Understanding the microstructural and macroscopic evolution of dynamic polymer networks through coarse-grained molecular dynamics
Keywords: Engineering.
Mechanical Engineering.

Due to their dynamic cross-linking bonds, highly stretchable and self-healable supramolecular elastomers are promising materials for future soft electronics, biomimetic systems, self-healing plastics, and smart textiles. The dynamic or reversible nature of the cross-links gives rise to interesting macroscopic responses in these materials such as self-healing and rapid stress-relaxation. Here, self-healing refers to the ability of the material to recover its shape and properties in its pristine state after it undergoes significant mechanical deformation such as extensive loading or material rupture. On the other hand, stress-relaxation refers to the relieving of stress in the elastomer when held indefinitely under deformation, a process that is accelerated due to the presence of dynamic cross-links. Though these properties of dynamic polymer networks are well documented, the relationship between bond activity and macroscopic mechanical response, and the self-healing properties of these dynamic polymer networks (DPNs) remains poorly understood. This dissertation aims to understand the dependence of the macroscopic responses of dynamic polymer networks on their microstructural evolution by using a two-pronged approach. The first is to identify a microstructural descriptor that can explain the macroscopic evolution of stress and the state of the material. The second is to identify the multiscale dynamic processes that precisely estimate the stress-relaxation response. For the first prong of our approach, using coarse-grained molecular dynamics (CGMD) simulations, we reveal a fundamental connection between the macroscopic behaviors of DPNs and the shortest paths between distant nodes in the polymer network. Notably, the trajectories of the material on the shortest path-strain map provide key insights into understanding the stress-strain hysteresis, anisotropy, stress relaxation, and self-healing of DPNs. Based on CGMD simulations under various loading histories, we formulate a set of empirical rules that dictate how the shortest path interacts with stress and strain. This lays the foundation for developing a physics-based theory centered around the non-local microstructural feature of shortest paths to predict the mechanical behavior of DPNs. However, these statistics can be costly to compute and difficult to study theoretically. To this end, we introduce a branching random walk (BRW) model to describe the SP statistics from the CGMD model of polymer networks. We postulate that the first passage time (FPT) of the BRW to a given termination site can be used to approximate the statistics of the SP between distant nodes in the polymer network. We develop a theoretical framework for studying the FPT of spatial branching processes and obtain an analytical expression for estimating the FPT distribution as a function of the cross-link density. We demonstrate by extensive numerical calculations that the distribution of the FPT of the BRW model agrees well with the SP distribution from the CGMD simulations. The theoretical estimate and the corresponding numerical implementations of BRW provide an efficient way of approximating the SP distribution in a polymer network. Our results have the physical meaning that by accounting for the realistic topology of polymer networks, extensive bond-breaking is expected to occur at a much smaller stretch than that expected from idealized models assuming periodic network structures. Our work presents the first analysis of polymer networks as a BRW and sets the framework for developing a generalizable spatial branching model for studying the macroscopic evolution of polymeric systems. This analysis identifies the SP between distant cross-links as a key microstructural parameter that governs material evolution and presents a theoretically tractable framework within which the SP evolution estimates can be made. The second prong of our approach is aimed at reconstructing or predicting the exact nature of the stress-relaxation behavior of the DPNs. The stress relaxation response obtained experimentally or from our CGMD simulations exhibits similar stretched exponential or non-exponential decay, which implies the contribution of multiple dynamic processes occurring at different time scales. We first probe the bond-breaking rates by using the transition state theory under different cross-link densities and polymer melt configurations. However, this limits us to the time scale and the length scale associated with a single cross-link. To access the dynamics at different length scales and time scales we computationally model a powerful experimental dynamics characterization technique called X-ray photon correlation spectroscopy (XPCS). Interpretation of the XPCS data regarding underlying physical processes is necessary to establish the connection between the macroscopic responses and the microstructural dynamics. To aid the interpretation of the XPCS data, we present a computational framework to model these experiments by computing the X-ray scattering intensity directly from the atomic positions obtained from CGMD simulations. The time scale of the dynamics accessed by XPCS is controlled by the sampling frequency of the CGMD configurations whereas the size of the CGMD simulation cell controls the extent of the length scales accessed. By repeating the XPCS analysis at different sampling frequencies we can obtain the multiscale dynamics of the DPN simulated by the CGMD method. We found that the distribution of rates revealed by computational XPCS is consistent with the stretched exponential decay of the stress-relaxation response of the system. This dissertation presents a thorough analysis of the SP between distant cross-links as a microstructural descriptor that governs the macroscopically observed mechanical evolution (self-healing and rapid stress relaxation) of the DPN system. In addition, the XPCS analysis of the CGMD simulation trajectory is successful in uncovering the characteristic rates of the dynamic processes that accurately predict the rapid stress-relaxation exhibited by the DPNs. The methods presented in this dissertation to study the microstructural and dynamic evolution are applicable to a large class of elastomeric systems and can aid in the design of the next generation of smart elastomers.