Goblet cell interactions reorient bundled mucus strands for efficient airway clearance

The respiratory tract of larger animals is cleared by sweeping bundled strands along the airway surface. These bundled strands can be millimetric in length and consist of MUC5B mucin. They are produced by submucosal glands, and upon emerging from these glands, the long axis of the bundled strands is oriented along the cilia-mediated flow toward the oral cavity. However, after release, the bundled strands are found to have turned orthogonal to the flow, which maximizes their clearance potential. How this unexpected reorientation is accomplished is presently not well understood. Recent experiments suggest that the reorientation process involves bundled strands sticking to MUC5AC mucus threads, which are tethered to the goblet cells. Such goblet cells are present in small numbers throughout the airway epithelium. Here, we develop a minimal model for reorientation of bundled mucus strands through adhesive interactions with surface goblet cells. Our simulations reveal that goblet cell interactions can reorient the bundled strands within 10 mm of release-making reorientation on the length scale of the tracheal tube feasible-and can stabilize the orthogonal orientation. Our model also reproduces other experimental observations such as strong velocity fluctuations and significant slow-down of the bundled strand with respect to the cilia-mediated flow. We further provide insight into the strand turning mechanism by examining the effect of strand shape on the impulse exerted by a single goblet cell. We conclude that goblet cell-mediated reorientation is a viable route for bundled strand reorientation, which should be further validated in future experiment.

Hydrodynamic stability criterion for colloidal gelation under gravity

Attractive colloids diffuse and aggregate to form gels, solidlike particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever-decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.

Frequency-controlled electrophoretic mobility of a particle within a porous, hollow shell

The unique properties of yolk-shell or rattle-type particles make them promising candidates for applications ranging from switchable photonic crystals, to catalysts, to sensors. To realize many of these applications it is important to gain control over the dynamics of the core particle independently of the shell.

HYPOTHESIS

The core particle may be manipulated by an AC electric field with rich frequency-dependent behavior.

EXPERIMENTS

Here, we explore the frequency-dependent dynamic electrophoretic mobility of a charged core particle within a charged, porous shell in AC electric fields both experimentally using liquid-phase electron microscopy and numerically via the finite-element method. These calculations solve the Poisson-Nernst-Planck-Stokes equations, where the core particle moves according to the hydrodynamic and electric forces acting on it.

FINDINGS

In experiments the core exhibited three frequency-dependent regimes of field-driven motion: (i) parallel to the field, (ii) diffusive in a plane orthogonal to the field, and (iii) unbiased random motion. The transitions between the three observed regimes can be explained by the level of matching between the time required to establish ionic gradients in the shell and the period of the AC field. We further investigated the effect of shell porosity, ionic strength, and inner-shell radius. The former strongly impacted the core's behavior by attenuating the field inside the shell. Our results provide physical understanding on how the behavior of yolk-shell particles may be tuned, thereby enhancing their potential for use as building blocks for switchable photonic crystals.

Amphibious Transport of Fluids and Solids by Soft Magnetic Carpets

One of the major challenges in modern robotics is controlling micromanipulation by active and adaptive materials. In the respiratory system, such actuation enables pathogen clearance by means of motile cilia. While various types of artificial cilia have been engineered recently, they often involve complex manufacturing protocols and focus on transporting liquids only. Here, soft magnetic carpets are created via an easy self-assembly route based on the Rosensweig instability. These carpets can transport not only liquids but also solid objects that are larger and heavier than the artificial cilia, using a crowd-surfing effect.This amphibious transportation is locally and reconfigurably tunable by simple micromagnets or advanced programmable magnetic fields with a high degree of spatial resolution. Two surprising cargo reversal effects are identified and modeled due to collective ciliary motion and nontrivial elastohydrodynamics. While the active carpets are generally applicable to integrated control systems for transport, mixing, and sorting, these effects can also be exploited for microfluidic viscosimetry and elastometry.

Tunability of Interactions between the Core and Shell in Rattle-Type Particles Studied with Liquid-Cell Electron Microscopy

Yolk-shell or rattle-type particles consist of a core particle that is free to move inside a thin shell. A stable core with a fully accessible surface is of interest in fields such as catalysis and sensing. However, the stability of a charged nanoparticle core within the cavity of a charged thin shell remains largely unexplored. Liquid-cell (scanning) transmission electron microscopy is an ideal technique to probe the core-shell interactions at nanometer spatial resolution. Here, we show by means of calculations and experiments that these interactions are highly tunable. We found that in dilute solutions adding a monovalent salt led to stronger confinement of the core to the middle of the geometry. In deionized water, the Debye length κ-1 becomes comparable to the shell radius Rshell, leading to a less steep electric potential gradient and a reduced core-shell interaction, which can be detrimental to the stability of nanorattles. For a salt concentration range of 0.5-250 mM, the repulsion was relatively long-ranged due to the concave geometry of the shell. At salt concentrations of 100 and 250 mM, the core was found to move almost exclusively near the shell wall, which can be due to hydrodynamics, a secondary minimum in the interaction potential, or a combination of both. The possibility of imaging nanoparticles inside shells at high spatial resolution with liquid-cell electron microscopy makes rattle particles a powerful experimental model system to learn about nanoparticle interactions. Additionally, our results highlight the possibilities for manipulating the interactions between core and shell that could be used in future applications.

Impact of surface charge on the motion of light-activated Janus micromotors

Control over micromotors' motion is of high relevance for lab-on-a-chip and biomedical engineering, wherein such particles encounter complex microenvironments. Here, we introduce an efficient way to influence Janus micromotors' direction of motion and speed by modifying their surface properties and those of their immediate surroundings. We fabricated light-responsive Janus micromotors with positive and negative surface charge, both driven by ionic self-diffusiophoresis. These were used to observe direction-of-motion reversal in proximity to glass substrates for which we varied the surface charge. Quantitative analysis allowed us to extract the dependence of the particle velocity on the surface charge density of the substrate. This constitutes the first quantitative demonstration of the substrate's surface charge on the motility of the light-activated diffusiophoretic motors in water. We provide qualitative understanding of these observations in terms of osmotic flow along the substrate generated through the ions released by the propulsion mechanism. Our results constitute a crucial step in moving toward practical application of self-phoretic artificial micromotors.

Erratum: Autonomously Probing Viscoelasticity in Disordered Suspensions [Phys. Rev. Lett. 125, 258002 (2020)]

This corrects the article DOI: 10.1103/PhysRevLett.125.258002.

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

 Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids.

Magnetic propulsion of colloidal microrollers controlled by electrically modulated friction

Precise control over the motion of magnetically responsive particles in fluidic chambers is important for probing and manipulating tasks in prospective microrobotic and bio-analytical platforms. We have previously exploited such colloids as shuttles for the microscale manipulation of objects. Here, we study the rolling motion of magnetically driven Janus colloids on solid substrates under the influence of an orthogonal external electric field. Electrically induced attractive interactions were used to tune the load on the Janus colloid and thereby the friction with the underlying substrate, leading to control over the forward velocity of the particle. Our experimental data suggest that the frictional coupling required to achieve translation, transitions from a hydrodynamic regime to one of mixed contact coupling with increasing load force. Based on this insight, we show that our colloidal microrobots can probe the local friction coefficient of various solid surfaces, which makes them potentially useful as tribological microsensors. Lastly, we precisely manipulate porous cargos using our colloidal rollers, a feat that holds promise for bio-analytical applications.

Autonomously Probing Viscoelasticity in Disordered Suspensions

Recent experiments show a strong rotational diffusion enhancement for self-propelled microrheological probes in colloidal glasses. Here, we provide microscopic understanding using simulations with a frictional probe-medium coupling that converts active translation into rotation. Diffusive enhancement emerges from the medium's disordered structure and peaks at a second-order transition in the number of contacts. Our results reproduce the salient features of the colloidal glass experiment and support an effective description that is applicable to a broader class of viscoelastic suspensions.

Regulating the aggregation of colloidal particles in an electro-osmotic micropump

Unrestricted particle transport through microfluidic channels is of paramount importance to a wide range of applications, including lab-on-a-chip devices. In this article, we study via video microscopy the electro-osmotic aggregation of colloidal particles at the opening of a micrometer-sized silica channel in the presence of a salt gradient. Particle aggregation eventually leads to clogging of the channel, which may be undone by a time-adjusted reversal of the applied electric potential. We numerically model our system via the Stokes-Poisson-Nernst-Planck equations in a geometry that approximates the real sample. This allows us to identify the transport processes induced by the electric field and salt gradient and to provide evidence that a balance thereof leads to aggregation. We further demonstrate experimentally that a net flow of colloids through the channel may be achieved by applying a square-waveform electric potential with an appropriately tuned duty cycle. Our results serve to guide the design of microfluidic and nanofluidic pumps that allow for controlled particle transport and provide new insights for anti-fouling in ultra-filtration.

Diffusion-Based Height Analysis Reveals Robust Microswimmer-Wall Separation

Microswimmers typically move near walls, which can strongly influence their motion. However, direct experimental measurements of swimmer-wall separation remain elusive to date. Here, we determine this separation for model catalytic microswimmers from the height dependence of the passive component of their mean-squared displacement. We find that swimmers exhibit "ypsotaxis," a tendency to assume a fixed height above the wall for a range of salt concentrations, swimmer surface charges, and swimmer sizes. Our findings indicate that ypsotaxis is activity induced, posing restrictions on future modeling of their still-debated propulsion mechanism.

Height distribution and orientation of colloidal dumbbells near a wall

Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles and can further contribute to the development of quantitative frameworks for arbitrarily shaped microparticle dynamics in confinement.

Slip Length Dependent Propulsion Speed of Catalytic Colloidal Swimmers near Walls

Catalytic colloidal swimmers that propel due to self-generated fluid flows exhibit strong affinity for surfaces. Here, we report experimental measurements of a significant dependence of such microswimmers' speed on the nearby substrate material. We find that speeds scale with the solution contact angle θ on the substrate, which relates to the associated hydrodynamic substrate slip length, as V∝(cosθ+1)^{-3/2}. We show that such dependence can be attributed to osmotic coupling between swimmers and substrate. Our work points out that hydrodynamic slip at nearby walls, though often unconsidered, can significantly impact microswimmer self-propulsion.

Self-thermoelectrophoresis at low salinity

A locally heated Janus colloid can achieve motion in an electrolyte by an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte using the finite-element method and analytic theory. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we employ Teubner's integral formalism to arrive at expressions for the speed, which agree semi-quantitatively with our numerical results for conducting swimmers. This lends credibility to the remarkably high swim speed at very low ionic strength, which we numerically obtain for a fully insulating swimmer. We also report on hot swimmers with a mixed electrostatic boundary conditions. Our results should benefit the realization and analysis of further experiments on thermo(di)electrophoretic swimmers.

Hydrodynamic mobility reversal of squirmers near flat and curved surfaces

Self-propelled particles have been experimentally shown to orbit spherical obstacles and move along surfaces. Here, we theoretically and numerically investigate this behavior for a hydrodynamic squirmer interacting with spherical objects and flat walls using three different methods of approximately solving the Stokes equations: The method of reflections, which is accurate in the far field; lubrication theory, which describes the close-to-contact behavior; and a lattice Boltzmann solver that accurately accounts for near-field flows. The method of reflections predicts three distinct behaviors: orbiting/sliding, scattering, and hovering, with orbiting being favored for lower curvature as in the literature. Surprisingly, it also shows backward orbiting/sliding for sufficiently strong pushers, caused by fluid recirculation in the gap between the squirmer and the obstacle leading to strong forces opposing forward motion. Lubrication theory instead suggests that only hovering is a stable point for the dynamics. We therefore employ lattice Boltzmann to resolve this discrepancy and we qualitatively reproduce the richer far-field predictions. Our results thus provide insight into a possible mechanism of mobility reversal mediated solely through hydrodynamic interactions with a surface.

A lattice Boltzmann model for squirmers

The squirmer is a simple yet instructive model for microswimmers, which employs an effective slip velocity on the surface of a spherical swimmer to describe its self-propulsion. We solve the hydrodynamic flow problem with the lattice Boltzmann (LB) method, which is well-suited for time-dependent problems involving complex boundary conditions. Incorporating the squirmer into LB is relatively straightforward, but requires an unexpectedly fine grid resolution to capture the physical flow fields and behaviors accurately. We demonstrate this using four basic hydrodynamic tests: two for the far-field flow-accuracy of the hydrodynamic moments and squirmer-squirmer interactions-and two that require the near field to be accurately resolved-a squirmer confined to a tube and one scattering off a spherical obstacle-which LB is capable of doing down to the grid resolution. We find good agreement with (numerical) results obtained using other hydrodynamic solvers in the same geometries and identify a minimum required resolution to achieve this reproduction. We discuss our algorithm in the context of other hydrodynamic solvers and present an outlook on its application to multi-squirmer problems.

Hydrodynamics strongly affect the dynamics of colloidal gelation but not gel structure

Colloidal particles with strong, short-ranged attractions can form a gel. We simulate this process without and with hydrodynamic interactions (HI), using the lattice-Boltzmann method to account for presence of a thermalized solvent. We show that HI speed up and slow down gelation at low and high volume fractions, respectively. The transition between these two regimes is linked to the existence of a percolating cluster shortly after quenching the system. However, when we compare gels at matched 'structural age', we find nearly indistinguishable structures with and without HI. Our result explains longstanding, unresolved conflicts in the literature.

The efficiency of self-phoretic propulsion mechanisms with surface reaction heterogeneity

We consider the efficiency of self-phoretic colloidal particles (swimmers) as a function of the heterogeneity in the surface reaction rate. The set of fluid, species, and electrostatic continuity equations is solved analytically using a linearization and numerically using a finite-element method. To compare spherical swimmers of different size and with heterogeneous catalytic conversion rates, a "swimmer efficiency" functional η is introduced. It is proven that in order to obtain maximum swimmer efficiency, the reactivity has to be localized at the pole(s). Our results also shed light on the sensitivity of the propulsion speed to details of the surface reactivity, a property that is notoriously hard to measure. This insight can be utilized in the design of new self-phoretic swimmers.

Microfluidic pumping by micromolar salt concentrations

An ion-exchange-resin-based microfluidic pump is introduced that utilizes trace amounts of ions to generate fluid flows. We show experimentally that our pump operates in almost deionized water for periods exceeding 24 h and induces fluid flows of μm s^-1 over hundreds of μm. This flow displays a far-field, power-law decay which is characteristic of two-dimensional (2D) flow when the system is strongly confined and of three-dimensional (3D) flow when it is not. Using theory and numerical calculations we demonstrate that our observations are consistent with electroosmotic pumping driven by μmol L^-1 ion concentrations in the sample cell that serve as 'fuel' to the pump. Our study thus reveals that trace amounts of charge carriers can produce surprisingly strong fluid flows; an insight that should benefit the design of a new class of microfluidic pumps that operate at very low fuel concentrations.

Ionic screening and dissociation are crucial for understanding chemical self-propulsion in polar solvents

Polar solvents like water support the bulk dissociation of themselves and their solutes into ions, and the re-association of these ions into neutral molecules in a dynamic equilibrium, e.g., H₂O₂ ⇌ H⁺ + HO₂^-. Using continuum theory, we study the influence of these association-dissociation reactions on the self-propulsion of colloids driven by surface chemical reactions (chemical swimmers). We find that association-dissociation reactions should have a strong influence on swimmers' behaviour, and therefore should be included in future modelling. In particular, such bulk reactions should permit charged swimmers to propel electrophoretically even if all species involved in the surface reactions are neutral. The bulk reactions also significantly modify the predicted speed of chemical swimmers propelled by ionic currents, by up to an order of magnitude. For swimmers whose surface reactions produce both anions and cations (ionic self-diffusiophoresis), the bulk reactions produce an additional reactive screening length, analogous to the Debye length in electrostatics. This in turn leads to an inverse relationship between swimmer radius and swimming speed, which could provide an alternative explanation for recent experimental observations on Pt-polystyrene Janus swimmers [S. Ebbens et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2012, 85, 020401]. We also use our continuum theory to investigate the effect of the Debye screening length itself, going beyond the infinitely-thin-screening-length approximation used by previous analytical theories. We identify significant departures from this limiting behaviour for micron-sized swimmers under typical experimental conditions and find that the approximation fails entirely for nanoscale swimmers.

Lattice-Boltzmann simulations of microswimmer-tracer interactions

Hydrodynamic interactions in systems composed of self-propelled particles, such as swimming microorganisms and passive tracers, have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force-counterforce-based lattice-Boltzmann (LB) algorithm [De Graaf et al., J. Chem. Phys. 144, 134106 (2016)JCPSA60021-960610.1063/1.4944962] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.

Selective Trapping of DNA Using Glass Microcapillaries

We show experimentally that an inexpensive glass microcapillary can accumulate λ-phage DNA at its tip and deliver the DNA into the capillary using a combination of electro-osmotic flow, pressure-driven flow, and electrophoresis. We develop an efficient simulation model based on the electrokinetic equations and the finite-element method to explain this phenomenon. As a proof of concept for the generality of this trapping mechanism we use our numerical model to explore the effect of the salt concentration, the capillary surface charge, the applied voltage, the pressure difference, and the mobility of the analyte molecules. Our results indicate that the simple microcapillary system has the potential to capture a wide range of analyte molecules based on their electrophoretic mobility that extends well beyond our experimental example of λ-phage DNA. Our method for separation and preconcentration of analytes therefore has implications for the development of low-cost lab-on-a-chip devices.

Understanding the onset of oscillatory swimming in microchannels

Self-propelled colloids (swimmers) in confining geometries follow trajectories determined by hydrodynamic interactions with the bounding surfaces. However, typically these interactions are ignored or truncated to the lowest order. We demonstrate that higher-order hydrodynamic moments cause rod-like swimmers to follow oscillatory trajectories in quiescent fluid between two parallel plates, using a combination of lattice-Boltzmann simulations and far-field calculations. This behavior occurs even far from the confining walls and does not require lubrication results. We show that a swimmer's hydrodynamic quadrupole moment is crucial to the onset of the oscillatory trajectories. This insight allows us to develop a simple model for the dynamics near the channel center based on these higher hydrodynamic moments, and suggests opportunities for trajectory-based experimental characterization of swimmers' hydrodynamic properties.

Tic-Tac-Toe Binary Lattices from the Interfacial Self-Assembly of Branched and Spherical Nanocrystals

The self-organization of nanocrystals has proven to be a versatile route to achieve increasingly sophisticated structures of materials, where the shape and properties of individual particles impact the final functionalities. Recent works have addressed this topic by combining various shapes to achieve more complex arrangements of particles than are possible in single-component samples. However, the ability to create intricate architectures over large regions by exploiting the shape of multiply branched nanocrystals to host a second component remains unexplored. Here, we show how the concave shape of a branched nanocrystal, the so-called octapod, is able to anchor a sphere. The two components self-assemble into a locally ordered monolayer consisting of an intercalated square lattice of octapods and spheres, which is reminiscent of the "tic-tac-toe" game. These tic-tac-toe domains form through an interfacial self-assembly that occurs by the dewetting of a hexane layer containing both particle types. By varying the experimental conditions and performing molecular dynamics simulations, we show that the ligands coating the octapods are crucial to the formation of this structure. We find that the tendency of an octapod to form an interlocking-type structure with a second octapod strongly depends on the ligand shell of the pods. Breaking this tendency by ligand exchange allows the octapods to assemble into a more relaxed configuration, which is able to form a lock-and-key-type structure with a sphere, when they have a suitable size ratio. Our findings provide an example of a more versatile use of branched nanocrystals in self-assembled functional materials.

The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells

The so-called "raspberry" model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.

The Raspberry model for hydrodynamic interactions revisited. II. The effect of confinement

The so-called "raspberry" model refers to the hybrid lattice-Boltzmann (LB) and Langevin molecular dynamics schemes for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. In this paper, we present a follow up to our study of the effectiveness of the raspberry model in reproducing hydrodynamic interactions in the Stokes regime for spheres arranged in a simple-cubic crystal [Fischer et al., J. Chem. Phys. 143, 084107 (2015)]. Here, we consider the accuracy with which the raspberry model is able to reproduce such interactions for particles confined between two parallel plates. To this end, we compare our LB simulation results to established theoretical expressions and finite-element calculations. We show that there is a discrepancy between the translational and rotational mobilities when only surface coupling points are used, as also found in Part I of our joint publication. We demonstrate that adding internal coupling points to the raspberry can be used to correct said discrepancy in confining geometries as well. Finally, we show that the raspberry model accurately reproduces hydrodynamic interactions between a spherical colloid and planar walls up to roughly one LB lattice spacing.

Site-specific growth of polymers on silica rods

Colloids specifically developed for self-assembly (SA) into advanced functional materials have rapidly become more complex, as this complexity allows for more ways to optimize both the SA process and the properties of the resulting materials. For instance, by creating 'patchy' particles more open structures can be achieved through directional interactions. However, the number of ways in which site-specific chemistry can be achieved on particle surfaces is still limited. Here, we show how polymer patches can be specifically grown onto only the flat end of bullet-shaped silica rods by utilizing a subtle anisotropy in surface tension and shape caused by the growth mechanism of the rods. Conversely, if the bullet-shaped silica rods are used as 'Pickering-emulsion' stabilizers the same surface tension effects exclusively direct the orientation of the rods into a 'hedgehog-morphology'. Finally, we demonstrate how an external electric field can direct the particles in a 'vectorial' way.

Phase diagram and structural diversity of a family of truncated cubes: degenerate close-packed structures and vacancy-rich states

Using Monte Carlo simulations and free-energy calculations, we determine the phase diagram of a family of truncated hard cubes, where the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. A remarkable diversity in crystal phases and close-packed structures is found, including a fully degenerate crystal structure, several plastic crystals, as well as vacancy-stabilized crystal phases, all depending sensitively on the precise particle shape. Our results illustrate the intricate relation between phase behavior and building-block shape, and can guide future experimental studies on polyhedral-shaped nanoparticles.

Low-dimensional semiconductor superlattices formed by geometric control over nanocrystal attachment

Oriented attachment, the process in which nanometer-sized crystals fuse by atomic bonding of specific crystal facets, is expected to be more difficult to control than nanocrystal self-assembly that is driven by entropic factors or weak van der Waals attractions. Here, we present a study of oriented attachment of PbSe nanocrystals that counteract this tuition. The reaction was studied in a thin film of the suspension casted on an immiscible liquid at a given temperature. We report that attachment can be controlled such that it occurs with one type of facets exclusively. By control of the temperature and particle concentration we obtain one- or two-dimensional PbSe single crystals, the latter with a honeycomb or square superimposed periodicity in the nanometer range. We demonstrate the ability to convert these PbSe superstructures into other semiconductor compounds with the preservation of crystallinity and geometry.

Ordered two-dimensional superstructures of colloidal octapod-shaped nanocrystals on flat substrates

We studied crystal structures in a monolayer consisting of anisotropic branched colloidal (nano)octapods. Experimentally, octapods were observed to form a monolayer on a substrate with a square-lattice crystal structure by drop-casting and fast evaporation of solvent. The experimental results were analyzed by Monte Carlo simulations using a hard octapod model consisting of four interpenetrating spherocylinders. We confirmed by means of free-energy calculations that crystal structures with a (binary-lattice) square morphology are indeed thermodynamically stable at high densities. The effect of the pod length-to-diameter ratio on the crystal structures was also considered and we used this to constructed the phase diagram for these hard octapods. In addition to the (binary-lattice) square crystal phase, a rhombic crystal and a hexagonal plastic-crystal (rotator) phase were obtained. Our phase diagram may prove instrumental in guiding future experimental studies.

Dense regular packings of irregular nonconvex particles

We present a new numerical scheme to study systems of nonconvex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, both from a nanoparticle and from a computational geometry perspective. Besides determining close-packed structures for 17 irregular shapes, we confirm several conjectures for the packings of a large set of 142 convex polyhedra and extend upon these. We also prove that we have obtained the densest packing for both rhombicuboctahedra and rhombic enneacontrahedra and we have improved upon the packing of enneagons and truncated tetrahedra.

Hierarchical self-assembly of suspended branched colloidal nanocrystals into superlattice structures

Self-assembly of molecular units into complex and functional superstructures is ubiquitous in biology. The number of superstructures realized by self-assembly of man-made nanoscale units is also growing. However, assemblies of colloidal inorganic nanocrystals are still at an elementary level, not only because of the simplicity of the shape of the nanocrystal building blocks and their interactions, but also because of the poor control over these parameters in the fabrication of more elaborate nanocrystals. Here, we show how monodisperse colloidal octapod-shaped nanocrystals self-assemble, in a suitable solution environment, on two sequential levels. First, linear chains of interlocked octapods are formed, and subsequently the chains spontaneously self-assemble into three-dimensional superstructures. Remarkably, all the instructions for the hierarchical self-assembly are encoded in the octapod shape. The mechanical strength of these superstructures is improved by welding the constituent nanocrystals together.

Triangular tessellation scheme for the adsorption free energy at the liquid-liquid interface: Towards nonconvex patterned colloids

We present a numerical technique, namely, triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently general to handle nonconvex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. It is verified that the numerical method presented is accurate and sufficiently stable to be applied to more general situations than presented in this paper. The merits of the tessellation method prove to outweigh those of traditionally used semianalytic approaches, especially when it comes to generality and applicability.

Curvature dependence of the electrolytic liquid-liquid interfacial tension

The interfacial tension of a liquid droplet surrounded by another liquid in the presence of microscopic ions is studied as a function of the droplet radius. An analytical expression for the interfacial tension is obtained within a linear Poisson-Boltzmann theory and compared with numerical results from nonlinear Poisson-Boltzmann theory. The excess liquid-liquid interfacial tension with respect to the pure salt-free liquid-liquid interfacial tension is found to decompose into a curvature-independent part due to short-ranged interfacial effects and a curvature-dependent electrostatic contribution. Several curvature-dependent regimes of different scalings of the electrostatic excess interfacial tension are identified. Symmetry relations of the interfacial tension upon swapping droplet and bulk liquid are found to hold in the low-curvature limit, which, e.g., lead to a sign change of the excess Tolman length. For some systems a low-curvature expansion up to the second order turns out to be applicable if and only if the droplet size exceeds the Debye screening length in the droplet, independent of the Debye length in the bulk.