Color coding in kJ mol-1. Deformation energy calculated at B3LYP/6â31G(d,p) level of theory with the flexible torsions fixed and the rest of the molecule ...
Creatine: Polymorphs Predicted and Found
Doris E. Braun, Maria Orlova and Ulrich J. Griesser
Electronic Supporting Information
Contents of Supporting Information 1
2 3 4 5 6
7 8 9
The crystal energy landscapes: generation and low energy crystal structures ................ 2 1.1 Conformational analysis of creatine..................................................................................... 2 1.2 Computational generation of the crystal energy landscape ................................................ 4 Representation of the experimental structures ..................................................................... 9 PIXEL calculations .................................................................................................................. 11 Hirshfeld 2D fingerprint plots ................................................................................................ 12 Comparison of computationally generated monohydrate structures .............................. 13 Experimental characterization of the creatine solid forms ............................................... 14 6.1 Materials and preparation ................................................................................................... 14 6.2 Infrared spectroscopy .......................................................................................................... 14 6.3 Hot-stage microscopy (HSM) ............................................................................................. 15 6.4 Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) ........ 16 6.5 Moisture sorption/desorption experiments ........................................................................ 18 6.5.1 Automated gravimetric moisture sorption/desorption experiments ......................... 18 6.5.2 Moisture controlled PXRD experiments .................................................................... 19 6.5.3 Water activity measurements ...................................................................................... 19 6.5.4 Isothermal Calorimetry................................................................................................ 20 Structure determination: anhydrate B and anhydrate C° crystal structures ................ 21 Structure comparison: conformations .................................................................................. 26 Comparison of calculated and experimental energy differences ...................................... 27 9.1 Differential scanning calorimetry ....................................................................................... 27 9.2 Isothermal calorimetry (RH perfusion cell) ....................................................................... 27 9.3 Lattice energy calculations ................................................................................................. 28
-1-
1
The crystal energy landscapes: generation and low energy crystal structures
1.1 Conformational analysis of creatine The deformation energy for CTN was computed on one 7x14x7 grid, equivalent to a 30° grid spacing for each dihedral angle in the range 0° to 180° for 1 and 3 and in the range 0° to 360° for 2. At each grid point the deformation energy was calculated with the flexible torsions fixed and the rest of the molecule optimized at the B3LYP/6–31G(d,p) level of theory.
Figure S1. (a) Atom numbering used throughout the study. The intramolecular degrees of freedom (torsions and HNC angles) that were optimized in the initial lattice energy minimizations are indicated with arrows (CrystalOptimizer: 1–6 and all HNC angles; 1: O1C4C2N1, 2: C4C2N1C1, : N3C3N1C1, HC1N1 C2HN2C3N1HN3C3N1). (b) Intermolecularly hydrogen bonded c1 conformation (1: 0/180°, 2: 270°, : 172°, 174° 159°153°). (c) Intramolecularly hydrogen bonded s5 conformation (1: 90°, 2: 90°, : 30/210°, 160° 159°162°). Dashed line denotes the intramolecular hydrogen bond. Eight intramolecularly hydrogen bonded low energy conformations, denoted s1-s8, were identified within 21 kJ mol1 of the global conformational energy minimum s5 (Figures S2-S3). The lowest CTN conformation exhibiting no intramolecular hydrogen bond, c1, was calculated to be 29.4 kJ mol1 less stable than the global conformational energy minimum s5. The second lowest non-intramolecularly hydrogen bonded conformation, c2, was estimated to be 41.6 kJ mol1 less stable than s5 and 12.2 less stable than c1. Minimum c1 can be related to the conformations observed in the anhydrate (AH-A) and monohydrate (MH) structures of CTN.
-2-
Figure S2. Potential energy surface scan for CTN with respect to 1 and 2. Dihedral 3 fixed to 0°. Color coding in kJ mol1. Deformation energy calculated at B3LYP/6–31G(d,p) level of theory with the flexible torsions fixed and the rest of the molecule optimized. Conformational energy minima are indicated with stars: white stars – conformation exhibiting an intramolecular hydrogen bond, black stars – conformation exhibiting no intramolecular hydrogen bond.
Figure S3. Potential energy surface scan for CTN with respect to 1 and 2. Dihedral 3 fixed to 30°. Color coding in kJ mol1. Deformation energy calculated at B3LYP/6–31G(d,p) level of theory with the flexible torsions fixed and the rest of the molecule optimized. Conformational energy minima are indicated with stars: white stars – conformation exhibiting an intramolecular hydrogen bond. -3-
Figure S4. Potential energy surface scan for CTN with respect to 1 and 2. Dihedral 3 fixed to 60°. Color coding in kJ mol1. Deformation energy calculated at B3LYP/6–31G(d,p) level of theory with the flexible torsions fixed and the rest of the molecule optimized. Conformational energy minimum is indicated with a star: white star – conformation exhibiting an intramolecular hydrogen bond. 1.2 Computational generation of the crystal energy landscape In the two experimental structures, AH-A and MH, creatine forms only intermolecular hydrogen bonds. Although, as evidenced from the conformational analysis, creatine is capable of forming an intramolecular NH∙∙∙O hydrogen bond. It is known that the combination of intermolecular electrostatics, calculated using distributed multipoles, combined with internal energies calculated ab initio tends to overestimate the stability of intramolecular hydrogen bonds relative to intermolecular hydrogen bonds, overestimating the stability of intramolecularly hydrogen bonded structures.1 Thus the inter- (c1,c2) and intramolecularly hydrogen bonded conformations (s1-s8) were treated independently in the initial generation of the crystal energy landscapes and the final crystal energy landscapes were derived using PBE-D calculations. Z=1 anhydrate and monohydrate crystal energy landscapes were generated using the 10 low energy conformations, obtained from the grid calculations using Gaussian09.2 Using the program CrystalPredictor2.0,3-5 750,000 Z'=1 anhydrate and 3,500,000 monohydrate crystal structures were randomly generated in 20 space groups, P1, P-1, P2 1, P21/c, P2 1212, P212121, Pna21, Pca21, -4-
Pbca, Pbcn, C2/c, Cc, C2, Pc, Cm, P2 1/m, C2/m, P2/c, C222 1, Pmn2 1. Each crystal structure was relaxed to a local minimum in the intermolecular lattice energy, calculated from the FIT6 exp-6 repulsion-dispersion potential and atomic charges which had been fitted to electrostatic potential around the B3LYP/6-31G(d,p) charge density using the CHELPG scheme.7 The 75,000 anhydrate and 100,000 hydrate lowest energy structures were reminimized using DMACRYS8 with a more realistic, distributed multipole model9 for the electrostatic forces which had been derived using GDMA2 10 to analyze the PBE0/6-31G(d,p) charge density. The lowest intermolecularly hydrogen bonded anhydrate was calculated to be 27.5 kJ mol–1 less stable than the most stable intramolecularly hydrogen bonded structure. The generated structures were used as starting point for further optimizations using more accurate, but computationally more time demanding, modelling methods. No constraints to prevent proton movement were necessary in the subsequent CrystalOptimizer or PBE-D structure optimizations. The more stable intermolecularly hydrogen bonded c1 and c2 crystal structures (400 anhydrates and 800 monohydrates) were refined allowing all of the conformational degrees of freedom depicted in Figure 1, the cell parameters and the molecular positions and orientations to be optimized using the CrystalOptimizer database method.11 The lattice energy (Elatt) was calculated as the sum of the intermolecular contribution (Uinter) and the conformational energy penalty paid for distortion of the molecular geometry to improve the hydrogen bonding geometries. Conformational energy penalties (Eintra, with respect to the global conformational energy minimum), and isolated molecule charge densities were computed at the PBE0/631G(d,p) level in the minimization of Elatt. The intramolecularly hydrogen bonded structures were not subjected to CrystalOptimizer calculations as the intramolecular structures were effectively rigid. Only three anhydrates, the experimentally observed ones, were within 10 kJ mol–1 of the lowest intermolecularly hydrogen bonded structure (AH-C°). In contrast 12 monohydrates were within 5 kJ mol–1 the lowest intermolecularly hydrogen bonded monohydrate structure, the experimental hydrate. Thus, all experimental structures were calculated as lowest in energy if intramolecularly hydrogen bonded structures were ignored. The most stable anhydrate (75 s1-s8 after DMACRYS and 160 c1-c2 after CryOpt) and monohydrate (210 s1-s8 after DMACRYS and 250 c1-c2 after CryOpt) structures were used as starting structures for periodic electronic structure calculations. The PBE-D calculations were
-5-
carried out with the CASTEP plane wave code12 using the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation density functional13 and ultrasoft pseudopotentials,14 with the addition of a semi-empirical dispersion correction, either the Tkatchenko and Scheffler (TS) model,15 or Grimme06 (G06)16. In a first step, the structures were geometry optimized using the TS dispersion correction. Brillouin zone integrations were performed on a symmetrized Monkhorst–Pack k-point grid with the number of k-points chosen to provide a maximum spacing of 0.07 Å−1 and a basis set cut-off of 560 eV. The self-consistent field convergence on total energy was set to 1x10−5 eV. Energy minimizations were performed using the Broyden–Fletcher–Goldfarb–Shanno optimization scheme within the space group constraints. The optimizations were considered complete when energies were converged to better than 2x10 −5 eV per atom, atomic displacements converged to 1x10 −3 Å, maximum forces to 5x10 −2 eV Å−1, and maximum stresses were converged to 1x10−1 GPa. Energy minimizations with variable unit cells were restarted after the first minimization to reduce the effects of changes in unit cell on the basis set. The energies for all anhydrates and monohydrates within 25 kJ mol−1 of the lowest anhydrate and monohydrate structure were recalculated, without optimization, with the number of k-points chosen to provide a maximum spacing of 0.04 Å−1 and a basis set cut-off of 780 eV, using the G06 dispersion correction. Isolated molecule minimizations to compute the creatine and water molecule energies (Ugas) were performed by placing a single molecule in a fixed cubic 25x25x25 Å3 unit cell and optimized with the same settings used for the crystal calculations. The PBE-D calculations reversed the stability order inter-/intramolecularly hydrogen bonded structures, making the intermolecularly hydrogen bonded structure more stable. All calculated structures are available in .res format from the authors on request. The lowest energy PBE-D structures are given in Tables S1 (anhydrates) and S2 (monohydrate).
-6-
Table S1. Hypothetical and known low-energy PBE-D anhydrate crystal structures of CTN. Str.
AH1 (C°) AH2 (B) AH3 (A) cAH4 cAH5 cAH6 cAH7 cAH8 cAH9 cAH10 cAH11 cAH12 cAH13 cAH14 cAH15 cAH16 cAH17 cAH18 cAH19 cAH20
Starting conf.
Space group
a/Å
b/Å
c1 c1 c1 c1 c1 s5 c2 c1 s3 c2 c1 c1 s7 c1 c1 c2 s5 c1 s3 c2
Pna21 P21/n P21/c Cc P21/c Pca21 P21/c P21/c Pbca Pbca Pc P21/c P21/c P21/c C2/c P21/c P21/n P21/n Pbca Pbca
11.990 5.507 9.833 6.713 6.835 12.571 7.045 11.269 11.968 9.003 6.739 7.879 6.483 9.836 8.947 6.720 9.288 5.153 11.946 9.712
5.283 11.375 5.988 9.799 9.748 4.122 10.030 5.001 8.174 9.547 5.214 9.430 11.984 4.816 11.299 13.837 6.683 16.740 8.080 8.917
Cell parameters c/Å α/° Anhydrates 9.506 90 9.973 90 11.429 90 9.566 90 9.522 90 11.609 90 8.788 90 11.979 90 12.534 90 14.243 90 9.388 90 8.051 90 8.277 90 13.261 90 13.017 90 6.790 90 9.341 90 7.004 90 12.230 90 14.808 90
-7-
β/°
γ/°
Elatt/ kJ mol-1
Elatt/ kJ mol-1
PI/ %
90 98.97 106.02 109.43 105.93 90 107.57 111.70 90 90 109.17 104.46 110.91 103.44 105.68 105.60 96.42 104.67 90 90
90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90
-267.94 -266.92 -266.61 -260.12 -258.01 -256.29 -256.15 -256.03 -254.86 -254.64 -254.40 -253.00 -252.07 -251.76 -251.40 -249.70 -249.50 -248.95 -248.34 -248.21
0 1.02 1.34 7.82 9.93 11.65 11.79 11.91 13.08 13.30 13.54 14.94 15.88 16.18 16.54 18.24 18.45 19.00 19.60 19.74
74.9 72.8 69.5 76.2 73.8 74.9 76.5 71.7 73.9 73.6 72.5 77.8 75.2 74.2 71.4 74.0 78.4 77.3 76.8 70.1
Table S2. Hypothetical and known low-energy PBE-D monohydrate crystal structures of CTN. Str.
MH1 (MH) cMH2 cMH3 cMH4 cMH5 cMH6 cMH7 cMH8 cMH9 cMH10 cMH11 cMH12 cMH13 cMH14 cMH15 cMH16 cMH17 cMH18 cMH19 cMH20 cMH21 cMH22 cMH23 cMH24 cMH25 cMH26 cMH27 cMH28 cMH29 cMH30 cMH31
Starting conf.
Space group
a/Å
b/Å
c1 c1 c1 c1 c1 c1 c1 c2 c1 c1 c1 c2 c1 c1 c1 c1 c1 c1 c1 c1 c1 c2 c1 c2 c1 c1 c2 c1 c2 c1 c2
P21/c C2/c P-1 Pbca P21/n P21/c P21/c Cc P2 12 121 C2/c P21/n Pbca P21/n Ic C2/c C2/c P21/c P21/c P21/c P21/n P2 12 121 P21/n Pna21 P21/c Pbca P21/n Cc C2/c P21/n P21/n P21/c
12.430 24.739 6.939 4.751 9.245 7.334 9.237 8.430 6.479 15.535 6.868 9.876 8.893 12.040 8.943 10.731 6.690 10.777 12.389 8.360 4.519 6.991 12.229 8.362 13.697 5.084 5.650 25.137 10.067 7.637 7.847
4.862 4.786 7.2571 12.273 7.699 7.033 5.929 9.541 9.088 6.909 15.511 10.496 9.315 5.028 14.279 14.219 9.460 5.372 4.636 9.052 8.322 9.510 4.813 6.878 7.119 16.461 12.191 4.545 7.343 6.699 6.814
Cell parameters c/Å α/° Monohydrates 12.273 90 12.254 90 7.652 108.04 24.356 90 9.829 90 13.316 90 12.856 90 9.746 90 12.423 90 15.188 90 6.998 90 15.068 90 9.085 90 12.720 90 11.149 90 9.714 90 11.600 90 12.424 90 12.469 90 9.395 90 18.410 90 11.097 90 12.611 90 12.502 90 13.859 90 8.827 90 10.756 90 12.681 90 10.459 90 13.974 90 14.473 90
-8-
β/°
γ/°
Elatt/ kJ mol-1
Elatt/ kJ mol-1
PI/ %
108.52 102.74 105.91 90 103.35 99.24 90378 114.17 90 115.46 102.10 90 107.99 105.26 98.00 90.45 101.09 94.07 92.20 101.62 90 107.22 90 98.76 90 106.67 102.92 91.34 99.54 102.43 104.54
90 90 94.66 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90
-340.52 -337.27 -336.16 -334.34 -332.51 -332.29 -332.20 -330.78 -329.76 -329.65 -329.53 -327.87 -327.33 -326.73 -326.53 -326.40 -325.48 -325.41 -325.39 -325.24 -324.80 -324.03 -323.63 -323.43 -323.33 -323.08 -322.80 -321.82 -321.66 -320.82 -320.54
0 3.25 4.36 6.19 8.01 8.23 8.53 9.75 10.76 10.87 11.00 12.66 13.20 13.80 14.00 14.12 15.04 15.11 15.13 15.28 15.73 16.49 16.90 17.10 17.20 17.44 17.72 18.70 18.87 19.70 19.98
73.0 72.6 74.2 72.2 75.7 76.1 73.4 71.7 70.2 69.9 70.6 65.9 72.2 69.6 73.5 69.3 71.3 71.9 72.5 73.9 74.6 73.1 69.4 72.7 76.6 72.9 71.6 71.4 67.4 74.2 68.8
2
Representation of the experimental structures
The final computational model was successful in reproducing the experimental structures (Table S3). The computationally generated low energy structures were compared using the Molecular Similarity Module in Mercury to determine the root mean square deviation of the non-hydrogen atoms in a cluster of n molecules (rmsdn).17
Table S3. Quality of representation of the PBE-D anhydrate and monohydrate structures.
a AH-A (exp.), RT K18 AH-A (CryOpt), 0 K AH-A (PBE-D), 0 K MH (exp.), 273 K19 MH (exp.), 20 K20 MH (CryOpt), 0 K MH (PBE-D), 0 K
9.767 9.712 9.833 12.168 12.492 12.018 12.430
Lattice parameters (cell vectors/Å, angles/o) b c α β 5.893 6.644 5.988 5.045 4.967 5.066 4.862
11.631 10.172 11.429 12.494 12.051 12.038 12.273
90 90 90 90 90 90 90
105.87 107.67 106.02 108.95 109.10 111.39 108.52
90 90 90 90 90 90 90
cell density g cm-3 1.352 1.393 1.347 1.366 1.402 1.452 1.409
rmsd15 (Å) 0.75 0.13
0.33 0.11
Figure S5. Overlay of the 15 molecule cluster of the observed structure of CTN AH-A (colored by element) and calculated PBE-D structure (green), rmsd15=0.13 Å.
-9-
Figure S6. Overlay of the 30 molecule cluster of the observed structure of CTN MH (colored by element) and calculated PBE-D structure (green), rmsd30=0.13 Å.
- 10 -
3
PIXEL calculations
PIXEL energies are intermolecular energies (i.e. Uinter) derived by integration over the isolated molecule charge densities placed in the crystal structures. The electrostatic contribution EC is rigorously derived by this procedure and various approximations are used to estimate the polarization (induction) EP, dispersion ED, and repulsion ER contribution to the intermolecular lattice energy. The calculations also provide an approximate breakdown into contributions from different pairs of molecules in the coordination shell. It has to be noted that the non-additivity of the molecule∙∙∙molecule polarization energies could not be taken into account for calculating the dimeric energies given in Table S4. This error was estimated by considering the lattice energies obtained by summing the molecule-molecule pairwise energies. These energies differ from the PIXEL lattice energies when the polarization is calculated from the net field (i.e. accounting for non-additivity of the electrostatic field around a molecule) by approximately a max. 5% overestimate. Thus the neglect of non-additivity and distant interactions does not qualitatively affect the results in the m/s. Table S4. PIXEL calculations on CTN AH-A, AH-B and AH-C° using the structures on Figure 1a. Only the most relevant intermolecular interactions for pairs of molecules are listed. EDd ERe Uinterf –1 kJ mol Form A Inversion (4.733) -161.9 -31.6 -52.0 52.9 -192.5 P2 1/c Inversion (5.253) -192.8 -31.1 -66.6 100.0 -190.4 glide (6.789) -164.6 -21.3 -56.5 97.7 -144.6 glide (6.789) -164.6 -21.3 -56.5 97.8 -144.6 Form B Inversion (5.319) -201.6 -31.2 -73.3 113.8 -192.3 P2 1/n Inversion (4.818) -151.2 -31.6 -48.4 47.9 -183.3 21 - screw (6.666) -166.8 -21.5 -56.6 98.0 -146.9 21 - screw (6.666) -166.8 -21.5 -56.5 98.0 -146.9 Form C 21 - screw (4.854) -187.5 -30.8 -61.7 86.5 -193.6 Pna2 1 21 - screw (4.854) -187.5 -30.8 -61.7 86.5 -193.6 glide (6.883) -159.0 -21.2 -53.2 89.7 -143.8 glide (6.883) -159.0 -21.2 -53.2 89.7 -143.8 a PIXEL energies are for a pair of molecules. The pairs of molecules are defined by the symmetry relationship and distance between their centres of mass in Å; belectrostatic (Coulombic) energy; cpolarization energy; ddispersion energy; erepulsion energy; ftotal intermolecular energy: U inter = EC + EP + ED + ER. The non-additivity of EP is not included. Structure
Interactiona
ECb
- 11 -
EPc
4
Hirshfeld 2D fingerprint plots
Hirshfeld surface 2D fingerprint plots of the CTN molecules representing the intermolecular interactions are given in Figure S7. For this analysis crystal structures of Figure 1a and 1b (ignoring the water molecule) were used. The fact that the 2D fingerprint plots of the anhydrates are similar is indicative of similar intermolecular interactions and environments. The spikes, present at low d e and d i values in all four plots, represent the strong hydrogen bonds.
(a) AH-C°
(b) AH-B
(c) AH-A
(d) MH
Figure S7. Hirshfeld surface 2D fingerprint plots of CTN molecules in anhydrates and monohydrate, where de is the distance from a point on the surface to the nearest nucleus outside the surface and di represents the distance from a point on the surface to the nearest nucleus inside the surface.21,22
- 12 -
5
Comparison of computationally generated monohydrate structures
The monohydrate structure (MH) and
three computationally generated
low-energy
monohydrates are contrasted in Figure S8. MH (exptl.) and cMH2, as well as MH and cMH4, exhibit 2D packing similarity. The cMH3 structure is the only low energy structure that has the R2,2(8) dimer motif interrupted.
Figure S8. Structural comparison of the computationally generated low energy monohydrate structures. Selected symmetry elements are shown for structures (a-c).
- 13 -
6 Experimental characterization of the creatine solid forms 6.1 Materials and preparation Creatine monohydrate puriss. was purchased from Fluka. Monohydrate: Creatine was dissolved in water at 95 °C. The Solution was filtered and then cooled to 4 °C. The crystallization product consisted of creatine MH. Anhydrate Form A: AH-A was obtained by dehydrating CTN MH at 110 °C. Anhydrate Form B: AH-B was prepared by drying MH above its peritectic temperature (dried at 130 °C), i.e. melting of the hydrate and recrystallization of AH-B. Otherwise a mixture of AHA and AH-B is observed. To avoid dehydration to AH-A the sample (MH) was dried in a drying oven at 130 to 135 °C with the drying vessel being preheated to the same temperature. Anhydrate Form C: Slurry experiments of CTN AH-A or AH-B in solvents with a water activity (aw) < 0.26 resulted in AH-C° (25 °C, rpm 700, ≥ 48 h).
6.2 Infrared spectroscopy Infrared spectra were recorded with a diamond ATR crystal on a Perkin Elmer Spectrum Two Fourier Transform spectrophotometer (Perkin Elmer, Norwalk Ct., USA) over a range of 4000 to 450 cm–1 with a resolution of 2 cm–1 (24 scans). The spectra were analyzed with the Opus v 5.5 software. The IR spectra of CTN and creatinine (Figure S9) allow a clear and easy discrimination of the two compounds in addition to the CTN solid forms. Similarities in the vibrational ranges of the (OH) and (NH) of CTN suggest that the four phases exhibit similar hydrogen bonding interactions. Furthermore, based on the IR spectra, all CTN forms can be expected to be Z=1.
- 14 -
Figure S9. FT-IR spectra of creatine (MH, AH-A, AH-B and AH-C°) and creatinine.
6.3 Hot-stage microscopy (HSM) A Reichert Thermovar polarization microscope equipped with a Kofler hot-stage (Reichert, A) was used for hot-stage thermomicroscopic investigations. Photographs were taken with an Olympus DP71 digital camera (Olympus, D). The dehydration process of MH to AH-A was followed with HSM (Figure S10). Upon heating the MH crystals start cracking at 55 °C, cf. jumping crystals. Dehydration is indicated by the appearance of dark regions (nucleation and growth of AH-A) that expand within the MH crystals on heating. The process starts at the surface and macroscopic defects. The overall dehydration process is dominated by the nucleation and growth of AH-A and results in the formation of aggregates of homogeneously sized AH-A crystals, with the outer shape of the original hydrate crystals being maintained. This “pseudomorphosis” is characteristic for the desolvation of stoichiometric solvates.23 The dehydration takes place within the temperature range of 60 to 75 °C. At a temperature above 210 °C needle-like shaped crystals start to sublime and in addition the decomposition of creatine starts. The sublimed needles and the decomposition product correspond to creatinine (2-amino-1-methyl-5H-imidazol-4-one, cyclization product of CTN
- 15 -
under the release of water). Melting and decomposition of creatinine is observed in the temperature range between 275 °C and 295 °C.
Figure S10. Photomicrographs of the dehydration process of CTN-MH (dry preparation).
By embedding the MH crystals in high viscosity silicon oil and applying a heating rate of about 10 to 15 K min–1 the incongruent melting of MH can be determined at 126.5 °C, accompanied by the formation of bubbles, the release of water vapor. Starting from temperatures above 240 °C the intramolecular cyclization of creatine to creatinine is again indicated by bubble formation.
6.4 Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) Thermogravimetric analysis (TGA) was carried out with a TGA7 system (Perkin-Elmer, USA) using the Pyris 2.0 software. Approximately 3 – 5 mg of sample was weighed into a platinum pan. A two-point calibration of the temperature was performed with ferromagnetic materials (Alumel and Ni, Curie-point standards, Perkin-Elmer). A Heating rate of 5 °C min–1 was applied and dry nitrogen was used as a purge gas (sample purge: 20 mL min–1, balance purge: 40 mL min–1). DSC thermograms were recorded on a Diamond DSC equipped with a Controlled Cooling Accessory (Intracooler 1P), controlled by the Pyris 7.0 software (Perkin-Elmer, Norwalk, CT, USA). A few milligrams of accurately weighed (Mettler UM3 ultramicrobalance) sample were heated in perforated or sealed Al-pans (30 µL) or sealed gold plated stainless steel high-pressure capsules. Heating rates of 5 °C min –1 were applied. The instruments was calibrated for temperature with pure benzophenone (m.p. 48.0 °C) and caffeine (m.p. 236.2 °C), and the energy - 16 -
calibration was performed with pure indium (m.p. 156.6 °C, heat of fusion 28.45 J g–1). The quoted error on temperature (extrapolated onset temperature) and enthalpy values correspond to 95% confidence intervals (derived from at least three measurements). The TGA curve of CTN MH (Figure S11) shows three distinct steps. The first mass loss corresponds to the loss of one mol of water per mol of CTN (measured mass loss: 12.09%, theoretical value for one mol of water relative to the monohydrate: 12.08%). The second indicates the intramolecular cyclization of CTN to creatinine and is accompanied by a mass loss of one mol of water per mol of CTN. The third step in the TGA curve corresponds to the thermal decomposition of creatinine and overlaps partly with the cyclization reaction. The dehydration process of CTN MH, measured in a one-pin holed DSC pan, is observed as a broad endothermic peak with a peak maximum temperature at 95 °C and a heat of dehydration, dehyH, of 51.1 ± 0.5 kJ mol–1. The peritectic temperature of MH was detected at 125.8 ± 0.5 °C by using sealed DSC pans (evaporation of water impeded) and faster heating rates ( 10 °C min – 1
). The DSC curves of the three anhydrates show an identical course. The first thermal event, an
overlay of several endothermic peaks, occurs in the temperature range between 230 °C and 275 °C. This event corresponds to the cyclization reaction of CTN to creatinine. At 291.3 ± 0.4 kJ mol–1 (heating rate 5 °C min–1) the melting and decomposition of creatinine is observed. No transformation was observed for any of the three anhydrates prior to their decomposition temperature, i.e. the metastable forms are kinetically stabilized. The DSC curve of creatinine shows only one enothermic peak, which corresponds to the melting and decomposition of the compound.
- 17 -
Figure S11. Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) thermograms of CTN and creatinine crystalline forms. TGA and DSC curves were recorded at a heating rate of 5 °C; One-pinhole lids were used for the anhydrate and MH-LK DSC experiments, a sealed pan for MH-GK.
6.5 Moisture sorption/desorption experiments 6.5.1
Automated gravimetric moisture sorption/desorption experiments
Moisture sorption and desorption studies were performed with the automatic multisample gravimetric moisture sorption analyzer SPS11-10µ (Proumid, Ulm, D). Approximately 450 - 700 mg of the forms were used for the investigations. The measurement cycles were started at 25% with a desorption cycle (decreasing humidity) to 0%, followed by a sorption cycle (increasing humidity) up to 95%, another desorption cycle to 0%, and a final sorption to 40% relative humidity (RH). RH changes were set to 5% for all cycles, except the last sorption cycle (single step from 0 to 40% RH). The equilibrium condition for each step was set to a mass constancy of ± 0.001% over 60 minutes. AH-A transforms to MH at RH > 35%, and AH-B and AH-C° transform to MH at RH > 60 % RH. The back-transformation of MH to AH-A occurs at RH < 20% (Figure 4a-d).
- 18 -
6.5.2
Moisture controlled PXRD experiments
PXRD patterns were recorded in transmission geometry on an X’Pert PRO diffractometer (PANalytical, Almelo, NL) equipped with a theta/theta coupled goniometer, programmable XYZ stage with well plate holder, Cu-K1,2 radiation source with a focussing mirror, 0.5° divergence slit and 0.02° Soller slit collimator on the incident beam side, 2 mm antiscattering slit and 0.02° Soller slit collimator on the diffracted beam side, and solid state PIXcel detector (tube voltage 40 kV, tube current 40 mA, 2step size 0.013°, 80s per step, 2 range 2° to 40°). For nonambient RH measurements a VGI stage (VGI 2000M, Middlesex, UK) was used. The moisture controlled PXRDs are shown in form of Guinier plots in Figure 4e-h. Reference PXRD patterns are given in Figure S12. Counts Anhydrate A
1000
0
Anhydrate B
2000
1000
0
Anhydrate C
3000 2000 1000 0
Monohydrate
3000 2000 1000 0 10
20
30
40
Position [°2Theta] (Copper (Cu))
Figure S12. Experimental powder X-ray diffraction patterns recorded at room temperature.
6.5.3
Water activity measurements
Excess of CTN AH-A, AH-B or AH-C° were stirred (750 r.p.m.) in 2.5 mL of each methanol and water mixture (each containing a different mole fraction of water corresponding to a defined water activity24,25) at 25.0 ± 0.1 °C for 21 days. Samples were withdrawn, filtered and the resulting phase was determined using powder X-ray diffraction and thermogravimetric analysis.
- 19 -
In contact with methanol/water, at a water activity (aw) ≤ 0.26, the AH-C° (AH-A and AH-B transformed to AH-C°) was the only solid phase at equilibrium. At aw ≥ 0.28 MH was obtained as the most stable form at equilibrium, suggesting that the system, CTN AH(-C°) ↔ MH, is in equilibrium at a w = 0.27 at 25 °C (Figure S13). AH-A was found to transform more quickly to MH than AH-B and AH-C°.
Figure S13. Phase diagram after equilibration for 21 days showing the dependence of CTN on water activity in methanol/water mixtures during CTN hydration process at 25 °C. Anhydrous CTN (AH-A, AH-B or AH-C°) was used as starting phase, the residual phase, after stirring for 21 days, was determined with PXRD (and TGA). 6.5.4
Isothermal Calorimetry
RH perfusion calorimetry experiments were performed with the TAM III nanocalorimeter unit in a 4 mL stainless steel RH perfusion ampoule. The relative humidity was controlled with two mass flow controllers and dry N2 was used as carrier gas at a constant flow rate of 100 mL h −1. Approximately 25-30 mg of sample was used. The humidity profiles (% RH vs. time) were executed as follows: 0 to 25% RH in one step, 25 to 80% in one step (anhydrates, Figure 4j-l) and 80 to 0% RH in one step (MH, Figure 4i). The RH perfusion cell was calibrated with saturated solutions of NaCl (75.3% RH), Mg(NO3)2 (52.8% RH) and LiCl (11.3% RH). The heat flow of the empty RH perfusion ampoule (baseline runs with the same humidity steps) was subtracted from the heat flow of the sample measurement. The errors on the stated (de)hydration enthalpy values are calculated at the 95% confidence intervals (CI) based on three measurements and are given in Table 1 and Figure 4i-l. - 20 -
7 Structure determination: anhydrate B and anhydrate C° crystal structures X-ray powder diffraction data were collected on a STOE STADI MP diffractometer using strictly monochromatic Cu-Kα1 radiation (λ = 1.54056 Å) from a focusing Ge(111) primary beam monochromator and a Mythen1k detector with 11° detection range. Measurements were taken in bisecting transmission geometry at ambient conditions, with a sample of 2 mm diameter placed between two zero-scattering foils. Data in the range from 5 to 111(B)/116(C°)° 2θ with the 0.009° step size were collected. The AH-B sample was prepared by dehydrating MH at 110 °C. AH-B, contaminated with traces of AH-A, was obtained. The purest batch was slurred for six hours in heptane at 20 ± 5 °C. This resulted in a transformation of the AH-A impurities to AH-C°, with form AH-B being stable. After three days of slurring in hepane at 20 ± 5 °C phase pure AH-C° was obtained and used for structure determination. Both models were refined, using the computationally generated structures as starting points, by the Rietveld method using the FULLPROF.2000 program26 and soft constraints. The background was modeled by a set of consecutive points with refineable intensities. Common isotropic displacement factors were refined for each type of atoms. FormB. Low intensity reflection belonging to AH-C° were found and taken in account during the calculations. The refinement converged at χ2 = 2.12, R wp = 4.53%, Rexp = 3.15%, Rp = 3.28 (not corrected for background). The resulting structure from the Rietveld refinement was further scrutinized by allowing all fractional coordinates to refine freely. The refinement converged at RB = 5.31%, Rf = 5.62 %, Rp = 3.00 %, Rwp = 4.05%, χ 2 = 1.65 (not corrected for background). As expected, the improvement in reliability factors came at the expense of some chemical sense (e.g. bond lengths), but otherwise, the geometry of the independent molecules was well preserved, confirming the correctness of restrained refined crystal structure. FormC. The refinement converged at χ2 = 2.01, Rwp = 4.40%, Rexp = 3.11%, Rp = 3.32 (not corrected for background).
- 21 -
Cell parameters for forms AH-B and AH-C° as well as details of the data collection and a list of atomic parameters can be found in Tables S5-S7, respectively. Observed and calculated PXRD patterns are shown in Figure S14.
Table S5. Crystallographic data for anhydrate B and anhydrate C° forms. AH-B
AH-C°
Crystal system, space group
Monoclinic, P 21/n (No.14)
Orthorhombic, P n a 2 1 (No.33)
a, Å
5.4857(3)
11.9504(3)
b, Å
11.4417(4)
5.3453(2)
c, Å
9.9624(5)
9.5314(3)
β, °
98.663(5)
90
Z
4
4
V, Å3
618.16(5)
608.86(3)
T, °C
20
20
M (g/mol)
131.13
131.13
λ, Å
1.54056
1.54056
- 22 -
Table S6. Powder diffraction data of the structure refinement of the creatine anhydrate B form. atom
AH-B x
y
z
Biso
occ.
C1
0.1390(5)
0.04627(5)
0.3797(5)
3.05(2)
1.0
C2
0.2776(5)
-0.0189(5)
0.1646(5)
3.05(2)
1.0
C3
0.4716(5)
0.1468(5)
0.2920(5)
3.05(3)
1.0
C4
0.4887(5)
-0.1084(5)
0.1925(5)
3.05(3)
1.0
N1
0.2862(5)
0.0680(5)
0.2733(5)
3.05(4)
1.0
N2
0.6028(5)
0.16928(5)
0.1924(5)
3.05(4)
1.0
N3
0.5354(5)
0.2037(5)
0.4115(5)
3.05(4)
1.0
O1
0.5680(5)
-0.1410(5)
0.3096(5)
3.05(3)
1.0
O2
0.5630(5)
-0.1495(5)
0.0835(5)
3.05(3)
1.0
H1
0.2374
-0.0071
0.4627
4.19(5)
1.0
H2
-0.0280
0.0005
0.3356
4.19(5)
1.0
H3
0.0849
0.1301
0.4205
4.19(5)
1.0
H4
0.1028
-0.0666
0.1575
4.19(5)
1.0
H5
0.2793
0.0235
0.0661
4.19(5)
1.0
H6
0.4755
0.1733
0.4993
4.19(5)
1.0
H7
0.6778
0.26081
0.4187
4.19(5)
1.0
H8
0.7312
0.2374
0.2041
4.19(5)
1.0
H9
0.5397
0.1468
0.0921
4.19(5)
1.0
- 23 -
Table S7. Powder diffraction data of the structure refinement of the creatine anhydrate C° form. AH-C° atom x
y
z
Biso
occ.
C1
0.0777(3)
0.6186(7)
-0.0012(7)
3.08(3)
1.0
C2
-0.0269(7)
0.7785(7)
0.2058(7)
3.08(3)
1.0
C3
0.1506(6)
0.9650(7)
0.1425(7)
3.08(3)
1.0
C4
-0.1152(7)
0.9748(7)
0.1627(7)
3.08(3)
1.0
N1
0.0747(4)
0.785(2)
0.1236(7)
3.08(3)
1.0
N2
0.1527(5)
0.1028(7)
0.2602(7)
3.08(3)
1.0
N3
0.2213(5)
0.0280(7)
0.0360(8)
3.08(3)
1.0
O1
-0.1010(4)
0.0948(7)
0.0475(8)
3.01(3)
1.0
O2
-0.1938(4)
1.0022(7)
0.2494(7)
3.01(3)
1.0
H1
0.0335
0.7007
-0.0919
4.69(3)
1.0
H2
0.0375
0.4387
0.0257
4.69(3)
1.0
H3
0.1644
0.5812
-0.0305
4.69(3)
1.0
H4
-0.0648
0.5902
0.1955
4.69(3)
1.0
H5
-0.0085
0.8035
0.3179
4.69(3)
1.0
H6
0.2001
0.0042
-0.0692
4.69(3)
1.0
H7
0.2818
0.1660
0.0531
4.69(3)
1.0
H8
0.2071
0.2566
0.2613
4.69(3)
1.0
H9
0.1270
0.0266
0.3546
4.69(3)
1.0
- 24 -
Figure S14. CTN AH-B (a) and AH-C° (b) Rietveld refinement from PXRD data. Experimental intensities (points), calculated intensities (line), difference plot (line at the bottom). Vertical bars indicate the positions of the Bragg peaks. For AH-B low intensity reflections belonging to AHC° were found and taken in account during refinement. λ = 1.54056 Å, T = 20 °C, 2θ range 5111(a)/116(b)°.
- 25 -
8 Structure comparison: conformations All four experimentally observed conformations can be related to the energy minimum c1 in Figure S2 and differ by less than 25° in all dihedral angles (Table S8). Overlay of the experimental conformations are given in Figure S15. Table S8. Comparison of dihedral angles (Figure computationally generated CTN solid forms. Form 1 / ° 2 / ° 3 / ° 18 11.41 -94.33 0.59 AH-A, exp. 13.17 -97.36 3.34 AH-A, calc. 34.27 -94.54 3.37 AH-B, exp. 32.43 -95.03 2.20 AH-B, calc. 11.47 -92.00 11.19 AH-C°, exp. 10.69 -91.15 7.74 AH-C°, calc. 20 MH, exp. -91.60 -5.41 9.40 -92.92 -3.23 MH, calc. 9.99
(a)
S1) observed in experimental and 4 / °
5 / °
6 / °
-147.26 -148.69 -150.93 -150.56 -157.89 -157.82 -142.11 -142.97
175.23 -178.89 172.68 172.97 -171.53 -173.55 179.17 179.65
-174.21 -178.23 179.14 176.91 -178.37 -176.58 -174.44 -174.78
(b)
(c) (d) Figure S15. Overlays of the CTN molecules in AH-A (black), AH-B (green), AH-C° (red) and MH (blue). H-atmos are drawn in (a and b), but are omitted in (c and d).
- 26 -
9 Comparison of calculated and experimental energy differences 9.1 Differential scanning calorimetry The dehydration process MH to AH-A, dehyHMH-A, measured in open DSC pans (Figure S11, Table S9), can be divided (application of Hess’s law) into the enthalpy of hydrate to anhydrate transformation, trsHMH-A, and the vaporization of the expelled water, vapHH2O. (1)
trs H MH A dehyH MH A vapH H 2O
If we subtract the known enthalpy value for the vaporization of water at the dehydration temperature (T dehy ~ 95 °C at which vapH° H2O = 40.657 kJ mol−1)27 from the measured enthalpy of dehydration according to eq. (1), we can estimate the enthalpy of MH to AHA phase transition as 10.5 ± 0.5 kJ mol−1.
9.2 Isothermal calorimetry (RH perfusion cell) With the aid of IC and a RH-perfusion cell the enthalpies of dehydration (dehyHMH-A) from MH to AH-A and hydration (hyHAH-MH) starting from all three anhydrates could be measured (Table S9) and the enthalpies of transition (trsHMH-A and trsHAH-MH, respectively) calculated according to eqs. (1) and (2): (2)
trsH AH MH hyH AH MH condH H 2O
For ΔvapHH2O = ΔcondHH2O we used the known enthalpy value of water27 at 25 °C of 43.99 kJ mol1. This resulted in:
trsHMH-A of 10.4 ± 0.1 kJ mol1 (MH to AH-A)
trsHA-MH of 10.5 ± 0.1 kJ mol1 (AH-A to MH)
trsHB-MH of 9.6 ± 0.1 kJ mol1 (AH-B to MH)
trsHC-MH of 8.7 ± 0.1 kJ mol1 (AH-C° to MH)
- 27 -
9.3 Lattice energy calculations A simple estimation of trsUMH-AH = –trsUAH-MH can be made by comparing the lattice energy, Elatt, of the hydrate to the lattice energies of the anhydrate and ice, using eq. (3): trsU MH AH trsU AH MH Elatt(MH) (Elatt( AH) ) (Elatt(ice) )
(3)
Using the lattice energy of the experimental structures (Table 1) and a value of –59 kJ mol–1 for ice,28,29 gives trsUA-MH of −14.92 kJ mol−1 (AH-A to MH), trsUB-MH of −14.60 kJ mol−1 (AH-B to MH), and trsUC-MH of −13.58 kJ mol−1 (AH-C° to MH).
Table S9. Thermodynamic Data and Lattice Energies Based on Periodic PBE-D Calculations for CTN Anhydrates and Monohydrate. Energya hyH / kJ mol1 trsH / kJ mol1
dehyH / kJ mol1 trsH / kJ mol1
AH-A
AH-B AH-C° Isothermal Calorimetry , 25 °C 53.5 ± 0.1 52.6 ± 0.1 51.7 ± 0.1 (AMH) (BMH) (C°MH) 1.8 (AC°) 0.9 (BC°) 10.5 ± 0.1 9.6 ± 0.1 8.7 ± 0.1 b b (AMH) (BMH) (C°MH)b Differential Scanning Calorimetry, 95 °C
MH 53.4 ± 0.1 (MHA) 10.4 ± 0.1 (MHA)b 51.1 ± 0.5 (MHA) 10.5± 0.1 (MHA)b
Lattice Energy Calculations, 273.15 °C Elatt / kJ 266.6 266.9 267.9 340.5 Elatt / kJ mol1 1.3 (AC°) 1.0 (BC°) 14.9 (AMH)c 14.6 (BMH)c 13.6 (C°MH)c 14.9 (MHA)c a hyH – enthalpy of hydration, dehyH – enthalpy of dehydration, trsH – enthalpy of transition, Elatt – lattice energy. bCalculated according to eqs. (1) and (2), using the heat of condensation of water (condHH2O) or the heat of vaporization of water (vapHH2O)27 at (de)hydration temperature. c Calculated according to eq. (3) using a value of –59 kJ mol–1 28,29 for ice. mol1
- 28 -
Figure S16. Comparison of experimental (isothermal calorimetry) and calculated (lattice) energy differences between MH/AH-A, MH/AH-B, MH/AH-C°. Tie lines have been added to show the differences in energy.
- 29 -
Reference List
1. Karamertzanis, P. G.; Day, G. M.; Welch, G. W. A.; Kendrick, J.; Leusen, F. J. J.; Neumann, M. A.; Price, S. L. J. Chem. Phys. 2008, 128, 244708-244717. 2. Gaussian 09, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, J. M. A.; Cheeseman, R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian Inc.: Wallingford CT, 2009 3. Karamertzanis, P. G.; Pantelides, C. C. J. Comput. Chem. 2005, 26, 304-324. 4. Karamertzanis, P. G.; Pantelides, C. C. Mol. Phys. 2007, 105, 273-291. 5. Pantelides, C. C.; Adjiman, C. S.; Kazantsev, A., V In Prediction and Calculation of Crystal Structures, 345 ed.; Atahan-Evrenk, S., Aspuru-Guzik, A., Eds.; Springer: Berlin Heidelberg, 2014; 25-58. 6. Coombes, D. S.; Price, S. L.; Willock, D. J.; Leslie, M. J. Phys. Chem. 1996, 100, 7352-7360. 7. Breneman, C. M.; Wiberg, K. B. J. Comput. Chem. 1990, 11, 361-373. 8. Price, S. L.; Leslie, M.; Welch, G. W. A.; Habgood, M.; Price, L. S.; Karamertzanis, P. G.; Day, G. M. Phys. Chem. Chem. Phys. 2010, 12, 8478-8490. 9. Stone, A. J. J. Chem. Theory Comput. 2005, 1, 1128-1132. 10. GDMA: A Program for Performing Distributed Multipole Analysis of Wave Functions Calculated Using the Gaussian Program System, version 2.2; Stone, A. J. University of Cambridge: Cambridge, United Kingdom, 2010 11. Kazantsev, A. V.; Karamertzanis, P. G.; Adjiman, C. S.; Pantelides, C. C. J. Chem. Theory Comput. 2011, 7, 1998-2016. 12. Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. J.; Refson, K.; Payne, M. C. Z. Kristallogr. 2005, 220, 567-570. 13. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865-3868. 14. Vanderbilt, D. Phys. Rev. B 1990, 41, 7892-7895. 15. Tkatchenko, A.; Scheffler, M. Phys. Rev. Lett. 2009, 102, 073005-1-073005/4. 16. Grimme, S. J. Comput. Chem. 2006, 27, 1787-1799. 17. Chisholm, J. A.; Motherwell, S. J. Appl. Crystallogr. 2005, 38, 228-231.
- 30 -
18. King, M. D.; Blanton, T. N.; Misture, S. T.; Korter, T. M. Cryst. Growth Des. 2011, 11, 5733-5740. 19. Goswami, S.; Jana, S.; Hazra, A.; Fun, H. K.; Anjum, S.; Atta, u. R. CrystEngComm 2006, 8, 712-718. 20. Frampton, C. S.; Wilson, C. C.; Shankland, N.; Florence, A. J. J. Chem. Soc. Faraday T. 1997, 93, 18751879. 21. Spackman, M. A.; Jayatilaka, D. CrystEngComm 2009, 11, 19-32. 22. CrystalExplorer, version 3.1; Wolff, S. K.; Grimwood, D. J.; McKinnon, J. J.; Turner, M. J.; Jayatilaka, D.; Spackman, M. A. University of Western Australia: Perth: 2012 23. Kuhnert-Brandstaetter, M.; Proell, F. Thermal analysis of hydrates of organic compounds. II. Mikrochimica Acta 3[5-6], 287-300. 1983. 24. Goelles, F. Monatsh. Chem. 1961, 92, 981-991. 25. Zhu, H.; Yuen, C.; Grant, D. J. W. Int. J. Pharm. 1996, 135, 151-160. 26. Rodriguez-Carvajal, J. Newsletter 2001, 26, 12-19. 27. Riddick, J. A.; Bunger, W. B. Techniques of Chemistry, Vol. 2: Organic Solvents: Physical Properties and Methods of Purification. 4th ed; Wiley-Interscience: New York, 1986. 28. Whalley, E. Transactions of the Faraday Society 1957, 53, 1578-1585. 29. Whalley, E. Hydrogen Bond 1976, 3, 1425-1470.
- 31 -
