Direct measurement of the free energy by optical microscopy.

We report the direct measurement of thermodynamic properties of colloidal hard spheres by optical microscopy. By using confocal microscopy, we obtain three-dimensional snapshots of a colloidal hard-sphere suspension over a wide range of densities. From these snapshots, the available volume to insert an additional sphere and the surface area of that volume are determined, which are directly related to the thermodynamics of the system. This procedure enables us to measure in a direct and noninterfering way, in principle, all thermodynamic properties, here demonstrated for the pressure, the chemical potential, and the free-energy density of a colloidal hard-sphere suspension. The "visual" determination of thermodynamic quantities opens up the possibility to experimentally study the relation between thermodynamics and geometry in real space beyond the hard-sphere potential.