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

Mean Field Fluid Behavior of the Gaussian Core Model

We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger (J. Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field fluid'' over a surprisingly wide density and temperature range. In the bulk the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated HNC integral equation. The resulting pressure deviates very little from a simple, mean-field like, quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against de-mixing at high densities. Possible implications for semi-dilute polymer solutions are discussed.Comment: 13 pages, 2 columns, ReVTeX epsfig,multicol,amssym, 15 figures; submitted to Phys. Rev. E (change: important reference added

Fluid and solid phases of the Gaussian core model

We study the structural and thermodynamic properties of a model of point particles interacting by means of a Gaussian pair potential first introduced by Stillinger [Stillinger F H 1976 J. Chem. Phys. 65, 3968]. By employing integral equation theories for the fluid state and comparing with Monte Carlo simulation results, we establish the limits of applicability of various common closures and examine the dependence of the correlation functions of the liquid on the density and temperature. We employ a simple, mean-field theory for the high density domain of the liquid and demonstrate that at infinite density the mean-field theory is exact and that the system reduces to an `infinite density ideal gas', where all correlations vanish and where the hypernetted chain (HNC) closure becomes exact. By employing an Einstein model for the solid phases, we subsequently calculate quantitatively the phase diagram of the model and find that the system possesses two solid phases, face centered cubic and body centered cubic, and also displays reentrant melting into a liquid at high densities. Moreover, the system remains fluid at all densities when the temperature exceeds 1% of the strength of the interactions.Comment: 22 pages, 10 figure

Can Polymer Coils be modeled as "Soft Colloids"?

We map dilute or semi-dilute solutions of non-intersecting polymer chains onto a fluid of ``soft'' particles interacting via a concentration dependent effective pair potential, by inverting the pair distribution function of the centers of mass of the initial polymer chains. A similar inversion is used to derive an effective wall-polymer potential; these potentials are combined to successfully reproduce the calculated exact depletion interaction induced by non-intersecting polymers between two walls. The mapping opens up the possibility of large-scale simulations of polymer solutions in complex geometries.Comment: 4 pages, 3 figures ReVTeX[epsfig,multicol,amssymb] references update

Exotic fluids and crystals of soft polymeric colloids

We discuss recent developments and present new findings in the colloidal description of soft polymeric macromolecular aggregates. For various macromolecular architectures, such as linear chains, star polymers, dendrimers and polyelectrolyte stars, the effective interactions between suitably chosen coordinates are shown to be ultrasoft, i.e., they either remain finite or diverge very slowly at zero separation. As a consequence, the fluid phases have unusual characteristics, including anomalous pair correlations and mean-field like thermodynamic behaviour. The solid phases can exhibit exotic, strongly anisotropic as well as open crystal structures. For example, the diamond and the A15-phase are shown to be stable at sufficiently high concentrations. Reentrant melting and clustering transitions are additional features displayed by such systems, resulting in phase diagrams with a very rich topology. We emphasise that many of these effects are fundamentally different from the usual archetypal hard sphere paradigm. Instead, we propose that these fluids fall into the class of mean-field fluids.Comment: 22 pages, uses iopart.cls and iopart10.clo; submitted to Journal of Physics Condensed Matter, special issue in honour of professor Peter Puse

Highly site-specific H2 adsorption on vicinal Si(001) surfaces

Experimental and theoretical results for the dissociative adsorption of H_2 on vicinal Si(001) surfaces are presented. Using optical second-harmonic generation, sticking probabilities at the step sites are found to exceed those on the terraces by up to six orders of magnitude. Density functional theory calculations indicate the presence of direct adsorption pathways for monohydride formation but with a dramatically lowered barrier for step adsorption due to an efficient rehybridization of dangling orbitals.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Lett. (1998). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Exact Criterion for Determining Clustering vs. Reentrant Melting Behavior for Bounded Interaction Potentials

We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials which do not diverge at the origin, are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity. By employing a mean field-density functional theory which is shown to become exact at high temperatures and/or densities, we establish a criterion which determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature.Comment: 5 pages, 3 figures, submitted to PRL on March 29, 2000 New version: 10 pages, 9 figures, forwarded to PRE on October 16, 200

Observation and Characterization of a Cosmic Muon Neutrino Flux from the Northern Hemisphere using six years of IceCube data

The IceCube Collaboration has previously discovered a high-energy astrophysical neutrino flux using neutrino events with interaction vertices contained within the instrumented volume of the IceCube detector. We present a complementary measurement using charged current muon neutrino events where the interaction vertex can be outside this volume. As a consequence of the large muon range the effective area is significantly larger but the field of view is restricted to the Northern Hemisphere. IceCube data from 2009 through 2015 have been analyzed using a likelihood approach based on the reconstructed muon energy and zenith angle. At the highest neutrino energies between 191 TeV and 8.3 PeV a significant astrophysical contribution is observed, excluding a purely atmospheric origin of these events at $5.6\,\sigma$ significance. The data are well described by an isotropic, unbroken power law flux with a normalization at 100 TeV neutrino energy of $\left(0.90^{+0.30}_{-0.27}\right)\times10^{-18}\,\mathrm{GeV^{-1}\,cm^{-2}\,s^{-1}\,sr^{-1}}$ and a hard spectral index of $\gamma=2.13\pm0.13$. The observed spectrum is harder in comparison to previous IceCube analyses with lower energy thresholds which may indicate a break in the astrophysical neutrino spectrum of unknown origin. The highest energy event observed has a reconstructed muon energy of $(4.5\pm1.2)\,\mathrm{PeV}$ which implies a probability of less than 0.005% for this event to be of atmospheric origin. Analyzing the arrival directions of all events with reconstructed muon energies above 200 TeV no correlation with known $\gamma$-ray sources was found. Using the high statistics of atmospheric neutrinos we report the currently best constraints on a prompt atmospheric muon neutrino flux originating from charmed meson decays which is below $1.06$ in units of the flux normalization of the model in Enberg et al. (2008).Comment: 20 pages, 21 figure