Uniform surface dissolution rate

After icorr is evaluated by any one of the foregoing methods, use of one of the Faraday-law expressions (Table 6.2 and Chapter 4) leads to either the average corrosion intensity (Cl) or average corrosion penetration rate (CPR). If the corrosion process is uniform, these average values relate directly to the uniform surface dissolution rate. If, on the other hand, the corrosion process is localized, the actual corrosion intensity and corrosion penetration rate at local areas can be orders of magnitude greater than the average values. 

Uniform corrosion is defined as a corrosion process with a uniform metal dissolution rate over the entire metal surface exposed to the corrosive environment. The result is a uniform loss of the metal, which leads to a smooth reduction of thickness. However, the uniformity of the corrosion attack depends on the observation technique. For instance, an electron... 

A silicon surface, no mater how well it is prepared, is not perfectly flat at the atomic scale, but has surface defects such as surface vacancies, steps, kinks sites, and dopant atoms. The dissolution of the surface is thus not uniform but modulated at the atomic scale with higher rates at the defects and depressed sites. The micro roughness of the surface will increase with the amount of dissolution due to the sensitivity of the reactions to surface curvature associated with the micro depressed sites. These sites, due to the higher dissolution rates, will evolve into pits and eventually into pores. Depending on the condition, a certain amount of dissolution is required before the initiation of pores on all types of materials. 

However, we have to reflect on one of our model assumptions (Table 5.1). It is certainly not justified to assume a completely uniform oxide surface. The dissolution is favored at a few localized (active) sites where the reactions have lower activation energy. The overall reaction rate is the sum of the rates of the various types of sites. The reactions occurring at differently active sites are parallel reaction steps occurring at different rates (Table 5.1). In parallel reactions the fast reaction is rate determining. We can assume that the ratio (mol fraction, %a) of active sites to total (active plus less active) sites remains constant during the dissolution that is the active sites are continuously regenerated after AI(III) detachment and thus steady state conditions are maintained, i.e., a mean field rate law can generalize the dissolution rate. The reaction constant k in Eq. (5.9) includes %a, which is a function of the particular material used (see remark 4 in Table 5.1). In the activated complex theory the surface complex is the precursor of the activated complex (Fig. 5.4) and is in local equilibrium with it. The detachment corresponds to the desorption of the activated surface complex. 

A common phenomenon in the dissolution of silicate minerals is the formation of etch pits at the surface (90-91.,93-94). When this occurs, the overall rate of mineral dissolution is non-uniform, and dissolution occurs preferentially at dislocations or defects that intercept the crystal surface. Preferential dissolution of the mineral could explain why surface spectroscopic studies have failed... 

When a powder of spheres of uniform size is stirred in water, 10% dissolves in 10 min. If the dissolution rate at the surface is rate controlling, after what time will the partieles eompletely dissolve [Answer -5 h.]... 

A certain amount of uniform dissolution may occur prior to and during the initiation of pores. For example, as reported in one study, before the formation of the macropores on lowly doped p-Si( 100) in anhydrous HF-MeCN solutions the entire surface is etched forming (111) facets of about l xm. Pores then start to grow at the base of these facets. Once macropores are developed the surface etch rate is greatly reduced, by a factor of 4. 

Statement of the problem. In the preceding chapters we considered processes of mass transfer to surfaces of particles and drops for the case of an infinite rate of chemical reaction (adsorption or dissolution.) Along with the cases considered in the preceding chapters, finite-rate surface chemical reactions (see Section 3.1) are of importance in applications. Here the concentration on the surfaces is a priori unknown and must be determined in the course of the solution. Let us consider a laminar fluid flow with velocity U past a spherical particle (drop or bubble) of radius a. Let R be the radial coordinate relative to the center of the particle. We assume that the concentration is uniform remote from the particle and is equal to C. Next, the rate of chemical reaction on the surface is given by Ws = KSFS(C), where Ks is the surface reaction rate constant and the function F% is defined by the reaction kinetics and satisfies the condition Fs(0) = 0. 

For polycrystalline metals, the dissolution rate of the various crystallographic orientations is different. Grain boundaries or precipitations will also show a different corrosion rate. There is no accepted definition for what constitutes uniform corrosion. A possible definition could be that the variation of thickness loss all over the surface should not he greater than 5%. 

Corrosion occurs at a rate determined by equilibrium between opposing electrochemical reactions. The rate of any given electrochemical process depends on the rates of two conjugate reactions proceeding at the surface of the metal. Transfer of metal atoms from the lattice to the solution (anodic reaction) with the liberation of electrons and consumption of these electrons by some depolarisers (cathodic reaction). When these two reactions are in equilibrium, the flow of electrons from each reaction of balanced and no net electron flow (current) occurs. Various methods are available for the determination of dissolution rate of metals in corrosive environments but electrochemical methods employing polarisation techniques are by far most widely used. The corrosion rate (CR) is evaluated by mass loss method considering uniform corrosion. The Corrosion rate is determined by the following formula as per standard [102]. 

The milled extrudate s particle size is often a critical quality attribute for the drug product performance for many reasons. It is well known that the dissolution rate of a particle is determined in part by the particle s size and surface area. For polymer-based materials such as extrudate, particle size can influence phenomena such as swelling and gelling, which may or may not be desirable for the product performance. Particle size may also affect powder flow in feeders and hoppers and can result in segregation risks that impact content uniformity in the final drug product. 

In contrast, there are no solvents used in HME processes for manufacturing amorphous solid dispersions. Instead, the mixture of crystalline drug and polymer are heated to a temperature at which the components melt or form a eutectic, and then flash cooled, resulting in a dense amorphous glassy solid. The solid is then milled to achieve uniform particle size distribution, which is then processed into the final formulation. Therefore, the milling step will determine particle size and surface area, which in turn is related to the dissolution rate of the solid. 

In his own paper, Frumkin also analyzed the effect of the sodium amalgam concentration on the rate of electrolysis of water, and arrived at the conclusirm that even for physically and chemically uniform surfaces, the processes of anodic metal dissolution and cathodic hydrogen evolution could occur simultaneously at the same potential. This same idea was later used by K. Wagner and W. Traud (1938) in their formulation of the theory of the mixed potential, the cornerstone of modem corrosion theory. 

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