The experimental realization of a two-dimensional colloidal model system

Liquid-hexatic transition for soft disks

We study the liquid-hexatic transition of soft disks with massively parallel simulations and determine the equation of state as a function of system size. For systems with interactions decaying as the inverse mth power of the separation, the liquid-hexatic phase transition is continuous for m=12 and m=8, while it is of first order for m=24. The critical power m for the transition between continuous and first-order behavior is larger than previously reported. The continuous transition for m=12 implies that the two-dimensional Lennard-Jones model has a continuous liquid-hexatic transition at high temperatures. We also study the Weeks-Chandler-Andersen model and find a continuous transition at high temperatures that is consistent with the soft-disk case for m=12. Pressure data as well as our implementation are available from an open-source repository.

Direct observation of crystal nucleation and growth in a quasi-two-dimensional nonvibrating granular system

We study a quasi-two-dimensional macroscopic system of magnetic spherical particles settled on a shallow concave dish under a temporally oscillating magnetic field. The system reaches a stationary state where the energy losses from collisions and friction with the concave dish surface are compensated by the continuous energy input coming from the oscillating magnetic field. Random particle motions show some similarities with the motions of atoms and molecules in a glass or a crystal-forming fluid. Because of the curvature of the surface, particles experience an additional force toward the center of the concave dish. When decreasing the magnetic field, the effective temperature is decreased and diffusive particle motion slows. For slow cooling rates we observe crystallization, where the particles organize into a hexagonal lattice. We study the birth of the crystalline nucleus and the subsequent growth of the crystal. Our observations support nonclassical theories of crystal formation. Initially a dense amorphous aggregate of particles forms, and then in a second stage this aggregate rearranges internally to form the crystalline nucleus. As the aggregate grows, the crystal grows in its interior. After a certain size, all the aggregated particles are part of the crystal and after that crystal growth follows the classical theory for crystal growth.

Relaxation moduli of glass-forming systems: temperature effects and fluctuations

Equilibrium and dynamical properties of a two-dimensional polydisperse colloidal model system are characterized by means of molecular dynamics (MD) and Monte Carlo (MC) simulations. We employed several methods to prepare quasi-equilibrated systems: in particular, by slow cooling and tempering with MD (method SC-MD), and by tempering with MC dynamics involving swaps of particle diameters (methods Sw-MD, Sw-MC). It is revealed that the Sw-methods are much more efficient for equilibration below the glass transition temperature T_g leading to denser and more rigid systems which show much slower self-diffusion and shear-stress relaxation than their counterparts prepared with the SC-MD method. The shear-stress relaxation modulus G(t) is obtained based on the classical stress-fluctuation relation. We demonstrate that the α-relaxation time τ_α obtained using a time-temperature superposition of G(t) shows a super-Arrhenius behavior with the VFT temperature T₀ well below T_g. We also derive novel rigorous fluctuation relations providing isothermic and adiabatic compression relaxation moduli in the whole time range (including the short-time inertial regime) based on correlation data for thermostatted systems. It is also shown that: (i) the assumption of Gaussian statistics for stress fluctuations leads to accurate predictions of the variances of the fluctuation moduli for both shear (μ_F) and compression (η_F) at T⪆T_g. (ii) The long-time (quasi-static) isothermic and adiabatic moduli increase on cooling faster than the affine compression modulus η_A, and this leads to a monotonic temperature dependence of η_F which is qualitatively different from μ_F(T) showing a maximum near T_g.

Colloidal monolayers with cell-like tessellations via interface assisted evaporative assembly

HYPOTHESIS

Evaporating sessile drops containing surface active colloids is a promising route to self-assemble two-dimensional nanostructures. The standard protocol is to first self-assemble surface active nanoscale particles at the water-vapour interface and subsequently transfer it on to a solid surface. Colloidal monolayers with very few morphologies have been fabricated, exploiting this bottom-up self-assembly technique. However, the evaporation kinetics under controlled humidity conditions may dramatically alter the microstructure of self-assembled colloidal monolayers at the liquid-vapor interface and that on the solid surfaces, an aspect that has not been fully addressed in the prior studies.

EXPERIMENTS

To this end, we present an experimental study of evaporation driven self-assembly of soft poly(N-isopropylacrylamide) (pNIPAM) microgel particles loaded in a sessile drop. The surface-active microgel particles spontaneously populate the water-vapour interface facilitating the suppression of the coffee-ring effect and the formation of monolayer stains. The role of evaporation kinetics under controlled humidity conditions on the colloid's microstructure adsorbed to the solvent-air interface and on the morphology of the colloidal monolayer transferred onto the solid surface are studied in detail.

FINDINGS

The formation of particle-free and particle-rich regions at the water-vapor interface is observed for sessile drops evaporated under saturated humidity conditions. We show that the evaporation induced shrinkage of the interface area and the enhancement of the areal density of microgel particles adsorbed onto the interface leads to a restructuring of the particle-laden interface. The rearrangement of microgel particles along the water-vapor interface resembling the de-wetting assisted patterns is transferred to the solid substrate upon complete evaporation of the solvent. The microgel particles in the deposit assemble into domains with enhanced crystalline order. The evolution of Voronoi entropy across the monolayer deposit patterns obtained by the standard and slow evaporation routes are presented.

Glass- and crystal-forming model based on a granular two-dimensional system

We study a two-dimensional system of magnetic particles under an alternating magnetic field. The particles are settled on the surface of a negative lens where they tend to sediment toward the center due to gravity. The effective temperature is controlled by the intensity of the applied magnetic field. The system is cooled down from a gaslike state to a solidlike state at different rates. We observe that for some slow cooling rates the final configuration of system is a hexagonal compact arrange, while for the faster cooling rates the final configurations are glasslike states. We followed the time evolution of the system, which allows us to determine in detail changes in quantities such as the interparticle distance. We determine the glass transition temperature for different cooling rates, finding that such temperature increases as the cooling rate decreases, in contrast with some other glass-forming liquids.

Dynamic ordering of driven spherocylinders in a nonequilibrium suspension of small colloidal spheres

The ordering effects of driven spherocylinder-shaped rods in a colloidal suspension of small spheres confined to a two-dimensional channel geometry are observed via Brownian dynamics simulations without hydrodynamics. To describe the ordering, an order parameter and an expression for a potential of mean force of an equivalent equilibrium system are defined and analyzed. By varying the application point of the external force along the rods and thus the resulting lever, a transition from a preferred orientation parallel to the direction of the force to a preferred orientation perpendicular to the direction of the force was observed. It is shown that this effect can only be found if the spheres and multiple rods are present. Furthermore, a dependency of the order parameter on the absolute value of the force was discovered. The analysis of the potential of mean force further indicates a transition between two different phases of mean orientation. An observation of the flow equilibrium mean velocity in channel direction led to a s-shaped progression regarding the lever dependency, also marking a transition between two states linked to the mean orientation of the rods. A finite size analysis was conducted. Its results indicate that the transition between the two orientation states is a general phenomenon of the observed rod-sphere mixture.

Dense colloidal mixtures in an external sinusoidal potential

Concentrated binary colloidal mixtures containing particles with a size ratio 1:2.4 were exposed to a periodic potential that was realized using a light field, namely, two crossed laser beams creating a fringe pattern. The arrangement of the particles was recorded using optical microscopy and characterized in terms of the pair distribution function along the minima, the occupation probability perpendicular to the minima, the angular bond distribution, and the average potential energy per particle. The particle arrangement was investigated in dependence of the importance of particle-potential and particle-particle interactions by changing the potential amplitude and particle concentration, respectively. An increase in the potential amplitude leads to a stronger localization, especially of the large particles, but also results in an increasing fraction of small particles being located closer to the potential maxima, which also occurs upon increasing the particle density. Furthermore, increasing the potential amplitude induces a local demixing of the two particle species, whereas an increase in the total packing fraction favors a more homogeneous arrangement.

Viscosity of a sheared correlated (near-critical) model fluid in confinement

Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including finite-size effects and critical Casimir forces. We explore here some non-equilibrium aspects of these effects in the stationary state resulting from the action of external forces: by analyzing a model of a correlated fluid under shear, spatially confined by two parallel plates, we study the resulting viscosity within the setting of (Gaussian) Landau-Ginzburg theory. Specifically, we introduce a model in which the hydrodynamic velocity field (obeying the Stokes equation) is coupled to an order parameter with dissipative dynamics. The well-known Green-Kubo relation for bulk systems is generalized for confined systems. This is shown to result in a non-local Stokes equation for the fluid flow, due to the correlated fluctuations. The resulting effective shear viscosity shows universal as well as non-universal contributions, which we study in detail. In particular, the deviation from the bulk behavior is universal, depending on the ratio of the correlation length and the film thickness L. In addition, at the critical point the viscosity is proportional to [Formula: see text], where [Formula: see text] is a dynamic length scale. These findings are expected to be experimentally observable, especially for systems where the bulk viscosity is affected by critical fluctuations.

Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions

Phase transitions significantly differ between 2D and 3D systems, but the influence of dimensionality on the glass transition is unresolved. We use microscopy to study colloidal systems as they approach their glass transitions at high concentrations and find differences between two dimensions and three dimensions. We find that, in two dimensions, particles can undergo large displacements without changing their position relative to their neighbors, in contrast with three dimensions. This is related to Mermin-Wagner long-wavelength fluctuations that influence phase transitions in two dimensions. However, when measuring particle motion only relative to their neighbors, two dimensions and three dimensions have similar behavior as the glass transition is approached, showing that the long-wavelength fluctuations do not cause a fundamental distinction between 2D and 3D glass transitions.

Mermin-Wagner fluctuations in 2D amorphous solids

In a recent commentary, J. M. Kosterlitz described how D. Thouless and he got motivated to investigate melting and suprafluidity in two dimensions [Kosterlitz JM (2016) J Phys Condens Matter 28:481001]. It was due to the lack of broken translational symmetry in two dimensions-doubting the existence of 2D crystals-and the first computer simulations foretelling 2D crystals (at least in tiny systems). The lack of broken symmetries proposed by D. Mermin and H. Wagner is caused by long wavelength density fluctuations. Those fluctuations do not only have structural impact, but additionally a dynamical one: They cause the Lindemann criterion to fail in 2D in the sense that the mean squared displacement of atoms is not limited. Comparing experimental data from 3D and 2D amorphous solids with 2D crystals, we disentangle Mermin-Wagner fluctuations from glassy structural relaxations. Furthermore, we demonstrate with computer simulations the logarithmic increase of displacements with system size: Periodicity is not a requirement for Mermin-Wagner fluctuations, which conserve the homogeneity of space on long scales.

Strain Pattern in Supercooled Liquids

Investigations of strain correlations at the glass transition reveal unexpected phenomena. The shear strain fluctuations show an Eshelby-strain pattern [∼cos(4θ)/r^{2}], characteristic of elastic response, even in liquids, at long times. We address this using a mode-coupling theory for the strain fluctuations in supercooled liquids and data from both video microscopy of a two-dimensional colloidal glass former and simulations of Brownian hard disks. We show that the long-ranged and long-lived strain signatures follow a scaling law valid close to the glass transition. For large enough viscosities, the Eshelby-strain pattern is visible even on time scales longer than the structural relaxation time τ and after the shear modulus has relaxed to zero.

Local collective motion analysis for multi-probe dynamic imaging and microrheology

Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches.

Glass transition of two-dimensional 80-20 Kob-Andersen model at constant pressure

We reconsider numerically the two-dimensional version of the Kob-Andersen model (KA2d) with a fraction of 80% of large spheres. A constant moderate pressure is imposed while the temperature T is systematically quenched from the liquid limit through the glass transition at [Formula: see text] down to very low temperatures. Monodisperse Lennard-Jones (mdLJ) bead systems, forming a crystal phase at low temperatures, are used to highlight several features of the KA2d model. As can be seen, e.g. from the elastic shear modulus G(T), determined using the stress-fluctuation formalism, our KA2d model is a good glass-former. A continuous cusp-singularity, [Formula: see text] with [Formula: see text], is observed in qualitative agreement with other recent numerical and theoretical work, however in striking conflict with the additive jump discontinuity predicted by mode-coupling theory.

Colloidal Microworms Propelling via a Cooperative Hydrodynamic Conveyor Belt

We study propulsion arising from microscopic colloidal rotors dynamically assembled and driven in a viscous fluid upon application of an elliptically polarized rotating magnetic field. Close to a confining plate, the motion of this self-assembled microscopic worm results from the cooperative flow generated by the spinning particles which act as a hydrodynamic "conveyor belt." Chains of rotors propel faster than individual ones, until reaching a saturation speed at distances where induced-flow additivity vanishes. By combining experiments and theoretical arguments, we elucidate the mechanism of motion and fully characterize the propulsion speed in terms of the field parameters.

Quantitatively mimicking wet colloidal suspensions with dry granular media

Athermal two-dimensional granular systems are exposed to external mechanical noise leading to Brownian-like motion. Using tunable repulsive interparticle interaction, it is shown that the same microstructure as that observed in colloidal suspensions can be quantitatively recovered at a macroscopic scale. To that end, experiments on granular and colloidal systems made up of magnetized particles as well as computer simulations are performed and compared. Excellent agreement throughout the range of the magnetic coupling parameter is found for the pair distribution as well as the bond-orientational correlation functions. This finding opens new ways to efficiently and very conveniently explore phase transitions, crystallization, nucleation, etc in confined geometries.

Entropy and kinetics of point defects in two-dimensional dipolar crystals

We study in experiment and with computer simulation the free energy and the kinetics of vacancy and interstitial defects in two-dimensional dipolar crystals. The defects appear in different local topologies, which we characterize by their point group symmetry; Cn is the n-fold cyclic group and Dn is the dihedral group, including reflections. The frequency of different local topologies is not determined by their almost degenerate energies but is dominated by entropy for symmetric configurations. The kinetics of the defects is fully reproduced by a master equation in a multistate Markov model. In this model, the system is described by the state of the defect and the time evolution is given by transitions occurring with particular rates. These transition rate constants are extracted from experiments and simulations using an optimization procedure. The good agreement between experiment, simulation, and master equation thus provides evidence for the accuracy of the model.

Dynamical properties and melting of binary two-dimensional colloidal alloys

A two-dimensional (2D) binary colloidal system consisting of interacting dipoles is investigated using an analytical approach. Within the harmonic approximation we obtain the phonon spectrum of the system as a function of the composition, dipole-moment ratio, and mass ratio between the small and big particles. Through a systematic analysis of the phonon spectra we are able to determine the stability region of the different lattice structures of the colloidal alloys. The gaps in the phonon frequency spectrum, the optical frequencies in the long-wavelength limit, and the sound velocity are discussed as well. Using the modified Lindemann criterion and within the harmonic approximation we estimate the melting temperature of the sublattice generated by the big particles.

Self-organized defect strings in two-dimensional crystals

Using experiments with single-particle resolution and computer simulations we study the collective behavior of multiple vacancies injected into two-dimensional crystals. We find that the defects assemble into linear strings, terminated by dislocations with antiparallel Burgers vectors. We show that these defect strings propagate through the crystal in a succession of rapid one-dimensional gliding and rare rotations. While the rotation rate decreases exponentially with the number of defects in the string, the diffusion constant is constant for large strings. By monitoring the separation of the dislocations at the end points, we measure their effective interactions with high precision beyond their spontaneous formation and annihilation, and we explain the double-well form of the dislocation interaction in terms of continuum elasticity theory.

Fluctuations of orientational order and clustering in a two-dimensional colloidal system under quenched disorder

Using both video microscopy of superparamagnetic colloidal particles confined in two dimensions and corresponding computer simulations of repulsive parallel dipoles, we study the formation of fluctuating orientational clusters and topological defects in the context of the KTHNY-like melting scenario under quenched disorder. We analyze cluster densities, average cluster sizes, and the population of noncluster particles, as well as the development of defects, as a function of the system temperature and disorder strength. In addition, the probability distribution of clustering and orientational order is presented. We find that the well-known disorder-induced widening of the hexatic phase can be traced back to the distinct development characteristics of clusters and defects along the melting transitions from the solid phase to the hexatic phase to the isotropic fluid.

Two-dimensional melting under quenched disorder

We study the influence of quenched disorder on the two-dimensional melting behavior of superparamagnetic colloidal particles, using both video microscopy and computer simulations of repulsive parallel dipoles. Quenched disorder is introduced by pinning a fraction of the particles to an underlying substrate. We confirm the occurrence of the Kosterlitz-Thouless-Halperin-Nelson-Young scenario and observe an intermediate hexatic phase. While the fluid-hexatic transition remains largely unaffected by disorder, the hexatic-solid transition shifts to lower temperatures with increasing disorder. This results in a significantly broadened stability range of the hexatic phase. In addition, we observe spatiotemporal critical(like) fluctuations, which are consistent with the continuous character of the phase transitions. Characteristics of first-order transitions are not observed.

Charged colloidal model systems under confinement in slit geometry: a new setup for optical microscopic studies

A new experimental setup for optical microscopic studies of charged colloidal model systems under confinement between two flat walls is presented. The measurement cell consists of optically flat quartz substrates attached to piezo actuators. Those facilitate fast and flexible adjustment of the confining geometry. Optionally, the local cell height can be quantitatively controlled by in situ interferometric measurements. Proper choice of materials guarantees sufficient chemical inertia against contamination with salt ions. For efficient preparation of charged colloidal suspensions under strongly deionized conditions, the cell can be connected to a conventional pump circuit including a mixed bed ion exchanger column. The usefulness of this setup, in particular for investigating the equilibrium phase behavior of colloids at low background salt concentrations, is demonstrated recalling recent experiments.

Sedimentation and polar order of active bottom-heavy particles

Self-propelled particles in an external gravitational field have been shown to display both an increased sedimentation length and polar order even without particle interactions. Here, we investigate self-propelled particles which additionally are bottom-heavy, that is they feel a torque aligning them to swim against the gravitational field. For bottom-heavy particles the gravitational field has the two opposite effects of i) sedimentation and ii) upward alignment of the particles' swimming direction. We perform a multipole expansion of the one-particle distribution of non-interacting particles with respect to orientation and derive expressions for sedimentation length and mean particle orientation which we check against Brownian Dynamics simulations. For large strength of gravity or small particle speeds and aligning torque, we observe sedimentation with increased sedimentation length compared with passive colloids but also active colloids without bottom-heaviness. Increasing, for example, swimming speed the sedimentation profile is inverted and the particles swim towards the top wall of the enclosing box. We find maximal orientational order at intermediate swimming speeds for both cases of particles with bottom-heaviness and those without. Ordering unsurprisingly is increased for the bottom-heavy particles, but this difference disappears at higher levels of activity and for very high activities ordering goes to zero in both cases.

Test of the universal scaling law of diffusion in colloidal monolayers

Using the techniques of optical microscopy and particle tracking, we measure the pair correlation function and Brownian diffusion in monolayers of strongly interacting colloidal particles suspended at or near three different interfaces and test the universal scaling law of the normalized diffusion coefficient, D[over ˜]≃e(αΔS), as a function of the excess entropy ΔS for a wide range of particle concentrations. It is found that the universal scaling law with α=1 holds well for highly charged polystyrene spheres suspended at an air-water interface, where the strong electrostatic interactions play a dominant role. For monolayer suspensions of hard-sphere-like particles, where hydrodynamic interactions become important, deviations from the universal scaling law are observed. The experiment indicates that the hydrodynamic corrections could be incorporated into the universal scaling law of diffusion with an exponent α<1.

Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model

A two-dimensional crystal of repulsive dipolar particles is studied in the vicinity of its melting transition by using Brownian dynamics computer simulation, dynamical density-functional theory, and phase-field-crystal modeling. A vacancy is created by taking out a particle from an equilibrated crystal, and the relaxation dynamics of the vacancy is followed by monitoring the time-dependent one-particle density. We find that the vacancy is quickly filled up by diffusive hopping of neighboring particles towards the vacancy center. We examine the temperature dependence of the diffusion constant and find that it decreases with decreasing temperature in the simulations. This trend is reproduced by the dynamical density-functional theory. Conversely, the phase-field-crystal calculations predict the opposite trend. Therefore, the phase-field model needs a temperature-dependent expression for the mobility to predict trends correctly.

Comparison of 2D melting criteria in a colloidal system

We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal equilibrium by two continuous phase transitions into the isotropic liquid state with an intermediate phase, commonly known as the hexatic phase. We verify the significance of several criteria based on dynamical and structural properties to identify the crystal-hexatic and hexatic-isotropic liquid phase transitions for the same experimental data of the given setup. The criteria are the bond orientational correlation function, the Larson-Grier criterion, the 2D dynamic Lindemann parameter, the bond orientational susceptibility, the 2D Hansen-Verlet rule, the Löwen-Palberg-Simon criterion as well as a criterion based on the shape factor of Voronoi cells and Minkowski functionals. For our system with long-range repulsion, the bond order correlation function and bond order susceptibility work best to identify the hexatic-isotropic liquid transition and the 2D dynamic Lindemann parameter identifies unambiguously the hexatic-crystalline transition.

Motion, relaxation dynamics, and diffusion processes in two-dimensional colloidal crystals confined between walls

The dynamical behavior of single-component two-dimensional colloidal crystals confined in a slit geometry is studied by Langevin dynamics simulation of a simple model. The colloids are modeled as pointlike particles, interacting with the repulsive part of the Lennard-Jones potential, and the fluid molecules in the colloidal suspension are not explicitly considered. Considering a crystalline strip of triangular lattice structure with n=30 rows, the (one-dimensional) walls confining the strip are chosen as two rigidly fixed crystalline rows at each side, commensurate with the lattice structure and, thus, stabilizing long-range order. The case when the spacing between the walls is incommensurate with the ideal triangular lattice is also studied, where (due to a transition in the number of rows, n → n-1) the confined crystal is incommensurate with the confining boundaries, and a soliton staircase forms along the walls. It is shown that mean-square displacements (MSDs) of particles as a function of time show an overshoot and then saturate at a horizontal plateau in the commensurate case, the value of the plateau being largest in the center of the strip. Conversely, when solitons are present, MSDs are largest in the rows containing the solitons, and all MSDs do not settle down at well-defined plateaus in the direction parallel to the boundaries, due to the lack of positional long-range order in ideal two-dimensional crystals. The MSDs of the solitons (which can be treated like quasiparticles at very low temperature) have also been studied and their dynamics are found to be about an order of magnitude slower than that of the colloidal particles themselves. Finally, transport of individual colloidal particles by diffusion processes is studied: both standard vacancy-interstitial pair formation and cooperative ring rotation processes are identified. These processes require thermal activation, with activation energies of the order of 10T(m) (T(m) being the melting temperature of the crystal), while the motions due to long-wavelength phonons decrease only linearly in temperature.

Glass elasticity from particle trajectories

Using positional data from video microscopy of a two-dimensional colloidal system and from simulations of hard disks, we determine the wave-vector-dependent elastic dispersion relations in glass. The emergence of rigidity based on the existence of a well defined displacement field in amorphous solids is demonstrated. Continuum elastic theory is recovered in the limit of long wavelengths which provides the glass elastic shear and bulk modulus as a function of temperature. The onset of a finite static shear modulus upon cooling marks the fluid-glass transition in an intuitive and unique way.

Electromagnetic torque tweezers: a versatile approach for measurement of single-molecule twist and torque

The well-established single-molecule force-spectroscopy techniques have recently been complemented by methods that can measure torque and twist directly, notably magnetic torque tweezers and the optical torque wrench. A limitation of the current torque measurement schemes is the intrinsic coupling between the force and torque degrees of freedom. Here we present electromagnetic torque tweezers (eMTT) that combine permanent and electromagnets to enable independent control of the force and torsional trap stiffness for sensitive measurements of single molecule torque and twist. Using the eMTT, we demonstrate sensitive torque measurements on tethered DNA molecules from simple tracking of the beads' (x,y)-position, obviating the need for any angular tracking algorithms or markers. Employing the eMTT for high-resolution torque measurements, we experimentally confirm the theoretically predicted torque overshoot at the DNA buckling transition in high salt conditions. We envision that the flexibility and control afforded by the eMTT will enable a range of new torque and twist measurement schemes from single-molecules to living cells.

The physics of the colloidal glass transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.

Langevin dynamics simulations of a two-dimensional colloidal crystal under confinement and shear

Langevin dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal (with implicit solvent) confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are crystalline. At even higher shear velocities, the effect of the shearing becomes smaller again. Also the effective temperature near the walls (deduced from the velocity distributions of the particles) decreases again when the wall velocity gets very large. When the walls are placed closer together, thereby introducing an incommensurability between the periodicity of the confined crystal and the walls, a structure containing a soliton staircase arises in simulations without shear. Introducing shear increases the disorder in these systems until no solitons are visible anymore. Instead, similar structures like in the case without mismatch result. At high shear rates, configurations where the incommensurability of the crystalline structure is compensated by the creation of holes become relevant.

Transitions between imperfectly ordered crystalline structures: a phase switch Monte Carlo study

A model for two-dimensional colloids confined laterally by "structured boundaries" (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance D between the confining walls is reduced at constant particle number from an initial value D(0), for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from n to n-1 to n-2, etc.) and are accompanied by an almost periodic strain pattern, due to "soliton staircases" along the boundaries. Since standard simulation studies of such transitions are hampered by huge hysteresis effects, we apply the phase switch Monte Carlo method to estimate the free energy difference between the structures as a function of the misfit between D and D(0), thereby locating where the transitions occur in equilibrium. For comparison, we also obtain this free energy difference from a thermodynamic integration method: The results agree, but the effort required to obtain the same accuracy as provided by phase switch Monte Carlo would be at least three orders of magnitude larger. We also show for a situation where several "candidate structures" exist for a phase, that phase switch Monte Carlo can clearly distinguish the metastable structures from the stable one. Finally, applying the method in the conjugate statistical ensemble (where the normal pressure conjugate to D is taken as an independent control variable), we show that the standard equivalence between the conjugate ensembles of statistical mechanics is violated.

Correlation between dynamical heterogeneities, structure and potential-energy distribution in a 2D amorphous solid

We investigate the collective properties of particles in a 2D experimental system which consists of a bi-disperse mixture of colloidal particles confined at an air/water interface. We find a direct correlation between structure and dynamical heterogeneities in this system: particles belonging to locally ordered structures have lower potential energy and are slower than other particles. In a more general way we show that particles with high potential energy are dominating the dynamics especially in the α-relaxation regime.

Tests of mode-coupling theory in two dimensions

We analyze the glassy dynamics of binary mixtures of hard disks in two dimensions. Predictions of the mode-coupling theory (MCT) are tested with extensive Brownian dynamics simulations. Measuring the collective particle density correlation functions in the vicinity of the glass transition, we verify four predicted mixing effects. For instance, for large size disparities, adding a small amount of small particles at a fixed packing fraction leads to a speedup in the long-time dynamics, while for small size disparities it leads to a slowing-down. Qualitative features of the nonergodicity parameters and the β relaxation, which both depend in a nontrivial way on the mixing ratio, are found in the simulated correlators. Studying one system in detail, we are able to determine its ideal MCT glass transition point as φ(c)=0.7948 and test MCT predictions quantitatively.

Computer simulations of colloidal transport on a patterned magnetic substrate

We study the transport of paramagnetic colloidal particles on a patterned magnetic substrate with kinetic Monte Carlo and Brownian dynamics computer simulations. The planar substrate is decorated with point dipoles in either parallel or zigzag stripe arrangements and exposed to an additional external magnetic field that oscillates in time. For the case of parallel stripes we find that the magnitude and direction of the particle current is controlled by the tilt angle of the external magnetic field. The effect is reliably obtained in a wide range of ratios between temperature and magnetic permeability. Particle transport is achieved only when the period of oscillation of the external field is greater than a critical value. For the case of zigzag stripes a current is obtained using an oscillating external field normal to the substrate. In this case, transport is possible only in the vertex of the zigzag, giving rise to a narrow stream of particles. The magnitude and direction of the particle current are found to be controlled by a combination of the zigzag angle and the distance of the colloids from the substrate. Metropolis Monte Carlo and Brownian dynamics simulations predict results that are in good agreement with each other. Using kinetic Monte Carlo we find that at high density the particle transport is hindered by jamming.

Entropic crystal-crystal transitions of Brownian squares

When a monolayer of hard microscale square platelets, produced lithographically, is osmotically concentrated in a flat plane to raise the particle area fraction Φ(A), an order-order transition occurs between a hexagonal rotator crystal and a rhombic crystal. Strikingly, phases having fourfold symmetry are not observed at any Φ(A). The rhombic lattice angle α increases continuously with Φ(A), as the system maximizes its total rotational and translational entropy. A cage model, based on packing rotationally swept squares, or "squaroids," reasonably predicts the measured α(Φ(A)), indicating that rotational entropy and the square particle shape combine to produce the rhombic unit cell.

Confined binary two-dimensional colloidal crystals: Monte Carlo simulation of crack formation

Binary mixtures (A, B) of colloidal particles of different sizes in two dimensions may form crystals with square lattice structure (the A-particles occupying the white sites and the B-particles the black sites of a checkerboard). Confining such a system by two parallel 'walls' a distance D apart, long-range order in the direction parallel to the walls is stabilized by 'corrugated walls' that are commensurate with the lattice structure but destabilized by structureless 'hard walls', even if there is no misfit between the strip width D and the crystal lattice spacing. The crossover to quasi-one-dimensional behavior is studied by Monte Carlo simulations, analyzing Lindemann parameters and displacement correlation functions. When D is reduced and thus a misfit created, the stress in the crystal increases up to a critical value, at which the stress jumps to much smaller values due to the formation of an (almost periodic) crack pattern. These cracks typically have a width of several particle diameters, and are mostly disordered, although sometimes small domains with hexagonal order can be identified. At very large misfits, glass-like structures appear. We discuss various methods to characterize order and disorder in such systems.

Dynamics of two-dimensional dipole systems

Using a combined analytical/molecular dynamics approach, we study the current fluctuation spectra and longitudinal and transverse collective mode dispersions of the classical two-dimensional (point) dipole system (2DDS) characterized by the ϕ{D}(r)=μ{2}/r{3} repulsive interaction potential; μ is the electric dipole strength. The interest in the 2DDS is twofold. First, the quasi-long-range 1/r{3} interaction makes the system a unique classical many-body system, with a remarkable collective mode behavior. Second, the system may be a good model for a closely spaced semiconductor electron-hole bilayer, a system that is in the forefront of current experimental interest. The longitudinal collective excitations, which are of primary interest for the liquid phase, are acoustic at long wavelengths. At higher wave numbers and for sufficiently high coupling strength, we observe the formation of a deep minimum in the dispersion curve preceded by a sharp maximum; this is identical to what has been observed in the dispersion of the zero-temperature bosonic dipole system, which in turn emulates so-called roton-maxon excitation spectrum of the superfluid 4He . The analysis we present gives an insight into the emergence of this apparently universal structure, governed by strong correlations. We study both the liquid and the crystalline solid state. We also observe the excitation of combination frequencies, resembling the roton-roton, roton-maxon, etc. structures in 4He .

Depinning dynamics of two-dimensional magnetized colloids on a random substrate

We perform Langevin simulations on the depinning dynamics of two-dimensional magnetized colloids on a random substrate. On increasing the magnetic field strength, we find for the first time a crossover from plastic to smectic flows as well as a crossover from smectic to elastic crystal flows above depinning. For both the smectic and elastic crystal flows, a power-law scaling relationship could be obtained between the average velocity and applied driving force. The scaling exponent is found to be larger than 1 for smectic flow. But, for the elastic crystal flow, the scaling exponent is found to be less than 1. For the plastic flow, no power-law scaling relationship between the average velocity and applied driving force can be derived and history dependence of the depinning occurs. Within the crossover from plastic to smectic flows, a sudden decrease in the critical driving force is observed, and a sudden increase is found in the critical driving force across the crossover from smectic to elastic crystal flows, accompanied by a crossing of the curves of average velocity versus driving force.

Frustrated rotator crystals and glasses of Brownian pentagons

Two-dimensional Brownian dispersions of microscale pentagonal platelets exhibit rich structural and dynamical behavior as the particle area fraction, phi(A), is increased. As phi(A) is raised above 0.66, a rotator crystal forms, and while in an equilateral hexagonal lattice, pentagons still explore all angles as they rotationally diffuse. At larger phi(A), the interference of the tips of neighboring pentagons causes rotational dynamical heterogeneity; particle rotations become nonergodic, the hallmark of a frustrated rotator crystal. Upon further compression, the quenched-in rotational disorder and inability of pentagons to fully tile a flat plane creates spatial defects, precluding access to a dense striped crystalline packing.