Nucleation, in crystallization

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

In view of secondary nucleation in crystallizers, Ten Cate et al. (2004) were interested in finding out locally about the frequencies of particle collisions in a suspension under the action of the turbulence of the liquid. To this end, they performed a DNS of a particle suspension in a periodic box subject to forced turbulent-flow conditions. In their DNS, the flow field around and between the interacting and colliding particles is fully resolved, while the particles are allowed to rotate in response to the surrounding turbulent-flow field. 

Bubble Nucleation in a Liquid Phase The above classical nucleation theory can be easily extended to melt nucleation in another melt. It can also be extended to melt nucleation in a crystal but with one exception. Crystal grains are usually small with surfaces or grain boundaries. Melt nucleation in crystals most likely starts on the surface or grain boundaries, which is similar to heterogeneous nucleation discussed below. Homogeneous nucleation of bubbles in a melt can be treated similarly using the above procedures. Because of special property of gases, the equations are different from those for the nucleation of a condensed phase, and are hence summarized below for convenience. 

To determine the relationship between hydrate nucleation (requiring three phases) and the more usual type (two-phase nucleation) consider the theory of homogeneous and heterogeneous nucleation in crystallization, as reviewed by Mullin (1993, p. 172) and Kashchiev and Firoozabadi (2002b), from which much of the below discussion has been excerpted. 

The effect of melt temperature on nucleation in crystallizing polymers. 

Markov, I.V. Crystal growth for beginners fundamentals of nucleation. In Crystal Growth, and Epitaxy-, World Scientific Singapore, 1995. 

HOMOGENOUS NUCLEATION. In crystallization from solution, homogenous nucleation almost never happens, except perhaps in some precipitation reactions. The fundamentals of the phenomenon, however, are important in understanding the more useful types of nucleation. 

Binsbergen, F. L. (1970). Heterogeneous nucleation in crystallization of pwlyolefins. I. Chemical and physical nature of nucleating agents. Polymer, VoLll, Issue 5, p>p. 253-267. 

S. Toshev, in Homogeneous Nucleation in Crystal Growth An Introduction, M. Hartman, ed., North-Holland, Amsterdam (1973), p. 1. 

It is independent of the number density, i.e., a specified function of z and t. This occurs obviously in systems in which the particles may appear or disappear because of events occurring in the continuous phase. An example of this would be homogeneous nucleation in crystallization or precipitation processes. 

The isotherms in Fig. 4.20 illustrate another important feature that is inherent to crystallization of polymers. A strong and dramatically negative temperature coefficient is apparent from these plots. As the temperature is decreased, the rate of crystallization becomes much more rapid. This behavior is quite the opposite of the usual case for chemical reactions. The negative temperature coefficient is rather severe. In the example given, the rate of crystallization changes by five orders of magnitude over a temperature interval of only 7 °C. This type of behavior is clearly indicative of a nucleation-controlled crystallization process [138]. It illustrates an extremely important principle that underlies and controls many aspects of the crystallization of polymers. The central role played by nucleation in crystallization of polymers will be presented in more detail when rates of growth of spherulites are discussed. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

A typical heat treatment cycle, as illustrated in Figure 1, comprises both nucleation and crystallization temperature holds, but some glass-ceramics are designed to nucleate and/or crystallize during the ramp itself, eliminating the need for multiple holds. 

Crystallization. Acidified aluminum sulfate solutions can be supercooled 10 °C or more below the saturation point. However, once nucleation begins, the crystallization rate is rapid and the supersaturated solution sets up. The onset of nucleation in a gentiy stirred supersaturated solution is marked by the appearance of silky, curling streamers of microscopic nuclei resulting from orientation effects of hydraulic currents on the thin, platelike crystals. Without agitation, nucleation in an acidified solution, in glass tubes, can yield extended crystalline membranes of such thinness to exhibit colors resulting from optical interference. 

Physical properties of the acid and its anhydride are summarized in Table 1. Other references for more data on specific physical properties of succinic acid are as follows solubiUty in water at 278.15—338.15 K (12) water-enhanced solubiUty in organic solvents (13) dissociation constants in water—acetone (10 vol %) at 30—60°C (14), water—methanol mixtures (10—50 vol %) at 25°C (15,16), water—dioxane mixtures (10—50 vol %) at 25°C (15), and water—dioxane—methanol mixtures at 25°C (17) nucleation and crystal growth (18—20) calculation of the enthalpy of formation using semiempitical methods (21) enthalpy of solution (22,23) and enthalpy of dilution (23). For succinic anhydride, the enthalpies of combustion and sublimation have been reported (24). 

Scaling is not always related to temperature. Calcium carbonate and calcium sulfate scaling occur on unheated surfaces when their solubiUties are exceeded in the bulk water. Metallic surfaces are ideal sites for crystal nucleation because of their rough surfaces and the low velocities adjacent to the surface. Corrosion cells on the metal surface produce areas of high pH, which promote the precipitation of many cooling water salts. Once formed, scale deposits initiate additional nucleation, and crystal growth proceeds at an accelerated rate. 

Several features of secondary nucleation make it more important than primary nucleation in industrial crystallizers. First, continuous crystallizers and seeded batch crystallizers have crystals in the magma that can participate in secondary nucleation mechanisms. Second, the requirements for the mechanisms of secondary nucleation to be operative are fulfilled easily in most industrial crystallizers. Finally, low supersaturation can support secondary nucleation but not primary nucleation, and most crystallizers are operated in a low supersaturation regime that improves yield and enhances product purity and crystal morphology. 

Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

Supersaturation has been observed to affect contact nucleation, but the mechanism by which this occurs is not clear. There are data (19) that infer a direct relationship between contact nucleation and crystal growth. This relationship has been explained by showing that the effect of supersaturation on contact nucleation must consider the reduction in interfacial supersaturation due to the resistance to diffusion or convective mass transfer (20). 

Crystal growth is a layer-by-layer process, and the retention time required in most commercial equipment to produce crystals of the size normally desired is on the order of 2 to 6 h. On the other hand, nucleation in a supersaturated solution can be generated in a fraction... 

The nucleation rate is, in fact, critically dependent on temperature, as Fig. 8.3 shows. To see why, let us look at the heterogeneous nucleation of b.c.c. crystals at grain boundaries. We have already looked at grain boundary nucleation in Problems 7.2 and 7.3. Problem 7.2 showed that the critical radius for grain boundary nucleation is given by... 

Initially, crystallization is a two-step process viz. nucleation and crystal growth requiring a change of free energy (Gibbs, 1928), as shown schematically in Figure 5.1. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

A number of authors have developed mechanistic descriptions of the processes causing secondary nucleation in agitated crystallizers (Ottens etal., 1972 Ottens and de Jong, 1973 Bennett etal., 1973 Evans etal., 1974 Garside and Jancic, 1979 Synowiec etal., 1993). The energy and frequency of crystal collisions are determined by the fluid mechanics of the crystallizer and crystal suspension. The numbers of nuclei formed by a given contact and those that proceed to survive can be represented by different functions. 

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