Rhombic preordering on a square substrate

Structural evolution of particle configurations: Zero-temperature phases under increasing confinement

In this study, we investigate the phase behavior and structural organization of colloidal particles in a two-dimensional (2D) system under isotropic harmonic confinement using overdamped Langevin dynamics simulations. We employ a modified mermaid potential, which introduces an additional short-distance term resulting in a null-force region, distinct from the conventional mermaid potential. This modification facilitates a richer exploration of self-assembled structures, revealing a variety of phases influenced by the interplay between confinement strength V0 and the interaction potential. Our analysis spans a wide range of parameters, resulting in a detailed phase diagram that captures transitions from dispersed clusters to well-ordered patterns, including square, triangular, rhomboidal, and mixed configurations, as the confinement strength increases. The findings underscore the intricate balance of forces governing the self-assembly of colloidal systems and offer valuable insights for future experimental realizations.

Computational self-assembly of a six-fold chiral quasicrystal

Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under real-space symmetry operations, quasicrystals possess symmetry that requires description by a space group in reciprocal space. In this study, we report the self-assembly of a six-fold chiral quasicrystal using molecular dynamics simulations of a two-dimensional particle system. The particles interact via the Lennard-Jones-Gauss pair potential and are subjected to a periodic substrate potential. We confirm the presence of chiral symmetry through diffraction patterns and order parameters, revealing unique local motifs in both real and reciprocal space. The quasicrystal's properties, including the tiling structure and symmetry and the extent of diffuse scattering, are strongly influenced by substrate potential depth and temperature. Our results provide insights into the mechanisms of chiral quasicrystal formation and the role and potential of external fields in tailoring quasicrystal structures.

Anti-matching effect in a two dimensional driven vortex lattice in the presence of periodic pinning

The dynamics of a driven superconducting vortex lattice in a two-dimensional (2D) periodic potential of square symmetry is studied using Brownian dynamics simulations. The range and strength of the vortex-substrate interaction are taken to be of the same order as that of the vortex-vortex interaction. The matching effect in a driven vortex lattice in the presence of a periodic array of pinning centers refers to the enhanced resistance to the vortex lattice motion when the ratio of the number of vortices to the number of pinning centers (called the filling fraction) takes simple fractional values. In particular, one expects a pronounced matching effect when the filling fraction is one. Contrary to this expectation, a drop in the vortex lattice mobility is observed as the filling fraction is increased from value one. This anti-matching effect can be understood in terms of the structural change in the vortex lattice as the filling fraction is varied. The dip observed in vortex mobility as a function of temperature when the filling fraction equals one (Joseph T 2020PhysicaA556124737), is studied for other values of filling above and below one. The behavior is found to persist for other fillings as well and is associated with the melting of the vortex lattice. The temperature at which the lattice melts is found to increase with drive and explains the shift in the temperature at which mobility is a minimum, locally.

Critical Role of Configurational Disorder in Stabilizing Chemically Unfavorable Coordination in Complex Compounds

The crystal structure of a material is essentially determined by the nature of its chemical bonding. Consequently, the atomic coordination intimately correlates with the degree of ionicity or covalency of the material. Based on this principle, materials with similar chemical compositions can be successfully categorized into different coordination groups. However, counterexamples have recently emerged in complex ternary compounds. For instance, covalent IB-IIIA-VIA2 compounds, such as AgInS2, prefer a tetrahedrally coordinated structure (TCS), while ionic IA-VA-VIA2 compounds, such as NaBiS2, would favor an octahedrally coordinated structure (OCS). One naturally expects that IB-VA-VIA2 compounds with intermediate ionicity or covalency, such as AgBiS2, should then have a mix-coordinated structure (MCS) consisting of covalent AgS4 tetrahedra and ionic BiS6 octahedra. Surprisingly, only the experimental presence of the OCS was observed for AgBiS2. To resolve this puzzle, we perform first-principles studies of the phase stabilities of ternary compounds at finite temperatures. We find that AgBiS2 indeed prefers MCS at the ground state, in agreement with the typical expectation, but under experimental synthesis conditions, disordered OCS becomes energetically more favorable because of its low mixing energy and high configurational entropy. Our work elucidates the critical role of configurational disorder in stabilizing chemically unfavorable coordination, providing a rigorous rationale for the anomalous coordination preference in IB-VA-VIA2 compounds.

Tuning the stability of a model quasicrystal and its approximants with a periodic substrate

Quasicrystals and their periodic approximants are complex crystalline phases. They have now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates, the type of complex phase was found to change depending on thermodynamic conditions and the type of substrate used. Here, we investigate the effect of a substrate on the relative thermodynamic stability of a two-dimensional model quasicrystal and its approximants. Our simulation model is particles interacting via the Lennard-Jones-Gauss potential. Our numerical methods are molecular dynamics simulations and free energy calculations that take into account phason flips explicitly. For substrates interacting weakly with the particles, we observe an incommensurate-commensurate transition, in which a continuous series of quasicrystal approximants locks into a small number of approximants. Interestingly, we observe that the 3/2 approximant exhibits phason mode fluctuations in thermodynamic equilibrium. Such fluctuations are reminiscent of random tiling and a phenomenon usually associated only with quasiperiodic order. For stronger substrates, we find an enhancement of the stability of the dodecagonal quasicrystal and variants of square lattices. We explain all observed phenomena by the interplay of the model system with the substrate. Our results demonstrate that designing novel complex periodic and quasiperiodic structures by choice of suitable substrates is a promising strategy.

Structural transitions in two-dimensional modulated systems under triangular confinement

We study numerically the structural transitions of two-dimensional systems of classic particles with competing interactions under a triangular confinement with two different types of soft-wall potentials. We observe a variety of novel confinement-induced equilibrium configurations as a function of particle density and confinement steepness for each considered confinement potential. The specific role played by the confining potentials on the ordering of the particle clusters is revealed. These findings allow us to control the self-organization of modulated systems through using external confinements.

Directional locking in a two-dimensional Yukawa solid modulated by a two-dimensional periodic substrate

Directional depinning dynamics of a two-dimensional (2D) dusty plasma solid modulated by a 2D square periodic substrate are investigated using Langevin dynamical simulations. We observe prominent directional locking effects when the direction of the external driving force is varied relative to the underlying square substrate. These locking steps appear when the direction of the driving force is close to the symmetry direction of the substrate, corresponding to the different dynamical flow patterns and the structures. In the conditions between the adjacent locking steps, moving ordered states are observed. Although the discontinuous transitions often occur between the locking steps and the nonlocking portion, the continuous transitions are also found around the locking step associated with the disordered plastic flow close to its termini. Our results show that directional locking also occurs for underdamped systems, which could be tested experimentally in dusty plasmas modulated by 2D substrates.

Hydrodynamic synchronization and clustering in ratcheting colloidal matter

Ratchet transport systems are widespread in physics and biology; however, the effect of the dispersing medium in the collective dynamics of these out-of-equilibrium systems has been often overlooked. We show that, in a traveling wave magnetic ratchet, long-range hydrodynamic interactions (HIs) produce a series of remarkable phenomena on the transport and assembly of interacting Brownian particles. We demonstrate that HIs induce the resynchronization with the traveling wave that emerges as a "speed-up" effect, characterized by a net raise of the translational speed, which doubles that of single particles. When competing with dipolar forces and the underlying substrate symmetry, HIs promote the formation of clusters that grow perpendicular to the driving direction. We support our findings both with Langevin dynamics and with a theoretical model that accounts for the fluid-mediated interactions. Our work illustrates the role of the dispersing medium on the dynamics of driven colloidal matter and unveils the growing process and cluster morphologies above a periodic substrate.

Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates

Phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.

Nonequilibrium pattern formation in circularly confined two-dimensional systems with competing interactions

We numerically investigate the nonequilibrium behaviors of classic particles with competing interactions confined in a two-dimensional logarithmic trap. We reveal a quench-induced surprising dynamics exhibiting rich dynamic patterns depending upon confinement strength and trap size, which is attributed to the time-dependent competition between interparticle repulsions and attractions under a circular confinement. Moreover, in the collectively diffusive motions of the particles, we find that the emergence of dynamic structure transformation coincides with a diffusive mode transition from superdiffusion to subdiffusion. These findings are likely useful in understanding the pattern selection and evolution in various chemical and biological systems in addition to modulated systems, and add a new route to tailoring the morphology of pattern-forming systems.

Commensurate states and pattern switching via liquid crystal skyrmions trapped in a square lattice

Using continuum based simulations we show that a rich variety of skyrmion liquid crystal states can be realized in the presence of a periodic obstacle array. As a function of the number of skyrmions per obstacle we find hexagonal, square, dimer, trimer and quadrimer ordering, where the n-mer structures are a realization of a molecular crystal state of skyrmions. As a function of external field and obstacle radius we show that there are transitions between the different crystalline states as well as mixed and disordered structures. We discuss how these states are related to commensurate effects seen in other systems, such as vortices in type-II superconductors and colloids interacting with two dimensional substrates.

Growth of two-dimensional dodecagonal colloidal quasicrystals: Particles with isotropic pair interactions with two length scales vs. patchy colloids with preferred binding angles

We explore the growth of colloidal quasicrystals with dodecagonal symmetry in two dimensions by employing Brownian dynamics simulations. On the one hand, we study the growth behavior of structures obtained in a system of particles that interact according to an isotropic pair potential with two typical length scales. On the other hand, we consider patchy colloids that possess only one typical interaction length scale but prefer given binding angles. In case of the isotropic particles, we show that an imbalance in the competition between the two distances might lead to defects with wrong nearest-neighbor distances in the resulting structure. In contrast, during the growth of quasicrystals with patchy colloids such defects do not occur due to the lack of a second interaction length scale. However, as a downside, the diffusion of patchy particles along a surface typically is slower such that domains occur where the particles possess different phononic and phasonic offsets. Our results are important to understand how soft matter quasicrystals can be grown as perfectly as possible and to obtain a deeper insight into the mechanisms of the growth of quasicrystals in general.

Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it

Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.

Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study

The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement.

Landscape-inversion phase transition in dipolar colloids: tuning the structure and dynamics of 2D crystals

We study the 2D crystalline phases of paramagnetic colloidal particles with dipolar interactions and constrained on a periodic substrate. Combining theory, simulation, and experiments, we demonstrate a new scenario of first-order phase transitions that occurs via a complete inversion of the energy landscape, featuring nonconventional properties that allow for (i) tuning of crystal symmetry, (ii) control of dynamical properties of different crystalline orders via tuning of their relative stability with an external magnetic field, (iii) an equivalent but independent control of the same dynamic properties via temporal modulations of that field, and (iv) nonstandard phase-ordering kinetics involving spontaneous formation of transient metastable domains.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.