Session: 12-07-04: Mechanics of Soft Materials
Paper Number: 100042
100042 - A Statistical Mechanics Framework for Polymer Chain Scission, Based on the Concepts of Distorted Bond Potential and Asymptotic Matching
To design increasingly tough, resilient, and fatigue-resistant elastomers, the relationship between controllable network parameters at the molecular level (bond type, non-uniform chain length, entanglement density, etc.) to macroscopic fracture toughness needs to be discovered, and remains a task of significant complexity. One of the most rigorous and predictive ways to try to find this relationship is by using the tools of statistical mechanics. To that end, a statistical mechanics-based and thermodynamically-consistent polymer chain model accounting for bond extensibility is formalized, where the chain responses at both low and high applied forces are asymptotically matched. This is achieved by extending the bond potential-supplemented freely jointed chain (uFJC) model derived in Buche and Silberstein, JMPS, 2021 with the work of Mao et al., EML, 2017. Along the way, a simple, quasi-polynomial bond potential energy function is proposed for use in this extended uFJC model, since it is derived to intrinsically comply with the asymptotically-matched chain response. In fact, this bond potential exhibits Morse potential-like behavior under low applied forces, and transitions to a more Lennard-Jones potential-like behavior at high applied forces. This bond potential exhibits these beneficial properties while being dependent only upon the material parameters of bond dissociation energy and equilibrium harmonic bond stiffness. Using this extended uFJC model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This statistical chain rupture framework is based upon a force-modified tilted bond potential that accounts for distortional bond energy, as guided by the novel work of Wang et al., Macromolecules, 2019. Dissipated chain scission energy is then derived, and this is used to calculate fracture toughness for elastomer networks. The cases of rate-dependent and rate-independent scission are accounted for throughout the rupture framework. Implications from this rupture framework are fed back to various statistical mechanics considerations in Buche and Silberstein, JMPS, 2021 to calculate the reference end-to-end chain length as a function of Kuhn segment number, bond dissociation energy, and equilibrium harmonic bond stiffness. In this way, the often-utilized reference end-to-end chain length calculated from the inextensible Gaussian chain assumption is corrected to account for bond extensibility. Matching single chain mechanical response data collected from atomic force microscopy tensile tests is used for model validation and for gleaning deeper insight into the molecular physics taking place within the chain. The extended uFJC model along with the chain rupture framework are straightforwardly implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.
Presenting Author: Nikolaos Bouklas Cornell University
Presenting Author Biography: Dr. Bouklas joined the Cornell MAE faculty in January 2018. Prior to that, he was a postdoctoral researcher at the Institute of Mechanical Engineering at EPFL, Switzerland, following a postdoctoral appointment at the Oden Institute, University of Texas at Austin. He received his PhD in Engineering Mechanics from the Aerospace Engineering and Engineering Mechanics department at the University of Texas at Austin in 2014, and obtained his Diploma in Mechanical Engineering from the Aristotle University of Thessaloniki, Greece in 2008.<br/>Dr. Bouklas' research focuses in the fields of theoretical and computational solid mechanics. Developing theoretical frameworks and advanced computational methods, he aims to improve the fundamental understanding of materials and structures, and enhance the predictive capabilities in relevant engineering applications. He is interested in the fundamental study of soft materials, active materials and biomaterials, fracture and instabilities, as well as multiscale modeling in coupled multi-physical systems. A recent thrust in his lab targets machine learning (ML)-enabled constitutive models and solutions of PDEs using a combination of data and guiding physical principles.
Authors:
Jason Mulderrig Cornell UniversityBrandon Talamini Lawrence Livermore National Laboratory
Nikolaos Bouklas Cornell University
A Statistical Mechanics Framework for Polymer Chain Scission, Based on the Concepts of Distorted Bond Potential and Asymptotic Matching
Paper Type
Technical Presentation