Bianca M. Mladek

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.

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.

Quantitative Prediction of the Phase Diagram of DNA-Functionalized Nanosized Colloids

We present a coarse-grained model of DNA-functionalized colloids that is computationally tractable. Importantly, the model parameters are solely based on experimental data. Using this highly simplified model, we can predict the phase behavior of DNA-functionalized nanocolloids without assuming pairwise additivity of the intercolloidal interactions. Our simulations show that, for nanocolloids, the assumption of pairwise additivity leads to substantial errors in the estimate of the free energy of the crystal phase. We compare our results with available experimental data and find that the simulations predict the correct structure of the solid phase and yield a very good estimate of the melting temperature. Current experimental estimates for the contour length and persistence length of single-stranded (ss) DNA sequences are subject to relatively large uncertainties. Using the best available estimates, we obtain predictions for the crystal lattice constants that are off by a few percent: this indicates that more accurate experimental data on ssDNA are needed to exploit the full power of our coarse-grained approach.

Phase coexistence of cluster crystals: Beyond the gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals, it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Reentrant and Isostructural Transitions in a Cluster-Crystal Former

We study the low-temperature behavior of a simple cluster-crystal forming system through simulation. We find the phase diagram to be hybrid between the Gaussian core model and the penetrable sphere model. The system additionally exhibits S-shaped doubly reentrant phase sequences as well as critical isostructural transitions between crystals of different average lattice site occupancy. Because of the possible annihilation of lattice sites and accompanying clustering, the system moreover shows an unusual softening upon compression.

Microscopically Resolved Simulations Prove the Existence of Soft Cluster Crystals

We perform extensive monomer-resolved computer simulations of suitably designed amphiphilic dendritic macromolecules over a broad range of densities, proving the existence and stability of cluster crystals formed in these systems, as predicted previously on the basis of effective pair potentials [B. M. Mladek et al., Phys. Rev. Lett. 96, 045701 (2006)]. Key properties of these crystals, such as the adjustment of their site occupancy with density and the possibility to heal defects by dendrimer migration, are confirmed on the monomer-resolved picture. At the same time, important differences from the predictions of the pair potential picture, stemming from steric crowding, arise as well, and they place an upper limit in the density for which such crystals can exist.

Monomer-Resolved Simulations of Cluster-Forming Dendrimers

We present results of monomer-resolved Monte Carlo simulations for a system of amphiphilic dendrimers of the second generation. Our investigations validate a coarse-grained level description based on the zero-density limit effective pair-interactions for low and intermediate densities, which predicted the formation of stable, finite aggregates in the fluid phase. Indeed, we find that these systems form a homogeneous fluid for low densities, which, on increasing the density, spontaneously transforms into a fluid of clusters of dendrimers. Although these clusters are roughly spherical in nature for intermediate densities, more complex structures are also detected for the highest densities considered.

Thermodynamically self-consistent liquid state theories for systems with bounded potentials

The mean spherical approximation (MSA) can be solved semianalytically for the Gaussian core model (GCM) and yields exactly the same expressions for the energy and the virial equations. Taking advantage of this semianalytical framework, we apply the concept of the self-consistent Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K is introduced in the MSA closure relation which is determined to enforce thermodynamic consistency between the compressibility route and either the energy or virial route. Utilizing standard thermodynamic relations this leads to two differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integrodifferential-equation-based formulation of the SCOZA which, although requiring a fully numerical solution, has the advantage that it is no longer restricted to the availability of an analytic solution for a particular system. Rather it can be used for an arbitrary potential and even in combination with other closure relations, such as a modification of the hypernetted chain approximation.

Erratum: Formation of Polymorphic Cluster Phases for a Class of Models of Purely Repulsive Soft Spheres [Phys. Rev. Lett.96, 045701 (2006)]

We present results from density functional theory and computer simulations that unambiguously predict the occurrence of first-order freezing transitions for a large class of ultrasoft model systems into cluster crystals. The clusters consist of fully overlapping particles and arise without the existence of attractive forces. The number of particles participating in a cluster scales linearly with density, therefore the crystals feature density-independent lattice constants. Clustering is accompanied by polymorphic bcc-fcc transitions, with fcc being the stable phase at high densities.