Self-assembly scenarios in inverse patchy colloid systems

The seemingly unlimited freedom in designing interactions in soft matter systems allows the synthesis of colloidal particles of increasingly complex architectures at an incredible pace. Among these entirely new classes of mesoscopic particles there is a new generation of colloids with chemically or physically patterned surfaces. Decorating the particles with synthetic organic or biological molecules provides valence to the colloids and introduces anisotropy in the inter-particle interaction. This can, for example, be achieved by coating spherically symmetric colloidal particles with biological ligands, such as proteins, DNA or RNA. With the mutually attractive patches being discrete and limited in number, these colloids are commonly referred to as "patchy particles". Due to the asymmetric, selective, and directional character of the interaction, novel scenarios of collective behaviour have been observed for this new class of colloidal particles, such as the gas-liquid phase separation, crystallization, cluster formation, or gelation. In the present project we want to study a novel class of patchy colloidal systems. We consider colloidal particles where the patches are repulsive while the spherical, isotropic interactions of the colloids is attractive. If, for instance, we decorate the poles of the particles by repulsive patches, then those parts of the surface that carry the same charge (i.e., patch-patch, equator-equator) will repel each other while oppositely charged zones (i.e., patch- equator) will feel an attraction. We will term these particles as inverse patchy particles. We are convinced that the resulting complex, highly anisotropic interaction will induce a rich wealth of new and unexpected self-assembly scenarios. The present project is dedicated to evaluate the full phase diagram of inverse patchy colloids. In an effort to evaluate the properties of the involved disordered (i.e., the gas and the fluid) phases and the ordered phases with high accuracy we will use statistical mechanics based, numerical concepts: the disordered phases will be treated with computer simulations and integral-equation theories; furthermore we will extend a recently developed thermodaynamic perturbation theory, which is based on Wertheim`s theory of associating fluids and on the Flory- Stockmayer approach of chemical gelation to our system. The identifications of the yet unknown self-assembly scenarios in the ordered phases will represent a particular challenge: here we will use accurate, efficient and highly reliable optimization tools that identify in unbiased search strategies the energetically most favourable ordered particle arrangements: genetic algorithms and metadynamics simulations will be the methods of our choice. While our investigations will start from a simplified model we plan to consider in a later stage a realistic inverse patchy system: by adsorbing soft polyelectrolyte stars on the surface of hard-sphere type colloids of opposite charge the features of inverse patchiness can indeed be realized in the lab.