1. Particle Sizing by DLS

2. DLS by Particles of Different Sizes particle of radius R 1 particle of radius R 2 total distribution function of  weighted by the scattering intensity intensity

3. Analysis of Autocorrelation Functions 1. Cumulant expansion (Unimodal analysis) 2. Inverse-Laplace transform (SDP analysis)

4. Cumulant Expansion (Unimodal analysis) where 1st cumulant 2nd cumulant Curve fitting by a second -order polynomial yields the coefficients. (polydispersity)

5. Inverse-Laplace Transform (SDP Analysis) is the Laplace transform of G(  ).

6. Examples of Inverse-Laplace Transform monodisperse unimodal distribution bimodal distribution

7. Relationship between Unimodal Analysis and SDP Analysis harmonic average weighted by the scattering intensity

8. Example of a Bimodal Distribution What is the average radius (estimated by DLS) for an equal mass mixture of spheres of two radii R 1 and R 2 ? Assume R 1 = 10 nm and R 2 = 100 nm. The average depends on k. Plot as a function of . Plot G 2 /G 1 as a function of .

9. Diffusion vs. Internal Relaxation

10. Examples of Internal Relaxation Rotation of a rodlike moleculeRouse normal modes Elastic motions of a gelReacting system