On the swelling properties of pom-pom polymers in dilute solutions. Part 1: Symmetric case

Abstract

The paper continues our previous study of complex polymers with two branching points of functionalities f 1 and f 2 known as pom-pom molecules [1]. Here, we analyze the asymmetric case, when f 1 = f 2 . Applying both the analytical approach, based on direct polymer renormalization, and computer simulations, we obtained the quantitative estimates for the set of universal size and shape characteristics of molecule as well as its individual branches. The main attention is pointed towards the impact of asymmetric architecture of molecule on its behaviour in a good solvent regime. In particular, we evaluate the size ratio of the gyration radii of symmetric and asymmetric pom-pom topologies of the same total molecular weight and quantitatively reveal an increase of effective size of molecule caused by anisotropy. We estimated the shift of center of mass position caused by presence of side stars which can serve as another charasteristic of the asymmetry of pom-pom structure.

Swelling of asymmetric pom-pom polymers in dilute solutions

“…An expression for 𝐶 𝑔 is provided in the Appendix in expression A.1. In the case of 𝑓 1 = 𝑓 2 we recover our previous result for the symmetric case [8].…”

“…This number of branches was chosen to show the effect of asymmetry and to avoid the effect of crowdedness which has been studied in our previous work [21]. Two cases of the arm length, 𝑁 𝑓 = 8 and 𝑁 𝑓 = 16 were examined, similarly to the case of a symmetric pom-pom polymer [8], the results were found to agree well. In work [19] it was shown that the reduced density is coupled to the amplitude 𝑎 of a repulsive force in equation (3.3).…”

“…A set of specific size characteristics can be defined for the pom-pom polymer. Some of them were introduced for a symmetric case in our previous study [8]. Here, we add a number of new characteristics that allow us to describe the asymmetry of pom-pom molecule when 𝑓 1 ≠ 𝑓 2 .…”

“…In our study, we concentrated on the conformational properties of such macromolecules in an infinite dilution regime. In our preceding work [8], we studied the simplified symmetric case with 𝑓 1 = 𝑓 2 . The main attention was focused on a set of universal conformational characteristics of macromolecules, which are independent of any details of the chemical structure and are governed only by the so-called global parameters.…”

“…These ratios characterize the averaged effect of crowdedness, caused by a mutual influence of adjacent branches on their respective conformations. Applying both the theoretical approach and the computer simulations, we quantitatively described the effects of the stretch and "compactization" of both the symmetric pom-pom polymer and of its individual branches by means of 9 universal size ratios [8].…”