Grow from Supersaturated Solutions

In a saturated solution, including one saturated with respect to protein, two states exist in equilibrium the solid phase and one consisting of molecules free in solution. At saturation, no net increase in the proportion of solid phase can accrue, since it would be counterbalanced by an equivalent dissolution. Thus crystals do not grow from a saturated solution. The system must be in a nonequilibrium, or supersaturated state to provide the thermodynamic driving force for crystallization. 

When the objective is to grow crystals of any compound, a solution of the molecule must be transformed or brought into a supersaturated state, whereby its return to equilibrium forces exclusion of solute molecules into the solid, the crystal. If, from a saturated solution, for example, solvent is gradually withdrawn by evaporation, temperature is lowered or raised appropriately, or some other property of the system is altered, then the solubility limit may be exceeded and the solution will become supersaturated. If a solid phase is present, or introduced, then strict saturation will be reestablished as molecules leave the solvent, join the solid phase, and equilibrium is regained. 

In terms of the phase diagram, ideal crystal growth would begin with nuclei formed in the labile region, but just beyond the metastable. There, growth would occur slowly the solution, by depletion, would return to the metastable state where no more stable nuclei could form and the few nuclei that had established themselves would continue to grow to maturity at a pace free of defect formation. Thus in growing crystals for X-ray diffraction analysis, one attempts, by either dehydration or alteration of physical conditions, to transport 

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The growth of the nanoparticles could have occurred either by the growth of CdSe on the seeds (growth from supersaturated solution) or by the process of Ostwald ripening whereby larger seed grow at the expense of the smaller ones. 

One example of this type of reactor is in the synthesis of catalyst powders and pellets by growing porous soHd oxides from supersaturated solution. Here the growth conditions control the porosity and pore diameter and tortuosity, factors that we have seen are crucial in designing optimal catalysts for packed bed, fluidized bed, or slurry reactors. 

Some conditions, however, are known which allow mineral crystallization from solution. The main agents of crystallization are the crystallization power and the crystallization rate crystallization is possible in systems out of equilibrium. The measure of a system s deviation from equilibrium is called the driving force of crystallization, and its actual expression is supersaturation and supercooling. The most important parameter allowing the growth of crystals from solution is solubility. The concentration of saturated solution quantitatively determines the solubility of the substance under particular conditions. Crystals do not grow from unsaturated solutions, crystals mainly dissolve in them. 

In the absence of a suitable soHd phase for deposition and in supersaturated solutions of pH values from 7 to 10, monosilicic acid polymerizes to form discrete particles. Electrostatic repulsion of the particles prevents aggregation if the concentration of electrolyte is below ca 0.2 N. The particle size that can be attained is dependent on the temperature. Particle size increases significantly with increasing temperature. For example, particles of 4—8 nm in diameter are obtained at 50—100°C, whereas particles of up to 150 nm in diameter are formed at 350°C in an autoclave. However, the size of the particles obtained in an autoclave is limited by the conversion of amorphous siUca to quartz at high temperatures. Particle size influences the stabiUty of the sol because particles <7 nm in diameter tend to grow spontaneously in storage, which may affect the sol properties. However, sols can be stabilized by the addition of sufficient alkaU (1,33). 

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... 

Crystallization is a phase transition phenomenon. Crystals grow from an aqueous protein solution when the solution is brought into supersaturation (Ataka, 1993). Supersaturation is achieved by varying the concentrations of precipitant, protein and additives, pH, temperature, and other parameters (McPherson, 1999 Ducruix and Giege, 1992 Ducruix and Giege, 1999). 

Even if crystals grow from the same aqueous solution, there are differences in Habitus. NaC103 crystals, for example, grow easily as polyhedral crystals, whereas NH Cl crystals always grow as dendrites, and NaCl crystals appear as hopper crystals. If Pb or Mn ions are added, cubic crystals of NaCl bounded by flat 100 faces may be obtained quite easily, but if NaCl is grown in pure solution all crystals take a hopper form, unless great care is taken to keep the supersaturation very low. These differences occur because the solute-solvent interaction energies, and, as a result, the values of Ap,/kT and A/x/kT, are different for different crystals. 

Growth Rate for Inclination-Dependent Interface Velocity. For a crystalline particle growing from a supersaturated solution, the surface velocity often depends on atomic attachment kinetics. Attachment kinetics depends on local surface structure, which in turn depends on the surface inclination, n, with respect to the crystal frame. In limiting cases, surface velocity is a function only of inclination the interfacial speed in the direction of n is given by v(h). The main aspects of a method for calculating the growth shapes for such cases when v(h) is known is described briefly in this section. 

Suspensions can be formed either by nudeation or by subdivision and dispersion. The nudeation process requires a phase change, such as condensation of vapour to yield solid, or precipitation of a salt from a supersaturated solution. In the latter case a supersaturated solution must be formed. The supersaturation condition is then alleviated by condensation on nudei (which need not be composed of the same material) already present, or else by formation of nuclei with subsequent condensation. The nudei eventually grow to microscopic, or macroscopic, size. Additional details of this process are discussed elsewhere [49,320],... 

Because of the difficulties associated with the characterisation of heteronuclei in solution, few studies have attempted to explain experimental results in a quantitative way. If it is assumed that, once nucleation occurs, the particles grow without recrystallisation, then it is possible to get information about the particle density from a consideration of the geometry of the particles and the growth kinetics. One approach is to add heteronuclei to supersaturated solutions and measure the crystallisation kinetics and, from the data obtained, estimate the surface area of the growing crystals. In this way, it is feasible to obtain information about the nucleation capability of different heteronuclei and the effects of pretreatments on the nucleation capability. An example of such an application will be discussed in Sect. 5.4. 

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