Monotropy

When a solid system undergoing a thermal change in phase exhibits a reversible transition point at some temperature below the melting points of either of the polymorphic forms of the solid, the system is described as exhibiting enantiotropic polymorphism, or enantiotropy. On the other hand, when a solid system undergoing thermal change is characterized by the existence of only one stable form over the entire temperature range, then the system is said to display monotropic polymorphism, or monotropy. 

Henck, J.-O. and Kuhnert-Brandstatter, M. (1999). Demonstration of the terms enan-tiotropy and monotropy in polymorphism research exemplified by flurbiprofen. J. Pharm. ScL, 88, 103-8. [33]... 

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 term monotropy applies in the case of an irreversible transition from one form to another. Monotropy is bound to the existence of metastable thermodynamic forms. The liquid-gas curve crosses the solid-gas curves for the two forms before their point of intersection. 

Knowing the relationship between the thermodynamic quantities H (enthalpy), G (free energy), S (entropy), and T (temperature), it is often simple to represent equilibrium states by plotting the free energy G as a function of the temperature for each form. If the two curves intersect before the melting point, there is reversibility, i.e., enantiotropy, and if the reverse is true, there is monotropy. 

Fig. 6 Energy diagrams showing plots of enthalpy H and Gibbs free energy G, against temperature T, for the solid and liquid phases of a single compound, showing (A) enantiotropy and (B) monotropy.

Fig. 7 illustrates the behavior of polymorphs A and B in case of enantiotropy (Fig. 7A) and monotropy (Fig. 7B) during heating. For all analysis where a temperature change is involved, kinetic factors have to be considered for proper interpretation of the results. The DSC scans will differ if the sample being analyzed is stable or metastable at ambient temperature. A is the stable form at ambient temperature in both cases. 

In the case of monotropy (Fig. 7B) only the form A should exist and the DSC scan should show the melting peak of the stable form A (scan 1). If the metastable form B is heated, then scan 2 or 3 may be observed the form B transforms exothermically into the stable form A (scan 2) or the form B melts and the stable form A grows from the melt and its melting peak is observed. 

Very often some substances have two melting points separated by an exotherm. Such a DSC scan can correspond to a monotropy or to an enantiotropy. The sample may be a pure form or a mixture. Using different heating rates and tempering in DSC, one... 

Fig. 7 Possible DSC curves for two polymorphs (A) Enan-tiotropy A B, B is the highest melting form, A is the stable form below the transition point. (B) Monotropy B A, A is the highest melting form. (For explanations of the scans, see text.)...

Although, as already stated, this explanation suffices for many cases, it does not prove that in all cases of monotropy the transitian... 

Enantiotropy combined with Monotropy.—N t-"ORiy oari. 4 ly-morghk exhihit enantiotropy Of ixtQUOtropy, but, if the sub-... 

Univariant Systems.—Equilibrium between liquid and vapour. Vaporisation curve. Upper limit of vaporisation curve. Theorems of van t Hoff and of Le Chatelier. The Clausius-Clapeyron equation. Presence of complex molecules. Equilibrium between solid and vapour. Sublimation curve. Equilibrium between solid and liquid. Curve of fusion. Equilibrium between solid, liquid, and vapour. The triple point. Complexity of the solid state. Theory of allotropy. Bivariant systems. Changes at the triple point. Polymorphism. Triple point Sj—Sg— V. Transition point. Transition curve. Enantiotropy and monotropy. Enantiotropy combined with monotropy. Suspended transformation. Metastable equilibria. Pressure-temperature relations between stable and metastable forms. Velocity of transformation of metastable systems. Metastability in metals produced by mechanical stress. Law of successive reactions. 

Generally speaking, the concepts of monotropy and enantiotropy in phase theory appear to coincide with the structural concepts of unrelated and related lattices. Nevertheless, one must avoid equating the two, for it is certainly possible that one of two related lattices of the same substance is less stable than the other under all conditions of temperature and pressure. This would indicate the existenced of monotropy in spite of the existence of related lattices. This situation becomes especially important for polymorphic organic compounds, which form molecular lattices. 

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