Shapes of macromolecules in good solvents: field theoretical renormalization group approach

• Main Authors: Blavatska, V., von Ferber, C., Holovatch, Yu.
• Format: Article
• Language: English
• Published: Інститут фізики конденсованих систем НАН України 2011
• Series: Condensed Matter Physics
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/120035

In this paper, we show how the method of field theoretical reno rmalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on the scaling exponents that govern conformational properties of polymer macromolecules. However, there are other observables that along with the scaling exponents are universal (i.e. independent of the chemical structure of macromolecules and of the solvent) and may be analyzed within the renormalization group approach. Here, we address the question of shape which is acquired by the long flexible polymer macromolecule when it is immersed in a solve nt in the presence of a porous environment. This question is of relevance for understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, and in cellular environment. To this end, we consider a previously suggested model of polymers in d-dimensions [V. Blavats’ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) ∼ r−a. We apply the field-theoretical renormalization group ap-proach and estimate the size ratio hR²ei/hR²Gi and the asphericity ratio Aˆd up to the first order of a double ε = 4−d, δ = 4−a expansion.