Fig. 4: Trapping and release of a flake.
From: Tunable critical Casimir forces counteract Casimir–Lifshitz attraction
a, Hydrophobic gold stripes (thickness 30 nm, width 3 μm, separation 3 μm) nanofabricated on a hydrophilic glass substrate with a hydrophilic gold flake (a = 1,450 nm) floating above. Inset: periodic raising and lowering of the temperature T to and away from the critical temperature Tc. The black scale bar corresponds to 2 μm. b–i, Trajectories of a hydrophilic gold flake when T is appreciably below Tc (white trajectories) so that the Casimir–Lifshitz force dominates and confines the flake over the gold stripes (dark stripes in background images) (b,d,f,h) and when T ≈ Tc (black trajectories) so that the critical Casimir force emerges, repelling the flake from the gold stripes to the glass regions (light stripes in background images) (c,e,g,i). j, Full trajectory of the flake under periodic heating and cooling of the sample, showing that transitions occur shortly after reaching T ≈ Tc (Supplementary Video S2). Its starting point is marked by the particle image. Scale bars 6 μm. k, Casimir–Lifshitz potential Uexp along the x-direction (see axes in j) in case of a trapped flake above gold stripes. The dotted lines represent the experimentally measured potentials for the trajectories in b, d, f and h, while the solid line represents the fitting to a harmonic potential with trap stiffness kx ≈ 0.1 pN μm−1.
