Metastable supersaturation

Calcium phosphate precipitation may also be involved in the fixation of phosphate fertilizer in soils. Studies of the uptake of phosphate on calcium carbonate surfaces at low phosphate concentrations typical of those in soils, reveal that the threshold concentration for the precipitation of the calcium phosphate phases from solution is considerably increased in the pH range 8.5 -9.0 (3). It was concluded that the presence of carbonate ion from the calcite inhibits the nucleation of calcium phosphate phases under these conditions. A recent study of the seeded crystal growth of calcite from metastable supersaturated solutions of calcium carbonate, has shown that the presence of orthophosphate ion at a concentration as low as 10-6 mol L" and a pH of 8.5 has a remarkable inhibiting influence on the rate of crystallization (4). A seeded growth study of the influence of carbonate on hydroxyapatite crystallization has also shown an appreciable inhibiting influence of carbonate ion.(5). 

In considering the state of supersaturation, Ostwald(20) introduced the terms labile and metastable supersaturation to describe conditions under which spontaneous (primary) nucle-ation would or would not occur, and Miers and Isaac(21) have represented the metastable zone by means of a solubility-supersolubility diagram, as shown in Figure 15.8. 

Ve see in Figure 7 that Tolman s representation of the radially dependent surface tension also leads to a vanishing thermodynamic barrier, at high but metastable supersaturations, when a value of 6 computed from solutions of the YBG equation on the planar interface is used. This value of the Tolman parameter is consistent with values obtained from simulation studies of the planar Lennard-Jones surface (28,29). It is apparent that the physical picture of nucleation is highly dependent upon the assumed radial dependence of the surface tension. 

The metastable (supersaturated) zone between lines AB and CD where spontaneous crystallization is improbable. However, if a crystal seed were placed in such a metastable solution, growth would occur on the seed. 

Numerous kinetic studies have been made of the spontaneous precipitation of calcium phosphates from solutions containing concentrations of lattice ions considerably in excess of the solubility values (33, 34). Although attempts, are usually made to control the mixing of reagent solutions, it is difficult to obtain reproducible results from such experiments since chance nucleation of solid phases may take place on foreign particles in the solution. Many of these difficulties can be avoided by studying the crystal growth of well-characterized seed crystals in metastable supersaturated solutions of calcium phos.phate. 

Hydrolysis equilibria can be interpreted in a meaningful way if the solutions are not oversaturated with respect to the solid hydroxide or oxide. Occasionally, it is desirable to extend equilibrium calculations into the region of oversaturation but quantitative interpretations for the species distribution must not be made unless metastable supersaturation can be demonstrated to exist. Most hydrolysis equilibrium constants have been determined in the presence of a swamping inert electrolyte of constant ionic strength (/ = 0.1, 1, or 3 M). As we have seen before, the formation of hydroxo species can be formulated in terms of acid-base equilibria. The formulation of equilibria of hydrolysis reactions is in agreement with that generally used for complex formation equilibria (see Table 6.2). 

Not only is timely seeding an excellent way to do away with batch-to-batch vagaries in the width and sensitivity ofthe metastable, supersaturated region, but the avoidance of nucleation is often crucial for achieving crystallization elegance—a requisite for enhanced rejection of impurities. To trade away such a powerful tool for the sake of trivially lessened inconveniences in record keeping in a GMP plant is most unsound as an operating principle. For those frequent and difficult purification tasks that crystallization from solution does so well, seed early, seed often and, above all, seed always. 

The removal of the metastable supersaturation is a slow process. A large amount of crystal surface is required to allow for the large number of random collisions necessary to remove the supersaturation generated during the cycle. The proper orientation of both the molecules in solution and the molecule on the crystal surface is required for deposition, and the increased complexity of the molecule increases the number of collisions required for proper orientation. 

Because thermodynamics deals only with equilibrium states, we can use it to show, for example, that calcite should dissolve in a certain solution, or that it should precipitate from another solution, but we are unable to say anything whatsoever about how fast such processes will occur, or indeed if they will occur at all (metastable supersaturated solutions are well known, after all). This is a serious limitation. Many important processes may be rate-limited by one or more slow reactions. 

Most precipitation systems exhibit a metastable supersaturation zone where supersaturation is too low for nucleation to take place. As the supersaturation is increased, the point at which nucleation just begins to occur corresponds to the maximum metastable (critical) supersaturation allowable without nucleation. If crystals are present at this moment in the precipitation vessel, they grow at a maximum (critical) growth rate. 

One method for overcoming the above mentioned difficulties is the use of external seeds so that initial nucleation can be controlled or minimized. Most crystallization systems exhibit a metastable supersaturation zone where crystal growth continues but the supersaturation is too low for nucleation to take place. Thus, if the supersaturation can be maintained below the metastable zone upper limit after seeding, then only growth on the seed crystals will occur. In this case, the initial condition for the population density will be the initial seed distribution. 

The state of supersaturation is an essential requirement for all crystallization operations. Ostwald (1897) first introduced the terms labile and metastable supersaturation to classify supersaturated solutions in which spontaneous (primary) nucleation (see section 5.1) would or would not occur, respectively. The work of Miers and Isaac (1906, 1907) on the relationship between supersaturation and spontaneous crystallization led to a diagrammatic representation of the metastable zone on a solubility-supersolubility diagram Figure 3.9). The... 

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