Sensitivity of chaotic behavior to low optical frequencies of a double-beam torsional actuator

Abstract

We investigate here how the optical properties at low frequencies affect the actuation dynamics and emerging chaotic behavior in a double-beam torsion actuator at nanoscale separations (<200 nm), where the Casimir forces and torques play a major role. In fact, we take into account differences of the Casimir force due to alternative modeling of optical properties at low frequencies, where measurements are not feasible, via the Drude and plasma models, and repercussions by different material preparation conditions. For conservative autonomous actuation, bifurcation and phase portrait analysis indicate that both factors affect the stability of an actuating device in such a way that stronger Casimir forces and torques will favor increased unstable behavior. The latter will be enhanced by unbalanced application of electrostatic voltages in double-beam actuating systems. For the case of a time-periodic driving force, we use a Melnikov function and a phase plane analysis to study the emerging chaotic behavior with respect to the Drude and plasma modeling and material preparation conditions. We find indications that any factor that leads to stronger Casimir interactions will aid chaotic behavior and prevent long term prediction of the actuating dynamics. Moreover, in a double-beam actuator chaoticity will be amplified by the application of unbalanced electrostatic voltages. Therefore, the details of modeling of optical properties and the material preparations conditions must be carefully considered in the design of actuating devices at nanoscale because here Casimir forces are omnipresent and broadband type interactions.

Recent progress in engineering the Casimir effect – applications to nanophotonics, nanomechanics, and chemistry

“…With a push toward further miniaturization (and the transition from MEMS to NEMS), movable parts in these systems begin to experience the Casimir force, which can lead to stiction and adhesion if not properly designed around [48,144]. Alternatively, the Casimir effect can be advantageous in these devices due to its sensitivity to small changes in distanceexamples include actuators [55], devices exploiting bistability and hysteresis [145][146][147], chaotic behavior [148], virtually frictionless bearings [149], etcetera.…”

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.…”

“…[41][42][43][44] So far, several works have shown the strong dependence of the normal Casimir force on the material optical properties and explored how these properties can be utilized to tune the actuation dynamics of devices that can exhibit transitions toward chaotic motion. [27][28][29][30] However, still unexplored is the actuation dynamic of devices under the influence of the lateral Casimir force by taking into account significant contrast in the material optical properties and conductivity of the interacting surfaces.…”

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

“…Moreover, it has been shown that the low optical frequency range, which is not accessible by experimental measurements, [14][15][16][17][18][19][20][21][22][23][24] is playing a significant role for an effective stable operation of devices. 3,4,[29][30][31] In fact, Casimir force measurements have revealed deviations from force predictions of dissipative models (e.g., the Drude model), 3,4,30 which lead to finite absorption at frequencies ω > 0 and singular absorption ∼1/ω for ω → 0 (static limit). On the other hand, the plasma (P) model, 3,4,30 which can also be thought as having infinite absorption at the frequency ω ∼ 0, and zero anywhere else, allowed calculations of the Casimir force that described the measured force data more precisely at separations above 160 nm.…”

“…3,4,30,31 Recently, we have shown that for systems at thermal equilibrium, the choice of the Drude or plasma models to describe the optical properties at low optical frequencies (farinfrared and below) in the range where any measured optical data are not available leads to remarkably different results regarding the stability and emerging chaotic motion of MEMS. 29,31 However, it is still remains unexplored how the optical properties in the low frequency range can affect the actuation of devices towards chaotic motion under the influence of thermal nonequilibrium Casimir forces taking into account the conductivity of interacting materials, and possible residual electrostatic interactions due to uncompensated contact potentials. This topic will be explored here for both good and poor conductive materials that are used in microdevices and can lead to irreversible adhesion of moving parts due to stiction on a long-term during operation.…”