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We analyse the effects of the environment (solvent quality, presence of extended structures -- crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the d = 3 case, the corresponding diverging ε = 4 - d expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension d = 2, the exponents are deduced from mapping the polymer model onto a two-dimensional random lattice, i.e., in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations. [ABSTRACT FROM AUTHOR]

In this work we focus on the dynamics of macromolecular networks formed by end-linking identical polymer stars. The resulting macromolecular network can then be viewed as consisting of spacers which connect branching points (the cores of the stars). We succeed in analyzing exactly, in the framework of the generalized Gaussian model, the eigenvalue spectrum of such networks. As applications we focus on several topologies, such as regular networks and dendrimers; furthermore, we compare the results to those found for regular hyperbranched structures. In so doing, we also consider situations in which the beads of the cores differ from the beads of the spacers. The analytical procedure which we use involves an exact real-space renormalization, which allows to relate the star network to a (much simpler) network, in which each star is reduced to its core. It turns out that the eigenvalue spectrum of the star-polymer structure consists of two parts: one follows in terms of polynomial equations from the relaxation spectrum of the corresponding renormalized structure, while the second part involves the motion of the spacer chains themselves. Finally, we show exemplarily the situation for copolymeric dendrimers, calculate their spectra, and from them their storage and the loss moduli. [ABSTRACT FROM AUTHOR]

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-δ, = 4-a expansion. [ABSTRACT FROM AUTHOR]

We analyze scaling laws that govern macromolecules of different topologies: polymer chains, homogeneous and miktoarm star polymers in a good solvent possibly constrained by a porous medium. The latter is modelled by long-range-correlated disorder with a pair correlation function g(r) that decays with a power law g(r) ∼ r-a at large distances r. We show that this type of disorder changes the universality class of the system. Within the framework of the field-theoretical renormalization group approach we obtain the corresponding new universal critical exponents for systems of homogeneous and star copolymers and discuss different consequences of the architecture dependent change of the scaling behavior. [ABSTRACT FROM AUTHOR]