Anomalous dynamics of intruders in a crowded environment of mobile obstacles.

Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collectives and vehicular traffic conditions. These are examples of motion through crowded environments, in which the host matrix may retain some glass-like dynamics. Here we investigate constrained transport in a colloidal model system, in which dilute small spheres move in a slowly rearranging, glassy matrix of large spheres. Using confocal differential dynamic microscopy and simulations, here we discover a critical size asymmetry, at which anomalous collective transport of the small particles appears, manifested as a logarithmic decay of the density autocorrelation functions. We demonstrate that the matrix mobility is central for the observed anomalous behaviour. These results, crucially depending on size-induced dynamic asymmetry, are of relevance for a wide range of phenomena ranging from glassy systems to cell biology.

Phase diagram of trivalent and pentavalent patchy particles.

We compute the equilibrium phase diagram of two simple models for patchy particles with three and five patches in a very broad range of pressure and temperature. The phase diagram presents low-density crystal structures which compete with the fluid phase. The phase diagram of the five-patch model shows re-entrant melting, in analogy with the previously studied four-patch case, a metastable gas-liquid critical point and a stable, high-density liquid. The three-patch model shows a stable gas-liquid critical point and, in the region of temperatures where equilibration is numerically feasible, a stable liquid phase, suggesting the possibility that in this small valence model the liquid retains its thermodynamic stability down to the vanishing range limit.

Silica through the eyes of colloidal models--when glass is a gel.

We perform molecular dynamics simulations of 'floating bond' (FB) models of network-forming liquids and compare the structure and dynamics against the BKS model of silica (van Beest et al 1990 Phys. Rev. Lett. 64 1955), with the aim of gaining a better understanding of glassy silica in terms of the variety of non-ergodic states seen in colloids. At low densities, all the models form tetrahedral networks. At higher densities, tailoring the FB model to allow a higher number of bonds does not capture the structure seen in BKS. Upon rescaling the time and length in order to compare mean squared displacements between models, we find that there are significant differences in the temperature dependence of the diffusion coefficient at high density. Additionally, the FB models show a greater range in variability in the behavior of the non-ergodicity parameter and caging length, quantities used to distinguish colloidal gels and glasses. Hence, we find that the glassy behavior of BKS silica can be interpreted as a 'gel' at low densities, with only a marginal gel-to-glass crossover at higher densities.

Association of limited valence patchy particles in two dimensions.

We investigate theoretically the phase behavior of particles with limited valence in two dimensions, by solving the first-order Wertheim theory form. As previously found for three dimensions, in two dimensions also the valence has a strong impact on the phase diagram, controlling the location of the gas-liquid coexistence. On decreasing the valence, the critical density and temperature decrease while the region of gas-liquid instability shrinks and vanishes. At low temperatures, the system reaches its ground state with particles forming a fully bonded network which spans the system.

A spherical model with directional interactions: II. Dynamics and landscape properties.

We study a binary non-additive hard-sphere mixture with square well interactions only between dissimilar particles. An appropriate choice of the inter-particle potential parameters favors the formation of equilibrium structures with tetrahedral ordering (Zaccarelli et al 2007 J. Chem. Phys. 127 174501). By performing extensive event-driven molecular dynamics simulations, we monitor the dynamics of the system, locating the iso-diffusivity lines in the phase diagram, and discuss their location with respect to the gas-liquid phase separation. We observe the formation of an ideal gel which continuously crosses towards an attractive glass upon increasing the density. Moreover, we evaluate the statistical properties of the potential energy landscape for this model. We find that the configurational entropy, for densities within the optimal network-forming region, is finite even in the ground state and obeys a logarithmic dependence on the energy.

Reversible gels of patchy particles: role of the valence.

We simulate a binary mixture of colloidal patchy particles with two and three patches, respectively, for several relative concentrations and hence relative average valences. For these limited-valence systems, it is possible to reach low temperatures, where the lifetime of the patch-patch interactions becomes longer than the observation time without encountering phase separation in a colloid-poor (gas) and a colloid rich (liquid) phase. The resulting arrested state is a fully connected long-lived network where particles with three patches provide the branching points connecting chains of two-patch particles. We investigate the effect of the valence on the structural and dynamic properties of the resulting gel and attempt to provide a theoretical description of the formation and of the resulting gel structure based on a combination of the Wertheim theory for associated liquids and the Flory-Stockmayer approach for modeling chemical gelation.

Gel formation through reversible and irreversible aggregation.

We study the kinetics of formation of branched loopless structures in mixtures of particles with different shapes and functionalities. These systems are treated with the appropriate Smoluchowski rate equations, including condensation and fragmentation terms, and it is shown that it is possible to provide a parameter-free description of the assembly process, including the limit of irreversible aggregation at low temperatures. Using dynamics simulations we provide evidence of a connection between physical and chemical gelation in low-valence particle systems, and the possibility of relating ageing time with temperature.

Theoretical and numerical estimates of the gas-liquid critical point of a primitive model for silica.

We present a numerical evaluation of the critical point location for a primitive model for silica recently introduced by Ford et al. [J. Chem. Phys. 121, 8415 (2004)]. We complement the numerical estimate with a theoretical description of the system free energy (and related thermodynamic quantities) by solving (i) the standard parameter-free first order thermodynamic perturbation Wertheim theory and (ii) an ad hoc modeling of the temperature and density dependences of the bonding free energy, inspired by the Wertheim theory but requiring one fitting parameter alpha(rho). This parameter takes into account the correlation between adjacent bonding induced by excluded volume effects. We compare the predicted critical point location in the temperature-density plane with the "exact" numerical Monte Carlo value. The critical temperature is correctly predicted by both theoretical approaches, while only approach (ii) is able to accurately predict the critical density.

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-ranged 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 the 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.

A spherical model with directional interactions. I. Static properties.

We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting only between particles of different sizes. The small particles provide the bonds between the large ones. With a proper choice of the interaction parameters, as well as of the relative concentration of the two species, it is possible to control the effective valence. Here we focus on a specific choice of the parameters which favors tetrahedral ordering and study the equilibrium static properties of the system in a large window of densities and temperatures. Upon lowering the temperature we observe a progressive increase in local order, accompanied by the formation of a four-coordinated network of bonds. Three different density regions are observed: At low density the system phase separates into a gas and a liquid phase; at intermediate densities a network of fully bonded particles develops; at high densities--due to the competition between excluded volume and attractive interactions--the system forms a defective network. The very same behavior has been previously observed in numerical studies of nonspherical models for molecular liquids, such as water, and in models of patchy colloidal particles. Different from these models, theoretical treatments devised for spherical potentials, e.g., integral equations and ideal mode coupling theory for the glass transition, can be applied in the present case, opening the way for a deeper understanding of the thermodynamic and dynamic behavior of low valence molecules and particles.

Viscoelasticity and Stokes-Einstein relation in repulsive and attractive colloidal glasses.

We report a numerical investigation of the viscoelastic behavior in models for steric repulsive and short-ranged attractive colloidal suspensions, along different paths in the attraction strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass, and in the reentrant region where viscosity shows a nonmonotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent of the microscopic dynamics by comparing Newtonian and Brownian simulations for the same model. Finally, we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass.

Fully solvable equilibrium self-assembly process: fine-tuning the clusters size and the connectivity in patchy particle systems.

Self-assembly is the mechanism that controls the formation of well-defined structures from disordered pre-existing parts. Despite the importance of self-assembly as a manufacturing method and the increasingly large number of experimental realizations of complex self-assembled nano-aggregates, theoretical predictions are lagging behind. Here, we show that for a nontrivial self-assembly phenomenon, originating branched loopless clusters, it is possible to derive a fully predictive parameter-free theory of equilibrium self-assembly by combining the Wertheim theory for associating liquids with the Flory-Stockmayer approach for chemical gelation.

Effective nonadditive pair potential for lock-and-key interacting particles: The role of the limited valence.

Theoretical studies of self-assembly processes and condensed phases in colloidal systems are often based on effective interparticle potentials. Here we show that developing an effective potential for particles interacting with a limited number of "lock-and-key" selective bonds (due to the specificity of biomolecular interactions) requires-in addition to the nonsphericity of the potential-a (many body) constraint that prevents multiple bonding on the same site. We show the importance of retaining both valence and bond selectivity by developing, as a case study, a simple effective potential describing the interaction between colloidal particles coated by four single-strand DNA chains.

Self-assembly of patchy particles into polymer chains: a parameter-free comparison between Wertheim theory and Monte Carlo simulation.

The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory. This comparison offers a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameters and liquid state correlation functions. The Wertheim theory has not been previously subjected to stringent tests against simulation data for ordering across the polymerization transition. The authors numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.

Slow dynamics in a primitive tetrahedral network model.

We report extensive Monte Carlo and event-driven molecular dynamics simulations of the fluid and liquid phase of a primitive model for silica recently introduced by Ford et al. [J. Chem. Phys. 121, 8415 (2004)]. We evaluate the isodiffusivity lines in the temperature-density plane to provide an indication of the shape of the glass transition line. Except for large densities, arrest is driven by the onset of the tetrahedral bonding pattern and the resulting dynamics is strong in Angell's classification scheme [J. Non-Cryst. Solids 131-133, 13 (1991)]. We compare structural and dynamic properties with corresponding results of two recently studied primitive models of network forming liquids-a primitive model for water and an angular-constraint-free model of four-coordinated particles-to pin down the role of the geometric constraints associated with bonding. Eventually we discuss the similarities between "glass" formation in network forming liquids and "gel" formation in colloidal dispersions of patchy particles.

Phase diagram of patchy colloids: towards empty liquids.

We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature T lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction (phi), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T-phi) plane, possibly favoring the establishment of homogeneous disordered materials at small phi, i.e., stable equilibrium gels.

Dynamics in the presence of attractive patchy interactions.

We report extensive Monte Carlo and event-driven molecular dynamics simulations of a liquid composed of particles interacting via hard-sphere interactions complemented by four tetrahedrally coordinated short-range attractive ("sticky") spots, a model introduced several years ago by Kolafa and Nezbeda (Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 87, 161). To access the dynamic properties of the model, we introduce and implement a new event-driven molecular dynamics algorithm suited to study the evolution of hard bodies interacting, beside the repulsive hard-core, with a short-ranged interpatch square well potential. We evaluate the thermodynamic properties of the model in deep supercooled states, where the bond network is fully developed, providing evidence of density anomalies. Different from models of spherically symmetric interacting particles, the liquid can be supercooled without encountering the gas-liquid spinodal in a wide region of packing fractions phi. Around an optimal phi, a stable fully connected tetrahedral network of bonds develops. By analyzing the dynamics of the model we find evidence of anomalous behavior: around the optimal packing, dynamics accelerate on both increasing and decreasing phi. We locate the shape of the isodiffusivity lines in the (phi - T) plane and establish the shape of the dynamic arrest line in the phase diagram of the model. Results are discussed in connection with colloidal dispersions of sticky particles and gel-forming proteins and their ability to form dynamically arrested states.

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 fractions, 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.

Physics of the liquid-liquid critical point.

Within the inherent structure thermodynamic formalism introduced by Stillinger and Weber [Phys. Rev. A 25, 978 (1982)]], we address the basic question of the physics of the liquid-liquid transition and of density maxima observed in some complex liquids such as water by identifying, for the first time, the statistical properties of the potential energy landscape responsible for these anomalies. We also provide evidence of the connection between density anomalies and the liquid-liquid critical point. Within the simple (and physically transparent) model discussed, density anomalies do imply the existence of a liquid-liquid transition.

Activated bond-breaking processes preempt the observation of a sharp glass-glass transition in dense short-ranged attractive colloids.

We study-using molecular dynamics simulations-the temperature dependence of the dynamics in a dense short-ranged attractive colloidal glass to find evidence of the kinetic glass-glass transition predicted by the ideal mode coupling theory. According to the theory, the two distinct glasses are stabilized, one by excluded volume and the other by short-ranged attractive interactions. By studying the density autocorrelation functions, we discover that the short-ranged attractive glass is unstable. Indeed, activated bond-breaking processes slowly convert the attractive glass into the hard-sphere one, preempting the observation of a sharp glass-glass transition.