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The red (blue) contour, dotted line, and dot represent the boundary, equivalent radius, and center of nanocylinder top (bottom) surface, respectively. (c) Tilted-view (60°) of a substrate with etched nanocylinders. The green dotted horizontal lines are crossing the centers of top and bottom surfaces, and the green vertical line indicates the height that will be converted to the actual height considering the tilting angle. (d-i) Nanocylinder dimensions extracted from the SEM images. The graphs display the (d) top diameter, (e) bottom diameter, (f) height, (g) top roundness, (h) bottom roundness, and (i) volume as a function of the radial distance from the substrate center. The roundness (defined as 4πA/P2, A: area, P: perimeter) measures how closely the shape of a nanocylinder’s cross section resembles that of a circle, where 1 corresponds to a perfect circle and smaller values imply deviations from circular.
Measurement points are spaced by 0.5 mm from the center of the substrate to its edge. At each point, the diameters (heights) are calculated from n = 12 (n = 10) different nanocylinders. The square markers and the error bars in the graphs represent the mean and the standard deviation of the local uniformity, respectively. The horizontal dotted black lines and the top and bottom sides of the gray shaded boxes in the graphs represent the mean and the standard deviation of the global uniformity, respectively.
Distributions of fabricated single-crystal TiO2 nanocylinder dimensions The comparison between single-crystal TiO2 nanocylinder dimensions presented in Fig. S4† and those presented earlier (Fig. 3) provides more information for the analysis of the nanocylinder dimensions. We etch the different batches of nanocylinders under the same conditions, except for the etch duration (Table S2†). The etch time of the nanocylinders analyzed in Fig. S4† (8 min) is approximately twice less than that of the S13 nanocylinders shown in Fig. 3 (15 min). Both etch times demonstrate a similar trend regarding the nanocylinder dimensions (analysis results are summarized in Table S3†). The observed irregular Cr mask erosion effect, which depends on the roughness of the mask surface, causes stronger deformation of the top surface geometry than the bottom of the nanocylinders; we expect that the bottom surface geometry is mostly determined by the initial round shape of etch mask while the top surface geometry is the same as the eroded etch mask until the end of the etching process. This geometry deformation is also observable in the roundness analysis, in which the top roundness values are smaller than the bottom roundness values for both batches of nanocylinders. For this reason, the top diameters show less local uniformity than the bottom diameters. As this effect is more profound for extended etch times, etch time of 15 min results in less local uniformity than etch time of 8 min for both top and bottom diameters. For each measurement point, the top and bottom diameters are directly correlated as observable in Fig. S4† and Fig. 3. However, variations in the top and bottom diameters across a substrate are random, possibly due to the instability of e-beam size or current during ebeam patterning process. Regardless of these variations, the top and bottom diameters exhibit still high global uniformity for both batches of nanocylinders (RSD ≤5%), which lie in the same order of magnitude as their local uniformity. Further, we observe high global uniformity in nanocylinder heights across the substrates (RSD ≤3%) regardless of the loading effect. These excellent global uniformity in both diameters and heights leads to nanocylinder volumes with high global uniformity (RSD ≤5%) across a substrate which is desirable for the application of torque in an OTW.1 S14 Fig. S5. Quantitative comparison of surface functionalization efficiencies on single-crystal TiO2 for different linker molecules. (a) Schematic of the different functionalization strategies. At left, the TiO2 (or other oxide materials, e.g.
SiO2) surface provides hydroxyl groups (-OH) to which the linkers bind covalently. In the center, the used linker molecules (ETA, GPDMES, APDMES, and BADMSCP) are shown with their molecular structures, including the PEGylation of ETA-coated surface. At right, target molecules are NHS-ester or amine modified ATTO 647N fluorophores (F), binding to the different functional group of each linker (ESI Methods†). The fluorophores allow quantitative measurements via fluorescence microscopy. However, in the same manner, other organic molecules, such as biomolecules or polymers, can be bound to the surface linkers. (b) Quantitative comparison of differently functionalized single-crystal rutile TiO2 (red bars) and quartz SiO2 (blue squares) substrates. The measured fluorescence intensity represents the surface coating density while the error bar (standard deviation) reflects the homogeneity of the coatings (ESI Methods†).
Comparison of TiO2 and SiO2 in surface functionalization efficiency It is known that TiO2 has lower functionalization efficiency compared to other widely used oxide materials, e.g.
SiO2 and Al2O3.19,20 To quantify this difference in functionalization efficiency, we compare the surface coating efficiency of TiO2 (rutile) with that of SiO2 (quartz). We select two linkers for this comparison: ETA, based on its highest coating efficiency on TiO2 surfaces (Fig. S5b†), and GPDMES that we used for TiO2 nanostructure functionalization (Fig. 4c) and OTW measurements (Fig. 5). For SiO2 substrates, which are functionalized under the same conditions as TiO2, both ETA and GPDMES coatings show ~30% higher functionalization density than on TiO2. However, the coating efficiencies of TiO2 are sufficient to perform single molecule OTW experiments (Fig. 5b,c). If higher coating density is required, TiO2 substrates can be treated with extended O2 plasmatreatment time to increase the density of surface hydroxyl groups.20 S15 Fig. S6. DLS measurements of single-crystal TiO2 nanocylinder aggregation in relation to surface coatings and buffer conditions. In the DLS graphs, each curve is an average of 10 measurements with a duration of 10 s each, with 2 min between successive curves (see legend at bottom of figure). Each green shaded box within the panels displays the range of nanocylinder sizes measured previously in SEM (left edge: diameter, right edge: height). Top-left corner denotes the individual test conditions, which are surface coating (1st row) and buffer solution (2nd row). (a-d) Results for non-coated nanocylinders dispersed in (a) DI water, (b) DI water with 2% (m/v) BSA (New England Biolabs, UK), (c) PBS buffer (pH 7.4), and (d) PBS buffer (pH 7.4) with 2% BSA. (e-g) DLS data for PEGylated nanocylinders in (e) DI water, and in PBS buffer (pH 7.4) after bioconjugation with (f) biotin and (g) DNA. (h) Result for GPDMES-coated nanocylinders with bound streptavidin
Measurements and analysis of DLS data We probe the aggregation of cleaved, isolated single-crystal TiO2 nanocylinders with different surface coatings and buffer solutions via DLS (Zetasizer Nano ZS, Malvern, UK). We compare the degree of nanocylinder aggregations by characterizing the nanocylinder size distributions with 173° backscattering angle at 25 °C. To achieve monodispersed nanocylinders in aqueous solution, we vortex the nanocylinder solutions for 1 min before each measurement. However, for the nanocylinders in Fig. S6a† and Fig. S6b†, vortexing is insufficient to obtain monodispersity. For these samples, we sonicate the solutions for 10 min before measurements. We attribute the mismatch between nanocylinder dimensions (green boxes) based on SEM image analysis and size measurements via DLS to the highly scattering nature of TiO2 and non-spherical shape of the nanocylinders.
Besides the aggregated nanocylinder solutions (Fig. S6a,b,d†) which are apparent from the severe broadening of the size distributions, the monodispersed nanocylinder solutions (Fig. S6c,e-h†) exhibit only sedimentation of nanocylinders over time, observable by intensity decrease.
S17 Fig. S7. Optical trap calibration of single-crystal TiO2 nanocylinders. The power spectral density (gray curve) of a trapped TiO2 nanocylinder with a Lorentzian fit (red dotted line) provides corner frequency (fc) and baseline amplitude (Ab). A piezo stage drives the flow cell sinusoidally in time (with amplitude of 1 µm and frequency of 25 Hz) along the z-axis (inset) to induce a drag force to the trapped nanocylinder. The driving frequency (fd) of this modulation appears as a spike in the power spectrum (blue arrow), with amplitude Ad. Analysis of the three
measured values (Ab, Ad, and fc) yields the three necessary parameters for the force calibration in an OTW:
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