Dissolution kinetics rate-limiting steps

QCM measurements directly give in-situ kinetic information of reactions inside the cell. Figure 8 shows the tight correlation of dissolution with the square root of time. The resonance frequency change was converted to that of surface mass using eq.(3). This linear dependency indicates a strong possibility of diffusion-controlled dissolution. The rate-limiting step, in this case, seems to be diffusion of Cu(acac)2 to the ambient fluid. 

Divalent dissolution is initiated by a hole from the bulk approaching the silicon-electrolyte interface which allows for nucleophilic attack of the Si atom (step 1 in Fig. 4.3). This is the rate-limiting step of the reaction and thereby the origin of pore formation, as discussed in Chapter 6. The active species in the electrolyte is HF, its dimer (HF)2, or bifluoride (HF2), which dissociates into HF monomers and l ions near the surface [Okl]. The F ions in the solution seem to be inactive in the dissolution kinetics [Se2], Because holes are only available at a certain anodic bias, the Si dissolution rate becomes virtually zero at OCP and the surface remains Si-H covered in this case, which produces a hydrophobic silicon surface. 

Fig. 2.3 Rate-limiting steps in mineral dissolution (a) transport-controlled, (b) surface reaction-controlled, and (c) mixed transport and surface reaction control. Concentration (C) versus distance (r) from a crystal surface for three rate-controUing processes, where is the saturation concentration and is the concentration in an infinitely diluted solution. Reprinted from Sparks DL (1988) Kinetics of soil chemical processes. Academic Press New York 210 pp. Copyright 2005 with permission of Elsevier...

This equation again demonstrates that particle size and solubility are the main parameters affecting dissolution kinetics of drug powders, which, in turn, could affect the release profile of dosage forms if dissolution is the rate-limiting step of in vivo absorption. Table 5.1 demonstrates several examples of dissolution times of spherical particles (assuming monodispersed systems) as a function of solubility and particle size. 

For water-soluble coatings that consist mainly of polymers, dissolution or erosion of the coat is the rate-limiting step toward the controlled release. After the coat is dissolved, the drug substance in the core is released, and the release kinetics depend on the core properties. Based on Eq. (5.2), solubility and dissolution/hydration behaviors of the pri-... 

Rate-Limiting Steps in Mineral Dissolution 146 Feldspar, Amphibole, and Pyroxene Dissolution Kinetics 148 Parabolic Kinetics 149 Dissolution Mechanism 155 Dissolution Rates of Oxides and Hydroxides 156 Supplementary Reading 161... 

LiBH4, NaBH4 and the ammonium salts all possess low solubility in the organic solvents in question, ivith slow dissolution kinetics. The slow dissolution of the reactants is the rate-limiting step and prohibits, together with the production of large amounts of by-products, the economic production of AB materials. 

Ligand-Promoted Dissolution. In some cases, organic matter-surface associations markedly increase oxide dissolution rates. The acceleration of oxide dissolution by organic ligands exhibits saturation kinetics that is, the dissolution rate reaches a plateau at high concentration of dissolved ligand as the surface becomes saturated. This behavior is characteristic of surface-controlled reactions (in which the reaction of a surface-bound species is the rate-limiting step) and is consistent with the direct dependence of the dissolution rate on the concentration of the reactive species at the surface (22-24). 

This mechanism is similar to the one occurring during liquid-phase sintering, where the dissolution of crystalline material into the glassy phase occurs at the interfaces loaded in compression and their reprecipitation on interfaces loaded in tension. The rate-limiting step in this case can be either the dissolution kinetics or transport through the boundary phase, whichever is slower. This topic was discussed in some detail in Chap. 10, and will not be repeated here. 

Quantification of the absorbed dose involves As dissolution and biological uptake. It is not yet fully understood whether absorption of soluble As is an active or passive mechanism. To further complicate the issue, the rate-limiting step (dissolution kinetics vs. absorption mechanism) has not yet been determined. 

Furthermore, the hydrolysis of butyl acetate and methyl pivalate in benzene in the presence of KOH at 25 °C as well as the reaction of potassium phenolate with benzyl chloride in boiling acetonitrile are accelerated by addition of polyoxyethylene [183]. The catalytic effect of POE is augmented by an increase in the number of oxyethylene units, i.e. 1 <6< 12. PEO is also an interfacial catalyst of the reaction of phenol and 2,4,6-trimethylphenol with methyl iodide in water-chloroform and dichloromethane. The kinetic study of the reaction between benzyl chloride and potassium acetate in the presence of PEO of variable molecular weight in toluene and butanol has been performed with IR spectroscopy [184]. The dissolution of a reagent of poor solubility is apparently a rate-limiting step of the reaction in a solution of low polarity (toluene). The presence of PEO impurities in toluene has been detected. Moreover, effect of PEO and crown ethers as phase transfer catalysts has been compared. In a low-polarity solvent, oligoethylene oxides are more effective catalysts, while in a polar solvent (butanol) the effectiveness of PEO and crown ethers as phase transfer catalysts is similar. 

Obviously, the parameter y is a measure of the kinetic situation when the rate-limiting step of the selective dissolution is the solid-phase diffusion mass transfer. It is clear that the increase in y contributes to the transition to the solid-phase diffusion control of the process the similar criterion was found in [4] for chronoampero- and chronopotentiometric diffusion problems of homogeneous binary alloys SD. 

Electroless deposition of Au in KAu(CN)2 -I- HF can be controlled by both the kinetic process and the diffusion process. The deposition is a two-step process, with initial diffusion-limited deposition of the intermediate species, followed by surface-limited reduction of this species. For electroless deposition of Pt, it has been reported that the rate-determining step is the deposition on n-Si, whereas it is the dissolution of silicon on p-Si. Electroless copper deposition does not occur on Si02-covered silicon surface due to the lack of anodic dissolution of silicon In a non-HF solution, the deposition of copper on a bare silicon surface results in the formation of oxide aroimd the metal particles. In HF solutions, the deposition of copper proceeds very slowly in the dark on both p-Si and n-Si samples due to the lack of carriers. The... 

The kinetics of several well-known electrochemical reactions have been studied in the presence of an ultrasonic field by Altukhov et al. [142], The anodic polarization curves of Ag, Cu, Fe, Cd, and Zn in various solutions of HC1 and H2S04 and their salts were measured in an ultrasonic field at various intensities. The effect of the ultrasonic field on the reaction kinetics was found to be dependent on the mechanism of metal anodic dissolution, especially on the effect of this field on the rate-determining step of the reaction. The results showed that the limiting factor of the anodic dissolving of Cu and Ag is the diffusion of reaction products, while in the case of Fe it is the desorption of anions of solution from the anode surface, and at Cd the limiting factor is the rate of destruction of the crystal lattice. Similar results were obtained by Elliot et al. [ 143] who studied reaction geometry in the oxidation and reduction of an alkaline silver electrode. 

The kinetics for a solvent mediated phase transformation will be governed by the kinetics of dissolution, nucleation, and crystal growth. These rates will depend directly on the solvent and any step may be rate limiting. As discussed in earlier sections of this chapter, the solvent influences the nucleation rate and crystal growth rate via two factors 1) solute solubility and 2) specific solvent-solute interactions. The dissolution rate will also be solvent dependent as pharmaceutical materials generally exhibit a wide range of dissolution rates in different solvents. 

---