Interface potentials

The combined effect of van der Waals and electrostatic forces acting together was considered by Derjaguin and Landau (5) and independently by Vervey and Overbeek (6), and is therefore called DLVO theory. It predicts that the total interaction energy per unit area, also known as the effective interface potential, is given by V(f) = ( ) + dl ( )- absence of externally imposed forces, the equiHbrium thickness of the Hquid film... 

Fig. 2. Effective interface potential (left) and corresponding disjoining pressure (right) vs film thickness as predicted by DLVO theory for an aqueous soap film containing 1 mM of 1 1 electrolyte. The local minimum in H(f), marked by °, gives the equiHbrium film thickness in the absence of appHed pressure as 130 nm the disjoining pressure 11 = —(dV/di vanishes at this minimum. The minimum is extremely shallow compared with the stabilizing energy barrier.

Disjoining Pressure. A static pressure difference can be imposed between the interior and exterior of a soap film by several means including, for example, gravity. In such cases the equiHbrium film thickness depends on the imposed pressure difference as weU as on the effective interface potential. When the film thickness does not minimize lV(f), there arises a disjoining pressure II = —dV/(U which drives the system towards mechanical equiHbrium. 

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

Thus, the expression for the total capacitance of the bare EIS structure, C(space-charge capacitance by means of the electrolyte solution-insulator interface potential (cp) (the capacitances C([Pg.216]

In addition to the aforementioned interactions with the surrounding gas environments, metallic interconnects also interact with adjacent components at their interfaces, potentially causing degradation of metallic interconnects and affecting the stability of the interfaces. One typical example is the rigid glass-ceramic seals, in particular those made from barium-calcium-aluminosilicate (BCAS) base glasses [205-209], FSS interconnect candidates have been shown to react extensively with... 

The potential difference (4>M - S), known as the interface potential, cannot be measured, in that it would need the insertion of another electrode, i.e. another interface. What one can measure is the electrochemical potential of the electrode, E, with respect to a reference electrode obviously every change of (M — < >s) is reflected in a variation of E, or vice versa. 

Fig. 8-14. Electron state density for a redox electron transfer reaction and profile of electrostatic inner potential, across an electrode interface = potential...

Unfortunately it is always impossible to change the potential only across a single interface - potentials are always changed between two points in two bulk phases. This means that the observed electrical... 

One complication which may be present, when the Helmholtz model is in other respects appropriate, is that of specific adsorption. If one of the mobile species is to some extent chemically bound rather than being simply electrostatically bound to the metal electrode, Cji may show a dependence on the dc bias potential. Indeed this is the normal method of inferring specific adsorption. Another possibility in this case is that dl exhibits different high frequency and low frequency limits because at high frequencies the specific adsorption being an activated process is too slow to follow changes in interface potential. A further complication which is often present in real systems is the presence of an oxide layer on the surface of the metal electrode. Such an oxide layer can generate a potential... 

Fig. 6.3 Schematic picture of the electrochemical potential ( > as a function of distance x in an oxide semiconductor electrolyte system a) bulk semiconductor potential b) solid/solution interface potential c) space charge potential d) flat band potential e) potential in the double layer (White, 1990, with permission.

Thus, since usually LH Lsc, then , and therefore № constitutes, as a rule, the main portion of the interface potential drop , 9 . This, however, does not hold true in the following cases ... 

A terminological remark is due. An equilibrium between two media with different fixed charge density (e.g., an ion-exchanger in contact with an electrolyte solution) is occasionally termed the Donnan equilibrium. The corresponding potential drop between the bulks of the respective media is then termed the Donnan potential. By the same token, we speak of the local Donnan equilibrium and the local Donnan potential, referring, respectively, to the local equilibrium and the interface potential jump at the surface of discontinuity of the fixed charge density, considered in the framework of the LEN approximation. 

The second important difference is that the interface potential is present at the (outer) Helmholtz layer of the semiconductor/soiution interface. The interface potential is produced by surface dipoles of surface bonds as well as surface charges due to ionic adsorption equilibria between the semiconductor surface and the solution. If the interface potential can be regulated by a change in the chemical structure of the semiconductor surface, then the semiconductor band energies can be shifted to match the energy levels of the solution species (oxidant or reductant). This is another advantage of the semiconductor system because this enables improvement of the electron transfer rate at the semiconductor/soiution interface and the energy conversion efficiency. 

One outstanding feature of the technique which deserves a particular emphasis is that mass transport properties coupled with interfacial kinetics can be analyzed without (or with a minimal) perturbation pf the interface potential, particularly for systems presenting locally high nonlinearities. 

In Fig. 5.19, the cyclic voltammogram versus the membrane potential M (given in Eq. (2.79)) obtained for a system with two polarizable interfaces (solid line) is presented. The i//cv curve has been also plotted versus the outer interface oul (dashed line) and the inner interface potential ilm (dotted line) with out and inn given by... 

Here I = denotes the identity matrix. The interface potential (( -potential) ( may by assumed to be constant. We consider a more general case where ( = ((x,T(e 1x)u>). Since we are interested in the macroscopic equations, we do not consider boundary conditions on dQe(uj). For the sake of simplicity we assume homogeneous initial conditions for ue, ve, (I> and r/ ) . 

Dietrich, S., (1991), Fluid interfaces - wetting, critical adsorption, van der Waals tails, and the concept of the effective interface potential , in Taub, H., Torzo, G., Lauter, HJ. and Fain, S.C., (eds), Phase. Transitions in Surface Films 2, NATO Advanced Science Series, Physics, Vol. 267, 391-423. 

The variation of the interface potential as a function of gate voltage is shown in Fig. 1.9. The value of the gate voltage is calculated for two values of the insulator capacitance, 10 and 100 nF cm-2. In most practical cases the actual value lies between these numbers, so it can be stated that Vs can be neglected in Eq. (11). 

At the beginning, the electric double layer at the solid-aqueous electrolyte solution interface was characterized by the measurements of the electrokinetic potential and stability of dispersed systems. Later, the investigations were supported by potentiometric titration of the suspension, adsorption and calorimetric measurements [2]. Now, much valuable information on the mechanism of the ion adsorption can be obtained by advanced spectroscopic methods (especially infrared ATR and diffuse spectroscopy) [3], Mosbauer spectroscopy [4] and X-ray spectroscopy [5]. Some data concerning the interface potential were obtained with MOSFET [6], and AFM [7]. An enthalpy of the reaction of the metal oxide-solution systems can be obtained by... 

The signs of x and p(cos d) are uniquely coupled. The direction of p is from the negative to the positive side. For a liquid with the negative side directed towards Its vapour, p and x are both positive. In this case the vapour is the reference. However at solid-liquid interfaces potentials are usually referred to the bulk liquid, in which case a minus sign is required. To remind us of that, the ( ) has been included. 

Our free energy calculations, using the thermodynamic integration technique [37], show different results for solvation in the bulk phases and for the ion transfer across the interface in the two-phase system, which may be understood by hypothesizing the existence of an electrostatic potential at the ice/water interface. Calculations of the free energy profiles across the ice/water interface show opposite tendencies of the ions in the bulk crystal phase, which may also can be explained by that same hypothesis, namely the existence of an interface potential attractive to Cl- ions and repulsive to Na+ ions. 

A water-splitting device has been invented [4], where photo-semiconductor and platinum are used as the cathode and the anode, respectively, instead of setting both the solar cell and the electrolyzer, separately. This method is called photoelectrochemical (PEC) water-splitting or photo semiconductor electrode method . The key phenomenon of PEC watersplitting is the steep rise (fall) of the potential at the interface between the n-(p-) semiconductor and the liquid electrolyte (e.g., KOH). If photons irradiate onto the interface, both the electrons (e ) and positive holes (IT) are excited to their conductive energy bands where they can move freely, so that e and h+ are separated by the interface potential difference. The h+ react with water by the equation ... 

Most capacitive evaluation circuits do not achieve the maximum possible resolution but are limited by the electromechanical interface, shortcomings in the electronic circuits, or stray signals coupling into the detector and corrupting the output. Section 6.1.2 below illustrates approaches to maximize the sensitivity of capacitive sensor interfaces, potential error sources, and approaches to minimize them. Electronic circuit options are discussed in Section 6.1.3. 

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