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We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending,…
Polymer entanglements lead to complicated topological constraints and interactions between neighbouring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they…
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…
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 propose a theoretical framework for dealing with a transient polymer network undergoing small deformations, based on the rate of breaking and re-forming of network crosslinks and the evolving elastic reference state. In this framework,…
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…
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,…
We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end…
Statistical mechanics is an important tool for understanding polymer electroelasticity because the elasticity of polymers is primarily due to entropy. However, a common approach for the statistical mechanics of polymer chains, the Gaussian…
This paper develops a damage model for unfilled cross-linked rubbers based on the concept of scission of polymer chains. The model is built up on the well-known Gent elastic potential complemented by a kinetic equation describing effects of…
This paper develops a damage model for unfilled cross-linked rubbers based on the concept of scission of polymer chains. The model is built up on the well-known Gent elastic potential complemented by a kinetic equation describing effects of…
Understanding the relationship between the microscopic structure and topology of a material and its macroscopic properties is a fundamental challenge across a wide range of systems. Here, we investigate the viscoelasticity of DNA nanostar…
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear…
We introduce an entropic network model for copolymer elastomers based on the evolution of microscopic chain conformations during deformation. We show that the stress results from additive contributions due to chain stretch at the global as…
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…
Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance,…
Live cells have ambiguous mechanical properties. They were often described as either elastic solids or viscoelastic fluids and have recently been classified as soft glassy materials characterized by weak power-law rheology. Nonlinear…
Stretching an elastic material along one axis typically induces contraction along the transverse axes, a phenomenon known as the Poisson effect. From these strains, one can compute the specific volume, which generally either increases or,…
Strain energy density is calculated for a network of flexible chains with weak excluded-volume interactions (whose energy is small compared with thermal energy). Constitutive equations are developed for an incompressible network of chains…
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”…