相关论文: Radius of Gyration of Randomly Branched Molecules
Suppose we have an embedding of a graph $\mathbf{G}$ created by subdividing the edges of a simpler graph $\mathbf{G'}$. The edges of $\mathbf{G}$ can be divided into subsets which join pairs of ``junction'' vertices in $\mathbf{G'}$. The…
It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers…
We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius $R$, at large $R$, obeys, in the scaling sense, $\Delta S \sim R^2/(a^2L)$, with $a$ bond…
We consider the topologically constrained random walk model for topological polymers. In this model, the polymer forms an arbitrary graph whose edges are selected from an appropriate multivariate Gaussian which takes into account the…
We present a semi-analytical approach to the determination of the dynamic properties of randomly branched polymers under the Rouse approximation. The principle procedure is based on examining a spectrum of eigenvalues which represents the…
The segment distribution around the center of gravity is investigated for a special comb polymer (triangular polymer) having the side chains of the same generation number, $g$, as the main backbone. Common to all the other polymers, the…
In this paper we continue our recent analysis [K. Haydukivska et al., J. Mol. Liq., 2021, 328, 115456] of complex molecules with two branching points at both ends of the linear backbone with $f_1$ and $f_2$ side arms starting from them,…
Several nontrivial properties are shown for the mean square radius of gyration $R_K^2$ of ring polymers with a fixed knot type K. Through computer simulation, we discuss both finite-size and asymptotic behaviors of the gyration radius under…
Building on and from the work of Brydges and Imbrie, we give an elementary calculation of the volume of the space of branched polymers of order $n$ in the plane and in 3-space. Our development reveals some more general identities, and…
We have derived long series expansions for the perimeter generating functions of the radius of gyration of various polygons with a convexity constraint. Using the series we numerically find simple (algebraic) exact solutions for the…
The conformational complexity of linear polymers far exceeds that of point-like atoms and molecules. Polymers can bend, twist, even become knotted. Thus they may also display a much richer phase structure than point particles. But it is not…
An explicit expression is derived for the scattering function of a self-avoiding polymer chain in a $d$-dimensional space. The effect of strength of segment interactions on the shape of the scattering function and the radius of gyration of…
The present research is dedicated to provide deeper understanding of the impact of complex architecture of branched polymers on their behaviour in solvents. The folding dynamics of macromolecules and hydrodynamics of polymer fluids are…
A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved…
We consider the simplest representative of the class of multiply branched polymer macromolecules, known as a pom-pom structure. The molecule consists of a backbone linear chain terminated by two branching points with functionalities…
Motivated by renewed interest in the physics of branched polymers, we present here a complete characterization of the connectivity and spatial properties of $2$ and $3$-dimensional single-chain conformations of randomly branching polymers…
The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…
We study the average number A_n per site of the number of different configurations of a branched polymer of n bonds on the Given-Mandelbrot family of fractals using exact real-space renormalization. Different members of the family are…
The interaction of polymers with small-scale velocity gradients can trigger a coil-stretch transition in the polymers. We analyze this transition within a direct numerical simulation of shear turbulence with an Oldroyd-B model for the…
We determine the density expansion of the radius of gyration, of the hydrodynamic radius, and of the end-to-end distance for a monodisperse polymer solution in good-solvent conditions. We consider the scaling limit (large degree of…