We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and modecoupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.

We introduce an order parameter for dynamical arrest. Dynamically available volume (unoccupied space that is available to the motion of particles) is expressed as holes for the simple lattice models we study. Near the arrest transition the system is dilute in holes, so we expand dynamical quantities in a series of hole density. Unlike the situation when presented in particle density, all cases of simple models that we examine have a quadratic dependence of the diffusion constant on hole density. This observation implies that in certain regimes ideal dynamical arrest transitions may possess a hitherto unnoticed degree of universality.

The dynamically arrested state of matter is discussed in the context of athermal systems, such as the hard sphere colloidal arrest. We believe that the singular dynamical behaviour near arrest expressed, for example, in how the diffusion constant vanishes may be 'universal', in a sense to be discussed in the paper. Based on this we argue the merits of studying the problem with simple lattice models. This, by analogy with the the critical point of the Ising model, should lead us to clarify the questions, and begin the program of establishing the degree of universality to be expected. We deal only with 'ideal' athermal dynamical arrest transitions, such as those found for hard sphere systems. However, it is argued that dynamically available volume (DAV) is the relevant order parameter of the transition, and that universal mechanisms may be well expressed in terms of DAV. For simple lattice models we give examples of simple laws that emerge near the dynamical arrest, emphasising the idea of a near-ideal gas of 'holes', interacting to give the power law diffusion constant scaling near the arrest. We also seek to open the discussion of the possibility of an underlying weak coupling theory of the dynamical arrest transition, based on DAV.

No abstract

We extend a previously studied lattice model of particles with infinite repulsions to the case of finite-energy interactions. The phase diagram is studied using grand canonical Monte Carlo simulation. Simulations of dynamical phenomena are made using the canonical ensemble. We find interesting order-disorder transitions in the equilibrium phase diagram and identify several anomalous regimes of diffusivity. These phenomena may be relevant to the case of strong orientational bonding near freezing. DOI: 10.1103/PhysRevE.71.030102 PACS number͑s͒: 61.20.Gy, 61.43.Fs Dynamical arrest ͓1-6͔ is a ubiquitous phenomenon in nature, with many manifestations. Well-known examples include conventional glasses ͓7-9͔, but in modern condensedmatter studies the range of systems where the issues have become relevant is remarkable. Thus, dynamical arrest is now believed to be a useful description for gellation ͓10-15͔, "solidification", glassification ͓7,8,16,17͔, jamming ͓18-20͔, and the ergodic-to-non-ergodic transition. Recent work tends to indicate that scientists increasingly see these phenomena as manifestations of a single underlying set of principles ͓12,18,20-22͔.Numerous attempts have been made to study simple models to develop ideas of dynamical arrest ͓9,23-31͔. Two approaches have been prominent in recent years, exemplified by the Kob-Andersen kinetically constrained models ͓32,33͔ and Hamiltonian-type models such as that introduced by Biroli and Mézard ͑BM͒. This model, introduced in Ref. ͓3͔, permits particles of any given type i to have a number of neighbors less than or equal to a prescribed number, c i . If c i is equal to the coordination number of the lattice, we have a lattice-gas model; elsewhere the model is believed to be an attempt to represent packing constraints ͓1,3,34͔. The relationship between these two different kinetic models has never been fully explored, although there has been a tendency to conclude that they are quite similar in spirit.In this paper we extend the concept of a Hamiltonian model to include "soft" repulsions, rather than simply hard constraints. Thus, we now stipulate that c i neighbors of a given type have zero energy and additional particles have a repulsive energy ⑀͑i͒ ͑in our case chosen to be V 0 ͒. Clearly, as we pass to the limit of infinite repulsions we expect to recover the original BM model. In what will follow the reader may assume that this is indeed the case, although that limit is not explicitly shown. Here we focus on this generalization and in particular two of its applications. First, it gives additional insights into the mechanisms involved in the dynamical arrest of such models, and second, such models may be applicable to systems with oriented bonding effects.In the work discussed below, we have calculated phase diagrams using the grand canonical Monte Carlo method. The initial configurations of these models are obtained by slowly annealing in the repulsions from a random lattice-gas configuration. Since we form crystals for a large portion of the phase diagr...

We discuss the ideal glass transition for two types of potential model of attractive colloidal systems, i.e. the square-well system and the Yukawa hard-sphere fluid. We use the framework of the ideal mode-coupling theory and we mostly focus our attention on the nature of the singularities predicted by the theory. We also study the phenomena that arise by varying the range of the attraction, since this parameter has been identified as one of the key parameters in colloidal systems.

No abstract

We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, and crystal, in characteristic relationship to each other. As the parameters of the model are varied, one obtains characteristic patterns of phase behavior reminiscent of continuum systems where the range of the interaction is varied. The model also possesses dynamical arrest, and although we have not studied it in detail, these "transitions" appear to have a reasonable relationship to the phases and their transitions. In many systems, one can observe a rich interplay between phase separation, critical phenomena, slowed dynamics, and solidification, the latter manifesting itself as both crystallization and glassification. These questions have a long and venerable past, but in modern condensed-matter theory the range of systems where the issues have become relevant [1-3] is remarkable. Recent interest in model systems extends from colloidal glasses [4], particle gels [3,5], polymeric gels [6], globular protein crystallization [7,8], and gellation. For example, it has recently transpired that even the simplest system with repulsive core and short-ranged attraction exhibits a large range of phase transitions, dynamical arrest (possibly with new dynamical logarithmic singularity [5,9]), and kinetic phenomena [10], the pertinent control parameter being the range of the attraction. So far it has not been possible to understand the inter-relation of all these effects. Such issues also lie at the heart of many important modern problems of materials science, including the formation of arrays of particles on optical wavelengths and knowledge-based materials design [11,12].To fully explore these questions, we would need to describe an extended range of density, across a number of different phase boundaries, dealing naturally with criticality [13], metastability, and arrest phenomena [14], all in a coherent fashion, with tools that were applicable and reliable across these regimes. In the interim, progress can be made in various aspects of the problem [8,11,15].The idea that the gas, liquid, crystal, and transitions between them can be studied within the same lattice model has been raised over the years in some interesting studies [16], and complex models have also been studied using such simple models [17]. However, there has never been any simple (lattice-based) general mechanism producing a liquid (considered as a large collection of attraction-dominated states with nearly degenerate energies) in an appropriate relation to gas and solid. Here, beginning from ideas introduced by Biroli and Mézard [18,19], we show that it is possible to caricature all the states, and their transitions, in a remarkably simple nearest-neighbor Ising model. In this model, dynamical arrest and glassy states are also naturally incorporated into the story.In the model, space is divided into cubes of side a, characteristic of the particle size and the microscopic length of the system. To the center of each cube we associate a site (coordination number c...