Lecture Information

Time&Place 11/29 (水) 13:30-15:00, 15:30-17:00 (Physics Building, Lecture Room #1)
11/30 (木) 13:30-15:00, 15:30-17:00 (Physics Building, Lecture Room #2)
Lecturer Prof. David Andelman
Affiliation School of Physics and Astronomy, Tel Aviv University
Title An introduction to electrostatics of soft and biological matter: electrolytes, polyelectrolytes and membranes
Abstract It is hard to under-estimate the crucial role that electrostatics (along with magnetism) plays in all physical, chemical and biological phenomena and processes. In a series of three lectures I will explain some of the key ingredients that are of importance when charges interact in liquids and in soft matter. At room temperature thermal fluctuations, and hence entropy of various conformational and translational degrees of freedom, will compete with electrostatic interactions giving rise to complex and sometimes poorly understood effects.
I will give an introduction to electrostatics in soft and biological matter. I will consider the theory and modeling and refer to experiments in a qualitative and phenomenological way. The lectures are intended for graduate and post-graduate students who are interested in the field and require knowledge of electromagnetism, statistical mechanics and thermodynamics. Other concepts and phenomenology will be clarified during the lectures.

The topics

0. Ions in solutions: free energies, boundary conditions, important
   length scales: Bjerrum length, Debye-Huckel length.

1. Explanation of the electric double layer problem.
 a. The Poisson-Boltzmann (PB) equation and its linearized Debye-Huckel form.
 b. Its solution in several cases: one flat charged surface, two flat charge surfaces and the pressure between them, counterions only case and added salt.
 c. Symmetric charged plates and non-symmetric ones.

2. Modifications of the PB theory to include finite size of ions, correlations and fluctuations.

3. Models of Polyelectrolytes (one dimensional systems).
 a. The chain persistence length.
 b. The PB solution for a rigid rod (cylinder) via the Katchalsky solution.
 c. the Manning-Oosawa condensation as a mapping from the cylinder to the asymmetric planar case.
 d. As an example: attractive interactions between DNA molecules in presence of multi-valent counterions.

4. Charged and flexible membranes and interfaces (two-dimensional systems)
 a. The bending rigidity of charged membranes.

5. Adsorption of macromolecules on charged surfaces.

6. Charged colloids and the DLVO theory (three dimensional systems)
 a. The PB solution for a charged sphere.
 b. Renormalization of the sphere charged in solution.