Pair interactions between complex mesoscopic particles from Widom's particle-insertion method

We demonstrate that Widom's particle insertion technique provides a convenient and efficient method to determine the effective pair interaction between complex, composite soft-matter particles in the zero-density limit. By means of three different test systems, i.e. amphiphilic dendrimers, electrostatic polymers and colloids coated with electrostatic polymers, we demonstrate the validity and the power of the presented method.Comment: 7 pages, 4 figures, to be published in Soft Matte

Are the energy and virial routes to thermodynamics equivalent for hard spheres?

The internal energy of hard spheres (HS) is the same as that of an ideal gas, so that the energy route to thermodynamics becomes useless. This problem can be avoided by taking an interaction potential that reduces to the HS one in certain limits. In this paper the square-shoulder (SS) potential characterized by a hard-core diameter $\sigma'$, a soft-core diameter $\sigma>\sigma'$ and a shoulder height $\epsilon$ is considered. The SS potential becomes the HS one if (i) $\epsilon\to 0$, or (ii) $\epsilon\to\infty$, or (iii) $\sigma'\to\sigma$ or (iv) $\sigma'\to 0$ and $\epsilon\to\infty$. The energy-route equation of state for the HS fluid is obtained in terms of the radial distribution function for the SS fluid by taking the limits (i) and (ii). This equation of state is shown to exhibit, in general, an artificial dependence on the diameter ratio $\sigma'/\sigma$. If furthermore the limit $\sigma'/\sigma\to 1$ is taken, the resulting equation of state for HS coincides with that obtained through the virial route. The necessary and sufficient condition to get thermodynamic consistency between both routes for arbitrary $\sigma'/\sigma$ is derived.Comment: 10 pages, 4 figures; v2: minor changes; to be published in the special issue of Molecular Physics dedicated to the Seventh Liblice Conference on the Statistical Mechanics of Liquids (Lednice, Czech Republic, June 11-16, 2006

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.Comment: 4 pages, 3 figure

Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental data

We present a quantitative, multi-scale coarse-grained model of DNA coated colloids. The parameters of this model are transferable and are solely based on experimental data. As a test case, we focus on nano-sized colloids carrying single-stranded DNA strands of length comparable to the colloids' size. We show that in this regime, the common theoretical approach of assuming pairwise additivity of the colloidal pair interactions leads to quantitatively and sometimes even qualitatively wrong predictions of the phase behaviour of DNA-grafted colloids. Comparing to experimental data, we find that our coarse-grained model correctly predicts the equilibrium structure and melting temperature of the formed solids. Due to limited experimental information on the persistence length of single-stranded DNA, some quantitative discrepancies are found in the prediction of spatial quantities. With the availability of better experimental data, the present approach provides a path for the rational design of DNA-functionalised building blocks that can self-assemble in complex, three-dimensional structures.Comment: 17 pages, 10 figures; to be published in Soft Matte

Formation of Polymorphic Cluster Phases for Purely Repulsive Soft Spheres

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.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

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.Comment: 4 pages, 4 figures, 1 tabl

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

The mean spherical approximation (MSA) can be solved semi-analytically for the Gaussian core model (GCM) and yields - rather surprisingly - exactly the same expressions for the energy and the virial equations. Taking advantage of this semi-analytical 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 virial or energy route. Utilizing standard thermodynamic relations this leads to two different differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integro-differential-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.Comment: 11 pages, 11 figures, submitted to J. Chem. Phy