Solvent monolayer models

With the addition of a pseudopotential interaction between electrons and metal ions, the density-functional approach has been used82 to calculate the effect of the solvent of the electrolyte phase on the potential difference across the surface of a liquid metal. The solvent is modeled as a repulsive barrier or as a region of dielectric constant greater than unity or both. Assuming no specific adsorption, the metal is supposed to be in contact with a monolayer of water, modeled as a region of 3-A thickness (diameter of a water molecule) in which the dielectric constant is 6 (high-frequency value, appropriate for nonorientable dipoles). Beyond this monolayer, the dielectric constant is assumed to take on the bulk liquid value of 78, although the calculations showed that the dielectric constant outside of the monolayer had only a small effect on the electronic profile. 

Two models have been proposed to describe the process of retention in liquid chromatography (Figure 3.3), the solvent-interaction model (Scott and Kucera, 1979) and the solvent-competition model (Snyder, 1968 and 1983). Both these models assume the existence of a monolayer or multiple layers of strong mobile-phase molecules adsorbed onto the surface of the stationary phase. In the solvent-partition model the analyte is partitioned between the mobile phase and the layer of solvent adsorbed onto the stationary-phase surface. In the solvent-competition model, the analyte competes with the strong mobile-phase molecules for active sites on the stationary phase. The two models are essentially equivalent because both assume that interactions between the analyte and the stationary phase remain constant and that retention is determined by the composition of the mobile phase. Furthermore, elutropic series, which rank solvents and mobile-phase modifiers according to their affinities for stationary phases (e.g. Table 3.1), have been developed on the basis of experimental observations, which cannot distinguish the two models of retention. 

Solvent competition model for normal-phase liquid chromatography. Like the solvent-interaction model, the solvent-competition model assumes that the stationary phase is covered with a monolayer of molecules of the strongest component of the mobile phase. This model also assumes that the concentration of analyte in the stationary phase is small compared with the concentration of solvent molecules and that solute-solvent interactions in the mobile phase are cancelled by identical interactions in the stationary phase. The competition between the analyte molecules, x, and the mobile phase molecules. A, for the active site or sites on the stationary phase is given by... 

Fig. 10.23 Models of the solvent monolayer at the electrode solution interface according to (a) the two-state model with spherical solvent dipoles in either the up (f) or down orientations ( ) (b) the three-state model in which a third state with solvent dipoles parallel ( ) to the interface has been added (c) the cluster model with clusters in the up (/ / ) and down ( / ) orientations, and single molecules up (t) and down (f,).

A more reasonable deseription of a solvent monolayer at the interfaee should inelude solvent dipoles in all possible orientations. However, if one is only interested in the potential drop due to the monolayer in a direetion perpendieular to the interface, and chemieal interaetions are ignored, it would be suffieient to eonsider three states, namely, those whieh result from veetor resolution of all possible orientations. These orientations are the two eonsidered above, up and down, and a third orientation with the dipole veetor parallel to the interfaee. The three-state model (fig. 10.23) has been applied to deseribe the strueture of aprotic solvents at charged interfaees [37]. If one extends the two-state model of Watts-Tobin, the electroehemical potential of the third state is given by... 

Fig. 9 The dependence of the effective thickness of the potential drop region in the metal surface layer, calculated by the Amokrane-Badiali model [19] (at constant capacitance of solvent monolayer, Cs), on the charge density for aqueous solution on different electrodes (a) 1, Sb(l 11) 2, Sb(OOl) 3, Bi(lll) 4, Hg 5, Bi(OOl) 6, Cd (0001) 7, Cd(1120) and 8, Ga and for Bi(OOl) in various solvents (b) 1, methanol 2, H2O 3, acetonitrile (updated from Ref [15, 15]).

Various functional forms for / have been proposed either as a result of empirical observation or in terms of specific models. A particularly important example of the latter is that known as the Langmuir adsorption equation [2]. By analogy with the derivation for gas adsorption (see Section XVII-3), the Langmuir model assumes the surface to consist of adsorption sites, each having an area a. All adsorbed species interact only with a site and not with each other, and adsorption is thus limited to a monolayer. Related lattice models reduce to the Langmuir model under these assumptions [3,4]. In the case of adsorption from solution, however, it seems more plausible to consider an alternative phrasing of the model. Adsorption is still limited to a monolayer, but this layer is now regarded as an ideal two-dimensional solution of equal-size solute and solvent molecules of area a. Thus lateral interactions, absent in the site picture, cancel out in the ideal solution however, in the first version is a properly of the solid lattice, while in the second it is a properly of the adsorbed species. Both models attribute differences in adsorption behavior entirely to differences in adsorbate-solid interactions. Both present adsorption as a competition between solute and solvent. 

Bead-spring models without explicit solvent have also been used to simulate bilayers [40,145,146] and Langmuir monolayers [148-152]. The amphi-philes are then forced into sheets by tethering the head groups to two-dimensional surfaces, either via a harmonic potential or via a rigid constraint. 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

Snyder and Soczewinski created and published, at the same time, another model called the S-S model describing the adsorption chromatographic process [19,61]. This model takes into account the role of the mobile phase in the chromatographic separation of the mixture. It assumes that in the chromatographic system the whole surface of the adsorbent is covered by a monolayer of adsorbed molecules of the mobile phase and of the solute and that the molecules of the mobile phase components occupy sites of identical size. It is supposed that under chromatographic process conditions the solute concentrations are very low, and the adsorption layer consists mainly of molecules of the mobile phase solvents. According to the S-S model, intermolecular interactions are reduced in the mobile phase but only for the... 

The ionic profile of the metal was modeled as a step function, since it was anticipated that it would be much narrower than the electronic profile, and the distance dx from this step to the beginning of the water monolayer, which reflects the interaction of metal ions and solvent molecules, was taken as the crystallographic radius of the metal ions, Rc. Inside the metal, and out to dl9 the relative dielectric constant was taken as unity. (It may be noted that these calculations, and subsequent ones83 which couple this model for the metal with a model for the interface, take the position of the outer layer of metal ion cores to be on the jellium edge, which is at variance with the usual interpretation in terms of Wigner-Seitz... 

Nucleic acids, DNA and RNA, are attractive biopolymers that can be used for biomedical applications [175,176], nanostructure fabrication [177,178], computing [179,180], and materials for electron-conduction [181,182]. Immobilization of DNA and RNA in well-defined nanostructures would be one of the most unique subjects in current nanotechnology. Unfortunately, a silica surface cannot usually adsorb duplex DNA in aqueous solution due to the electrostatic repulsion between the silica surface and polyanionic DNA. However, Fujiwara et al. recently found that duplex DNA in protonated phosphoric acid form can adsorb on mesoporous silicates, even in low-salt aqueous solution [183]. The DNA adsorption behavior depended much on the pore size of the mesoporous silica. Plausible models of DNA accommodation in mesopore silica channels are depicted in Figure 4.20. Inclusion of duplex DNA in mesoporous silicates with larger pores, around 3.8 nm diameter, would be accompanied by the formation of four water monolayers on the silica surface of the mesoporous inner channel (Figure 4.20A), where sufficient quantities of Si—OH groups remained after solvent extraction of the template (not by calcination). 

A Au-coated substrate is another model surface, to which many surface characterization methods can be applied. To achieve surface-initiated ATRP on Au-coated substrates, some haloester compounds with thiol or disulflde group were developed [80-84]. Self-assembled monolayers (SAM) of these compounds were successfully prepared on a Au-coated substrate and used for ATRP graft polymerization. Because of the limited thermal stability of the S - Au bond, the ATRP was carried out at a relatively low temperature, mostly at room temperature, by using a highly active catalyst system and water as a (co)solvent (water-accelerated ATRP). 

The water-shell-model, strictly speaking, will only apply to very hydrophilic enzymes which do not contain hydrophobic parts. Many enzymes, like lipases, are surface active and interact with the internal interface of a microemulsion. In fact, lipases need a hydrophobic surface in order to give the substrate access to the active site of the enzyme. Nevertheless, Zaks and Klibanov found out that it is often not necessary to have a monolayer of water on the enzyme surface in order to perform a catalytic reaction in an organic solvent [98]. 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

The method has been applied, for example, in electrochemical investigations (110) and also for surface catalytic reactions in the presence of a gas phase 111). When PM-IRRAS is used with a thin-layer cell, as depicted in Fig. 37, the contribution from dissolved molecules in the liquid phase can be minimized. Still, the layer thickness has to be small to prevent complete absorption of the IR radiation by the solvent. The combination of polarization modulation and ATR for metal films was demonstrated recently and applied in an investigation of self-assembled octadecylmercaptan monolayers on thin gold films 112). This combination could emerge as a valuable technique for the investigation of model catalysts. 

Figure 2.13 illustrates what is currently a widely accepted model of the electrode-solution interphase. This model has evolved from simpler models, which first considered the interphase as a simple capacitor (Helmholtz), then as a Boltzmann distribution of ions (Gouy-Chapman). The electrode is covered by a sheath of oriented solvent molecules (water molecules are illustrated). Adsorbed anions or molecules, A, contact the electrode directly and are not fully solvated. The plane that passes through the center of these molecules is called the inner Helmholtz plane (IHP). Such molecules or ions are said to be specifically adsorbed or contact adsorbed. The molecules in the next layer carry their primary (hydration) shell and are separated from the electrode by the monolayer of oriented solvent (water) molecules adsorbed on the electrode. The plane passing through the center of these solvated molecules or ions is referred to as the outer Helmholtz plane (OHP). Beyond the compact layer defined by the OHP is a Boltzmann distribution of ions determined by electrostatic interaction between the ions and the potential at the OHP and the random jostling of ions and... 

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