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Interest in colloidal physics has grown at an incredible pace over the past few decades. To a great extent this remarkable development is due to the fact that colloidal systems are highly relevant in everyday applications as well as in basic research.

On the one hand, colloids are ubiquitous in our daily lives and a deeper understanding of their physical properties is therefore highly relevant in applied areas ranging from biomedicine over food sciences to technology. On the other hand, a seemingly unlimited freedom in designing colloidal particles with desired properties in combination with new, low-cost experimental techniques, make them—compared to hard matter systems—considerably more attractive for a wide range of basic investigations. All these investigations are carried out with close cooperation between experimentalists, theoreticians and simulators, reuniting thereby, on a highly interdisciplinary level, physicists, chemists, and biologists.

In an effort to give credit to some of these new developments in colloidal physics, two proposals for workshops were submitted independently to CECAM in the fall of 2008; both of them were approved and organized as consecutive events. This decision undoubtedly had many practical and organizational advantages. Furthermore, and from the scientific point of view more relevant, the organizers could welcome in total 69 participants, presenting 42 oral and 21 poster contributions. We are proud to say that nearly all the colleagues that we contacted at submission time accepted our invitation, and we are happy to say that the number of additional participants was rather high. Due to the fact that both workshops took place within one week, quite a few participants, registered originally for one of these meetings, extended their participation to the other event also. In total, 23 contributions have been submitted to this special issue, which cover the main scientific topics addressed in these workshops. We consider this relatively high number of contributions as an indicator that the topics presented at these workshops represent substantial scientific developments.

The particular motivation to organize these two workshops came from the fact that experimental work in colloidal physics is advancing rapidly around the globe. In contrast, theoretical and simulation approaches to investigate the wide range of new and surprising physical phenomena of colloidal systems is lagging behind this experimental progress. This is the more deploring since theory and simulation might provide a more profound understanding of many phenomena in soft and bio-related physics, such as phase behaviour, self-assembly strategies, or rheological properties, to name but a few. Furthermore this insight might help to guide experiment to design new colloid-based materials with desired properties. The declared aim of the two workshops was thus to bring together scientists who have contributed in recent time to new developments in colloidal physics and to share and discuss their latest innovations.

While CECAM workshops traditionally bring together scientists from the theoretical and simulator communities, from the very beginning the organizers considered it an indispensable necessity to invite experimentalists. And indeed, the organizers are happy to confirm that the participation of experimentalists, theoreticians, and simulators was highly fruitful and mutually inspiring: discussions between all communities did help to understand the possibilities and limitations imposed by experiment, theory, and simulations. Reuniting thus all forces, the workshop did contribute to a deeper understanding in colloidal physics and has helped to address future aspects that might lead to more applied problems of technological relevance.

The first workshop, entitled 'Computer Simulation Approaches to Study Self-Assembly: From Patchy Nano-Colloids to Virus Capsides', (organized by Jonathan Doye—University Of Oxford, Ard A Louis—University Of Oxford and Athanassios Panagiotopoulos—University Of Princeton) focused on the remarkable ability of colloidal systems to self-organize in well-defined composite objects. New simulation techniques and theoretical approaches were presented and discussed that offer a deeper understanding of self-assembly phenomena in colloidal physics and, eventually to uncover design rules for self-assembly. Particular emphasis was put on an emerging new class of colloidal particles, so-called patchy colloids. The second workshop, entitled 'New Trends in Simulating Colloids: From Models to Applications', (organized by Giuseppe Foffi—Ecole Polytechnique Fédérale De Lausanne, Gerhard Kahl—Vienna Technical University and Richard Vink—Georg-August-Universität Göttingen) focused on new methodological devices in theoretical and simulation approaches that provided a more profound insight in colloidal physics in general. A large variety of theoretical tools, ranging from different simulation techniques over classical density functional theory to efficient optimization techniques were presented. For details about the tools presented in both workshops we refer the reader to the contributions of this special issue. The 'round table' discussion meetings were highly useful in providing an overview of yet unsolved problems and to point out directions for future work. From the phenomenological point of view, among those are the question on the relevance of hydrodynamic interactions, the problem whether to treat solvents in an explicit or implicit way, or the relevance of multibody interactions, to name but a few. With respect to the methods it was agreed that future developments on dynamic Monte Carlo simulations or on rare events and multiscale techniques are urgently required. The presence of the experimentalists was also of great help in focusing attention on the systems that are going to represent the scientific challenges in the next years. It was interesting that while new materials like dna-coated colloids or janus and patchy particles are generating a lot of interest, more traditional systems, like colloidal glasses/gels and proteins, are far from being completely understood.

The relevance of these two workshops was reflected by the general consent that within a few years' time events with similar aims should be organized to discuss the progress that has been achieved.

We use computer simulations to study a model, first proposed by Wales (2005 Phil. Trans. R. Soc. A 363 357), for the reversible and monodisperse self-assembly of simple icosahedral virus capsid structures. The success and efficiency of assembly as a function of thermodynamic and geometric factors can be qualitatively related to the potential energy landscape structure of the assembling system. Even though the model is strongly coarse-grained, it exhibits a number of features also observed in experiments, such as sigmoidal assembly dynamics, hysteresis in capsid formation and numerous kinetic traps. We also investigate the effect of macromolecular crowding on the assembly dynamics. Crowding agents generally reduce capsid yields at optimal conditions for non-crowded assembly, but may increase yields for parameter regimes away from the optimum. Finally, we generalize the model to a larger triangulation number T = 3, and observe assembly dynamics more complex than that seen for the original T = 1 model.

For systems that self-assemble into finite-sized objects, it is sometimes convenient to compute the thermodynamics for a small system where a single assembly can form. However, we show that in the canonical ensemble the use of small systems can lead to significant finite-size effects due to the suppression of concentration fluctuations. We introduce methods for estimating the bulk yields from simulations of small systems and for following the convergence of yields with system size, under the assumptions that the various species behave ideally.

The self-assembly of rigid three-legged building blocks into polyhedral cages is investigated by patchy particle simulations. A four-site anisotropic interaction potential is introduced to make pairs of overlapping legs bind in an anti-parallel fashion, thereby forming the edges of a polyhedron of pentagons and hexagons. A torsional potential, reflecting an asymmetry or polarity in the legs' binding potential, proves crucial for the successful formation of closed fullerene-like cages. Self-assembly proceeds by a nucleation-and-growth mechanism, with a high success rate of cage closure. The size distribution of the self-assembled buckyballs is largely determined by the pucker angle of the particle. Nature explores a similar building block, the clathrin triskelion, to regulate vesicle formation at the cell membrane during endocytosis.

Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.

We have investigated the self-assembly scenario of patchy colloidal particles in a two-dimensional system. The energetically most favourable ordered particle arrangements have been identified via an optimization tool that is based on genetic algorithms. Assuming different simple models for patchy colloidal particles, which include binary mixtures as well as attraction and repulsion between the patches, we could identify a broad variety of highly non-trivial ordered structures. The strategies of the systems to self-assemble become evident from a systematic variation of the pressure: (i) saturation of patch bonds at low pressure and close packing at high pressure and (ii) for intermediate pressure values, the strategy is governed by a trade-off between these two energetic aspects. The present study is yet another demonstration of the efficiency and the high reliability of genetic algorithms as versatile optimization tools.

The simulation of colloidal particles suspended in solvent requires an accurate representation of the interactions between the colloids and the solvent molecules. Using the multiparticle collision dynamics method, we examine several proposals for stick boundary conditions, studying their properties in both plane Poiseuille flow (where fluid interacts with the boundary of a stationary macroscopic solid) and particle-based colloid simulations (where the boundaries are thermally affected and in motion). In addition, our simulations compare various collision rules designed to remove spurious slip near solid surfaces, and the effects of these rules on the thermal motion of colloidal particles. Furthermore, we demonstrate that stochastic reflection of the fluid at solid boundaries fails to faithfully represent stick boundary conditions, and conclude that bounce-back conditions should be applied at both mobile and stationary surfaces. Finally, we generalize these ideas to create partial slip boundary conditions at both stationary and mobile surfaces.

We investigate the stable crystalline configurations of a nematic liquid crystal made of soft parallel ellipsoidal particles interacting via a repulsive, anisotropic Gaussian potential. For this purpose, we use genetic algorithms (GA) in order to predict all relevant and possible solid phase candidates into which this fluid can freeze. Subsequently we present and discuss the emerging novel structures and the resulting zero-temperature phase diagram of this system. The latter features a variety of crystalline arrangements, in which the elongated Gaussian particles in general do not align with any one of the high-symmetry crystallographic directions, a compromise arising from the interplay and competition between anisotropic repulsions and crystal ordering. Only at very strong degrees of elongation does a tendency of the Gaussian nematics to align with the longest axis of the elementary unit cell emerge.

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.

The Euler characteristic of an object is a topological invariant determined by the number of handles and holes that it contains. Here, we use the Euler characteristic to profile the topology of model three-dimensional gel-forming fluids as a function of increasing length scale. These profiles act as a 'topological fingerprint' of the structure, and can be interpreted in terms of three types of topological events. As model fluids we have considered a system of dipolar dumbbells, and suspensions of adhesive hard spheres with isotropic and patchy interactions in turn. The correlation between the percolation threshold and the length scale on which the Euler characteristic passes through zero is examined and found to be system-dependent. A scheme for the efficient calculation of the Euler characteristic with and without periodic boundary conditions is described.

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.

We present a confocal microscopy study of the quasi-two-dimensional crystallization of a binary mixture of spherical colloids coated with long DNA strands. Our experiments show that in the crystalline phase the two colloidal species are completely demixed. Analysis of the lattice spacings in the two types of colloidal crystal shows that the diameters of the two species of colloids differ by 10%. We argue that the demixing in the crystalline phase is due to size segregation during crystallization. This phenomenon had been predicted in several theoretical studies. To our knowledge, the present study provides the first 'real-space' experimental confirmation of this effect.

The recently developed fundamental measure density functional theory (Hansen-Goos and Mecke 2009 Phys. Rev. Lett.102 018302) for an inhomogeneous anisotropic hard body fluid is used as a basic ingredient in treating the Brownian dynamics of hard spherocylinders. After discussing the relevance of a free parameter in the fundamental measure density functional for the isotropic–nematic transition in equilibrium, we discuss the equilibrium phase behaviour of hard spherocylinders in a static external potential which couples only to the orientations. For external potentials favouring rod orientations along the poles of the unit sphere, there is a well-known paranematic–nematic transition which ceases to exist above a threshold of the strength V₀ of the external potential. However, when orientations along the equator are more favoured, in the plane of the potential energy V₀ and density, there is a phase transition from paranematic to nematic for any strength, which becomes second order above a critical threshold of V₀. The full equilibrium phase diagram in the V₀–density plane is computed for a fixed rod aspect ratio of 5. For the equatorial cases, strength V₀ is then oscillating in time and dynamical density functional theory is used to compute the evolution of the orientational distribution. A subtle resonance for increasing oscillation frequencies is detected if the oscillating V₀ crosses the paranematic–nematic phase transition.

We study the phase behaviour of symmetric binary mixtures of hard core Yukawa (HCY) particles via thermodynamic perturbation theory (TPT). We show that all the topologies of phase diagram reported for the symmetric binary mixtures are correctly reproduced within the TPT approach. In a second step we use the capability of TPT to be straightforwardly extended to mixtures that are nonsymmetric in size. Starting from mixtures that belong to the different topologies of symmetric binary mixtures we investigate the effect on the phase behaviour when an asymmetry in the diameters of the two components is introduced. Interestingly, when the energy of interaction between unlike particles is weaker than the interaction between like particles, the propensity for the solution to demix is found to increase strongly with size asymmetry.

We use extensive event-driven molecular dynamics simulations to study the thermodynamic, structural and dynamic properties of hard-sphere glasses. We determine the equation of state of the metastable fluid branch for hard spheres with a size polydispersity of 10%. Our results show a clear jump in the slope of the isothermal compressibility. The observation of a thermodynamic signature at the transition from a metastable fluid to a glassy state is analogous to the abrupt change in the specific heat or thermal expansion coefficient as observed for molecular liquids at the glass transition. The dynamic glass transition becomes more pronounced and shifts to higher densities for longer equilibration times.

Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit solvent and the nature of the events along their growth pathways; the results provide further evidence of the importance of reversibility in the assembly process. The underlying goal of this approach is the modeling of virus capsid growth, a phenomenon at the submicroscopic scale that, despite its importance, is little understood.

Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker–Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.

We analyze connectivity and space-filling properties of colloidal gels obtained in a model with directional interactions. We compare gels formed upon slow cooling with the ones produced via quenching. The aggregation process is qualitatively different upon quenching: the cluster size distribution shows a percolation type of behavior but not the fully connected network achieved upon slow cooling. Because quenching favors the formation of defects, differently from systems where quenching tends to produce lower local connectivity and more open structures, here it favors instead more connected, but less space-filling, structures.

Using a highly efficient and reliable optimization tool that is based on ideas of genetic algorithms, we have systematically studied the pattern formation of the two-dimensional square-shoulder system. An overwhelming wealth of complex ordered equilibrium structures emerge from this investigation as we vary the shoulder width. With increasing pressure three structural archetypes could be identified: cluster lattices, where clusters of particles occupy the sites of distorted hexagonal lattices, lane formation, and compact particle arrangements with high coordination numbers. The internal complexity of these structures increases with increasing shoulder width.

We study the structure of colloidal fluids with reference to colloid–polymer mixtures. We compare the one-component description of the Asakura–Oosawa (AO) idealization of colloid–polymer mixtures with the full two-component model. We also consider the Morse potential, a variable range interaction, for which the ground state clusters are known. Mapping the state points between these systems, we find that the pair structure of the full AO model is equally well described by the Morse potential and the one-component AO approach. We employ a recently developed method to identify in the bulk fluid the ground state clusters relevant to the Morse potential. Surprisingly, when we measure the cluster populations, we find that the Morse fluid is significantly closer the full AO fluid than the one-component AO description.

A coarse-grained model for colloid–polymer mixtures is investigated where both colloids and polymer coils are represented as point-like particles interacting with spherically symmetric effective potentials. Colloid–colloid and colloid–polymer interactions are described by Weeks–Chandler–Andersen potentials, while the polymer–polymer interaction is very soft, of strength k_BT/2 for maximum polymer–polymer overlap. This model can be efficiently simulated both by Monte Carlo and molecular dynamics methods, and its phase diagram closely resembles that of the well-known Asakura–Oosawa model. The static and dynamic properties of the model are presented for systems at critical colloid density, varying the polymer density in the one-phase region. Applying Lees-Edwards boundary conditions, colloid–polymer mixtures exposed to shear deformation are considered, and the resulting anisotropy of correlations is studied. Whereas for the considered shear rate, , radial distribution functions and static structure factors indicate only small structural changes under shear, an appropriate projection of these correlation functions onto spherical harmonics is presented that allows us to directly quantify the structural anisotropies. However, the considered shear rate is probably not high enough to see anisotropies in static structure factors at small wavenumbers that have been predicted by Onuki and Kawasaki (1979 Ann. Phys.121 456) for the critical behavior of systems under shear. The anomalous dependence of the polymer's self-diffusion constant on polymer density is referred to the clustering of the colloid particles when approaching the critical point.

We present simulations of the aging of a quasi-hard-sphere glass, with Newtonian and Brownian microscopic dynamics. The system is equilibrated at the desired density (above the glass transition in hard spheres) with short-range attractions, which are removed at t = 0. The structural part of the decay of the density correlation function can be time rescaled to collapse onto a master function independent of the waiting time, t_w, and the timescale follows a power law with t_w, with exponent z ∼ 0.89; the non-ergodicity parameter is larger than that of the glass transition point (the localization length is smaller) and oscillates in harmony with S_q. The aging with both microscopic dynamics is identical, except for a scale factor from the age in Newtonian to the age in Brownian dynamics. This factor is approximately the same as that which scales the α-decay of the correlation function in fluids close to the glass transition.

The problem of successfully simulating ionic fluids at low temperature and low density states is well known in the simulation literature: using conventional methods, the system is not able to equilibrate rapidly due to the presence of strongly associated cation–anion pairs. In this paper we present a numerical method for speeding up computer simulations of the restricted primitive model (RPM) at low temperatures (around the critical temperature) and at very low densities (down to 10 ^{− 10}σ ^{− 3}, where σ is the ion diameter). Experimentally, this regime corresponds to typical concentrations of electrolytes in nonaqueous solvents. As far as we are aware, this is the first time that the RPM has been equilibrated at such extremely low concentrations. More generally, this method could be used to equilibrate other systems that form aggregates at low concentrations.

Computer simulations of first-order phase transitions using 'standard' toroidal boundary conditions are generally hampered by exponential slowing down. This is partly due to interface formation, and partly due to shape transitions. The latter occur when droplets become large such that they self-interact through the periodic boundaries. On a spherical simulation topology, however, shape transitions are absent. We expect that by using an appropriate bias function, exponential slowing down can be largely eliminated. In this work, these ideas are applied to the two-dimensional Widom–Rowlinson mixture confined to the surface of a sphere. Indeed, on the sphere, we find that the number of Monte Carlo steps needed to sample a first-order phase transition does not increase exponentially with system size, but rather as a power law , with α≈2.5, and V the system area. This is remarkably close to a random walk for which α_RW = 2. The benefit of this improved scaling behavior for biased sampling methods, such as the Wang–Landau algorithm, is investigated in detail.