Transport-controlled kinetics, crystal

There are basically three, rate-limiting mechanisms for mineral dissolution assuming a fixed degree of undersaturation. They are (1) transport of solute away from the dissolved crystal or transport-controlled kinetics. 

From the above statements it follows that it should be possible to derive the growth kinetics and calculate the growth rate of uncontaminated electrolyte crystals when the following parameters are known molecular weight, density, solubility, cation dehydration frequency, ion pair stability coefficient, and the bulk concentration of the solution (or the saturation ratio). If the growth rate is transport controlled, one shall also need the particle size. In table I we have made these calculations for 14 electrolytes of common interest. For the saturation ratio and particle size we have chosen values typical for the range where kinetic experiments have been performed (29,30). The empirical rates are given for comparison. 

Fig. 2.3 Rate-limiting steps in mineral dissolution (a) transport-controlled, (b) surface reaction-controlled, and (c) mixed transport and surface reaction control. Concentration (C) versus distance (r) from a crystal surface for three rate-controUing processes, where is the saturation concentration and is the concentration in an infinitely diluted solution. Reprinted from Sparks DL (1988) Kinetics of soil chemical processes. Academic Press New York 210 pp. Copyright 2005 with permission of Elsevier...

In contrast to fluids, crystals have a greater number of control parameters crystal structure, strain and stress, grain boundaries, line defects (dislocations), and the size and shape of crystallites, etc. These are all relevant to kinetics. Treatments that go beyond transport and diffusion in this important field of physical chemistry are scarce. 

In order to undergo a redox process, the reactant must be present within the electrode-reaction layer, in an amount limited by the rate of mass transport of Yg, to the electrode surface. In electrolyte media, four types of mass-transport control, namely convection, diffusion, adsorption and chemical-reaction kinetics, must be considered. The details of the voltammetric procedure, e.g., whether the solution is stirred or quiet, tell whether convection is possible. In a quiet solution, the maximum currents of simple electrode processes may be governed by diffusion. Adsorption of either reactant or product on the electrode may complicate the electrode process and, unless adsorption, crystallization or related surface effects are being studied, it is to be avoided, typically... 

For PEIMs (n = odds), crystallization at temperatures above the liquid crystalline transition may result in spherulitic morphology development. Kinetics analysis of these PEIMs indicates that the phase transition is mainly determined by the number of methyl units in the spacers. The liquid crystallization formation can be either transport-controlled or nucleation-controlled, depending on how far apart the liquid crystalline transition is from the glass transition temperature of the polymer. As all of these PEIMs form a monoclinic system, the lifetime of mesophase may be very short (in seconds). Therefore, kinetics analysis may involve two stages mesophase formation followed by true crystallization (Table 3.2). 

The usual practice for avoiding the plugging of production facilities by hydrates is to add thermodynamic inhibitors, such as methanol or glycol. A newer concept is the injection of low-dosage additives either kinetic inhibitors, which delay nucleation or prevent the growth of hydrate crystals, or hydrate dispersants, which prevent the agglomeration of hydrate particles and allow them to be transported within the flow [880,1387]. Hydrate control is discussed extensively in Chapter 13. Classes of hydrate control agents are shown in Table 11-9, and additives are shown in Table 11-10. 

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. 

All seven steps require time, resulting in a rate of incorporating clusters into the growing crystal surface, which is called crystal growth kinetics. The following two sections consider translation of such a rate into a macroscopic equation for correlation and prediction. It is difficult to say which of the steps control the process, or even if the conceptual picture is valid. However, the first step—species transport to the solid surface—is well established and a brief description is given in Section 3.2.1.2. 

One of the most controversial topics in the recent literature, with regard to partition coefficients in carbonates, has been the effect of precipitation rates on values of the partition coefficients. The fact that partition coefficients can be substantially influenced by crystal growth rates has been well established for years in the chemical literature, and interesting models have been produced to explain experimental observations (e.g., for a simple summary see Ohara and Reid, 1973). The two basic modes of control postulated involve mass transport properties and surface reaction kinetics. Without getting into detailed theory, it is perhaps sufficient to point out that kinetic influences can cause both increases and decreases in partition coefficients. At high rates of precipitation, there is even a chance for the physical process of occlusion of adsorbates to occur. In summary, there is no reason to expect that partition coefficients in calcite should not be precipitation rate dependent. Two major questions are (1) how sensitive to reaction rate are the partition coefficients of interest and (2) will this variation of partition coefficients with rate be of significance to important natural processes Unless the first question is acceptably answered, it will obviously be difficult to deal with the second question. 

The next step is to produce nearly perfect single-crystal boules of silicon from the ultrapure polycrystalline silicon. Many techniques have been developed to accomplish this, and they all rely on a similar set of concepts that describe the transport process, thermodynamically controlled solubility, and kinetics [8]. Three important methods are the vertical Bridgman-Stockbarger, Czochralski, and floating zone processes, fully described in Fundamentals of Crystal Growth by Rosenberger [9]. 

If the growth kinetics are controlled by the transport of ions from the bulk solution to the surface of the crystal, it is essential to perform experiments in well-defined hydrodynamic conditions. This is possible using the rotating... 

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