Analytical model for the dynamics of semiflexible dendritic polymers

Abstract

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.

Relaxation Dynamics of Semiflexible Fractal Macromolecules

“…Such a procedure was first introduced for fully flexible dendrimers of functionality f = 3 [43] and later extended to arbitrary functionalities [47,48]; see also recent general results [49] for flexible dendritic structures. The works in [39,40] illustrate that an extension of the procedure is also applicable to semiflexible dendrimers and semiflexible Vicsek fractals. Here, we find (G + 1) groups of eigenvectors for a T-fractal of generation G. Among them, the first G groups are based on the branches Z (1) to Z (G) , whereas the (G + 1)-th group involves the motion of all beads, including the central one (in the case of semiflexible dendrimers [39], the groups 1 to G represent the dynamics of dendrons of the generations 1 to G, and the (G + 1)-th group involves the motion of all dendrimer's beads).…”

“…The works in [39,40] illustrate that an extension of the procedure is also applicable to semiflexible dendrimers and semiflexible Vicsek fractals. Here, we find (G + 1) groups of eigenvectors for a T-fractal of generation G. Among them, the first G groups are based on the branches Z (1) to Z (G) , whereas the (G + 1)-th group involves the motion of all beads, including the central one (in the case of semiflexible dendrimers [39], the groups 1 to G represent the dynamics of dendrons of the generations 1 to G, and the (G + 1)-th group involves the motion of all dendrimer's beads). A branch Z (G Z ) of generation G Z = 1 consists of a single terminal bead.…”

“…for fully-flexible dendrimers [42] that has been recently extended to semiflexible structures, namely 43 dendrimers [38] and Vicsek fractals [39]. This procedure reduces the numerical effort and gives an 44 intuitive sense of the structure of eigenmodes and of the corresponding relaxation spectra.…”

“…An improved description of the polymer's dynamics is achieved by introducing local semiflexibility in the GGS model, which turns out to be very important for dendritic structures [29,30]. Semiflexibility was first introduced to the dynamics of discrete chains by Bixon and Zwanzig [31]; later, it was included to the description of other macromolecular architectures [32][33][34][35][36][37][38][39][40][41][42]. This work employs the framework of semiflexible treelike polymers (STP) [35], which allows one to study arbitrary treelike architectures and to obtain many results in closed form.…”

“…This work employs the framework of semiflexible treelike polymers (STP) [35], which allows one to study arbitrary treelike architectures and to obtain many results in closed form. In particular, the STP framework allows us to determine in this work a complete set of eigenmodes of semiflexible T-fractals, following the procedure put forward by Cai and Chen for fully-flexible dendrimers [43] that has been recently extended to semiflexible structures, namely dendrimers [39] and Vicsek fractals [40]. This procedure reduces the numerical effort and gives an intuitive sense to the structure of eigenmodes and of the corresponding relaxation spectra.…”