COURSE LAYOUT
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, 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 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, thermodynamic origin of diffusion.
Week 7 : Lattice model of solutions, Flory-Huggins theory of polymer solutions, Definition of partition function and free energy, binodal and spinodal curve, critical point, 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 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 stress tensor.
Week 12 : Experimental rheology: rheometers, linear viscoelasticity, superposition principle, relaxation modulus, storage modulus, loss modulus.
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