Dissolution percolation modeling

On the basis of the results of preferential dissolution and starting from the percolation model, McCafferty [133, 134] developed a graph theory for the formation of oxide networks on binary alloys that is in agreement with the experimental findings on alloys such Fe-Cr, Co-Cr, Al-Cr, Ni-Cr, Fe-Si and Cu-Ni. 

Inductive Cluster Polarization. Reiser 21) noted that the rate changes caused by dissolution inhibitors are disproportionate to the amount of inhibitor used. For example, the dissolution rate of novolac is decreased by several orders of magnitude with an inhibitor loading of only 10 % (wt/wt). The percolation model predicts that the inhibitor must block the active sites of the novolac to the point that p falls below Pc. Reiser concluded that for such small loadings of inhibitor to block so many active sites each inhibitor must block several phenolic sites in the percolation field. 

The percolation model of selective dissolution, an extension of the surface diffusion mechanism, based on preexisting interconnected paths of like elements in the binary alloy and effects of curvature on dissolution potential [24, 25]. 

In the percolation model, it is the interconnectedness of atoms of the LN component that allows the dealloying front to proceed into the alloy. However, without allowing for surface diffusion, the dissolution process stops after penetrating a short distance into the crystal as the MN component covers the surface and prevents further dissolution [11],... 

The reason for the decrease in the polymer percolation threshold was suggested to be that the polymer experiences a sintering phenomenon that results in an almost continuum medium inside the US tablets. The drug particles are practically surrounded by the inert polymer, which diminished the contact with the dissolution medium and therefore slows down the release rate. So, in the case in which a component experiences a thermoplastic deformation, the continuum percolation model can be employed to explain the changes in the system with respect to a tablet obtained by a traditional... 

The percolation argument is based on the idea that with an increasing Cr content an insoluble interlinked cliromium oxide network can fonn which is also protective by embedding the otherwise soluble iron oxide species. As the tlireshold composition for a high stability of the oxide film is strongly influenced by solution chemistry and is different for different dissolution reactions [73], a comprehensive model, however, cannot be based solely on geometrical considerations but has in addition to consider the dissolution chemistry in a concrete way. 

The second model extends the surface diffusion model to include the importance of the atomic placement of atoms in the randomly packed alloy. The model considers that a continuous connected cluster of the less noble atoms must exist to maintain the selective dissolution process for more than just the few monolayers of the alloy. This percolating cluster of atoms provides a continuous active pathway for the corrosion process as well as a pathway for the electrolyte to penetrate the solid. This is expected to depend on a sharp critical composition of the less noble element, below which dealloying does not occur.54, (Corcoran)5... 

In 1991, Bonny and Leuenberger [40] explained the changes in dissolution kinetics of a matrix controlled-release system over the whole range of drug loadings on the basis of percolation theory. For this purpose, the tablet was considered a disordered system whose particles are distributed at random. These authors derived a model for the estimation of the drug percolation thresholds from the diffusion behavior. 

Reiser expanded the diffusion model for dissolution of novolac 13-24) using percolation theory (25, 2d) as a theoretical framework. Percolation theory describes the macroscopic event, the dissolution of resist into the developer, without necessarily understanding the microscopic interactions that dictate the resist behavior. Reiser views the resist as an amphiphilic material a hydrophobic solid in which is embedded a finite number of hydrophilic active sites (the phenolic hydrogens). When applied to a thin film of resist, developer diffuses into the film by moving from active site to active site. When the hydroxide ion approaches an active site, it deprotonates the phenol generating an ionic form of the polymer. In Reiser s model, the rate of dissolution of the resin. .. is predicated on the deprotonation process [and] is controlled by the diffusion of developer into the polymer matrix (27). 

Fig. 108. Model for the monodispefse dissolution of Ca-123 in an Y-123 matrix so that all NN are Y-I23. Clusters in the form of crosses, consisting of 4 distorted molecules of Y-123 surrounding 1 molecule of Ca-123 are proposed. A percolation is expected at 12% Ca. This is in good agreement with the experiment (fig. 107). Based on this model one would expect that the holes introduced by the Ca into the Y matrix will be screened by the Y-123 NN. After Rohler et al. (1999b).

Atomistic Modeling of Selective Dissolution and Related Passivation by Percolation Theory... 

The Critical Potential The nature of the critical potential, (see Fig. 30) was addressed in the framework of this model. No definite conclusions are established. may be the balance point between the smoothing action of surface diffusion and the roughening action of dissolution. Another explanation regards E as a threshold potential above which percolation becomes possible within a connected subset of A-type atoms with lowered reactivity due to their atomic surrounding (high-density percolation problem). 

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