The physics of polymer chains: returning to simple theory

This thesis explores the physics of polymer chains in solution, covering both theoretical models and computational methods. It begins with an overview of key concepts such as ideal chains, excluded volume effects, the Flory–Huggins equation, and polymer dynamics in dilute solutions.
A central challenge addressed is how to simulate long polymer behavior using short chains, since simulating long chains with explicit solvents is computationally expensive. By using a simplified model, the study shows that choosing a specific parameter ratio allows short chains to mimic long-chain behavior, enabling accurate predictions of diffusion and viscoelastic properties.
The thesis also develops thermodynamic models to describe polymer size in solvents. Treating the system as two phases, it derives expressions for the excluded volume parameter and demonstrates how solvent properties influence polymer expansion or collapse. Extensions of the model incorporate asymmetry between monomers and solvent, revealing conditions under which polymers shrink or collapse, including the existence of multiple theta temperatures.
Further refinements include accounting for correlations between monomers, improving agreement with simulations. The nature of the collapsed polymer state is also examined, showing higher local solvent density around polymers than in the bulk.
Finally, the work connects and extends existing theories, showing relationships between equations of state and improving scaling models for polymer solutions across dilute and semidilute regimes. Overall, the thesis provides both theoretical insights and practical methods for understanding and simulating polymer behavior in solution.