Supersaturated region

This represents a straight line of slope CS 9 — 90) + X/1. Both Cs(9 — 9q) and X/ are negative and therefore the slopes of all these isothermals are negative. When 9 = 9a, the slope is Xf. In the supersaturated region therefore, there are two distinct isothermals at temperature 9a one corresponds to the condition where the excess vapour is present in the form of liquid droplets and the other to the condition where it is present as solid particles. The region between these isothermals represents conditions where a mixture of liquid and solid is present in the saturated gas at the temperature 9o-... 

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. 

Particles within the supersaturated region develop in a two-step process nucleatton and growth. Nucleation may proceed spontaneously through the formation of M(OH) entities or be initiated with "seed materials. These are solid impurities such as dust, particle fragments, or rough edges on... 

The solubility chart divides the field of the solution into two regions the subsaturated region where the solution will dissolve more of the solute at fhe existing conditions, and file supersaturated region. 

Direct measurements of ambient supersaturations in clouds have been extremely challenging. Not only does one try to measure a small deviation from saturation, but clouds are frequently patchy with supersaturated regions next to subsaturated ones corresponding to dry entrained masses. Previous measurements have indicated that ambient supersaturations are usually less than 1% and almost never exceed 2% (Warner 1968). A median value of 0.1% was reported in these measurements. Most of our knowledge of these supersaturations is based on theoretical calculations using measurements of atmospheric conditions and are rather similar to that presented here as an example. Ranges of supersaturations expected in various cloud types are given in Table 17.3. 

The diffusivity of KCl in aqueous solutions is shown in Figure 1.26. In electrolytes, the diffusivity initially decreases with increasing concentration, reaches a minimum, and then increases until saturation. The diffusivity then rapidly declines with increasing concentration in the supersaturated region. 

These, and all other equations for concentration-dependent diffusion, consist of an infinite dilution diffusivity and a thermodynamic correction term. The thermodynamie correction term in all cases is equivalent to the derivative dGildx. The definition of the thermodynamic metastable limit (the spinodal curve) is the locus of points where dG2ldx = 0. This means that concentration-dependent diffusion theory predicts a diffusivity of zero at the spinodal. Thermodynamics tells us that the diffusivity goes from some finite value at saturation to zero at the spinodal. Unfortunately, it does not tell us how the diffusion coefficient declines. In addition, lack of thermodynamic data makes prediction of the spinodal difficult. We are, therefore, left with only the fact that as the concentration is increased in the supersaturated region, the diffusivity should decline towards zero but we do not know at what concentration the diffusivity becomes zero. 

Preliminary tests must be carried out to determine which of the process quantities -mixing intensity, temperature differences, supersaturation (metastable region with weak seed formation and labile, highly supersaturated region with spontaneous seed formation), seeding, mechanical loading - are of decisive influence for a particular application. If necessary, modified test apparatus must be used in individual cases. 

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 structure of a supersaturated solution is probably more complex than that of an unsaturated or saturated solution. As reported by Khamskii (1969) a number of attempts have been made to find the distinguishing features of supersaturated solutions by investigating the dependences of various physical properties on concentration. In most cases, however, no evidence of discontinuity of the property-concentration curves at the equilibrium saturation point has been found, although an observation that light transmittancy could decrease sharply in the supersaturated region was regarded as evidence for solute clustering. 

In contrast to sustaining an equilibrium state, crystal growth by human interference is achieved by continuous, intentional distortion of equilibration. The art of growing crystals is the ability to maintain the supersaturation region, which is metastable from a thermodynamic point of view, over such long periods of time as they are required for the built-up of single crystals [1]. A situation is intentionally created where higher than equilibrium pressures drive the system to produce the. .. solid desired. The maximum quantity of... solid that can be produced is simply the amount (the supersaturation) that would establish equihbrium, and is, thus, fundamentally limited by thermodynamics. .. [2]. 

Classical mechanism of particle formation follows nucleation of nanoparticles in supersaturated regions created by solvent diffusion. It is an intricate process, which... 

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