Related papers: A Tube Model of Rubber Elasticity
Dense rubbery networks are highly entangled polymer systems, with significant topological restrictions for the mobility of neighbouring chains and crosslinks preventing the reptation constraint release. In a mean field approach,…
Reptation theory has been highly successful in explaining the unusual material properties of entangled polymer solutions. It reduces the complex many-body dynamics to a single-polymer description where each polymer is envisaged to be…
The reptation concept in polymer dynamics is studied for model chains with added stiffness. The main idea of a chain diffusing inside a tube can be transferred from fully flexible chains. However, the picture, which renormalizes the chain…
In the first part of the paper we show that the constraining potentials introduced to mimic entanglement effects in Edwards' tube model and Flory's constrained junction model are diagonal in the generalized Rouse modes of the corresponding…
We numerically examine the nonlinear rubber elasticity of topologically constrained polymer networks. We propose a simple and effective model based on Graessley and Pearson's topological model (GP model) for describing the topological…
Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…
Constitutive equations are derived for the viscoelastic response of rubbery polymers at finite strains. A polymer is thought of as a network of long chains connected to temporary junctions. At a random time, a chain detaches from a…
Constitutive equations are derived for the time-dependent behavior of particle-reinforced elastomers at isothermal loading with finite strains. A rubbery polymer is modelled as a network of macromolecules bridged by junctions which can slip…
Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff…
Semi-flexible polymers in crowded environments exhibit complex dynamics that play a crucial role in various biological and material design processes. Based on the classic reptation theory, it is generally believed that semiflexible polymers…
A constitutive model is derived for the time-dependent response of particle-reinforced elastomers at finite strains. An amorphous rubbery polymer is treated as a network of long chains linked by permanent junctions (chemical crosslinks,…
A thermodynamically related model is developed for describing elastic rubber-like behavior of amorphous and crystallizing polymers and demonstrated on example of simple extension. Both the “entropic” and “energetic”…
The two approaches to analyzing the large strain behavior of rubbery networks are phenomenologically, using strain energy functions drawn from continuum mechanics, and molecular models, which apply statistical mechanics to compute the…
The non-linear stress-strain relation for crosslinked polymer networks is studied using molecular dynamics simulations. Previously we demonstrated the importance of trapped entanglements in determining the elastic and relaxational…
The elastic response is studied of a single flexible chain grafted on a rigid plane and an ensemble of non-interacting tethered chains. It is demonstrated that the entropic theory of rubber elasticity leads to conclusions that disagree with…
We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated…
Classical network elasticity theories are based on the concept of flexible volumeless polymers fixed into a network in which there are no excluded volume, or even topological interactions, and where the chains explore accessible…
We construct a micromechanical version of an early model for topologically constrained polymers -- a 2D chain amongst point-like uncrossable obstacles -- which allows us to explicitly elucidate the role of topological forces beyond…
In this work, we explore the dynamics of active entangled chains using molecular dynamics simulations of a modified Kremer-Grest model. The active chains are diluted in a mesh of very long passive linear chains, to avoid constraint release…
Herein an alternative model to reptation to describe concentrated polymer dynamics is developed. The model assumes that the chains act as blobs that are able to diffuse past each other in a compressed state. Allowing that the local…