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

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

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

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

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

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

Quantitative prediction of the phase diagram of DNA-functionalized nano-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 nano-colloids without assuming pairwise additivity of the inter-colloidal interactions. Our simulations show that for nano-colloids, 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 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.Comment: 4 pages, 2 figures; accepted for publication in Phys. Rev. Let

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-definite 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 L = 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.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor changes in structure of pape

Exotic phenomena in the phase behaviour of soft matter systems

Zsfassung in dt. SpracheFür bestimmte Systeme der weichen Materie, wie etwa Makromoleküle mit niedriger Monomerdichte in ihrem Inneren, kann man die effektiven Wechselwirkungen zwischen den Molekülen durch rein abstoßende, beschränkte Potentiale darstellen. FÜr das Phasenverhalten solcher Systeme wurden zwei unterschiedliche Szenarien vorausgesagt: einerseits ``re-entrant melting'', wo eine Flüssigkeit bei Kompression zuerst friert und schließlich wieder schmilzt, und andererseits das ``clustering'' Phänomen, wo überlappende Teilchen Klumpen bilden, die sich an den Gitterplätzen von Kristallen anordnen. Das erste Szenario wurde sowohl theoretisch als auch experimentell an zahlreichen Systemen der weichen Materie untersucht und bestätigt.Der Bildung von Cluster-Phasen ist hingegen bislang noch wenig Interesse geschenkt worden. In dieser Arbeit wird dieses Phänomen daher eingehend studiert:einerseits wird aufgezeigt, wie man geeignete Makromoleküle, die dieses Phasenverhalten zeigen, synthetisieren kann. Andererseits wird eine eingehende Analyse der Eigenschaften und Thermodynamik dieser exotischen Systeme präsentiert. Somit werden in dieser Arbeit sowohl die mikroskopischen als auch die mesoskopischen Aspekte dieses Phänomens behandelt.Effective interactions in particular soft matter systems, such as macromolecules of low inner monomer concentration, can be described by purely repulsive, bounded potentials. For such systems, two different phase behaviours have been predicted: re-entrant melting, where a fluid freezes and re-melts again upon compression, and clustering, where particles agglomerate in groups at the lattice sites of perfect crystals. The former has been studied and confirmed by both theory and experiments for a wide range of soft matter systems. Clustering, however, has not yet received due attention despite its intriguing and counterintuitive character. Our investigations range from tailoring suitable macromolecules---demonstrating that clustering can indeed be realised in certain soft matter systems---to an thorough examination of the properties and thermodynamics of such exotic systems.In our detailed study of this phenomenon we thus bridge the scales between the microscopic and the mesoscopic level.16