8.592 - HST.452J (Spring 2026)

Statistical Physics in Biology

Lecture 9

Phases of Polymers

1. Interacting polymers:
   • Entropy; excluded volume; and solvent-mediated interactions
   • Mean-field estimate of the partition function
2. Swollen (coil) phase in good solvents
   • Self-avoiding walks on a lattice
   • Flory exponent
   • Scaling behavior in other dimensions
3. Compact (globular) phase in poor solvents
   • Hamiltonian paths
   • 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
   • Levinthal's paradox
   • Designed REM as a model of protein folding

(Lecture notes)