Interfacial capacitor

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... 

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

Such a comparison has formed the basis, for example, for the assertion that the double layer can be emersed essentially intact from solution /8/. A common ambiguity, although for different reasons, in both emersion and UHV model experiments is the difference in the amount of solvent present either at the emersed or synthesized interface, compared to the in-situ situation. In the UHV the total amount of solvent adsorbed, and its distribution into the first and subsequent layers, can in many instances directly be determined, but this information is difficult to obtain and not yet available for the emersed and the real interface. To gather such missing pieces in the interfacial puzzle is the motivation for the work described in this paper. One important prerequisite for any model of the double layer is, for example, the density of solvent molecules in the inner layer as a function of the charge on the interfacial capacitor. 

Alkali 10ns in aqueous solution are probably the most typical and most widely studied representatives of non-specific adsorption. The electrochemical term of non-specific adsorption is used to denote the survival of at least the primary hydration shell when an ion is interacting with a solid electrode. As pointed out previously, the generation of such hydrated ions at the gas-solid interface would be of great value because it would provide an opportunity to simulate the charging of the interfacial capacitor at the outer Helmholtz plane or perhaps even in the diffuse layer. 

Since the interface behaves like a capacitor, Helmholtz described it as two rigid charged planes of opposite sign [2]. For a more quantitative description Gouy and Chapman introduced a model for the electrolyte at a microscopic level [2]. In the Gouy-Chapman approach the interfacial properties are related to ionic distributions at the interface, the solvent is a dielectric medium of dielectric constant e filling the solution half-space up to the perfect charged plane—the wall. The ionic solution is considered as formed... 

The expressions for the rates of the electrochemical reactions given in Section II. A have not taken into account the detailed structure of the interfacial region. In general, the solution adjacent to the electrode will consist of at least two regions. Immediately adjacent to the metal there will be a compact layer of ions and solvent molecules which behaves as a capacitor. A potential difference will be established between... 

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,... 

Huang LJ, Rajesh K, Lau WM, Ingrey S, Landheer D, Noel JP, Lu Z (1995) Interfacial properties of metal-insulator-semiconductor capacitors on GaAs(llO). J Vac Sci Technol A 13 792-796... 

Even though this contribution is always negative, the total capacity must be positive - otherwise the capacitor would accumulate charge spontaneously. Thus Eq. (17.4) is only valid if f > rjm, so that there is no electronic overlap between the two plates. Similarly the use of a macroscopic dielectric constant in Eq. (17.5) presupposes a plate separation of macroscopic dimensions, and again the total capacity is positive. Only unphysical models or bad mathematical approximations can produce negative interfacial capacities, which enjoyed a brief spell of fame under the name of the Cooper-Harrison catastrophe [2]. 

Helmholtz [71] first described the interfacial behavior of a metal and electrolyte as a capacitor, or so-called electrical double layer, with the excess surface charge on the metallic electrode remaining separated from the ionic counter charge in the electrolyte by the thickness of the solvation shell. Gouy and Chapmen subsequently... 

In drawing an appropriate equivalent circuit, it is clear that the resistance of the solution should be placed first in the intended diagram, but how should the capacitative impedance be coupled with that of the interfacial resistance One simple test decides this issue. We know that electrochemical interfaces pass both dc and ac. It was seen in Eq. (7.103) that for a series arrangement of a capacitor and a resistor, the net resistance is infinite for = 0, i.e., for dc. Our circuit must therefore have its capacitance and resistance in parallel for under these circumstances, for = 0, a direct current can indeed pass the impedance has become entirely resistive.51... 

Fig. 8.2. An early transient. Current density is constant. Potential builds up first through charging of the double layer, but at a higher potential, electrons pass across the interface, i.e., current flows and the double layer behaves as a leaky capacitor. The very early sections of the transient (double-layer condenser not leaking) can be used to obtain the capacity of the double layer because, there, there is a negligible Faradaic current through the interfacial region and the current goes overwhelmingly to charging the double layer. C = (dq/dV) = (idt/dV).

This an important step in determining the charge at the interface. If Equations D3.5.37 and D3.5.39 are combined, an expression that directly relates the interfacial charge to the electrical potential is obtained. In the simplified capacitor model, a linear increase in the potential between interface and ion shell was assumed. Hence, the d p/dx differential in Equation D3.5.39 can be replaced with the absolute difference A j//8, where 5 is the distance between interface and ion shell. Using the total differential, the desired relationship is obtained. 

At this interface, charges are separated and form the double-layer capacitor, but because electrons can transfer freely between the two phases, the interfacial charge <2i is fixed at only one value by the equilibrium potential Eeq. 

When a periodically changing excitation signal is chosen for the operation of chemiresistors, they can be used to detect changes of capacitance (Fig. 8.1b). Therefore, the dielectrometric sensors rely on the chemical modulation of one or more equivalent circuit capacitors, either through the change of the dielectric constant of the chemically sensitive layer or through the chemical modulation of the interfacial charge. 

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