1. Kinetic Properties (see Chapter 2 in Shaw, pp. 21-45) Sedimentation and Creaming: Stokes’ Law Brownian Motion and Diffusion Osmotic Pressure Next lecture: Experimental Methods Centrifugal Sedimentation (Chapter 2) Light Scattering (Chapter 3)

2. 11 22 FgFg FbFb FvFv g  2 >  1 sedimentation  2 <  1 creaming Now we need to find an expression for f... Gravitation and Sedimentation: Stokes’ Law Independent of shape No solvation (which changes the density)

3. Stokes’ Law Assumptions: Spherical particles, (no solvation) Particle size much larger than size of particles making up the medium (i.e.much larger than solvent molecules) Infinitely dilute solution Particles travelling slowly (no turbulence)

4. Effects of Non-Sphericity & Solvation absorbs solvent m increases measured f increases Solvation Non-sphericity dry absorbs solvent R s increases measured f increases ideal particle of radius R s sphere excluded by tumbling ellipsoid of same volume is larger R s increases measured f increases

5. Consider quantitatively The actual measured friction factor The ideal friction factor: unsolvated sphere given by Stokes’ law as Minimum possible value of f friction factor for spherical particle having same volume as solvated one of mass m Ratio measuring increase due to asymmetry Ratio measuring increase due to solvation

6. Analyses also exist for the asymmetry contribution but are complex. Sedimentation allows for unambiguous particle mass determination, and upper limits on size and shape. mass of bound solvent

7. Furthermore, if intrinsic viscosity measurements are also performed we can determine unambiguously particle hydration and axis ratio

8. Brownian Motion and Diffusion All suspended particles have kinetic energy 1/2mv 2 = 3/2kT. Smaller the particle, the faster is moves. Moving particles trace out a complex and random path in solution as they hit other particles or walls--Brownian motion (Robert Brown, 1828). Average distance travelled by a particle:

9. Diffusion - tendency for particles to move from regions of high concentration to regions of low concentration.  S > 0, second law of thermodymanics Two laws govern diffusion: From these laws, we may derive (text) Einstein’s law of diffusion (pp.27-29) Fick’s first lawFick’s second law A dm c x

10. No assumptions! Any particle shape or size. D and f determined experimentally Stokes-Einstein equation Assumes spheres No solvation Original use: --finding Avogadro’s number! Note the two are complementary: measurement of diffusion coefficient gives a friction factor with NO assumptions: can determine particle masses

11. Competition between sedimentation and diffusion Note tables 2.1 and 2.2 in the text At particle sizes ca. 10 -7 m radius (0.1  m) the sedimentation is perturbed to a significant step by Brownian motion: i.e particles of this size don’t sediment. Spheres of  2 = 2.0 g/cm 3 in water at 20 o C

12. Experimental Methods Diffusion Constants: Free boundary method Must thermostat (no convection effects) Must remove any mechanical vibration x cdc/dx 0

13. Porous Plug Method