Structural characterization of systems with competing interactions confined in narrow spherical shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. In fact, confinement has been proven to be a good strategy to induce the formation of novel ordered microphases that might be appealing to the development of functional nanomaterials. Using Grand Canonical Monte Carlo (GCMC) simulations, we study a model colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions under which the hexagonal phase is stable in bulk. We observe the formation of three parent ordered structures formed by toroidal clusters and two spherical clusters (Type I), toroidal clusters and one spherical cluster (Type II), and toroidal clusters alone (Type III), depending on the radius of the confining shell, that can often coexist with other related structures derived from these parent ones by a simple transformation, in which the system is divided into two hemispheres that are rotated with respect to each other by a given angle. We propose a general method to characterize and predict the structures obtained under confinement in spherical shells in systems able to self-assemble into a hexagonal phase in bulk. We also show that deforming the spherical shells into ellipsoidal ones affects the structure of the system in such a way that helical structures are favoured by prolate ellipsoids and toroidal structures by oblate ellipsoids.

Self-Assembly of Optimally Packed Cylindrical Clusters inside Spherical Shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. Using grand canonical Monte Carlo simulations, we study a colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions at which the hexagonal phase of cylindrical clusters is stable in bulk. We observe spontaneous formation of different ordered structures. The results of the simulations are in a very good agreement with the predictions of a simple mathematical model based on the geometry and optimal packing of colloidal clusters. The results of the simulations and the explanation provided by a relatively simple geometric model may be helpful in manufacturing copolymer nanocapsules and may indicate possible ways of coiling DNA strands on spherical objects.

Spontaneous organization and phase separation of skyrmions in chiral active matter.

Skyrmions are topologically protected vortex-like excitations that hold promise for applications such as information processing and electron manipulation. Here we combine theoretical analysis and numerical simulations to show that skyrmions can spontaneously emerge in chiral active matter without external confinements or regulation. Strikingly, these activity-driven skyrmions can either self-organize into a periodic, stable square lattice consisting of half Néel skyrmions and antiskyrmions, where the in-plane flows display an antiferromagnetic vortex array, or undergo phase separation between skyrmions with different topological numbers. We identify that the emerging skyrmion dynamics stems from the competition between the chiral and polar coherence length scales dictated by the interplay of intrinsic chirality, polarity, and elasticity in the system. Our results reveal unanticipated topological excitations, self-organization, and phase separation in non-equilibrium systems and also suggest a potential way towards engineering complicated bespoke skyrmionic structures through manipulating active matter.

Structural and Dynamical Behaviour of Colloids with Competing Interactions Confined in Slit Pores.

Systems with short-range attractive and long-range repulsive interactions can form periodic modulated phases at low temperatures, such as cluster-crystal, hexagonal, lamellar and bicontinuous gyroid phases. These periodic microphases should be stable regardless of the physical origin of the interactions. However, they have not yet been experimentally observed in colloidal systems, where, in principle, the interactions can be tuned by modifying the colloidal solution. Our goal is to investigate whether the formation of some of these periodic microphases can be promoted by confinement in narrow slit pores. By performing simulations of a simple model with competing interactions, we find that both the cluster-crystal and lamellar phases can be stable up to higher temperatures than in the bulk system, whereas the hexagonal phase is destabilised at temperatures somewhat lower than in bulk. Besides, we observed that the internal ordering of the lamellar phase can be modified by changing the pore width. Interestingly, for sufficiently wide pores to host three lamellae, there is a range of temperatures for which the two lamellae close to the walls are internally ordered, whereas the one at the centre of the pore remains internally disordered. We also find that particle diffusion under confinement exhibits a complex dependence with the pore width and with the density, obtaining larger and smaller values of the diffusion coefficient than in the corresponding bulk system.

Formation and internal ordering of periodic microphases in colloidal models with competing interactions.

Theory and simulations predict that colloidal particles with short-range attractive and long-range repulsive interactions form periodic microphases if there is a proper balance between the attractive and repulsive contributions. However, the experimental identification of such structures has remained elusive to date. Using molecular dynamics simulations, we investigate the phase behaviour of a model system that stabilizes a cluster-crystal, a cylindrical and a lamellar phase at low temperatures. Besides the transition from the fluid to the periodic microphases, we also observe the internal freezing of the clusters at a lower temperature. Finally, our study indicates that, for the chosen model parameters, the three periodic microphases are kinetically accessible from the fluid phase.

Confinement of Colloids with Competing Interactions in Ordered Porous Materials.

In this work, we explore the possibility of promoting the formation of ordered microphases by confinement of colloids with competing interactions in ordered porous materials. For that aim, we consider three families of porous materials modeled as cubic primitive, diamond, and gyroid bicontinuous phases. The structure of the confined colloids is investigated by means of grand canonical Monte Carlo simulations in thermodynamic conditions at which either a cluster crystal or a cylindrical phase is stable in bulk. We find that by tuning the size of the unit cell of these porous materials, numerous novel ordered microphases can be produced, including cluster crystals arranged into close packed and open lattices as well as nonparallel cylindrical phases.

Mechanical adaptions of collective cells nearby free tissue boundaries.

Mechanical adaptions of cells, including stiffness variation, cytoskeleton remodeling, motion coordination, and shape changing, are essential for tissue morphogenesis, wound healing, and malignant progression. In this paper, we take confluent monolayers of Madin-Darby canine kidney (MDCK) and mouse myoblast (C2C12) cells as model systems to probe how cells collectively adapt their mechanical features in response to a free tissue boundary. We show that the free boundary not only can trigger unjamming transition but also induces cell fluidization nearby the boundary. The Young's moduli of cells near the boundary are found to be much lower than those of interior cells. We demonstrate that the stiffness of cells in monolayers with a free tissue boundary exhibits negative dependence on the projected cell area, in contrast to previous studies where cells were found to stiffen as cellular area increases in a confluent MDCK monolayer without boundary. In addition, the free tissue boundary may activate cell remodeling, rendering volume enlargement and cell-specified cytoskeleton organization. Our study emphasizes the important role of geometrical boundary in regulating biomechanical properties of cell aggregates.

The influence of confinement on the structure of colloidal systems with competing interactions.

Colloidal systems with competing interactions have a complex phase diagram with several periodic microphases, in which particles are arranged in lamellae, cylinders or clusters. Using grand canonical Monte Carlo simulations, we investigate how the structure of the colloidal fluid can be modified by confinement in channels with different cross-section geometries and sizes. We pay particular attention to the hexagonal cylindrical phase since it is the most susceptible to form new structures from. In particular, we considered pores with elliptical, triangular, squared, hexagonal, and wedged-cylindrical cross-sections. Our results show that the structure of the confined fluid depends on the commensurability of the bulk periodic structure with the confining cross-section of the channel. We also find that the structure of the confined fluid can be modified by inserting wedges of appropriate geometry and size. These geometrical modifications of the confining pores can be exploited for the controlled assembly of colloidal structures.

Predicting the orientation of lipid cubic phase films.

Lipid cubic phase films are of increasingly widespread importance, both in the analysis of the cubic phases themselves by techniques including microscopy and X-ray scattering, and in their applications, especially as electrode coatings for electrochemical sensors and for templates for the electrodeposition of nanostructured metal. In this work we demonstrate that the crystallographic orientation adopted by these films is governed by minimization of interfacial energy. This is shown by the agreement between experimental data obtained using grazing-incidence small-angle X-ray scattering (GI-SAXS), and the predicted lowest energy orientation determined using a theoretical approach we have recently developed. GI-SAXS data show a high degree of orientation for films of both the double diamond phase and the gyroid phase, with the [111] and [110] directions respectively perpendicular to the planar substrate. In each case, this matches the lowest energy facet calculated for that particular phase.

Giant hexagonal superstructures in diblock-copolymer membranes.

We have observed polymersomes of high genus with their vesicle wall organized on the micrometer scale either in a double bilayer connected by a lattice of passages or a tubular network with hexagonal symmetry. Experimentally found shape classes are identified within a theoretical phase diagram based on the bending energy of the polymer membrane. Pronounced morphological changes could be induced and controlled by temperature.