Temperatures energy—temperature diagrams

Figs. 6A and B illustrate the plots of the functions G and H versus temperature (energy/temperature diagrams) for each polymorph and for the liquid. The thermodynamic reversibility of the solid transition between two crystalline forms is characteristic of enantiotropic systems. Each form has its thermodynamic stability range. The lower melting form is... 

Figure 2-33. Energy/temperature diagram of the tripie pressure HRSG.

Free Energy - Temperature Diagrams (Ellingham Diagrams)... 

Fig. 16. Gibbs energy-temperature diagram if FCC and ECC are present in the system. Ai-isotropic (undeformed) melt, A2-deformed melt (nematic phase) points 1 and 4 - melting temperatures of FCC and ECC under unconstrained conditions (transition into isotropic melt) points V and 2 -melting temperatures of FCC and ECC under isometric conditions (transition into nematic phase), point 3 - melting temperature of nematic phase (transition into isotropic melt but not completely randomized)...

Figure 3.6 Free energy-temperature diagram with scales showing oxygen pressures, C0/C02 and H2/H20 pressure gas ratios.

Grunenberg, A., Flenck, J-O., Siesler, FI.W., 1996, Theoretical Derivation and practical Application of Energy / Temperature Diagrams as an Instmment in Preformulation Studies of Polymorphic Drug Substances, International Journal of Pharmaceutics, 129, 147-158. 

Fig. 9.2. Flowchart of prilocaine hydrochloride solid state forms and melt with transformation temperatures under ambient pressure conditions (left) and semi-schematic energy/temperature diagram of the polymorphs (right). Key H, enthalpy G, Gibbs free energy AHf, heat of fusion Liq, liquid phase (melt). Reproduced from [36]...

Grunenberg A, Henck JO, Siesler HW. 1996. Theoretical derivation and practical application of energy/temperature diagrams as an instrument in preformulation studies of polymorphic drug substances. Int. J. Pharm. 129 147-158. 

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. 

Obtaining the thermodynamically metastable form in an enantiotropic system the information for obtaining and maintaining this form is essentially found in the energy-temperature diagram. 

The energy temperature diagram and characteristic DSC traces for the monotropic case are given in Fig. 4.14, while that for the enantiotropic case is given in Fig. 4.15. The connections between the diagram and the traces are described in the figure... 

Fig. 4.15 Characteristic free-energy temperature diagram (a) and DSC traces (b) for the enantiotropic relationship between polymorphs. The Gi and Gu curves cross at the transition temperature 7[ n below their melting points mpi, and mpn all indicated on the temperature axis. DSC trace A at the transition temperature modification I undergoes an endothermic transition to modification II, and the heat absorbed is A/fi n for that transition. Modification II then melts at mpn, with the accompanying AHfu. DSC trace B Modification I melts at mpi with A//n followed by crystaUization of II with A//ni at the intermediate temperature. Modification II then melts with details as above. DSC trace C modification II, metastable at room temperature, transforms exothermically to modification I with A/fn i at that transition temperature. Continued heating leads to the events in trace A. DSC trace D modification II exists at room temperature and no transition takes place prior to melting at mpn, with the appropriate A//ni- (After Giron 1995, with permission.)...

Burger, A. Henck, J.O. The presentation of polymorphic systems by energy/temperature diagrams. Biopharm. Pharm. Technol. 1995,1, 10-11. 

Figure 1 Energy-temperature diagrams, (a) For a hypothetical enantiotropic system T and T, melting points of forms I and II 7, transition temperature, (b) For a hypothetical monotropic system 7 and 7n, melting points of forms I and II.

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... 

Fig. 42 Energy-temperature diagrams for a monotropic system (top) and an enantio-tropic system (bottom).

Figure 7 Energy/temperature diagrams of polymorphic systems (a) an enantio-tropic system, (b) a monotropic system. (From Ref. 22. Reproduced by permission of Springer, Vienna.)...

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