Supersaturation measurement techniques

There are a number of experimental methods that can be used to obtain the crystal growth rate data needed to obtain kinetics. Unfortunately, unless great care is taken, these methods can provide very different results for the same system at the same supersaturation. We will first review the measurement techniques and then describe the various problems and pitfalls that may be encountered. 

All of the direct measurement techniques are time consuming and require a significant number of experiments to obtain sufficient data to obtain kinetic parameters. This has led a number of investigators (Garside et al. 1982 Tavare and Garside 1986 Qiu and Rasmussen 1990 Witkowski et al. 1990) to look at indirect methods for the estimation of both growth and nucleation kinetics. Most of the indirect methods are based on the measurement of the solution concentration versus time in a seeded isothermal batch experiment. This is often called the desupersaturation curve since the concentration and the solubility can be used to calculate the supersaturation of the system versus time. 

Also discussed are precipitation specific experimental techniques, such as supersaturation measurements, constant composition (CC) method, instantaneous mixing devices, maximum (critical) growth rate experiments, and sizing. Due to the intrinsic difficulties with the direct supersaturation measurements and the microsecond characteristic time scale of precipitation reaction and nucleation, the CC method is used to study the precipitation kinetics. For the same reasons, the critical growth experiments are used to delineate the domain of the reactant feed rate that assures a renucleation-free process and a unimodal CSD. 

As (In S) appears in the exponential in Eq. (42) for the nucleation rate, J depends very strongly on the supersaturation S. This is illustrated in Fig. 6, where the nucleation rates calculated from Eq. (42) are shown for water at 0°C. The magnitude of the nucleation rates, expressed in the number of nuclei formed in a volume of 1 cm in 1 sec can b st be appreciated by example. Typical measuring techniques cannot detect less than 1 drop per cm. At a supersaturation of 3 the nucleation rate is 2x 10 cm sec Thus one... 

In experimental studies, it is common practice to attempt to bracket a measured solubility by reacting a sample with undersaturated as well as supersaturated solutions. As is shown in Figure 26.2, however, this technique might equally well identify a steady-state condition as an equilibrium state. 

Results obtained in this way were helpful, but of limited value. The analyses told us whether or not the bile was supersaturated with cholesterol, but did not tell us whether the abnormality was due to too much cholesterol, too few bile acids, too few phospholipids or to some combined defect. The next step, therefore, was to measure the hour-by-hour bile lipid-secretion rates using marker-corrected perfusion techniques. These assume that, in response to the perfusion stimulus (such as an intra-duodenal amino acid mixture), the gallbladder remains tonically contracted throughout and steady-state conditions ensue. 

Another parameter often used to characterise nucleation is the induction time or period, t. This is defined as the time taken for the formation of crystals after creating a supersaturated solution. Hence, the measured induction period does depend upon the sensitivity of the recording technique. It is generally assumed that t is inversely proportional to the nucleation rate, i.e. 

While nucleation phenomena have their origin at the molecular level, they are often described in terms of macroscopic properties owing to the scarcity of experimental techniques that allow for monitoring events at the molecular level. Nucleation rates can be determined by measuring the induction time, rjnd, for nucleation. The induction time represents the time elapsed between the creation of a supersaturated state to the appearance of a solid phase and is represented by... 

The linear growth rate of a face can be expressed in terms of the step velocity, step height, and step spacing. Techniques used for in situ measurement of crystal growth rates as a function of supersaturation include the following ... 

Myerson (2002), Mullin (2001), and Mersmann (2001) provide excellent descriptions of methods for crystal growth rate measurements. These methods involve measurements of either single crystals or suspensions. Much information can be gained from the traditional technique of measuring ( grab samples or in-line) solute concentration versus time in batch crystallization on a seed bed. Initial and later slopes on such a plot can provide multiple data points of growth rate versus supersaturation. 

The technique of thermoparticulate analysis (TPA) consists of the detection of evolved particulate material in the evolved gases as a function of temperature. In the presence of supersaturated water vapor, these particles provide condensation sites for water, and hence can be detected by light-scattering techniques. Water droplets grow very rapidly on the particulate matter (condensation nuclei) until they are of a sufficient size to scatter light. The scattered light, as detected by a phototube in a dark-field optical system, is proportional to the number of condensation nuclei initially present. It is an extremely sensitive measurement, with the capability of detecting one part of material in 1015 parts of air. The technique was first employed by Doyle (90) and has been reviewed by Murphy (91. 92). 

Two common errors in solubility measurement that produce large errors involve using nonisothermal techniques. In one technique a solution of known concentration is made at a given temperature above room temperature and cooled until the first crystals appear. It is assumed that this temperature is the saturation temperature of the solution of the concentration initially prepared. This is incorrect. As we will see in Section 1.5, solutions become supersaturated (exceed their solubility concentration) before they crystallize. The temperature that the crystals appeared is likely to be significantly below the saturation temperature for that concentration so that the solubility has been significantly overestimated. 

Estimation of Crystal Growth Kinetics. The techniques for crystal growth measurement discussed in the last section all involved direct measurement of the change in mass or size of a crystal (or crystals) at a fixed temperature and supersaturation. To obtain kinetic parameters, these experiments are repeated at a several different supersaturations at each temperature of interest and then fit to a power law model given by Eqs. (2.55) or (2.56). In the MSMPR method, which will be described in detail in Chapter 4... 

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