Chemical physics of polymer solutions

Advanced course, Semester A, 2003/2004
0351.4809
Mondays 12:00-15:00, Schreiber 8

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Bibliography

General agenda

• Models of chain-like molecules
• Dilute, semi-dilute and concentrated polymer solutions
• Phase transitions and phase diagrams of polymer solutions
• Analogies to random walks, quantum mechanics, critical phemomena
• Dynamics of polymer solutions
• Biopolymers

Prerequisites

Requirements

• Submission of 75% of exercises
• Written work submitted until May 2, 2004. Subjects for works

Program

• Lecture 1 (27/10/03)
  • Introduction: what is special about polymer solutions
  • Dilute solutions and single-chain description
  • Specific example: polyethylene and the rotational-isomeric model
  • From the RI model to a Gaussian chain
  • Gaussian chain in 1D: exact calculation, the continuum limit, the diffusion equation
  Exercise #1
   
• Lecture 2 (3/11/03)
  • The path-integral representation
  • Analogy with quantum-mechanics
  • Gaussian chain in external potential
  • Tutorial: freely-rotating chain and the persistence length
  Exercise #2
   
• Lecture 3 (10/11/03)
  • Surface adsorption of a Gaussian chain (quantum-mechanical analogy)
  • Semiflexible polymers; the Worm-Like-Chain model
  • Tutorial: Gaussian chain under tension
  Exercise #3
   
• Lecture 4 (17/11/03)
  • Mechanical response of biopolymers (DNA): rescaled freely-jointed chain
  
  
• Lecture 5 (24/11/03)
  • Mechanical response of biopolymers (DNA): worm-like chain
  Exercise #4
   
• Lecture 6 (8/12/03)
  • Self-similarity and fractal nature of Gaussian chains
  • Introducing excluded volume and other short-range interactions
  • The Edwards Hamiltonian
  • The Flory argument
  
  
• Lecture 7 (15/12/03)
  • Solvent quality
  • The theta (coil-globule) transition
  • Scaling arguments (thermal "blobs")
  • Tutorial: statistics of contacts in a Gaussian chain
  Exercise #5
   
• Lecture 8 (22/12/03)
  Tutorial: scaling theory of real chains
  • Real chain under tension
  • End-to-end distance distribution of a real chain
  • Surface adsorption of a real chain
  
  
• Lecture 9 (29/12/03)
  Scattering from dilute polymer solutions
  • Ideal chains (the Debye form factor)
  • Real chains; fractal pair correlation functions
  • Tutorial: "bubbles" in DNA melting
  Exercise #6
   
• Lecture 10 (5/1/04)
  Thermodynamics of polymer solutions: the Flory-Huggins theory
   
• Lecture 11 (12/1/04)
  Phase diagrams of polymer solutions
   
• Lecture 12 (15/1/04, extra class)
  Melts, concentrated solutions, and semidilute solutions
  • Flory-Huggins theory
  • Scaling theory
  • Edwards' screening
  Exercise #7
   
• Lecture 13 (19/1/04)
  • Semidilute theta solutions
  • Osmotic pressure in dilute and semidilute solutions
  Exercise #8
   
• Lecture 14 (26/1/04)
  Single-chain dynamics
  • Rouse model
  • Zimm relaxation time