Crystal formation nucleation

Leubner, I. H. Crystal formation (nucleation) under kinetically controlled and diffusion-controlled growth conditions. J. Phys. Chem. 91,6069-6073 (1987). 

In ciysiallization, nuciention is the formation of a solid phase from a liquid phase. The process differs from growth in that a naw ciystal results from the transfer of solute from the liquid to (he solid in growth, solid is deposited on an existing ciystal. Because it is the phenomenon of crystal formation, nucleation sets the cheracter of the ciystailization process, and it is tharefore the most critical component in relating ciystallizer desiga and operation to ciystal size distribution . 

Secondary nucleation is crystal formation through a mechanism involving the solute crystals crystals of the solute must be present for secondary nucleation to occur. Thorough reviews have been given (8,9). 

Crystal Formation There are obviously two steps involved in the preparation of ciystal matter from a solution. The ciystals must first Form and then grow. The formation of a new sohd phase either on an inert particle in the solution or in the solution itself is called nucle-ation. The increase in size of this nucleus with a layer-by-layer addition of solute is called growth. Both nucleation and ciystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, ciystals can neither form nor grow. Supersaturation refers to the quantity of solute present in solution compared with the quantity which would be present if the solution were kept for a veiy long period of time with solid phase in contac t with the solution. The latter value is the equilibrium solubility at the temperature and pressure under consideration. The supersaturation coefficient can be expressed... 

A reduction in the magma density will generally increase nucleation and decrease the particle size. This technique has the disadvantage that crystal formation on the equipment surfaces increases because lower shiny densities create higher levels of supersaturation within the equipment, particularly at the critical boiling surface in a vaporization-type ciystaUizer. 

Secondary nucleation is an important particle formation process in industrial crystallizers. Secondary nucleation occurs because of the presence of existing crystals. In industrial crystallizers, existing crystals in suspension induce the formation of attrition-like smaller particles and effectively enhance the nucleation rate. This process has some similarity with attrition but differs in one important respect it occurs in the presence of a supersaturated solution. 

The size of crystals produced in the gas-liquid system varied from 10 to 100 pm by controlling the level of supersaturation, while the liquid-liquid system produced crystals of 5—30 pm. The wide variation of crystal size is due to the marked sensitivity of the nucleation rate on the level of supersaturation, while the impurity content is another variable that can affect the crystal formation. 

Brown, C.M., Ackemiann, D.K., Puricli, D.L. and Finlayson, B., 1991. Nucleation of calcium oxalate monoliydrate use of turbidity measurements and computer-assisted simulations in characterising early events in crystal formation. Journal of Crystal Growth, 108, 455 64. 

The basic science behind nucleation and forces between materials have been treated in Chapter 1. For those interested in this section, it is assumed that this basic science is (more or less, at least) understood. However, the basics treated in Chapter 1, while important to an understanding of film (as opposed to isolated crystal) formation, are not enongh by themselves to provide a phenomenological explanation of film formation. We would ideally like to be able to predict in advance, from fundamental principles, whether a particular bath formulation will result in adherent films or not. We cannot However, if we cannot reliably predict adhesion, we can at least choose conditions so that the probability of adhesion is good. 

Disodium Tetraborate Decahydrate (Borax Decahydrate). Disodium tetraborate decahydrate, Na2B40 101I, 0 or Na20 2B203 1 HI I (). formula wt, 381.36 monoclinic sp gr, 1.71 specific heat 1.611 kj/ (kg-K) [0.385 kcal/(g°C] at 25—50°C (68) heat of formation, —6.2643 MJ/mol (—1497.2 kcal/mol) (69) exists in nature as the mineral borax. Its crystal habit, nucleation, and growth rate are sensitive to inorganic and surface active otganic modifiers (70). 

Metastability with respect to ice crystal formation was not apparent in this freezer, probably because particulate matter in the salt solution induced nucleation. Nevertheless, more ice may be produced for a given pressure difference and surface when the slurry is recycled. The ice in the flowing slurry presents more surface and precludes the necessity of high driving forces to induce nucleation. Also, the size of the ice crystals is increased by recycle of slurry. 

In view of the importance of macroscopic structure, further studies of liquid crystal formation seem desirable. Certainly, the rates of liquid crystal nucleation and growth are of interest in some applications—in emulsions and foams, for example, where formation of liquid crystal by nonequilibrium processes is an important stabilizing factor—and in detergency, where liquid crystal formation is one means of dirt removal. As noted previously and as indicated by the work of Tiddy and Wheeler (45), for example, rates of formation and dissolution of liquid crystals can be very slow, with weeks or months required to achieve equilibrium. Work which would clarify when and why phase transformation is fast or slow would be of value. Another topic of possible interest is whether the presence of an interface which orients amphiphilic molecules can affect the rate of liquid crystal formation at, for example, the surfaces of drops in an emulsion. 

Crystal formation depends not only on the interaction energy of a particular synthon but on a wide variety of other factors, particular crystal nucleation and growth kinetics and nucleus-solution interfacial energy. Other important factors are lattice enthalpy and lattice entropy, long range interactions... 

There are several cases, however, where the most negative lattice energy does not correspond with the preferred guest in a competition experiment. We attribute this to imprecise force-field parameters and kinetic effects which may be controlling the nucleation step in crystal formation [20]. 

It is clear that an accurate prediction of the CP, PP, or CFPP is almost impossible, certainly since presence of crystallizable minor components can have a significant effect. Some of these components, such as phytosterol glycoside esters in soy-based FAME, can speed nucleation and crystallization other molecules creating steric hindrance in the growing nucleus will retard crystallization. Such components are often added to biodiesel to reduce the size of crystals or inhibit crystal formation by preventing nucleation. 

To circumvent such seemingly insurmountable difficulties, approximations and simplifications can often be made. For example, even though the formation of a solid from a saturated solution can involve several successive reactions, one may judiciously select for analysis or prediction the one that presents the slowest rate. The so-called Oswald s phase rule states that a supersaturated solution that undeigoes a sudden alteration that takes it out of such a state will produce a metastable solid (instead of the expected thermodynamically stable solid). It is a very useful rule, although it is not always obeyed. Three limiting cases are shown in Figure 5.8 for different values of the overall crystallization rate (nucleation -1- crystal growth), v. 

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