We attempt a classification of different colloidal gels based on colloid‐ colloid interactions. We discriminate primarily between non-equilibrium and equilibrium routes to gelation, the former case being slaved to thermodynamic phase separation while the latter is individuated in the framework of competing interactions and of patchy colloids. Emphasis is put on recent numerical simulations of colloidal gelation and their connection to experiments. Finally, we underline typical signatures of different gel types, to be looked at, in more detail, in experiments. (Some figures in this article are in colour only in the electronic version)

https://iopscience.iop.org/article/10.1088/0953-8984/19/32/323101/pdf

Colloidal gels: equilibrium and non-equilibrium routes

The addition of non-adsorbing polymer to a colloidal suspension induces an interparticle 'depletion' attraction whose range and depth can be 'tuned' independently by altering the polymer's molecular weight and concentration respectively. Over the past decade, one particularly simple experimental realization of such a mixture has been studied in considerable detail: nearly-hard-sphere particles of poly(methyl methacrylate) and random-coil polystyrene dispersed in simple hydrocarbon solvents (mainly cis-decalin). The simplicity of the system has enabled rather detailed comparison of experimental findings with theory and simulation. Here I review the current understanding of the equilibrium phase behaviour, structure, phase transition kinetics, and metastability of this model colloid–polymer mixture. These findings form a useful reference point for understanding more complex mixtures. Moreover, in some cases, insights gained from studying this model system have relevance beyond soft-condensed-matter physics, e.g. in understanding the liquid state, in controlling protein crystallization, and in elucidating the nature of glasses.

https://iopscience.iop.org/article/10.1088/0953-8984/14/33/201/pdf

The physics of a model colloid–polymer mixture

Colloids have increasingly been used to characterize or mimic many aspects of atomic and molecular systems. With confocal microscopy these colloidal particles can be tracked spatially in three dimensions with great precision over large time scales. This review discusses equilibrium phases such as crystals and liquids, and non-equilibrium phases such as glasses and gels. The phases that form depend strongly on the type of particle interaction that dominates. Hard-sphere-like colloids are the simplest, and interactions such as the attractive depletion force and electrostatic repulsion result in more non-trivial phases which can better model molecular materials. Furthermore, shearing or otherwise externally forcing these colloids while under microscopic observation helps connect the microscopic particle dynamics to the macroscopic flow behaviour. Finally, directions of future research in this field are discussed.

/pdf/confocal-microscopy-of-colloids-4pulp0rera.pdf

Confocal microscopy of colloids

The field of ab initio molecular dynamics (AIMD), in which finite temperature molecular dynamics (MD) trajectories are generated with forces obtained from accurate 'on the fly' electronic structure calculations, is a rapidly evolving and growing technology that allows chemical processes in condensed phases to be studied in an accurate and unbiased way. This article is intended to present the basics of the AIMD method as well as to provide a broad survey of the state of the art of the field and showcase some of its capabilities. Beginning with a derivation of the method from the Born–Oppenheimer approximation, issues including the density functional representation of electronic structure, basis sets, calculation of observables and the Car–Parrinello extended Lagrangian algorithm are discussed. A number of example applications, including liquid structure and dynamics and aqueous proton transport, are presented in order to highlight some of the current capabilities of the approach. Finally, advanced topics such as inclusion of nuclear quantum effects, excited states and scaling issues are addressed.

https://iopscience.iop.org/article/10.1088/0953-8984/14/50/202/pdf

Ab initio molecular dynamics: basic concepts, current trends and novel applications

Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bulk phenomenologies. The complexity of the confined molecular species is varied from simple building blocks, like noble gas atoms, normal alkanes and alcohols to liquid crystals, polymers, ionic liquids, proteins and water. Mostly, experiments with mesoporous solids of alumina, gold, carbon, silica, and silicon with pore diameters ranging from a few up to 50 nm are presented. The observed peculiarities of nanopore-confined condensed matter are also discussed with regard to applications. A particular emphasis is put on texture formation upon crystallisation in nanoporous media, a topic both of high fundamental interest and of increasing nanotechnological importance, e.g. for the synthesis of organic/inorganic hybrid materials by melt infiltration, the usage of nanoporous solids in crystal nucleation or in template-assisted electrochemical deposition of nano structures.

https://iopscience.iop.org/article/10.1088/0953-8984/27/10/103102/pdf

Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media

Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble. However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in nanopore systems could certainly benefit from a mesoscopic DFT in the CE. The stumbling block is the fixed N constraint which is responsible for the failure in proving the interchangeability of density profiles and external potentials as independent variables. Here we prove that, if in the CE the correlation functions are stripped of their asymptotic behaviour (which is not in the form of a properly irreducible n-body function), the HKSM theorem can be extended to the CE. In proving that, we generate new hierarchies of N-modified distribution and correlation functions with the same formal structure that the more conventional ones have (but with the proper irreducible n-body behaviour) and show that, if they are employed, either a modified external field or the density profiles can indistinctly be used as independent variables. We also write down the N-modified free energy functional and prove that the thermodynamic potential is minimized by the equilibrium values of the new hierarchy, completing in this way the extension of the HKSM theorem to the CE.

https://iopscience.iop.org/article/10.1088/0953-8984/14/3/302/pdf

Density functional theory in the canonical ensemble: I. General formalism

Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE). However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in nanopore systems could certainly benefit from a mesoscopic DFT in the CE. The stumbling block is the fixed $N$ constraint which is responsible for the failure in proving the interchangeability of density profiles and external potentials as independent variables. Here we prove that, if in the CE the correlation functions are stripped off of their asymptotic behaviour (which is not in the form of a properly irreducible $n$-body function), the HKSM theorem can be extended to the CE. In proving that, we generate a new {\it hierarchy} of $N$-modified distribution and correlation functions which have the same formal structure that the more conventional ones have (but with the proper irreducible $n$-body behaviour) and show that, if they are employed, either a modified external field or the density profiles can indistinctly be used as independent variables. We also write down the $N$-modified free energy functional and prove that the thermodynamic potential is minimized by the equilibrium values of the new hierarchy.

J. A. Hernando

Papers

Density functional theory in the canonical ensemble: I. General formalism

Density functional theory in the canonical ensemble I General formalism