Polymer physics is important to understand the structure-property relation in polymers.
An understanding of the structural features and interactions responsible for Polymer physics properties can aid in tuning the desirable properties. This introductory course will discuss the models for ideal polymer chains, and thermodynamics of polymer solutions and blends, focusing on miscibility. The course will also cover the different methods to measure polymer molar mass, which has a strong effect on polymer properties. The physics of branching and network formation will be introduced concerning branched polymers, dendrimers, and cross-linked polymers. The course will also discuss the mechanical properties of polymers with a focus on viscoelasticity and rubber elasticity. Finally, a brief introduction to polymer dynamics will be provided.
Week 1: Macromolecules and Life, Molecular flexibility, Classification of polymers, Types of polymerization, Average molecular weights and polydispersity, Concept of universality
Week 2: Random walk models in polymer physics: 1-D random walk (drunkard walk), 2-D random walk on a lattice, freely jointed chain, modified freely jointed chain, freely rotating chain
Week 3: Elastic energy of polymer chain, bead-spring model, ideal polymer chain and finite extension models, the radius of gyration, pair correlation function, scattering experiments
Week 4: Review of programming concepts, Monte Carlo simulations of a polymer chain, Importance Sampling, Metropolis criteria, Practical aspects of Monte Carlo simulation
Week 5: Excluded volume interaction. Flory theory in a good solvent, bad solvent, and theta solvent. Monte Carlo simulations in good solvent and bad solvent regime.
Week 6: Concentrated polymer solutions. Review of Solution thermodynamics: Mixing and phase separation, osmotic pressure, chemical potential, the thermodynamic origin of diffusion.
Week 7: Lattice model of solutions, Flory-Huggins theory of polymer solutions, Definition of the partition function and free energy, binodal and spinodal curve, critical point, an extension to polymer blends, and melt
Week 8: Brownian motion, Correlation functions, Time translational invariance and time-reversal symmetry, Brownian motion of a free particle, Einstein relation
Week 9: Brownian motion in a potential field, Introduction to Molecular Dynamics and Brownian Dynamics
Week 10: Rouse model of the polymer chain, normalized coordinates and basis functions, Rouse modes, problems with Rouse model
Week 11: Review of continuum mechanics: equations of motion, stress tensor, deformation tensor, deformation gradient tensor, constitutive relations of solids, liquids, and rubber. Microscopic definition of the stress tensor.
Week 12: Experimental rheology: rheometers, linear viscoelasticity, superposition principle, relaxation modulus, storage modulus, loss modulus.