Networks of Limited-Valency Patchy Particles.

Equilibrium gels provide physically attractive counterparts of nonequilibrium gels, allowing statistical understanding and design of the equilibrium gel structure. Here, we assemble two-dimensional equilibrium gels from limited-valency "patchy" colloidal particles and follow their evolution at the particle scale to elucidate cluster-size distributions and free energies. By finely adjusting the patch attraction with critical Casimir forces, we let a mixture of two-valent and pseudo-three-valent patchy particles approach the percolated network state through a set of equilibrium states. Comparing this equilibrium route with a deep quench, we find that both routes approach the percolated state via the same equilibrium states, revealing that the network topology is uniquely set by the particle bond angles, independent of the formation history. The limited-valency system follows percolation theory remarkably well, approaching the percolation point with the expected universal exponents.

Activity affects the stability, deformation and breakage dynamics of colloidal architectures.

Living network architectures, such as the cytoskeleton, are characterized by continuous energy injection, leading to rich but poorly understood non-equilibrium physics. There is a need for a well-controlled (experimental) model system that allows basic insight into such non-equilibrium processes. Activated self-assembled colloidal architectures can fulfill this role, as colloidal patchy particles can self-assemble into colloidal architectures such as chains, rings and networks, while self-propelled colloidal particles can simultaneously inject energy into the architecture, alter the dynamical behavior of the system, and cause the self-assembled structures to deform and break. To gain insight, we conduct a numerical investigation into the effect of introducing self-propelled colloids modeled as active Brownian particles, into self-assembling colloidal dispersions of dipatch and tripatch particles. For the interaction potential, we use a previously designed model that accurately can reproduce experimental colloidal self-assembly via the critical Casimir force [Jonas et al., J. Chem. Phys., 2021, 135, 034902]. Here, we focus primarily on the breakage dynamics of three archetypal substructures, namely, dimers, chains, and rings. We find a rich response behavior to the introduction of self-propelled particles, in which the activity can enhance as well as reduce the stability of the architecture, deform the intact structures and alter the mechanisms of fragmentation. We rationalize these findings in terms of the rate and mechanisms of breakage as a function of the direction and magnitude of the active force by separating the bond breakage process into two stages: escaping the potential well and separation of the particles. The results set the stage for investigating more complex architectures.

Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement.

Colloidal patchy particles with divalent attractive interaction can self-assemble into linear polymer chains. Their equilibrium properties in 2D and 3D are well described by Wertheim's thermodynamic perturbation theory, which predicts a well-defined, exponentially decaying equilibrium chain length distribution. In experimental realizations, due to gravity, particles sediment to the bottom of the suspension, forming a monolayer of particles with a gravitational height smaller than the particle diameter. In accordance with experiments, an anomalously high monomer concentration is observed in simulations, which is not well understood. To account for this observation, we interpret polymerization as taking place in a highly confined quasi-2D plane and extend the Wertheim thermodynamic perturbation theory by defining additional reaction constants as functions of chain length. We derive the theory, test it on simple square well potentials, and apply it to the experimental case of synthetic colloidal patchy particles immersed in a binary liquid mixture, which are described by an accurate effective critical Casimir patchy particle potential. The important interaction parameters entering the theory are explicitly computed using the integral method in combination with Monte Carlo sampling. Without any adjustable parameter, the predictions of the chain length distribution are in excellent agreement with explicit simulations of self-assembling particles. We discuss the generality of the approach and its application range.

Structural modification enhances the optoelectronic properties of defect blue phosphorene thin films.

Active enhancement of the optical absorption coefficient to improve the light converting efficiency of thin-film solar cell materials is crucial to develop the next-generation solar cell devices. Here we report first-principles calculations with generalized gradient approximation to study the optoelectronic properties of pristine and divacancy (DV) blue phosphorene (BlueP) thin films under structural deformation. We show that instead of formingsp-like covalent bonds as in the pristine BlueP layer, a DV introduces two particular dangling bonds between the voids. Using a microscopic (non-) affine deformation model, we reveal that the orbital hybridization of these dangling bonds is strongly modified in both the velocity and vorticity directions depending on the type of deformation, creating an effective light trap to enhance the material absorption efficiency. Furthermore, this successful light trap is complemented by a clear signature ofσ+πplasmon when a DV BlueP layer is slightly compressive. These results demonstrate a practical approach to tailor the optoelectronic properties of low-dimensional materials and to pave a novel strategy to design functionalized solar cell devices from the bottom-up with selective defects.

A temperature-dependent critical Casimir patchy particle model benchmarked onto experiment.

Synthetic colloidal patchy particles immersed in a binary liquid mixture can self-assemble via critical Casimir interactions into various superstructures, such as chains and networks. Up to now, there are no quantitatively accurate potential models that can simulate and predict this experimentally observed behavior precisely. Here, we develop a protocol to establish such a model based on a combination of theoretical Casimir potentials and angular switching functions. Using Monte Carlo simulations, we optimize several material-specific parameters in the model to match the experimental chain length distribution and persistence length. Our approach gives a systematic way to obtain accurate potentials for critical Casimir induced patchy particle interactions and can be used in large-scale simulations.

Revealing pseudorotation and ring-opening reactions in colloidal organic molecules.

Colloids have a rich history of being used as 'big atoms' mimicking real atoms to study crystallization, gelation and the glass transition of condensed matter. Emulating the dynamics of molecules, however, has remained elusive. Recent advances in colloid chemistry allow patchy particles to be synthesized with accurate control over shape, functionality and coordination number. Here, we show that colloidal alkanes, specifically colloidal cyclopentane, assembled from tetrameric patchy particles by critical Casimir forces undergo the same chemical transformations as their atomic counterparts, allowing their dynamics to be studied in real time. We directly observe transitions between chair and twist conformations in colloidal cyclopentane, and we elucidate the interplay of bond bending strain and entropy in the molecular transition states and ring-opening reactions. These results open the door to investigate complex molecular kinetics and molecular reactions in the high-temperature classical limit, in which the colloidal analogue becomes a good model.

Size dependence of quantum efficiency of red emission from GaN:Eu structures for application in micro-LEDs.

GaN-based micro-LEDs typically suffer from a size-dependent efficiency due to the relatively long carrier lifetime and sidewall-related recombination effects. We demonstrate that for red-emitting Eu-doped GaN, sidewall-related recombination is hardly an issue for emission efficiency. We determine the photoluminescence quantum efficiency (PL QE) of Eu-related emission as a function of the size of square structures ranging from 3 to 192 µm. With the support of finite-difference time-domain simulations, we show that the light extraction efficiency and material losses are responsible for the decrease in PL QE for large sizes. For sizes smaller than 24 µm, there is an influence of the sidewall-related non-radiative recombination of carriers on the PL QE; however, it is only minor as a result of the limited carrier diffusion lengths in the Eu-doped material. These properties combined with the high efficiency of luminescence indicate the potential of this material for micro-LED applications.

Measurement of the Curvature-Dependent Surface Tension in Nucleating Colloidal Liquids.

The curvature dependence of the surface tension is central to the nucleation of liquids, but remains difficult to access experimentally and predict theoretically. This curvature dependence arises from the curvature-dependent molecular structure, which, for small nuclei, can deviate significantly from that of the planar liquid interface. Simulations and density functional theory have been used to predict this curvature dependence, however with contradicting results. Here, we provide the first direct measurement of the curvature-dependent surface tension in nucleating colloidal liquids. We employ critical Casimir forces to finely adjust colloidal particle interactions and induce liquid nucleation, and image individual nuclei at the particle scale to measure their curvature-dependent surface tension directly from thermally excited surface distortions. Using continuum models, we elucidate the interplay between nucleus structure, particle pair potential, and surface tension. Our results reveal a 20% lower surface tension for nuclei of critical size compared to bulk liquids, leading to 3 orders of magnitude higher nucleation rates, thus highlighting the importance of surface tension curvature corrections for accurate prediction of nucleation rates.

Critical Casimir interactions between colloids around the critical point of binary solvents.

Critical Casimir interactions between colloidal particles arise from the confinement of fluctuations of a near-critical solvent in the liquid gap between closely-spaced particles. So far, the comparison of theoretical predictions and experimental measurements of critical Casimir forces (CCFs) has focused on the critical solvent composition, while it has been lacking for off-critical compositions. We address this issue by investigating CCFs between spherical colloidal particles around the critical point of a binary solvent through a combination of experiments, previous Ising Monte Carlo simulation results and field-theoretical methods. By measuring the correlation length of the near-critical solvent and the pair potentials of the particles in terms of radial distribution functions and by determining the second virial coefficient, we test in detail theoretical predictions. Our results indicate that the critical Casimir theory gives quantitative correct predictions for the interaction potential between particles in a near critical binary mixture if weak preferential adsorption of the particle surface is taken into account.

Reversibility and hysteresis of the sharp yielding transition of a colloidal glass under oscillatory shear.

The mechanical response of glasses remains challenging to understand. Recent results indicate that the oscillatory rheology of soft glasses is accompanied by a sharp non-equilibrium transition in the microscopic dynamics. Here, we use simultaneous x-ray scattering and rheology to investigate the reversibility and hysteresis of the sharp symmetry change from anisotropic solid to isotropic liquid dynamics observed in the oscillatory shear of colloidal glasses (D. Denisov, M.T. Dang, B. Struth, A. Zaccone, P. Schall, Sci. Rep. 5 14359 (2015)). We use strain sweeps with increasing and decreasing strain amplitude to show that, in analogy with equilibrium transitions, this sharp symmetry change is reversible and exhibits systematic frequency-dependent hysteresis. Using the non-affine response formalism of amorphous solids, we show that these hysteresis effects arise from frequency-dependent non-affine structural cage rearrangements at large strain. These results consolidate the first-order-like nature of the oscillatory shear transition and quantify related hysteresis effects both via measurements and theoretical modelling.

Universality of slip avalanches in flowing granular matter.

The search for scale-bridging relations in the deformation of amorphous materials presents a current challenge with tremendous applications in material science, engineering and geology. While generic features in the flow and microscopic dynamics support the idea of a universal scaling theory of deformation, direct microscopic evidence remains poor. Here, we provide the first measurement of internal scaling relations in the deformation of granular matter. By combining macroscopic force fluctuation measurements with internal strain imaging, we demonstrate the existence of robust scaling relations from particle-scale to macroscopic flow. We identify consistent power-law relations truncated by systematic pressure-dependent cutoff, in agreement with recent mean-field theory of slip avalanches in elasto-plastic materials, revealing the existence of a mechanical critical point. These results experimentally establish scale-bridging relations in the flow of matter, paving the way to a new universal theory of deformation.

Critical Casimir forces for colloidal assembly.

Critical Casimir forces attract increasing interest due to their opportunities for reversible particle assembly in soft matter and nano science. These forces provide a thermodynamic analogue of the celebrated quantum mechanical Casimir force that arises from the confinement of vacuum fluctuations of the electromagnetic field. In its thermodynamic analogue, solvent fluctuations, confined between suspended particles, give rise to an attractive or repulsive force between the particles. Due to its unique temperature dependence, this effect allows in situ control of reversible assembly. Both the force magnitude and range vary with the solvent correlation length in a universal manner, adjusting with temperature from fractions of the thermal energy, k B T, and nanometre range to several ten kT and micrometer length scale. Combined with recent breakthroughs in the synthesis of complex particles, critical Casimir forces promise the design and assembly of complex colloidal structures, for fundamental studies of equilibrium and out-of-equilibrium phase behaviour. This review highlights recent developments in this evolving field, with special emphasis on the dynamic interaction control to assemble colloidal structures, in and out of equilibrium.

Totally asymmetric simple exclusion process simulations of molecular motor transport on random networks with asymmetric exit rates.

Using the totally asymmetric simple-exclusion-process and mean-field transport theory, we investigate the transport in closed random networks with simple crossing topology-two incoming, two outgoing segments, as a model for molecular motor motion along biopolymer networks. Inspired by in vitro observation of molecular motor motion, we model the motor behavior at the intersections by introducing different exit rates for the two outgoing segments. Our simulations of this simple network reveal surprisingly rich behavior of the transport current with respect to the global density and exit rate ratio. For asymmetric exit rates, we find a broad current plateau at intermediate motor densities resulting from the competition of two subnetwork populations. This current plateau leads to stabilization of transport properties within such networks.

Sharp symmetry-change marks the mechanical failure transition of glasses.

Glasses acquire their solid-like properties by cooling from the supercooled liquid via a continuous transition known as the glass transition. Recent research on soft glasses indicates that besides temperature, another route to liquify glasses is by application of stress that drives relaxation and flow. Here, we show that unlike the continuous glass transition, the failure of glasses to applied stress occurs by a sharp symmetry change that reminds of first-order equilibrium transitions. Using simultaneous x-ray scattering during the oscillatory rheology of a colloidal glass, we identify a sharp symmetry change from anisotropic solid to isotropic liquid structure at the crossing of the storage and loss moduli. Concomitantly, intensity fluctuations sharply acquire Gaussian distributions characteristic of liquids. Our observations and theoretical framework identify mechanical failure as a sharp atomic affine-to-nonaffine transition, providing a new conceptual paradigm of the oscillatory yielding of this technologically important class of materials, and offering new perspectives on the glass transition.

Shear banding of colloidal glasses: observation of a dynamic first-order transition.

We demonstrate that application of an increasing shear field on a glass leads to an intriguing dynamic first-order transition in analogy with equilibrium transitions. By following the particle dynamics as a function of the driving field in a colloidal glass, we identify a critical shear rate upon which the diffusion time scale of the glass exhibits a sudden discontinuity. Using a new dynamic order parameter, we show that this discontinuity is analogous to a first-order transition, in which the applied stress acts as the conjugate field on the system's dynamic evolution. These results offer new perspectives to comprehend the generic shear-banding instability of a wide range of amorphous materials.

Criterion for condensation in kinetically constrained one-dimensional transport models.

We study condensation in one-dimensional transport models with a kinetic constraint. The kinetic constraint results in clustering of immobile vehicles; these clusters can grow to macroscopic condensates, indicating the onset of dynamic phase separation between free-flowing and arrested traffic. We investigate analytically the conditions under which this occurs and derive a necessary and sufficient criterion for phase separation. This criterion is applied to the well-known Nagel-Schreckenberg model of traffic flow to analytically investigate the existence of dynamic condensates. We find that true condensates occur only when acceleration out of jammed traffic happens in a single time step, in the limit of strong overbraking. Our predictions are further verified with simulation results on the growth of arrested clusters. These results provide analytic understanding of dynamic arrest and dynamic phase separation in one-dimensional traffic and transport models.

Visualizing the strain evolution during the indentation of colloidal glasses.

We use an analog of nanoindentation on a colloidal glass to elucidate the incipient plastic deformation of glasses. By tracking the motion of the individual particles in three dimensions, we visualize the strain field and glass structure during the emerging deformation. At the onset of flow, we observe a power-law distribution of strain indicating strongly correlated deformation, and reflecting a critical state of the glass. At later stages, the strain acquires a Gaussian distribution, indicating that plastic events become uncorrelated. Investigation of the glass structure using both static and dynamic measures shows a weak correlation between the structure and the emerging strain distribution. These results indicate that the onset of plasticity is governed by strong power-law correlations of strain, weakly biased by the heterogeneous glass structure.

SODI-COLLOID: a combination of static and dynamic light scattering on board the International Space Station.

Microgravity research in space is a complex activity where the often scarce resources available for the launch, accommodation, and operation of instrumentation call for a careful experiment planning and instrument development. In this paper we describe a module of the Selectable Optical Diagnostic Instrument, that has been designed as a compact optical diagnostic instrument for colloidal physics experiments. The peculiarity of the instrument is the combination of a novel light scattering technique known as near field scattering and standard microscopy with a low-coherence laser light source. We describe its main design features, as well as measurement results on colloidal aggregation taken on the International Space Station.

Resolving structural modifications of colloidal glasses by combining x-ray scattering and rheology.

Glasses have liquid-like structure, but exhibit solid-like properties. A central question concerns the relation between the structure and mechanical properties of glasses, but structural changes remain difficult to resolve. We use a novel combination of rheology and x-ray scattering to resolve structural changes in colloidal glasses and link them directly to their mechanical behavior. By combining stress and structure factor measurements, we resolve shear induced changes in the nearest neighbor configuration as a function of applied stress, allowing us to elucidate the structural origin of the genuine shear banding transition of glasses.

Probing incipient plasticity by indenting colloidal glasses.

Glasses are lucrative engineering materials owing to their superior mechanical properties such as high strength and large elastic strain. A central question concerns incipient plasticity - the onset of permanent deformation - that is central to their relaxation, aging, yield and fracture. Here, we use an analogue of nano-indentation performed on a colloidal glass to obtain direct images of the incipient plasticity, allowing us to elucidate the onset of permanent deformation. We visualize the microscopic strain by following distorted nearest neighbor configurations, and observe a surprising hierarchical structure of deformation: at the onset of irreversible deformation, the strain acquires a robust fractal structure, and we measure its fractal dimension. These results give direct evidence that the onset of permanent deformation has the hallmarks of a critical point, in agreement with recent theoretical works.