Soft electrostatic trapping in nanofluidics

Trapping and manipulation of nano-objects in solution are of great interest and have emerged in a plethora of fields spanning from soft condensed matter to biophysics and medical diagnostics. We report on establishing a nanofluidic system for reliable and contact-free trapping as well as manipulation of charged nano-objects using elastic polydimethylsiloxane (PDMS)-based materials. This trapping principle is based on electrostatic repulsion between charged nanofluidic walls and confined charged objects, called geometry-induced electrostatic (GIE) trapping. With gold nanoparticles as probes, we study the performance of the devices by measuring the stiffness and potential depths of the implemented traps, and compare the results with numerical simulations. When trapping 100 nm particles, we observe potential depths of up to Q≅24 kBT that provide stable trapping for many days. Taking advantage of the soft material properties of PDMS, we actively tune the trapping strength and potential depth by elastically reducing the device channel height, which boosts the potential depth up to Q~200 kBT, providing practically permanent contact-free trapping. Due to a high-throughput and low-cost fabrication process, ease of use, and excellent trapping performance, our method provides a reliable platform for research and applications in study and manipulation of single nano-objects in fluids.


DEVICE FABRICATION
All features were patterned on a silicon wafer with a thermally grown SiO 2 layer of 400 nm thickness (Supplementary Figure S2a). To etch the microfluidic reservoir channels, inlets, outlets and the alignment markers, a chromium layer of 120 nm (Univex 450, Leybold GmbH, 50968 Koeln, Germany) was first evaporated, which served as a hard mask during the RIE etching of the deep channels. After spin-coating a photoresist (Microposit S1813, Dow (Shipley), Newark, DE 19713, USA; 2000 rpm, 500 rpm/s, 40 s) and UV-light exposure (Suess MA 6, Suess Microtec AG, 85748 Garching, Germany; λ = 365 nm, 120 mJ/cm 2 , 12 s) using a chromium mask (Compugraphics Jena GmbH, 07751 Jena, Germany) with the design of the microfluidic system, the wafer was developed in MF-24A (Shipley, Megaposit MF-24A, Dow (Shipley)) for 40 s. The structures were etched through the chromium layer (BMP Plasmatechnology GmbH, O 2 :Cl 2 with a ratio of 5:1) and further etched 3 μm into the SiO 2 (Ar 38 sccm, CHF 3 12 sccm, 100 W) and Si (SF 6  acetone and the wafer was cleaned in a piranha bath (H 2 SO 4 (%): H 2 O 2 (%) = 2:1) for 20 min at 90°C. The remaining chromium was dissolved in chromium mask etchant (Chrome ETCH No. 1, Microchemicals GmbH, 89079 Ulm, Germany) and the wafer was rigorously rinsed in DI water and dried under a nitrogen air stream. To further fabricate the nanofluidic GIE trapping region, a new chromium layer of 25 nm was evaporated on the silicon wafer. This layer was again used as a hard mask for RIE etching. After spin-coating PMMA (PMMA 950 k, Allresist GmbH, 15344 Strausberg, Germany; 4 % ethylacetate; 4000 rpm, 1000 rpm/s, 60 s) on the chromium layer, the design of parallel channels of 10 μm width and 0.5 mm length including supporting pillars were exposed using e-beam lithography (Vistec EBPG 5000 Plus, Vistec Electron Beam GmbH, 07743 Jena, Germany), developed in a mixture of methyl isobutyl ketone and isopropyl alcohol (MIBK: IPA = 1:2 (v/v), 60 s) and etched into the chromium hard mask using BMP. After removing the PMMA layer in acetone, the channels were further etched 160 nm or 210 nm deep into the silicon dioxide layer, using RIE as shown in Supplementary Figure S2c   (a) Schematics of the PDMS-based nanofluidic device demonstrating the path of the incident laser beam (green) and the fields scattered from the nano-object and reflected from the glasswater and water-PDMS interfaces. Similar to glass-based nanofluidic systems, PDMS devices have a reduced reflection of the incident beam, which leads to higher SNR and contrast imaging using iSCAT. (b) Example of iSCAT images and the corresponding contrast profiles of 60, 80 and 100 nm gold particles as used in this paper. The contrast profiles were multiplied by 1/2, 1/3 and 1/5 for better visualization. (c) Mean contrast and SNR measurements as a function of particle diameter.

Figure S4
Standard deviation of the intensity fluctuation of the 100 nm Au NP trapped at different applied compression pressures. Figure S2d). The wafer was cleaned in a freshly made piranha solution (H 2 SO 4 (%):H 2 O 2 (%) = 2:1 (v/v)) and silanized (mixture of trichloro(1H, 1H, 2H 2H-perfluorooctyl)-silane and (tridecafluoro-1,1,2,2-tetrahydrooctyl) dimethylchlorosilane with a ratio of 1:1 (v/ v)) in an evacuation chamber. The silicon wafer then served as a master to fabricate several OrmoStamp-based negative masters. Before each replica molding step from the silicon master to OrmoStamp, a new silanization of the silicon master was carried out to insure high quality OrmoStamp masters and non-sticking to the silicon wafer.
In the second main step, a cleaned 700 μm thick borofloat glass wafer (Borofloat 33, 700 μm, Schott AG, 55122 Mainz, Germany) was plasma activated for 2 min (Oxford 80, Oxford Instruments plc, O 2 20 sccm, 20 W), spincoated with an adhesion layer (OrmoPrime, micro resist technology GmbH, 4000 rpm, 45 s) for better adhesion of the OrmoStamp resin to the glass wafer and baked at 180°C for 5 min. A 2 ml droplet of OrmoStamp hybrid polymer was placed in the middle of the silicon wafer and the glass wafer was gently aligned upside down onto the droplet and left for about 30 min until the droplet reached the edge of the two wafers. Then the silicon-OrmoStamp-glass stack was placed under a UV lamp (ELC-500, Electro-Lite Corporation, Bethel, CT 06801, USA) for 10 min to cure the hybrid polymer. After detaching the two wafers, a negative OrmoStamp-glass wafer was received. Each OrmoStamp wafer was silanized (mixture of trichloro(1H, 1H, 2H 2H-perfluorooctyl)-silane and (tridecafluoro-1,1,2,2-tetrahydrooctyl) dimethylchlorosilane with a ratio of 1:1 (v/v)) once in an evacuation chamber before the first PDMS replica molding.
The OrmoStamp wafer was used in the third main step as a negative master to obtain the PDMS-based devices. To reduce sagging and roof collapse of the thin nanometer height fluidic channels, PDMS was mixed at a ratio of 5:1 (prepolymer: crosslinker) to achieve a higher elastic modulus 1-3 of E = 3.6 MPa 1 and degassed in a vacuum chamber to remove air bubbles. The PDMS devices were cured on a hotplate at 150°C for 3 h which reduced the viscosity of the PDMS prepolymer before crosslinking to achieve high resolution replication into PDMS 4,5 . The PDMS was removed from the OrmoStamp master and devices were cut out using a scalpel. Finally, inlet and outlet reservoirs of 4 mm diameter were punched into the PDMS device as seen in Figure 2b.

HIGH CONTRAST AND SNR IMAGING USING PDMS
Interferometric scattering detection (iSCAT) is used for many applications as a detection method, since it provides high sensitivity and nanometer precision detection of nano-objects down to 5 nm in diameter [6][7][8] . In our device configuration, the iSCAT signal is based on the interference between the scattered light from a particle and a reference beam reflected from the water-solid interface. The interference signal scales with the third power of the object diameter (d 3 ) whereas the pure scattering signal is proportional to d 6 .
In comparison to glass-based devices 9 , PDMS also has the key advantage that it is transparent from UV to IR (240-1100 nm) with a refractive index of~1.4 10 in the visible range, making it possible to enclosure fluidic optical components and highly suitable for high signal-to-noise detection using iSCAT imaging. The background intensity in PDMS-based GIE trapping devices originates mainly from the reflected field of the glass-water interface E r1 and the water-PDMS interface E r2 with a reflectivity of R 1 = 0.26% and R 2 = 0.11% respectively, as sketched in Supplementary Figure S3a Figure S3c. We would like to point out that, using PDMS-based GIE trapping devices, the contrast and SNR values for detecting Au NPs are comparable to glass based devices and one order of magnitude higher than compared to silicon based devices 9 . This is explained due to the limited incident laser power used in silicon based devices, preventing an overexposure of the camera detector, caused by the high reflection of the Si-SiO 2 interface in the device.

REDUCTION OF AXIAL MOVEMENT OF THE PARTICLE AT REDUCED NANOFLUIDIC CHANNEL HEIGHTS
Additional to the lateral trajectories, iSCAT imaging provides information on the axial movement of the particle due to the interference signal between the scattered field of the particle and the reflected background field 8,[11][12][13] . This information can be extracted from the intensity fluctuation of the particle and thus from the amplitude of each acquired Gaussian profile fit. For the individual trapped particle in Figure 6 of the manuscript, we obtain a decrease of the standard deviation of the intensity fluctuation of the particle for increased compression pressure (see Supplementary Figure S4). This confirms, that the reduction of the nanofluidic channel height results additionally in a stronger confinement in z-direction.

SURFACE ZETA POTENTIAL MEASUREMENT OF ACTIVATED GLASS AND PDMS
In glass-based GIE trapping devices, the top and bottom surface layer consist of the same material, which results in an energy minimum at the midplane of the nanofluidic channel without implemented traps. However, PDMS-based GIE trapping devices consist of a top PDMS surface and a bottom glass surface. To determine the charge properties of the glass and PDMS, surface zeta potential measurements were carried out at pH = 6.2 (Surface zeta potential cell ZEN1020, Malvern Instruments Ltd) using 1 μm polystyrene beads (micromere 01-54-103, micromod Partikeltechnologie GmbH, 18119 Rostock, Germany). The beads were diluted 1:1000 (v/v) in fresh DI water (18 MΩ). After activating a PDMS and glass sample, respectively, the apparent mobility of the tracer particles was measured at several distances away from the surfaces. Close to the surfaces, the tracer mobility is dominated by the electro-osmotic surface flow whereas far from the surface, the electrophoretic motion of the tracer particles itself dominates the mobility. By extrapolating the reported zeta potential values to zero displacement (see Supplementary Figure S5) and using the equation ζ surface = − ζ tracer (0)+ζ tracer (∞), the surface zeta potentials of the materials were obtained 14 . At pH 6.2, a zeta potential of the Figure S5 Surface zeta potential measurements of non-activated and activated glass and of activated PDMS in water. For activated glass and activated PDMS a similar surface zeta potential of around − 80 mV was obtained ensuring that PDMS can be used as a material for GIE trapping devices.
tracer particles of ζ tracer (∞) = − 43.8 (±0.9) mV was measured. For activated glass and activated PDMS a surface zeta potential of ζ surface,glass = − 79.9 (±0.9) mV and ζ surface,PDMS = − 78.2 (±1.2) mV was obtained ensuring that the energy minimum in GIE trapping devices made from PDMS and glass as substrates results in the slit midplane of the nanofluidic channels without the trap implementations.

SIMULATION OF THE ELECTROSTATIC POTENTIALS
The simulated electrostatic potentials of a point charge of − 1 e for all three device geometries (see Supplementary Figure S6) were obtained by numerically solving the nonlinear Poisson-Boltzmann equation in 3D using the COMSOL Multiphysics package 4.2 (COMSOL) 11 . An ionic strength of a monovalent ionic salt concentration of c 0 = 0.1 mM and a surface charge density of the Au NPs of σ p~8 ·10 − 3 e nm − 2 were measured and taken as a boundary condition. The surface charge density of the glass and PDMS of σ s~3 ·10 − 3 e nm − 2 were estimated to fit the simulations to the experimentally observed data in agreement with literature 15 .
The circular pockets were rotationally symmetric about the r = 0 axis in the nanofluidic channels. The potential depths ΔQ of a point charge of − 1 e were extracted by calculating the energy difference between the minimum potential along the z-axis for r = 0 nm (center of the pocket, blue dashed lines) and r = 400 nm (midplane of the nanofluidic channels outside the trap potential, red dashed lines).

Figure S6
Two-dimensional electrostatic potentials and electrostatic energy plots along the z-axis for r = 0 nm and r = 400 nm for a point charge of − 1 e for the two device geometries and pocket sizes used in the experiments.