User:Benjah-bmm27/degree/4/PB

=Soft Matter II, PB= =Diffusion=

RMS displacements
=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

=Microscopic expressions for the diffusion constant, D=

Diffusion on macroscopic scales is very slow
=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 + &tau;
 * If &tau; is short enough, the two intensities will be correlated (i.e. similar)

$$g_2(q,\tau) = \left ( \frac{ \left \langle I(q,t)I(q,t+\tau) \right \rangle }{ \left \langle I(q) \right \rangle ^2 } \right )$$
 * The normalised IACF is

Rotational diffusion
=Optical tweezers=