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Introduction: Polymer structure, properties and universality: The basic approach of polymer physics.

Mathematical and Statistical Preliminaries: Probability distribution (Gausian, Poisson), Binomial and multinomial distributions, Large N limit, Stirling's approximation, Discrete and continuous Fourier Transform.

Brief Recap of Thermodynamics and Statistical Mechanics: The laws of thermodynamics; Internal energy, free energy and entropy. Introduction to statistical mechanics. Illustration with a simple example.

Properties of an Isolated Polymer Chain: Conformations, bond rotation and polymer size: the random walk model (Ideal chain), effect of short range interactions (freely-rotating chain, hindered rotation etc), Stiffness measures: concept of statistical segment length (persistence length/ Kuhn length), Radius of gyration, The Gaussian chain model, Probability distribution for polymer conformation: Self-avoiding chains and the excluded-volume effect. Reaal polymeric systems: Molecular weight distributions and polydispersity.

Statistical Thermodynamics of Polymer solutions: Lattice model for a binary fluid mixture; Flory-Huggins theory for polymer solutions: Osmotic pressure; Flory Chi parameter and Theta temperature; Phase behavior of polymer solution and blends; Good solvents, Poor solvents and Theta solvents; Excluded volume effect revisited; Coil-Globule transition; Concentration regimes; Chain size in concentrated solutions and melts. Brief overview of scaling arguments.

Continuum aspects of Rheology: Introdution to various rheological response functions: viscosity, modulus and compliance; Normal stress differences; Stress relaxation and Creep response; Dynamic response functions (storage and loss moduli); Linear vs. Non-linear response; Intrinsic viscosity of polymer solutions; steady shear and elongational flows; Introduction to Rheometry; Phenomenological models to illustrate viscoelastic effects; Some commonly used continuum constitutive relations for polymer solutions: Differential and Integral representations.

Molecular theories of Dynamics and Rheology of Polymer Solutions: Polymer chains as an entropic spring; Theory of rubber elasticity; General theory of Brownian motion; Microscopicexpression for stress tensor; Dilute solutions: The bead-spring model for a polymer; Rouse theory; Hydrodynamic interactions and the Zimm model; Concentrated polymer solutions and melts: entanglement and reptation model

Rheology of other complex fluids (if time permits): Solid-liquid suspensions, liquid crystals, emulsions and foams.

Scheme of Assesment:
One Mid-semester exam: 30% of the grade
End-semester exam: 40% of the grade
Assignments: 10% of the grade
Course Mini-project: 20% of the grade