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*Suspensions and polymer solutions*

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Advanced course, Semester A, 2006/2007

0351.4809

Mondays 10:00-13:00, Ornstein 102

**Announcements:**

Contact the lecturer

Mailing
list

**Course fact sheet including detailed syllabus**
(pdf
doc)

Bibliography

**Prerequisites:**
*Thermodynamics & Statistical Mechanics* (chemistry students)
or *Thermal Physics* (physics students)
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General agenda

- Interactions between suspended particles; suspension stability
- Dynamics of suspensions
- Models of chain-like molecules
- Phase diagrams and phase transitions of polymer solutions
- Polymer dynamics
- Biopolymers

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Program

**Lecture 1** (23/10/06)
- Introduction: particulate liquids
- Electrostatic interactions: Poisson-Boltzmann theory, Debye-Huckel approximation, potential near a charged plane

Exercise #1
Solution #1

**Lecture 2** (30/10/06)
- Electrostatic interactions (cont.): potential near a charged
sphere, interaction between two charges planes

**Lecture 3** (6/11/06)
- Derjaguin approximation (force between curved surfaces)
- Electrostatic interaction between two charged spheres
- van der Waals interactions: Keesom interaction, Debye interaction, London (dispersion) interaction

Exercise #2
Solution #2

**Lecture 4** (13/11/06)
- van der Waals interaction (cont.): interaction between two planes, interaction between two spheres
- DLVO theory of suspension stability
- Additional interactions
- Depletion interaction

Exercise #3
Solution #3

**Lecture 5** (20/11/06)
- Brownian motion: random walk, Langevin equation, Einstein relation, Stokes-Einstein fromula
- Hydrodynamics: Navier-Stokes equation, Reynolds number

**Lecture 6** (27/11/06)
- Hydrodynamics (cont.): Oseen tensor
- Hydrodynamic interactions: pair mobility, correlated Brownian motion, pair diffusivity

Exercise #4
Solution #4

**Lecture 7** (7/12/06)
- Hydrodynamic screening and effective viscosity of a suspension

**Lecture 8** (11/12/06)
- Models of single polymer chains:
- Rotational-isomeric chain
- Freely jointed chain; Gaussian chain
- Freely rotating chain
- Semiflexible polymer; persistence length
- Worm-like chain

Exercise #5
Solution #5

**Lecture 9** (18/12/06)

**Lecture 10** (1/1/07)
- Relevance of interactions in real chains; fractal dimension
- Flory argument; swelling exponent
- Solvent quality
- Theta collapse

Exercise #6
Solution #6

**Lecture 11** (8/1/07)
- Scaling theory for single chains
- Thermal blobs
- Tension blobs

- Many chains: Flory-Huggins theory

Exercise #7
Solution #7

**Lecture 12** (15/1/07)
- Flory-Huggins theory:
- Phase separation
- Melts; screening of correlations

- Semi-dilute solutions: scaling theory; Edwards' screening
- Generic phase diagram of a polymer solution

Exercise #8
Solution #8

**Lecture 13** (22/1/07)