arXiv subjects
Publications and source records attributed to Thomas Vogel.
We prove a theorem formulated by V. I. Arnold concerning a relation between the asymptotic linking number and the Hopf invariant of divergence-free vector fields. Using a modified definition for the system of short paths, we prove their existence in the general case.
In their tubelike phase, nanowire-adsorbed polymers exhibit strong structural similarities to morphologies known from single-walled carbon (hexagonal) and boron (triangular) nanotubes. Since boron/boron nitride tubes require some disorder for stability the triangular polymer tubes provide a closer analog to the carbon tubes. By means of computer simulations of both two and three dimensional versions of a coarse-grained bead-spring model for the polymers, we investigate their structural properties and make a detailed comparison with structures of carbon nanotubes.
In a recent computational study, we found highly structured ground states for coarse-grained polymers adsorbed to ultrathin nanowires in a certain model parameter region. Those tubelike configurations show, even at a first glance, exciting morphological similarities to known atomistic nanotubes such as single-walled carbon nanotubes. In order to explain those similarities in a systematic way, we performed additional detailed and extensive simulations of coarse-grained polymer models with various parameter settings. We show this here and explain why standard geometrical models for atomistic nanotubes are not suited to interpret the results of those studies. In fact, the general structural behavior of polymer nanotubes, as well as specific previous observations, can only be explained by applying recently developed polyhedral tube models.
Low-energy structures of a hybrid system consisting of a polymer and an attractive nanowire substrate as well as the thermodynamics of the adsorption transition are studied by means of Monte Carlo computer simulations. Depending on structural and energetic properties of the substrate, we find different adsorbed polymer conformations, amongst which are spherical droplets attached to the wire and monolayer tubes surrounding it. We identify adsorption temperatures and the type of the transition between adsorbed and desorbed structures depending on the substrate attraction strength.
We study ground states of a hybrid system consisting of a polymer and an attractive nanowire by means of computer simulations. Depending on structural and energetic properties of the substrate, we find different adsorbed polymer conformations, amongst which are spherical droplets attached to the wire and monolayer tubes surrounding it. We construct the complete conformational phase diagram and analyze in more detail particularly interesting polymer-tube conformations.
Investigating thermodynamic properties of liquid-solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of Lennard-Jones clusters. This allows us to set up a structural classification scheme for finite-length flexible polymers and their freezing mechanism in analogy to atomic cluster formation. Crystals of polymers with "magic length" turn out to be perfectly icosahedral.
In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of such tubelike objects.
We study the conformational behavior of a polymer adsorbed at an attractive nanostring and construct the complete structural phase diagram in dependence of the binding strength and effective thickness of the string. For this purpose, Monte Carlo optimization techniques are employed to identify lowest-energy structures for a coarse-grained hybrid polymer-wire model. Among the representative conformations in the different phases are, for example, compact droplets attached to the string and also nanotube-like monolayer films wrapping the string in a very ordered way. We here systematically analyze low-energy shapes and structural order parameters to elucidate the transitions between the structural phases.
In this work we present the general phase behavior of short tubelike flexible polymers. The geometric thickness constraint is implemented through the concept of the global radius of curvature. We use sophisticated Monte Carlo sampling methods to simulate small bead-stick polymer models with Lennard-Jones interaction among non-bonded monomers. We analyze energetic fluctuations and structural quantities to classify conformational pseudophases. We find that the tube thickness influences the thermodynamic behavior of simple tubelike polymers significantly, i.e., for given temperature, the formation of secondary structures strongly depends on the tube thickness.
We analyze the freezing and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well-separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.
By means of sophisticated Monte Carlo methods, we investigate the conformational phase diagram of a simple model for flexible polymers with explicit thickness. The thickness constraint, which is introduced geometrically via the global radius of curvature of a polymer conformation, accounts for the excluded volume of the polymer and induces cooperative effects supporting the formation of secondary structures. In our detailed analysis of the temperature and thickness dependence of the conformational behavior for classes of short tubelike polymers, we find that known secondary-structure segments like helices and turns, but also ringlike conformations and stiff rods are dominant intrinsic topologies governing the phase behavior of such cooperative tubelike objects. This shows that the thickness constraint is indeed a fundamental physical parameter that allows for a classification of generic polymer structures.
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well-separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.