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 f c linear branches and f r closed loops grafted to the central core. We determine size measures such as the gyration radius R g and the hydrodynamic radii R H , and obtain the estimates for the size ratio R g /R H with its dependence on the functionality f = f c + f r of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops f r as compared to linear or star-shape molecules of the same total molecular weight. numerical simulations corroborate theoretical prediction that R g /R H decreases towards unity with increasing f. These findings provide qualitative description of polymers with complex architecture in θ solvents.
We analyze the universal size characteristics of flexible ring polymers in solutions in presence of structural obstacles (impurities) in d dimensions. One encounters such situations when considering polymers in gels, colloidal solutions, intra- and extracellular environments. A special case of extended impurities correlated on large distances r according to a power law ~r(-a) is considered. Applying the direct polymer renormalization scheme, we evaluate the estimates for averaged gyration radius ⟨R(g ring)⟩ and spanning radius ⟨R(1/2 ring)⟩ of typical ring polymer conformation up to the first order of double ɛ = 4 - d, δ = 4 - a expansion. Our results quantitatively reveal an extent of the effective size and anisotropy of closed ring macromolecules in disordered environment. In particular, the size ratio of ring and open (linear) polymers of the same molecular weight grows when increasing the strength of disorder according to ⟨R(g ring)(2)⟩/⟨R(g chain)(2)⟩=½(1+(13/48)δ).
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.
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