Finding a relationship between the transport coefficient of a molecule and its surrounding energy landscape has always being an interesting and challenging problem in physics, chemistry and biology. The well-known Arrhenius-Kramers equation, k ≃ k₀ve^-E_b/k_BT, links the reaction rate k to the energy barrier height E_b with k₀ being an attempt frequency and ν the Arrhenius pre-factor. However, direct experimental investigations on Arrhenius-Kramers-like equations are rare because it is quite difficult to obtain information about the energetics and transport coefficients simultaneously at the single-particle level. In this thesis, I report three related experiments using colloidal monolayers as a model system to study colloidal diffusion over different energy landscapes. In the first...[ Read more ]

Finding a relationship between the transport coefficient of a molecule and its surrounding energy landscape has always being an interesting and challenging problem in physics, chemistry and biology. The well-known Arrhenius-Kramers equation, k ≃ k₀ve^-E_b/k_BT, links the reaction rate k to the energy barrier height E_b with k₀ being an attempt frequency and ν the Arrhenius pre-factor. However, direct experimental investigations on Arrhenius-Kramers-like equations are rare because it is quite difficult to obtain information about the energetics and transport coefficients simultaneously at the single-particle level. In this thesis, I report three related experiments using colloidal monolayers as a model system to study colloidal diffusion over different energy landscapes. In the first experiment, the gravitational energy landscape U(x, y) on the corrugated surface of a colloidal crystal is characterized using the Boltzmann distribution. Simultaneously, we also measure the mean first passage time t_R and diffusion coefficient D of the colloidal particles diffusing on top of the colloidal crystal. The experimental results verify the exact solution of Lifson and Jackson, and demonstrate that the Arrhenius-Kramers equation works well only for large energy barriers ( E_b ≳ 6-7k_BT). The second experiment studies the mean drift velocity v, diffusion coefficient D, and the probability distribution function (PDF) of the diffusing particles over a tilted periodic energy landscape, so that the energy barrier is lowered in the direction of the gravitational forcing. In addition to testing the exact results of Stratonovich and Reimann, we also use the steepest-descent approximation to obtain an Arrhenius-Kramers-like scaling law for v and D. A good agreement is found between the experimental and theoretical results. In the third experiment, I study the universal scaling law of diffusion at the single part level using colloidal monolayers suspended at/near different liquid-liquid and liquid-solid interfaces. It is found that the universal scaling law proposed by Dzugotov holds for highly charged colloidal suspensions where the strong electrostatic force dominates the colloidal interaction. For hard-sphere-like particles, however, deviations from the scaling law are observed due to the hydrodynamic interactions between the colloidal particles.