Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces

Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically stable phases of polyhedrally-shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, {\beta}-tin, and high- pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces.Comment: Article + supplementary information. 23 pages, 10 figures, 2 table

Coarsening and Pinning in the Self-consistent Solution of Polymer Blends Phase-Separation Kinetics

We study analytically a continuum model for phase-separation in binary polymer blends based on the Flory-Huggins-De Gennes free energy, by means of the self-consistent large-$n$ limit approach. The model is solved for values of the parameters corresponding to the weak and strong segregation limits. For deep quenches we identify a complex structure of intermediate regimes and crossovers characterized by the existence of a time domain such that phase separation is pinned, followed by a preasymptotic regime which in the scalar case corresponds to surface diffusion. The duration of the pinning is analytically computed and diverges in the strong segregation limit. Eventually a late stage dynamics sets in, described by scaling laws and exponents analogous to those of the corresponding small molecule systems.Comment: 16 pages, 5 figures. Submitted to Phys. Rev.

Heterogeneities in systems with quenched disorder

We study the strong role played by structural (quenched) heterogeneities on static and dynamic properties of the Frustrated Ising Lattice Gas in two dimensions, already in the liquid phase. Differently from the dynamical heterogeneities observed in other glass models in this case they may have infinite lifetime and be spatially pinned by the quenched disorder. We consider a measure of local frustration, show how it induces the appearance of spatial heterogeneities and how this reflects in the observed behavior of equilibrium density distributions and dynamic correlation functions.Comment: 8 page

Effect of Ordering on Spinodal Decomposition of Liquid-Crystal/Polymer Mixtures

Partially phase-separated liquid-crystal/polymer dispersions display highly fibrillar domain morphologies that are dramatically different from the typical structures found in isotropic mixtures. To explain this, we numerically explore the coupling between phase ordering and phase separation kinetics in model two-dimensional fluid mixtures phase separating into a nematic phase, rich in liquid crystal, coexisting with an isotropic phase, rich in polymer. We find that phase ordering can lead to fibrillar networks of the minority polymer-rich phase

Device-detected atrial fibrillation and risk for stroke: an analysis of >10 000 patients from the SOS AF project (Stroke preventiOn Strategies based on Atrial Fibrillation information from implanted devices)

Objective: The aim of this study was to assess the association between maximum daily atrial fibrillation (AF) burden and risk of ischaemic stroke. Background: Cardiac implanted electronic devices (CIEDs) enhance detection of AF, providing a comprehensive measure of AF burden. Design, setting, and patients A pooled analysis of individual patient data from five prospective studies was performed. Patients without permanent AF, previously implanted with CIEDs, were included if they had at least 3 months of follow-up. A total of 10 016 patients (median age 70 years) met these criteria. The risk of ischaemic stroke associated with pre-specified cut-off points of AF burden (5 min, 1, 6, 12, and 23 h, respectively) was assessed. Results: During a median follow-up of 24 months, 43% of 10 016 patients experienced at least 1 day with at least 5 min of AF burden and for them the median time to the maximum AF burden was 6 months (inter-quartile range: 1.3–14). A Cox regression analysis adjusted for the CHADS2 score and anticoagulants at baseline demonstrated that AF burden was an independent predictor of ischaemic stroke. Among the thresholds of AF burden that we evaluated, 1 h was associated with the highest hazard ratio (HR) for ischaemic stroke, i.e. 2.11 (95% CI: 1.22–3.64, P = 0.008). Conclusions: Device-detected AF burden is associated with an increased risk of ischaemic stroke in a relatively unselected population of CIEDs patients. This finding may add to the basis for timely and clinically appropriate decision-making on anticoagulation treatment

A cluster theory for a Janus fluid

Recent Monte Carlo simulations on the Kern and Frenkel model of a Janus fluid have revealed that in the vapour phase there is the formation of preferred clusters made up of a well-defined number of particles: the micelles and the vesicles. A cluster theory is developed to approximate the exact clustering properties stemming from the simulations. It is shown that the theory is able to reproduce the micellisation phenomenon.Comment: 27 pages, 8 figures, 6 table

Multiple-Point and Multiple-Time Correlations Functions in a Hard-Sphere Fluid

A recent mode coupling theory of higher-order correlation functions is tested on a simple hard-sphere fluid system at intermediate densities. Multi-point and multi-time correlation functions of the densities of conserved variables are calculated in the hydrodynamic limit and compared to results obtained from event-based molecular dynamics simulations. It is demonstrated that the mode coupling theory results are in excellent agreement with the simulation results provided that dissipative couplings are included in the vertices appearing in the theory. In contrast, simplified mode coupling theories in which the densities obey Gaussian statistics neglect important contributions to both the multi-point and multi-time correlation functions on all time scales.Comment: Second one in a sequence of two (in the first, the formalism was developed). 12 pages REVTeX. 5 figures (eps). Submitted to Phys.Rev.

Percolation transition and the onset of non exponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in 2 and 3 dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the ``large scale'' effects of frustration, present below the percolation threshold. Moreover these results are consistent with the picture suggested by Campbell et al. in space of configurations.Comment: 8 pages, 11 figures, revised versio

Phase-separation of binary fluids in shear flow: a numerical study

The phase-separation kinetics of binary fluids in shear flow is studied numerically in the framework of the continuum convection-diffusion equation based on a Ginzburg-Landau free energy. Simulations are carried out for different temperatures both in d=2 and in d=3. Our results confirm the qualitative picture put forward by the large-N limit equations studied in \cite{noi}. In particular, the structure factor is characterized by the presence of four peaks whose relative oscillations give rise to a periodic modulation of the behavior of the rheological indicators and of the average domains sizes. This peculiar pattern of the structure factor corresponds to the presence of domains with two characteristic thicknesses whose relative abundance changes with time.Comment: 6 pages, 11 figures in .gif forma

Non exponential relaxation in fully frustrated models

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature T_p corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q=1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q=1/2-state Potts model.Comment: 7 pages, RevTeX, 11 figs, to appear on Physical Review