Dissolution-controlled growth

If the growth rate of particles B is governed by the dissolution rate of particles A (dissolution-controlled growth), it must holds that KASA KBSB. In this case, Eq. (4) reduces to... 

Consequently, drA/dt is proportional to SA/SK for the dissolution-controlled growth, whereas it is independent of SA/SB for the deposition-controlled growth. Obviously, information on the growth mechanism is obtained only in the case of deposition-controlled growth. 

Consider two separate particles with a radius of r and ri, respectively, in a liquid. Draw schematically the solute distributions in the liquid between the particles for diffusion and reaction-controlled growth, respectively. For reaction-controlled growth, are there any differences between the solute distribution in the LSW theory and those in dissolution-controlled growth and precipitation-controlled growth Explain. 

Growth or dissolution controlled by diffusion or heat conduction... 

Crystal dissolution/melting/growth may be controlled by interface reaction rate (Figure 1-lla), meaning that mass/heat transfer rate is very high and interface reaction rate is low. Examples include dissolution of minerals with low... 

Crystal dissolution and growth may also be controlled by both mass or heat transport and interface reaction (Figure 1-1 Id). In this case, the interface reaction... 

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. 

Murphy W. M., Oelkers E. H., and Lichtner P. C. (1989) Surface reaction versus diffusion control of mineral dissolution and growth rates in geochemical processes. Chem. Geol. 78, 357-380. 

Rate expressions of this form were derived for calcite precipitation with = 1 (Nancollas and Reddy, 1971 Reddy and Nancollas, 1971), and with mj = 0 and = 0.5 (Sjoberg, 1976 Kazmierczak et al, 1982 Rickard and Sjoberg, 1983 Sjoberg and Rickard, 1983). Rate equations such as (57) wherein rates are linearly proportional to AG close to equilibrium have been attributed to adsorption-controlled growth (Nielsen, 1983 Shiraki and Brantley, 1995). Such rate models have been used by some researchers to model dissolution and precipitation of quartz over a wide range in temperature and pressure (Rimstidt and Barnes, 1980) however, it has been pointed out that this has only been confirmed with experiments at high temperature (Dove, 1995). 

Fig. 23 Current transients ofthe dissolution of a Cu UPD MLon Pt(lll) in 1 mM Cu + +0.1 M H2SO4, obtained when stepping the potential from 1 = 0.50 V to various final potentials as indicated in the figure. The transients with final potentials lower than 0.67 V could be modeled by assuming two successive hole nucleation processes according to an exponential law coupled with surface diffusion-controlled growth (cf Eq. (30) and Eq. (33)). The inset shows, as an example, the fit (----) for the experimental transient (-----) 1 = 0.50 V —> 2 = 0.65 V [407].

The Avrami-exponent m = 1.48 points to nucleation according to an exponential law coupled with surface diffusion-controlled growth (Eq. (34) and Eq. (35), solid line). The experimental results in panels (b) and (c) indicate that the spectroscopic and the electrochemical transients probe different interfacial properties of the dissolution process and illustrate the complementary information of both approaches (reproduced from Ref. [475]). 

Thermoreversible polymer hydrogels also represent a medium for synthesis of nanosized zeolite crystals. This support is recyclable and stable in the temperature range of interest for zeolite synthesis. In aqueous media, the voids between monodisperse polymer spheres can serve as a nanoreactor for controlled growth [157]. Recycling of the support can be done via dissolution of... 

Equation (2.3-47), the pseudo-steady-state solution for die flux, could be used to predict the diffusion-controlled growth or dissolution rate of the crystal in a manner analogous to the Stefan problem solution. The result would indicate that the square of the particle radius varies linearly with time. 

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