Brownian Motion

(0.5,1.1, and 1.9 polystyrene particles in water, from Exploring Squishy Mterials at Emory University)

Robert
Brown, Phil. Mag. **4**, 171 (1828)

- Irregular motions of small grains in water were observed soon after advent of microscopes.
- Early microscopy observations were interpreted as motions of living creatures.
- Brown showed that inorganic grains in suspension show similiar irregular motion.

Exploring Squishy Mterials at Emory University (Brownian Motion Movies - offline)

A.
Einstein, Ann. d. Physik **17**, 549 (1905)

- "Investigations on the theory of the Brownian Movement:"
- The large particle performs random motion as a result of collisoins with smaller (unseen) particles.
- A plethora of Java Applets to demostrate this:
- Michael Fowler Physics Applets (Virginia) (offline)
- Sturm/Dolgert (UCSB) (offline)
- Wolfgang Christian (Davidson)
- Mai Zhou (Kentucky)

Langevin
(C.R. Acad. Sci **146** 530, 1908) equation for the particle:

- For a sphere of radius a , in a fluid of viscosity η , the mobility is given by μ=1/(6πηa)
- The stochastic force is uncorrelated at different times, <f(t)
f(t')>∝δ(t-t')D ,
where D is the diffusion coefficient.

- To ensure the correct Maxwell-Boltzmann distribution at
a temperature T
,
mobility and diffusion must be related by

Jean Baptiste Perrin was awarded the 1926 Nobe Prize (lecture, offline) for expeimental verification (1905-12)