Activated complex dissolution

Hiemstra T. and van Riemsdijk W. H. (1990) Multiple activated complex dissolution of metal (hydr)oxides a thermodynamic approach to quartz. J. Coll. Interface Sci. 136, 132-150. 

Activated complex theory for the surface-controlled dissolution of a mineral far from equilibrium. A is the precursor, i.e., a surface site that can be activated to A. The latter is in equilibrium with the precursor. The activation energy for the conversion of the precursor into the product is given by AG. ... 

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. 

The backward reaction (detachment) must also be considered to obtain the net crystal growth (or dissolution) rate. The detachment goes through the same activated complex ... 

Three different ways have been developed to produce nanoparticle of PE-surfs. The most simple one is the mixing of polyelectrolytes and surfactants in non-stoichiometric quantities. An example for this is the complexation of poly(ethylene imine) with dodecanoic acid (PEI-C12). It forms a solid-state complex that is water-insoluble when the number of complexable amino functions is equal to the number of carboxylic acid groups [128]. Its structure is smectic A-like. The same complex forms nanoparticles when the polymer is used in an excess of 50% [129]. The particles exhibit hydrodynamic diameters in the range of 80-150 nm, which depend on the preparation conditions, i.e., the particle formation is kinetically controlled. Each particle consists of a relatively compact core surrounded by a diffuse corona. PEI-C12 forms the core, while non-complexed PEI acts as a cationic-active dispersing agent. It was found that the nanoparticles show high zeta potentials (approximate to +40 mV) and are stable in NaCl solutions at concentrations of up to 0.3 mol l-1. The stabilization of the nanoparticles results from a combination of ionic and steric contributions. A variation of the pH value was used to activate the dissolution of the particles. 

For a large number of reactions of Cr(III) complexes with Cr++, a bridged activated complex is obviously also involved. Among these is a reaction of almost classical interest the catalysis by Cr++ of the dissolution of anhydrous CrCls (f). The product of the reaction has been shown to be CrCl++ [rather than Cr(OH2)e+ + as would be expected for ordinary dilute solutions if complete equilibrium were rapidly established], and the Cl retained has been proved not to have passed through the solution (129). The reaction can be formulated as... 

Surface Reactions As we have seen from the dissolution of oxides, the surface-controlled dissolution mechanism would have to be interpreted in terms of surface reactions one can reasonably expect that these reactions constitute the elementary steps in the formation of the surface-activated complex. 

Combining concepts of surface coordination chemistry with established models of lattice statistics and activated complex theory, Wieland et al. (8) proposed a general rate expression for the proton-catalyzed dissolution of oxide minerals ... 

The partial orders with respect to [OH ] observed for most silicate mineral dissolution reactions can be explained by the surface complexation model (Blum and Lasaga, 1988 Brady and Walther, 1989). Brady -and Walther (1989) showed that slope plots of log R vs. pH for quartz and other silicates at 25 °C is not inconsistent with a value of 0.3. Plots of the log of absorbed OH vs. pH also have slopes of about 0.3, suggesting a first-order dependence on negative charge sites created by OH adsorption. Because of the similarity of quartz with other silicates and difference with the dependence of aluminum oxides and hydroxide dissolution on solution [OH ], Brady and Walther (1989) concluded that at pH >8 the precursor site for development of the activated complex in the dissolution of silicates is Si. This conclusion is supported by the evidence that the rates (mol cm s ) at pH 8 are inversely correlated with the site potential for Si (Smyth, 1989). Thus it seems that at basic pH values, silicate dissolution is dependent on the rate of detachment of H3SiO4 from negative charge sites. 

Rimstidt and Barnes (1980) use the shorthand notation (Si02 2H20)t for the activated complex in the dissolution and precipitation of silica. While this approach is satisfactory for the purposes in their paper, it is important to remember that it is only a heuristic label we expect the reaction itself to proceed with several elementary reactions, as illustrated in Figure 2. The last example raises another serious misuse of the theory [not to be attributed to Rimstidt and Barnes (1980)]. Activated complexes are specific to a particular elementary reaction. One cannot discuss the activated complex without specifying the nature of the elementary reaction taking place nor can one speak of the activated complex of an overall reaction. 

I hose molecular moieties are the ones relevant to surface reactions. To be able to probe actual molecular mechanisms, the details of activated complexes and even obtain a first-principles movie of the adsorption and dissolution processes on uirfaces is an exciting prospect. In turn, this result truly opens a new era for the. ludy of surface reactions. 

Transition-state theory may be useful in testing the dissolution mechanisms presented above. According to TST, for any elementary chemical reaction the reactants should pass through a free-energy maximum, labeled the activated complex , before they are converted to products. It is assumed that the reaction rate-determining step is related to the decomposition of this activated complex ... 

THE RATE-DETERMINING STEP IN DISSOLUTION KINETICS THE SURFACE SPECIES AS THE PRECURSOR OF THE ACTIVATED COMPLEX... 

Dissolution kinetics of single carbonates such as calcite, aragonite, and magnesite exhibit simple dependence with respect to a limited number of reactants, specifically, H +, H2C03, and H20. It is thus easy to identify the elementary steps leading to the formation of the surface activated complex and the nature of the products of the detachment process following the decomposition of the activated complex. 

The concentration of constituent B becomes negligible at the surface of the mineral grain. Gradually, the rate of mass diffusion of B (Eq. 1) through an increasing depleted layer (y) becomes slower, and it is equal to the rate of surface-controlled dissolution of A (Eq. 2). Thus, a pseudosteady state is attained, and the depleted layer thickness stabilizes. For a 1 1 stoichiometry, the rates of reaction of solid layer diffusion (Eq. 1) and surface reaction (Eq. 2) become equal (Eq. 3). The thickness of the cation depleted layer is related to the concentration of B in the original mineral AB and the rate of detachment of the activated complex (Eq. 4). 

Figure 2. Schematic of an aluminum oxide mineral undergoing hydrolysis and protonation. Dissolution occurs when the surface-coordinated-activated complex (A1-3H20)3 + detaches from the surface and goes into solution, thereby renewing the surface.

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