Crystal diffusion control

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. 

This deceleratory reaction obeyed the parabolic law [eqn. (10)] attributed to diffusion control in one dimension, normal to the main crystal face. E and A values (92—145 kJ mole-1 and 109—10,s s-1, respectively) for reaction at 490—520 K varied significantly with prevailing water vapour pressure and a plot of rate coefficient against PH2o (most unusually) showed a double minimum. These workers [1269] also studied the decomposition of Pb2Cl2C03 at 565—615 K, which also obeyed the parabolic law at 565 K in nitrogen but at higher temperatures obeyed the Jander equation [eqn. (14)]. Values of E and A systematically increased... 

Figure 1.55. The relationships between the concentration product, (Ba " )i(S04 )i, at the initiation of barite precipitation, and morphologies of barite crystals (Shikazono, 1994). The dashed line represents the boundary between dendritic barite crystals and well-formed rhombohedral, rectangular, and polyhedral barite crystals. The 150°C data are from Shikazono (1994) the others from other investigations. D dendritic (spindle-like, rodlike, star-like, cross-like) barite Dp feather-like dendritic barite W well-formed rectangular, rhombohedral, and polyhedral barite. The boundary between the diffusion-controlled mechanism (Di) and the surface reaction mechanism (S) for barite precipitation at 25°C estimated by Nielsen (1958) The solubility product for barite in 1 molal NaCl solution at 150°C based on data by Helgeson (1969) and Blount (1977). A-B The solubility product for barite in 1 molal NaCl solution from 25 to 150°C based on data by Helgeson (1969).

It is usually believed that the growth of dendritic crystals is controlled by a bulk diffusion-controlled process which is defined as a process controlled by a transportation of solute species by diffusion from the bulk of aqueous solution to the growing crystals (e.g., Strickland-Constable, 1968 Liu et al., 1976). The appearances of feather- and star-like dendritic shapes indicate that the concentrations of pertinent species (e.g., Ba +, SO ) in the solution are highest at the corners of crystals. The rectangular (orthorhombic) crystal forms are generated where the concentrations of solute species are approximately the same for all surfaces but it cannot be homogeneous when the consumption rate of solute is faster than the supply rate by diffusion (Nielsen, 1958). 

Nielsen, A.E. (1959b) The kinetics of crystal growth in barium sulphate precipitation. 111. Mixed surface reaction and diffusion-controlled rate of growth. Acta Chem. Scand., 13, 1680-1686. 

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 ... 

The following reactions have been employed in the syntheses of tri-and tetrametaphosphimates. Since most often the compounds are very soluble in water, single crystals were grown by evaporation of the solvent or by diffusion controlled addition of an organic solvent such as acetone, ethanol, or methanol. 

During the studies carried out on this process some unusual behavior has been observed. Such results have led some authors to the conclusion that SSP is a diffusion-controlled reaction. Despite this fact, the kinetics of SSP also depend on catalyst, temperature and time. In the later stages of polymerization, and particularly in the case of large particle sizes, diffusion becomes dominant, with the result that the removal of reaction products such as EG, water and acetaldehyde is controlled by the physics of mass transport in the solid state. This transport process is itself dependent on particle size, density, crystal structure, surface conditions and desorption of the reaction products. 

These newer PET formulations utilize not only a nucleating agent, but also a plasticizing agent [3-9], The crystallization rate of polymeric materials can be broken down into two different regions, i.e. nucleation-controlled and diffusion-controlled (Figure 15.3). In the injection molding process, hot polymer is injected... 

The dynamics of upd reactions have also been examined by STM. The formation of the ordered copper/sulfate layer [354] and copper chloride layer [355] on Au(lll) was examined in a dilute solution of Cu where the reaction was under diffusion control so that growth proceeded on a time scale compatible with STM measurements [354]. In another study, the importance of step density on nucleation was examined and the voltammetric and chronoamperometric response for Cu upd on vicinal Au(lll) was shown to be a sensitive function of the crystal miscut, as... 

In addition to the above, there are further possibihties. When the rate of guest diffusion between individual layers is very large compared with the rate of nucleation at the edge of the crystal, there exists a situation in which the individual layers appear to fill instantly. In this case, when Avrami kinetics are applied to the system, the diffusion process being observed is not the diffusion of guest species between the layers, but the diffusion of filled layers parallel to the c-axis. Such ID processes will consist of nucleation followed by diffusion control in the vast majority of cases, although phase boundary control is also possible if the rate of advancement of the phase boundary is also very rapid with respect to nucleation. In this case, instantaneous nucleation is not a possibility [18]. 

Early work by Boyd et al. (1947), performed on zeohtes, showed that the ion exchange process is diffusion controlled and the reaction rate is limited by mass transfer phenomena that are either film-diffusion (ED) or particle-diffusion (PD) dependent. Under natural conditions, the charge compensation cations are held on a representative subsurface solid phase as follows within crystals in interlayer... 

Under conditions leading to a porous shell of magnetite, the kinetic curve displayed an induction period corresponding to formation of nuclei and the subsequent reaction followed the cube root law. Diffusion of the reducing gas to the reactant/ product interface took place readily with a porous product. Whether chemical or diffusion control predominated depended on reaction conditions. With small crystals... 

Figure 1-11 Concentration profile for (a) crystal growth controlled by interface reaction (the concentration profile is flat and does not change with time), (b) diffusive crystal growth with t2 = 4fi and = 4t2 (the profile is an error function and propagates according to (c) convective crystal growth (the profile is an exponential function and does not change with time), and (d) crystal growth controlled by both interface reaction and diffusion (both the interface concentration and the length of the profile vary).

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