1. Ionic solutions:
   • Why do electrolytes dissociate (ionize) in water?
   • The bare Coulomb interaction and the Bjerrum length
   • Acids, bases, and salts
   • The importance of Coulomb repulsion in biological systems
   • Macroions, counterions, salt ions
   • Restricted partition function
2. Statistical treatments of ionic solutions:
• `Mean-field' potential and charge density via the self-consistent Poisson-Boltzmann equation
• Screening in salt solutions
  • Linearized Poisson-Boltzman
  • Debye-Hückel theory
• Dissociation from a charged membrane
  • Solution of the 1d equation
  • The Gouy-Chapman layer
• Interaction between charged parallel plates
• Importance of fluctuations; like charges can attract

1. Polymers are long covalently bonded macromolecules, with N>>1 monomers
• Biological polymers: Polynucleotides, polypeptides, polysaccharides
• Homopolymers, heteropolymers
• Artificial polymers, e.g (-CHH-)N
2. How straight is a polymer?
• Thermal excitation of rotational isomores
• Bending rigidity and Persistence length
3. Entropic elasticity:
   • Random walks, Kuhn segments, and the central limit theorem
   • Polymer spring
4. Interactions:
   • Excluded volume; role of solvent
   • Mean-field estimate of the partition function
   • Applet for self-avoiding walks

1. Interacting polymers:
   • Entropy; excluded volume; and solvent-mediated interactions
   • Mean-field estimate of the partition function
2. Swollen (coil) phase in good solvents
   • Flory exponent
   • Scaling behavior in other dimensions
3. Compact (globular) phase in poor solvents
   • Polymer collapse, theta-point
   • Thermodynamic behavior at the transition; reduction in entropy
4. Frozen (folded) state of heteropolymers
   • The Random Energy Model (REM)
   • The freezing transition and associated singularities
   • Designed REM as a model of protein folding

[Lecture Notes]

[Exercises]

Related links

• DNA-Inspired Electrostatics, Gelbart et al, Physics Today 53, 38 (2000).
• Electrostatics in DNA-peptide complexes; from a course on Principles of Protein Structure
• Ten years of tension: single-molecule DNA mechanic; Bustamante, et al, Nature 421, 423 (2003).
• On Electrostatic Screening; John Marko at Northwestern
• On DNA elasticity; Philip Nelson at UPenn
• The residual potential; Bruce Tidor at MIT