Stability: of polymorphs

C. H. Gu and D. J. Grant, Estimating the relative stability of polymorphs and hydrates from heats of solution and solubility data, /. Pharm. Sci. 90 (2001), 1277-1287. 

None of these rules is foolproof. However, they are useful guidelines, and the combination of relatively simple techniques can often be used to get a good estimate of the relative stability of polymorphs under a variety of conditions, information which is useful in understanding polymorphic systems, the properties of different polymorphs and the methods to be used to selectively obtain any particular polymorph (see Section 3.2). As noted above, much of that information can be included in the energy/temperature diagram, and the actual preparation of that diagram from experimentally determined quantities is described in Sections 4.2 and 4.3 following the description of the techniques used to obtain those physical data. 

Ojala etal. (1998) reported on the crystallization of two conformational polymorphs (Bernstein 1987) (see Chapter 5) of acetone tosyUiydrazone 3-XX. A triclinic form and a monoclinic form are both obtained from anhydrous ethanol—sometimes together. If the crystallizing solution is allowed to evaporate completely, only the monoclinic form is obtained, suggesting that it is the thermodynamically preferred form at room temperature. This is consistent with Ostwald s Rule of Stages and McCrone s (1965) test for relative stability of polymorphs according to which the more stable polymorph... 

One of the tests described for the relative stability of polymorphs (Sections 3.5.1 and 4.12) involves the observation of competitive growth rates in a particular solvent (Fig. 1.4). Such experiments may be easily followed and recorded on the microscope (at different temperatures) as demonstrated in Fig. 3.5. 

Whereas hot stage microscopy can be used to obtain qualitative information on polymorphic behaviour, thermal analysis provides quantitative information about the relative stability of polymorphic modifications, the energies involved in phase changes between them and the monotropic or enantiotropic nature of those transitions. The two techniques are best used in conjunction. 

Stability of polymorphs in general. As noted in Section 2.2.2 the relative stability of polymorphs depends on the free energy (AG = AH — TAS) between them. The relative importance of the two terms on the right can be measured by the ratio between them (say TAS/AH). As seen in Fig. 2.5 at absolute zero T = 0, AG = AH and TAS/AH = 0. At a transition temperature between two polymorphic phases, AG = 0 so the ratio TAS/AH = 1. Above a transition temperature this ratio will be > 1. Applied to some of the polymorphs of 5-Xn, for example, for the pair Y-R at the melting point of R the ratio is 0.85, which means that while Y is the more stable form at that temperature, the entropy is an important contributor to the free energy. Other similar comparisons based on the data in Table 5.2 strengthen the notion of the importance of entropy in the consideration of thermodynamic relationships among polymorphs. 

Microcalorimeters have the ability of directly measuring the order of the reaction (n), the rate constant (k), the reaction enthalpy (Ar//), and the equilibrium constant (ATeq). " For example, solution microcalorimetry may be used to determine the free energy of dissolution of a solid compound, which is particularly important in pharmaceutical research for dissolution studies and in the determination of the relative thermodynamic stability of polymorphs. " The change in the Gibbs-Helmholtz free energy, AGsoi, on dissolution is... 

A number of empirical rules have been proposed to deduce the relative order of stability of polymorphs and the nature of the process that interconverts these (i.e., enantiotropy vs. monotropy). Among the better known are the Heat of Transition Rule, which states that if an endothermic transition is observed at some temperature, it may be assumed that there must be a transition point located at a lower temperature where the two forms bear an enantiotropic relationship. Conversely, if an exothermic transition is noted at some temperature, it may be assumed that there is no transition point located at a lower temperature. This in turn implies that either the two forms bear a monotropic relationship to each other or that the transition temperature is higher than the temperature of the exotherm. 

The simplest and most straightforward application of thermal analysis is concerned with studies of the relative stability of polymorphic forms. For example, DTA thermograms enabled the deduction that one commercially available form of chloroquine diphosphate was phase pure, while another consisted of a mixture of two polymorphs. DTA analysis was used to demonstrate that in spite of the fact that different crystal habits of sulfamethazine could be obtained, these in fact consisted of the same anhydrous poly-morph.f In a study aimed at profiling the dissolution behavior of the three polymorphs and five solvates of spironlactone, DTA analysis was used in conjunction with powder X-ray diffraction to establish the character of the various materials. ... 

Grant has comprehensively discussed the thermodynamics of polymorphs (9). The stability of polymorphs and the driving force for polymorphic transitions is governed by the difference in Gibbs free energy, AG, between two polymorphs ... 

Free Energy Relationships Between Solvates and Non-Solvates While the relative thermodynamic stability of polymorphs depends only on the temperature at constant pressure, the stability relationship between a solvate and a non-solvated form, or of two solvates, depends not only on the temperature but also on the activity of the solvent at constant pressure. Most of the following discussion will focus on hydrates but the concepts can also be applied to other solvates. 

The stability of polymorphs is thermod5mamicaUy related to their free energy. The more stable polymorph has the lower free energy at a given temperature. The aforementioned classification of polymorphic substances into monotropic and enantiotropic classes, from the lattice theory perspective is not always appropriate. There is a need to explore the way the crystal lattice structures of... 

If left in solution, crystals of a polymorph can convert into other polymorphs (a solvent-mediated transformation). The products of these transformations might be unpredictable and irreproducible. Through kinetic factors in the crystallization, the so-called slurry experiments might mislead in attempts to estimate the relative stability of polymorphs from observations of their interconversion in the presence of solvents. In slurry experiments not the most stable polymorph is formed, but the polymorph growing best under these particular conditions. Preferential crystallization of a polymorph does not directly depend on its relative stability. 

The relative stability of polymorphs at a given temperature and pressure is determined by their differences in Gibbs energy, AG ... 

Also Na20 and K O are stabilizing p phase [146]. Thilo and Funk [146] are stating that a very small Na O eontent (from 0.17 to 0.27%) is sufficient for phase p stabilization. This opinion is, however, not confirmed by others authors [127,132], However, the stabilization of polymorph p by covering the ciystals with the glass coating is known, which assumes the formed internal stress. 

Computational assessment of the likelihoods of occurrence and the relative stabilities of polymorphs is not necessarily more effective than the experimental approach. Whilst great advances have been made in the field of ab initio crystal structure prediction (CSP), as documented in five international blind tests spanning the years 1999-2010 [5], it is still not routinely possible to predict whether a molecule is likely to be polymorphic or to confirm whether the most thermodynamically stable structure has been found experimentally, especially for molecules of the complexity of a typical drug. It is possible to compute the polymorph landscape for a specific flexible molecule, but the calculations require considerable expertise, and the timescales and computing resources can render CSP impractical for application to even a limited portfolio of candidate APIs. 

A series of rules have been formulated for understanding the relative thermodynamic stabilities of polymorphs. These rules also help to determine whether a polymorphic system belongs to the monotropic or the enantiotropic category. Tammann was the first to develop these rules in the 1920s, and they were later extended by Burger and Ramberger who applied these rules to several polymorphic systems. ... 

As there are exceptions to one or more of these rules, it is important to caution that the relative stabilities of polymorphs should be estimated by applying more than one of the above rules. A combined application of these rules provides valuable data to construct qualitative E-T diagrams, which in turn give information about the operating regions to obtain a particular polymorph. 

Drug stability is an important consideration in pharmacenti-cal unit operations and prolonged storage. It is possible that one polymorph is unstable/metastable (a kinetic polymorph) compared to another form of the same dmg (the thermodynamic polymorph). For example, differences in the chemical and thermal/photochenfical stability of polymorphs are observed for drugs such as carbamazepine, furosemide, ... 

Given the practical relevance of the relative thermodynamic relationship of various solid-state forms, rules have been developed to predict the relative thermodynamic stability of polymorphs and whether the relationship between polymorphs is monotropic or enantiotropic. First rules were developed by Tammann in 1926... 

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