Interfacial layer model

Zhou C B, Chen Y F, Jiang Q H, etc. 2008, An interfacial layer model for coupled hydro mechanical analysis in geological discontinuities[J]. Chinese Journal of Rock Mechanics and Engineering, 27[6] 1081-1093. (in Chinese). 

Figure 7.6 Non-polar interfacial layer model proposed for the alcohol/room-temperarnre ionic liquid interface [461.

Novotny et al. [41] used p-polarized reflection and modulated polarization infrared spectroscopy to examine the conformation of 1 -1,000 nm thick liquid polyperfluoropropy-lene oxide (PPFPO) on various solid surfaces, such as gold, silver, and silica surfaces. They found that the peak frequencies and relative intensities in the vibration spectra from thin polymer films were different from those from the bulk, suggesting that the molecular arrangement in the polymer hlms deviated from the bulk conformation. A two-layer model has been proposed where the hlms are composed of interfacial and bulk layers. The interfacial layer, with a thickness of 1-2 monolayers, has the molecular chains preferentially extended along the surface while the second layer above exhibits a normal bulk polymer conformation. 

The theoretical approach by Samec based on the ion-free compact layer model established that the true apparent transfer coefficient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide-Fc system provided values of a smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on defining effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that k i is... 

The competition model and solvent interaction model were at one time heatedly debated but current thinking maintains that under defined r iitions the two theories are equivalent, however, it is impossible to distinguish between then on the basis of experimental retention data alone [231,249]. Based on the measurement of solute and solvent activity coefficients it was concluded that both models operate alternately. At higher solvent B concentrations, the competition effect diminishes, since under these conditions the solute molecule can enter the Interfacial layer without displacing solvent molecules. The competition model, in its expanded form, is more general, and can be used to derive the principal results of the solvent interaction model as a special case. In essence, it seems that the end result is the same, only the tenet that surface adsorption or solvent association are the dominant retention interactions remain at variance. 

One approach to the study of solubility is to evaluate the time dependence of the solubilization process, such as is conducted in the dissolution testing of dosage forms [70], In this work, the amount of drug substance that becomes dissolved per unit time under standard conditions is followed. Within the accepted model for pharmaceutical dissolution, the rate-limiting step is the transport of solute away from the interfacial layer at the dissolving solid into the bulk solution. To measure the intrinsic dissolution rate of a drug, the compound is normally compressed into a special die to a condition of zero porosity. The system is immersed into the solvent reservoir, and the concentration monitored as a function of time. Use of this procedure yields a dissolution rate parameter that is intrinsic to the compound under study and that is considered an important parameter in the preformulation process. A critical evaluation of the intrinsic dissolution methodology and interpretation is available [71]. 

Fig. 15 Two of the simplest theories for the dissolution of solids (A) the interfacial barrier model, and (B) the diffusion layer model, in the simple form of Nemst [105] and Brunner [106] (dashed trace) and in the more exact form of Levich [104] (solid trace). c is the concentration of the dissolving solid, cs is the solubility, cb is the concentration in the bulk solution, and x is the distance from the solid-liquid interface of thickness h or 8, depending on how it is defined. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., from Ref. 1, p. 478.)...

The description of the sorption of charged molecules at a charged interface includes an electrostatic term, which is dependent upon the interfacial potential difference, Ai//(V). This term is in turn related to the surface charge density, electric double layer model. The surface charge density is calculated from the concentrations of charged molecules at the interface under the assumption that the membrane itself has a net zero charge, as is the case, for example, for membranes constructed from the zwitterionic lecithin. Moreover,... 

The triple layer model has been described in detail elsewhere (11, 16, 17) however, the model as reported here has been slightly modified from the original versions (11, 15) in two ways (i) metal ions are allowed to form surface complexes at either the o- or 8-plane insted of at the 8-plane only, and (ii) the thermodynamic basis of the TLM has been modified leading to a different relationship between activity coefficients and interfacial potentials. The implementation and basis for these modifications are described below. 

In a biphasic system, the same rules as above apply, however, the rate of the reaction and the position of the equilibrium are determined by the concentration of the reactants and products in the phase where the reaction takes place, rather than their overall concentration in the system. Exactly where the reaction actually takes place is still a matter of debate, with two locations proposed, specifically, at the interfacial layer between the two phases (model 1) and in the bulk of the catalyst-containing phase (model 2), as shown in Figure 2.9. 

In the three layer model shown in Fig. 5-8, the electric capacity C of an interfacial electric double layer is represented by a series connection of three... 

In comparing Eqn. 5-39 with Eqn. 5-9 (4< >h = gia.+ M.d - s,dip), which is based on the classical double layer model, it appears that the sum of the first, second and third terms on the right hand side of Eqn. 5-39 corresponds to the sum of gbm due to the interfadal charge and gM,dii> due to the interfacial dipole on the metal side and the fourth term corresponds to gs.dip due to the interfadal dipole of adsorbed water molecules on the solution side. These equivalences give Eqns. 6-40 and 5-41 ... 

The presence of a low-viscosity interfacial layer makes the determination of the boundary condition even more difficult because the location of a slip plane becomes blurred. Transitional layers have been discussed in the previous section, but this is an approximate picture, since it stiU requires the definition of boundary conditions between the interfacial layers. A more accurate picture, at least from a mesoscopic standpoint, would include a continuous gradient of material properties, in the form of a viscoelastic transition from the sohd surface to the purely viscous liquid. Due to limitations of time and space, models of transitional gradient layers will be left for a future article. 

To summarize, to properly model liquid water transport and ensuing flooding effect on cell performance, one must consider four submodels (1) a model of catalytic surface coverage by liquid water inside the catalyst layer, (2) a model of liquid water transport through hydrophobic microporous layer and GDL, (3) an interfacial droplet model at the GDL surface, and last (4) a two-phase flow model in the gas channel. Both experimental and theoretical works, in academia and industry alike, are ongoing to build models for the four key steps of water generation, transport, and removal from a PEFC. 

G. Pirug, H. P. Bonzel, Electrochemical double-layer modeling under idtrahigh vacuum conditions in Interfacial Electrochemistry. Theory, Experiment and Applica tions (Eds. A. Wifckowski), Marcel Dekker New York-Basel, 1999, p. 269. 

In addition to these experimental methods, there is also a role for computer simulation and theoretical modelling in providing understanding of structural and mechanical properties of mixed interfacial layers. The techniques of Brownian dynamics simulation and self-consistent-field calculations have, for example, been used to some advantage in this field (Wijmans and Dickinson, 1999 Pugnaloni et al., 2003a,b, 2004, 2005 Parkinson et al., 2005 Ettelaie et al., 2008). 

Among what have been widely employed as model compounds for Chi, are porphyrins, phthalocyanines, and some photoactive transition metal complexes, which are more stable and easier to obtain than Chi. Interfacial layers of these insoluble compounds are generally prepared by means of vacuum sublimation or solvent evaporation. 

FIGURE 17.1 (a) Diffusion-layer model of dissolution, (b) Interfacial barrier model of dissolution. 

Two of the simplest theories to explain the dissolution rate of solutes are the interfacial barrier model and the diffusion-layer model (Figures 17.1 and 17.2). Both of these theories make the following two assumptions ... 

Emulsions are two-phase systems formed from oil and water by the dispersion of one liquid (the internal phase) into the other (the external phase) and stabilized by at least one surfactant. Microemulsion, contrary to submicron emulsion (SME) or nanoemulsion, is a term used for a thermodynamically stable system characterized by a droplet size in the low nanorange (generally less than 30 nm). Microemulsions are also two-phase systems prepared from water, oil, and surfactant, but a cosurfactant is usually needed. These systems are prepared by a spontaneous process of self-emulsification with no input of external energy. Microemulsions are better described by the bicontinuous model consisting of a system in which water and oil are separated by an interfacial layer with significantly increased interface area. Consequently, more surfactant is needed for the preparation of microemulsion (around 10% compared with 0.1% for emulsions). Therefore, the nonionic-surfactants are preferred over the more toxic ionic surfactants. Cosurfactants in microemulsions are required to achieve very low interfacial tensions that allow self-emulsification and thermodynamic stability. Moreover, cosurfactants are essential for lowering the rigidity and the viscosity of the interfacial film and are responsible for the optical transparency of microemulsions [136]. 

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