Diffusion controlled dissolution

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. 

R Braun, E Parrot. Effect of various parameters upon diffusion-controlled dissolution of benzoic acid. J Pharm Sci 61 592, 1972. 

Leblanc and Fogler developed a population balance model for the dissolution of polydisperse solids that included both reaction controlled and diffusion-controlled dissolution. This model allows for the handling of continuous particle size distributions. The following population balance was used to develop this model. 

As was mentioned in the introduction to this chapter "diffusion-controlled dissolution" may occur because a thin layer either in the liquid film surrounding the mineral or on the surface of the solid phase (that is depleted in certain cations) limits transport as a consequence of this, the dissolution reaction becomes incongruent (i.e., the constituents released are characterized by stoichiometric relations different from those of the mineral. The objective of this section is to illustrate briefly, that even if the dissolution reaction of a mineral is initially incongruent, it is often a surface reaction which will eventually control the overall dissolution rate of this mineral. This has been shown by Chou and Wollast (1984). On the basis of these arguments we may conclude that in natural environments, the steady-state surface-controlled dissolution step is the main process controlling the weathering of most oxides and silicates. 

Cable M. and Frade J.R. (1987a) The diffusion-controlled dissolution of spheres. /. Mater. Sci. 22, 1894-1900. 

Figure 16-6. Electrochemical set-up for the registration of a) the diffusion controlled dissolution of A in B b) an interface controlled dissolution of A in B. At = A , ttA(t) is determined by a solid emf probe. AX = electrolyte.

J. Wang and D. R. Flanagan, General Solution for Diffusion-Controlled Dissolution of Spherical Particles. 1. Theory, J. Pharm. Sci., 88, 731 (1999). 

Both Peterson (41) and Berger (42) found that dissolution started at approximately 0.5 km water depth and the rate of dissolution increased slowly with increasing water depth until a depth of approximately 3.8 km was reached. Below this depth the rate of dissolution rapidly increased with increasing water depth. The change in the saturation state of seawater, with respect to calcite, in the deep water of this region is close to linear with depth (43). Consequently, the results of these experiments indicated that the rate of dissolution was not simply related to saturation state. Edmond (44) proposed that the rapid increase in dissolution rate could be attributed to a change in water velocity. Morse and Berner (45) pointed out that this could be true only if the rate of dissolution was transport controlled. Their calculations indicated that the rate of dissolution measured by Peterson (41) was over 20 times too slow for diffusion controlled dissolution, this being the slowest transport process. 

In addition to characterizing mass losses, textural features can be used to discern the mechanisms and chemical environment associated with silicate dissolution. It is widely accepted that pitted surfaces, such as that shown in Figure 5, indicate surface reaction whereas smooth rounded surfaces result from diffusion-controlled dissolution (Lasaga, 1998 see Chapter 5.03). 

Release characteristics diffusion-controlled dissolution-controlled... 

The slowest transport-controlled dissolution/precipitation is that governed by aqueous diffusion. Diffusion rates can be estimated (cf. Bodek et al. 1988 Fetter 1988), thus we can estimate the lower limit of rates attributable to transport control. Berner (1978) suggests that the rate of diffusion-controlled dissolution R is given by... 

FIG. 18 SECM approach curves (measurement time 0.6 s after a potential step) of normalized current for the reduction of Cu2+ versus separation between a 25 /rm diameter Pt tip and the (100) face of CuS04 -5H20. Data are shown for saturated copper sulfate solutions containing 2.3 (A), 3.6 ( ), 6.4 ( ), 7.3 ( ), and 10.2 ( ) mol dm-3 sulfuric acid. The solid lines through each data set represent the best fits for a first-order dissolution process characterized by log K, = 0.46 (A), log K, = 0.60 ( ), and log K, = 0.91 ( ). The dashed line shows the theoretical behavior predicted for a diffusion-controlled dissolution process, while the dotted line shows the behavior expected for an inert surface. 

FIG. 25 SECM experimental approach curves showing the variation of the initially attained steady-state current for ferrocyanide oxidation at UMEs with a = (a, ) 12.5 /r,m, (b, ) 5 fim, and (c, ) 2.5 /rm, with distance between the tip and the potassium ferrocyanide trihydrate (010) surface. The data were derived from chronoamperometric measurements. For comparison, the theoretical behavior for a diffusion-controlled dissolution process (.) is also shown along with the best fits to the experimental... 

FIG. 35 Steady-state approach curves of the diffusion-limited current for the oxidation of Br to BrJ at a Pt tip (a = 2.5 /xm), as a function of distance from a glass surface ( ) and the (100) face of KBr (o), in an acetonitrile solution containing 0.05 mol dm-3 LiC104 and saturated with respect to potassium bromide. The theoretical characteristics for (a) negative feedback (----) and (b) a diffusion-controlled dissolution process (-----) are also shown. 

The Tafel constant was b = 0.20 V decade-1 for iron electrodes [55] and b = 0.20 V decade-1 for austenitic stainless steels [54] in acid solution. It is noticed that these Tafel constants are greater than those (0.03-0.1 V) usually observed with general dissolution of metals in acid solution. The other mode of localized corrosion is the active mode of corrosion that prevails in the potential range less positive (more cathodic) than the passivation potential, EP, in which potential range the localized corrosion is mainly controlled by the acidity of the occluded pit solution. In the potential range of active metal dissolution, the anodic dissolution current density is also an exponential function of the electrode potential, except for diffusion-controlled dissolution. 

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. 

Ultrasonic wave clearly enhances the solubilization process (Figure 7, 8). Figure 8 also indicates that diffusion-controlled dissolution maintained even under ultrasonic pulses. The diffusivity under ultrasonic pulses was measured to increase about 3-4 times at the given geometry and power used in this experiment. There are two known effects of ultrasonic waves on solubilization i) acoustic streaming, and ii) cavitation/implosion[24,25]. 

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. 

The simulations predict both diffusion-controlled dissolution (Fig. 5) and disassodation-controlled dissolution (Fig. 6). Different forms of the functions fi and (2 were used in the simulations and it was shown that the concentration dependence of the diffusion coefficient is very crucial. The disassociation rate, Rd, was treated as a model parameter and the simulations failed to yield more insight into the actual nature of that rate. 

The roughness of an electrode, irrespective of the irregularities shape and their distribution on the surface, leads to additional increase in the current on voltammograms of selective diffusion-controlled dissolution. The peak current dependence on the square root of the potential scan rate is non-linear in general, flattened only in two cases where the moment of reaching the voltammetric peak tm ti and tm > t2. The characteristic times ti and t2 are... 

Recalling that crystal-medium interfacial layer is composed of the rigid layer 1 - 2 atomic diameters wide and the diffuse layer extends up to some 10 cm deep into the solution, we may view the diffusion-controlled dissolution process as one in which the reactant species and reaction products have to traverse the wide diffuse layer in order to enable the surface reactions to proceed. In this case, the rate of dissolution, expressed as the amount, m, of material removed per unit time, t, is described by Pick s first law, namely ... 

Etching kinetics of semiconductors may be diffusion-controlled in two ways (24). In the first case, the reduction reaction is diffusion limited and controls the etching kinetics. Under these conditions a well defined crystallographic facet is obtained. This behavior is observed at low pH. In the second case of high pH, the rate of anodic dissolution of the semiconductor wafer depends on the mass transport of OH ions to the electrode. Electroless etching based on this limitation shows rounded profiles typical of diffusion-controlled dissolution. 

Spinning disc Dissolution of solid or liquid Small Easy Large Concentration vs. time requires chemical analysis Good requires diffusion-controlled dissolution, a stringent restraint... 

---