Numerical Investigation of Glassy Dynamics in Low Density Systems

Vitrification in colloidal systems typically occurs at high densities driven by sharply varying, short-ranged interactions. The possibility of glassy behavior arising from smoothly varying, long-ranged particle interactions has received relatively little attention. Here we investigate the behavior of screened charged particles, and explicitly demonstrate that these systems exhibit glassy properties in the regime of low temperature and low density. Properties close to this low density (Wigner) glass transition share many features with their hard-sphere counterparts, but differ in quantitative aspects that may be accounted for via microscopic theoretical considerations.Comment: 4 pages, 4 figures, revised versio

Numerical study of the glass-glass transition in short-ranged attractive colloids

We report extensive numerical simulations in the {\it glass} region for a simple model of short-ranged attractive colloids, the square well model. We investigate the behavior of the density autocorrelation function and of the static structure factor in the region of temperatures and packing fractions where a glass-glass transition is expected according to theoretical predictions. We strengthen our observations by studying both waiting time and history dependence of the numerical results. We provide evidence supporting the possibility that activated bond-breaking processes destabilize the attractive glass, preventing the full observation of a sharp glass-glass kinetic transition.Comment: 15 pages, 9 figures; Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted to J. Phys.: Condens. Matt.

Equilibrium cluster phases and low-density arrested disordered states: The role of short-range attraction and long-range repulsion

We study a model in which particles interact with short-ranged attractive and long-ranged repulsive interactions, in an attempt to model the equilibrium cluster phase recently discovered in sterically stabilized colloidal systems in the presence of depletion interactions. At low packing fraction particles form stable equilibrium clusters which act as building blocks of a cluster fluid. We study the possibility that cluster fluids generate a low-density disordered arrested phase, a gel, via a glass transition driven by the repulsive interaction. In this model the gel formation is formally described with the same physics of the glass formation.Comment: RevTeX4, 4 pages, 4 eps figure

Competing interactions in arrested states of colloidal clays

Using experiments, theory and simulations, we show that the arrested state observed in a colloidal clay at intermediate concentrations is stabilized by the screened Coulomb repulsion (Wigner glass). Dilution experiments allow us to distinguish this high-concentration disconnected state, which melts upon addition of water, from a low-concentration gel state, which does not melt. Theoretical modelling and simulations reproduce the measured Small Angle X-Ray Scattering static structure factors and confirm the long-range electrostatic nature of the arrested structure. These findings are attributed to the different timescales controlling the competing attractive and repulsive interactions.Comment: Accepted for publication in Physical Review Letter

Theoretical and numerical study of the phase diagram of patchy colloids: ordered and disordered patch arrangements

We report theoretical and numerical evaluations of the phase diagram for a model of patchy particles. Specifically we study hard-spheres whose surface is decorated by a small number f of identical sites ("sticky spots'') interacting via a short-range square-well attraction. We theoretically evaluate, solving the Wertheim theory, the location of the critical point and the gas-liquid coexistence line for several values of f and compare them to results of Gibbs and Grand Canonical Monte Carlo simulations. We study both ordered and disordered arrangements of the sites on the hard-sphere surface and confirm that patchiness has a strong effect on the phase diagram: the gas-liquid coexistence region in the temperature-density plane is significantly reduced as f decreases. We also theoretically evaluate the locus of specific heat maxima and the percolation line.Comment: preprint, 32 pages, 6 figures, 3 tables, J. Chem. Phys. in pres

Harmonic damped oscillators with feedback. A Langevin study

We consider a system in direct contact with a thermal reservoir and which, if left unperturbed, is well described by a memory-less equilibrium Langevin equation of the second order in the time coordinate. In such conditions, the strength of the noise fluctuations is set by the damping factor, in accordance with the Fluctuation and Dissipation theorem. We study the system when it is subject to a feedback mechanism, by modifying the Langevin equation accordingly. Memory terms now arise in the time evolution, which we study in a non-equilibrium steady state. Two types of feedback schemes are considered, one focusing on time shifts and one on phase shifts, and for both cases we evaluate the power spectrum of the system's fluctuations. Our analysis finds application in feedback cooled oscillators, such as the Gravitational Wave detector AURIGA.Comment: 17 page

Star-Like Micelles with Star-Like Interactions: A quantitative Evaluation of Structure Factor and Phase Diagram

PEP-PEO block copolymer micelles offer the possibility to investigate phase behaviour and interactions of star polymers (ultra-soft colloids). A star-like architecture is achieved by an extremely asymmetric block ratio (1:20). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by SANS can be quantitatively described in terms of an effective potential developed for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid/solid transition. Whereas for intermediate f a bcc phase is observed, for high f the formation of a fcc phase is preempted by glass formation.Comment: 5 pages, 4 figures, PRL in pres

Dynamics of supercooled liquids: density fluctuations and Mode Coupling Theory

We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the exact Newtonian equations. Following established ideas, we choose to separate these trial functions into a set representing integrable motions of density waves, and a set containing all effects of non-integrability. It transpires that the static structure factor is fixed by this minimum condition to be the solution of the Yvon-Born-Green (YBG) equation. The residual interactions between density waves are explicitly isolated in their Newtonian representation and expanded by choosing the dominant objects in the phase space of the system, that can be represented by a dissipative term with memory and a random noise. This provides a mapping between deterministic and stochastic dynamics. Imposing the Fluctuation-Dissipation Theorem (FDT) allows us to calculate the memory kernel. We write exactly the expression for it, following two different routes, i.e. using explicitly Newtons equations, or instead, their implicit form, that must be projected onto density pairs, as in the development of the well-established Mode Coupling Theory (MCT). We compare these two ways of proceeding, showing the necessity to enforce a new equation of constraint for the two schemes to be consistent. Thus, while in the first `Newtonian' representation a simple gaussian approximation for the random process leads easily to the Mean Spherical Approximation (MSA) for the statics and to MCT for the dynamics of the system, in the second case higher levels of approximation are required to have a fully consistent theory

Gaussian density fluctuations and Mode Coupling Theory for supercooled liquids

The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the memory function. The resulting equations, solved under the assumption that the noise, and consequently density fluctuations, of the liquid are gaussian distributed, are equivalent to the random-phase-approximation for the static structure factor and to the well known ideal mode coupling theory (MCT) equations for the dynamics. This finding suggests that MCT is the canonical mean-field theory of the fluid dynamics.Comment: 4 pages, REVTE

Multiple glass transitions in star polymer mixtures: Insights from theory and simulations

The glass transition in binary mixtures of star polymers is studied by mode coupling theory and extensive molecular dynamics computer simulations. In particular, we have explored vitrification in the parameter space of size asymmetry $\delta$ and concentration $\rho_2$ of the small star polymers at fixed concentration of the large ones. Depending on the choice of parameters, three different glassy states are identified: a single glass of big polymers at low $\delta$ and low $\rho_2$, a double glass at high $\delta$ and low $\rho_2$, and a novel double glass at high $\rho_2$ and high $\delta$ which is characterized by a strong localization of the small particles. At low $\delta$ and high $\rho_2$ there is a competition between vitrification and phase separation. Centered in the $(\delta, \rho_2)$-plane, a liquid lake shows up revealing reentrant glass formation. We compare the behavior of the dynamical density correlators with the predictions of the theory and find remarkable agreement between the two.Comment: 15 figures, to be published in Macromolecule