Dynamical arrest in attractive colloids: the effect of long-range repulsion

We study gelation in suspensions of model colloidal particles with short-ranged attractive and long-ranged repulsive interactions by means of three-dimensional fluorescence confocal microscopy. At low packing fractions, particles form stable equilibrium clusters. Upon increasing the packing fraction the clusters grow in size and become increasingly anisotropic until finally associating into a fully connected network at gelation. We find a surprising order in the gel structure. Analysis of spatial and orientational correlations reveals that the gel is composed of dense chains of particles constructed from face-sharing tetrahedral clusters. Our findings imply that dynamical arrest occurs via cluster growth and association.     

Aggregation kinetics in a model colloidal suspension

We present molecular dynamics simulations of aggregation kinetics in a colloidal suspension modeled as a highly asymmetric binary mixture. Starting from a configuration with largely uncorrelated colloidal particles the system relaxes by coagulation-fragmentation dynamics to a structured state of low-dimensionality clusters with an exponential size distribution. The results show that short-range repulsive interactions alone can give rise to so-called cluster phases. For the present model and probably other, more common colloids, the observed clusters appear to be equilibrium phase fluctuations induced by the entropic intercolloidal attractions.     

Phase separation and structure in a concentrated colloidal dispersion of uniform plates

The structure and phase behaviour of a colloidal dispersion of plate-like particles are described. The plates are nickel (II) hydroxide and have short-range, repulsive interactions and a low polydispersity. As the concentration of the plates is increased, an equilibrium phase separation between a columnar phase and a less ordered phase is observed. Complementary measurements using small-angle neutron and small-angle X-ray scattering have been used to distinguish the columnar phase from other possible ordered structures. Previously isotropic-nematic phase transitions have been observed [#!ref1!#], however this dispersion forms the more highly ordered columnar phase, due to the aspect ratio and the low polydispersity of the plate-like particles. The concentration at which phase separation occurs, increases as the range of the particle interactions is reduced. This system provides an interesting model for comparison with theory and calculations of structures in liquid crystal and mesophase in which the particle interactions can be altered. Received 24 February 1999     

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.     

Heterogeneous diffusion in a reversible gel

We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line determined by geometric percolation, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is only supported by a fractal network. The gel dynamics is highly heterogeneous and we propose a theoretical model to quantitatively describe dynamic heterogeneity in gels. We elucidate several differences between the dynamics of gels and that of glass formers.     

Free cooling phase-diagram of hard-spheres with short- and long-range interactions

We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.     

Out-of-equilibrium states as statistical equilibria of an effective dynamics in a system with long-range interactions

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Nonequilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, such as two-dimensional incompressible fluids and wave-particle interaction in a plasma.     

Different orderings in the narrow-band limit of the extended Hubbard model on the Bethe lattice

We present the exact solution of a system of Fermi particles living on the sites of a Bethe lattice with coordination number z and interacting through on-site U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. Within the Green’s function and equations of motion formalism, we provide a comprehensive analysis of the model and we study the phase diagram at finite temperature in the whole model’s parameter space, allowing for the on-site and nearest-neighbor interactions to be either repulsive or attractive. We find the existence of critical regions where charge ordering (V > 0) and phase separation (V < 0) are observed. This scenario is endorsed by the study of several thermodynamic quantities.     

Jamming percolation and glass transitions in lattice models

A new class of lattice gas models with trivial interactions but constrained dynamics is introduced. These models are proven to exhibit a dynamical glass transition: above a critical density rhoc ergodicity is broken due to the appearance of an infinite spanning cluster of jammed particles. The fraction of jammed particles is discontinuous at the transition, while in the unjammed phase dynamical correlation lengths and time scales diverge as exp[C(rhoc-rho)-mu]. Dynamic correlations display two-step relaxation similar to glass formers and jamming systems.     

A density-functional theory study of microphase formation in binary Gaussian mixtures

We use density-functional theory to study the formation of inhomogeneous phases in a binary mixture of particles interacting by repulsive, athermal Gaussian potentials with suitably chosen strengths and ranges. Both the potential parameters and the free-energy functional are the same as those adopted in a previous investigation by other authors (Archer A J, Likos C N and Evans R 2004 J. Phys.: Condens. Matter 16 L297), but here a fully numerical minimization of the functional is performed, without any assumption about the functional form of the density profile. We find lamellar, rod and cluster phases. In the lamellar phase, the two species arrange into intercalating stripes; in the rod and cluster phases, the minority species is localized at the site of a periodic lattice, either triangular (for rods) or body-centred cubic (for clusters), while the other species is distributed non-uniformly in the remaining region, so that it forms a percolating network. The order of the transition from the homogeneous to the inhomogeneous phase and the phase diagram of the mixture are also discussed.     

Exact relaxation dynamics of a localized many-body state in the 1D Bose gas

Through an exact method, we numerically solve the time evolution of the density profile for an initially localized state in the one-dimensional bosons with repulsive short-range interactions. We show that a localized state with a density notch is constructed by superposing one-hole excitations. The initial density profile overlaps the plot of the squared amplitude of a dark soliton in the weak coupling regime. We observe the localized state collapsing into a flat profile in equilibrium for a large number of particles such as N=1000. The relaxation time increases as the coupling constant decreases, which suggests the existence of off-diagonal long-range order. We show a recurrence phenomenon for a small number of particles such as N=20.     

Coexistence of s-wave superconductivity and antiferromagnetism

We study the phase diagram of a new model that exhibits a first order transition between s-wave superconducting and antiferromagnetic phases. The model, a generalized Hubbard model augmented with competing spin-spin and pair-pair interactions, was investigated using the projector quantum Monte Carlo method. Upon varying the Hubbard U from attractive to repulsive, we find a first order phase transition between superconducting and antiferromagnetic states.     

Sequential desorption of dimers from square lattices: A novel mechanism for phase transitions

This work describes a novel mechanism for phase transitions during desorption, involving the formation of lattice size dependent intermediate states when there is enough adsorbate mobility. Monte Carlo simulations are performed to analyze the mechanism of the thermal desorption for adsorbed homonuclear dimers on two-dimensional square lattices. The lattice-gas model with nearest-neighbor repulsive interactions between particles is implemented to study the cases of mobile (with diffusion) and immobile desorption. The number of peaks for the immobile desorption spectra is related to the connectivity of the adsorbed species for both monomer and dimer molecules. However, for the case of mobile desorption, the spectra give information about the desorption mechanism, which differs significantly for monomers and dimers, particularly when the initial temperatures correspond to the critical region.     

Dissolution arrest and stability of particle-covered bubbles

Experiments show that bubbles covered with monodisperse polystyrene particles, with particle to bubble radius ratios of about 0.1, evolve to form faceted polyhedral shapes that are stable to dissolution in air-saturated water. We perform Surface Evolver simulations and find that the faceted particle-covered bubble represents a local minimum of energy. At the faceted state, the Laplace overpressure vanishes, which together with the positive slope of the bubble pressure-volume curve, ensures phase stability. The repulsive interactions between the particles cause a reduction of the curvature of the gas-liquid interface, which is the mechanism that arrests dissolution and stabilizes the bubbles.     

Colloidal assembly on magnetically vibrated stripes

We investigate the collective organization of paramagnetic colloidal particles externally driven above the periodic stripes of a uniaxial ferrimagnetic garnet film. An external field modulation induces vibration of the stripe walls and produces random motion of the particles. Defects in the stripe pattern break the symmetry of the potential and favor particle nucleation into large clusters above a critical density. Mismatch between particle size and pattern wavelength generates assemblies with different morphological order. At even higher field strengths, repulsive dipolar interactions between the particles induce cluster melting. We propose a novel approach to generate and externally control a variety of colloidal assemblies.     

Absence of conventional quantum phase transitions in itinerant systems with disorder

Effects of disorder are examined in itinerant systems close to quantum critical points. We argue that spin fluctuations due to the long-range part of the RKKY interactions generically induce non-Ohmic dissipation due to rare disorder configurations. This dissipative mechanism is found to destabilize quantum Griffiths phase behavior in itinerant systems with arbitrary symmetry of the order parameter, leading to the formation of a "cluster glass" phase preceding uniform ordering.     

Lattice model for colloidal gels and glasses

We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied, it reproduces many characteristic phenomena of liquids, glasses, and colloidal systems such as ideal gel formation, liquid-glass phase coexistence, jamming, or the re-entrance of the glass transition.     

Different magic number behaviors in supported metal clusters

Two different magic number behaviors in supported metal clusters, which contain several to hundreds of atoms, are revealed on a series of fcc(001) metal surfaces based on the calculations with the tight-binding potential. The magic number sequence persists on some surfaces while gradually disappears on the others with the increasing cluster size. A theory is proposed to explain these behaviors in terms of atomic interactions. We find in surprise that the different magic number behaviors are triggered by the relatively weak adatom–adatom interactions between next nearest-neighbor (NNN) atoms, although the closed shell of the magic cluster is enhanced by nearest-neighbor interactions. For an attractive NNN interaction, the closed shell of the magic cluster is gradually destabilized and eventually broken, leading to the disappearance of the magic number sequence with increasing cluster size. For a repulsive one, the closed shell and magic number sequence persists. Besides, our theory also allows a good understanding of the equilibrium shape of Cu islands on the Cu(001) surface.     

Effective potential method for active particles

ABSTRACT

We investigate the steady-state properties of an active fluid modelled as an assembly of soft repulsive spheres subjected to Gaussian coloured noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified coloured noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of coloured noise and interactions enhances the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.     

Clustering and cooperative dynamics in a reactive system

We study the dependence of the dynamics on the size of particle clusters that grow by stepwise aggregation in a reactive epoxy-amine mixture. The data reveal the cluster property involved in the glasslike arrest and its quantitative link with the structural relaxation time. We find that the number-average cluster size xn governs the formation of a glassy phase as distinct from a gel phase, and that xn correlates to the size of the "cooperatively rearranging regions" postulated by the Adam-Gibbs model for glass forming liquids. These results suggest that the step polymerization process generates clusters that behave much like dynamical heterogeneities observed in supercooled liquids.