Gerhard Kahl

Fundamental measure theory for hard-sphere mixtures revisited: the White Bear version

We develop a density functional for hard-sphere mixtures which keeps the structure of Rosenfelds fundamental measure theory (FMT) whilst inputting the Mansoori–Carnahan–Starling–Leland bulk equation of state. Density profiles for the pure hard-sphere fluid and for some binary mixtures adsorbed at a planar hard wall obtained from the present functional exhibit some improvement over those from the original FMT. The pair direct correlation function c(2) (r) of the pure hard-sphere fluid, obtained from functional differentiation, is also improved. When a tensor weight function is incorporated for the pure system our functional yields a good description of fluid–solid coexistence and of the properties of the solid phase.

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.

Computer assembly of cluster-forming amphiphilic dendrimers.

Recent theoretical studies have predicted a new clustering mechanism for soft matter particles that interact via a certain kind of purely repulsive, bounded potentials. At sufficiently high densities, clusters of overlapping particles are formed in the fluid, which upon further compression crystallize into cubic lattices with density-independent lattice constants. In this work we show that amphiphilic dendrimers are suitable colloids for the experimental realization of this phenomenon. Thereby, we pave the way for the synthesis of such macromolecules, which form the basis for a novel class of materials with unusual properties.

Ionic microgels as model systems for colloids with an ultrasoft electrosteric repulsion: Structure and thermodynamics

We present a theoretical analysis of the structural properties and phase behavior of spherical, loosely cross-linked ionic microgels that possess a low monomer concentration. The analysis is based on the recently derived effective interaction potential between such particles [A. R. Denton, Phys. Rev. E 67, 011804 (2003)]. By employing standard tools from the theory of the liquid state, we quantitatively analyze the pair correlations in the fluid and find anomalous behavior above the overlap concentration, similar to the cases of star-branched neutral and charged polymers. We also employ an evolutionary algorithm in order to predict the crystalline phases of the system without any a priori assumptions regarding their symmetry class. A very rich phase diagram is obtained, featuring two reentrant melting transitions and a number of unusual crystal structures. At high densities, both the Hansen-Verlet freezing criterion [J.-P. Hansen and L. Verlet, Phys. Rev. 184, 151 (1969)] and the Lindemann melting criterion [F. A. Lindemann, Phys. Z. 11, 609 (1910)] lose their validity. The topology of the phase diagram is altered when the steric interactions between the polymer segments become strong enough, in which case the lower-density reentrant melting disappears and the region of stability of the fluid is split into two disconnected domains, separated by intervening fcc and bcc regions.

Self-assembly scenarios of patchy colloidal particles in two dimensions

We have investigated the self-assembly scenario of patchy colloidal particles in a two-dimensional system. The energetically most favourable ordered particle arrangements have been identified via an optimization tool that is based on genetic algorithms. Assuming different simple models for patchy colloidal particles, which include binary mixtures as well as attraction and repulsion between the patches, we could identify a broad variety of highly non-trivial ordered structures. The strategies of the systems to self-assemble become evident from a systematic variation of the pressure: (i) saturation of patch bonds at low pressure and close packing at high pressure and (ii) for intermediate pressure values, the strategy is governed by a trade-off between these two energetic aspects. The present study is yet another demonstration of the efficiency and the high reliability of genetic algorithms as versatile optimization tools.

Predicting equilibrium structures in freezing processes

We propose genetic algorithms as a new tool that is able to predict all possible solid candidate structures into which a simple fluid can freeze. In contrast to the conventional approach where the equilibrium structures of the solid phases are chosen from a preselected set of candidates, genetic algorithms perform a parameter-free, unbiased, and unrestricted search in the entire search space, i.e., among all possible candidate structures. We apply the algorithm to recalculate the zero-temperature phase diagrams of neutral star polymers and of charged microgels over a large density range. The power of genetic algorithms and their advantages over conventional approaches is demonstrated by the fact that new and unexpected equilibrium structures for the solid phases are discovered. Improvements of the algorithm that lead to a more rapid convergence are proposed and the role of various parameters of the method is critically assessed.

Multiple occupancy crystals formed by purely repulsive soft particles

Recently, particular interest has been placed in the study of a strikingly counter-intuitive phenomenon: the clustering of purely repulsive soft particles. This contribution serves the purpose of both reviewing our current understanding of the multiple occupancy crystals and presenting details of recently developed tailor-cut approaches to the problem. We first indicate, by use of analytically tractable examples, how such a phenomenon can arise at all. We then show that the thermodynamic formalism has to be adapted when studying such systems and present a novel computer simulation technique apt to do so. Finally, we discuss the intriguing mechanical and structural responses of such systems upon increasing the density.

The structure of the elements in the liquid state

It is by now well established that the structures of the elements in the liquid state follow characteristic trends reminiscent of the trends among the crystal structures of the elements. The crystal structures have been discussed very recently by Hafner and Heine (1983) in terms of the systematic variations of the effective interatomic pair potentials with electron density and pseudopotential. The present analysis of the liquid structures is based on the same set of interatomic potentials and on the optimised random-phase approximation (ORPA) for the calculation of the liquid structure. The authors show that the structural trends in the liquid and crystalline states have the same physical origin. The complex structures of the light polyvalent liquid metals (Ga, Si, Ge) are shown to arise from the interplay of two characteristic distances: the effective diameter of the hard repulsive core expressing the geometrical requirements of sphere packing and the Friedel wavelength of the oscillatory part of the potentials characterising the electronic effects in the metallic bonding. The return to hard-sphere-like structures for the heavy elements stems from the disappearance of the leading term of the Friedel oscillations as the core radius Rc approaches a value for which 2kFRc=1/2 pi .

Zero temperature phase diagram of the square-shoulder system

Particles that interact via a square-shoulder potential, consisting of an impenetrable hard core with an adjacent, repulsive, steplike corona, are able to self-organize in a surprisingly rich variety of rather unconventional ordered, three-dimensional structures. Using optimization strategies that are based on ideas of genetic algorithms, we encounter, as we systematically increase the pressure, the following archetypes of aggregates: low-symmetry cluster and columnar phases, followed by lamellar particle arrangements, until at high pressure values compact, high-symmetry lattices emerge. These structures are characterized in the isobaric-isothermal ensemble as configurations of minimum Gibbs free energy. Based on simple considerations, i.e., basically minimizing the number of overlapping coronas while maximizing at the same time the density, the sequence of emerging structures can easily be understood. In contrast to a previous contribution [G. J. Pauschenwein and G. Kahl, Soft Matter 4, 1396 (2008)], we present here a systematic investigation of this phenomenon, considering a short, an intermediate, and a large shoulder width.

Self-assembly of heterogeneously charged particles under confinement.

Self-assembly—the spontaneous organization of microscopic units into well-defined mesoscopic structures—is a fundamental mechanism for a broad variety of nanotechnology applications in material science. The central role played by the anisotropy resulting from asymmetric shapes of the units and/or well-defined bonding sites on the particle surface has been widely investigated, highlighting the importance of properly designing the constituent entities in order to control the resulting mesoscopic structures. Anisotropy driven self-assembly can also result from the multipolar interactions characterizing many naturally occurring systems, such as proteins and viral capsids, as well as experimentally synthesized colloidal particles. Heterogeneously charged particles represent a class of multipolar units that are characterized by a competitive interplay between anisotropic attractive and repulsive interactions, due to the repulsion/attraction between charged-like/oppositely charged regions on the particle surface. In the present work, axially symmetric quadrupolar colloids are considered in a confined planar geometry; the role of both the overall particle charge and the patch extension as well as the effect of the substrate charge are studied in thermodynamic conditions such that the formation of extended structures is favored. A general tendency to form quasi-two-dimensional aggregates where particles align their symmetry axes within the plane is observed; among these planar self-assembled scenarios, a clear distinction between the formation of microcrystalline gels—branched networks consisting of purely crystalline domains—as opposed to disordered aggregates can be observed based on the specific features of the particle–particle interaction. Additionally, the possible competition of interparticle and particle–substrate interactions affects the size and the internal structure of the aggregates and can possibly inhibit the aggregation process.