Abstract

Abstract People Publications Cooperations Alumni

S. Matthias and F. Müller

Introduction

Brownian motion is omnipresent in the movement of mesoscopic particles, but it does not only lead to random motion - it may also enable mechanisms of directed motion. These mechanisms are exploited by nature in many biological processes like molecular motors or intra-cell transport. In manmade devices directed particle transport has been demonstrated for several variants of ratchet concepts in one or two dimensions like molecular motors or quantum ratchets. These experiments have proven the validity of the basic concept in many fields of physics, chemistry and biology. We present a first experimental realization of a massively parallel system based on a three-dimensional arrangement of one-dimensional ratchets in macroporous silicon. Applying a periodic pressure profile with zero mean value causes a periodic flow of water and suspended particles through ratchet-shaped channels. A net motion for the colloidal particles is observed although the liquid itself is not moving on average. The pressure dependence agrees well with microscopic calculations and exhibits the predicted current inversion with a remarkably narrow transition region. The highly efficient transport due to many stages in series and the potentially high throughput due to the millions of pores acting in parallel are the main advantages of the new device.

Setup and samples

Our experimental setup consists of two basins filled with water and dispersed particles. The basins are separated by a horizontally mounted ratchet membrane (Fig. 1). Whereas the upper basin is open, the lower one is closed and connected to an electrically driven pressure oscillator. The pore arrays were grown by a photo-electrochemical etching process, which has been extended to allow very strong diameter modulations. The luminescent particles were commercial polystyrene spheres with well-defined diameters of 0.1 µm, 0.32 µm, 0.53 µm and 1 µm, respectively. The total number of particles in the upper basin was measured by photoluminescence (PL).

Fig. 1. Experimental setup:a: Schematic representation. The horizontally mounted membrane structure with asymmetric diameter modulated pores separates 2 basins (U) and (L).b: Scanning electron micrograph of a cleaved modulated macroporous silicon wafer. The macropores are arranged in a triangular lattice with a pitch of 6 µm and a depth of about 150 µm.c: Scanning electron micrograph of a cleaved modulated macroporous silicon ratchet membrane. After drying, some colloidal spheres with a diameter of 1 µm stick to the silicon surface. The maximum pore diameter is 4.8 µm and the minimum 2.5 µm. The length of one period is 8.4 µm.

Fig. 2. Schematic cross­-section of the setup. The carrier liquid, including the dispersed particles of different size, is driven periodically through the membran with the asymmetrically shaped pores. After some time different sized particles accumulate in different basins. Click to view as an animation (gif).

Results

We modulated our whole experiment and toggled the driving pressure oscillations on and off every 60 seconds to exclude long term drifts caused, e. g., by water evaporation. Additionally, by this toggling we get more information on the system. Together with the macroscopic simulations presented below, this helps to understand in more detail the drift and diffusion contributions.

In figure 3a the curve labeled U shows the evolution of the PL-signal, starting from a homogenous particle distribution. The "on"-phases of the cycles are highlighted in grey. Switching on for the first time at t = 60 s, the PL signal starts to increase nearly linearly with time. After 60 s the total PL intensity and therefore the total number of particles in the upper basin has increased by about 8%. Turning off the periodic pressure oscillations leads to a nearly constant signal. Only a very slight decrease is visible. Repeating this cycle several times, we observe an increase of the signal during the "on"-phases of the cycles although for longer times the number of added particles is reduced. On the other hand, during the "off"-phases the number of vanishing particles strongly increases with time. The profile changes from a stepwise function to a sawtooth like behaviour and suggests the onset of a mechanism that pushes the particles back into the membrane.

To understand the experimental data of Fig. 3a, we modelled the macroscopic system by a one-dimensional diffusion equation for the particle density n(z,t).