Condensed Matter Physics, 2011, vol. 14, No. 3, 33701: 1-20
DOI:10.5488/CMP.14.33701           arXiv:1106.2042

Title: Shapes of macromolecules in good solvents: field theoretical renormalization group approach
  V. Blavatska (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine),
  C. von Ferber (Applied Mathematics Research Centre, Coventry University, CV1 5FB Coventry, UK; Theoretische Polymerphysik, Universität Freiburg, 79104 Freiburg, Germany),
  Yu. Holovatch (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine)

In this paper, we show how the method of field theoretical renormalization 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 solvent 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 approach and estimate the size ratio < Re2>/< RG2 > and the asphericity ratio Âd up to the first order of a double ε=4-d, δ=4-a expansion.

Key words: polymer, quenched disorder, renormalization group
PACS: 75.10.Hk, 11.10.Hi, 12.38.Cy

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