Fig. 2.

a An example graph of Clausius–Mossotti factor ($f_{\text{CM}}$) of 100 nm diameter silica nanoparticles. The sign of $f_{\text{CM}}$ determines PDEP or NDEP. The critical frequency of the sign is almost 3 MHz in this case. b Schematic diagram of the experiment with arrows for the X- and Z-directions. The phase of electrodes is determined by the simulation in Fig. S1. c Simulation graph of PDEP ($f_{\text{CM}}$ = 1.0) trap energy vs. Brownian motion along the X-axis. $V_{\text{peak}}$ = 1.0 V, 15 MHz frequency of AC voltage, 100 nm diameter of the particle, 2.0 µm gap size, and 2.35 µm outer diameter of the pipette with a 0.7 $R_{\text{inner}}/R_{\text{outer}}$ ratio. The trap energy rapidly increases around the edge of electrodes near the outer diameter of the pipette at ① (±1.175 µm) and substrate at ② (±1.0 µm), so the particles affected by the PDEP force are supposed to move to the edge of the electrodes. The inset image shows an expanded graph near the center; it shows the same direction for the PDEP force. The NDEP case shown in Fig. S3 and the particles affected by NDEP gather around the center near zero. d Simulation graph of the DEP trap energy vs. Brownian motion along the Z-axis with the same conditions as c. The particles affected by PDEP force are supposed to move downward at ⓐ but the particles affected by NDEP go upward. However, in the inset graph, the Brownian motion energy is much bigger than the z-direction DEP trap energy at ⓑ, so particles are not affected by the DEP force in the Z-direction except near ⓐ