Dynamics of a Polymer Network Based on Dual Sierpinski Gasket and Dendrimer: A Theoretical Approach

Relaxation dynamics of semiflexible treelike small-world polymer networks

We study the relaxation dynamics of the polymer networks that are constructed based on a degree distribution specific to small-world networks. The employed building algorithm generates polymers with a large variety of architectures, thus allowing for a detailed study of the structural transition from a pure linear chain to dendritic polymer networks. This is done by varying a single parameter p, which measures the randomness in the degree of the network's nodes. The dynamics is investigated in the framework of the generalized Gaussian structures model by monitoring the influence of the parameter p and of the stiffness parameter q on the behavior of the relaxation quantities: averaged monomer displacement, storage modulus, and loss modulus. The structure properties of the constructed polymers are described by the mean-square radius of gyration. In the absence of stiffness, in the intermediate frequencies domain of the dynamical quantities we encounter different behaviours, such as a dendritic behavior followed by a linear one for very small values of p or a single well-marked dendritic behavior for higher values of p. The stiffness parameter q influences drastically the relaxation dynamics of these polymer networks and in general no evident scaling regions were encountered. However, for some values of the parameter set (p,q), such as (0.8,0.4), an extremely short constant slope region, less than one order of magnitude, was found.

Mechanisms of the Complex Thermo-Mechanical Behavior of Polymer Glass Across a Wide Range of Temperature Variations

This paper aims to explore the mechanisms of the complex thermo-mechanical behavior of polymer glass across a wide range of temperature variations. To this end, the free vibration frequency spectrum of simply supported poly(methyl methacrylate) (PMMA) beams was thoroughly investigated with the aid of the impulse excitation technique. It was found that the amplitude ratio of the multiple peaks in the frequency spectrum is a strongly dependent on temperature, and that the peaks correspond to the multiple vibrational modes of the molecular network of PMMA. At a low temperature, the vibration is dominated by the overall microstructure of PMMA. With increasing the temperature, however, the contribution of the sub-microstructures is retarded by β relaxation. Above 80 °C, the vibration is fully dominated by the microstructure after relaxation. The relaxation time at the transition temperature is of the same order of the vibration period, confirming the contribution of β relaxation. These findings provide a precise method for establishing reliable physical-based constitutive models of polymer glass.

Dynamics of a Polymer Network Modeled by a Fractal Cactus

In this paper, we focus on the relaxation dynamics of a polymer network modeled by a fractal cactus. We perform our study in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. By performing real-space renormalization transformations, we determine analytically the whole eigenvalue spectrum of the connectivity matrix, thereby rendering possible the analysis of the Rouse-dynamics at very large generations of the structure. The evaluation of the structural and dynamical properties of the fractal network in the Rouse type-approach reveals that they obey scaling and the dynamics is governed by the value of spectral dimension. In the Zimm-type approach, the relaxation quantities show a strong dependence on the strength of the hydrodynamic interaction. For low and medium hydrodynamic interactions, the relaxation quantities do not obey power law behavior, while for slightly larger interactions they do. Under strong hydrodynamic interactions, the storage modulus does not follow power law behavior and the average displacement of the monomer is very low. Remarkably, the theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results from the literature.

NMR studies of excluded volume interactions in peptide dendrimers

Peptide dendrimers are good candidates for diverse biomedical applications due to their biocompatibility and low toxicity. The local orientational mobility of groups with different radial localization inside dendrimers is important characteristic for drug and gene delivery, synthesis of nanoparticles, and other specific purposes. In this paper we focus on the validation of two theoretical assumptions for dendrimers: (i) independence of NMR relaxations on excluded volume effects and (ii) similarity of mobilities of side and terminal segments of dendrimers. For this purpose we study 1H NMR spin-lattice relaxation time, T1H, of two similar peptide dendrimers of the second generation, with and without side fragments in their inner segments. Temperature dependences of 1/T1H in the temperature range from 283 to 343 K were measured for inner and terminal groups of the dendrimers dissolved in deuterated water. We have shown that the 1/T1H temperature dependences of inner groups for both dendrimers (with and without side fragments) practically coincide despite different densities of atoms inside these dendrimers. This result confirms the first theoretical assumption. The second assumption is confirmed by the 1/T1H temperature dependences of terminal groups which are similar for both dendrimers.

Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer

In this paper, we focus on the mechanical relaxation of a multilayer polymer network built by connecting identical layers that have, as underlying topologies, the dual Sierpinski gasket and the regular dendrimer. Additionally, we analyze the dynamics of dipolar energy transfer over a system of chromophores arranged in the form of a multilayer network. Both dynamical processes are studied in the framework of the generalized Gaussian structure (GSS) model. We develop a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multilayer network can be determined iteratively, thereby rendering possible the analysis of the dynamics of networks consisting of a large number of layers. This fact allows us to study in detail the crossover from layer-like behavior to chain-like behavior. Remarkably, we highlight the existence of two bulk-like behaviors. The theoretical findings with respect to the decomposition of the intermediate domain of the relaxation quantities, as well as the chain-like behavior, are well supported by experimental results.

Dynamics of Dual Scale-Free Polymer Networks

We focus on macromolecules which are modeled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units. The transition towards the networks of complete graphs is controlled by the probability p of adding a link between non-neighboring nodes of the same initial ring. The relaxation dynamics of the polymer networks is studied in the framework of generalized Gaussian structures by using the full eigenvalue spectrum of the Laplacian matrix. The dynamical quantities on which we focus here are the averaged monomer displacement and the mechanical relaxation moduli. For several intermediate values of the parameters' set ( γ , p ) , we encounter for these dynamical properties regions of constant in-between slope.