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.     

Formation of polymorphic cluster phases for a class of models of 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.     

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.     

The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

Heat-treated biodegradable films and foils of collagen hydrolysate crosslinked with dialdehyde starch

Gels of collagen hydrolysate (H) crosslinked with dialdehyde starch (DAS) are marked by a strong tendency to aging, which means a certain problem during their processing into biodegradable packaging materials. Applying casting technology and drying these materials by heating air-dry films and foils for a limited time (1–4 h) at 105 °C may eliminate the aging problem. Solubility of heat-treated films in an aqueous environment remains preserved, but depending on how long this temperature acts and on the DAS content in the film, time of film disintegration prolongs from 1–1.5 h to 1300 h (≈54 days). It is probably caused by the functional groups initially blocked by sorbed water, which get released to produce hydrogen inter-chain crosslinks. The decrease in glass transition temperature (T _g) of such films varies with content of water sorbed in films in an interval of 90.2–189 °C.     

Design rule for colloidal crystals of DNA-functionalized particles

We report a Monte Carlo simulation study of the phase behavior of colloids coated with long, flexible DNA chains. We find that an important change occurs in the phase diagram when the number of DNAs per colloid is decreased below a critical value. In this case, the triple point disappears and the condensed phase that coexists with the vapor is always liquid. Our simulations thus explain why, in the dilute solutions typically used in experiments, colloids coated with a small number of DNA strands cannot crystallize. We understand this behavior in terms of the discrete nature of DNA binding.     

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.     

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.     

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.     

Clustering in the absence of attractions: density functional theory and computer simulations

We numerically investigate the formation of stable clusters of overlapping particles in certain systems interacting via purely repulsive, bounded pair potentials. In close vicinity of a first-order phase transition between a disordered and an ordered structure, clusters are encountered already in the fluid phase which then freeze into crystals with multiply occupied lattice sites. These hyper-crystals are characterized by a number of remarkable features that are in clear contradiction to our experience with harshly repulsive systems: upon compression, the lattice constant remains invariant, leading to a concomitant linear growth in the cluster population with density; further, the freezing and melting lines are to high accuracy linear in the density-temperature plane, and the conventional indicator that announces freezing, that is, the Hansen-Verlet value of the first peak of the structure factor, attains for these soft systems much higher values than for their hard-matter counterparts. Our investigations are based on the generalized exponential model of index 4 (i.e., Phi(r) approximately exp[-(r/sigma)4]). The properties of the phases involved are calculated via liquid state theory and classical density functional theory. Monte Carlo simulations for selected states confirm the theoretical results for the structural and thermodynamic properties of the system. These numerical data, in turn, fully corroborate an approximate theoretical framework that was recently put forward to explain the clustering phenomenon for systems of this kind (Likos, C. N.; Mladek, B. M.; Gottwald, D.; Kahl, G. J. Chem. Phys. 2007, 126, 224502).