Interfacial structure models

Certainly these approaches represent a progress in our understanding of the interfacial properties. All the phenomena taken into account, e.g., the coupling with the metal side, the degree of solvation of ions, etc., play a role in the interfacial structure. However, it appears that the theoretical predictions are very sensitive to the details of the interaction potentials between the various species present at the interface and also to the approximations used in the statistical treatment of the model. In what follows we focus on a small number of basic phenomena which, probably, determine the interfacial properties, and we try to use very transparent approximations to estimate the role of these phenomena. 

In the previous section we saw on an example the main steps of a standard statistical mechanical description of an interface. First, we introduce a Hamiltonian describing the interaction between particles. In principle this Hamiltonian is known from the model introduced at a microscopic level. Then we calculate the free energy and the interfacial structure via some approximations. In principle, this approach requires us to explore the overall phase space which is a manifold of dimension 6N equal to the number of degrees of freedom for the total number of particles, N, in the system. 

In principle, a measurement of upon water adsorption gives the value of the electrode potential in the UHV scale. In practice, the interfacial structure in the UHV configuration may differ from that at an electrode interface. Thus, instead of deriving the components of the electrode potential from UHV experiments to discuss the electrochemical situation, it is possible to proceed the other way round, i.e., to examine the actual UHV situation starting from electrochemical data. The problem is that only relative quantities are measured in electrochemistry, so that a comparison with UHV data requires that independent data for at least one metal be available. Hg is usually chosen as the reference (model) metal for the reasons described earlier. 

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 interpretation of phenomenological electron-transfer kinetics in terms of fundamental models based on transition state theory [1,3-6,10] has been hindered by our primitive understanding of the interfacial structure and potential distribution across ITIES. The structure of ITIES was initially studied by electrochemical and thermodynamic analyses, and more recently by computer simulations and interfacial spectroscopy. Classical electrochemical analysis based on differential capacitance and surface tension measurements has been extensively discussed in the literature [11-18]. The picture that emerged from... 

The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler-Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (k j). The potential dependence of the ET rate constant normalized by as obtained from the optical analysis of the TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a mixed-solvent layer type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (A 0) is zero. The potential drop in the aqueous side was estimated by the Gouy-Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). 

The good agreement between electrochemical and UHV data, documented in Figure 4, is a very important result, because it proves for the first time that the microscopic information which one obtains with surface science techniques in the simulation studies is indeed very relevant to interfacial electrochemistry. As an example of such microscopic information, Figure 5 shows a structural model of the inner layer for bromide specific adsorption at a halide coverage of 0.25 on Ag 110 which has been deduced from thermal desorption and low energy electron diffraction measurements /12/. Qualitatively similar models have been obtained for H2O / Br / Cu( 110) /18/and also for H2O/CI /Ag 110. ... 

It is important to establish the origin and magnitude of the acidity (and hence, the charge) of mineral surfaces, because the reactivity of the surface is directly related to its acidity. Several microscopic-mechanistic models have been proposed to describe the acidity of hydroxyl groups on oxide surfaces most describe the surface in terms of amphoteric weak acid groups (14-17), but recently a monoprotic weak acid model for the surface was proposed (U3). The models differ primarily in their description of the EDL and the assumptions used to describe interfacial structure. "Intrinsic" acidity constants that are derived from these models can have substantially different values because of the different assumptions employed in each model for the structure of the EDL (5). Westall (Chapter 4) reviews several different amphoteric models which describe the acidity of oxide surfaces and compares the applicability of these models with the monoprotic weak acid model. The assumptions employed by each of the models to estimate values of thermodynamic constants are critically examined. 

From a survey of the literature in chemically modified electrodes [13], one can identify simple phenomenological models that have been very successful for the analysis of a particular aspect of the experimental data. Such models are, for instance, the Dorman partition model [24, 122], the Laviron [158], Albery [159] and Anson models [127] to account for the nonideal peak width, the Smith and White model for the interfacial potential distribution [129], and so on. Most of these models contain one or more adjustable parameters that give some partial information about the system. For example, the lateral interaction model proposed by Anson [127] provides a value for the lateral interactions between oxidized and reduced sites, but does not explain the origin of the interactions, neither does it predict how they depend on the experimental conditions or the polymer structure. In addition, none of these models provide information on the interfacial structure. 

O Keeffe (1991Z)) has used bond valences to model the coherent interface that occurs between the semiconductors Si and MSi2 with M = Ni or Co (27139). Although these systems contain Si-Si bonds and therefore do not obey the assumptions of the bond valence model (condition 3.2), the mathematical formalism of the model still works because of the high symmetry. As both Si-Si and Si-Ni bonds are found in NiSi2, the cubic structure is strained (cf. BaTiOs in Section 13.3.2) and this strain affects the structure of the interface. Of the six possible interfacial structures examined, the two with the lowest BSI eqn (12.1) are those that are believed to occur in NiSi2 and CoSi2 respectively, and in both cases the strain introduced at the interface is correctly predicted. 

Fig. 10. Schematic structure models of the bulk-crystallized polyethylene samples. 1, II, and 111 indicate the crystalline, interfacial, and interzonal regions, respectively. Models A, B, C, D, and E express the molecular crystal, unpeeled crystal, disheveled unpeeled crystal, and lamellar crystals for medium and large molecular weight samples, respectively66), f and x designate the lamellar thickness and the extended molecular chain length, respectively...

An understanding of equilibrium phenomena in naturally occurring aqueous systems must, in the final analysis, involve understanding the interaction between solutes and water, both in bulk and in interfacial systems. To achieve this goal, it is reasonable to attempt to describe the structure of water, and when and if this can be achieved, to proceed to the problems of water structure in aqueous solutions and solvent-solute interactions for both electrolytes and nonelectrolytes. This paper is particularly concerned with two aspects of these problems—current views of the structure of water and solute-solvent interactions (primarily ion hydration). It is not possible here to give an exhaustive account of all the current structural models of water instead, we shall describe only those which may concern the nature of some reported thermal anomalies in the properties of water and aqueous solutions. Hence, the discussion begins with a brief presentation of these anomalies, followed by a review of current water structure models, and a discussion of some properties of aqueous electrolyte solutions. Finally, solute-solvent interactions in such solutions are discussed in terms of our present understanding of the structural properties of water. 

Mechanisms and Interfacial Structures. Meanwhile, we may provide some schematic models (see Figure 9) and a critical assay of the mechanisms that reflect the views either expressed in the literature or presented in this communication. 

Throughout, we have used the lattice constant of CaF2 (only 0.6% greater than in bulk Si) except for the interfacial Si-Ca distance, which is taken to be 3.15 A, as found [174,175] experimentally. Our structural model follows the experimental outcomes [174,175] with the first monolayer of CaF2 losing... 

Fig. 20. (a) Atomic model for the trihydride termination of Si(lll) after etching in 1% HF (after [118]), (b) UHV-STM image of Si(lll) showing a boundary between the two domains of -SiHj in (a) (after [118]). (c) Hypothetical Si/SiOj interfacial structure explaining trihydride formation upon etching in HF (see text). 

Recently, detailed molecular pictures of the interfacial structure on the time and distance scales of the ion-crossing event, as well as of ion transfer dynamics, have been provided by Benjamin s molecular dynamics computer simulations [71, 75, 128, 136]. The system studied [71, 75, 136] included 343 water molecules and 108 1,2-dichloroethane molecules, which were separately equilibrated in two liquid slabs, and then brought into contact to form a box about 4 nm long and of cross-section 2.17 nmx2.17 nm. In a previous study [128], the dynamics of ion transfer were studied in a system including 256 polar and 256 nonpolar diatomic molecules. Solvent-solvent and ion-solvent interactions were described with standard potential functions, comprising coulombic and Lennard-Jones 6-12 pairwise potentials for electrostatic and nonbonded interactions, respectively. While in the first study [128] the intramolecular bond vibration of both polar and nonpolar solvent molecules was modeled as a harmonic oscillator, the next studies [71,75,136] used a more advanced model [137] for water and a four-atom model, with a united atom for each of two... 

The proportion of a-helix in native proteins is variable and sometimes not very great. It is a mistake to over emphasize its role in interfacial structures, but where it is present its radial distribution of side chains means that its orientation in the interface will be governed by its over-all hydrophobicity. The presence of hydrophobic groups directed into the water is then possible as well as others contributing to cohesion between adjacent molecules as in the monolayers considered here. Those directed into the water may function as sites for the binding of other molecules in the aqueous phase. This is also a possibility for the p conformation but not for extended chain conformations where under pressure the hydrophobic side chains are directed away from the surface and the hydrophilic ones into the water. While this latter model has been accepted by surface chemists 37), the conformation appears unlikely both from a biological and a stereochemical standpoint. Indeed except where there is a regular alternation of hydrophobic and hydrophilic side chains, the conformation is probably not one acceptable within the usual criteria for polypeptide structures (5). 

Ellipsometry Spectroscopic ellipsometry Imaging ellipsometry Adsorbed amounts/coverages phase transitions thickness and refractive indices. Identification of interfacial molecules. Domain formation eind shape (coexisting phases) internal structure of condensed phases resolution O (1 gm). For interpretation in terms of molecular structure model profiles across the Interface are needed. Problems mono-layer anisotropy, and different profiles may match the experimental data additional (independent) information required. 

In the next few pages we shall discuss the question of local interfacial structures bounding idealised aggregates, tiled by blocks of fixed dimensions. The model represents one extreme idealisation of the molecular constituents that form the aggregate, most applicable to small surfactant molecules. At the other extreme, the block dimensions are not set a priori, they must be determined as a function of the temperature, concentration, etc. This case will be dealt with later. The welding of two concepts, a fluid-like mixture of hydrocarbons, with that of an idealised block is at first sight contradictory. However it can be shown to be consistent in a first order theory [2]. 

The current structural model for microemulsions was advanced by Hoar and Schulman (1 ). These authors pictured the transparent dispersions of oil in water or of water in oil as consisting of small spherical droplets of the dispersed phase within the continuous phase. Later, this model was refined to include an interfacial film of surfactant and cosurfactant coating the droplets (2). It has also been pointed out that the compositions leading to microemulsions could be related... 

The total interfacial surface area can be simply related to the dispersed phase volume in terms of the microemulsion droplet radius. Calculated radii for the systems studied are shown in Table 1. As expected, the droplets increasingly grow in size as the volume of dispersed phase increases. Thus, the observed decrease in X is merely a consequence of the decreasing surface-to-volume ratio needing a correspondingly smaller fraction of the MMA to create new interface. The droplet sizes predicted are consistent with the observed transparency of our systems which requires droplet sizes of under 100 A in radius. Thus, the simple swollen micelle serves as an adequate structural model for this microemulsion system. 

The simulations with both models demonstrated the existence of an inhomogeneous interfacial structure normal to the surface layer. In the outmost surface layer, the cation is likely to lie on the surface with the imidazolium ring parallel to the interface, while there is a second region with enhanced density from that in the bulk where the cation tended to be perpendicular to the surface. It was found that the cation is likely to be segregated at the IL surface for the polarizable model, while for the nonpolarizable model, the anion was found to be more likely exhibiting such behavior. The surface tension obtained from the polarizable model was much smaller (>28%) than that obtained from the nonpolarizable model, in better agreement with extrapolated experiments [107],... 

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