A physical model describing the electro-optic behavior of switchable optical elements based on electrowetting

Recently, we have demonstrated reflective display pixels based on the voltage-controlled two-dimensional movement of an oil/water interface across a hydrophobic fluoropolymer insulator [R. A. Hayes and B. J. Feenstra, Nature (London) 425, 383 (2003)]. Here a physical model is reported that describes the basic electro-optic behavior of these electrowetting-based optical elements. The model extends the classical electrowetting theory developed for a free water droplet on an insulator surface to the controlled two-dimensional movement of a confined oil/water interface. The model takes into account the spatial extent of the oil layer (<5mm), where the oil film is well approximated by a spherical cap. The calculated results are in very good agreement with experimental data without employing fitting parameters. The model can be used to predict and optimize the electro-optic behavior of devices as a function of a range of well-defined parameters including the oil film thickness, the thickness of the insulating layer, the size of the optical element, and the oil/water interfacial tension.