Browse
Submit Data
Databases
API
Help

Dataset Information

39 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Size distribution of ring polymers.

ABSTRACT: We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4 - d are equivalent, thus the celebrated Airy distribution describing the areal distribution of the d = 1 Brownian excursion describes also a polymer in three dimensions. For a self-avoiding polymer in dimension d we find numerically that the fluctuations of the scaled averaged distance are nearly identical in dimension d = 2, 3 and are well described to a first approximation by the non-interacting excursion model in dimension 5.

SUBMITTER: Medalion S

PROVIDER: S-EPMC4908590 | biostudies-literature | 2016 Jun

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Size distribution of ring polymers.

Medalion Shlomi S Aghion Erez E Meirovitch Hagai H Barkai Eli E Kessler David A DA

Scientific reports 20160615

We present an exact solution for the distribution of sample averaged monomer to monomer distance of ring polymers. For non-interacting and local-interaction models these distributions correspond to the distribution of the area under the reflected Bessel bridge and the Bessel excursion respectively, and are shown to be identical in dimension d ≥ 2, albeit with pronounced finite size effects at the critical dimension, d = 2. A symmetry of the problem reveals that dimension d and 4 - d are equivale ...[more]

PMID: 27302596

Similar Datasets

Architecture-Induced Size Asymmetry and Effective Interactions of Ring Polymers: Simulation and Theory.

Project description:We investigate, by means of Monte Carlo simulations, the role of ring architecture and topology on the relative sizes of two interacting polymers as a function of the distance between their centers-of-mass. As a general rule, polymers swell as they approach each other, irrespectively of their topologies. For each mutual separation, two identical linear polymers adopt the same average size. However, unknotted rings at close separations adopt different sizes, with the small one being "nested" within the large one over long time intervals, exchanging their roles in the course of the simulation. For two rings of different architectures and identical polymerization degree, the knotted one is always smaller, penetrating the unknotted one. On the basis of these observations, we propose a phenomenological theory for the effective interactions between rings, modeling them as unequal-sized penetrable spheres. This simple approximation provides a good description of the simulation results. In particular, it rationalizes the non-Gaussian shape and the short-distance plateau observed in the effective potential between unknotted ring polymers and pairs of unequal-sized unknotted/knotted ones. Our results demonstrate the crucial role of the architecture on both the effective interactions and the molecular size for strongly interpenetrating polymers.

| S-EPMC3859368 | biostudies-other

Large ring polymers align FtsZ polymers for normal septum formation.

Project description:Cytokinesis in bacteria is initiated by polymerization of the tubulin homologue FtsZ into a circular structure at midcell, the Z-ring. This structure functions as a scaffold for all other cell division proteins. Several proteins support assembly of the Z-ring, and one such protein, SepF, is required for normal cell division in Gram-positive bacteria and cyanobacteria. Mutation of sepF results in deformed division septa. It is unclear how SepF contributes to the synthesis of normal septa. We have studied SepF by electron microscopy (EM) and found that the protein assembles into very large (?50 nm diameter) rings. These rings were able to bundle FtsZ protofilaments into strikingly long and regular tubular structures reminiscent of eukaryotic microtubules. SepF mutants that disturb interaction with FtsZ or that impair ring formation are no longer able to align FtsZ filaments in vitro, and fail to support normal cell division in vivo. We propose that SepF rings are required for the regular arrangement of FtsZ filaments. Absence of this ordered state could explain the grossly distorted septal morphologies seen in sepF mutants.

| S-EPMC3034016 | biostudies-literature

Random Knotting in Fractal Ring Polymers.

Project description:Many ring polymer systems of physical and biological interest exhibit both pronounced topological effects and nontrivial self-similarity, but the relationship between these two phenomena has not yet been clearly established. Here, we use theory and simulation to formulate such a connection by studying a fundamental topological property-the random knotting probability-for ring polymers with varying fractal dimension, d f . Using straightforward scaling arguments, we generalize a classic mathematical result, showing that the probability of a trivial knot decays exponentially with chain size, N, for all fractal dimensions: P 0(N) ∝ exp(-N/N 0). However, no such simple considerations can account for the dependence of the knotting length, N 0, on d f , necessitating a more involved analytical calculation. This analysis reveals a complicated double-exponential dependence, which is well supported by numerical data. By contrast, functional forms typical of simple scaling theories fail to adequately describe the observations. These findings are equally valid for two-dimensional ring polymer systems, where "knotting" is defined as the intersection of any two segments.

| S-EPMC9520986 | biostudies-literature

Cluster Glasses of Semiflexible Ring Polymers.

Project description:We present computer simulations of concentrated solutions of unknotted nonconcatenated semiflexible ring polymers. Unlike in their flexible counterparts, shrinking involves a strong energetic penalty, favoring interpenetration and clustering of the rings. We investigate the slow dynamics of the centers-of-mass of the rings in the amorphous cluster phase, consisting of disordered columns of oblate rings penetrated by bundles of prolate ones. Scattering functions reveal a striking decoupling of self- and collective motions. Correlations between centers-of-mass exhibit slow relaxation, as expected for an incipient glass transition, indicating the dynamic arrest of the cluster positions. However, self-correlations decay at much shorter time scales. This feature is a manifestation of the fast, continuous exchange and diffusion of the individual rings over the matrix of clusters. Our results reveal a novel scenario of glass formation in a simple monodisperse system, characterized by self-collective decoupling, soft caging, and mild dynamic heterogeneity.

| S-EPMC4111402 | biostudies-literature

A topologically driven glass in ring polymers.

Project description:The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in polymer physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work, we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly interpenetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work both demonstrates the existence of long-lived inter-ring penetrations and realizes a novel, topologically induced, glass transition.

| S-EPMC4868430 | biostudies-literature

Minimal size of coffee ring structure.

Project description:A macroscopic evaporating water droplet with suspended particles on a solid surface will form a ring-like structure at the pinned contact line due to induced capillary flow. As the droplet size shrinks, the competition between the time scales of the liquid evaporation and the particle movement may influence the resulting ring formation. When the liquid evaporates much faster than the particle movement, coffee ring formation may cease. Here, we experimentally show that there exists a lower limit of droplet size, D(c), for the successful formation of a coffee ring structure. When the particle concentration is above a threshold value, D(c) can be estimated by considering the collective effects of the liquid evaporation and the particle diffusive motion within the droplet. For suspended particles of size approximately 100 nm, the minimum diameter of the coffee ring structure is found to be approximately 10 microm.

| S-EPMC2902562 | biostudies-literature

A photo-Favorskii ring contraction reaction: the effect of ring size.

Project description:The effect of ring size on the photo-Favorskii induced ring-contraction reaction of the hydroxybenzocycloalkanonyl acetate and mesylate esters (7a-d, 8a-c) has provided new insight into the mechanism of the rearrangement. By monotonically decreasing the ring size in these cyclic derivatives, the increasing ring strain imposed on the formation of the elusive bicyclic spirocyclopropanone 20 results in a divergence away from rearrangement and toward solvolysis. Cycloalkanones of seven or eight carbons undergo a highly efficient photo-Favorskii rearrangement with ring contraction paralleling the photochemistry of p-hydroxyphenacyl esters. In contrast, the five-carbon ring does not rearrange but is diverted to the photosolvolysis channel avoiding the increased strain energy that would accompany the formation of the spirobicyclic ketone, the "Favorskii intermediate 20". The six-carbon analogue demonstrates the bifurcation in reaction channels, yielding a solvent-sensitive mixture of both. Employing a combination of time-resolved absorption measurements, quantum yield determinations, isotopic labeling, and solvent variation studies coupled with theoretical treatment, a more comprehensive mechanistic description of the rearrangement has emerged.

| S-EPMC3502675 | biostudies-literature

Programming Photodegradability into Vinylic Polymers via Radical Ring-Opening Polymerization.

Project description:Incorporation of photolabile moieties into the polymer backbone holds promise to remotely-control polymer degradation. However, suitable synthetic avenues are limited, especially for radical polymerizations. Here we report a strategy to program photodegradability into vinylic polymers by exploiting the wavelength selectivity of photocycloadditions for radical ring-opening polymerization (rROP). Irradiation of coumarin terminated allylic sulfides with UVA light initiated intramolecular [2+2] photocycloaddition producing cyclic macromonomers. Subsequent RAFT-mediated rROP with methyl acrylate yielded copolymers that inherited the photoreactivity of the cyclic parent monomer. Irradiation with UVB initiated efficient photocycloreversion of the coumarin dimers, causing polymer degradation within minutes under UVB light or days under sunlight exposure. Our synthetic strategy may pave the way to insert photolabile linkages into vinylic polymers, tuning degradation for specific wavelengths.

| S-EPMC10108003 | biostudies-literature

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers.

Project description:The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.

| S-EPMC5379250 | biostudies-literature

Synthesis of functionalizable and degradable polymers by ring-opening metathesis polymerization.

Project description: Not available

| S-EPMC3808988 | biostudies-literature