Swelling of asymmetric pom-pom polymers in dilute solutions

Abstract

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 f1 and f2 side arms starting from them, known as the pom-pom polymers. Here, we analyze the asymmetric case, f1 ≠ f2, by applying both the analytical approach, based on the direct polymer renormalization, and computer simulations using both dissipative particle dynamics and Monte Carlo methods. We study the role played by the molecular asymmetry of average polymer conformations, considering the infinite dilution regime and good solvent conditions.The quantitative estimates are reported for the set of universal size and shape characteristics of such molecules and for their individual branches, all the functions of f1 and f2. In particular, we evaluate the size ratio of the gyration radii of symmetric and asymmetric pom-pom topologies with the same molecular weight and quantitatively reveal an increase of the effective size of a molecule caused by its asymmetry. We also introduce and analyse the asymmetry factor and estimate the shift of the center of mass caused by the presence of side stars, which can serve as another characteristic of the asymmetry of pom-pom structure.

On the swelling properties of pom-pom polymers: impact of backbone length

“…This work is a continuation of a cycle of our studies devoted to the analysis of universal conformational properties of pom-pom polymers. Our previous works [26,27] mainly concentrated on the influence of the branching parameters of side stars on side and shape properties of macromolecule, whereas here we finally address the question of the impact of the backbone length. Within the frames of the continuous chain model, we evaluated the estimates for the size ratio 𝑔 𝑐 that compares the effective size of the pom-pom topology in a solvent to that of a linear chain with the same molecular mass.…”

“…To calculate 𝜉 (k) within the path integration approach, we use a diagrammatic technique for which the diagrams for the Gaussian approximation are given in figures 1. These diagrams should be accounted for with some prefactors, as was discussed in our previous works [26,27]. The Gaussian approximation for the pom-pom structure will thus read:…”

“…In order to get a reliable result on their basis, which can be compared with the data of computer simulations or experiments, we need to consider at least the second order of perturbation theory, which is usually a tricky task from mathematical point of view. One of the possibilities is to make use of a Douglas-Freed (DF) approximation (details are provided in the appendix) that gives a good quantitative agreement with simulations [26,27] and experiment [31].…”

“…As typical examples of such universal properties, one consideres, e.g., the so-called size ratio 𝑔 of mean-squared gyration radii of the complex molecule ⟨𝑅 2 𝑔 ⟩ complex and that of the simplest linear polymer chain ⟨𝑅 2 𝑔 ⟩ chain of the same total molecular weight [25], describing the effective extention of the shape of complex polymer architecture in solution, as compared with the linear one. More subtle size characteristics, specific to branched polymers, are the individual backbone and side branches swelling ratios as well as backbone-to-side branches ratio, sudied in detail in our previous works [26,27]. The elongation of the macromolecule may be also characterised by considering the universal shape characteristics like the asphericity 𝐴 𝑑 .…”

“…In our previous studies [26,27], we analyzed a case of pom-pom polymer, where both the backbone and side arms are of equal length 𝐿. Here, we consider the central backbone of variable length 𝑎𝐿 (with variable 𝑎), which is assumed to be longer than the side chains.…”