Thermodynamics polymorphism

The measured density can be neatly accounted for by assuming that these cavities contain about 4 % benzenedicarboxylic acids plus 4 % TMA. It has been shown that TMA decarboxylates at high temperatures our NMR analysis of a solution of y -TMA showed an impurity content of about 4% benzenedicarboxylic adds. Our interpretation of these results is that the so-called y -TMA is actually a clathrate inclusion compound stabilized by the presence of interstitial impurities. This is why we have been careful not to designate it as a true thermodynamic polymorph. 

The most common crystalline forms are polymorphs, hydrates, and solvates (pseudopolymorphs). Polymorphs are formed when a substance crystallizes in two or more crystal structures. Polymorphism significantly impacts on physicochemical properties of materials, such as stability, density, melting point, solubility, bioavailability, and so on. Hence the characterization of all possible polymorphs, identifying the stable (thermodynamic) polymorph, and design of reliable processes for consistent production are critical in modem day drug development. 

Polymorphism is ubiquitous in the pharmaceutical industry. The approval of a new drug substance by the USFDA requires that all data on polymorphs of the lead molecule be documented. In general, a given substance can have any number of polymorphs but, under given experimental conditions, only one polymorph will be stable and all other polymorphs will be metastable. Since the presence of a metastable polymorph during processing often leads to phase transformation to the more stable polymorph, it is desirable to choose the thermodynamic polymorph for drug development. 

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, ... 

Many different approaches have been suggested as possible approaches to this problem, from the 1960s onwards [Verwer and Leusen 1998]. What is obvious from all of these ellorts is that this is an extremely difficult problem. Both thermodynamics and kinetics can be important in determining which crystalline form is obtained under a certain se1 of experimental conditions. Kinetic effects are particularly difficult to take into accouni and so are usually ignored. A proper treatment of the thermodynamic factors would lequire one to deal with the relative free energies of the different possible polymorphs... 

Polymorphism. Many crystalline polyolefins, particularly polymers of a-olefins with linear alkyl groups, can exist in several polymorphic modifications. The type of polymorph depends on crystallisa tion conditions. Isotactic PB can exist in five crystal forms form I (twinned hexagonal), form II (tetragonal), form III (orthorhombic), form P (untwinned hexagonal), and form IP (37—39). The crystal stmctures and thermal parameters of the first three forms are given in Table 3. Form II is formed when a PB resin crystallises from the melt. Over time, it is spontaneously transformed into the thermodynamically stable form I at room temperature, the transition takes about one week to complete. Forms P, IP, and III of PB are rare they can be formed when the polymer crystallises from solution at low temperature or under pressure (38). Syndiotactic PB exists in two crystalline forms, I and II (35). Form I comes into shape during crystallisation from the melt (very slow process) and form II is produced by stretching form-1 crystalline specimens (35). 

The thermodynamically most stable polymorph of boron is the /3-rhombohedral modification which has a much more complex structure with 105 B atoms in the unit cell (no 1014.5 pm, a 65.28°). The basic unit can be thought of as a central Bn icosahedron surrounded by an icosahedron of icosahedra this can be visualized as 12 of the B7 units in Fig. 6.1b arranged so that the apex atoms form the central Bn surrounded by 12 radially disposed pentagonal dishes to give the Bg4 unit shown in Fig. 6.3a. The 12 half-icosahedra are then completed by means of 2 complicated Bjo subunits per unit cell,... 

The following section deals with the crystallization and interconversion of polymorphic forms of polymers, presenting some thermodynamic and kinetic considerations together with a description of some experimental conditions for the occurrence of solid-solid phase transitions. 

The thermodynamic transition between different forms as the above described is formally discontinuous. The difference between polymorphs is shown in general also by a different metrical description of the corresponding lattices. 

Crystallizations and Interconversions of Polymorphic F orms 3.1 Thermodynamic and Kinetic Considerations... 

The obtainment of a particular polymorph, under given crystallization conditions, corresponds in most cases to the one which is thermodynamically more stable. In some cases, however, (when more than one minimum of free energy is available) the form which is obained is simply that one produced more rapidly (indicated as kinetically favored). 

As usual, this can be due both to thermodynamic and kinetic reasons. In fact, the presence of comonomeric units increases, in general, the energy content of all the crystalline forms, but, since the extent of increase may be different, it may destabilize some chain conformation or some kind of packing more than other ones. On the other hand, the influence of the comonomeric units on the polymorphic behavior of a polymer can be due to a change in the crystallization rates of the various forms. 

Abstract Protoberberine alkaloids and related compounds represent an important class of molecules and have attracted recent attention for their various pharmacological activities. This chapter deals with the physicochemical properties of several isoquinoline alkaloids (berberine, palmatine and coralyne) and many of their derivatives under various environmental conditions. The interaction of these compounds with polymorphic DNA structures (B-form, Z-form, H -form, protonated form, triple helical form and quadruplex form) and polymorphic RNA structures (A-form, protonated form, triple helical form and quadruplex form) reported by several research groups, employing various analytical techniques such as spectrophotometry, spectrofluorimetry, circular dichro-ism, NMR spectroscopy, viscometry as well as molecular modelling and thermodynamic analysis to elucidate their mode and mechanism of action for structure-activity relationships, are also presented. 

It is important to have an understanding of the competing thermodynamic and kinetic factors that govern crystallization. Situations exist where one polymorph formation is kinetically controlled, while another is thermodynamically controlled. 

If a compound exhibits polymorphism, one of the forms will be more stable (physically) than the other forms that is, of n existing forms n -1 forms will possess thermodynamic tendency to convert to the nth, stable form (which then has the lowest Gibbs energy it should be noted that in the preformulation stage it is not known whether the form on hand is the stable polymorph or not). 

Oosawa F, Higashi S. Statistical thermodynamics of polymerization and polymorphism of protein. In Snell FM, ed. Progress in Theoretical Biology. New York Academic Press, 1967 79-164. 

Measurements of the dissolution behavior of polymorphic forms of relatively insoluble drugs are a convenient way of measuring thermodynamic parameters which, in turn, provide a rational approach to selection of the more energetic polymorphic forms of these drugs for absorption. Large differences in free energy... 

Tables 3 and 4 list thermodynamic values calculated for polymorphs of chloramphenicol palmitate and mefenamic acid, respectively. Absorption studies of chloramphenicol palmitate in humans show that suspensions containing polymorph B of chloramphenicol palmitate gave blood levels approximately 10 times higher than those produced by suspensions of polymorph A [49], This may be due to the significant (-774 cal/mol) free energy difference between the polymorphs resulting in a substantial difference in their solubility and dissolution behavior. This theory is supported by the almost identical blood levels due to polymorphs I and n of mefenamic acid, which have a small free energy difference (-231 cal/mol) and similar solubility and dissolution behavior (Table 4).

Table 3 Thermodynamic Values for Polymorphs of Chloramphenicol Palmitate... 

For a polymorphic drug, the polymorph obtained depends on the physical conditions, such as temperature, pressure, solvent, and the rate of desupersaturation. For a solvated drug, in addition to these conditions, the thermodynamic activity of the solvating solvent may also determine the solvate obtained. However, kinetic factors may sufficiently retard the crystallization of a stable form or the solid-state transition to the stable form that an unstable form may be rendered metastable. 

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