Based on the LBS Approach

The models of this category are based on the pioneering work by Levine, Bell and Smith in 1969, who modeled the inner layer of a charged interface in the absence of solute molecules as a two-dimensional sheet of polarizable point dipoles situated in vacuo. The dipoles are randomly distributed over the sites of a hexagonal lattice. This model has been extended to describe adsorption of solute molecules on electrode surfaces by Sangaranarayanan, Rangarajan and their col- 

The adsorbed layer is modeled as a two-dimensional sheet with a hexagonal lattice structure composed of adsorbate and solvent molecules, which behave as polarizable point dipoles. The solvent molecules in the form of either monomers or clusters may be in different polarization states (orientations) treated as independent species. Each adsorbed species i may occupy ri lattice sites. In addition, the thickness of the adsorbed layer may vary upon adsorption. For this reason we denote by h the thickness of the adsorbed layer when it is composed exclusively of the i-th species. 

If A(()V/i is the effective electric field acting on each adsorbed species i, then the electrical energy of the monolayer U is eqnal to the energy required to charge the monolayer in vacuo, i.e., to increase A( ) from zero to its final value, plus the work needed to bring the adsorbed species from an infinite distance outside the interface into the adsorbed layer when it is subject to a constant potential difference Aij), plus the work needed to produce induced dipoles. Therefore, If may be expressed as 

Indeed, the first term of Eq. (10) expresses the electrical energy enclosed in the monolayer when A( ) is increased in vacuo from zero to its final value, the second term represents the interaction energy of the permanent dipoles with the electric field, the third term is the interaction energy of the induced dipoles with the electric field, and the last term expresses the work needed to produce induced dipoles. 

Differentiation ofEq. (10) with respect to TV/ at constant A ( yields the electrical contribution to the chemical potential ofi 

---

The adsorbed layer is the scene of various interesting phenomena, like re-orientation of the adsorbate molecules, co-adsorption, polylayer formation, surface aggregation, adsorption of oligomers and, finally, surface phase transformations. All these phenomena can be treated within the frames of either the STE model or the models based on the LBS approach in precisely the same way We express the equilibrium equations first in terms of chemical potentials and next we introduce into these equations the expressions of the chemical potentials given by Eqs. (13) and (14). In some cases certain modifications are needed, as discussed below. 

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. 

The order of these 2D systems is produced by a chemical reaction at the interface as the system approaches equilibrium. Unfortunately, they appear to contain a significant number of pinholes and other defects [443-445]. Constrains exist also for monolayers based on the LB technique. These studies are limited to the choice of molecules with a very low solubility in the subphase [438, 439]. 

Another total synthesis of pamamycin-607 (lb) was reported in 2001 by our own group [6] at about the same time as the Lee synthesis. Here, the approach was based on the stereoselective intramolecular Diels-Alder reaction of vinyl-sulfonates and novel methods for elaboration of the resulting sultones [13,14]. 

The computational approach couples the two-phase LB model for the liquid water transport and the DNS model for the species and charge transport for the CL.25-27,68 The two-phase simulation using the LB model is designed based on the ex-situ, steady-state flow experiment for porous media, detailed earlier in the section 4.3, in order to obtain the liquid water distributions within the CL microstructure for different saturation levels resulting from the dynamic interactions between the two phases and the underlying pore morphology. The details of the simulation setup are provided in our work.27,61 62 Once steady state is achieved, 3-D liquid water distributions can be obtained within the CL, as shown in Fig. 13. From the liquid water distributions within the CL structure, the information about the catalytic site coverage effect can be extracted directly. 

There is an alternate approach to introducing the time dependence into electron transfer which is based on the adiabatic approximation. In the adiabatic approximation the effect of electronic coupling on the potential curves (Figure lb) is included from the beginning. The emphasis is on calculating the time dependence of the redistribution of electron density within the ground state, D—A V D —At, rather than calculating the transition rate between weakly perturbed but... 

Molecularly layered systems with built-in control of defects would therefore be highly interesting as an alternative to LB-films and we have developed 2 different approaches that are based on the self-organization of liquid crystals and on layer-by-layer adsorption from solution. Advantages and drawbacks of both techniques are briefly discussed below. 

Yet more elaborate super-molecular models were smdied by Balbuena et al. by introducing a co-solvent to EC in the solvation shell of LB, to take into account the presence of additives in real electrolytes. First the effects of VC [37] and later DMC, EMC, or DEC [39], were investigated. A similar approach was taken also for PC with VC as co-solvent [38]. Interestingly, in the super-molecules Li(EC) ,(VC)j, the preferential reduction of EC or VC depended on if the initial cychc reduction products or the final open-chain products were considered super-molecules with a cyclic VC anion were found to be the products of lowest energy in the first reduction step, but in the subsequent step the super-molecules with an open-chain EC anion formed the most stable products [37]. These differences, observed for all mixed solvent super-molecules - also for the combination PC and VC [38] - indicate the importance of the choice of reference state for predicting E. Should the predictions of relative stabilities be based on the initial step only or a multi-step reaction sequence,... 

---