User:Benjah-bmm27/degree/4/PB

Microscopic dynamics of single particles

Brownian motion

• Brownian motion
• A single diffusing particle can be modelled by a 3D random walk model

Comparison of random walk with bulk diffusion

• Particles flow from higher to lower concentrations only because of probabilities
• Distance travelled depends on √t rather than just t because of this stochastic nature
• Particles ultimately move in the direction that has fewer collisions

Dynamic light scattering

Intensity autocorrelation function

• The IACF is quite complicated
• It compares scattered light or X-ray intensity at time t with that at time t + τ
• If τ is short enough, the two intensities will be correlated (i.e. similar)

• The normalised IACF is

$g_{2}(q,\tau )=\left({\frac {\left\langle I(q,t)I(q,t+\tau )\right\rangle }{\left\langle I(q)\right\rangle ^{2}}}\right)$