Colloidal diffusion over a quasicrystalline-patterned surface

Abstract

We report a systematic study of colloidal diffusion over a substrate with quasicrystalline-patterned holes. Silica spheres of diameter comparable to the hole diameter diffuse over the patterned substrate and experience a gravitational potential U(x, y). Using optical microscopy, we track the particle trajectories and find two distinct states: a trapped state when the particles are inside the holes and a freediffusion state when they are on the flat surface outside the holes. The potential U(x, y) and dynamic properties of the diffusing particle, such as its mean dwell time, mean square displacement, and longtime diffusion coefficient D L , are measured simultaneously. The measured D L is in good agreement with the prediction of two theoretical models proposed for diffusion over a quasicrystal lattice. The experiment demonstrates the applications of this newly constructed potential landscape.

Lattice diffusion of a single molecule in solution

“…In order to validate our simulations against theoretical expectations, we apply a mean-squared-displacement (MSD) analysis to about five particle trajectories and extract effective lattice diffusion coefficients, D eff , for the particle. We verify that the simulated D eff values satisfy the Lifson-Jackson relation in both one and two dimensions for values of W ranging from 3 to 8 k B T [29,33] [34] and demonstrated a measurement of the effective diffusion coefficient, D eff , of a particle [9]. However, knowledge of D eff alone yields neither the well depth, W, nor the particle's free diffusion coefficient, D, which reflects its hydrodynamic radius, r H .…”

“…Our goal is to accurately determine both the trapped and free diffusive time scales for a single particle migrating in a periodic lattice in order to obtain measures for both W and D (r H ) from a single transport trajectory. A recent study on colloidal particle transport in a quasicrystalline lattice illustrates the subtleties involved and shows how the lack of crystalline order in the landscape introduces more complex free diffusive behavior, thus necessitating averaging over an ensemble of particles in order to measure both W and r H [34].…”

Active colloidal propulsion over a crystalline surface

“…Pt-coated) surfaces. Our study touches also fundamental questions concerning hydrodynamic coupling phenomena in the lubrication regime [22] and non-equilibrium transport near crystalline [33] or quasi-crystalline [34] surfaces.…”

Transport of a colloidal particle driven across a temporally oscillating optical potential energy landscape

“…Creating a model system of colloidal particles in an optical potential energy landscape leads to a far more accessible system with increased control. Particle motion across random potential energy landscapes has led to observed subdiffusion [15][16][17][18][19][20], which can be controlled with surface roughness [15]. Exact particle motion has been shown to heavily rely on the form of the landscape and can give rise to freely diffusive as well as trapped particles [16,21].…”

“…Particle motion across random potential energy landscapes has led to observed subdiffusion [15][16][17][18][19][20], which can be controlled with surface roughness [15]. Exact particle motion has been shown to heavily rely on the form of the landscape and can give rise to freely diffusive as well as trapped particles [16,21]. Further to this, the study of colloidal particle transport across periodic potential energy surfaces has led to many interesting observations such as subdiffusion [22,23], superdiffusion [23][24][25][26], ballistic motion [26,27] and synchronisation [28][29][30].…”