Lectures
Lecture 1: Introduction to polymer physics
Basic polymer properties, concepts, and considerations;
introduction to polymer chain models.
Lecture 2: Structures and conformations of polymers in solution
Kuhn model, worm-like chain model, and Gaussian chain model;
scattering wave vector, form factor, and structure factor.
Lecture 3: Polymer-solvent interactions
Excluded volume interactions/parameter;
Flory temperature/parameter;
Flory theory of chain swelling;
coil-globule transition;
rods, coils, and globules.
Lecture 4: Dilute and semi-dilute polymer solutions
Osmotic pressure, virial equation, and Zimm plot at dilute solution conditions;
overlap concentration and semi-dilute conditions;
screening of intrachain excluded volume interactions;
osmotic pressure and virial equation at semi-dilute conditions.
Lecture 5: Thermodynamics of mixed solutions
Monomer correlation length in dilute, semi-dilute, and concentrated solutions;
lattice model;
free energy of mixing of small molecules (Bragg-Williams theory).
Lecture 6: Flory-Huggins solution theory
Flory-Huggins interaction parameter and (im)miscibility;
Flory-Huggins solution theory of polymer blends and polymer solutions;
chemical potential, osmotic pressure, and phase diagrams from Flory-Huggins solution theory.
Lecture 7: Phase behavior of dilute polymer solutions
Spinodal and binodal curves;
critical values of Flory-Huggins solution theory;
Ornstein-Zernike/Landau-Ginzberg theory;
concentration fluctuations;
upper/lower critical solution temperature;
determination of Flory-Huggins interaction parameter.
Lecture 8: Rod-like polymers, block copolymers, and phase separation kinetics
Introduction to rod-like polymers and nematic phase;
introduction to block copolymers and morphology;
lamellar morphology and the strong and weak segregation limits;
phase separation kinetics and spinodal decomposition.
Lecture 9: Nucleation and growth
Spherical droplet formation;
free energy and interfacial tensions of droplets;
nucleation barrier;
nucleation rate.
Lecture 10: Polymer dynamics
Introduction to polymer dynamics;
Brownian motion;
Newton's equation of motion.
Lecture 11: Langevin equation and diffusion
Langevin equation;
characteristic time;
mean square displacement;
Einstein relation;
dynamic light scattering, dynamic structure factor, and determination of diffusion coefficient.
Lecture 12: Dynamics of a Brownian particle
Solving Langevin equation for a Brownian particle;
dynamic light scattering of Brownian particle.
Lecture 13: Gaussian chain dynamics and Rouse model
Dynamics of a Gaussian chain;
probability of conformation of chain;
Rouse model/equation/mode/time;
dynamics of a labeled monomer;
incoherent dynamic structure factor;
comparison of Brownian dynamics of a particle to Rouse model.
Lecture 14: Zimm model and polymer dynamics in semi-dilute solutions
Hydrodynamic interactions/Zimm model;
Zimm relaxation time;
comparison between Rouse and Zimm models;
polymer dynamics in semi-dilute solutions;
hydrodynamic screening length;
self and mutual diffusion coefficients;
generalized Stokes-Einstein law.
Lecture 15: Entanglement dynamics
Polymer melt viscosity;
reptation model;
disengagement time and diffusion in reptation regime;
stress-relaxation function (Doi-Edwards theory);
scaling laws in entangled regime.
Lecture 16: Introduction to crystalline polymers
Free energy above, at, and below melting temperature;
semi-crystallinity;
equilibrium melting temperature;
polymer crystallization thermodynamics;
crystal growth kinetics and nucleation rate.
Lecture 17: Kinetics of polymer crystallization
Lauritzen-Hoffman theory;
crystal growth kinetics at lamellar growth front.
