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.

The problem of phase behaviour of solutions of globular proteins is approached by means of a Hard Core Yukawa fluid model with short-ranged attractions. We have determined the phase behaviour of this model system for different well widths, using a variety of high quality methods. The essential phase behaviour of systems with short-ranged attractions is reproduced. The typical phase behaviour of solutions of globular proteins is well represented by the Hard Core Yukawa fluid with short-ranged attractions. The formation of amorphous precipitates in protein crystal growth experiments is identified on our model phase diagram with the formation of an attractive glass. As the range of attraction is decreased, the formation of an attractive glass state dominates the phase behaviour in the meta-stable regime above the critical point. We show how the addition of a long-ranged attraction, in the Two-Yukawa model, has the effect of eliminating the formation of attractive glass, while preserving the equilibrium features of the short-ranged attractive system. This opens the possibility of using attractive long-range interactions to avoid the formation of an attractive glass state.

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.

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.

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.

Using dynamically available volume (DAV) as an order parameter, we study the ideal dynamical arrest for some simple lattice glass models. For these models the dynamically available volume is expressed as holes, or vacant sites into which particles can move. We find that on approach to the arrest the holes, which are the only mediators of transport, become increasingly rare. Near the arrest, dynamical quantities can be expanded in a series of hole density, in which the leading term is found to quadratic, as opposed to unfrustrated systems which have a linear dependence. Dynamical quantities for the models we have studied show universal behaviour when expressed in terms of the hole density. The dynamically available volume is shown to be a useful characterisation of the slow aging in lattice glasses.

We discuss the phase behaviour of spherical hard-core particles, with an attractive potential, as described by a hard-core Yukawa model. The ratio of the range of the attraction to the diameter of the particles is an important control parameter of the problem. Upon decreasing the range of the attraction, the phase diagram changes quite significantly, with the liquid–gas transition becoming metastable, and the crystal being in equilibrium with the fluid, with no intervening liquid. We also study the glass transition lines and, crucially, find that the situation, being very simple for pure repulsive potentials, becomes much richer in competition between glass and crystal phases for short-range attractions. Also a transition between attractive and repulsive glass appears somewhat in analogy with the isostructural equilibrium transition between two crystals.

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.

We have studied a model of a complex fluid consisting of particles interacting through a hard-core and 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 mode-coupling 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, nanoparticle aggregation, and globular protein crystallization.