General

We theoretically study aspects of soft condensed matter, mainly phase behaviour, structure, and interfaces of colloidal suspensions, nanoparticle dispersions, (Pickering) emulsions, electrolytes, etc. Many of these fluids are multicomponent systems consisting of mesoscopic solid particles (the colloidal nanoparticles), solvent molecules, often salt ions, and possibly additional components such as polymers. The colloidal nanoparticles come in various sizes (ranging from a few nanometer up to several microns) and shapes (spheres, rods, discs, cubes, octapods). This regime of sizes is such that the particles can perform Brownian motion in the liquid, which allows many microstates the be explored at the fixed temperature of the medium ---larger particles are more passive as they sink to the bottom as a brick or float on the air-water meniscus as a cork. The Brownian dynamics of sub-micron particles in suspensions or dispersions renders these systems a genuine thermodynamic character, featuring phase transitions and self-assembly into (hopefully new and functional) structures, e.g. crystals, liquid crystals, monolayers, demixed states separated by a vapour-liquid meniscus or a liquid-liquid interface. The structures that form depend not only on the properties of the particles (size, shape, surface charge, polarisability, surface coating etc.) but also on those of the liquid medium (pH, salt concentration, dielectric constant, etc).    The statistical mechanics of these systems is challenging because of the large length- and time-scale differences between the mesoscopic colloidal particles and the microscopic molecules and ions of the liquid medium. Often one is interested in the effective interactions between the particles in the liquid medium ---once these are known one can treat the actual multicomponent system as an effective one-component system. The effective interaction are, in principle, obtained by integrating out all the degrees of freedom of the microscopic particles, in the partition sum, at a fixed configuration of the particles. In other words, the effective colloidal interactions are essentially given by the free energy (or grand potential) of an inhomogeneous fluid of solvent, ions, polymers etc. in the external field of the colloids. By tuning parameters such as temperature, salinity, pH, dielectric constant etc., one can tune the effective interactions, and hence influence the phase behaviour, self-assembly, and structure of the particle dispersion. It is this tunability that is responsible for a zoo of interesting phenomena and new structures.
 

There is a number of effective interactions to be distinguished:

• Short-ranged steric excluded volume interactions, which stem essentially from Pauli-exclusion of the electrons in surface layers that approach each other. They determine the size and the shape of a particle.
• Dispersion forces due to fluctuating atomic dipoles, with a strength that depends on the dielectric contrast between the particle and the liquid medium.
• Coulomb interactions due to charged groups on the surface of a particle, often screened by diffuse ionic clouds in the liquid medium;
• Depletion interactions due to non-adsorbing polymers, which exert a usually attractive osmotic force on pairs of particle at small separations. The range of this interaction is set by the size of the polymers, the strength by the polymer concentration.
• Many more, including hydrophobic and capillary forces.

We study and have studied several aspects of all of these forces.

Under appropriate conditions the effective colloid-colloid interactions can be made "hard", i.e. the interactions are harshly repulsive at short distances such that colloid-colloid overlap is not allowed. Colloidal hard-sphere, hard-rod, or hard-disc systems are athermal, i.e. there is no energy scale and no cohesive energy, and the thermodynamic properties (e.g. phase behaviour) are therefore solely determined by entropy . Despite this purely entropic nature there is a plethora of phase transitions from disordered to ordered, e.g. a hard-sphere fluid crystallises into a face-centered-cubic lattice at high enough density, hard rods form nematic and smectic liquid crystal phases upon compression. Moreover, when hard particles of different size and/or shape are mixed together, they may spontaneously demix , again because the entropy of the demixed phases is higher(!) than in the mixed phase. We study, as discussed below in more detail, the behaviour of such hard-core systems theoretically. We consider both homogeneous bulk systems and inhomogeneous systems, where the inhomogeneity may be caused by external fields or by a spontaneous phase separation into two bulk phases separated by an interface.

Most (colloidal) surfaces acquire, when exposed to water, a net electric charge due to the dissociation of chemical groups: a positive ion "jumps" into the water leaving behind a negatively charged group on the surface (or vice versa). The effective interaction between two of these charged colloids is conventionally described by screened-Coulomb (Yukawa) repulsions, where the screening is more efficient at high salinity than at low.

Our published work can be found here.

More specifically some current research topics include:

1. The calculation of effective interactions that result from  ionic screening of patchy and charge-regulated surfaces;
2. The calculation of crystal structures formed by odd-shaped particles (Platonic, Archimedean, and Johnson solids, polyhedra, or branched particles such as tetra- and octapods) using triangular tessellation techniques combined with Monte Carlo methods.
3. The calculation, within Onsager-type density functional theory, of  phase diagrams of liquid crystals, in particular involving (i) the elusive biaxial nematic state of brick-shaped particles, (ii) the effect of flexibility on needle-shaped virus particles, and (iii) carbon nanotubes dispersed in a matrix of flexible particles.
4. The calculation of the polarisability tensor of odd-shaped nanoparticles, and their resulting effective interactions in and out of external electric fields, on the basis of a microscopic "Drude" model for the fluctuating atomic dipoles. This involves large-matrix manipulations, and incorporates many-body effects at a level similar to Lifshitz' fluctuating quantumelectrodynamics theory.