Norman Hoffmann

Partial Clustering in Binary Two-Dimensional Colloidal Suspensions

Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation, and experiment. The mixture exhibits a partial clustering in equilibrium: in the voids of the matrix of unclustered big particles, the small particles form subclusters with a spongelike topology which is accompanied by a characteristic small-wave vector peak in the small-small structure factor. This partial clustering is a general phenomenon occurring for strongly coupled negatively nonadditive mixtures.

Exotic fluids and crystals of soft polymeric colloids

We discuss recent developments and present new findings in the colloidal description of soft polymeric macromolecular aggregates. For various macromolecular architectures, such as linear chains, star polymers, dendrimers, and polyelectrolyte stars, the effective interactions between suitably chosen coordinates are shown to be ultrasoft, i.e., they either remain finite or diverge very slowly at zero separation. As a consequence, the fluid phases have unusual characteristics, including anomalous pair correlations and mean-field-like thermodynamic behaviour. The solid phases can exhibit exotic, strongly anisotropic as well as open crystal structures. For example, the diamond and the A15 phase are shown to be stable at sufficiently high concentrations. Re-entrant melting and clustering transitions are additional features displayed by such systems, resulting in phase diagrams with a very rich topology. We emphasize that many of these effects are fundamentally different from the usual archetypal hard-sphere paradigm. Instead, we propose that these fluids fall into the class of mean-field fluids.

Linear screening of the electrostatic potential around spherical particles with non-spherical charge patterns

We derive analytical expressions for the screened electrostatic potential caused by a charged spherical colloid that contains point charges distributed in an arbitrary manner in its interior. We consider both the cases of uniform and discontinuous dielectric constants. The solution is based on an expansion of the electrostatic potentials on the various regions of space in spherical harmonics involving spherical Bessel functions of the third kind. Tetrahedral charge arrangements as well as a random charge distribution inside the confining sphere are considered explicitly as representative examples.

Structure and phase behavior of polyelectrolyte star solutions

Using the recently developed effective interaction potentials between polyelectrolyte stars, we examine the structure and phase behavior of solutions of the same. The effective interaction is ultrasoft and density dependent, owing to the integration of the counterionic degrees of freedom. The latter contribute extensive volume terms that must be taken into account in drawing the phase diagram of the system. The structural behavior of the uniform fluid is characterized by anomalous structure factors, akin to those found previously for solutions of uncharged star polymers. The phase diagram of the system is very rich, featuring a fluid phase at low arm numbers of the stars, two reentrant melting regions, as well as a variety of crystal structures with unusual symmetry. The physical origin of these features can be traced back to the ultrasoft nature of the effective interaction potential.

Microphase structuring in two-dimensional magnetic colloid mixtures

Suspensions of super-paramagnetic colloids trapped in the water–air interface are an excellent model system for the study of two-dimensional systems. Here, we investigate the structural behaviour of two-component mixtures of such particles. The interparticle interactions are tunable through the application of a magnetic field perpendicular to the air–water surface. Further, they can be influenced by the choice of the relative magnetic susceptibilities of the two colloidal species. We have performed integral equation theory and computer simulations to study the static properties of such a binary superparamagnetic system. For all susceptibility ratios studied, no macroscopic phase separation takes place; the fluid phase remains macroscopically homogeneous but microphase structuring occurs: the interactions with the large particles lead to a clustering of the smaller particles. We combine structural information in reciprocal space together with morphological measures in real space to characterize the ordering of the two species in the binary mixture.

Charged colloids, polyelectrolytes and biomolecules viewed as strongly coupled Coulomb systems

Ab rief review is given on recent studies of charged soft matter solutions, as modelled by the ‘primitive’ approach of strongly coupled Coulomb systems, where the solvent just enters as a dielectric background. These include charged colloids, biological macromolecules such as proteins and DNA, polyelectrolytes and polyelectrolyte stars. Also some original results are presented on colloid–polyelectrolyte complex formation near walls and on the anomalous fluid structure of polyelectrolyte stars as a function of increasing concentration.

Density functional theory of freezing for soft interactions in two dimensions

A density functional theory of two-dimensional freezing is presented for a soft interaction potential that scales as inverse cube of particle distance. This repulsive potential between parallel, induced dipoles is realized for paramagnetic colloids on an interface, which are additionally exposed to an external magnetic field. An extended modified weighted density approximation which includes correct triplet correlations in the liquid state is used. The theoretical prediction of the freezing transition is in good agreement with experimental and simulation data.

Colloidal layers in magnetic fields and under shear flow

The behaviour of colloidal mono- and bilayers in external magnetic fields and under shear is discussed and recent progress is summarized. Superparamagnetic colloidal particles form monolayers when they are confined to a air–water interface in a hanging water droplet. An external magnetic field allows us to tune the strength of the mutual dipole–dipole interaction between the colloids and the anisotropy of the interaction can be controlled by the tilt angle of the magnetic field relative to the surface normal of the air–water interface. For sufficiently large magnetic field strength crystalline monolayers are found. The role of fluctuations in these two-dimensional crystals is discussed. Furthermore, clustering phenomena in binary mixtures of superparamagnetic particles forming fluid monolayers are predicted. Finally, we address sheared colloidal bilayers and find that the orientation of confined colloidal crystals can be tailored by a previously applied shear direction.

Correlations of two-dimensional super-paramagnetic colloids in tilted external magnetic fields

We outline the formalism of liquid integral equation theory for anisotropic interactions in two dimensions and subsequently apply this theory to one-component super-paramagnetic particles exposed to a tilted magnetic field. Inhomogeneous local ordering of the particles is observed for different in-plane directions. The anisotropy of the interaction as well as of the liquid structure is increased by increasing the tilt angle. Furthermore, the particles favour an alignment in the direction of the in-plane component of the magnetic field. For increasing tilt angle, the anisotropy of the structural correlations is qualitatively similar to that of the corresponding solid lattice which is stable at lower temperatures. However, the mean-square displacements behave qualitatively different in the solid and fluid phases as a function of the tilt angle.

Interactions and phase behaviour of polyelectrolyte star solutions

In this work, we first briefly review recent results regarding effective interactions of charged star polymers (polyelectrolyte stars) and then we present new results for many-body systems obtained by employing this interaction. The dominant role is played by the trapped counterions that bring about an entropic repulsion between the centres of these macromolecular aggregates. Subsequently, we explicitly derive density-dependent effective interaction potentials between the polyelectrolyte stars and calculate liquid structure factors and solid-state zero-temperature phase diagrams, discovering thereby a large variety of different crystal phases, similar to those found for the case of neutral star polymers.