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Figure 2. Solubility curves for two polymorphs I and I, related either enantiotropically (a) or monotropically (b) At equilibrium, i.e. if the solid phase is in contact with its saturated solution, the chemical potentials are identical for both species in solid and liquid phases:

Figure 2 Solubility curves for two polymorphs I and I, related either enantiotropically (a) or monotropically (b) At equilibrium, i.e. if the solid phase is in contact with its saturated solution, the chemical potentials are identical for both species in solid and liquid phases:

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Figure 1. Growth of a BPTI crystal in 350 mM KSCN at pH = 4.9. (a—c) Frames of a time sequence obtained at different temperatures showing the evolution of the growth form as illustrated in (d), in which arrows indicate the face displacement with time (after ref 16).
Figure 1. Growth of a BPTI crystal in 350 mM KSCN at pH = 4.9. (a—c) Frames of a time sequence obtained at different temperatures showing the evolution of the growth form as illustrated in (d), in which arrows indicate the face displacement with time (after ref 16).
Figure 4. Uric acid phase II epitaxially grown on phase I. Figure 3. van’t Hoff plot of solubility for a dimorphic system related either enantiotropically (a) or monotropically (b).
Figure 4. Uric acid phase II epitaxially grown on phase I. Figure 3. van’t Hoff plot of solubility for a dimorphic system related either enantiotropically (a) or monotropically (b).
measurement. In this configuration, the curves plotted in Figure 2 become straight lines (Figure 3). T, is thus given by the intersection of the straight lines. However, bear in mind that the slope discontinuity does not necessarily mean a new polymorph but could also be due to the nonideal nature of the solution, for instance the presence of a miscibility gap in the phase diagram.”°
measurement. In this configuration, the curves plotted in Figure 2 become straight lines (Figure 3). T, is thus given by the intersection of the straight lines. However, bear in mind that the slope discontinuity does not necessarily mean a new polymorph but could also be due to the nonideal nature of the solution, for instance the presence of a miscibility gap in the phase diagram.”°
Figure 5. Schematic representation of the solubility curves of two phases, depending on temperature, in the case of a monotropic system.
Figure 5. Schematic representation of the solubility curves of two phases, depending on temperature, in the case of a monotropic system.
Figure 6. Concentration vs time during a polymorphic transition in solution, C*; and C*,; are the solubilities of the two phases, (a) general profile and (b) limit profiles; curve (1) transformation is controlled by growth of the stable form (II) and curve (2) transformation is controlled by dissolution of the metastable form (I).
Figure 6. Concentration vs time during a polymorphic transition in solution, C*; and C*,; are the solubilities of the two phases, (a) general profile and (b) limit profiles; curve (1) transformation is controlled by growth of the stable form (II) and curve (2) transformation is controlled by dissolution of the metastable form (I).
Table 1. Classification of organic solvents for the screening of polymorphs Finally, the temperature can be varied. The metastable zones are narrower at high temperature, and nucleation is, therefore, favored. If the system is enantiotropic and if the phase transition temperature is lower than the solvent boiling point, crystalliza- tion at low and high temperatures should be able to produce the two polymorphs, whether or not the Ostwald rule of stages applies.
Table 1. Classification of organic solvents for the screening of polymorphs Finally, the temperature can be varied. The metastable zones are narrower at high temperature, and nucleation is, therefore, favored. If the system is enantiotropic and if the phase transition temperature is lower than the solvent boiling point, crystalliza- tion at low and high temperatures should be able to produce the two polymorphs, whether or not the Ostwald rule of stages applies.
calibration is necessary, and this technology can be used both in the laboratory and in the plant. FBRM measurements are highly dependent on the shape of the crystal, which means that it is reasonable to assume that a change in crystal habit can be monitored. The study performed on paracetamol, which exhibits three different polymorphic forms, illustrates that it is possible to detect the occurrence of SMPT between Form I crystals (octahedrons) and Form II crystals (needlelike) when parac- etamol is crystallized in ethanol.®° The use of a model is necessary to determine the influence of crystal shape on the chord length distribution. Considerable additional work is required to overcome the obstacle presented by a population of several solid forms exhibiting different habits and to enable, thereby, a more precise estimation of the kinetics of the transformation.®° Modeling SMPT can be carried out in two ways, either by considering a “pseudoglobal process”, or by separately distin- guishing each mechanism. The former approach makes it quite easy to determine the impact of several process parameters such as temperature or supersaturation level.®° Nevertheless, the incidence of the volume of the solution, of the specific power input from the stirring system is not taken into account. Results obtained in laboratory-scale experiment cannot be translated quantitatively to higher scales and are merely indications of trends. The second approach is a two-stage approach. First, the kinetic rate expression of each mechanism involved is obtained through specific experiments conducted with only one solid phase in suspension. For instance dissolution of the metastable phase is monitored in order to determine the values of the kinetic parameter of the dissolution law. Secondary nucleation and growth rate expressions of the stable form can be estimated though batch experiments. Second, these dissolution and growth kinetic expressions are then combined with population balance equations in order to estimate the time evolution of the crystal size distributions corresponding to the populations of metastable and stable forms and to calculate the supersatu- ration profile. This approach has been found to satisfactorily describe the SMPT process,®* revealing the intensity of each mechanism during the transformation. This allows the mechanisms which govern the transition to be deter- mined. For instance, in the case of citric acid, the key role of the population of metastable particles in the secondary nucleation rate of the stable form has been demonstrated.®? The model reveals the effects of the operating parameters whatever the scale considered. This approach is more valuable than the former, but requires
calibration is necessary, and this technology can be used both in the laboratory and in the plant. FBRM measurements are highly dependent on the shape of the crystal, which means that it is reasonable to assume that a change in crystal habit can be monitored. The study performed on paracetamol, which exhibits three different polymorphic forms, illustrates that it is possible to detect the occurrence of SMPT between Form I crystals (octahedrons) and Form II crystals (needlelike) when parac- etamol is crystallized in ethanol.®° The use of a model is necessary to determine the influence of crystal shape on the chord length distribution. Considerable additional work is required to overcome the obstacle presented by a population of several solid forms exhibiting different habits and to enable, thereby, a more precise estimation of the kinetics of the transformation.®° Modeling SMPT can be carried out in two ways, either by considering a “pseudoglobal process”, or by separately distin- guishing each mechanism. The former approach makes it quite easy to determine the impact of several process parameters such as temperature or supersaturation level.®° Nevertheless, the incidence of the volume of the solution, of the specific power input from the stirring system is not taken into account. Results obtained in laboratory-scale experiment cannot be translated quantitatively to higher scales and are merely indications of trends. The second approach is a two-stage approach. First, the kinetic rate expression of each mechanism involved is obtained through specific experiments conducted with only one solid phase in suspension. For instance dissolution of the metastable phase is monitored in order to determine the values of the kinetic parameter of the dissolution law. Secondary nucleation and growth rate expressions of the stable form can be estimated though batch experiments. Second, these dissolution and growth kinetic expressions are then combined with population balance equations in order to estimate the time evolution of the crystal size distributions corresponding to the populations of metastable and stable forms and to calculate the supersatu- ration profile. This approach has been found to satisfactorily describe the SMPT process,®* revealing the intensity of each mechanism during the transformation. This allows the mechanisms which govern the transition to be deter- mined. For instance, in the case of citric acid, the key role of the population of metastable particles in the secondary nucleation rate of the stable form has been demonstrated.®? The model reveals the effects of the operating parameters whatever the scale considered. This approach is more valuable than the former, but requires
Table 3. Summary of four possible situations and the strategies to be adopted for the control of the polymorphic forms
Table 3. Summary of four possible situations and the strategies to be adopted for the control of the polymorphic forms
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