Characteristic properties of the Casimir free energy for metal films deposited on metallic plates

The Casimir free energy and pressure of thin metal films deposited on metallic plates are considered using the Lifshitz theory and the Drude and plasma model approaches to the role of conduction electrons. The bound electrons are taken into account by using the complete optical data of film and plate metals. It is shown that for films of several tens of nanometers thickness the Casimir free energy and pressure calculated using these approaches differ by hundreds and thousands percent and can be easily discriminated experimentally. According to our results, the free energy of a metal film does not vanish in the limiting case of ideal metal if the Drude model approach is used in contradiction with the fact that the fluctuating field cannot penetrate in its interior. Numerical computations of the Casimir free energy and pressure of Ag and Au films deposited on Cu and Al plates have been performed using both theoretical approaches. It is shown that the free energy of a film can be both negative and positive depending on the metals used. For a Au film on a Ag plate and vice versa the Casimir energy of a film changes its sign with increasing film thickness. Applications of the obtained results for resolving the Casimir puzzle and the problem of stability of thin films are discussed.

Figure 1

The magnitudes of (a) the Casimir free energy per unit area and (b) the Casimir pressure of a Ag film on a Cu plate computed using the tabulated optical data extrapolated to zero frequency by the Drude (the solid line 1) and plasma (the solid line 2) models are shown as functions of the film thickness. The dashed lines 1 and 2 present the same quantities computed using the simple Drude and plasma models, respectively.

Figure 2

The magnitudes of the Casimir free energy per unit area of a Au film on a Cu plate computed using the tabulated optical data extrapolated to zero frequency by the Drude (the solid line 1) and plasma (the solid line 2) models are shown as functions of the film thickness. The dashed lines 1 and 2 present the same quantities computed using the simple Drude and plasma models, respectively.

Figure 3

(a) The Casimir free energies per unit area and (b) the Casimir pressures of a Au film on an Al plate computed using the tabulated optical data extrapolated to zero frequency by the Drude (the solid line 1) and plasma (the solid line 2) models are shown as functions of the film thickness. The dashed lines 1 and 2 present the same quantities computed using the simple Drude and plasma models, respectively.

Figure 4

The Casimir free energies per unit area of a Ag film on an Al plate computed using the tabulated optical data extrapolated to zero frequency by the Drude (the solid line 1) and plasma (the solid line 2) models are shown as functions of the film thickness. The dashed lines 1 and 2 present the same quantities computed using the simple Drude and plasma models, respectively.

Figure 5

(a) The Casimir free energies per unit area of a Au film on a Ag plate and (b) the same free energies multiplied by the film thickness squared computed using the tabulated optical data extrapolated to zero frequency by the Drude (the solid line 1) and plasma (the solid line 2) models are shown as functions of the film thickness. The dashed lines 1 and 2 present the free energies computed using the simple Drude and plasma models, respectively.

Figure 6

(a) The magnitudes of the Casimir free energy per unit area of a Ag film on a Au plate and (b) the Casimir free energies multiplied by the film thickness squared computed using the tabulated optical data extrapolated to zero frequency by the Drude (the solid line 1) and plasma (the solid line 2) models are shown as functions of the film thickness. The dashed lines 1 and 2 present the magnitudes of the free energies computed using the simple Drude and plasma models, respectively.