1. Transport Phenomena and Diffusion (24.1-24.2) Net motion of particles occurs when a system is disturbed from equilibrium (e.g., concentration gradients)concentration gradients – Flux is the movement of particles through a given area in a given amount of time – Flux opposes concentration gradients (i.e., it restores equilibrium) Diffusion is the natural motion of particles in response to a spatial concentration gradient – Particles naturally want disperse into an even distribution in space (e.g., odors from volatile liquids) Fick’s first law relates particle flux to spatial concentration gradients – Diffusion coefficient (D) is related to how large the flux is, which in turn determines how quickly equilibrium is re-established (related to physical properties of particles)

2. Concentration Gradients and Equilibrium (24.3) Flux is related to how quickly equilibrium is accomplished – Larger flux allows equilibrium to be established faster (depends on D and conc. gradient) – Fick’s second law relates concentration changes to time and spaceconcentration changes The root mean square (rms) distance is a measure of how far particles translate in the system in a given amount of time – Particles don’t move in a linear fashion due to collisions, they go on random walksrandom walks – The distance particles travel depends on how much time has passed (t) and on how quickly the particles diffuse (D) Since D is so important, how do we relate it to easy to understand physical quantities? – We use classical physics (whew!)

3. Diffusion Coefficients and Friction (24.5) Einstein came up with a relationship for the diffusion coefficient and other physical quantities – Diffusion rates depend on temperature and on the frictional forces of the medium in which the particle moves For spherical molecules, the frictional force has a simple form (Stokes- Einstein) – Friction is proportional to the size of the molecule and the viscosity of the medium Biomolecules are not usually spherical, but frictional forces are still useful – The fraction of the true frictional force to that of the idealized sphere (f/f 0 ) is always greater than one (shape or Perrin factors) – Shape of biomolecules can be elucidated from the shape factors

4. Concentration Gradient and Flux

5. Concentration Gradients and Time

6. Time Evolution of Diffusion

7. RMS Displacement and Random Walks