Elastic capacitor

This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the elastic dimer and the elastic capacitor. They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This real applications only the total charge or the applied voltage can be fixed. We then show that predictions of C < 0 under a-control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state the initial uniformity assumption is erroneous. Most... 

From the previous analysis it follows that the harmonic elastic capacitor collapses when approaches its critical value... 

Elastic capacitors (Section II) are very useful as electromechanical analogs of microscopic interfacial capacitors [22,31,34], But most importantly, they demonstrate that nega-... 

Under these conditions, corresponding to so-called cr-control [37], the elastic capacitor is described by the Hamiltonian, Eq. (7). In dimensionless units this becomes... 

In the analysis of molecular capacitors, the diffuse layer and elastic capacitors, we have always assumed that the electrode charge density a could be controlled. Under such conditions it is generally possible for C to become negative while the system remains stable. For example, contraction of the gap z in an elastic capacitor proceeds smoothly with cr growing until the plates come in contact, while C becomes negative for z < 2/3. At the same time, as shown in Section II for an EC connected to a battery, the EC collapses after z 0.6 is reached. How can these seemingly contradictory results be reconciled And how can cr-control be related to reality Is C < 0 observable These questions are addressed in this section. 

Recently [7] we constructed an example showing that interfacial flexibility can cause instability of the uniform state. Two elastic capacitors, C and C2, were connected in parallel. The total charge was fixed, but it was allowed to redistribute between C and C2. It was shown that if the interface was absolutely soft , i.e., contraction of the two gaps was not coupled, the uniform distribution became unstable at precisely the point where the dimensionless charge density s reached the critical value, = (2/3). In other words, the uniform distribution became unstable at the point where, under a control,... 

Initially the effect of applied voltage on membrane capacitance was attributed to the uniform electrostriction, in the manner of the elastic capacitor model [1,103], The effect of undulations was first considered by Leikin [78], In Ref. 89 the combined effect of undulations and uniform compression is studied, including the possible influence of nonlocality. The differential capacitance C is presented as... 

If isolated, the EC remains stable for all values of q corresponding to / > 0, as can be seen from Eq. (7). The major difference from the elastic dimer is that electrical energy of an isolated EC is positive and finite for all q and / while for the dimer it goes to —oo when / 0. In the next section we reexamine this result and show that the uniformity assumption for the charge distribution a across the plates of a capacitor can fail, and this can influence the stability condition for an isolated EC. 

Another observation should be made with respect to the term elastic in describing interfacial capacitors. It was originally introduced by Crowley [1] for membranes and reflects the compressibility of lipid layers which behave in some respects like an elastic film. Its relation to electrochemical interfaces is less obvious. Consider an interface between a metal electrode and an electrolyte. As we will see in Section III, the effective gap of the interfacial capacitor is the distance between the centers of mass of the electronic, e, and ionic, i, charge density distributions... 

In order to incorporate both tendencies, Lazare, Sundheim, and Gregor developed an improved model, where the elastic and electrostatic interactions were included. In this model, the resin was regarded as a set of charged planar capacitors, with the plates interconnected by elastic springs (Figure 7.24) [126], The balance between forces is attained when the elastic forces provided by the polymeric resin stabilize the dissolution propensity. 

Since the unloaded QCM is an electromechanical transducer, it can be described by the Butterworth-Van Dyke (BVD) equivalent electrical circuit represented in Fig. 12.3 (box) which is formed by a series RLC circuit in parallel with a static capacitance C0. The electrical equivalence to the mechanical model (mass, elastic response and friction losses of the quartz crystal) are represented by the inductance L, the capacitance C and the resistance, R connected in series. The static capacitance in parallel with the series motional RLC arm represents the electrical capacitance of the parallel plate capacitor formed by both metal electrodes that sandwich the thin quartz crystal plus the stray capacitance due to the connectors. However, it is not related with the piezoelectric effect but it influences the QCM resonant frequency. 

Workplace exposure to PCBs can occur during repair and maintenance of PCB transformers accidents, fires, or spills involving PCB transformers and older computers and instruments and disposal of PCB materials. In addition to older electrical instruments and fluorescent lights that contain PCB-filled capacitors, caulking materials, elastic sealants, and heat insulation have also been known to contain PCBs. Contact with PCBs at hazardous waste sites can happen when workers breathe air and touch soil containing PCBs. Exposure in the contaminated workplace... 

The actuation of DEs can be approximated as the lateral electrostatic compression and planar expansion of an incompressible Unearly elastic material where the electrical component is treated as a parallel plate capacitor [141], The incompressibility constraint can be expressed as ... 

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