Table of contents

This special issue of Journal of Physics: Condensed Matter collects together a series of contributions first reported at the workshop `Structural Arrest Transitions in Colloidal Systems With Short-Range Attractions' which was held in Messina (Italy) on 17-20 December 2003. The aim of the workshop was to discuss, in depth, the recent progress on both the mode coupling theory predictions and their experimental tests on various aspects of structural arrest transitions in colloidal systems with short-range attractions. Indeed, the last five years had seen an incredible progress in the understanding of the slow dynamics in colloidal suspensions and of the formation of disordered arrested states in these systems, both at low and at high packing fraction. The time was ripe for an open discussion, not only of the previous achievements, but also of foreseeable future developments.

Browsing through this issue, the reader will immediately notice the presence of words and ideas indicating a flowering of the original novel idea of the structural arrest transition in densely packed systems. The dynamical arrest phenomena close to the colloidal glass transition is discussed together with several other types of dynamic arrest, in particular the ones also able to generate arrested states at extremely low packing fractions. In this issue, studies of glass and gel formation are often found together. Novel and/or deeper connections between dynamical arrest and cluster formation, both in equilibrium and out of equilibrium conditions were presented and discussed during the workshop and reported in the accompanying articles. The theoretical frontier is pushed toward systems where short-range attractions are complemented by long-range repulsions, favouring the description of supramolecular ordering in protein solutions, in the same theoretical framework developed for charged colloidal systems. Mode-coupling theory calculations, strengthened by the notable agreement between theoretical predictions and experimental results, are tackling more sophisticated dynamical phenomena, the dynamics close to higher-order singularity points which are expected to exist in these types of systems.

The seventeen articles included in this issue provide a state-of-the-art description of the experimental, theoretical and numerical studies reported at the workshop.

We believe these articles will be of interest not only to scientist interested in colloidal sciences, but also to the wider community of researchers interested in basic dynamical properties of soft and bio-matter, of the liquid state and of disordered systems in general.

We are grateful to the Bonino-Pulejo Foundation (Messina, Italy) for the patronage and enthusiatic support during the workshop. Our thanks also go to the Messina University, the Department of Energy (USA), the MIUR-PRIN-02 UCJTCS (Italy), the European Community Marie-Curie Project MRTN-CT-2003-504712 and the Bonino-Pulejo Foundation which contributed financial support to the Congress.

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A₃- and A₄-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: , where g_n(x) = p_n(lnx)/xⁿ with p_n denoting some polynomial and x = ln(t/t₀). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.

We review some results on the dynamics of gelation phenomena, obtained via a lattice model and via molecular dynamics using a DLVO potential. This study allowed us to make a connection between classical gelation and the phenomenology of colloidal systems, suggesting that gelation phenomena in attractive colloids at low temperature and low volume fraction can be described in terms of a two-line scenario.

We present the concept of dynamically available volume as a suitable order parameter for dynamical arrest. We show that dynamical arrest can be understood as a de-percolation transition of a vacancy network or available space. Beyond the arrest transition we find that droplets of available space are disconnected and the dynamics is frozen. This connection of the dynamics to the underlying geometrical structure of empty space provides us with a rich framework for studying the arrest transition.

We report extensive numerical simulations in the glass region for a simple model of short-ranged attractive colloids, the square well model. We investigate the behaviour 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.

We present some recent theory and simulation results addressing the phenomena of colloidal gelation at both high and low volume fractions, in the presence of short-range attractive interactions. We discuss the ability of mode-coupling theory and its adaptations to address situations with strong heterogeneity in density and/or dynamics. We include a discussion of the effect of attractions on the shear-thinning and yield behaviour under flow.

The combination of short-range attractions and long-range repulsions can lead to interesting clustering phenomena. In particular there are strong indications that the colloidal cluster phase is in fact a manifestation of such a competition. Here we compute the stability boundary of the cluster phase by invoking counter-ion condensation. It is found that a condensation catastrophe leading to an infinite cluster sets in if the level of charge on the colloid is too low.

The same ingredients leading to the cluster phase are found in nuclear physics: strong short-range attractions due to nuclear force and weak long-range Coulomb repulsions. We will show explicitly here the equivalence of a semi-empirical mass formula for the binding energy of the nucleus and the free energy of a cluster in a colloidal cluster phase. This identification enables an exploitation of theoretical results from nuclear physics to the colloidal domain and, perhaps, the construction of a colloidal system mimicking various aspects of nuclear matter.

We discuss the derivation and use of a key feature of a new version of thermodynamic perturbation theory (TPT) that Ben-Amotz and Stell have developed recently—the choice of a hard-core diameter to be used in modelling soft-core systems. We go on to show the way the new version of TPT can be used as input for the self-consistent Ornstein–Zernike approach (SCOZA) of Høye and Stell to obtain highly accurate static structure factors and thermodynamics for fluids and glasses. In obtaining quantitatively useful results for the structural arrest and other dynamic features in colloidal systems with pair potentials that include strong short-range attraction, accurate structure factors are a necessity.

The structure of the Baxter adhesive hard sphere fluid is examined using computer simulation. The radial distribution function (which exhibits unusual discontinuities due to the particle adhesion) and static structure factor are calculated with high accuracy over a range of conditions and compared with the predictions of Percus–Yevick theory. We comment on rigidity in percolating clusters and discuss the role of the model in the context of experiments on colloidal systems with short range attractive forces.

We studied clustering and gelation in low-volume-fraction () hard-sphere colloids, some with charge, with added non-adsorbing polymers. The range of the effective 'depletion' attraction induced by the polymers between the particles is of the particles' diameter. The effects of density mismatch between the particles and the solvent and unscreened charges on the particles were investigated. The onset of aggregation and gelation in a neutral, density-matched system is discussed in terms of mode-coupling theory (MCT) and a recent 'renormalized' version of MCT respectively. Gravity causes sedimentation of growing clusters and shifts the gelation boundary. In the charged and density-matched system, a 'cluster phase' in which finite-size aggregates 'coexisted' with monomers occurred before gelation. Its origins remain unclear.

We report theoretical and simulation studies of phase coexistence in model globular protein solutions, based on short-range, central, pair potential representations of the interaction among macro-particles. After reviewing our previous investigations of hard-core Yukawa and generalized Lennard-Jones potentials, we report more recent results obtained within a DLVO-like description of lysozyme solutions in water and added salt. We show that a one-parameter fit of this model, based on static light scattering and self-interaction chromatography data in the dilute protein regime, yields demixing and crystallization curves in good agreement with experimental protein-rich–protein-poor and solubility envelopes. The dependence of cloud and solubility point temperatures of the model on the ionic strength is also investigated. Our findings highlight the minimal assumptions on the properties of the microscopic interaction sufficient for a satisfactory reproduction of the phase diagram topology of globular protein solutions.

We have studied by dynamic light scattering the glass transition dynamics of a binary mixture of polystyrene microgel particles with a size ratio of R_small/R_large = 0.81 and a number ratio of , where a short-ranged depletion attraction () was induced by addition of linear polystyrene. This system shows a reentrant glass transition. We have determined the glass transition lines of this system in the experimental control parameter space given by the colloid volume fraction φ and the polymer concentration c_p by employing the power law of mode coupling theory (MCT) for the α-relaxation times. We find a reentry region which is much larger than predicted by theory and reported for another colloidal system with depletion attractions. Analysing the fluid dynamics along the transition lines with the β-scaling law of MCT we extract the c_p dependence of the exponent parameter λ and the non-ergodicity parameter f_q^c. The results are in qualitative agreement with the prediction of MCT for increasing attraction strength. The observed 'jump' of f_q^c is indicative of a change of the close by glass phase from a packing-driven to a bonding-driven glass. The increase of λ to 0.91 and its subsequent decrease may indicate the neighbourhood of an A₄ singularity.

We summarize the results of analyses of a series of small angle neutron scattering (SANS) experiments on dense L64 copolymer micellar solutions in heavy water. The system is modelled as a suspension of micellar particles that interact among themselves with a hard core plus a short range square well attractive interaction. The observed phase behaviour in the plane of temperature and polymer concentration is described. Characteristic features such as the existence of the glass-to-liquid-to-glass re-entrance transition and the line of glass-to-glass transition with its associated end point (A₃ singularity) are found which are quantitatively consistent with the recent mode coupling theory calculations using the same model potential. Supplementary to SANS experiments, photon correlation spectroscopy experiments on the same system have been performed. They show that although the Debye–Waller factors (the long time limits of the coherent intermediate scattering functions) of the two glasses do indeed become identical at the A₃ point as predicted, the intermediate scattering functions exhibit distinctly different intermediate time relaxations. Furthermore, we show that the Debye–Waller factors obtained from volume fractions beyond the A₃ point have the same magnitude as for the repulsive glass obtained before the A₃ point. In addition, the effect of applied pressure on the kinetic glass transition (KGT) is explored for the first time. We observe that, for the KGT in L64/D₂O micellar system, increasing applied pressure at constant temperature has a similar effect to reducing temperature at constant pressure. The preliminary observation of the ageing effect on quenching into the attractive glass state with the SANS technique is reported as well.

We report a set of viscoelastic measurements in concentrated aqueous solutions of a copolymer micellar system with short-range inter-micellar attractive interactions, a colloidal system characterized, in different regions of the composition–temperature phase diagram, by the existence of a percolation line (PT) and a kinetic glass transition (KGT). Both these transitions cause dramatic changes in the system viscoelasticity. Whereas the observed variations of the shear moduli at the PT are described in terms of percolation models, for the structural arrest at the KGT we investigate the frequency-dependent shear modulus behaviours by using a mode coupling theory (MCT) approach.

We study the nonlinear rheological behaviour and the microscopic particle dynamics for a colloidal glass. The measurements allow us to relate the microscopic diffusion dynamics to the macroscopic viscosity of the system. We demonstrate that the competition between the spontaneous restructuration (ageing) and the destruction of the internal structure by the shear ('shear rejuvenation') leads to a bifurcation in rheological behaviour. For a stress smaller than a (time-dependent) critical value, the viscosity increases in time and the material eventually stops flowing. For slightly larger stresses the viscosity decreases continuously with time and the flow accelerates. Thus the viscosity jumps discontinuously to infinity at the critical stress.

At variance with previous determinations, recent investigations on water suspension of a synthetic clay (Laponite) have shown the presence of an arrested phase also at very low clay concentrations (down to C_w = 0.003). This surprising behaviour has been studied in a wide clay concentration range. As a result the existence of two different routes towards the arrested phase, applying to low and high Laponite concentrations, has been found. We can speculate that at high clay concentration the system would form a Wigner glass whose elementary units are single Laponite platelets, as already indicated in previous works. At low clay concentrations, in contrast, the Wigner glass is supposed to be composed of clusters of Laponite platelets; in this case the clusters would be stabilized by the competition of long-range electrostatic repulsion and short-range attractive interactions. A similar behaviour has been recently found in a simulation work (Sciortino et al 2003 Preprint cond-mat/0312161).

The effect of pH and different anions of sodium salts on concentrated solutions of cytochrome C protein have been investigated by means of small angle neutron scattering and viscosity measurements. The control and a fine tuning of protein–protein interactions leads to the formation of protein clusters that eventually evolve into a structural arrested state. The appearance of a low Q peak in the small angle neutron scattering intensity distributions is also accompanied by a strong increase in the relative viscosity. These phenomena taken together can be considered as the signature of the gelation process. This structural arrest is induced by salt addition and specifically depends on the nature of anions, according to the Hofmeister series.

Experimental determination of stability conditions or instability boundaries in protein solution is a powerful tool for testing interaction models and for use in seeking an understanding of the mechanisms leading to protein aggregation. In a recent work on lysozyme solutions at different NaCl concentrations, we have determined the instability boundaries (spinodal line) of a liquid–liquid phase separation, metastable with respect to crystallization. Here, we review previous results, pointing out the scaling critical behaviour of isothermal compressibility with respect to spinodal temperatures, and discuss interaction models and the addition of an entropic term. The measured slowing down of concentration fluctuation dynamics is clearly related to the divergence of the fluctuation correlation length on approaching each point of the spinodal line. This observed off-critical slowing down calls for a crucial role for enhanced fluctuations in the crystallization process.