Dynamics of semiflexible treelike polymeric networks

Abstract

We study the dynamics of general treelike networks, which are semiflexible due to restrictions on the orientations of their bonds. For this we extend the generalized Gaussian structure model, in which the dynamics obeys Langevin equations coupled through a dynamical matrix. We succeed in formulating analytically this matrix for arbitrary treelike networks and stiffness coefficients. This allows the straightforward determination of dynamical characteristics relevant to mechanical and dielectric relaxation. We show that our approach also follows from the maximum entropy principle; this principle was previously implemented for linear polymers and we extend it here to arbitrary treelike architectures.

Relaxation Dynamics of Semiflexible Fractal Macromolecules

“…In this section, the model of semiflexible treelike polymers (STP) is briefly recalled; details of the STP model can be found in [35].…”

“…The structure of potential (3) can be obtained based on maximum entropy methods [35,44] or by construction of the covariance matrix (consisting of the mean values…”

“…This restriction comes from the observation of f i rays emanating from the same origin, for which in three-dimensional space the sum of cosines of the angles between them ( f i rays lead to f i ( f i − 1)/2 angles) is restricted by − f i /2 from below [45]. A detailed presentation of the explicit matrix elements of W, taking into account the above conditions, can be found in [35].…”

“…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. 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].…”

“…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.…”