Supersaturation

Supersaturation is the driving force in nucleation and growth. After dissolving the chemical species in a solvent, whether or not of a predetermined nature, the solution must be supersaturated in order to observe nucleation or growth. Supersaturation is the difference between the chemical potential of the solute molecules in the supersaturated (ji) and saturated states, respectively. For one molecule the expression of this difference is  

TABLE 16.2. Maximum Allowable Supercooling AT (°C) and Corre onding Supersaturation AC (g/100 g water) at 25°C  

Working values usually are not more than one-half the maxima. 

The questions of interest are how to precipitate the crystals and how to make them grow to suitable sizes and size distributions. Reqnired sizes and size distributions are established by the need for 

A precipitate may be formed as a result of chemical reaction between separately soluble gases or liquids. Commercial examples are productions of sodium sulfate, ammonium sulfate, and ammonium phosphate. 

Precipitation also can be induced by additives, a process generally called salting out because salts with ions common to those whose precipitation is desired are often used for this purpose. For instance, ammonium chloride is recovered from spent Solvay liquors by addition of sodium chloride and the solubility of BaCl2 can be reduced from 32% to 0.1% by addition of 32% of CaClj. Other kinds of precipitants also are used, for instance, alcohol to precipitate aluminum sulfate from aqueous solutions. 

Foreign substances even in minute amounts may have other kinds of effects on crystallization They may inhibit or accelerate growth rate or change the shape of crystals, say from rounded to needlelike, or otherwise. One of the problems sometimes encountered with translating laboratory experience to full scale operation is that the synthetic liquors used in the laboratory may not contain the actually occurring impurities, and thus give quite different performance. Substances that modify crystal formation are very important industrially and many such materials have been the subject of patents. 

The basic phenomena influencing crystalhzation include solid-hquid equihbria and the material will not crystallize unless the solution is supersaturated. Supersaturation is the driving force for the crystalhzation process and is expressed in terms of concentration. It can be expressed as a difference (AG) in the concentration of the 

The above thermodynamic information gives an idea about the maximum amount of material that will crystallize as a solid however, to get an insight into the rate of the prodnction of crystals we need information about its kinetics. The crystallization kinetics provide design information like crystal production rate, size distribution, and its shape. 

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Gas bubble separation time of petroleum oils NFT 60-149 ASTM D 3427 Time for air liberation after supersaturation (measurement of density)... 

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

The dynamic picture of a vapor at a pressure near is then somewhat as follows. If P is less than P , then AG for a cluster increases steadily with size, and although in principle all sizes would exist, all but the smallest would be very rare, and their numbers would be subject to random fluctuations. Similarly, there will be fluctuations in the number of embryonic nuclei of size less than rc, in the case of P greater than P . Once a nucleus reaches the critical dimension, however, a favorable fluctuation will cause it to grow indefinitely. The experimental maximum supersaturation pressure is such that a large traffic of nuclei moving past the critical size develops with the result that a fog of liquid droplets is produced. 

The figures in the table show clearly how rapidly / increases with x, and it is generally sufficient to define the critical supersaturation pressure such that In / is some arbitrary value such as unity. 

Frequently, vapor-phase supersaturation is studied not by varying the vapor pressure P directly but rather by cooling the vapor and thus changing If To is the temperature at which the saturation pressure is equal to the actual pressure P, then at any temperature T, Pjf = x is given by... 

Still another situation is that of a supersaturated or supercooled solution, and straightforward modifications can be made in the preceding equations. Thus in Eq. IX-2, x now denotes the ratio of the actual solute activity to that of the saturated solution. In the case of a nonelectrolyte, x - S/Sq, where S denotes the concentration. Equation IX-13 now contains AH, the molar heat of solution. 

In principle, nucleation should occur for any supersaturation given enough time. The critical supersaturation ratio is often defined in terms of the condition needed to observe nucleation on a convenient time scale. As illustrated in Table IX-1, the nucleation rate changes so rapidly with degree of supersaturation that, fortunately, even a few powers of 10 error in the preexponential term make little difference. There has been some controversy surrounding the preexponential term and some detailed analyses are available [33-35]. 

Supersaturation phenomena in solutions are, of course, very important, but, unfortu-... 

Once nuclei form in a supersaturated solution, they begin to grow by accretion and, as a result, the concentration of the remaining material drops. There is thus a competition for material between the processes of nucleation and of crystal growth. The more rapid the nucleation, the larger the number of nuclei formed before relief of the supersaturation occurs and the smaller the final crystal size. This, qualitatively, is the basis of what is known as von Weimam s law [86] ... 

Calculate the value of the Zeldovich factor for water at 20°C if the vapor is 5% supersaturated. 

Because of the large surface tension of liquid mercury, extremely large supersaturation ratios are needed for nucleation to occur at a measurable rate. Calculate rc and ric at 400 K assuming that the critical supersaturation is x = 40,000. Take the surface tension of mercury to be 486.5 ergs/cm. ... 

Calculate what the critical supersaturation ratio should be for water if the frequency factor in Eq. IX-10 were indeed too low by a factor of 10 . Alternatively, taking the observed value of the critical supersaturation ratio as 4.2, what value for the surface tension of water would the corrected theory give ... 

Again consider a single spherical droplet of minority phase ( [/ = -1) of radius R innnersed m a sea of majority phase. But now let the majority phase have an order parameter at infinity that is (slightly) smaller than +1, i.e. [i( ) = < 1. The majority phase is now supersaturated with the dissolved minority species,... 

In the LS analysis, an assembly of drops is considered. Growth proceeds by evaporation from drops withi < R and condensation onto drops R > R. The supersaturation e changes in time, so that e (x) becomes a sort of mean field due to all the other droplets and also implies a time-dependent critical radius. R (x) = a/[/"(l)e(x)]. One of the starting equations in the LS analysis is equation (A3.3.87) withi (x). 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

Dissolve 12 g. of aniline hydrochloride and 6 g. of urea in 50 ml. of warm water, and then filter the solution through a fluted filter to remove any suspended impurities which may have been introduced with the aniline hydrochloride. Transfer the clear filtrate to a 200 ml. conical flask, fit the latter with a reflux water-condenser, and boil the solution gently over a gauze for about hours. Crystals of diphenylurea usually start to separate after about 30-40 minutes boiling. Occasionally however, the solution becomes supersaturated with the diphenylurea and therefore remains clear in this case, if the solution is vigorously shaken after about 40 minutes heating, a sudden separation of the crystalline diphenyl compound will usually occur. The further deposition of the crystals during the re-... 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

Occasionally substances form supersaturated solutions from which the first crystals separate with difficulty this is sometimes caused by the presence of a little tar or viscous substance acting as a protective colloid. The following methods should be tried in order to induce crystallisation —... 

Inulin. This polysaccharide melts with decomposition at about 178°. It is insoluble in cold but dissolves readily in hot water giving a clear solution which tends to remain supersaturated. It does not reduce Fehling s solution. Inulin gives no colouration with iodine solution. 

Method 1. Dissolve 76 g. of thiourea in 200 ml. of warm water in a 750 ml. or 1 litre round-bottomed flask. Dilute the solution with 135 ml. of rectified spirit and add 126-5 g. of benzyl chloride. Heat the mixture under reflux on a water bath until the benzyl chloride dissolves (about 15 minutes) and for a further 30 minutes taking care that the mixture is well shaken from time to time. Cool the mixture in ice there is a tendency to supersaturation so that it is advisable to stir (or shake) the cold solution vigorously, when the substance crystallises suddenly. Filter off the sohd at the pump. Evaporate the filtrate to about half bulk in order to recover a further small quantity of product. Dry the compound upon filter paper in the air. The yield of hydrochloric acid filter off the sohd which separates on cooling. Concentrate the filtrate to recover a further small quantity. The yield of recrystalhsed salt, m.p. 175° is 185 g. some of the dimorphic form, m.p. 150°, may also separate. 

There are, however, practical limitations to minimizing RSS. Precipitates that are extremely insoluble, such as Fe(OH)3 and PbS, have such small solubilities that a large RSS cannot be avoided. Such solutes inevitably form small particles. In addition, conditions that yield a small RSS may lead to a relatively stable supersaturated solution that requires a long time to fully precipitate. For example, almost a month is required to form a visible precipitate of BaS04 under conditions in which the initial RSS is 5. ... 

Superplasticiy Superplasticizers Super Radiometal Supersaturation Superseed Supersensitization... 

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