Sensitivity of nonequilibrium Casimir forces on low frequency optical properties toward chaotic motion of microsystems: Drude vs plasma model

Abstract

Here, we investigate the sensitivity of nonequilibrium Casimir forces to optical properties at low frequencies via the Drude and plasma models and the associated effects on the actuation of microelectromechanical systems. The stability and chaotic motion for both autonomous conservative and nonconservative driven systems were explored assuming good, e.g., Au, and poor, e.g., doped SiC, interacting conductors having large static conductivity differences. For both material systems, we used the Drude and plasma methods to model the optical properties at low frequencies, where measurements are not feasible. In fact, for the conservative actuating system, bifurcation and phase space analysis show that the system motion is strongly influenced by the thermal nonequilibrium effects depending on the modeling of the optical properties at low frequencies, where also the presence of residual electrostatic forces can also drastically alter the actuating state of the system, depending strongly on the material conductivity. For nonconservative systems, the Melnikov function approach is used to explore the presence of chaotic motion rendering predictions of stable actuation or malfunction due to stiction on a long-term time scale rather impossible. In fact, the thermal effects produce the opposite effect for the emerging chaotic behavior for the Au-Au and SiC-SiC systems if the Drude model is used to model the low optical frequencies. However, using the plasma model, only for the poor conducting SiC-SiC system, the chance of chaotic motion is enhanced, while for the good conducting Au-Au system, the chaotic behavior will remain unaffected at relatively short separations (<2 µm).

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics

“…This theory describes the attractive interaction due to quantum fluctuations for all separations covering both the Casimir (long-range) and van der Waals (shortrange) regimes. [1][2][3][4][5][14][15][16][17] Besides the optical properties [18][19][20][21][22][23][24][25][26][27][28][29][30] and thermal contributions, [31][32][33][34][35] by engineering the boundary surface between interacting components, it is feasible to tailor the direction and strength of the Casimir force and consequently drive the actuation dynamic of NEMS/MEMS in a multitude of different ways.…”

Nonlinear Actuation of Casimir Oscillators toward Chaos: Comparison of Topological Insulators and Metals

“…In terms of the Lifshitz theory [9,10], the van der Waals and Casimir forces are the short-and long-range asymptotic limits, respectively, of the same force [1][2][3][4][8][9][10][11][12][13][14]. Nevertheless, the strong dependence of the Casimir force on the material optical properties can be utilized to tune the actuation of devices by proper choice of the interacting materials [5][6][7][15][16][17][18][19]. Several studies have shown that strong Casimir forces exist between components made of metals due to their high absorption of conduction electrons in the infrared range, while the less conductive materials can provide weaker Casimir forces and enhance the stability of microdevices suitable for operation in harsh environments [5][6][7][15][16][17][18][19].…”

Casimir force from complex systems

“…In other words, by the advancement in micro/nanofabrication and consequent reduction of the scale of microdevices into the submicron range, the role of Casimir and electrostatic forces could become comparable [71,72]. Although the electrostatic forces can be utilized to actuate MEMS/NEMS, the Casimir force is omnipresent and, in principle, it can always influence the actuation dynamics of operating devices leading to chaotic behavior towards stiction [73,74]. distance ratio of the involved miniaturized bodies is very large.…”