The effects of an electrolyte solution on screening the Casimir interaction between two symmetric double-layered media

Abstract

Using the scattering approach besides the Matsubara formalism, this paper aims at investigating screening and intensifying the thermal Casimir force in an electrolyte solution surrounded by two layers of local media within two semispaces. The electric field in an electrolyte solution is decomposed into its transverse and longitudinal components. We construct the reflection matrix describing the combination of the transverse and the longitudinal modes contribution to the incident wave to make the reflection wave for zero and nonzero Matsubara frequencies, individually. It is shown that the longitudinal modes contribution to the Casimir interaction in the Hamaker coefficient is significant only at zero frequency, and it shows that the presence of layers on the substrates intensifies the transverse modes contribution to the Hamaker coefficient in both the conductor and insulator media. It is illustrated that screening in the Hamaker coefficient shows similar behavior for different layers of the conductor and the insulator. Our calculations reveal that increasing the electrolyte’s concentration increases the Hamaker coefficient. Furthermore, the longitudinal modes contribution to the Hamaker coefficient—present due to the ions—is weaker if the electrolyte is surrounded by a conductor rather than being surrounded by a dielectric media. Interestingly, the zero-frequency portion of this coefficient asymptotically reaches its longitudinal contribution at zero frequency for different layers and different concentrations. Our investigation illustrates that in the presence of an electrolyte solution within two dielectric layers surrounded by two other dielectric semispaces, the intensification of the Casimir force per unit area becomes weaker in comparison to the case in which the solution is absent in such a system.