Reaction-limited dissolution

In recent years two novel models [122,123] have appeared that were proposed to describe the heterogeneous features of drug dissolution. They are considered here as continuous (in well-stirred media) or discrete (in understirred media) reaction-limited dissolution models. Their derivation and relevance is discussed below. 

Figure 5.6 A discrete, reaction-limited dissolution process interpreted with the population growth model of dissolution.

Figure 7.7. Comparison of the CaS04 fluxes predicted for reaction limited dissolution, transport limited dissolution, and mixed kinetics...

In situ SAXS investigations of a variety of sol-gel-derived silicates are consistent with the above predictions. For example, silicate species formed by hydrolysis of TEOS at pH 11.5 and H20/Si = 12, conditions in which we expect monomers to be continually produced by dissolution, are dense, uniform particles with well defined interfaces as determined in SAXS experiments by the Porod slope of -4 (non-fractal) (Brinker, C. J., Hurd, A. J. and Ward, K. D., in press). By comparison, silicate polymers formed by hydrolysis at pH 2 and H20/Si = 5, conditions in which we expect reaction-limited cluster-cluster aggregation with an absence of monomer due to the hydrolytic stability of siloxane bonds, are fractal structures characterized by D - 1.9 (Porod slope — -1.9) (29-30). 

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,... 

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. 

Further, when k takes values much larger than 1/0, (5.24) exhibits chaotic behavior following the period-doubling bifurcation (cf. Chapter 3). For example, (5.24) leads to chaos when 1 /9 = 0.25 and k is greater than 0.855. Despite the aforementioned disadvantages, the model offers the sole approach that can be used to describe supersaturated dissolution data. In addition, the derivation of (5.24) relies on a model built from physical principles, i.e., a reaction-limited... 

Figure 3. Illustration of the pH dependence of the hydrolysis, condensation, and dissolution rates of silica. Condensation rates are judged by the reciprocal of gel times. RLCA denotes reaction-limited cluster aggregation. (Reproduced with permission from reference 30. Copyright 1988.)...

The solubility of silica is also important. Figure 48.7 shows the relative dissolution rate for aqueous silicates as a function of pH [23]. The rate is slow at low pH so there is little bond redistribution. SAXS studies coupled with computer simulations have shown that under these conditions reaction-limited cluster-cluster aggregation is... 

This model assumes laminar flow past a flat plate with L = 0.001 m and q = 0.001 m/sec (Table 7.3). Figure 7.7 shows that the rate of gypsum dissolution changes from reaction limited at T < 0°C to transport limited for T > 100° C. The apparent activation energy for the mixed kinetics model ranges from 22 kJ/ mol at 0°C to 5 kJ/mol at 100°C. 

Hydrolysis and condensation occur by bimolecular nucleophilic displacement reactions involving OH and Si-0 anions. For w > 4, the hydrolysis of all polymeric species is expected to be complete. Dissolution reactions provide a continual source of monomers. Because condensation occurs preferentially between weakly acidic species that tend to be protonated and strongly acidic species that are deprotonated, growth occurs primarily by reaction-limited monomer-cluster aggregation (equivalent to nucleation and growth), leading to compact, nonfractal structures. 

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