Supersolubility curves

This observation is in accordance with the phenomena of the crystallization in the resolution operation mentioned above in the following points. There are no clear, definite critical supersaturations above which nucleation of D-threonine occurs. Ohtsuki (2), however, reported supersolubility curve for this system, who gave the value of the supersaturation width At=7 C at 50 C. Their definition of the metastablllty was that no nucleation of the enantiomer other than seeded one was observed for two hours of resolution experiments. According to this definition, the supersolubility can be determined to lie somewhere between At=8 and 5 C from the present experimental data, this being in agreement with his result. If the crystallization proceeds further, however, D-threonine crystals may start to crystallize from the solution even if the initial supersaturation is 5 C. In this sense it is no longer the metastablllty limit. 

The area of conditions called the metastable zone is situated between the solubility and supersolubility curves on the crystallization phase diagram (Fig. 3.1). The supersolubility curve is defined as the line that separates the conditions where spontaneous nucleation (or phase separation or precipitation) occurs, from those where the crystallization solution remains clear if left undisturbed (Ducruix and Giege, 1992 Ducruix and Giege, 1999). 

Plot the results and you will obtain the supersolubility curve. Figure 3.3 shows a practical example if a screen has produced hits at conditions of 10-15 mg/ml of protein and 5-10% PEG, the experiments are set at concentrations ranging from 5-20 mg/ml protein versus 2.5-15 or 20% PEG, thus covering a range of conditions above and below the hits. ... 

Saridakis, E. and Chayen, N. E. (2003). Systematic improvement of protein crystals by determining the supersolubility curves of phase diagrams. Biophys. 84, 1218-1222. 

The true picture (Schoen 1961) is far more complex than indicated in Figure 6.8. In reality, a series of supersolubility curves should be pictured whose locations depend on specific seed surface, rate of supersat-... 

Figure 7. Solubility plot also showing the supersolubility curve.

When the nuclei of the precursor to be precipitated interact significantly with the surface of the support, the rate of precipitation is measurable at much lower concentrations. Accordingly it is possible to perform precipitation exclusively on the surface of the support by maintaining the concentration of the precursor between that of the solubility and supersolubility curve. Control of the concentration of catalytically active precursors within the above range is the basis of the deposition-precipitation procedure. With sparingly soluble solids, the concentration difference between the solubility and supersolubility curves is small. The concentration therefore has to be controlled fairly accurately. 

Figure 8 shows the case when the active precursor reacts with the surface of the support to yield a compound of a lower solubility. Now both the solubility and the supersolubility curve have been shifted to lower concentrations. We will see that reaction to form a compound with the support often takes place. 

With the usual addition of a precipitant to a solution, as schematically represented in Fig. 9, the local concentration rises temporarily above that of the super-solubility curve, which causes rapid nucleation of the precipitate. When after homogenizing the liquid, the final concentration is lower than that of the supersolubility curve, nucleation has already proceeded and the crystallites precipitated are stable. Consequently, the concentration has to be maintained continuously... 

Interaction with the support is a prerequisite to achieve the desired dense and uniform coverage of the surface of the support with the precursor of the active component. Precipitation from a homogeneous solution without interaction with the support leads usually to relatively large precipitated crystallites. The interaction with the support can be easily assessed by measuring the pH as a function of time or of the amount of alkali injected both with and without a suspended support. If there is a significant interaction with the support. the level of the pH remains with a suspended support considerably below that of the pH measured without a suspended support. Without a support, the concentration of the supersolubility curve is often apparent from the pH curve passing through a maximum. 

When the concentration of the supersolubility curve has been attained, nucleation proceeds rapidly and the subsequent growth of the nuclei proceeds faster than the generation or addition of hydroxy ions. 

The effect of solution concentration on nucleation rate is shown qualitatively in Fig. 9. At low levels of supersaturation, the rate is essentially zero but, as concentration is increased, a fairly well defined critical supersaturation is reached (point 1), beyond which nucleation rate rises steeply (curve 1-2). Point 1 may be regarded as the threshold of the labile region. Data from a series of such curves at different temperatures establish the locus of points at which nucleation starts, i.e., the Miers supersolubility curve discussed in Section II. 

Although the existence of a supersolubility curve has been demonstrated as characteristic of most crystallizing systems, its position depends on a number of external factors. These include the presence of solid... 

Using this formula for a measured solubility at low temperatures immediately gives an idea about potential yield and about the feasibility of a cooling crystallization process. In the metastable zone no nucleation is observed even though the solution is supersaturated. Spontaneous nucleation will only occur when the supersolubility curve is reached. 

A given supersaturation thus corresponds to a crystal seed of length in labile equilibrium. Aggregation of molecules to form clusters (ca. 20-100 molecules) with the critical crystallite size is only possible in the case of a local deviation in the supersaturation of the solution. Figure 2.3.5-3 shows a schematic plot of the supersolubility curves, which lie above the saturation curve and run approximately parallel to it. They indicate to which degree of supersaturation spontaneous crystallization is not observed in a technically acceptable time (20-30 min).This experimentally determined time is an important quantity in the design of industrial crystallizers. 

Fig. 2.3.S-3 Schematic depiction of a solubility curve c (7) and two supersolubility curves Cs T, l-j.

Jennings [11] was of the opinion that the curve I (5 inFig. 3.7), which according to Barret is the C-S-H supersolubility curve, is in fact the dissolution curve of the second C-S-H modification, different from the C-S-H which dissolves along the A curve (Fig. 3.7). He supports his view by presenting many results reported by different authors, which fit to the well-defined curve. Moreover, he... 

In spite of the fact that the supersolubility curve is ill-defined, there is no doubt that a region of metastability exists in the supersaturated region above the solubility curve. The diagram is therefore divided into three zones, one well-defined and the other two variable to some degree ... 

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

Supersaturation can also be achieved by removing some of the solvent from the solution by evaporation. Line AB C represents such an operation carried out at constant temperature. Penetration beyond the supersolubility curve into the labile zone rarely happens, as the surface from which evaporation takes place is usually supersaturated to a greater degree than the bulk of the solution. 

Agitation is frequently used to induce crystallization. Stirred water, for example, will allow only about 1°C of supercooling before spontaneous nucle-ation occurs, whereas undisturbed water will allow over 5 °C. Actually, very pure water, free from all extraneous matter, has been supereooled some 40 °C. Most agitated solutions nucleate spontaneously at lower degrees of supereool-ing than quiescent ones. In other words, the supersolubility curve Figure 3.9) tends to approach the solubility curve more closely in agitated solutions, i.e. the width of the metastable zone is reduced. 

Interaction between the soluble metal precursor and the surface of the support is required. In such a case, the supersolubility curve SS in Figure 14.1 is shifted towards lower concentrations in the presence of the support (curve... 

SSsupport in Figure 14.1). As a consequence, when the concentration of the precursor increases, this supersolubility curve is encountered before the other. 

The concentration of the precursor must be maintained between the concentrations of the solubility (curve S) and the supersolubility curves (curve SS) to avoid the precipitation in solution (Figure 14.1). 

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