Double layer 322 Subject

There are many questions remaining and many puzzUng, unexplained effects such as the effect of cation size and valence on film stability. These questions point to the need to develop a better understanding of the crystal-like structure of LB films, the role of molecular and structural forces in creating these structures, and the nature and stability of electrical double layers subject to mechanical perturbations in the underlying subphase. 

The treatment may be made more detailed by supposing that the rate-determining step is actually from species O in the OHP (at potential relative to the solution) to species R similarly located. The effect is to make fi dependent on the value of 2 and hence on any changes in the electrical double layer. This type of analysis has permitted some detailed interpretations to be made of kinetic schemes for electrode reactions and also connects that subject to the general one of this chapter. 

The existence of a double layer determines the properties of many systems in electrochemistry, in colloidal sciences, in biology, etc. [1-4]. Owing to their importance, electrical double layers have long been and remain a subject of intense research on both experimental and theoretical aspects. This is covered by some recent textbooks and review articles [3,5-10]. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The role of electrolyte is critical in these nanoscopic interfaces, but is difficult to predict and quantify. For sufficiently large rigid interfacial structures, one can apply the model of electrolyte interaction with a single charged surface in Figure 1(a). The double-layer theories or the recent integral-equation theories have been applied. Reviews of this subject are available in the literature [4,5]. For electrolytes in a nanostructure, the double layers from two surfaces overlap and behave differently from the case of a single surface. Ad-... 

The effect of the phospholipids on the rate of ion transfer has been controversial over the last years. While the early studies found a retardation effect [6-8], more recent ones reported that the rate of ion transfer is either not retarded [9,10] or even enhanced due to the presence of the monolayer [11 14]. Furthermore, the theoretical efforts to explain this effect were unsatisfactory. The retardation observed in the early studies was explained in terms of the blocking of the interfacial area by the phospholipids, and therefore was related to the size of the transferring ion and the state of the monolayer [8,15]. The enhancement observed in the following years was attributed to electrical double layer effects, but a Frumkin-type correction to the Butler Volmer (BV) equation was found unsuitable to explain the observations [11,16]. Recently, Manzanares et al. showed that the enhancement can be described by an electrical double layer correction provided that an accurate picture of the electrical double layer structure is used [17]. This theoretical approach will be the subject of Section III.C. 

Although not the subject of this article, double layer studies are briefly discussed in this paragraph in order to demonstrate that ex situ XPS studies indeed provide information about the state of the electrode exposed to an electrochemical environment at a defined potential. A crucial step in any ex situ experiment is the emersion of the electrode. Here the question arises whether the electrochemical double layer or part of it is preserved at the interface after emersion and transfer. Winograd et al. [10,11] first demonstrated that the electrode under UHV conditions still remembers the electrode potential applied at the time of emersion. These authors investigated oxide formation on Pt and the underpotential deposition of Cu and Ag on Pt by means of XPS and proved that the electrochemically formed oxide layer and... 

The structure of alumina on NiAl(l 1 0) was the subject of a surface X-ray diffraction study by Stierle et al. [46]. The model derived by Stierle et al. from the analysis of the X-ray diffraction data was based on a strongly distorted double layer of hexagonal oxygen ions, where the Al ions are hosted with equal probability on octahedral- and tetrahedral-coordinated sites the resulting film structure was closely related to bulk k-A1203. An attractive feature of Stierle s model was that it provided a natural explanation of the domain structure of the alumina overlayer, which is induced by a periodic row matching between film and substrate lattices. However, as pointed out recently by Kresse et al. [47], this structure model has two bonds with... 

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

While the lipid bilayer has a very low water content, and therefore behaves quite hydrophobically, especially in its core (see Chapter 2 of this volume), the cell wall is rather hydrophilic, with some 90% of water. Physicochemically, the cell wall is particularly relevant because of its high ion binding capacity and the ensuing impact on the biointerphasial electric double layer. Due to the presence of such an electric double layer, the cell wall possesses Donnan-like features, leaving only a limited part of the interphasial potential decay in the diffuse double layer in the adjacent medium. For a detailed outline, the reader is referred to recent overviews of the subject matter [1,2]. 

Lateral transfer of ionic species through the biointerphasial double layer has only recently received attention. Yet it is a subject of significant relevance, because it may play a crucial role in the interactions of organisms with their surroundings, for example in bacterial adhesion processes, biofilm formation (and removal), etc. 

The theoretical modeling of electron transfer reactions at the solution/metal interface is challenging because, in addition to the difficulties associated with the quantitative treatment of the water/metal surface and of the electric double layer discussed earlier, one now needs to consider the interactions of the electron with the metal surface and the solvated ions. Most theoretical treatments have focused on electron-metal coupling, while representing the solvent using the continuum dielectric media. In keeping with the scope of this review, we limit our discussion to subjects that have been adi essed in recent years using molecular dynamics computer simulations. 

The simplified description presented here did not consider the processes that give rise to activation polarization, except for attributing it to sluggish electrode kinetics. A detailed discussion of the subject is outside the scope of this presentation, but processes involving absorption of reactant species, transfer of electrons across the double layer, desorption of product species, and the nature of the electrode surface can all contribute to activation polarization. 

The main properties of the double layer of solid lead electrodes have been already described in the Encyclopedia [1]. New achievements in this field have been the subject of reviews [for example [2-6]. Some of the new results relate to impedance of polycrystalline Pb electrodes in aqueous [7-9] and nonaqueous solvents (references in [3, 6[). Special attention has been paid to chemically and electrochemically polished polycrystalline electrodes, mainly in aqueous [10-12] and methanolic [13] fluoride solutions. 

Though not discussed in this book, the role of non-aqueous solvents in determining the structures and properties of electrical double-layer has been the subject of numerous studies dating from 1920s. For the recent results, see, for example, Trasatti, S. Electrochim. Acta 1987, 32, 843 Borkowska, Z. J. Electroanal. Chem. 1988, 244, 1 Bagotskaya, I.A., Kazarinov, V.E. J. Electroanal. Chem. 1992, 329, 225. 

When transient techniques are employed for fundamental research on these and other subjects, the effect of double-layer charging has to be accounted for in the analysis procedures. It has been observed frequently that at solid—solution interfaces, this process does not obey the capacitive behaviour predicted by double-layer theories. For example, the doublelayer admittance, Fc, cannot be represented by Yc = jciCd, but rather follows the relation [118]... 

These examples show that our knowledge of ion radical chemistry in homogenous soluction is far from complete and that extrapolation of this knowledge to ion radicals produced at electrodes is a risky procedure, especially if one contemplates the additional complexities involved. The composition of the medium in the vicinity of the electrode is not the same as in the bulk of the solution (Sect 5.2), the structure of the double-layer can at its best be the subject of educated guesses, and due allowance must be made for the possibility that reactions may take place between adsorbed intermediates. 

Thus, in practice, the potential distribution within the electrolyte is obtained by solving Laplace s equation subject to a time-dependent, Dirichlet-type boundary condition at the end of the double layer of the WE, a given value of (j> at the end of the double layer of the CE and zero-flux or periodic boundary conditions at all other domain boundaries. Knowing the potential distribution, the electric field at the WE can be calculated, and the temporal evolution of the double layer potential is obtained by integrating Eq. (11) in time, which results in changed boundary conditions (b.c.) at the WE. 

The rate of deposition of Brownian particles is predicted by taking into account the effects of diffusion and convection of single particles and interaction forces between particles and collector [2.1] -[2.6]. It is demonstrated that the interaction forces can be incorporated into a boundary condition that has the form of a first order chemical reaction which takes place on the collector [2.1], and an expression is derived for the rate constant The rate of deposition is obtained by solving the convective diffusion equation subject to that boundary condition. The procedure developed for deposition is extended to the case when both deposition and desorption occur. In the latter case, the interaction potential contains the Bom repulsion, in addition to the London and double-layer interactions [2.2]-[2.7]. Paper [2.7] differs from [2.2] because it considers the deposition at both primary and secondary minima. Papers [2.8], [2.9] and [2.10] treat the deposition of cancer cells or platelets on surfaces. 

To calculate the double-layer force, the nonlinear Poisson-Boltzmann equation was solved for the case of two plane parallel plates, subject to boundary conditions which arise from consideration of the simultaneous dissociation equilibria of multiple ionizable groups on each surface. Deijaguin s approximation is then used to extend these results to calculate the force between a sphere and a plane. Details of the method can be found in Ref. (6). 

In another part of this study we wished to see the effects of post-modification treatments on the properties of the modified LDPE surface. Polyethylene samples were photosulfonated for different periods of time. Afterwards they were subjected to an after-treatment by conditioning in an electrolyte solution (aqueous KC1, 10-3 M) for 48 hours and then characterized by zeta potential measurements. This conditioning process resulted in a shift of f to even less negative values (see Fig. 8). This finding may be explained by the swelling of the polymer samples (water adsorption) in water that causes a shift of the shear plane of the electrochemical double layer into the liquid phase. This effect demonstrates that storage conditions and pre-conditioning may exert a pronounced influence on the zeta potential recorded for surface-modified polymers. Phenomena of this kind have already been described in previous literature [26,27],... 

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