Inertial Effects on Polymers - Theoretical Derivation and Molecular Dynamic Simulations

 Abstract

This master's thesis expands upon the Rouse model by introducing an inertia term into the equation of motion, thereby incorporating inertial effects. The thesis derives precise analytical expressions for various quantities, including the Rouse mode correlation function, the end-to-end relaxation, monomer mean squared displacements, velocity correlation function, and time-dependent shear modulus. The inclusion of the inertia term introduces two additional characteristic timescale, namely the inertial time and the vibrational time. In the limit of infinitesimally small inertial time, the derived expressions converge to those of the standard Rouse model. Specifically, when the inertial time is much smaller than the Rouse time, the modes exhibit overdamped exponential decay over time. Conversely, for significantly larger inertial times compared to the Rouse time, the modes display underdamped oscillations with a period comparable to the vibrational time. The validity of the obtained analytical expressions is substantiated through the utilization of molecular dynamics simulations. The implications of this study are significant for simulations, as enhanced simulation dynamics are often achieved by increasing the simulation mass. Consequently, a comprehensive understanding of the inertial effects becomes imperative. Future investigations may involve the removal of the inertial effects from the simulation data as a potential avenue for further research.