Dynamics of a three-dimensional inextensible chain

In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to the $z-$axis is studied using a path integral approach. It is shown that it is possible to reduce this problem to a two-dimensional case, in a way which is similar to the reduction of the statistical mechanics of a directed polymer to the random walk of a two-dimensional particle.Comment: 15 pages, 3 figures, LaTeX, version accepted for publicatio

The size and shape of snowflake star polymers in dilute solutions: analytical and numerical approaches

We investigate the conformational properties of a multi-branched polymer structure with a dendrimer-like topology, known as a snowflake polymer. This polymer is characterized by two parameters: $f_s$, which represents the functionality of the central star-like core, and $f$, which represents the functionality of the side branching points. To analyze the conformational properties, we have employed various approaches, including analytical methods based on direct polymer renormalization and the Wei's approach as well as numerical molecular dynamics simulations. These methods have allowed us to estimate a size and shape characteristics of the snowflake polymer as functions of $f$ and $f_s$. Our findings consistently demonstrate the effective compactification of the typical polymer conformation as the number of branching points increases. Overall, our study provides valuable insights into the conformational behavior of the snowflake polymer and highlights the impact of branching parameters on its overall compactness

Description of the dynamics of a random chain with rigid constraints in the path integral framework

In this work we discuss the dynamics of a three dimensional chain which is described by generalized nonlinear sigma model The formula of the probability distribution of two topologically entangled chain is provided. The interesting case of a chain which can form only discrete angles with respect to the $z-$axis is also presented.Comment: 4 pages. To appear in the proceedings of `Path Integrals - New Trends and Perspectives`, 23-28 September 2007, Dresden, German

Super-soft and super-elastic dry gels

Molecular combs and bottlebrushes are a new class of polymer architecture allowing for anomalously low density of entanglements in polymer melts. The conformations and rheological properties of melts of these branched macromolecule composed of a flexible backbone and side chains densely tethered to it are investigated theoretically, experimentally and by computer simulations.1,2 We develop the rule for dialing in the desired value of the melt plateau modulus of these molecules as low as 1000 times below the conventional values for linear polymer melts and experimentally verify the validity of our theory. The theory also predicts that elastomers made from these melts should be super-elastic and reversibly stretch up to ten times more than elastomers made from linear polymers. Hybrid networks with both permanent and reversible bonds made with this novel architecture are predicted to be super-tough and self-healing. References W.F.M. Daniel, J. Burdynska, M. Vatankhah-Varnoosfaderani, K. Matyjaszewski, J. Paturej, M. Rubinstein, A.V. Dobrynin and S.S. Sheiko, Nature Materials, 2016, 15, 183-190. L.H Cai, T.E. Kodger, R.E. Guerra, A.F. Pegoraro, M. Rubinstein, and D.A. Weitz, Advanced Materials 2015, 27, 5132–5140

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 \div 4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time declines with growing contour length $L$ as $\propto L^{-0.17}$, and with side chain length as $\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.Comment: 15 pages, 7 figure