Fig. 1: Casimir–Lifshitz and critical Casimir forces between parallel plates.
From: Tunable critical Casimir forces counteract Casimir–Lifshitz attraction
a, Schematic (not to scale) of a hydrophilic (−) gold flake hovering at an equilibrium height h above a glass surface coated with a gold layer and treated with SAMs to control the preferential surface adsorption. b, Forces acting on a hydrophilic flake above a hydrophilic (blue layer, inset) surface as a function of its height h. Since the boundary conditions are symmetric (−, −), both the Casimir–Lifshitz forces (dashed orange line, Eq. (5)) and the critical Casimir forces (dashed blue line, Eq. (2) at ΔT = T − Tc = −0.1 K, where T is the solution temperature and Tc is the critical temperature of the critical binary mixture) are attractive. The total force (black line) including also a repulsive electrostatic component (dashed green line) vanishes at h ≈ 80 nm. c, Forces on a hydrophilic (−) flake above a hydrophobic (+) surface (red layer, top inset) as a function of h. Here, the antisymmetric (−, +) boundary conditions induce a repulsive critical Casimir force (dashed red line, Eq. (2) at ΔT = −0.1 K), while the Casimir–Lifshitz force (dashed orange line, Eq. (5)) remains attractive. Accordingly, the total force vanishes at much larger h ≈ 210 nm (bottom inset shows a zoom-in view of this region). The presence of repulsive critical Casimir forces greatly raises the equilibrium height of the flake above the surface. The forces shown in b and c are calculated for a 34-nm-thick 1,520-nm-wide gold flake suspended in water–2,6-lutidine above a 40-nm-thick gold layer.
