Nanometer-Scale-Resolution Multichannel Separation of Spherical Particles in a Rocking Ratchet with Increasing Barrier Heights

Philippe Nicollier, Christian Schwemmer, Francesca Ruggeri, Daniel Widmer, Xiaoyu Ma, and Armin W. Knoll

Phys. Rev. Applied 15, 034006 – Published 2 March 2021

Abstract

We present a nanoparticle size-separation device based on a nanofluidic rocking Brownian motor. It features a ratchet-shaped electrostatic particle potential with increasing barrier heights along the particle transport direction. The sharp drop of the particle current with barrier height is exploited to separate a particle suspension into multiple subpopulations. By solving the Fokker-Planck equation, we show that the physics of the separation mechanism is governed by the energy landscape under forward tilt of the ratchet. For a given device geometry and sorting duration, the applied force is thus the only tunable parameter to increase the separation resolution. For the experimental conditions of 3.5 V applied voltage and 20 s sorting, we predict a separation resolution of approximately $2$ nm, supported by experimental data for separating spherical gold particles of nominal diameters of 80 and 100 nm.

Received 24 March 2020
Revised 10 November 2020
Accepted 25 January 2021

DOI:https://doi.org/10.1103/PhysRevApplied.15.034006

Physics Subject Headings (PhySH)

Brownian motion Classical transport Confinement Diffusion Electrostatic double layer forces Nanofluidics Particle-laden flows

Nanoparticles

Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Philippe Nicollier ^†, Christian Schwemmer ^†, Francesca Ruggeri , Daniel Widmer, Xiaoyu Ma, and Armin W. Knoll ^*

IBM Research—Zurich, Säumerstrasse 4, Rüschlikon 8803, Switzerland

^*ark@zurich.ibm.com
^†These authors contributed equally to this work.

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Vol. 15, Iss. 3 — March 2021

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Images

Figure 1
(a) Schematic side view of the nanofluidic slit (not to scale). A central pillar of $40 μ m$ in height is etched from a cover slip and surrounded by four Cr–Au electrodes. The ratchet structure in ${Si O}_{2}$ is covered with a thin layer of OTL polymer. (b) Topography of the sorting device in PPA after $t$ -SPL patterning. From the inclined ratchet (top), particles can be driven into reservoirs (R1 to R19) by linear ratchets after being sorted. Force and diffusivity are measured in D1. (c) Cross section through the device after transfer to ${Si O}_{2}$ measured by atomic force microscopy. The 19 teeth in the sorting ratchet span a vertical distance of 28 nm, corresponding to $Δ z = 1.6$ nm per tooth. (d) Extrapolated potential $V_{\exp} (x)$ for a gap distance of $64 \pm 2$ nm (black dots) and the input potential $V_{sim} (x)$ for simulating the device (red line). We use an initial probability density $ρ_{0} (x) \propto \exp [- V (x) / k_{B} T]$ with $0 < x < 10 μ m$ (dashed line) for our simulations (violet).
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Figure 2
(a) Top: iSCAT images of the sorting process after 1, 10, and 20 s of an applied ac voltage of 3.5 V at 5 Hz. Bottom: comparison of the experimental, $P_{\exp} (n)$ , and simulated, $P_{sim} (n)$ , particle distributions. (b) Expected average travel distance for particles of radii between 25 and 35 nm with 1 nm difference in radius as a function of time. (c) Simulated probability distribution $P_{r} (n)$ after 20 s of sorting. The width of the distributions of single particle types, marked by separate colors, indicates the simulated resolution of the sorting device. The color code corresponds to that used in (b).
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Figure 3
(a) Forward bias potential barriers for particles with radius 35 to 25 nm (left to right) and a force of $20.7 k_{B} T / μ m$ (colored lines). The intercept with the black lines marks the average travel distances and barrier heights reached after 5, 10, 15, and 20 s. (b) Standard deviation $σ_{r}$ of the radius distribution in the central tooth for each particle size. The inset shows an enlarged view for longer sorting durations. (c) Remaining energy barriers under forward bias for particles with a radius of 30 nm and applied forces of 15, 20, 25, and $30 k_{B} T / μ m$ . (d) $σ_{r}$ as a function of applied force and different separation durations.
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Figure 4
(a) SEM (left) and AFM (right) scans of the different particle types present in a mixture with nominal radii of 40 and 50 nm. The white scale bar indicates 100 nm. (b) AFM scan across particles from (a). (c) Quantification of the sorting, with colors corresponding to the particle types shown in (b). The spherical particles (red) follow a linear trend of particle radius $r$ and tooth number $n$ . The slope of the dashed line is obtained from simulation and its position is shifted in $r$ to obtain a good fit to the data. The shaded area corresponds to a width of $\pm 2 σ_{r}$ . The plates (blue) and diamonds (green) show a different behavior because they experience a reduced interaction energy compared with spherical particles.
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