A pinboard by
Youjin Lee

Research Assistant , University of Chicago


Unprecedented Directionality in Random Walk has been Observed in High Aspect Ratio Nanowires

What is Brownian motion?

It is a random motion of a small particle suspended in a medium like water caused by collisions with molecules comprising the medium.
Silicon nanowires (SiNWs) suspended in water were examined using a microscope. Cylindrical NWs with higher aspect ratios than have previously been studied were examined.

How can a random motion be directional?

These SiNWs displayed high anisotropy (or directionality) in their BM. Because the movement along the long axis experiences less drag due to its smaller cross sectional area, we expected the translational diffusivity along the NW’s long axis (D∥) be greater than that along the short axis (D⊥). In our experiment, the quotient values (D∥/D⊥) obtained from 30 different NWs ranged between 2 and 25, which exceeded those of previously reported smaller aspect ratio particles in non-crowded environments. Interestingly, no theoretical expressions gave D∥/D⊥ higher than 2: all the theories for diffusion of rods converged monotonically to a limit less than 2.

Can NEW PHYSICS be Understood?

The new empirical results highlight the lack of robust theories for understanding diffusion of high aspect ratio particles. Regression analysis of my experimental result for translational BM of the NWs showed a clear deviation from the Stokes-Einstein relation, which relates diffusivity of a spherical particle to its radius. Experimental data will serve as an integral part to expand old theories and to shed light on the physics of high aspect ratio particle


Brownian motion: from kinetics to hydrodynamics

Abstract: Brownian motion has served as a pilot of studies in diffusion and other transport phenomena for over a century. The foundation of Brownian motion, laid by Einstein, has generally been accepted to be far from being complete since the late 1960s, because it fails to take important hydrodynamic effects into account. The hydrodynamic effects yield a time dependence of the diffusion coefficient, and this extends the ordinary hydrodynamics. However, the time profile of the diffusion coefficient across the kinetic and hydrodynamic regions is still absent, which prohibits a complete description of Brownian motion in the entire course of time. Here we close this gap. We manage to separate the diffusion process into two parts: a kinetic process governed by the kinetics based on molecular chaos approximation and a hydrodynamics process described by linear hydrodynamics. We find the analytical solution of vortex backflow of hydrodynamic modes triggered by a tagged particle. Coupling it to the kinetic process we obtain explicit expressions of the velocity autocorrelation function and the time profile of diffusion coefficient. This leads to an accurate account of both kinetic and hydrodynamic effects. Our theory is applicable for fluid and Brownian particles, even of irregular-shaped objects, in very general environments ranging from dilute gases to dense liquids. The analytical results are in excellent agreement with numerical experiments.

Pub.: 02 Jun '17, Pinned: 28 Jun '17