E M Terentjev

  • Introduction:
    What is soft matter? Forces, energies and timescales.
  • Elements of fluid dynamics:
    Navier-Stokes equation; Reynolds number; Laminar and boundary layer flows; Stokes Law and drag; Viscosity of a hard sphere suspension; Hydrodynamic interaction between colloidal particles; Implications for living systems; How bacteria swim.
  • Viscoelasticity and Brownian motion:
    Non-Newtonian behaviour; Idea of complex viscosity; Linear viscoelasticity; Simple phenomenological models pf viscoelastic response. Stochastic force and Langevin equation; Free Brownian motion; Brownian motion in external potentials; Diffusion equation; Fokker-Planck and Smoluchowski equations; Kramers problem - escape over a potential barrier.
  • Surface energy and interactions:
    Surface energy and tension; Cahn-Hilliard model of a liquid interface; Wetting: Young’s equation and contact angles; Hydrophobicity and hydrophilicity; Electrolyte solutions: Debye-Huckel theory; Interactions between colloidal particles, DLVO potential.
  • Self assembly:
    Chemical potential of systems that aggregate; Aggregation equilibria; Aggregation of amphiphilic molecules; Critical micelle concentration; Shape of micelles; Lipid bilayers; Nature of the cell membrane; Curvature elasticity; Fluctuations of membranes; Examples of self assembly: viruses and nanotechnology.
  • Polymers and biological macromolecules:
    Examples of polymers; Single-chain statistics, self-avoiding walks; Gaussian correlations in the chain; Entropic forces and excluded volume; Wormlike (semiflexible) chain and persistence length, DNA; Single chain in good and poor solvents: coil-globule transition and protein folding; Phase transitions: Flory Huggins free energy for solutions; Good, {theta} and poor solvent conditions; Osmotic pressure in dilute conditions; Scaling in semi-dilute solutions; Chain dynamics: Rouse model; Rubber elasticity.