Kinetics of topological defects in systems with competing interactions

Multiple scale model for cell migration in monolayers: Elastic mismatch between cells enhances motility

We propose a multiscale model for monolayer of motile cells that comprise normal and cancer cells. In the model, the two types of cells have identical properties except for their elasticity; cancer cells are softer and normal cells are stiffer. The goal is to isolate the role of elasticity mismatch on the migration potential of cancer cells in the absence of other contributions that are present in real cells. The methodology is based on a phase-field description where each cell is modeled as a highly-deformable self-propelled droplet. We simulated two types of nearly confluent monolayers. One contains a single cancer cell in a layer of normal cells and the other contains normal cells only. The simulation results demonstrate that elasticity mismatch alone is sufficient to increase the motility of the cancer cell significantly. Further, the trajectory of the cancer cell is decorated by several speed “bursts” where the cancer cell quickly relaxes from a largely deformed shape and consequently increases its translational motion. The increased motility and the amplitude and frequency of the bursts are in qualitative agreement with recent experiments.

Real-time observation of domain fluctuations in a two-dimensional magnetic model system

Domain patterns of perpendicularly magnetized ultra-thin ferromagnetic films are often determined by the competition of the short range but strong exchange interaction favouring ferromagnetic alignment of magnetic moments and the long range but weak antiferromagnetic dipolar interaction. Detailed phase diagrams of the resulting stripe domain patterns have been evaluated in recent years; however, the domain fluctuations in these pattern forming systems have not been studied in great detail so far. Here we show that domain fluctuations can be observed in ultra-thin two-dimensional ferromagnetic Fe/Ni/Cu(001) films with perpendicular magnetization in the stripe domain phase. Non-stroboscopic time-resolved threshold photoemission electron microscopy with high temporal resolution allows analysing the dynamic fingerprint of the topological excitations in the nematic domain phase. Furthermore, proliferation of domain ending defects in the vicinity of the spin reorientation transition is witnessed.

Lamellar order, microphase structures, and glassy phase in a field theoretic model for charged colloids

In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation.

Morphologies of expansion ridges of elastic thin films onto a substrate

A model of a thin film elastically attached to a rigid substrate is considered. In the case in which the film expands relative to the substrate and assuming certain nonlinear elastic behavior of the film, expansion ridges may appear, in which the material collapses, and the density is higher on average. By studying numerically this process, the possible morphologies of these collapsed regions are presented. They range from circular spots and straight stripes, to wiggle polygonal patterns and ring-shaped domains. The similarity of some of these results with patterns observed in delamination of thin films and biphase epitaxial growth is emphasized.

Thermodynamic equilibrium of domains in a two-component Langmuir monolayer

This [corrected] article outlines the results from a combined experimental and theoretical study on the properties of circular domains in a mixed Langmuir monolayer at thermodynamic equilibrium. The mixed monolayer consisted of a binary mixture of dimyristoyl-phosphatidyl-choline and dihydrocholesterol. A long-term fluorescence microscopy study of these domains was carried out over the course of approximately 60 h. Image analysis of the domains over time revealed that the domains ripened slowly with an [corrected] increase in mean domain radius and a [corrected] decrease in domain number density. At the end of the measurement, the domains remained polydisperse, and true thermodynamic equilibrium was not reached. Theoretically, collective thermodynamic equilibrium properties such as mean domain size and size distribution were calculated by combining micelle self-assembly theory and the "equivalent dipole" model for the self-energy of two-dimensional domains. The calculations predicted existence of finite-sized circular domains at equilibrium. This suggests that equilibrium circular monolayer domains of single- or multicomponent lipids with a finite size distribution should form only at very limited experimental conditions. Both the predicted mean domain size and size distribution are strongly affected by line tension and dipole moment density difference. A comparison between the theoretical and experimental results is made.

Pattern formation and glassy phase in the phi4 theory with a screened electrostatic repulsion

We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar, and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.

Self-assembled patterns and strain-induced instabilities for modulated systems

The self-assembled domain patterns of modulated systems are characteristic of a wide variety of chemical and physical systems, and are the result of competing interactions. From a technological point of view, there is considerable interest in these domain patterns, as they form suitable templates for the fabrication of nanostructures. We have analyzed the domains and instabilities that form in modulated systems, and show that a large variety of patterns--based on long-lived metastable or glassy states--may be formed as a compromise between the required equilibrium modulation period and the strain present in the system. The strain results from topologically constrained trajectories in phase space, that effectively preclude the equilibrium configuration.

New and exotic self-organized patterns for modulated nanoscale systems

The self-assembled domain patterns of modulated systems are the result of competing short-range attractive and long-range repulsive interactions found in diverse physical and chemical systems. From an application point of view, there is considerable interest in these domain patterns, as they form templates suitable for the fabrication of nanostructures. In this work we have generated a variety of new and exotic patterns, which represent either metastable or glassy states. These patterns arise as a compromise between the required equilibrium modulation period and the strain resulting from topologically constrained trajectories in phase space that effectively preclude the equilibrium configuration.

Numerical simulations of two-dimensional magnetic domain patterns

I show that a model for the interaction of magnetic domains that includes a short range ferromagnetic and a long range dipolar antiferromagnetic interaction reproduces very well many characteristic features of two-dimensional magnetic domain patterns. In particular bubble and stripe phases are obtained, along with polygonal and labyrinthine morphologies. In addition, two puzzling phenomena, namely, the so called "memory effect" and the "topological melting" observed experimentally, are also qualitatively described. Very similar phenomenology is found in the case in which the model is changed to be represented by the Swift-Hohenberg equation driven by an external orienting field.

Dynamics of growth in a three-component mixture with competing interactions

We study numerically the dynamics, in two dimensions, of phase separation in ternary mixtures with dipolar interactions which lead to the formation of modulated phases. We distinguish three different modulated phases: a hexagonal phase of droplets, a lamellar phase, and a hexagonal phase of bubbles. Inside the crystal structures an additional phase separation occurs "coloring" the texture. The dynamics in the droplet phase mixes the two kinds of droplets of different composition. The lamellar phase does not evolve toward parallel lamellae, and the phase separation inside the channels proceeds until they reach a grain boundary. The hexagonal bubble phase is never formed due to the phase separation that forms an interface of bubbles which blocks the contact between the two phases. In its place we find an unsuspected lamellar phase.

Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: Lattice-Boltzmann simulations

By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-assembly of sponge mesophases and gyroid liquid-crystalline cubic mesophases, hence confirming that (a) amphiphile-amphiphile interactions need not be long-ranged in order for periodically modulated structures to arise in a dynamics of competing interactions, and (b) a chemically specific model of the amphiphile is not required for the self-assembly of cubic mesophases, contradicting claims in the literature. We also observe a structural order-disorder transition between sponge and gyroid phases driven by amphiphile concentration alone or, independently, by the amphiphile-amphiphile and the amphiphile-binary fluid coupling parameters. For the growth-arrested mesophases, we also observe temporal oscillations in the structure function at all length scales; most of the wave numbers show slow decay, and long-term stationarity or growth for the others. We ascribe this behavior to a combination of complex amphiphile dynamics leading to Marangoni flows.

Ordering of the lamellar phase under a shear flow

The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free energy and the evolution follows a convection-diffusion equation. Lamellas order preferentially with the normal along the vorticity direction. Typical lengths grow as gamma t(5/4) (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3.

Domain Shapes and Patterns: The Phenomenology of Modulated Phases

A wide variety of two- and three-dimensional physical-chemical systems display domain patterns in equilibrium. The phenomenology of these patterns, and of the shapes of their constituent domains, is reviewed here from a point of view that interprets these patterns as a manifestation of modulated phases. These phases are stabilized by competing interactions and are characterized by periodic spatial variations of the pertinent order parameter, the corresponding modulation period generally displaying a dependence on temperature and other external fields. This simple picture provides a unifying framework to account for striking and substantial similarities revealed in the prevalent "stripe" and "bubble" morphologies as well as in commonly observed, characteristic domain-shape instabilities. Several areas of particular current interest are discussed.