2019, Ferrari, Franco, Paturej, Jarosław, Pia̧tek, Marcin, Zhao, Yani

The field theory approach to the statistical mechanics of a system of N polymer rings linked together is extended to the case of links whose paths in space are characterized by a fixed number 2s of maxima and minima. Such kind of links are called 2s-plats and appear for instance in the DNA of living organisms or in the wordlines of quasiparticles associated with vortices nucleated in a quasi-two-dimensional superfluid. The path integral theory describing the statistical mechanics of polymers subjected to topological constraints is mapped here into a field theory of quasiparticles (anyons). In the particular case of s=2, it is shown that this field theory admits vortex solutions with special self-dual points in which the interactions between the vortices vanish identically. The topological states of the link are distinguished using two topological invariants, namely the Gauss linking number and the so-called bridge number which is related to s. The Gauss linking number is a topological invariant that is relatively weak in distinguishing the different topological configurations of a general link. The addition of topological constraints based on the bridge number allows to get a glimpse into the non-abelian world of quasiparticles, which is relevant for important applications like topological quantum computing and high-TC superconductivity. At the end an useful connection with the cosh-Gordon equation is shown in the case s=2. © 2019

2016, Paturej, Jarosław, Sheiko, Sergei S., Panyukov, Sergey, Rubinstein, Michael

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of both individual bottlebrushes and their assemblies. We delineate fundamental correlations between molecular architecture, mesoscopic conformation, and macroscopic properties of polymer melts. Numerical simulations corroborate theoretical predictions for the effect of grafting density and side-chain length on the dimensions and rigidity of bottlebrushes, which effectively behave as a melt of flexible filaments. These findings provide quantitative guidelines for the design of novel materials that allow architectural tuning of their properties in a broad range without changing chemical composition.

2020, Haydukivska, Khristine, Blavatska, Viktoria, Paturej, Jarosław

We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing fc linear branches and fr closed loops grafted to the central core. We determine size measures such as the gyration radius Rg and the hydrodynamic radii RH, and obtain the estimates for the size ratio Rg/RH with its dependence on the functionality f=fc+fr of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops fr as compared to linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that Rg/RH decreases towards unity with increasing f. These findings provide qualitative description of polymers with complex architecture in θ solvents.