Relaxation of polymers modeled by generalized Husimi cacti

Galiceanu, Mircea

doi:10.1088/1751-8113/43/30/305002

Cited by 26 publications

(19 citation statements)

References 36 publications

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“…IV, SD; scaling behavior is, on the other hand, the rule for linear chains and for fractals. [28][29][30][31] In fact, for FD the corresponding curves in the region of intermediate frequencies can be approximated through logarithmic forms. 8 The broadening of the spectra with growing q, as discussed above, manifests itself through a broadening of the [G (ω)]-shapes.…”

Section: Discussionmentioning

confidence: 99%

Analytical model for the dynamics of semiflexible dendritic polymers

Fürstenberg

Dolgushev

Blumen

2012

The Journal of Chemical Physics

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We study the dynamics of semiflexible dendritic polymers following the method of Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. The scheme allows to formulate in analytical form the corresponding Langevin equations. We determine the eigenvalues by first block-diagonalizing the problem, which allows to treat even very large dendritic objects. A basic ingredient of the procedure is the observation that a set of eigenmodes in the semiflexible case is similar to that chosen by Cai and Chen [Macromolecules 30, 5104 (1997)] for fully flexible dendritic structures. Varying the flexibility of the macromolecules allows us to better understand their mechanical loss moduli G"(ω) based on their eigenvalue spectra. We present the G"(ω) for a series of stiffness parameters and for different functionalities of the branching points.

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Section: Discussionmentioning

confidence: 99%

Analytical model for the dynamics of semiflexible dendritic polymers

Fürstenberg

Dolgushev

Blumen

2012

The Journal of Chemical Physics

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“…For semiflexible chains Equation 16 was derived by Bixon and Zwanzig [35] using projection operator techniques. [33,34] We note that for STP the average of d a Á d b with respect to the Boltzmann distribution expðÀV STP =k B TÞ is…”

Section: Simulation Proceduresmentioning

confidence: 99%

“…For several classes of macromolecules the GGS method has been applied (in many cases semi-analytically) to dendrimers, [4] to mesh-like [5,6] and star-based networks, [7,8] to dendritic [9,10] and regular hyperbranched structures [11,12] and to several kinds of fractals. [13][14][15][16] However, the GGS concept neglects important aspects, such as the excluded volume and the hydrodynamic interactions, as well as the role of stiffness. It is the latter aspect on which we focus here, since stiffness is often fundamental, e.g.…”

Section: Introductionmentioning

confidence: 99%

Branched Semiflexible Polymers: Theoretical and Simulation Aspects

Dolgushev

Berezovska

Blumen

2011

Macro Theory & Simulations

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Recent approaches for taking stiffness effects into account when modeling multifunctional polymer structures are reported. The theoretical part is focused on arbitrary tree‐like polymers, modeled through extensions of the GGS scheme that allows the inclusion of local constraints. The theoretical findings are compared to the results of numerical simulations in which stiffness is included into the bond fluctuation model with the help of additional bending potentials. The procedure is illustrated by evaluating the static properties of semiflexible linear chains, stars, cospectral polymers and rings. The dynamical properties are exemplified by the mechanical relaxation of semiflexible polymers, including situations in which the local conditions at different sites are the same or different.magnified image

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“…Thus far, the Laplacian eigenvalues for some classes of graphs have been determined exactly, including regular hypercubic lattices, 1,9 dual Sierpinski gaskets, 10,11 Vicsek fractals, 12,13 dendrimer also known as Cayley tree, 14 and Husimi cacti. 15,16 Recent empirical research indicated that some real-life networks (e.g., power grid) display small-world behavior. 17 Moreover, these networks are simultaneously characterized by an exponentially decaying degree distribution, 18 which cannot be described by the above-mentioned networks.…”

Section: Introductionmentioning

confidence: 99%

Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications

Liu

Zhang²

2013

The Journal of Chemical Physics

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A central issue in the study of polymer physics is to understand the relation between the geometrical properties of macromolecules and various dynamics, most of which are encoded in the Laplacian spectra of a related graph describing the macrostructural structure. In this paper, we introduce a family of treelike polymer networks with a parameter, which has the same size as the Vicsek fractals modeling regular hyperbranched polymers. We study some relevant properties of the networks and show that they have an exponentially decaying degree distribution and exhibit the small-world behavior. We then study the Laplacian eigenvalues and their corresponding eigenvectors of the networks under consideration, with both quantities being determined through the recursive relations deduced from the network structure. Using the obtained recursive relations we can find all the eigenvalues and eigenvectors for the networks with any size. Finally, as some applications, we use the eigenvalues to study analytically or semi-analytically three dynamical processes occurring in the networks, including random walks, relaxation dynamics in the framework of generalized Gaussian structure, as well as the fluorescence depolarization under quasiresonant energy transfer. Moreover, we compare the results with those corresponding to Vicsek fractals, and show that the dynamics differ greatly for the two network families, which thus enables us to distinguish between them.

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Relaxation of polymers modeled by generalized Husimi cacti

Cited by 26 publications

References 36 publications

Analytical model for the dynamics of semiflexible dendritic polymers

Analytical model for the dynamics of semiflexible dendritic polymers

Branched Semiflexible Polymers: Theoretical and Simulation Aspects

Laplacian spectra of recursive treelike small-world polymer networks: Analytical solutions and applications

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