Nonlinear capacitance

Recall the original ion flux (4.7). In Section 4.2 we have noted that the 

Due to the nonlinear terms in (4.37), an explicit solution like that for (4.9) is not feasible. Instead, we seek to analyze (4.37) at its equihbrimn imder an applied step voltage and find the mapping from the applied voltage to the accumulated charge. The latter mapping will represent the nonlinear capacitance associated with ion transport, which can be used in a circuit model to represent electrical djmamics for IPMCs. 

Taking a systems perspective, we can further use (4.38) to obtain an analytical mapping from the applied DC voltage V to the total transferred charge Q [Chen et al. (2009)] for U 0, 

When y —0, one can approximate r(y) using its Taylor series expansion around = 0. This results in 

2 Nonlinear circuit model and its experimental validor-tion 

---

Generally, a linear SPICE primitive capacitor is not the best way to model the nonlinear capacitance of a MOSFET. The capacitance of the MOSFET s gate is dependent on the gate-to-source voltage, and to a lesser extent, the drain-to-source voltage. However, the fixed capacitance used in this simulation is adequate for our purposes. 

The investigated resonance circuit consists of a linear inductance Lo and the dielectric nonlinear capacitance C-nl (see Figure 14.1). Let us consider the case, that a ferroelectric triglycine sulfate crystal (tgs) is used as nonlinear capacitance. 

List of Abbreviations ACh, acetylcholine DPOAE, distortion product otoacoustic emission IHCs, inner hair cells MET, mechanoelectric transducel NEC, nonlinear capacitance OHCs, outer hair cells PFAE, promyclocytic leukemia zinc finger protein RC, resistance and capacitance SEC, solute-carrier family SSC, sub-surface cistern... 

Santos-Sacchi J, Huang G. 1998. Temperature dependence of outer hair cell nonlinear capacitance. Hear Res 116 99-106. 

First models of liquid-liquid interfaces in electrochemistry treated them as flat and sharp [289, 290]. The nonlinear capacitance due to two back-to-back ionic double layers at such an interface is given simply by [289]... 

Unlike rectangular Fit), bisinusoidal F t) can be generated virtually exactly. However, circuits with nonlinear capacitance approximate Equation 3.26 by a waveform with the form-factor (for n= 1) lower by l/4, or l/3 versus the rectangular F t). Such forms were not adopted broadly, perhaps because of low form-factor, and will not be further discussed. 

In this section we present a nonlinear circuit model for IPMC actuators. A key component of the circuit is the nonlinear capacitance, derived based on the original PDEs governing the ion dynamics. In addition, the circuit includes ion diffusion resistance [Bonomo et al. (2007) Porfiri (2008)], pseu-... 

While the nonlinear capacitance captmes ion transport djmamics, a good model needs to accommodate other relevant djmamics. Fig. 4.21 shows a nonlinear circuit model for IPMC actuators, which incorporates the nonhn-ear capacitance Ci, the pseudocapacitance due to the electrochemical adsorption process at the polymer-metal interface, ion diffusion resistance i c) electrode resistance and nonhnear DC resistance of polymer R c-The pseudocapacitance Cg, and nonlinear DC resistance R c are further elaborated below. 

By substituting the charges in the summation in Equation El.7, in remarking that the grouping operators in a sum is not possible in the general case of nonlinear capacitances one writes... 

---