THESIS
2014

xiv, 136 pages : illustrations ; 30 cm

**Abstract**
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 ≃ k

_{0}ve

^{-Eb/kBT}, links the reaction rate k to the energy barrier height E

_{b} with k

_{0} 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...[

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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 ≃ k

_{0}ve

^{-Eb/kBT}, links the reaction rate k to the energy barrier height E

_{b} with k

_{0} 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

_{B}T). 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.

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