Statistical mechanical model for crack growth.

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation.

Modeling single-molecule stretching experiments using statistical thermodynamics.

Single-molecule stretching experiments are widely utilized within the fields of physics and chemistry to characterize the mechanics of individual bonds or molecules, as well as chemical reactions. Analytic relations describing these experiments are valuable, and these relations can be obtained through the statistical thermodynamics of idealized model systems representing the experiments. Since the specific thermodynamic ensembles manifested by the experiments affect the outcome, primarily for small molecules, the stretching device must be included in the idealized model system.

Freely jointed chain models with extensible links.

Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable.

Force-mediated molecule release from double network hydrogels.

The incorporation of mechanosensitive linkages into polymers has led to materials with dynamic force responsivity. Here we report oxanorbornadiene cross-linked double network hydrogels that release molecules through a force-mediated retro Diels-Alder reaction. The molecular design and tough double network of polyacrylamide and alginate promote significantly higher activation at substantially less force than pure polymer systems.

Statistical mechanical constitutive theory of polymer networks: The inextricable links between distribution, behavior, and ensemble.

A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation permits the consideration of arbitrary polymer chain behaviors when interactions among chains may be neglected. This careful treatment highlights the naturally occurring correspondence between single-chain mechanical behavior and the equilibrium distribution of chains in the network, as well as the correspondences between different single-chain thermodynamic ensembles.

Bridging experiments and theory: isolating the effects of metal-ligand interactions on viscoelasticity of reversible polymer networks.

Polymer networks cross-linked by reversible metal-ligand interactions possess versatile mechanical properties achieved simply by varying the metal species and quantity. Although prior experiments have revealed the dependence of the network's viscoelastic behavior on the dynamics of metal-ligand interaction, a theoretical framework with quantitative relations that would enable efficient material design, is still lacking. One major challenge is isolating the effect of metal-ligand interaction from other factors in the polymer matrix.