Combining statistical-mechanical theories and neutron-scattering techniques, we show that the effective pair potential between star polymers is exponentially decaying for large distances and crosses over, at a density-dependent corona diameter, to an ultrasoft logarithmic repulsion for small distances. We also make the theoretical prediction that in concentrated star polymer solutions, this ultrasoft interaction induces an anomalous fluid structure factor which exhibits an unusually pronounced second peak.

Recently, an increasing experimental effort has been devoted to the synthesis of complex colloidal particles with chemically or physically patterned surfaces and possible specific shapes that are far from spherical. These new colloidal particles with anisotropic interactions are commonly named patchy particles. In this Perspective article, we focus on patchy systems characterized by spherical neutral particles with patchy surfaces. We summarize most of the patchy particle models that have been developed so far and describe how their basic features are connected to the physical systems they are meant to investigate. Patchy models consider particles as hard or soft spheres carrying a finite and small number of attractive sites arranged in precise geometries on the particle's surface. The anisotropy of the interaction and the limited valence in bonding are the salient features determining the collective behavior of such systems. By tuning the number, the interaction parameters and the local arrangements of the patches, it is possible to investigate a wide range of physical phenomena, from different self-assembly processes of proteins, polymers and patchy colloids to the dynamical arrest of gel-like structures. We also draw attention to charged patchy systems: colloidal patchy particles as well as proteins are likely charged, hence the description of the presence of heterogeneously distributed charges on the particle surface is a promising perspective for future investigations.

In this review we present a summary of recent progress achieved in examining the equilibrium and dynamical properties of concentrated solutions of two novel kinds of soft matter systems: star-shaped polymers and starburst molecules known as dendrimers. The two systems share a host of interesting properties. The both consist of highly branched polymers, they allow for tuning of their properties through modification of the macromolecular architecture and they are both representatives of a quite novel class of colloidal particles, termed ultrasoft colloids. On the other hand there are also important differences, reflecting the fundamental difference in their architecture. It will be shown that a combination of scattering techniques and rheology with computer simulations and analytical methods from the realm of theoretical physics can shed light on the unusual properties of such systems. In this fashion, new ways appear for the manipulation of soft matter systems under external influences and promising perspectives for the fabrication of new materials are opened up and the versatility in manipulating soft matter is underlined.

We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials that do not diverge at the origin, are free of attractive parts, and decay fast enough to zero as the interparticle separation r goes to infinity. By employing a mean field-density functional theory which is shown to become exact at high temperatures and/or densities, we establish a criterion that determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature.