic field and a time-dependent magnetic field. The method works without detailed knowledge about the particle positions and for arbitrary initial particle distributions. With these features, it paves the way for the future application of motile particles as vehicles for targeted drug delivery in nanomedicine.

Vesicles Balance Osmotic Stress with Bending Energy That Can Be Released to Form Daughter Vesicles.

The bending energy of the lipid membrane is central to biological processes involving vesicles, such as endocytosis and exocytosis. To illustrate the role of bending energy in these processes, we study the response of single-component giant unilamellar vesicles (GUVs) subjected to external osmotic stress by glucose addition. For osmotic pressures exceeding 0.15 atm, an abrupt shape change from spherical to prolate occurs, showing that the osmotic pressure is balanced by the free energy of membrane bending. After equilibration, the external glucose solution was exchanged for pure water, yielding rapid formation of monodisperse daughter vesicles inside the GUVs through an endocytosis-like process. Our theoretical analysis shows that this process requires significant free energies stored in the deformed membrane to be kinetically allowed. The results indicate that bending energies stored in GUVs are much higher than previously implicated, with potential consequences for vesicle fusion/fission and the osmotic regulation in living cells.

Thermal fluctuations and osmotic stability of lipid vesicles.

Biological membranes constantly change their shape in response to external stimuli, and understanding the remodeling and stability of vesicles in heterogeneous environments is therefore of fundamental importance for a range of cellular processes. One crucial question is how vesicles respond to external osmotic stresses, imposed by differences in solute concentrations between the vesicle interior and exterior. Previous analyses of the membrane bending energy have predicted that micron-sized giant unilamellar vesicles (GUVs) should become globally deformed already for nanomolar concentration differences, in contrast to experimental findings that find deformations at much higher osmotic stresses. In this article, we analyze the mechanical stability of a spherical vesicle exposed to an external osmotic pressure in a statistical-mechanical model, including the effect of thermally excited membrane bending modes. We find that the inclusion of thermal fluctuations of the vesicle shape changes renders the vesicle deformation continuous, in contrast to the abrupt transition in the athermal picture. Crucially, however, the predicted critical pressure associated with global vesicle deformation remains the same as when thermal fluctuations are neglected, approximately six orders of magnitude smaller than the typical collapse pressure recently observed experimentally for GUVs. We conclude by discussing possible sources of this persisting dissonance between theory and experiments.

On the role of softness in ionic microgel interactions.

Thermoresponsive microgels are a popular model system to study phase transitions in soft matter, because temperature directly controls their volume fraction. Ionic microgels are additionally pH-responsive and possess a rich phase diagram. Although effective interaction potentials between microgel particles have been proposed, these have never been fully tested, leading to a gap in our understanding of the link between single-particle and collective properties. To help resolve this gap, four sets of ionic microgels with varying crosslinker density were synthesised and characterised using light scattering techniques and confocal microscopy. The resultant structural and dynamical information was used to investigate how particle softness affects the phase behaviour of ionic microgels and to validate the proposed interaction potential. We find that the architecture of the microgel plays a marked role in its phase behaviour. Rather than the ionic charges, it is the dangling ends which drive phase transitions and interactions at low concentration. Comparison to theory underlines the need for a refined theoretical model which takes into consideration these close-contact interactions.

ArGSLab: a tool for analyzing experimental or simulated particle networks.

Microscopy and particle-based simulations are both powerful techniques to study aggregated particulate matter such as colloidal gels. The data provided by these techniques often contains information on a wide array of length scales, but structural analysis methods typically focus on the local particle arrangement, even though the data also contains information about the particle network on the mesoscopic length scale. In this paper, we present a MATLAB software package for quantifying mesoscopic network structures in colloidal samples. ArGSLab (Arrested and Gelated Structures Laboratory) extracts a network backbone from the input data, which is in turn transformed into a set of nodes and links for graph theory-based analysis. The routines can process both image stacks from microscopy as well as explicit coordinate data, and thus allows quantitative comparison between simulations and experiments. ArGSLab furthermore enables the accurate analysis of microscopy data where, e.g., an extended point spread function prohibits the resolution of individual particles. We demonstrate the resulting output for example datasets from both microscopy and simulation of colloidal gels, in order to showcase the capability of ArGSLab to quantitatively analyze data from various sources. The freely available software package can be used either with a provided graphical user interface or directly as a MATLAB script.

Crystal-to-Crystal Transitions in Binary Mixtures of Soft Colloids.

In this article, we demonstrate a method for inducing reversible crystal-to-crystal transitions in binary mixtures of soft colloidal particles. Through a controlled decrease of salinity and increasingly dominating electrostatic interactions, a single sample is shown to reversibly organize into entropic crystals, electrostatic attraction-dominated crystals, or aggregated gels, which we quantify using microscopy and image analysis. We furthermore analyze crystalline structures with bond order analysis to discern between two crystal phases. We observe the different phases using a sample holder geometry that allows both in situ salinity control and imaging through confocal laser scanning microscopy and apply a synthesis method producing particles with high resolvability in microscopy with control over particle size. The particle softness provides for an enhanced crystallization speed, while altering the re-entrant melting behavior as compared to hard sphere systems. This work thus provides several tools for use in the reproducible manufacture and analysis of binary colloidal crystals.

Tube to ribbon transition in a self-assembling model peptide system.

Peptides that self-assemble into ß-sheet rich aggregates are known to form a large variety of supramolecular shapes, such as ribbons, tubes or sheets. However, the underlying thermodynamic driving forces for such different structures are still not fully understood, limiting their potential applications. In the AnK peptide system (A = alanine, K = lysine), a structural transition from tubes to ribbons has been shown to occur upon an increase of the peptide length, n, from 6 to 8. In this work we analyze this transition by means of a simple thermodynamic model. We consider three energy contributions to the total free energy: an interfacial tension, a penalty for deviating from the optimal ß-sheet twist angle, and a hydrogen bond deformation when the ß-sheets adopt a specific self-assembled structure. Whilst the first two contributions merely provide similar constant energy offsets, the hydrogen bond deformations differ depending on the studied structure. Consequently, the tube structure is thermodynamically favored for shorter AnK peptides, with a crossover at n≈ 13. This qualitative agreement of the model with the experimental observations shows, that we have achieved a good understanding of the underlying thermodynamic features within the self-assembling AnK system.

Symmetric Mixtures of Pusher and Puller Microswimmers Behave as Noninteracting Suspensions.

Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as "pushers" and "pullers," display qualitatively different collective behaviors: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher-puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction χ of pullers is increased and disappears for χ≥0.5. We then show analytically and numerically that the two-point hydrodynamic correlations of the 1∶1 mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer-swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in 1∶1 pusher-puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium long-range interacting systems.

Anisotropic dynamics of a self-assembled colloidal chain in an active bath.

Anisotropic macromolecules exposed to non-equilibrium (active) noise are very common in biological systems, and an accurate understanding of their anisotropic dynamics is therefore crucial. Here, we experimentally investigate the dynamics of isolated chains assembled from magnetic microparticles at a liquid-air interface and moving in an active bath consisting of motile E. coli bacteria. We investigate both the internal chain dynamics and the anisotropic center-of-mass dynamics through particle tracking. We find that both the internal and center-of-mass dynamics are greatly enhanced compared to the passive case, i.e., a system without bacteria, and that the center-of-mass diffusion coefficient D features a non-monotonic dependence as a function of the chain length. Furthermore, our results show that the relationship between the components of D parallel and perpendicular with respect to the direction of the applied magnetic field is preserved in the active bath compared to the passive case, with a higher diffusion in the parallel direction, in contrast to previous findings in the literature. We argue that this qualitative difference is due to subtle differences in the experimental geometry and conditions and the relative roles played by long-range hydrodynamic interactions and short-range collisions.

Derivation of the Derjaguin approximation for the case of inhomogeneous solvents.

The Derjaguin approximation (DA) relates the force between curved surfaces to the interaction free energy between parallel planes. It is typically derived by considering the direct interaction between the bodies involved, thus treating the effect of an intervening solvent implicitly by a rescaling of the corresponding Hamaker constant. Here, we provide a generalization of DA to the case of a molecular medium between the bodies, as is the case in most applications. The derivation is based on an explicit statistical-mechanical treatment of the contribution to the interaction force from a molecular solvent using a general expression for intermolecular and molecule-surface interactions. Starting from an exact expression for the force, DA is arrived at by a series of well-defined approximations. Our results show that DA remains valid in a molecular solvent as long as (i) the surface-molecule interactions are of a much shorter range than the radius R of the sphere and (ii) the density correlation length in the solvent is smaller than R. We then extend our analysis to the case where a phase transition occurs between the surfaces, which cannot easily be covered using a statistical-mechanical formalism due to the discontinuous change in the density of the medium. Instead, using a continuum thermodynamic description, we show that this phase transformation induces an attractive force between the bodies and that the force between curved surfaces can be related to the free energy in the corresponding planar case, in accordance with DA.

Pair-distribution function of active Brownian spheres in two spatial dimensions: Simulation results and analytic representation.

We investigate the full pair-distribution function of a homogeneous suspension of spherical active Brownian particles interacting by a Weeks-Chandler-Andersen potential in two spatial dimensions. The full pair-distribution function depends on three coordinates describing the relative positions and orientations of two particles, the Péclet number specifying the activity of the particles, and their mean packing density. This five-dimensional function is obtained from Brownian dynamics simulations. We discuss its structure taking into account all of its degrees of freedom. In addition, we present an approximate analytic expression for the product of the full pair-distribution function and the interparticle force. We find that the analytic expression, which is typically needed when deriving analytic models for the collective dynamics of active Brownian particles, is in good agreement with the simulation results. The results of this work can thus be expected to be helpful for the further theoretical investigation of active Brownian particles as well as nonequilibrium statistical physics in general.

Using Patchy Particles to Prevent Local Rearrangements in Models of Non-equilibrium Colloidal Gels.

Simple models based on isotropic interparticle attractions often fail to capture experimentally observed structures of colloidal gels formed through spinodal decomposition and subsequent arrest: the resulting gels are typically denser and less branched than their experimental counterparts. Here, we simulate gels formed from soft particles with directional attractions ("patchy particles"), designed to inhibit lateral particle rearrangement after aggregation. We directly compare simulated structures with experimental colloidal gels made using soft attractive microgel particles, by employing a "skeletonization" method that reconstructs the three-dimensional backbone from experiment or simulation. We show that including directional attractions with sufficient valency leads to strongly branched structures compared to isotropic models. Furthermore, combining isotropic and directional attractions provides additional control over aggregation kinetics and gel structure. Our results show that the inhibition of lateral particle rearrangements strongly affects the gel topology and is an important effect to consider in computational models of colloidal gels.

Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence.

Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to N = 3 × 106) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.

Reversible Formation of Thermoresponsive Binary Particle Gels with Tunable Structural and Mechanical Properties.

We investigate the collective behavior of suspended thermoresponsive microgels that expel solvent and subsequently decrease in size upon heating. Using a binary mixture of differently thermoresponsive microgels, we demonstrate how distinctly different gel structures form, depending on the heating profile used. Confocal laser scanning microscopy (CLSM) imaging shows that slow heating ramps yield a core-shell network through sequential gelation, while fast heating ramps yield a random binary network through homogelation. Here, secondary particles are shown to aggregate in a monolayer fashion upon the first gel, which can be qualitatively reproduced through Brownian dynamics simulations using a model based on a temperature-dependent interaction potential incorporating steric repulsion and van der Waals attraction. Through oscillatory rheology it is shown that secondary microgel deposition enhances the structural integrity of the previously formed single species gel, and the final structure exhibits higher elastic and loss moduli than its compositionally identical homogelled counterpart. Furthermore, we demonstrate that aging processes in the scaffold before secondary microgel deposition govern the final structural properties of the bigel, which allows a detailed control over these properties. Our results thus demonstrate how the temperature profile can be used to finely control the structural and mechanical properties of these highly tunable materials.

Generalized thermodynamics of phase equilibria in scalar active matter.

Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy. We illustrate our approach on two well-known models: self-propelled particles interacting either through a density-dependent propulsion speed or via direct pairwise forces. Our theory accounts quantitatively for their phase diagrams, providing a unified description of MIPS.

Directed Self-Assembly of Polarizable Ellipsoids in an External Electric Field.

The interplay between shape anisotropy and directed long-range interactions enables the self-assembly of complex colloidal structures. As a recent highlight, ellipsoidal particles polarized in an external electric field were observed to associate into well-defined tubular structures. In this study, we systematically investigate such directed self-assembly using Monte Carlo simulations of a two-point-charge model of polarizable prolate ellipsoids. In spite of its simplicity and computational efficiency, we demonstrate that the model is capable of capturing the complex structures observed in experiments on ellipsoidal colloids at low volume fractions. We show that, at sufficiently high electric field strength, the anisotropy in shape and electrostatic interactions causes a transition from three-dimensional crystal structures observed at low aspect ratios to two-dimensional sheets and tubes at higher aspect ratios. Our work thus illustrates the rich self-assembly behavior accessible when exploiting the interplay between competing long- and short-range anisotropic interactions in colloidal systems.

Role of Correlations in the Collective Behavior of Microswimmer Suspensions.

In this Letter, we study the collective behavior of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedentedly large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is nonperturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its nontrivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.