Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks

We demonstrate that a semiflexible bundle of wormlike chains exhibits a state-dependent bending stiffness that alters fundamentally its scaling behavior with respect to the standard wormlike chain. We explore the equilibrium conformational and mechanical behavior of wormlike bundles in isolation, in crosslinked networks, and in solution.

We investigate theoretically the effect of polymer tension on the collective behavior of reversibly binding cross-links. For this purpose, we employ a model of two weakly bending wormlike chains aligned in parallel by a tensile force, with a sequence of inter-chain binding sites regularly spaced along the contours. Reversible cross-links attach and detach at the sites with an affinity controlled by a chemical potential. In a mean-field approach, we calculate the free energy o...

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 with segment interactions at finite deformations. These relations are applied to the study of uniaxial and equi-biaxial tension (compression), where the stress--strain diagrams are analyzed numerically. It is demonstrated that intra-chain in...

The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, ...

We image semi-flexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 micron. The degree of nonaffine strain depends on polymer length and crosslink density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of t...

Molecular dynamics simulations are used to study a unique expanded jammed state. Tension transforms many glassy polymers from a dense glass to a network of fibrils and voids called a craze. Entanglements between polymers and interchain friction jam the system after a fixed increase in volume. As in dense jammed systems, the distribution of forces is exponential, but they are tensile rather than compressive. The broad distribution of forces has important implications for fibri...

The structural properties of a linear polymer and its evolution in time have a strong bearing on its anisotropic stress response. The mean-square bond length and mean bond angle are the critical parameters that influence the time-varying stress developed in the polymer. The bond length distribution along the chain is uniform without any abrupt changes at the ends. Among the externally set parameters such as density, temperature, strain rate, and chain length, the density as w...

The stretchability of polymeric materials is critical to many applications such as stretchable electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as ...

Motivated by recent experiments showing that stiff biopolymer gels exhibit highly unusual negative normal elastic stresses, we develop a computational model for stiff polymer networks subject to large strains. In all cases, we find that such networks develop normal stresses that are both negative and of magnitude comparable to the corresponding shear stress. We find that these normal stresses coincide with other nonlinearities in our networks, and specifically with compressiv...

We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, $G(t)$, into the plateau regime for chains with $Z=40$ entanglements and into the terminal relaxation regime for $Z=10$. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the mic...