POLYMORPHISM CALCULATION

Fig. 7.5 Comparison of the PXRD pattern of a production sample of 2-[(2-nitrophenyl)amino]-5-methyl-3-thiophenecarbonitrile to those of six coloured polymorphs calculated from single-crystal data. The ticks below the PXRD pattern of the production sample (with an expanded intensity scale) correspond to the major peaks of the red and yellow prisms forms. Peaks in the production sample that are not found in the patterns of the six known forms are indicated with arrows.

Figure 5 (a) Structures and (b) relative energies of FeOOH polymorphs calculated with parameterized model, plane-wave pseudopotential methods, and experiment (Laberty and Navrotsky, 1998). 

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

The detailed first principles study of the three stable polymorphs has been performed recently using the LCAO technique The main drawback of that work is that no cell optimization was performed for anatase or brookite. The energy-volume curves that were used to calculate the bulk modulus, B, and its pressure derivative, B, have been produced by varying the volume with the c/a ratio and fractional atomic coor nates being fixed at experimental values which makes results unreliable. 

The fluorite phase is found to be extremely high in energy (it falls outside the energy range of Figure 1). Its equilibrium volume at P=0 would be 27.648 A /mol, and calculated equation of state gives B=287 GPa and B"=4.18. These values make fluorite structure the least compressible of all titanium dioxide polymorphs studied here, but still leaves the observation of a phase with B>500 GPa unexplained. ... 

Calculated valence band (VB) densities of states (DOS) for all six polymorphs studied are presented in Figure 2. These plots correspond to zero pressure geometries. 

The different chain conformations observed in different polymorphic forms of a polymer are generally associated to nearly equivalent minima in the conformational energy maps, calculated for isolated chain models [2, 3],... 

It is also well known that different polymorphic forms can present largely different crystallite moduli along the chain axis (both observed and calculated). These differences can be large if large variations in the chain conformations are involved, and can have a significant influence on the bulk properties... 

Perhaps the most interesting aspect of this set of studies is the question posed in the recent paper by Schmidt et al. (2004) and deals with the reality of the patterns they observed. Is the polymorphism observed a result of the calculation methods used in the study, neural network (NN), and multivariate statistical analysis (MVA) Would increased sampling result in a greater number of chemo-types It is entirely possible, of course, that the numbers obtained in this study are a true reflection of the biosynthetic capacities of the plants studied. The authors concluded—and this is a point made elsewhere in this review—that ... for a correct interpretation a good knowledge of the biosynthetic background of the components is needed. ... 

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).

Li, W.K., Gong, X.Q., Lu, G., and Selloni, A. (2008) Different reactivities of Ti02 polymorphs comparative DFT calculations of water and formic acid adsorption at anatase and brookite Ti02 surfaces. Journal of Physical Chemistry C, 112 (17), 6594-6596. 

Table 7 shows the calculated weight percent of calcium carbonate and titanium dioxide in the white-colored paint sample. These levels are based on the calcium and titanium levels shown in Table 6. Calcium carbonate was evident by the FTIR spectrum acquired from the dried paint sample, shown in Figure 13. (Flad it been available, Raman spectroscopy, which gives ready access to the low wavenumber region, could have been used to confirm the presence (and polymorphic form) of titanium dioxide [4].) Given the white color of the paint, it is likely that the titanium present was present as titanium dioxide, and this was assumed in the calculations. The calculated weight percentage of calcium carbonate in the dried paint is 21.7 wt%, and 12.6 wt% in the paint containing the solvents. The titanium dioxide levels were calculated to be 30.6 and 17.7 wt% in the dried and solvent-containing paint sample, respectively.

An experimental study of barbituric acid found one new polymorph where molecules in the asymmetric unit adopted two different conformations [10]. The conformational aspect was investigated through the use of ab initio calculations, which permitted the deduction that the new form found would have a lower lattice energy than would the known form. It was also found that many hypothetical structures characterized by a variety of hydrogen-bonding structures were possible, and so the combined theoretical and experimental studies indicated that a search for additional polymorphs might yield new crystal structures. 

A derived crystal packing model proved to be useful in resolving the crystal structure of a metastable polymorph of racemic modafinil, where details of the solved crystal structure of one polymorph was used as a basis for developing the structure of the other [12]. It was found that the calculated XRPD pattern matched well with the experimental data, indicating the correctness of the analysis. The powder diffraction of two polymorphs of chlorothalonil were solved to obtain... 

Crystallization conditions can often be manipulated to favor the nucleation of alternate crystal forms. A metastable polymorph of metformin hydrochloride has been isolated using capillary crystallization techniques, and subsequently studied using thermal microscopy [24]. Calculations based on classical nucleation theory indicated that a metastable form could be obtained using high degrees of... 

The existence of two polymorphs was reported for a NO-releasing derivative of acetyl-salicylic acid [28]. Selection crystallization of one form or the other was achieved from a number of solvent systems (14 solvents and 3 preparative methods), but several systems were identified that yielded mixtures of the two forms. The single-crystal structure of Form I was reported, but the habit of the Form II crystals precluded their characterization. The transition point of the two forms was calculated from intrinsic dissolution data to be higher than the melting points of both polymorphs and thus the two forms bear a monotropic relationship. 

Fig. 18 Solubilities at 20°C of the two polymorphs of cimetidine, form A (<9>-) and form B (0), as a function of the mole fraction of 2-propanol in the 2-propanol/water system. Also shown are the solubility ratios (form A/form B) calculated at each solvent composition. (The data are adapted from Ref. 128.)...

According to Mottl and McConachy (1990), amorphous silica (SiC>2) is the only silica polymorph present in the smoke at the site. To allow it to form in the calculation, we suppress each of the more stable silica polymorphs. We also suppress hematite (Fe203) in order to give the iron oxy-hydroxide goethite (FeOOH) a chance to form. 

To keep our discussion simple for the moment, we suppress the silica polymorphs tridymite and chalcedony. In the calculation results (Fig. 26.1), the silica concentration gradually decreases from its initial value and, as in the previous calculation, approaches equilibrium with quartz after about half a year. 

Fig. 26.3. Silica concentration (bold lines) in a fluid packet that cools from 300 °C as it flows along a quartz-lined fracture of 10 cm aperture, calculated assuming differing traversal times At. Fine lines show solubilities of the silica polymorphs quartz, cristobalite, and amorphous silica.

---