Model interfacial barrier

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 interfacial barrier theory is illustrated in Fig. 15A. Since transport does not control the dissolution rate, the solute concentration falls precipitously from the surface value, cs, to the bulk value, cb, over an infinitesimal distance. The interfacial barrier model is probably applicable when the dissolution rate is limited by a condensed film absorbed at the solid-liquid interface this gives rise to a high activation energy barrier to the surface reaction, so that kR kj. Reaction-controlled dissolution is somewhat rare for organic compounds. Examples include the dissolution of gallstones, which consist mostly of cholesterol,... 

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 ... 

It is worth repeating the above. T o date, the effects of the presence of interfacial barriers or interface regions have not been explicitly considered in models of charge injection at such interfaces. The... 

Figure 5.2 Schematic representation of the dissolution mechanisms according to (A) the diffusion layer model, and (B) the interfacial barrier model.

In the interfacial barrier model of dissolution it is assumed that the reaction at the solid-liquid interface is not rapid due to the high free energy of activation requirement and therefore the reaction becomes the rate-limiting step for the dissolution process (Figure 5.1), thus, drug dissolution is considered as a reaction-limited process for the interfacial barrier model. Although the diffusion layer model enjoys widespread acceptance since it provides a rather simplistic interpretation of dissolution with a well-defined mathematical description, the interfacial barrier model is not widely used because of the lack of a physically-based mathematical description. 

Stochastic variation may be introduced in other models as well. In this context, Lansky and Weiss [130] have also considered random variation for the parameter k of the interfacial barrier model (5.20). 

The previous model erases aU electrical fields and interfacial barriers in the mesostructure, which is viewed in effect as a homogeneous medium. However, in semiconductor mesostructures, filled with an HTM, one can also allow for the presence of an electrical field and semiconductor barrier at the internal interface ETM/HTM. The prevalence of one approach or the other, i.e., a macrohomogeneous model that only contemplates the Fermi level or the explicit presence of internal interface barriers, depends on doping densities, size of semiconductor particles or wires, and Debye length both in the semiconductor nanostructure and in the HTM [95-97]. 

Studies based on the Frenkel-Kontorova model reveal that static friction depends on the strength of interactions and structural commensurability between the surfaces in contact. For surfaces in incommensurate contact, there is a critical strength, b, below which the depinning force becomes zero and static friction disappears, i.e., the chain starts to slide if an infinitely small force F is applied (cf. Section 3). This is understandable from the energetic point of view that the interfacial atoms in an incommensurate system can hardly settle in any potential minimum, or the energy barrier, which prevents the object from moving, can be almost zero. 

It has been proposed recently [28] that static friction may result from the molecules of a third medium, such as adsorbed monolayers or liquid lubricant confined between the surfaces. The confined molecules can easily adjust or rearrange themselves to form localized structures that are conformal to both adjacent surfaces, so that they stay at the energy minimum. A finite lateral force is required to initiate motion because the energy barrier created by the substrate-medium system has to be overcome, which gives rise to a static friction depending on the interfacial substances. The model is consistent with the results of computer simulations [29], meanwhile it successfully explains the sensitivity of friction to surface film or contamination. 

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