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Hydrodynamic interactions as modeled by Multi-Particle Collision Dynamics can dramatically influence the dynamics of fully flexible, ring-shaped polymers in ways not known for any other polymer architecture or topology. We show that steady shear leads to an inflation scenario exclusive to ring polymers, which depends not only on Weissenberg number but also on contour length of the ring. By analyzing velocity fields of the solvent around the polymer, we show the existence of a hydrodynamic pocket which allows the polymer to self-stabilize at a certain alignment angle to the flow axis. This self-induced stabilization is accompanied by transitioning of the ring to a non-Brownian particle and a cessation of tumbling. The ring swells significantly in the vorticity direction, and the horseshoe regions on the stretched and swollen ring are effectively locked in place relative to the ring's center-of-mass. The observed effect is exclusive to ring polymers and stems from an interplay between hydrodynamic interactions and topology. Furthermore, knots tied onto such rings can serve as additional "stabilization anchors". Under strong shear, the knotted section is pulled tight and remains well-localized while tank-treading from one horseshoe region to the opposite one in sudden bursts. We find knotted polymers of high contour length behave very similarly to unknotted rings of the same contour length, but small knotted rings feature a host of different configurations. We propose a filtering technique for rings and chains based on our observations and suggest that strong shear could be used to tighten knots on rings., Comment: 12 pages, 8 figures, 2 Tables

By employing monomer-resolved computer simulations and analytical considerations based on polymer scaling theory, we analyze the conformations and interactions of multiarm star polymers strongly adsorbed on a smooth, two-dimensional plane. We find a stronger stretching of the arms as well as a stronger repulsive, effective interaction than in the three dimensional case. In particular, the star size scales with the number of arms $f$ as $\sim f^{1/4}$ and the effective interaction as $\sim f^{2}$, as opposed to $\sim f^{1/5}$ and $\sim f^{3/2}$, respectively, in three dimensions. Our results demonstrate the dramatic effect that geometric confinement can have on the effective interactions and the subsequent correlations of soft colloids in general, for which the conformation can be altered as a result of geometrical constraints imposed on them., Comment: 17 pages, LaTeX, 5 figures, to appear in Macromolecules

We analyze the phonon spectra of periodic structures formed by two-dimensional mixtures of dipolar colloidal particles. These mixtures display an enormous variety of complex ordered configurations [J. Fornleitner {\it et al.}, Soft Matter {\bf 4}, 480 (2008)], allowing for the systematic investigation of the ensuing phonon spectra and the control of phononic gaps. We show how the shape of the phonon bands and the number and width of the phonon gaps can be controlled by changing the susceptibility ratio, the concentration and the mass ratio between the two components., Comment: 4 pages 3 figures

Using extensive Brownian dynamics computer simulations, the long-time self-diffusion coefficient is calculated for Gaussian-core particles as a function of the number density. Both spherical and rod-like particles interacting via Gaussian segments ar$ For increasing concentration we find that the translational self-diffusion behaves non-monotonically reflecting the structural reentrance effect in the equilibrium phase diagram. Both in the limits of zero and infinite concentration, it approaches its short-time value. The microscopic Medina-Noyola theory qualitatively accounts for the translational long-time diffusion. The long-time orientational diffusion coefficient for Gaussian rods, on the other hand, remains very close to its short-time counterpart for any density. Some implications of the weak translation-rotation coupling for ultrasoft rods are discussed., Comment: 5 pages, 5 figures

We derive effective interaction potentials between hard, spherical colloidal particles and star-branched polyelectrolytes of various functionalities and smaller size than the colloids. The effective interactions are based on a Derjaguin-like approximation, which is based on previously derived potentials acting between polyelectrolyte stars and planar walls. On the basis of these interactions we subsequently calculate the demixing binodals of the binary colloid--polyelectrolyte star mixture, employing standard tools from liquid-state theory. We find that the mixture is indeed unstable at moderately high overall concentrations. The system becomes more unstable with respect to demixing as the star functionality and the size ratio grow., Comment: 24 pages, 9 figures, submitted to Journal of Physics: Condensed Matter

The effective pair potentials between different kinds of dendrimers in solution can be well approximated by appropriate Gaussian functions. We find that in binary dendrimer mixtures the range and strength of the effective interactions depend strongly upon the specific dendrimer architecture. We consider two different types of dendrimer mixtures, employing the Gaussian effective pair potentials, to determine the bulk fluid structure and phase behavior. Using a simple mean field density functional theory (DFT) we find good agreement between theory and simulation results for the bulk fluid structure. Depending on the mixture, we find bulk fluid-fluid phase separation (macro-phase separation) or micro-phase separation, i.e., a transition to a state characterized by undamped periodic concentration fluctuations. We also determine the inhomogeneous fluid structure for confinement in spherical cavities. Again, we find good agreement between the DFT and simulation results. For the dendrimer mixture exhibiting micro-phase separation, we observe rather striking pattern formation under confinement., Comment: 8 pages, 10 figures

We examine the vitrification and melting of asymmetric star polymers mixtures by combining rheological measurements with mode coupling theory. We identify two types of glassy states, a {\it single} glass, in which the small component is fluid in the glassy matrix of the big one and a {\it double} glass, in which both components are vitrified. Addition of small star polymers leads to melting of {\it both} glasses and the melting curve has a non-monotonic dependence on the star-star size ratio. The phenomenon opens new ways for externally steering the rheological behavior of soft matter systems., Comment: 4 pages, 4 figures, accepted in Phys. Rev. Lett

Large-scale Monte Carlo simulations of a phase-separating colloid-polymer mixture are performed and compared to recent experiments. The approach is based on effective interaction potentials in which the central monomers of self-avoiding polymer chains are used as effective coordinates. By incorporating polymer nonideality together with soft colloid-polymer repulsion, the predicted binodal is in excellent agreement with recent experiments. In addition, the interfacial tension as well as the capillary length are in quantitative agreement with experimental results obtained at a number of points in the phase-coexistence region, without the use of any fit parameters, Comment: 4 pages, 4 figures

We employ monomer-resolved computer simulations of model dendrimer molecules, to examine the significance of many-body effects in concentrated solutions of the same. In particular, we measure the radial distribution functions and the scattering functions between the centres of mass of the dissolved dendrimers at various concentrations, reaching values that slightly exceed the overlap density of the macromolecules. We analyse the role played by many-body effective interactions by comparing the structural data to those obtained by applying exclusively the previously obtained two-body effective interactions between the dendrimers [G{\"o}tze I O, Harreis H M and Likos C N 2004 {\it J. Chem. Phys.} {\bf 120} 7761]. We find that the effects of the many-body forces are small in general and they become weaker as the dendrimer flexibility increases. Moreover, we test the validity of the oft-used factorisation approximation to the total scattering intensity into a product of the form- and the scattering factors, finding a breakdown of this factorisation at high concentrations., Comment: Submitted to Journal of Physics: Condensed Matter

By employing computer simulations for a model binary mixture, we show that a reentrant glass transition upon adding a second component only occurs if the ratio $\alpha$ of the short-time mobilities between the glass-forming component and the additive is sufficiently small. For $\alpha \approx 1$, there is no reentrant glass, even if the size asymmetry between the two components is large, in accordance with two-component mode coupling theory. For $\alpha \ll 1$, on the other hand, the reentrant glass is observed and reproduced only by an effective one-component mode coupling theory., Comment: 4 pages, 3 figures

The concept of effective depletion forces between two fixed big colloidal particles in a bath of small particles is generalized to a non-equilibrium situation where the bath of small Brownian particles is flowing around the big particles with a prescribed velocity. In striking contrast to the equilibrium case, the non-equilibrium forces violate Newton's third law, are non-conservative and strongly anisotropic, featuring both strong attractive and repulsive domains., Comment: 4 pages, 3 figures

The dynamics of star polymers has been investigated via extensive Molecular- and Brownian Dynamics simulations for a large range of functionality $f$ and packing fraction $\eta$. The calculated isodiffusivity curves display both minima and maxima as a function of $\eta$ and minima as a function of $f$. Simulation results are compared with theoretical predictions based on different approximations for the structure factor. In particular, the ideal glass transition line predicted by mode-coupling theory is shown to exactly track the isodiffusivity curves, offering a theoretical understanding for the observation of disordered arrested states in star polymer solutions., Comment: 4 pages, Revtex, to be published in PRL

We examine the out-of-equilibrium dynamical evolution of density profiles of ultrasoft particles under time-varying external confining potentials in three spatial dimensions. The theoretical formalism employed is the dynamical density functional theory (DDFT) of Marini Bettolo Marconi and Tarazona [J. Chem. Phys. {\bf 110}, 8032 (1999)], supplied by an equilibrium excess free energy functional that is essentially exact. We complement our theoretical analysis by carrying out extensive Brownian Dynamics simulations. We find excellent agreement between theory and simulations for the whole time evolution of density profiles, demonstrating thereby the validity of the DDFT when an accurate equilibrium free energy functional is employed., Comment: 8 pagers, 4 figures

The pair interaction between two stiff parallel linear DNA molecules depends not only on the distance between their axes but on their azimuthal orientation. The positional and orientational order in columnar B-DNA assemblies in solution is investigated, based on the DNA-DNA electrostatic pair potential that takes into account DNA helical symmetry and the amount and distribution of adsorbed counterions. A phase diagram obtained by lattice sum calculations predicts a variety of positionally and azimuthally ordered phases and bundling transitions strongly depending on the counterion adsorption patterns., Comment: 4 pages, 3 figures, submitted to PRL

We examine sedimentation density profiles of star polymer solutions as an example of colloidal systems in sedimentation equilibrium which exhibit reentrant melting in their bulk phase diagram. Phase transitions between a fluid and a fluid with an intercalated solid are observed below a critical gravitational strength $\alpha^{*}$. Characteristics of the two fluid-solid interfaces in the density profiles occurring in Monte Carlo simulations for $\alpha < \alpha^{*}$ are in agreement with scaling laws put forth in the framework of a phenomenological theory. Furthermore we detect density oscillations at the fluid-gas interface at high altitudes for high gravitational fields, which are verified with density functional theory and should be observable in surface scattering experiments., Comment: 10 pages, 6 figures

Using monomer-resolved Molecular Dynamics simulations and theoretical arguments based on the radial dependence of the osmotic pressure in the interior of a star, we systematically investigate the effective interactions between hard, colloidal particles and star polymers in a good solvent. The relevant parameters are the size ratio q between the stars and the colloids, as well as the number of polymeric arms f (functionality) attached to the common center of the star. By covering a wide range of q's ranging from zero (star against a flat wall) up to about 0.75, we establish analytical forms for the star-colloid interaction which are in excellent agreement with simulation results. A modified expression for the star-star interaction for low functionalities, f < 10 is also introduced., Comment: 37 pages, 14 figures, preprint-version

Using small-angle neutron scattering and liquid integral equation theory, we relate the structure factor of flexible dendrimers of 4th generation to their average shape. The shape is measured as a radial density profile of monomers belonging to a single dendrimer. From that, we derive an effective interaction of Gaussian form between pairs of dendrimers and compute the structure factor using the hypernetted chain approximation. Excellent agreement with the corresponding experimental results is obtained, without the use of adjustable parameters. The present analysis thus strongly supports the previous finding that flexible dendrimers of low generation present fluctuating structures akin to star polymers., Comment: 20 pages, 4 figures, submitted to Macromolecules on July 24, 2000

We examine the demixing transition in star polymer-colloid mixtures for star arm numbers f=2,6,16,32 and different star-colloid size ratios. Theoretically, we solve the thermodynamically self-consistent Rogers-Young integral equations for binary mixtures using three effective pair potentials obtained from direct molecular computer simulations. The numerical results show a spinodal instability. The demixing binodals are approximately calculated, and found to be consistent with experimental observations., Comment: 4 pages, 4 figures, submitted to PRL

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 figures

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, 2000

The phase diagram of star polymer solutions in a good solvent is obtained over a wide range of densities and arm numbers by Monte Carlo simulations. The effective interaction between the stars is modeled by an ultrasoft pair potential which is logarithmic in the core-core distance. Among the stable phases are a fluid as well as body-centered cubic, face-centered cubic, body-centered orthogonal, and diamond crystals. In a limited range of arm numbers, reentrant melting and reentrant freezing transitions occur for increasing density., Comment: final version as published

The core-core structure factor of dense star polymer solutions in a good solvent is shown theoretically to exhibit an unusual behaviour above the overlap concentration. Unlike usual liquids, these solutions display a structure factor whose first peak decreases by increasing density while the second peak grows. The scenario repeats itself with the subsequent peaks as the density is further enhanced. For low enough arm numbers $f$ ($f \leq 32$), various different considerations lead to the conclusion that the system remains fluid at all concentrations., Comment: ReVTeX, 13 pages, 14 figures in eps-format

We consider a system of spherical particles interacting by means of a pair potential equal to a finite constant for interparticle distances smaller than the sphere diameter and zero outside. The model may be a prototype for the interaction between micelles in a solvent [C. Marquest and T. A. Witten, J. Phys. France 50, 1267 (1989)]. The phase diagram of these penetrable spheres is investigated using a combination of cell- and density functional theory for the solid phase together with simulations for the fluid phase. The system displays unusual phase behavior due to the fact that, in the solid, the optimal configuration is achieved when certain fractions of lattice sites are occupied by more than one particle, a property that we call `clustering'. We find that freezing from the fluid is followed, by increasing density, by a cascade of second-order, clustering transitions in the crystal., Comment: 16 pages and 10 figures in ps-format, fig. 5 corrected, final version as published

We apply density functional theory to study the freezing of superfluid {$^{4}\rm{He}$}, charged bosons and charged fermions at zero temperature. We employ accurate Quantum Monte Carlo data for the linear response function in the uniform phase of these systems, a quantity that has different behavior for large values of the wavevector than previously assumed. We find that, as a result of this {\it{exact}} behavior, different approximations in the density functional theory of freezing that involve linear response, all fail to correctly describe the crystallization in {\it{three dimensions}}, while yielding satisfactory predictions in {\it{two dimensions}}. This demonstrates the shortcomings of the currently popular density functional approximate theories to describe $3d$-freezing in the quantum regime. We also investigate the consequences of the exact asymptotic behavior of response functions on the form of effective interactions and polarization potentials in the electron gas, at small distances., Comment: 15 pages, REVTeX, 10 figures

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of different sublattices of the given lattice and it generates as many flow equations as coupling constants without arbitrary truncations on the renormalized Hamiltonian. We obtain good results for the test case of Ising systems with an additional second-neighbor coupling in two and three dimensions. An application of the method is also done to a morphological model of interacting surfaces introduced recenlty by Likos, Mecke and Wagner [J. Chem. Phys. {\bf{102}}, 9350 (1995)]. PACS: 64.60.Ak, 64.60.Fr, 05.70.Jk, Comment: Tex file and three macros appended at the end. Five figures available upon request to: christos@iris.ts.infn.it, Fax: [+]39-40-224-601