Inner interface

Shanahan and Carre [31-36, 55, 56] have done extensive theoretical work on the coating of viscoelastic surfaces and the effect of soft surfaces on hydrodynamic forces. Again, we have considered this area in a recent review [44]. This area is important in how energy is transferred or lost at the interface. Coupling changes at an inner interface can result in either an increase or decease in the energy dissipated. This has been discussed and observed for a number of acoustic systems [40, 41, 54, 57, 58]. 

From this definition it follows that at the outer interface pj of the innermost slice s = 1, and at the inner interface pg i of the outermost slice s = S, the immittance matrix takes the values... 

Solution. The outer interface is concave and the inner interface is convex with respect to the 0 phase. The concentrations of B maintained in equilibrium in the a phase at the outer interface, c (ft, and at the inner interface, c f, are given by Eq. 15.4. The concentration difference across the shell is therefore... 

The membrane system considered here is composed of two aqueous solutions wd and w2, separated by a liquid membrane M, and it involves two aqueous solution/ membrane interfaces WifM (outer interface) and M/w2 (inner interface). If the different ohmic drops (and the potentials caused by mass transfers within w1 M, and w2) can be neglected, the membrane potential, EM, defined as the potential difference between wd and w2, is caused by ion transfers taking place at both L/L interfaces. The current associated with the ion transfer across the L/L interfaces is governed by the same mass transport limitations as redox processes on a metal electrode/solution interface. Provided that the ion transport is fast, it can be considered that it is governed by the same diffusion equations, and the electrochemical methodology can be transposed en bloc [18, 24]. With respect to the experimental cell used for electrochemical studies with these systems, it is necessary to consider three sources of resistance, i.e., both the two aqueous and the nonaqueous solutions, with both ITIES sandwiched between them. Therefore, a potentiostat with two reference electrodes is usually used. 

In Scheme 2.2b interface Wj/M is the outer or working interface, and interface M/w2 is the inner interface (not a reference interface). 

At interface M/w2 The concentration profiles of the cation R+ of the supporting electrolyte of the membrane at both sides of this interface (c + and c"j) and the potential drop E2. Note that it has been assumed that R+ is being transferred at the inner interface, coupled with the transfer of X+ at the outer one, in order to maintain electroneutrality. 

Indeed, this is a problem with five unknown variables, the four concentrations above indicated and one of the potential differences at the two interfaces, E or E2. since they can be reduced to one potential difference because Em = E — 2 is known. Four differential equations and the additional condition of equality of the fluxes of the target ion X+ and the cation R+ at the outer and inner interfaces, respectively, will be used to obtain the explicit I/EM curve and the concentration profiles of all the species. 

In line with what is observed for other techniques, the response obtained in CV for a system with two liquid/liquid polarizable interfaces is lower and broader than that obtained for ion transfers at a single water/organic interface. This has been attributed to different polarization rates at the outer and inner interfaces [66]. 

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... 

From these curves, it is clear that the difference between peak potentials for the y/cy-EM curve (AEp = 88 mV) is equal to the sum of those obtained from the cyclic voltammograms plotted versus out and illn (61 mV and 27 mV, respectively). The different voltammetric responses obtained at outer and inner interfaces are the result of different potential drops at each of them, in agreement with Eq. (5.113). 

In order to show the distribution of the applied potential between the outer and the inner interface in the case of systems with two polarized interfaces, the potential time waveform used in SWV is depicted in Scheme 7.5. The applied potential, E (red line), and the outer ( out, blue line) and inner potentials ( "", green line) have been plotted. 

It can be seen that in the central part of the cyclic sweep, the outer potential, out, follows the same trend as the applied potential, E, so in this zone the outer interface presents a behavior similar to that of a system with a single polarizable interface. Concerning the inner interface, "ml is quite sensitive to the external polarization at both extremes of the cyclic sweep, becoming independent of the potential in the central zone of the same. In the inset, it can be seen how the potential pulses are distributed unequally between both outer and inner interfaces [38],... 

Scheme 7.5 Potential-time waveform of SWV obtained from Eq. (7.5) ( , red line), and its distribution between the outer interface ( °ul, dark blue line) and the inner interface ( "", green line). The three index potentials (the outer index potential, out,mdex, the inner index potential, """ index, and the membrane index potential, mdex) are also included (blue line, dark green line, and black line, respectively). Inset figure Distribution of the applied potential red line), between the outer and the inner interfaces (dark blue line and green line, respectively). jnitiai = —450mV,...

In both types of membrane systems, the current-potential curves corresponding to the first and second scans must be mirror images, which indicates that the ion transfer processes taking place at both the outer and inner interfaces are reversible. Thus, CSWV can be used as an excellent tool for analyzing the reversibility of charge transfer processes. 

In addition, the dielectric constant at the pzt top surface was found to be dramatically reduced compared to the bulk value. Our measurements therefore suggest a dead layer to be present. Similar experiments of deducing the local dielectric constant are now necessary for the inner interface. 

An extension of the kinetic theory on cases when a mechanical pressure interacts with kinetic processes inside solid volume and on interfaces has wide application interests. The elastic deformations in solid are presented from influence of external forces and from presence of internal defects of crystal structure point defects (vacancy, intersite atoms, complexes of atoms, etc.), extended defects (dislocations and inner interfaces in polycrystals), and three-dimensional defects (heterophases crystals, polycrystals). 

The first communication about the Chl-sensitized water oxidation to 02 on the outer vesicle interface conjugated with Fe(CN)g reduction at the inner interface appeared in 1977 [42] (see System 2 in Table 1). However an attempt to reproduce this result was a failure [273]. Thus the possibility of water photooxidation in vesicular systems which contain either only Chi molecules or Chi molecules in combination with other photosynthetic pigments is still under discussion. However, embedding of the intact fragments of thylakoids in the vesicle membranes was found to provide the evolution of 02 from water upon illumination [273], But again this process was not conjugated with PET across the membranes. 

P.7.d.2. Continuously changing e(z), continuous de/dz at inner interface quadratic variation over finite layers, retardation neglected... 

P.7.d.l. Power-law variation in a finite layer of thickness D, symmetric structures, no discontinuities in e but discontinuity in de/dz at interfaces, retardation neglected P.7.d.2. Continuously changing e(z), continuous de/dz at inner interface quadratic variation over finite layers, retardation neglected 134 P.7.e. Gaussian variation of dielectric response in an infinitely thick layer, no discontinuities in e or in de/dz, symmetric profile, retardation neglected 135... 

Extinction spectra for nanoparticles represented as a silver core covered by a carbon sheath in an insulating matrix (PMMA) will be analyzed in terms of the Mie relationships for sheathed cores [53, 54]. Here, an additional interface for which electrodynamic boundary conditions must be set up arises. Plasmon-polariton modes may be excited in both the core and the sheath. These modes, interacting through the inner interface, are responsible for the resulting extinction spectrum. 

Similar to an electrolyte-covered metal surface, an electrode potential of the inner interface would be measured. However, the physical meaning of this electrode potential is not as obvious, as it cannot be interpreted by conventional electrochemical kinetics. The electrode potential could in the absence of any faradaic currents be determined by dipole orientation of segments of the polymer chain. If, however. 

Wagner was well aware that these processes also may affect or even control the kinetics of oxidation, sulfidation, and so on, and he initiated research on the phase boundary reaction kinetics [10-18]. Some cases of surface reaction control are described in Sect. 6.2.3.2. The surface reactions generally have no electrochemical character, but as shown, electron transfer steps are involved [10-12]. Least is known about the reactions at the inner interface, but studies on sulfidation [13-18] have proven its role. 

Figure 16 Photomicrographs of double emulsions (W/O/W) stabilized with fat crystals and PGPR (polyglycerol pol)nicinoleate) at the inner interface and Tween 80 at the outer interface (a) after 24 h and (b) after 3 weeks.

For such a polysurface system to exist, the drop in electronic cmiductivity at each inner interface must be less than the drop at the neighbouring interface (closer to the electrolyte). However, the calculations showed that such situation could not be stable dynamically on sufficiently large timescales. We have so far no distinct evidence for the formation of such deposits, neither in molten nor in aqueous electrolytes. 

In such kind of systems, the winning of a pure metal is only possible by means of a solid-phase reduction mechanism, in a FS with a high ionic conductivity. Moreover, not just ionic but predominantly anionic conductivity is required. Otherwise, the cations of the alkali metals would migrate through the film to the inner interface... 

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