We study the conformational properties of charged polymers in a solvent in the presence of structural obstacles correlated according to a power law $sim x^{-a}$. We work within the continuous representation of a model of linear chain considered as a
random sequence of charges $q_i=pm q_0$. Such a model captures the properties of polyampholytes -- heteropolymers comprising both positively and negatively charged monomers. We apply the direct polymer renormalization scheme and analyze the scaling behavior of charged polymers up to the first order of an $epsilon=6-d$, $delta=4-a$-expansion.
We present an analysis of the impact of structural disorder on the static scattering function of f-armed star branched polymers in d dimensions. To this end, we consider the model of a star polymer immersed in a good solvent in the presence of struct
ural defects, correlated at large distances r according to a power law sim r^{-a}. In particular, we are interested in the ratio g(f) of the radii of gyration of star and linear polymers of the same molecular weight, which is a universal experimentally measurable quantity. We apply a direct polymer renormalization approach and evaluate the results within the double varepsilon=4-d, delta=4-a-expansion. We find an increase of g(f) with an increasing delta. Therefore, an increase of disorder correlations leads to an increase of the size measure of a star relative to linear polymers of the same molecular weight.
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 scalin
g 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. Blavatska, 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) sim r-a. We apply the field-theoretical renormalization group approach and estimate the size ratio <R_e^2>/<R_G^2 > and the asphericity ratio hat{A}_d up to the first order of a double epsilon=4-d, delta=4-a expansion.
