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Soft Matter II, PB[edit]
Diffusion[edit]
Particle flux[edit]
Concentration gradients cause fluxes[edit]
Diffusion from a point source[edit]
RMS displacements[edit]
Microscopic dynamics of single particles[edit]
Brownian motion[edit]
- Brownian motion
- A single diffusing particle can be modelled by a 3D random walk model
Comparison of random walk with bulk diffusion[edit]
- 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[edit]
Friction in fluids[edit]
Effect of shape on friction coefficients[edit]
Einstein-Smoluchowski equation[edit]
Diffusion constants[edit]
Characteristic time for diffusion[edit]
Diffusion on macroscopic scales is very slow[edit]
Dynamic light scattering[edit]
Formation of a speckle pattern[edit]
Twinkling[edit]
Instrumentation[edit]
Intensity autocorrelation function[edit]
- 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)
Analysis of DLS data to determine diffusion constant[edit]
Rotational diffusion[edit]
Optical tweezers[edit]
How optical traps work[edit]
Applications: evidence for reptation[edit]
Nano-building blocks[edit]
