Fig. 2: Hydrodynamic measurement of flake height above the substrate.
From: Tunable critical Casimir forces counteract Casimir–Lifshitz attraction
a, Scanning electron microscopy image of gold flakes with various sizes and shapes. The scale bar corresponds to 5 μm. b, Microscope image and trajectory (blue) recorded for 100 s of a diffusing flake shaped as an equilateral hexagon with side a = 840 nm (inset) in a critical water–2,6-lutidine mixture at ΔT = −0.5 K (Supplementary Video 1). c, Experimental data (blue circles) and theoretical fit (orange line) of the mean square displacement (MSD) of the flake’s trajectory in b, which provides an estimate of the diffusion constant D = 0.067 μm2 s−1, compared with D ≈ 5.98 μm2 s−1 for free diffusion (black line). The s.d. of the experimental points is much smaller than the symbols. d, Theoretical diffusion D of a hexagonal flake with side a = 840 nm as a function of its height h above the surface (Fig. 1a) obtained from hydrodynamic simulations (see Methods and Supplementary Information Section IV). The experimentally measured D = 0.067 μm2 s−1 corresponds to height h = 100 nm.
