Physical chemistry
Brownian motion
Random motion of small particles in a fluid evidences molecular thermal motion and allows diffusion to be measured.
Small particles jitter because collisions with solvent molecules are momentarily unbalanced. The observed motion is random although molecules obey dynamics.
Diffusion and evidence
Random motion of small particles in a fluid evidences molecular thermal motion and allows diffusion to be measured.
Definition: Core definition
In one dimension, mean-square displacement after time t is 2Dt; D depends on temperature, viscosity and particle size.
Example: Worked example
Apply the model to a simple case: Einstein derived D=kBT/(6πηa) for a sphere of radius a in fluid viscosity η. Tracking many particles over time estimates D and tests diffusion.
Solution
Einstein derived D=kBT/(6πηa) for a sphere of radius a in fluid viscosity η. Tracking many particles over time estimates D and tests diffusion.
In one dimension, mean-square displacement after time t is 2Dt; D depends on temperature, viscosity and particle size.
| Quantity | Model / rule |
|---|---|
| Key relation | Random motion of small particles in a fluid evidences molecular thermal motion and allows diffusion to be measured. |
| Meaning / use | Einstein derived D=kBT/(6πηa) for a sphere of radius a in fluid viscosity η. Tracking many particles over time estimates D and tests diffusion. |
In one dimension, what is the mean-square displacement after time t?
Which statement best matches the model described?
References
- Albert Einstein (1956). Investigations on the Theory of the Brownian Movement