Christos Tzoumanekas

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A pairwise parameter, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their stren...

Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

We present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field ‘target’ model. Most previous works used the Doi–Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well-entangled chains, with the parameters determined ab initio, lies in the range of experimental data for the materials investigated.

A Study of the Entanglement in Systems with Periodic Boundary Conditions

We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking to assess the extent of entanglement in a polymer melt we study the effect of CReTA algorithm on the entanglement of polyethylene chains. Our numerical results show that the statistics of the local periodic linking number observed for polymer melts before and after the application of CReTA are the same.

Atomistic simulations of cavitation in a model polyethylene network

A molecular-level understanding of cavitation in polymer networks upon imposition of mechanical stress is still lacking. Molecular Dynamics simulations of crosslinked amorphous Polyethylene (PE) were conducted in order to study cavitation as a function of the prevailing stress. We first show that the characteristic relaxation times related to tube confinement and chain connectivity can be obtained by examining the mean square displacement of middle chain monomers. Then, we present a methodology for predicting the cavitation strength and understanding its dependence on cohesive interactions and entropic elasticity. Our simulations show that experimental observations and predictions of continuum mechanics analysis, which relate the critical stress for cavitation to the Young’s modulus of the rubber, are in agreement with the observed tensile triaxial stress below which a pre-existing cavity cannot survive in a cavitated sample.

Molecular Modeling and Simulation of Polymer Nanocomposites at Multiple Length Scales

The complexity of intermolecular interactions and confinement in polymer-nanoparticle systems leads to spatial variations in structure and dynamics at both the meso and nanoscale. Molecular simulation holds great promise as a means of predicting these effects and understanding their microscopic origin. In order to shed some light onto local structure and segmental dynamics of atactic polystyrene/silica (PS/SiO2) and atactic polystyrene/fullerene (PS/C60) melt systems, molecular simulations have been conducted using two interconnected levels of representation: 1) A coarse-grained representation. Equilibration of coarse-grained polymer-nanoparticle systems at all length scales is achieved via connectivity-altering Monte Carlo simulations. 2) An atomistic representation. Initial configurations for atomistic molecular dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse-grained configurations. The local structure around a silica nanoparticle immersed in the PS matrix, PS segmental, and local dynamics in both composites and mechanical properties and entanglements in PS/SiO2 are studied.

Molecular modeling and simulation of atactic polystyrene/amorphous silica nanocomposites

The local structure, segmental dynamics, topological analysis of entanglement networks and mechanical properties of atactic polystyrene - amorphous silica nanocomposites are studied via molecular simulations using two interconnected levels of representation: (a) A coarse - grained level. Equilibration at all length scales at this level is achieved via connectivity - altering Monte Carlo simulations. (b) An atomistic level. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well- equilibrated coarse-grained configurations. By analyzing atomistic MD trajectories, the polymer density profile is found to exhibit layering in the vicinity of the nanoparticle surface. The dynamics of polystyrene (in neat and filled melt systems) is characterized in terms of bond orientation. Well-equilibrated coarse-grained long-chain configurations are reduced to entanglement networks via topological analysis with the CReTA algorithm. Atomistic simulation results for the mechanical properties are compared to the experimental measurements and other computational works.

Molecular modeling and simulation of polymer nanocomposites at multiple length scales

The complexity of intermolecular interactions and confinement in polymer - nanoparticle systems leads to spatial variations in structure and dynamics at both the meso- and nanoscale. Molecular simulation holds great promise as a means of predicting these effects and understanding their microscopic origin. In order to shed some light onto local structure and segmental dynamics of PS/SiO2 silica and PS/C60 fullerene melt systems, molecular simulations have been conducted using two interconnected levels of representation: (a) A coarse-grained representation. Equilibration of coarse-grained polymer-nanoparticle systems at all length scales is achieved via connectivity-altering Monte Carlo (MC) simulations. (b) An atomistic representation. Initial configurations for atomistic Molecular Dynamics (MD) simulations are obtained by reverse mapping well-equilibrated coarse-grained configurations. The local structure around a silica nanoparticle immersed in polystyrene matrix, PS segmental and local dynamics in both composites and mechanical properties and entanglements in PS/SiO2 are studied.