Polymorphs thermodynamic rules

A Burger, R Ramberger. On the polymorphism of pharmaceuticals and other molecular crystals. I. Theory of thermodynamic rules. Mikrochim Acta (Wein) 2 259-271, 1979. 

When a decision needs to be made on whether two polymorphs are enantio-tropes or monotropes, it is very useful to use the thermodynamic rules developed by Burger and Ramberger, which are tabulated in Table 3. 

A Burger, R Ramberger. On the polymorphism of pharmaceuticals and other molecular crystals. I. Theory of thermodynamic rules. Mikrochim Acta [Wien] 11 259— 271, 1979. A Burger, R Ramberger. On the polymorphism of pharmaceuticals and other molecular crystals, n. Applicability of thermodynamic rules. Mikrochim Acta [Wien] 11 273-316, 1979. 

To help decide whether two polymorphs are enantiotropes or monotropes. Burger and Ramberger developed four thermodynamic rules [14]. The application of these rules was extended by Yu [15]. The most useful and applicable of the thermodynamic rules of Burger and Ramberger are the heat of transition rule and the heat of fusion rule. Figure 11, which includes the liquid phase as well as the two polymorphs, illustrates the use of these rules. The heat of fusion rule states that, if an endothermic polymorphic transition is observed, the two forms are enantiotropes. Conversely, if an exothermic polymorphic transition is observed, the two forms are monotropes. 

Table 4 Thermodynamic Rules for Polymorphic Transitions According to Burger and Ramberger [14], Where Form I is the Higher-Melting Form...

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. ... 

BeUantone RA, Patel P, Sandhu H, Choi D, Singhal D, Chokshi H, Malick AW, Shah NH (2012) A method to predict the equilibrium solubility of dmgs in solid polymers near room temperature using thermal analysis. J Pharm Sd 101 4549-4558 Burger A, Ramberger R (1979) On the polymorphism of pharmaceutical and other molecular crystals I. Theory of thermodynamic rules. Mikrochimica Acta 11 259-281 Chiou WL, Riegelman S (1971) Pharmaceutical applications of solid dispersion systems. J Pharm Sd 60 1281-1302... 

Table 8.2 Thermodynamic rules for polymorphic transitions according to Burger and Ramburger [10]...

Ostwald s step rule holds that a thermodynamically unstable mineral reacts over time to form a sequence of progressively more stable minerals (e.g., Morse and Casey, 1988 Steefel and Van Cappellen, 1990 Nordeng and Sibley, 1994). The step rule is observed to operate, especially at low temperature, in a number of min-eralogic systems, including the carbonates, silica polymorphs, iron and manganese oxides, iron sulfides, phosphates, clay minerals, and zeolites. 

Transformations between phases follow the Ostwald step rule, which states When a number of phase transformations, from a less stable state to more and more stable states are possible, usually the closest more stable modification is formed and not the most stable one corresponding to the least free energy (Ostwald 1897). The phase transition from the metastable to the lowest free-energy polymorph is unavoidable due to the thermodynamic driving force to minimize free energy. 

Polymorphic structures of molecular crystals are different phases of a particular molecular entity. To understand the formation of those phases and relationships between them we make use of the classic tools of the Phase Rule, and of thermodynamics and kinetics. In this chapter we will review the thermodynamics in the context of its relevance to polymorphism and explore a number of areas in which it has proved useful in understanding the relationship between polymorphs and polymorphic behaviour. This will be followed by a summary of the role of kinetic factors in detecting the growth of polymorphic forms. We will then provide some guidelines for presenting and comparing the structural aspects of different polymorphic structures, with particular emphasis on those that are dominated by hydrogen bonds. 

By making use of Volmer s equations some attempts have been made by Becker and Doring (1935), Stranski and Totomanov (1933), and Davey (1993) to explain the Rule in kinetic terms. In doing this, it becomes apparent that the situation is by no means as clear cut as Ostwald might have us believe. Figure 2.11 shows the three possible simultaneous solutions of the nucleation equations which indicate that by careful control of the occurrence domain there may be conditions in which the nucleation rates of two polymorphic forms are equal, and hence their appearance probabilities are nearly equal. Under such conditions we might expect the polymorphs to crystallize concomitantly (see Section 3.3). In other cases, there is a clearer distinction between kinetic and thermodynamic crystallization conditions, and that distinction may be utilized to selectively obtain or prevent the crystallization of a particular polymorph. 

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... 

---