A finite-temperature study of the degeneracy of the crystal phases in systems of soft aspherical particles.

We employ classical density-functional theory to investigate the phase diagram of an assembly of mutually penetrable, parallel ellipsoids interacting via the generalized exponential model of index four (GEM-4) pair potential. We show that the crystal phases of the system are obtained from those of the spherically symmetric GEM-4 model by rescaling the lattice vectors. Performing this rescaling in combination with an arbitrary rotation of the lattice leads to infinitely many different structures with the same free energy, thereby implying their infinite degeneracy. These findings generalize to non-zero temperature the results formerly obtained by us [Pini et al., J. Chem. Phys. 153, 164901 (2020)] for the ground state of a similar system of ellipsoids interacting via a Gaussian potential. According to the mean-field free-energy functional used here, our conclusions apply to soft-core potentials both when they form cluster crystals as the GEM-4 and when they form single-occupancy crystals as the Gaussian itself.

Two-stage assembly of patchy ellipses: From bent-core particles to liquid crystal analogs.

We investigate the two-dimensional behavior of colloidal patchy ellipsoids specifically designed to follow a two-step assembly process from the monomer state to mesoscopic liquid-crystal phases via the formation of the so-called bent-core units at the intermediate stage. Our model comprises a binary mixture of ellipses interacting via the Gay-Berne potential and decorated by surface patches, with the binary components being mirror-image variants of each other-referred to as left-handed and right-handed ellipses according to the position of their patches. The surface patches are designed so as in the first stage of the assembly the monomers form bent-cores units, i.e., V-shaped dimers with a specific bent angle. The Gay-Berne interactions, which act between the ellipses, drive the dimers to subsequently form the characteristic phase observed in bent-core liquid crystals. We numerically investigate-by means of both Molecular Dynamics and Monte Carlo simulations-the described two-step process: we first optimize a target bent-core unit and then fully characterize its state diagram in temperature and density, defining the regions where the different liquid crystalline phases dominate.

Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system.

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.

Phase separation dynamics in a symmetric binary mixture of ultrasoft particles.

Phase separation plays a key role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft, i.e., they can significantly overlap at a small energy cost. From a computer simulation point of view, these complex macromolecular aggregates are generally modeled by soft particles. The effective interaction between two particles is defined via the generalized exponential model of index n, with n = 4. Here, using molecular dynamics simulations, we study the phase separation dynamics of a size-symmetric binary mixture of ultrasoft particles. We find that when the mixture is quenched to a temperature below the critical temperature, the two components spontaneously start to separate. Domains of the two components form, and the equal-time order parameter reveals that the domain sizes grow with time in a power-law manner with an exponent of 1/3, which is consistent with the Lifshitz-Slyozov law for conserved systems. Furthermore, the static structure factor shows a power-law decay with an exponent of 4, consistent with the Porod law.

Ordered ground state configurations of the asymmetric Wigner bilayer system-Revisited with unsupervised learning.

We have reanalyzed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [Antlanger et al., Phys. Rev. Lett. 117, 118002 (2016)], comprising roughly 60 000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out "by hand," we have used for the present contribution machine learning concepts, notably based on a principal component analysis and a k-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters), we were able to reanalyze these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed, we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, thereby identifying a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states.

Elasticity in crystals with a high density of local defects: Insights from ultra-soft colloids.

In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a microscopic basis to include and account for the motion of point defects in an otherwise ordered crystalline structure. We study the elastic properties of a point-defect rich crystal within a first principles theoretical framework derived from the microscopic equations of motion. This framework allows us to make specific predictions pertaining to the mechanical properties that we can validate through deformation experiments performed in molecular dynamics simulations.

On the yielding of a point-defect-rich model crystal under shear: insights from molecular dynamics simulations.

In real crystals and at finite temperatures point defects are inevitable. Under shear their dynamics severely influence the mechanical properties of these crystals, giving rise to non-linear effects, such as ductility. In an effort to elucidate the complex behavior of crystals under plastic deformation it is crucial to explore and to understand the interplay between the timescale related to the equilibrium point-defect diffusion and the shear-induced timescale. Based on extensive non-equilibrium molecular dynamics simulations we present a detailed investigation on the yielding behavior of cluster crystals, an archetypical model for a defect-rich crystal: in such a system clusters of overlapping particles occupy the lattice sites of a regular (FCC) structure. In equilibrium particles diffuse via site-to-site hopping while maintaining the crystalline structure intact. We investigate these cluster crystals at a fixed density and at different temperatures where the system remains in the FCC structure: temperature allows us to vary the diffusion timescale appropriately. We then expose the crystal to shear, thereby choosing shear rates which cover timescales that are both higher and lower than the equilibrium diffusion timescales. We investigate the macroscopic and microscopic response of our cluster crystal to shear and find that the yielding scenario of such a system does not rely on the diffusion of the particles - it is rather related to the plastic deformation of the underlying crystalline structure. The local bond order parameters and the measurement of local angles between neighboring clusters confirm the cooperative movement of the clusters close to the yield point. Performing complementary, related simulations for an FCC crystal formed by harshly repulsive particles reveals similarities in the yielding behavior between both systems. Still we find that the diffusion of particles does influence characteristic features in the cluster crystal, such as a less prominent increase of order parameters close to the yield point. Our simulations provide for the first time an insight into the role of the diffusion of defects in the yielding behavior of a defect-rich crystal under shear. These observations will thus be helpful in the development of theories for the plastic deformation of defect-rich crystals.

Microswimmers learning chemotaxis with genetic algorithms.

Various microorganisms and some mammalian cells are able to swim in viscous fluids by performing nonreciprocal body deformations, such as rotating attached flagella or by distorting their entire body. In order to perform chemotaxis (i.e., to move toward and to stay at high concentrations of nutrients), they adapt their swimming gaits in a nontrivial manner. Here, we propose a computational model, which features autonomous shape adaptation of microswimmers moving in one dimension toward high field concentrations. As an internal decision-making machinery, we use artificial neural networks, which control the motion of the microswimmer. We present two methods to measure chemical gradients, spatial and temporal sensing, as known for swimming mammalian cells and bacteria, respectively. Using the genetic algorithm NeuroEvolution of Augmenting Topologies, surprisingly simple neural networks evolve. These networks control the shape deformations of the microswimmers and allow them to navigate in static and complex time-dependent chemical environments. By introducing noisy signal transmission in the neural network, the well-known biased run-and-tumble motion emerges. Our work demonstrates that the evolution of a simple and interpretable internal decision-making machinery coupled to the environment allows navigation in diverse chemical landscapes. These findings are of relevance for intracellular biochemical sensing mechanisms of single cells or for the simple nervous system of small multicellular organisms such as Caenorhabditis elegans.

Deformable hard particles confined in a disordered porous matrix.

With suitably designed Monte Carlo simulations, we have investigated the properties of mobile, impenetrable, yet deformable particles that are immersed into a porous matrix, the latter one realized by a frozen configuration of spherical particles. By virtue of a model put forward by Batista and Miller [Phys. Rev. Lett. 105, 088305 (2010)], the fluid particles can change in their surroundings, formed by other fluid particles or the matrix particles, their shape within the class of ellipsoids of revolution; such a change in shape is related to a change in energy, which is fed into suitably defined selection rules in the deformation "moves" of the Monte Carlo simulations. This concept represents a simple yet powerful model of realistic, deformable molecules with complex internal structures (such as dendrimers or polymers). For the evaluation of the properties of the system, we have used the well-known quenched-annealed protocol (with its characteristic double average prescription) and have analyzed the simulation data in terms of static properties (the radial distribution function and aspect ratio distribution of the ellipsoids) and dynamic features (notably the mean squared displacement). Our data provide evidence that the degree of deformability of the fluid particles has a distinct impact on the aforementioned properties of the system.

On the degeneracy of ordered ground state configurations of the aspherical Gaussian core model.

We provide rigorous evidence that the ordered ground state configurations of a system of parallel oriented, ellipsoidal particles, interacting via a Gaussian potential (termed in the literature as Gaussian core nematics), must be infinitely degenerate; we have demonstrated that these configurations originate from the related ground state configuration of the corresponding symmetric Gaussian core system via a suitable stretching operation of this lattice in combination with an arbitrary rotation. These findings explain related observations in former investigations, which then remained unexplained. Our conclusions have far reaching consequences for the search of ground state configurations of other nematic particles.

Reliable Computational Prediction of the Supramolecular Ordering of Complex Molecules under Electrochemical Conditions.

We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide reference data for the energies (evaluated for archetypical configurations) to fit the parameters of a conceptually much simpler and computationally less expensive force field of the molecules: classical, spherical particles, representing the respective atomic entities; a flat and perfectly conducting wall represents the metallic surface. Stage two feeds the energies that emerge from this force field into highly efficient and reliable optimization techniques to identify via energy minimization the ordered ground-state configurations of the molecules. We demonstrate the power of our approach by successfully reproducing, on a semiquantitative level, the intricate supramolecular ordering observed experimentally for PQP+ and ClO4- molecules at an Au(111)-electrolyte interface, including the formation of open-porous, self-host-guest, and stratified bilayer phases as a function of the electric field at the solid-liquid interface. We also discuss the role of the perchlorate ions in the self-assembly process, whose positions could not be identified in the related experimental investigations.

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations.

The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by the multiparticle collision dynamics (MPC) approach is studied. The fluid is composed of flexible, Gaussian phantom polymers that interact by local momentum-conserving stochastic MPCs. For comparison, the analytical solution of the linearized Navier-Stokes equation is calculated, where viscoelasticity is taken into account by a time-dependent shear relaxation modulus. The fluid properties are characterized by the transverse velocity autocorrelation function in Fourier space as well as in real space. Various polymer lengths are considered-from dumbbells to (near-)continuous polymers. Viscoelasticity affects the fluid properties and leads to strong correlations, which overall decay exponentially in Fourier space. In real space, the center-of-mass velocity autocorrelation function of individual polymers exhibits a long-time tail, independent of the polymer length, which decays as t-3/2, similar to a Newtonian fluid, in the asymptotic limit t → ∞. Moreover, for long polymers, an additional power-law decay appears at time scales shorter than the longest polymer relaxation time with the same time dependence, but negative correlations, and the polymer length dependence L-1/2. Good agreement is found between the analytical and simulation results.

Controlled self-aggregation of polymer-based nanoparticles employing shear flow and magnetic fields.

Star polymers with magnetically functionalized end groups are presented as a novel polymeric system whose morphology, self-aggregation, and orientation can easily be tuned by exposing these macromolecules simultaneously to an external magnetic field and to shear forces. Our investigations are based on a specialized simulation technique which faithfully takes into account the hydrodynamic interactions of the surrounding, Newtonian solvent. We find that the combination of magnetic field (including both strength and direction) and shear rate controls the mean number of magnetic clusters, which in turn is largely responsible for the static and dynamic behavior. While some properties are similar to comparable non-magnetic star polymers, others exhibit novel phenomena; examples of the latter include the breakup and reorganization of the clusters beyond a critical shear rate, and a strong dependence of the efficiency with which shear rate is translated into whole-body rotations on the direction of the magnetic field.

Structure and stimuli-responsiveness of all-DNA dendrimers: theory and experiment.

We present a comprehensive theoretical and experimental study of the solution phase properties of a DNA-based family of nanoparticles - dendrimer-like DNA molecules (DL-DNA). These charged DNA dendrimers are novel macromolecular aggregates, which hold high promise in targeted self-assembly of soft matter systems in the bulk and at interfaces. To describe the behaviour of this family of dendrimers (with generations ranging from G1 to G7), we use a theoretical model in which base-pairs of a single DL-DNA molecule are modeled by charged monomers, whose interactions are chosen to mimic the equilibrium properties of DNA correctly. Experimental results on the sizes and conformations of DL-DNA are based on static and dynamic light scattering; and molecular dynamics simulations are employed to model the equilibrium properties of DL-DNA, which compare favorably to the findings from experiments while at the same time providing a host of additional information and insight into the molecular structure of the nanostructures. We also examine the salt-responsiveness of these macromolecules, finding that despite the strong screening of electrostatic interactions brought about by the added salt, the macromolecules shrink only slightly, their size robustness stemming from the high bending rigidity of the DNA-segments. The study of these charged dendrimer systems is an important field of research in the area of soft matter due to their potential role for various interdisciplinary applications, ranging from molecular cages and carriers for drug delivery in a living organism to the development of dendrimer- and dendron-based ultra-thin films in the area of nanotechnology. These findings are essential to determine if DL-DNA is a viable candidate for the experimental realization of cluster crystals in the bulk, a novel form of solid with multiple site occupancy.

Molecular dynamics simulations of inverse patchy colloids.

Inverse patchy colloids are patchy particles with differently charged surface regions. In this paper we focus on inverse patchy colloids with two different polar patches and an oppositely charged equatorial belt, and we describe a model and a reliable and efficient numerical algorithm that can be applied to investigate the properties of these particles in molecular dynamics simulations.

The asymmetric Wigner bilayer.

We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates and form there ordered sublattices. Using complementary tools (analytic and numerical), we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: net charge neutrality on each of the plates on the one hand and particles' self-organization into commensurate sublattices on the other hand. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows us to study on a quantitative level phenomena such as over- and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive, complementary Monte Carlo simulations in the canonical ensemble, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy. The simple setup of the Wigner bilayer system offers an attractive possibility to study and to control complex scenarios and strategies of colloidal self-assembly, via the variation of two system parameters.

On the applicability of density dependent effective interactions in cluster-forming systems.

We systematically studied the validity and transferability of the force-matching algorithm for computing effective pair potentials in a system of dendritic polymers, i.e., a particular class of ultrasoft colloids. We focused on amphiphilic dendrimers, macromolecules which can aggregate into clusters of overlapping particles to minimize the contact area with the surrounding implicit solvent. Simulations were performed for both the monomeric and coarse-grained models in the liquid phase at densities ranging from infinite dilution up to values close to the freezing point. The effective pair potentials for the coarse-grained simulations were computed from the monomeric simulations both in the zero-density limit (Φeff0) and at each investigated finite density (Φeff). Conducting the coarse-grained simulations with Φeff0 at higher densities is not appropriate as they failed at reproducing the structural properties of the monomeric simulations. In contrast, we found excellent agreement between the spatial dendrimer distributions obtained from the coarse-grained simulations with Φeff and the microscopically detailed simulations at low densities, where the macromolecules were distributed homogeneously in the system. However, the reliability of the coarse-grained simulations deteriorated significantly as the density was increased further and the cluster occupation became more polydisperse. Under these conditions, the effective pair potential of the coarse-grained model can no longer be computed by averaging over the whole system, but the local density needs to be taken into account instead.

Spontaneous assembly of a hybrid crystal-liquid phase in inverse patchy colloid systems.

Materials with well-defined architectures are heavily sought after in view of their diverse technological applications. Among the desired target architectures, lamellar phases stand out for their exceptional mechanical and optical features. Here we show that charged colloids, decorated on their poles with two oppositely charged regions possess the unusual ability to spontaneously assemble in different morphologies of (semi-)ordered, layered particle arrangements which maintain their structural stability over a surprisingly large temperature range. This remarkable capacity is related to a characteristic bonding mechanism: stable intra-layer bonds guarantee the formation of planar aggregates, while strong inter-layer bonds favor the stacking of the emerging planar assemblies. These two types of bonds together are responsible for the self-healing processes occurring during the spontaneous assembly. The resulting phases are characterized by parallel, densely packed, particle layers connected by a relatively small number of intra-layer particles. We investigate the properties of the (semi-)ordered phases in terms of static and dynamic correlation functions, focusing in particular on a novel hybrid crystal-liquid phase that prevails at intermediate temperatures where the inter-layer particles form a mobile, fluid phase.

Rich Polymorphic Behavior of Wigner Bilayers.

Self-assembly into target structures is an efficient material design strategy. Combining analytical calculations and computational techniques of evolutionary and Monte Carlo types, we report about a remarkable structural variability of Wigner bilayer ground states, when charges are confined between parallel charged plates. Changing the interlayer separation, or the plate charge asymmetry, a cascade of ordered patterns emerges. At variance with the symmetric case phenomenology, the competition between commensurability features and charge neutralization leads to long range attraction, appearance of macroscopic charges, exotic phases, and nonconventional phase transitions with distinct critical indices, offering the possibility of a subtle, but precise and convenient control over patterns.