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We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First, we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.

We investigate hyperbranched polymers (HBPs) and highlight the relation between their architecture and their viscoelastic behavior, while paying special attention to the role of the chainlike spacer segments between branching points. For this we study the dynamics of HBP in solution, based on the generalized Gaussian structure formalism, an extension of the Rouse model, which disregards hydrodynamical and excluded volume effects. For HBP the dynamical effects display, beside the obvious contributions of localized modes on the spacers, also remarkable features, as we highlight based on the exact renormalization procedure recently developed by us in J. Chem. Phys. 123, 034907 (2005). We exemplify these features by analyzing the dynamics of randomly linked star polymers and study the impact both of the length and of the spacers’ mobility on the normal modes’ spectra. We compute these modes both by numerical diagonalization and also by employing our renormalization procedure; the excellent agreement between these methods allows us to extend the range of investigations to very large HBP. [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]

We focus on the dynamical properties of dendrimers and of randomly built branched polymers, which allows us to assess theoretically the role of disorder on the relaxation forms. We model the random polymers through a stochastic growth algorithm. Our studies are carried out both in the Rouse and also in the Zimm framework; the latter accounts for hydrodynamic interactions. Moreover, we also mimic the local geometry by imposing conditions on the average values of the angles between neighboring segments. Excluded volume interactions, however, are neglected throughout. The storage G′(ω) and the loss G″(ω) moduli, which we calculate, turn out to depend more on the hydrodynamic and the angular restrictions than on randomness. Furthermore, we find that both the randomness and the angular restrictions slow down the relaxation. Given that G′(ω), G″(ω) and also C(t), a function related to the radius of gyration, are all connected to the relaxation function G(t), a fact which we recall, we also calculate numerically G(t) and C(t); moreover we fit, following previous works, C(t) to stretched-exponential forms. Interestingly, it appears that from all functions considered G(t) is most sensitive to disorder. [ABSTRACT FROM AUTHOR]

We study the conformational properties of charged polymers in a solvent in the presence of structural obstacles correlated according to a power law ~ x-a . We work within the continuous representation of a model of linear chain considered as a random sequence of charges qi = ±q0. 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 ε= 6-d, δ= 4-a-expansion. [ABSTRACT FROM AUTHOR]

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 structural defects, correlated at large distances r according to a power law ~ 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 ε = 4-d, δ = 4-a-expansion. We find an increase of g( f ) with an increasing δ. 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. [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]

We extend existing renormalization group calculations for the exponents describing scaling of star polymers and polymer networks constituted by chains of different species (the so-called copolymer star exponents). Our four loop results find application in the description of various phenomena involving self-avoiding and random walks that interact. [Copyright &y& Elsevier]