Crystal dissolution diffusion-controlled

Diffusive crystal dissolution means that crystal dissolution is controlled by diffusion, which requires high interface reaction rate and absence of convection. In nature, diffusive crystal dissolution is rarely encountered, because there is almost always fluid flow, or crystal falling or rising in the fluid. That is, crystal dissolution in nature is often convective dissolution, which is discussed in the next section. One possible case of diffusive crystal dissolution is for crystals on the roof or floor of a magma chamber if melt produced by dissolution does not sink or rise. For these... 

Under diffusion-controlled dissolution conditions (in the anodic direction) the crystal orientation has no influence on the reaction rate as only the mass transport conditions in the solution detennine the process. In other words, the material is removed unifonnly and electropolishing of the surface takes place. 

Firstly, they might be expected to have an effect when corrosion occurs under conditions of active (film-free) anodic dissolution and is not limited by the diffusion of oxygen or some other species in the environment. However, if the rate of active dissolution is controlled by the rate of oxygen diffusion, or if, in general terms, the rate-controlling process does not take place at the metal surface, the effect of crystal defects might be expected to be minimal. 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

To use this method to obtain diffusivity, the dissolution must be diffusion controlled. The diffusion aspect was discussed in Section 3.5.5.1, and the heterogeneous reaction aspect is discussed later. The melt growth distance (L, which differs from the crystal dissolution distance by the factor of the density ratio of crystal to melt) may be expressed as (Equation 3-115d)... 

Comparing the rate of crystal dissolution versus complete melting versus partial melting, one finds that complete melting is the most rapid (controlled by heat transfer), dissolution is slower, and partial melting controlled by diffusion in the solid phase is the slowest. 

For convective crystal dissolution, the dissolution rate is u = (p/p )bD/8. For diffusive crystal dissolution, the dissolution rate is u = diffusive boundary layer thickness as 5 = (Df), the diffusive crystal dissolution rate can be written as u = aD/5, where a is positively related to b through Equation 4-100. Therefore, mass-transfer-controlled crystal dissolution rates (and crystal growth rates, discussed below) are controlled by three parameters the diffusion coefficient D, the boundary layer thickness 5, and the compositional parameter b. The variation and magnitude of these parameters are summarized below. 

Clearly, under conditions of diffusion control the rate of dissolution expressed in terms of the concentration of dissolving elements in the melt does not depend upon the atomic packing density of the crystallographic faces of any substance under investigation. Therefore, dissolution of single crystals of different orientation (line 2 in Fig. 5.7) is characterised by the... 

When an ionic single crystal is immersed in solution, the surrounding solution becomes saturated with respect to the substrate ions, so, initially the system is at equilibrium and there is no net dissolution or growth. With the UME positioned close to the substrate, the tip potential is stepped from a value where no electrochemical reactions occur to one where the electrolysis of one type of the lattice ion occurs at a diffusion controlled rate. This process creates a local undersaturation at the crystal-solution interface, perturbs the interfacial equilibrium, and provides the driving force for the dissolution reaction. The perturbation mode can be employed to initiate, and quantitatively monitor, dissolution reactions, providing unequivocal information on the kinetics and mechanism of the process. 

FIG. 28 Dissolution rate image of the (010) surface of potassium ferrocyanide trihydrate recorded in the same area of the crystal as the topographic image shown in Figure 27. The tip was held at a potential to establish the diffusion-controlled oxidation of ferrocyanide and scanned at a speed of 50 gm s... 

Equation 9.30 describes a diffusion-controlled dissolution process (4). It is visualized that when solid drug particles are introduced to the fluids at the absorption sites, the drug promptly saturates the diffusion layer (Fig. 9.17). This is followed by the diffusion of drug molecules from the diffusion layer into the bulk solution, which is instantly replaced in the diffusion layer by molecules from the solid crystal or particle. This is a continuous process. Although it oversimplifies the dynamics of the dissolution process. Equation 9.30 is a qualitatively useful equation and clearly indicates the effects of some important factors on the dissolution and, therefore, the absorption rate of drugs. When dissolution is the rate-limiting factor in the absorption, then bioavailability is affected. These factors are listed in Table 9.4. 

If both crystallization and dissolution processes were purely diffusion controlled in nature, they should exhibit a true reciprocity the rate of crystallization should equal the rate of dissolution at a given temperature and under equal concentration driving forces, i.e. at equal displacements away from the equilibrium saturation conditions. In addition, all faces of a crystal would grow and dissolve at the same rate. These conditions rarely, if ever, occur in practice. 

Different crystallographic planes of a semiconductor electrode usually exhibit different reaction kinetics. It was found in III-V compounds in indifferent electrolytes that the (lll)B face terminated with the anion plane (P, As) etched faster than the (lll)A face containing the cations (Ga, In) [47]. The planes composed entirely of metal atoms react more slowly than any other crystal plane because of the stable metal oxide layer, which can be formed on such planes. Consequently on these planes termed etch stop planes, provision of reactants (diffusion control) is not rate-limiting. In Si, the (100) planes are known to etch faster than (111) planes in alkaline solutions. This property is at the origin of various apphcations, such as texturization of silicon surface [formation of pyramids on (100) planes], which allows reduction of reflectivity of the front surface of solar cells and Si micromachining [48]. The semiconductor surface may be shaped during the anodic dissolution... 

Investigation of the dissolution of ionic solids by SECM is based on the use of the UME tip to oxidize or reduce a component of the crystal in order to generate a controllable undersaturation at the crystal surface [20-24]. This induces crystal dissolution and the rate of dissolution determines the extent of feedback [20]. Two limiting cases of the Bur-ton-Cabrera-Frank Model corresponding to detachment (n = 1) and surface diffusion n = 2) as the rate limiting steps were simulated in Eq. (11) ... 

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