Mode-coupling theory predictions for a limited valency attractive square-well model

Recently we have studied, using numerical simulations, a limited valency model, i.e. an attractive square well model with a constraint on the maximum number of bonded neighbors. Studying a large region of temperatures $T$ and packing fractions $\phi$, we have estimated the location of the liquid-gas phase separation spinodal and the loci of dynamic arrest, where the system is trapped in a disordered non-ergodic state. Two distinct arrest lines for the system are present in the system: a {\it (repulsive) glass} line at high packing fraction, and a {\it gel} line at low $\phi$ and $T$. The former is essentially vertical ($\phi$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(\phi-T)$ plane. We here complement the molecular dynamics results with mode coupling theory calculations, using the numerical structure factors as input. We find that the theory predicts a repulsive glass line -- in satisfactory agreement with the simulation results -- and an attractive glass line which appears to be unrelated to the gel line.Comment: 12 pages, 6 figures. To appear in J. Phys. Condens. Matter, special issue: "Topics in Application of Scattering Methods for Investigation of Structure and Dynamics of Soft Condensed Matter", Fiesole, November 200

A closer look at arrested spinodal decomposition in protein solutions

Concentrated aqueous solutions of the protein lysozyme undergo a liquid solid transition upon a temperature quench into the unstable spinodal region below a characteristic arrest temperature of Tf=15C. We use video microscopy and ultra-small angle light scattering in order to investigate the arrested structures as a function of initial concentration, quench temperature and rate of the temperature quench. We find that the solid-like samples show all the features of a bicontinuous network that is formed through an arrested spinodal decomposition process. We determine the correlation length Xi and demonstrate that Xi exhibits a temperature dependence that closely follows the critical scaling expected for density fluctuations during the early stages of spinodal decomposition. These findings are in agreement with an arrest scenario based on a state diagram where the arrest or gel line extends far into the unstable region below the spinodal line. Arrest then occurs when during the early stage of spinodal decomposition the volume fraction phi2 of the dense phase intersects the dynamical arrest threshold phi2Glass, upon which phase separation gets pinned into a space-spanning gel network with a characteristic length Xi

Aging in short-ranged attractive colloids: A numerical study

We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at large packing fractions, kinetically arrested disordered states can be created both on cooling (attractive glass) and on heating (repulsive glass). The possibility of having two distinct glasses, at the same packing fraction, with two different dynamics offers the unique possibility of comparing -- within the same model -- the differences in aging dynamics. We find that, while the aging dynamics of the repulsive glass is similar to the one observed in atomic and molecular systems, the aging dynamics of the attractive glass shows novel unexpected features.Comment: 8 pages, 11 figures, submited to Journal of Chemical Physic

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.

Gelation as arrested phase separation in short-ranged attractive colloid-polymer mixtures

We present further evidence that gelation is an arrested phase separation in attractive colloid-polymer mixtures, based on a method combining confocal microscopy experiments with numerical simulations recently established in {\bf Nature 453, 499 (2008)}. Our results are independent of the form of the interparticle attractive potential, and therefore should apply broadly to any attractive particle system with short-ranged, isotropic attractions. We also give additional characterization of the gel states in terms of their structure, inhomogeneous character and local density.Comment: 6 figures, to be published in J. Phys. Condens. Matter, special issue for EPS Liquids Conference 200

Effect of bond lifetime on the dynamics of a short-range attractive colloidal system

We perform molecular dynamics simulations of short-range attractive colloid particles modeled by a narrow (3% of the hard sphere diameter) square well potential of unit depth. We compare the dynamics of systems with the same thermodynamics but different bond lifetimes, by adding to the square well potential a thin barrier at the edge of the attractive well. For permanent bonds, the relaxation time $\tau$ diverges as the packing fraction $\phi$ approaches a threshold related to percolation, while for short-lived bonds, the $\phi$-dependence of $\tau$ is more typical of a glassy system. At intermediate bond lifetimes, the $\phi$-dependence of $\tau$ is driven by percolation at low $\phi$, but then crosses over to glassy behavior at higher $\phi$. We also study the wavevector dependence of the percolation dynamics.Comment: Revised; 9 pages, 9 figure

Energy landscape of a simple model for strong liquids

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks.Comment: Revised versio

Non-Gaussian energy landscape of a simple model for strong network-forming liquids: accurate evaluation of the configurational entropy

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square well potential, with an additional constraint that limits the maximum number of bonds, $N_{\rm max}$, per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and $N_{\rm max}$. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e. features defining strong glass-forming liquids. This model has two important features: (i) landscape basins can be associated with bonding patterns; (ii) the configurational volume of the basin can be evaluated in a formally exact way, and numerically with arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e. configurations in which all particles are bonded to $N_{\rm max}$ neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state, and show that it follows a logarithmic functional form, differently from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.Comment: Final version. Journal of Chemical Physics 124, 204509 (2006

A random walk description of the heterogeneous glassy dynamics of attracting colloids

We study the heterogeneous dynamics of attractive colloidal particles close to the gel transition using confocal microscopy experiments combined with a theoretical statistical analysis. We focus on single particle dynamics and show that the self part of the van Hove distribution function is not the Gaussian expected for a Fickian process, but that it reflects instead the existence, at any given time, of colloids with widely different mobilities. Our confocal microscopy measurements can be described well by a simple analytical model based on a conventional continuous time random walk picture, as already found in several other glassy materials. In particular, the theory successfully accounts for the presence of broad tails in the van Hove distributions that exhibit exponential, rather than Gaussian, decay at large distance.Comment: 13 pages, 5 figs. Submitted to special issue "Classical and Quantum Glasses" of J. Phys.: Condens. Matter; v2: response to refere

Confirmation of Anomalous Dynamical Arrest in attractive colloids: a molecular dynamics study

Previous theoretical, along with early simulation and experimental, studies have indicated that particles with a short-ranged attraction exhibit a range of new dynamical arrest phenomena. These include very pronounced reentrance in the dynamical arrest curve, a logarithmic singularity in the density correlation functions, and the existence of `attractive' and `repulsive' glasses. Here we carry out extensive molecular dynamics calculations on dense systems interacting via a square-well potential. This is one of the simplest systems with the required properties, and may be regarded as canonical for interpreting the phase diagram, and now also the dynamical arrest. We confirm the theoretical predictions for re-entrance, logarithmic singularity, and give the first direct evidence of the coexistence, independent of theory, of the two coexisting glasses. We now regard the previous predictions of these phenomena as having been established.Comment: 15 pages,15 figures; submitted to Phys. Rev.