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*Suspensions and polymer solutions*

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Advanced course, Semester B, 2010/2011

0351.4809

Wednesdays 16:00-19:00, Ornstein 110

**Announcements:**

Contact the lecturer

Mailing
list

Course fact sheet including detailed syllabus

Bibliography

**Prerequisites:**
*Statistical Thermodynamics* (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** (23/2/11)
- Introduction: particulate liquids
- Electrostatic interactions:
- Poisson-Boltzmann theory
- Debye-Huckel approximation
- potential near a charged plane

**Lecture 2** (2/3/11)
- Electrostatic interactions (cont.):
- potential near a charged plane - nonlinear theory
- potential near a charge sphere
- interaction between two charged planes

Exercise #1
Solution #1

**Lecture 3** (9/3/11)
- Derjaguin approximation (force between curved surfaces)
- Electrostatic interaction between two charged spheres
- van der Waals interactions between molecules

**Lecture 4** (16/3/11)
- van der Waals interaction between molecules (cont.)
- van der Waals interaction between two planes; between two spheres

Exercise #2
Solution #2

**Lecture 5** (23/3/11)
- DLVO theory of suspension stability
- Additional interactions
- Depletion interaction

Exercise #3
Solution #3

**Lecture 6** (30/3/11)
- Brownian motion: random walk, Langevin equation, Einstein relation

**Lecture 7** (6/4/11)
- Stokes-Einstein fromula
- Hydrodynamics: Navier-Stokes equation, Reynolds number
- Hydrodynamics: Oseen tensor

**Lecture 8** (13/4/11)
- Hydrodynamic interactions: pair mobility, correlated Brownian motion, pair diffusivity
- Models of single polymer chains: rotational-isomeric chain

Exercise #4
Solution #4

**Lecture 9** (27/4/11)
- Gaussian chain; Kuhn length
- Semiflexible polymer; persistence length
- Worm-like chain
- Stretching a biopolymer

Exercise #5
Solution #5

**Lecture 10** (4/5/11)
- Stretching a biopolymer (cont.)
- Relevance of interactions in real chains

**Lecture 11** (11/5/11)
- Relevance of interactions (cont.): fractal dimension
- Flory argument; swelling exponent
- Solvent quality
- Theta collapse
- Scaling theory for single chains: thermal blobs

Exercise #6
Solution #6

**Lecture 12** (18/5/11)
- Scaling theory for single chains: tension blobs
- PDF of a real chain
- Many chains: Flory-Huggins theory

Exercise #7
Solution #7

**Lecture 13** (25/5/11)
- Flory-Huggins theory:
- Phase separation
- Melts; screening of correlations

Exercise #8
Solution #8

**Lecture 14** (1/6/11)
- Semi-dilute solutions: scaling theory; Edwards' screening
- Generic phase diagram of a polymer solution