Diffusion over complex potential landscapes is a common problem in many areas of science. In this thesis, I studied the dynamics of single particle diffusion over various potential landscapes. Colloidal spheres in a thin layer over different potential templates are used as an experimental model system and information about the potentials and dynamics of single particles are obtained simultaneously using the techniques of optical microscopy and particle tracking. In the first project, colloidal diffusion over a substrate with micron-sized holes arranged on a quasicrystalline lattice made by photolithography was studied. The particle can be trapped temporarily by the holes and also diffuse freely over the flat portion of the substrate. The measured long time diffusion coefficient D...[ Read more ]

Diffusion over complex potential landscapes is a common problem in many areas of science. In this thesis, I studied the dynamics of single particle diffusion over various potential landscapes. Colloidal spheres in a thin layer over different potential templates are used as an experimental model system and information about the potentials and dynamics of single particles are obtained simultaneously using the techniques of optical microscopy and particle tracking. In the first project, colloidal diffusion over a substrate with micron-sized holes arranged on a quasicrystalline lattice made by photolithography was studied. The particle can be trapped temporarily by the holes and also diffuse freely over the flat portion of the substrate. The measured long time diffusion coefficient D_L is in good agreement with the predictions of two theoretical models, which link D_L to the local properties such as local diffusivities and transition times between traps. In the second project, colloidal diffusion over a more complex potential with both the spatial positions of traps and their barrier heights being randomized was studied. This gravitational random potential is realized by the rugged surface of a randomly close-packed monolayer of bidisperse silica spheres fixed on a glass substrate. The measured D_L of the top diffusing particles is in good agreement with theoretical predictions. The measured mean-squared-displacement reveals a wide subdiffusion region caused by structural disorders. The crossover from subdiffusion to normal diffusion is explained by the Lorentz model. In the third project, the statistical knowledge and tools developed from the previous projects was used to investigate the anomalous diffusion of acetylcholine receptors (AChRs) on live cell membranes. From the measured AChR trajectories, the distribution P(Δx(τ)) of displacement Δx(τ) and the distribution f(δ) of the “instantaneous” diffusion coefficient δ was obtained . By comparing the results with those for colloidal diffusion, we found that the motion of the AChRs has large dynamic heterogeneity, which may arise from the partition of cell membranes by the immobile transmembrane proteins. The short-time subdiffusion of the mobile AChRs may result from active agitations of the cortical actin network. The research presented in this thesis represents a comprehensive and quantitative experimental study of the effects of spatial disorder in the external potential on colloidal diffusion. It also demonstrates that the thin layer colloidal system is a versatile experimental platform for the study of a range of interesting problems in equilibrium diffusion dynamics over complex potential landscapes and non-equilibrium steady-state physics involving external forces.