Polymorphic system stability

In terms of thermodynamics, one of the key questions regarding polymorphic systems is the relative stability of the various crystal modifications and the changes in thermodynamic relationships accompanying phase changes and different domains of temperature, pressure, and other conditions. Buerger s (1951) treatment of these questions provides the fundamentals upon which to base further discussion. 

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. 

In spite of these caveats, there is intense activity in the application of these methods to polymorphic systems and considerable progress has been made. Two general approaches to the use of these methods in the study of polymorphism may be distinguished. In the first, the methods are utilized to compute the energies of the known crystal structures of polymorphs to evaluate lattice energies and determine the relative stabilities of different modifications. By comparison with experimental thermodynamic data, this approach can be used to evaluate the methods and force fields employed. The ofher principal application has been in fhe generation of possible crystal structures for a substance whose crystal structure is not known, or which for experimental reasons has resisted determination. Such a process implies a certain ability to predict the crystal structure of a system. However, the intrinsically approximate energies of different polymorphs, the nature of force fields, and the inherent imprecision and inaccuracy of the computational method still limit the efificacy of such an approach (Lommerse et al. 2000). Nevertheless, in combination with other physical data, in particular the experimental X-ray powder diffraction pattern, these computational methods provide a potentially powerful approach to structure determination. The first approach is the one applicable to the study of conformational polymorphs. The second is discussed in more detail at the end of this chapter. 

One generally finds, therefore, that absolute values for thermodynamic parameters are less important than are relationships that predict the relative stability of the various phases of a polymorphic system. Although it is possible to calculate such energy differences from considerations of the lattice energies of the different structures,most workers instead employ the time-honored empirical rules that have been developed over time. For instance, since Gmetastabie > G tabie, then the vapor pressure of the stable form must be less than the vapor pressure of the metastable form. 

Since different crystal forms have different structures, they can, potentially, exhibit different physical properties and different responses to experimental analytical methods. Some of the more commonly used of these methods have been demonstrated above. A central question for any polymorphic system is the relative stability of the various crystal forms. As noted above, these may be investigated qualitatively by HSM methods, and more quantitatively using thermal analytical techniques. The combined results of these measurements are conveniently summarized on a semi-empirical energy-temperature diagram [31], as shown in Fig. 3.3.16. The thermal... 

When considering questions of equilibria, one ordinarily thinks of chemical reactions taking place in a suitable medium. However, it is well known that a variety of physical equilibria are also possible, and thermodynamics is a powerful tool for the characterization of such equilibria. The existence of alternate crystal structures for a given compound can be successfully examined from an equilibrium viewpoint, and this approach is especially useful when establishing the relative stability of such polymorphic systems and their possible ability to interconvert. 

The equilibrium thermodynamics of stoichiometric hydrates has been described by several authors. The overview presented here is intended both to review the basic thermodynamics of crystalline hydrate formation/stability and to highlight the intrinsic differences between polymorphic systems and hydrate systems (a discussion of the kinetics of dehydration/hydration will be given in Section IV). The following description is a hybrid based on the work of Grant and Higuchi [7] and that of Carstensen [8]. 

While heats of solution data are frequently used to establish differences in enthalpy within a polymorphic system, they cannot be used to deduce accurately the relative phase stability. 

Polymorphism Ca2[SiOJ and stractuies of phases stable at different range of temperature are relatively well known. On Fig. 2.51 the range of temperature of individual polymorphic phases stability after Niesel and Thormann [127] are shown. Dicalcium silicate forms four phases which are stable at different temperature ranges, however, fifth phase P is unstable. Ntmse [128] gives the hypothetical system for C2S in which phase P is thermodynamically stable, at high pressme. 

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. ... 

In conclusion, S-LMHA SAMs were used to stabilize the conglomerate form of DL-glutamic acid crystals. The results offer a powerful tool in the development of processes for controlling chiral polymorphic systems and can further develop into a novel method for chiral resolution by crystallization. 

Pressure-induced phase transitions in the titanium dioxide system provide an understanding of crystal structure and mineral stability in planets interior and thus are of major geophysical interest. Moderate pressures transform either of the three stable polymorphs into the a-Pb02 (columbite)-type structure, while further pressure increase creates the monoclinic baddeleyite-type structure. Recent high-pressure studies indicate that columbite can be formed only within a limited range of pressures/temperatures, although it is a metastable phase that can be preserved unchanged for years after pressure release Combined Raman spectroscopy and X-ray diffraction studies 6-8,10 ave established that rutile transforms to columbite structure at 10 GPa, while anatase and brookite transform to columbite at approximately 4-5 GPa. 

Studies of polymorphs in recent years have pointed out the effects of polymorphism on solubility and, more specifically, on dissolution rates. The aspect of polymorphism that is of particular concern to the parenteral formulator is physical stability of the product [8]. Substances that form polymorphs must be evaluated so that the form used is stable in a particular solvent system. Physical stresses that occur during suspension manufacture may also give rise to changes in crystal form [9]. 

As indicated above, evaluation of the thermodynamics of a polymorphic or solva-tomorphic system provides valuable insight into the nature of the system, but is all too often overlooked in many studies. However, Sacchetti [6] used aqueous/organic slurries of the anhydrate and hydrate forms of GW2016 to determine the relative stability of crystal forms interrelated by solution-mediated transformation. It was reported that the use of slurries enabled experiments to be completed in a day that enabled an understanding of the relative stability of the forms as a function of relative humidity. 

Olanzapine appears to exist in at least five polymorphic forms, and the structure of Form II has been reported [32]. Two molecules form centrosymmetric dimmers stabilized by a series of C—H - rc interactions, and the dimmers are connected by a system of intermolecular N—C—and C—H S hydrogen bonds. The structure of a monoclinic polymorph of isoxsuprine hydrochloride has been reported [33], The molecular conformation existing in the new monoclinic polymorph was found to be very similar to that existing in the known triclinic polymorph. 

Based on the reversibility of their phase transformation behavior, polymorphs can easily be classified as being either enantiotropic (interchange reversibly with temperature) or monotropic (irreversible phase transformation). Enantiotropic polymorphs are each characterized by phase stability over well-defined temperature ranges. In the monotropic system, one polymorph will be stable at all temperatures, and the other is only metastable. Ostwald formulated the rule of successive reactions, which states that the phase that will crystallize out of a melt will be the state that can be reached with the minimum loss of free... 

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