Figure 1

Left: Scheme of the TIRF setup. A laser beam is collimated through a high numerical aperture objective ($100\times$ $\mathrm{NA}=1.46$) with an incidence angle higher than the critical angle for total reflection. Laser is focused in the back focal plane of the objective with an achromatic doublet (focal length $150\mathrm{mm}$) and the incidence angle is tunable by a rotating mirror in the optical path. The evanescent wave created within the channel restricts fluorescence to tracers (black dots) in the vicinity of the surface. Right: Typical images obtained by TIRF illumination: the two images are acquired in frame-transfer mode with an exposure/acquisition time of 40 ms. Scale bar represents $5\mu \mathrm{m}$.Reuse & Permissions

Figure 2

(a) Electrostatic interaction energy between NPs and surface, as deduced from the NP concentration profile (see inset): open circles (○), hydrophilic; plain circles (●), hydrophobic. Salt concentration is $1.5\times {10}^{-4}\mathrm{mol}·{\mathrm{L}}^{-1}$. Dashed lines are fits to the PB predictions, providing the Debye length ${\lambda }_D=49\pm 5\mathrm{nm}$ and the energy of interaction of the NPs with the surface: $U_0=8.1\pm 0.7k_{B}T$ (hydrophilic) and $U_0=7.5\pm 0.7k_{B}T$ (hydrophobic). (b) Debye length as a function of salt concentration ${\rho }_{\mathrm{salt}}$ (black dots). The dashed red line is the theoretically expected form, ${\lambda }_D({\rho }_{\mathrm{salt}})\propto {\rho }_{\mathrm{salt}}^{-1/2}$ [14].Reuse & Permissions

Figure 3

Top: Velocity profiles, respectively, above a hydrophilic (a) and OTS-coated (b) glass. Symbols are experimental data and error bar are the uncertainty due to Brownian diffusion. Plain lines are a fit of the normalized data by a Poiseuille law with $b$ as a free parameter. The maximal speed $v_{\max }$ and the width of the channel $w$ are experimentally known, leaving the slip length $b$ as the only free parameter: $b=3\pm 7\mathrm{nm}$ (a) and $b=29\pm 11\mathrm{nm}$ (b). Bottom: Diffusion coefficient profiles on hydrophilic (c) and OTS-coated (d) glass. Experimental data are the triangles; plain curves are a fit using $D/D_0=1-\frac{9}{16}[r/(z+b)]$ [9, 26], where $r$ is the NP radius. This yields is, respectively $b=-3\pm 7\mathrm{nm}$ (a) and $b=21\pm 12\mathrm{nm}$ (b). Dotted lines in (b)–(d) are predictions with $b=0\mathrm{nm}$.Reuse & Permissions

Figure 4

Electro-osmotic flows close to hydrophilic glass (●) and hydrophobic OTS (▪), corrected for the electrophoretic velocity of the NPs. The deduced zeta potentials are $\zeta =-66\pm 8\mathrm{mV}$ (glass) and $\zeta =-123\pm 15\mathrm{mV}$ (OTS). The salt concentration is $1.5\times {10}^{-4}\mathrm{mol}·{\mathrm{L}}^{-1}$ and the driving electric field is $E=500\mathrm{V}·{\mathrm{m}}^{-1}$. Dashed lines are fits to the theoretical predictions using Eq. (1), yielding ${\lambda }_D=51\pm 10\mathrm{nm}$ [in agreement with Fig. 2a] and $b=0\pm 10\mathrm{nm}$ (bottom) and $b=38\pm 6\mathrm{nm}$ (top) for the slip lengths. Note the large slip velocity at the wall in the hydrophobic case, thereby confirming a strong effect of slippage on EO [$=\mathcal{O}(b/{\lambda }_D)$].Reuse & Permissions