Influence of polymer topologies under shear flow
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Authors
Wang, Xiaoyan
Issue Date
2025-12
Type
Electronic thesis
Thesis
Thesis
Language
en_US
Keywords
Chemical engineering
Alternative Title
Abstract
Polymers are the foundation of countless modern materials, and their mechanical and rheological behavior under flow is strongly depends on molecular topology, whether the chain is linear, ring, or star. Understanding how these architectures deform, relax, and transmit stress in dilute solution is essential to link molecular scale structure with macroscopic response. Most classical polymer models assume polymers undergo Gaussian deformation, which overlook the finite extensibility and correlated motion that emerge in strong flows. This work provides a unified picture that moves beyond the Gaussian assumption to quantitatively characterize non-Gaussian deformation across different topologies. We use Brownian dynamics simulations of the coarse-grained bead-spring model to study linear, ring, and star polymers under steady shear flow. The spring force laws are varied among Hookean, Finite Extensible Nonlinear Elastic (FENE), and FENE-Fraenkel to tune chain flexibility and rigidity, while hydrodynamic interactions (HI) are incorporated through the Rotne-Prager-Yamakawa tensor to capture solvent-mediated coupling. Simulation trajectories are analyzed using a Gram-Charlier expansion, which decomposes each segmental probability distribution into Gaussian and higher-order cumulant terms. The results reveal that the topology governs both the extent and the nature of the deformation. These distinct behaviors arise because different topologies possess different relaxation spectra, which set the pathways through which deformation develops under flow. Linear chains exhibit the largest end-to-end extension and most pronounced non-Gaussian fluctuations, whereas ring and star polymers remain more compact and resistant to extreme deformation. Finite extensibility introduces shear thinning and limits chain elongation, whereas hydrodynamic interactions suppress average stretch but enhance non-Gaussian fluctuations. For smaller, stiffer molecules modeled with FENE-Fraenkel springs, deformation is reduced and the distribution shows smaller fluctuations around the mean, reflecting rigid-segment motion where the spring behaves more like a fixed bond rather than an entropic, stretchable connector. Together, these findings establish a quantitative framework for non-Gaussian polymer dynamics. Using the Gram-Charlier expansion, we can not only detect the presence of non-Gaussianity but also measure its magnitude, something previously inaccessible in most polymer theories. This approach provides new physical insight into how topology, hydrodynamic coupling, and finite extensibility jointly determine polymer response under flow, advancing predictive modeling for both fundamental research and materials design.
Description
December2025
School of Engineering
School of Engineering
Full Citation
Publisher
Rensselaer Polytechnic Institute, Troy, NY