Model Guidelli

Models for the compact layer of the metal-electrolyte interface have become more and more elaborate, providing better and better representations of observed electrocapillary data for different metals, solvents, and temperatures, but almost always leaving the metal itself out of consideration, except for consideration of image interactions of the solvent dipoles. For reviews of these models, see Parsons,13 Reeves,14 Fawcett et a/.,15 and Guidelli,16 who gives detailed discussion of the mathematical as well as the physical assumptions used. 

Guidelli,16 reviewing work on the capacitance of the metal-electrolyte interface, writes the equation for calculating capacitances from models for the inner layer as ... 

Guidelli model of, 899 Habib and Bockris, 899 at the interface, importance of, 918 -ion interaction energy, 924 -metal interactions, 896 chemical forces, 897, 972 lateral forces, 897 monomers of, definition, 899 orientation of, 898 Parsons model of, 899 and potential of the electrode. 900. 924 preferential orientation of, 912 and solvent excess entropy, 912 the "three-state water model 898, 899 Wave nature of electrons, 788 Wavenumber, 799 Waves... 

These two orientations of water molecules, the flip-up and flip-down states, are extreme cases. However, there are several other possible states for the water molecules on the electrode. Evidence exists suggesting that water molecules in the interfacial region may be associated into groups (see Fig. 6.77). This gave rise to several models proposed to describe the water structure at the interface Damaskin and Fmmkin (1974), Parsons (1975), Fawcett (1978), and Guidelli (1986) (Fig. 6.78). 

Parson s monolayer model, Fawcett s three-state model, and Guidelli s model, (a) Allowed orientations of water molecules with H bonds directed toward the vertices of the unit cell, (b) Rotations required to form H bonding between two water molecules of the monolayer, (c) H bonding of a chemisorbed water molecule in the monolayer with two bulk water molecules. (Reprinted from R. 

R. Guidelli. Molecular Models of Organic Adsorption at Metal-Water Interfaces. in Adsorption of Molecules at Metal Electrodes, J. Lipkowski and P. N. Ross, eds., p. 1, VCH Publishers, New York (1992). 

The molecular models adopt a statistical mechanical treatment of the adsorbed layer. In most cases a lattice structure is assumed and the differences of the various models lie in the effects on which the emphasis is put. There are two main molecular approaches one has been developed by Guidelli and his colleagues and the other is based on the LBS theory. Guidelli s approach emphasizes local order and hydrogen bonding among adsorbed water (solvent) molecules, whereas the models based on the LBS theory disregard local order and focus their attention on the polarizability of the adsorbed molecules. 

Guidelli was the first to develop a strict statistical mechanical model for the adsorption of neutral organic compounds on electrodes and he continued with his colleagues to present some novel ideas in this area. 9,29,36,59-64 jjjg adsorbcd layer is treated as a two-... 

Figure 1, Plot of A vj., 9 at constant = 0.02, 0, -0.02, -0.04, -0.06 C m (from top to bottom) predicted by Ouidelli s et al two-dimensional model when r- = 3 and c = 5.5. (Reprinted from J. Electroanal. Chem., 197, R. Guidelli, M. L. Foresti, Statistical-Mechanical Treatment of an Adsorbed Monolayer with Local Order. Part III. p. 103, Copyright 1986, with permission from Elsevier Science).

The two-dimensional lattice model disregards completely any direct correlation between the adsorbed water molecules and the adjacent water molecules of the solution phase. In order to overcome this weakness Guidelli and Aloisi have developed a three-dimensional lattice model, the main features of which are the described next. 

On this issue Guidelli et al. expressed the view that phase transitions take plaee when the shape of the solute molecules hinders H-bond formation between water (solvent) molecules. In this case the water molecules are squeezed out of the adsorbed layer, leaving behind a compact film of solute molecules. This view seems to be verified by the three-dimensional lattice model, which in the presence of non-polar trimeric solute molecules does predict the occurrence of a phase transition. However, due to an inappropriate statistical mechanical approach based on the use of the grand ensemble H instead of the generalized ensemble A, it is not possible to know whether this model predicts correctly or not the properties of the phase transitions. ... 

Figure 20. Effect of electron spillover (- - -) on the adsorption isotherms predicted by Guidelli s et al three-dimensional model for a polar monomeric solute pointing towards the metal (A) and away from the metal (B) at = -...

The most important macroscopic and statistical thermodynamic models developed to describe adsorption phenomena on electrodes are presented critically in a concise and authoritative chapter by Panos Nikitas. The reader is guided through the seminal contributions of Frumkin, Butler, Bockris, Guidelli and others, to the current state of the art adsorption isotherms, which are both rigorous, and in good agreement with experiment. 

Modern theories have abandoned the idea that the water dipoles can take up only two orientations, though it occasionally still crops up in the literature. A significant conceptual progress was achieved in the work of Guidelli [10, 11]. He modeled the inner layer as a two-dimensional lattice. 

Figure 3. Adsurption isotherm predicted by Guidelli s ei al. three-dimensional model (—for (A) a polar dimeric solute adsorbed vertical or flat at o = 0, 0.05, 0.1 C m (from left to right), and (B) a polar monomeric solute at o 0.04, 0, -0.04, -0.08, -0.12 C m (from left to right). Broken lines represent the best Frumkin s isotherms. (Solid lines were reprinted from J. Electraanal. Chem., 329, R. Guidelli, and G..Aloisi, A three Dimensional Lattice Model of TIP4P Water Molecules and of Polar Monomeric and Dimeric Solute Molecules Against a Charged Wall., p.39, Copyright 1992, with permission from Elsevier Science).

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