Topologically controlled synthesis of active colloidal bipeds.

Topological growth control allows to produce a narrow distribution of outgrown colloidal rods with defined and adjustable length. We use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of a chosen length. The rods reside above a metamorphic hexagonal magnetic pattern. The periodic repetition of specific loops of the orientation of an applied external field renders paramagnetic colloidal particles and their assemblies into active bipeds that walk on the pattern. The metamorphic patterns allow the robust and controlled polymerization of single colloids to bipeds of a desired length. The colloids are exposed to this fixed external control loop that causes multiple simultaneous responses: Small bipeds and single colloidal particles interpret the external magnetic loop as an order to walk toward the active zone, where they assemble and polymerize. Outgrown bipeds interpret the same loop as an order to walk away from the active zone. The topological transition occurs solely for the growing biped and nothing is changed in the environment nor in the magnetic control loop. As in many biological systems the decision of a biped that reached its outgrown length to walk away from the reaction site is made internally, not externally.

Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes.

Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous magnetic patterns, revealing that transport complexity can be encoded in both the driving loop and the pattern. Complex patterns support intricate transport modes when the microparticles are subjected to simple time-periodic loops of a uniform magnetic field. We design a pattern featuring a topological defect that functions as an attractor or a repeller of microparticles, as well as a pattern that directs microparticles along a prescribed complex trajectory. Using simple patterns and complex loops, we simultaneously and independently control the motion of several identical microparticles differing only in their positions above the pattern. Combining complex patterns and complex loops we transport microparticles from unknown locations to predefined positions and then force them to follow arbitrarily complex trajectories concurrently. Our findings pave the way for new avenues in transport control and dynamic self-assembly in colloidal science.

Energy Dissipation in the Human Red Cell Membrane.

The membrane of the human red cell consists of a lipid bilayer and a so-called membrane skeleton attached on the cytoplasmic side of the bilayer. Upon the deformation of red cells, energy is dissipated in their cytoplasm and their membrane. As to the membrane, three contributions can be distinguished: (i) A two-dimensional shear deformation with the membrane viscosity as the frictional parameter; (ii) A motion of the membrane skeleton relative to the bilayer; (iii) A relative motion of the two monolayers of the bilayer. The frictional parameter in contributions (ii) and (iii) is a frictional coefficient specific for the respective contribution. This perspective describes the history up to recent advances in the knowledge of these contributions. It reviews the mechanisms of energy dissipation on a molecular scale and suggests new ones, particularly for the first contribution. It proposes a parametric fitting expected to shed light on the discrepant values found for the membrane viscosity by different experimental approaches. It proposes strategies that could allow the determination of the frictional coefficients pertaining to the second and the third contribution. It highlights the consequences characteristic times have on the state of the red cell membrane in circulation as well as on the adaptation of computer models to the red cell history in an in vitro experiment.

Colloidal transport in twisted lattices of optical tweezers.

We simulate the transport of colloidal particles driven by a static and homogeneous drift force, and subject to the optical potential created by two lattices of optical tweezers. The lattices of optical tweezers are parallel to each other, shifted, and rotated by a twist angle. Due to a negative interference between the potential of the two lattices, flat channels appear in the total optical potential. At specific twist angles, known as magic angles, the flat channels percolate the entire system and the colloidal particles can then be transported using a weak external drift force. We characterize the transport in both square and hexagonal lattices of twisted optical tweezers.

The Shape of Human Red Blood Cells Suspended in Autologous Plasma and Serum.

(1) Background: In almost all studies of the shape of the human red blood cell (RBC), the suspending medium was a salt solution supplemented with albumin. However, the ratio of thickness across the dimple region to the thickness of the rim (THR) depends on the albumin concentration. Values of the THR in the literature range from 0.27 to 0.627 whereas in the present work it was 0.550 or 0.601 whether measured in plasma or serum. (2) Methods: 9911 RBCs of eight donors were suspended in autologous plasma or serum. Sedimented RBCs were observed under bright field illumination at 416 nm. From the profiles of gray value, the THR was determined. (3) Results: The THR displays a wide distribution within a single blood sample. A direct correlation of THR and spontaneous curvature of the membrane is likely. The variation of the mean THR between different donors is large. The aspect ratio of RBCs viewed face-on ranged on average from 1 to 1.48. In oval RBCs, the rim is thicker along the major axis than along the minor axis, an effect increasing with increasing aspect ratio. Remodeling of the membrane skeleton occurs in vivo with a characteristic time (τ) on the order of 1 h. (4) Conclusions: Consideration of these data in models of RBC behavior might improve the agreement with observations. τ≈1 h suggests a more general type of reference configuration of the membrane skeleton than a stress free shape.

Gauge invariant and gauge dependent aspects of topological walking colloidal bipeds.

Paramagnetic colloidal spheres assemble to colloidal bipeds of various length in an external magnetic field. When the bipeds reside above a magnetic pattern and we modulate the direction of the external magnetic field, the rods perform topologically distinct classes of protected motion above the pattern. The topological protection allows each class to be robust against small continuous deformations of the driving loop of the external field. We observe motion of the rod from a passive central sliding and rolling motion for short bipeds toward a walking motion with both ends of the rod alternately touching down on the pattern for long bipeds. The change of character of the motion occurs in form of discrete topological transitions. The topological protection makes walking a form of motion robust against the breaking of the non symmorphic symmetry. In patterns with non symmorphic symmetry walking is reversible. In symmorphic patterns lacking a glide plane the walking can be irreversible or reversible involving or not involving ratchet jumps. Using different gauges allows us to unravel the active and passive aspects of the topological walks.

Simultaneous polydirectional transport of colloidal bipeds.

Detailed control over the motion of colloidal particles is relevant in many applications in colloidal science such as lab-on-a-chip devices. Here, we use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of several lengths. The rods reside above a square magnetic pattern and are transported via modulation of the direction of the external magnetic field. The rods behave like bipeds walking above the pattern. Depending on their length, the bipeds perform topologically distinct classes of protected walks. We design parallel polydirectional modulation loops of the external field that command up to six classes of bipeds to walk on distinct predesigned paths. Using such loops, we induce the collision of reactant bipeds, their polymerization addition reaction to larger bipeds, the separation of product bipeds from the educts, the sorting of different product bipeds, and also the parallel writing of a word consisting of several letters. Our ideas and methodology might be transferred to other systems for which topological protection is at work.

Colloidal trains.

Single and double paramagnetic colloidal particles are placed above a magnetic square pattern and are driven with an external magnetic field processing around a high symmetry direction of the pattern. The external magnetic field and that of the pattern confine the colloids into lanes parallel to a lattice vector of the pattern. The precession of the external field causes traveling minima of the magnetic potential along the direction of the lanes. At sufficiently high frequencies of modulation, only the doublets respond to the external field and move in direction of the traveling minima along the lanes, while the single colloids cannot follow and remain static. We show how the doublets can induce a coordinated motion of the single colloids building colloidal trains made of a chain of several single colloids transported by doublets.

Hard topological versus soft geometrical magnetic particle transport.

The question of how a dissipative geometrical transport system changes towards a topological transport system is important to render a fragile transport into a robust transport. We show how a macroscopic magnetic topological transport of solid state spheres changes to a geometrical transport of ferrofluid droplets, when instead of a solid state object, soft matter is transported. The key difference when comparing solid objects with fluid droplets is the possibility to split a ferrofluid droplet into two droplets. It is shown how this fundamental difference also fundamentally changes the transport properties. Hence, experimentally and theoretically the transport on top of a periodic two-dimensional hexagonal magnetic pattern of (i) a single macroscopic steel sphere, (ii) a doublet of wax/magnetite composite spheres, and (iii) an immiscible mixture of ferrofluid droplets with a perfluorinated liquid is analyzed. The transport of all these magnetic objects is achieved by moving an external permanent magnet on a closed modulation loop around the two-dimensional magnetic pattern. The transport of one and also that of two objects per unit cell is topologically protected and characterized by discrete displacements of the particles as we continuously scan through a family of modulation loops. The direction and the type of transport are characterized by the winding numbers of the modulation loops around special objects in control space, which is the space for the possible directions of the external magnetic field. The winding numbers necessary for characterizing the topological transport increase with the number of particles per unit cell. The topological character of the transport is destroyed, when transporting a large collection of particles per unit cell, like it is in the case of a macroscopic assembly of magnetic nanoparticles in a ferrofluid droplet for which the transport is geometrical and no longer topological. To characterize the change in the transport from topological to geometrical, we perform computer simulations of the transport of an increasing number of particles per unit cell.

Edge transport at the boundary between topologically equivalent lattices.

Edge currents of paramagnetic colloidal particles propagate at the edge between two topologically equivalent magnetic lattices of different lattice constant when the system is driven with periodic modulation loops of an external magnetic field. The number of topologically protected particle edge transport modes is not determined by a bulk-boundary correspondence. Instead, we find a rich variety of edge transport modes that depend on the symmetry of both the edge and the modulation loop. The edge transport can be ratchet-like or adiabatic, time or non-time reversal symmetric. The topological nature of the edge transport is classified by a set of winding numbers around bulk fence points extended by winding numbers around edge specific bifurcation points that cannot be deduced from the two bulk lattices.

Blood Crystal: Emergent Order of Red Blood Cells Under Wall-Confined Shear Flow.

Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report numerical simulations and an analytical model revealing that deformable particles and, in particular, red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The pattern wavelength concurs well with our experimental observations. The order is of a pure hydrodynamic and inertialess origin, and it emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls that drives deformable cells towards the channel midplane and (ii) intercellular hydrodynamic interactions that can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on the RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order.

Wrinkled labyrinths in critical demixing ferrofluid.

A thin film of a critical ferrofluid mixture undergoes a sequence of transitions in a magnetic field. First the application of a field induces a critical demixing of the fluid into cylindrical droplets of the minority phase immersed in an extended majority phase. At a second critical field the cylindrical shape is destabilized and transforms into a labyrinth pattern. A third wrinkling transition occurs at even higher field if the liquid has a liquid/air interface. The wrinkling is absent if the droplet has a cover-slide on top. We explain the wrinkling by the wetting behavior of the liquid/air interface that shifts the surface region away from a critical demixing point.

Lattice symmetries and the topologically protected transport of colloidal particles.

The topologically protected transport of colloidal particles on top of periodic magnetic patterns is studied experimentally, theoretically, and with computer simulations. To uncover the interplay between topology and symmetry we use patterns of all possible two dimensional magnetic point group symmetries with equal lengths lattice vectors. Transport of colloids is achieved by modulating the potential with external, homogeneous but time dependent magnetic fields. The modulation loops can be classified into topologically distinct classes. All loops falling into the same class cause motion in the same direction, making the transport robust against internal and external perturbations. We show that the lattice symmetry has a profound influence on the transport modes, the accessibility of transport networks, and the individual transport directions of paramagnetic and diamagnetic colloidal particles. We show how the transport of colloidal particles above a two fold symmetric stripe pattern changes from universal adiabatic transport at large elevations via a topologically protected ratchet motion at intermediate elevations toward a non-transport regime at low elevations. Transport above four-fold symmetric patterns is closely related to the two-fold symmetric case. The three-fold symmetric case however consists of a whole family of patterns that continuously vary with a phase variable. We show how this family can be divided into two topologically distinct classes supporting different transport modes and being protected by proper and improper six fold symmetries. We discuss and experimentally demonstrate the topological transition between both classes. All three-fold symmetric patterns support independent transport directions of paramagnetic and diamagnetic particles. The similarities and the differences in the lattice symmetry protected transport of classical over-damped colloidal particles versus the topologically protected transport in quantum mechanical systems are emphasized.

Molecular Explanation for the Abnormal Flux of Material into a Hot Spot in Ester Monolayers.

Langmuir monolayers of certain surfactants show a negative derivative of the surface pressure with respect to temperature. In these monolayers, a local temperature gradient leads to local yielding of the solid phase to a kinetically flowing liquid, so that the material flows toward the hotter regions that act as sinks. The accumulation of material leads to the formation of nonequilibrium multilamellar bubbles of different sizes. Here we investigate the molecular factors leading to such a peculiar behavior. First, we identify the required structural molecular moieties, and second we vary the composition of the subphase in order to analyze its influence. We conclude that esters appear to be unique in two key aspects: they form monolayers whose compression isotherms shift to lower areas as the temperature increases, and thus collapse into a hot spot; and they bind weakly to the aqueous subphase, i.e., water does not attach to the monolayer at the molecular level, but only supports it. Molecular simulations for a selected system confirm and help explain the observed behavior: surfactant molecules form a weak hydrogen bonding network, which is disrupted upon heating, and also the molecular tilting changes with temperature, leading to changes in the film density.

Creep and stress relaxation of human red cell membrane.

In contrast to most mechanical properties of the red cell, experimental information on stress relaxation (SR) of the membrane skeleton is scarce. On the other hand, many postulates or assumptions as to the value of the characteristic time of SR [Formula: see text] can be found in the literature. Here, an experiment is presented that allows measurement of [Formula: see text] up to values of about 10 h. The membrane skeleton was deformed passively by changing the spontaneous curvature of the bilayer thus transforming the natively biconcave red cells into echinocytes. This shape and the concomitant deformation of the skeleton were kept up to 4 h by incubation at 37 â„ƒ. During this period, no plastic deformation (creep) was observed. After the incubation, the spontaneous curvature was returned to normal. The resulting shape was smooth showing no remnants of the echinocytic shape. Both observations indicate [Formula: see text] 10 h. This result is in gross disagreement to postulates or assumptions existing in the literature.

Non reciprocal skewed rolling of a colloidal wheel due to induced chirality.

We use a rotating magnetic field to assemble an oblate cluster of paramagnetic colloidal particles. If the field is rotating about a horizontal axis, the cluster acts as a colloidal wheel rolling across the supporting glass surface. The motion is reversible upon switching the direction of rotation. Surprisingly, the reversibility is lost if the axis of field rotation is tilted with respect to the surface. The wheel then rolls in a direction that is not perpendicular to the field rotation axis. We explain the skewed rotation with an interplay between a magnetic driving torque, magnetic anisotropy and an anisotropy in the hydrodynamic mobility tensor in the vicinity of a surface. The opposing forward and backward drive induce opposite chirality in the degrees of freedom of the mechanically achiral colloidal wheel.

Magnetic field induced modulated phases in a ferrofluid lutidine silicone oil mixture.

A mixture of an ester based ferrofluid with silicone oil and 2,6-lutidine is exposed to an external magnetic field. We find a region of composition of the ternary mixture, where weak magnetic fields of the order of a few kA m-1 induce a modulated phase with a pattern characterized by equilibrium size droplets of the minority phase immersed into the extended majority phase. While the pattern resembles in many ways the pattern of immiscible magnetic fluids, the dependence of the characteristic parameters of the pattern on the magnetic field are completely different than in immiscible fluids. We theoretically explain the pattern formation as a magnetic field induced polymerization of magnetic particles into magnetic chains that goes along with a reduction of the entropy of mixing. This entropy reduction causes the Ostwald ripening of chains into mesoscopic droplets the size of which is limited by repulsive dipolar interactions between the chains.

Transport on Active Paramagnetic Colloidal Networks.

We dynamically self-assemble an active paramagnetic colloidal network that ballistically transports nonmagnetic fluorescent colloidal particles on top of the network. The transport mechanism is put into effect by a directed hydrodynamic flow, created by the rotation of individual colloids forming the network. The ballistic transport is confined to the network, and tracer beads in meshes show a diffusive instead of a ballistic transport. We develop a simple model to explain the transport.

Topological protection of multiparticle dissipative transport.

Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.

Magnetic guidance of the magnetotactic bacterium Magnetospirillum gryphiswaldense.

Magnetospirillum gryphiswaldense is a magnetotactic bacterium with a permanent magnetic moment capable of swimming using two bipolarly located flagella. In their natural environment these bacteria swim along the field lines of the homogeneous geomagnetic field in a typical run and reversal pattern and thereby create non-differentiable trajectories with sharp edges. In the current work we nevertheless achieve stable guidance along curved lines of mechanical instability by using a heterogeneous magnetic field of a garnet film. The successful guidance of the bacteria depends on the right balance between motility and the magnetic moment of the magnetosome chain.