Fig. 2: Microdisk alignment by critical Casimir forces.
a Diffusion coefficient of a microdisk (radius R = 1.2μm) above a circular pattern (radius a = 0.92R) as a function of temperature ΔT = T − Tc. Far from Tc (black circles), the microdisks are freely diffusing in the fluid. As the temperature rises (cyan squares), the microdisks get trapped above the pattern parallel to the surface. As the temperature rises even further (blue triangles), critical Casimir torques can also flip the microdisks into a configuration perpendicular to the surface. b Experimental (purple pentagons) and theoretical (green diamonds) probability of a parallel configuration, \({{{{{{{{\mathcal{P}}}}}}}}}_{\parallel }\), of the microdisk above a circular pattern as a function of a at ΔT = T − Tc = − 100mK (see Methods “Measurement of the configuration''). c Theoretical \({{{{{{{{\mathcal{P}}}}}}}}}_{\parallel }\) as a function of a and ΔT (right axis) and R/ξ (left axis), where \(\xi={\xi }_{0}{({{\Delta }}T/{T}_{{{{{{{{\rm{c}}}}}}}}})}^{-\nu }\) is the fluid correlation length, ξ0 is the bare correlations length, and ν ≈ 0.63 is the bulk critical exponent. The green diamonds separate the two phases corresponding to \({{{{{{{{\mathcal{P}}}}}}}}}_{\parallel }\, > \,50\%\) (red region) and \({{{{{{{{\mathcal{P}}}}}}}}}_{\parallel } \, < \, 50\%\) (blue region). The insets schematically illustrate the two configurations. d Experimental \({{{{{{{{\mathcal{P}}}}}}}}}_{\parallel }\) as a function of a and ΔT. The squares indicate the points for which the experiment was performed, and the purple pentagons locate the boundary between the two phases corresponding to \({{{{{{{{\mathcal{P}}}}}}}}}_{\parallel }\, > \,50\%\) (red points) and \({{{{{{{{\mathcal{P}}}}}}}}}_{\parallel } \, < \, 50\%\) (blue points). The lines are guides for the eye. The insets show the microscope images of the two configurations. Source data are provided as a Source Data file.
