An exceptional series of phase transitions in hydrophobic amino acids with linear side chains

Four amino acids with linear, hydrophobic side chains display an unprecedented series of solid-state phase transitions between 100 and 470 K. These involve hydrogen-bond rearrangements, sliding of molecular bilayers in one or two dimensions and development of side-chain disorder. The first modulated structures of amino acids are reported.

In the anticipation that temperature-induced phase transitions of the four amino acids with linear, hydrophobic side chains may not be limited to just the racemates, we have undertaken a systematic investigation of the enantiomeric substances in the temperature range between 100 and 470 K. We report here 18 single-crystal structures, refined from X-ray diffraction data collected at temperatures above and below transition temperatures recorded by differential scanning calorimetry (DSC).

Materials
The amino acids l-Abu, l-Nva, l-Nle and l-Met were purchased from Sigma and used as received.

Crystal growth
For each amino acid approximately 0.3 mg was dissolved in 30 mL of water in a 30 Â 6 mm test tube and sealed with parafilm. A small hole was then pricked in the parafilm and the tube placed inside a larger test tube filled with 2 ml of acetonitrile. The system was capped and left for 5 d at 20 C. Thin platelets crystallized as the organic solvent diffused into the aqueous solutions.

Differential Scanning Calorimetry (DSC) measurements
A liquid-nitrogen operated Perkin-Elmer Pyris 1 instrument was used to perform heating and cooling DSC cycles for $ 30 mg of the dried crystalline powders, sealed in aluminium pans of 30 mL volume, upon a decrease in scanning rate from 40 to 20 to 10 K min À1 . The instrument was calibrated against the enthalpy and temperature standards of n-dodecane, mnitrotoluene, p-nitrotoluene and indium of higher than 99.7% purity. Transition temperatures were evaluated by extrapolating peak-top temperatures to the zero scanning rate, transition enthalpies and entropies via integrating heat-flow peaks versus time as described by Karen (2003).

X-ray data collection and structure solution
Single-crystal X-ray data collections were carried out with APEX2 software (Bruker, 2014) on a D8 Venture singlecrystal CCD diffractometer equipped with an Oxford Cryosystems Cryostream Plus cooling unit and Mo K radiation ( = 0.71069 Å ). Data sets were collected on cooling and heating from room temperature, except that data for l-Nle at 180 K were collected after first cooling the crystal to 100 K. Data integration and cell refinement were performed with SAINT-Plus (Bruker, 2014) with subsequent absorption correction by SADABS (Bruker, 2014) and structure solution with SHELXLT (Sheldrick, 2015a). All structures are monoclinic and have a b-axis close to 5.2 Å . There is always a second axis of 9.5-9.6 Å in length, which, in order to facilitate comparison between the different structures, is here always taken to be the a-axis. The remaining c-axis is more variable (13-23 Å ). Consequently, the unconventional space group I2 (rather than C2) is used for l-Nva at 220 K; analogous to the form of l-Abu at 110 K (Gö rbitz, 2010).

Structure refinement
Least-squares refinements were carried out with SHELXL (Sheldrick, 2015b) against F 2 . All structures except l-Nva at 100 and 190 K exhibit disorder, which becomes quite extensive above 300 K, making it tedious to match geometrically reasonable side-chain orientations with the electron density maps. Usually the whole molecule was regarded as disordered, but in some cases just one set of coordinates was used for the  Table 1 Crystal data for l-Abu (C 4 H 9 NO 2 ). effectively putting restraints on covalent angles. Furthermore, at 405 K the four atoms defining a trans torsion angle were restrained to be coplanar within a 0.05 Å or 0.07 Å standard deviation (SHELXL FLAT command) and 1,2-, 1,3-and 1,4distances were restrained to preset values. Details are in the CIF files in the supporting information.
Crystal data and refinement results are listed in Tables 1-4, while a summary of the conformational disorder in terms of refined rotamers and their occupancies are given in Table 5. Complete lists of torsions angles and hydrogen-bond geometries are provided as supporting information, Tables S1 and S2. Illustrations of molecules and their crystal packing arrangements were prepared by Mercury (Macrae et al., 2008).

Refinement of modulated phases
Least-squares refinements for l-Nle were carried out with JANA2006 (Petříček et al., 2014) against F 2 . For comparison, both incommensurate and commensurate refinements were performed on each modulated phase. A so-called rigid-body modulation approach was used to fix the molecular geometry of each conformer at all its positions and occupancies generated from their complementing modulation waves on the periodicity refined in the (3 + 1)-dimensional superspace with either  Table 2 Crystal data for l-Nva (C 5 H 11 NO 2 ).  Table 3 Crystal data for l-Nle (C 6 H 13 NO 2 ).

Table 4
Crystal data for l-Met (C 5 H 11 NO 2 S). harmonic (Fourier series) or crenel (Petříček et al., 1995) functions. Experimental and refinement details are provided in the supporting information, Tables S3 and S4.

Results and discussion
3.1. Phase transitions between 100 and 470 K from DSC The results from the DSC analysis are summarized in Table  6 and Fig. 1, a schematic illustration is shown in the supporting information, Fig. S1. Upon warming, two reproducible endothermic events are recorded for l-Abu. The first is sharp, while the second develops gradually from 270 K to a peak at 356 K and ceases abruptly around 360 K. For l-Nva transition 1 is rather broad, while transition 3 is very weak. Regarding transition 2 at 273 K, repeated measurement with a carefully dried sample confirmed the absence of water. Four reproducible endothermic events take place for l-Nle. The first (observable only upon heating) and second events overlap. Finally, for l-Met, three endothermic events are recorded between 100 and 470 K. The first is broad and develops between 250 and 340 K.

L-Abu
A P2 1 form and a I2 form, both with Z 0 = 4 ( Fig. 2a), were previously identified for l-Abu at 110 K (Gö rbitz, 2010). We have now heated and cooled a selected crystal a number of times across the transition temperature at $ 207 K. Unit-cell determinations at 190 K always reproduced the form, while the form prevailed at 215 K. Accordingly, transition 1 in Fig.  1 represents a full and reversible conversion between the two l-Abu polymorphs. From this we conclude that the form is unstable below transition 1, and that the P2 1 crystal previously investigated at 110 K (Gö rbitz, 2010), the only one with this symmetry out of about ten tested, represented a freak occurrence of a specimen that failed to undergo the normal phase transition upon cooling.
The packing diagrams in Fig. 3 show the typical construction of a crystal of a hydrophobic amino acid with stacking of molecular bilayers, each with two hydrogen-bonded sheets in its core. Four different types of sheets have been observed for enantiomeric amino acids (Gö rbitz et al., 2009). The one observed here (Fig. 4) is called Lx (see the supporting information for notation). Notably, all molecules of such a sheet take part in equivalent intermolecular interactions, even when Z 0 > 1 (here Z 0 = 4).
A special property of the I2 and the P2 1 l-Abu polymorphs, seen among previous amino acid structures only for form (I) (Ihlefeldt et al., 2014) and form (III) (Mossou et al., 2014) of lphenylalanine, is the presence of two distinct types of molecular bilayers, one constructed from A and B molecules and one from C and D molecules. The latter is unperturbed by the phase change (Figs. 3a and b), but some subtle yet intriguing changes occur for the AB-bilayers as only A:::B heterodimers are present in the P2 1 structure, while the I2 structure has A:::A and B:::B homodimers. It would be unreasonable to assume that transitions between the two forms take place by  Table 5 Occupancies for side-chain conformations as a function of temperature (K).
Side-chain conformations are listed in Table  5. At 215 K, molecule B is disordered over two gauche positions (Fig. 2b), with gauche+ as the most populated conformation (Table 5) (7) to 0.100 (6) (Fig. S4), and at 110 K only gaucheÀ remains (Fig.  2a). It follows from the previous data (Gö rbitz, 2010) that this ordering upon cooling occurs regardless of whether the phase transition 1 takes place or not (see above). As the temperature increases between 209 and 355 K, there is a gradual introduction of disorder for molecules A, B and C, while molecule D remains fully ordered even at 330 K (Fig.  2c). At transition 2 the disorder reaches a state where the distinction between A and B and between C and D is lost, leaving just two crystallographically independent molecules at 365 K (Fig. 2d), each with its own distribution of side-chain rotamers, Table 5. Symmetry consequently increases as the pseudo-twofold rotation axes of the P2 1 structure at 215 K in Fig. 3(b) become proper symmetry elements of a C2 unit cell at 365 K (Fig. 3c).

L-Nva
The two molecules in the asymmetric unit of l-Nva at 100 K ( Fig. 5a) participate in L2-type hydrogen-bonded sheets (Fig.  4), not Lx sheets as l-Abu, l-Nle and most other amino acids that do not branch at C or C (Gö rbitz et al., 2009). At low temperatures, l-Nva is thus isostructural to its analog with an isopropyl side chain, l-Val (Dalhus & Gö rbitz, 1996a). There is no side-chain disorder below transition 1 (Fig. S5).
Upon heating through transition 1 at 207 K (Fig. 1), sliding of molecular bilayers occurs both along the monoclinic axis ( Figs. 6a and b) and the 9.6 Å a-axis (Fig. S6). These displacive changes, linked with a shift in space group from P2 1 to I2, are equivalent to those observed for the amino acid racemates and quasiracemates described above. Simultaneously, disorder is introduced for both side chains (Fig. 5b).
While all other amino acids investigated so far retain their basic hydrogen-bonding pattern during a phase transition, transition 2 of l-Nva at 273 K (Fig. 1) Table 5. The asymmetric unit of the P2 1 form of l-Abu at 110 K looks exactly as the I2 asymmetric unit shown in (a).  L2-L2 to Lx-Lx with Z 0 being reduced from 2 (space group I2, Z = 8) to 1 (C2, Z = 4, Fig. 5c). Major shifts in molecular positions upon the change of crystal symmetry are not required, but minor reorientations can be seen by comparing Figs. 6(b) and (c). This unprecedented transition appears sharp in DSC, but a plot of the positions of H atoms accepted by the carboxylate syn lone pairs (Fig. 7) makes it evident that H1A and H1B atoms gradually migrate towards more centered positions between 100 and 270 K (i.e. through transition 1). An abrupt final shift results in a single three-centered interaction in an Lx sheet at 293 K (Fig. 4).
The unit-cell volume and density of l-Nva are in Table 7 compared with corresponding values for l-Val. The large 15% difference at room temperature is associated with the inefficient stacking of the long l-Nva side chains compared with the isopropyl chain of l-Val (Figs. 6c and d).
Regarding transition 3 in Fig. 1 at 300 K, the angle increases from 104.770 (5) at 293 K to 112.2 (2) at 320 K (Table S7). As the thermal effect is very weak, any significant change in disorder can be excluded, so this transition is probably associated with minor bilayer sliding and rearrangements of the side chains. As the structure at 293 K is already disordered over four positions, further efforts to resolve this matter were considered futile.

Figure 5
Molecular structure of l-Nva at (a) 100, (b) 220 and (c) 293 K with atomic coloring scheme as in Fig. 2. Side-chain H atoms have been omitted for disordered structures, and only the most populated conformation is shown in ellipsoid representation; the side chains of minor orientations being shown in ball-and-stick style with spheres of arbitrary size (the polar heads are omitted due to extensive overlap).

Figure 4
Hydrogen-bonded sheet of type Lx (Gö rbitz et al., 2009) of l-Abu at 215 K and l-Nva at 293 K (top) and type L2 of l-Nva at 100 and 220 K (bottom). Side chains are shown as small spheres. Hydrogen bonds accepted by syn and anti carboxylate lone pairs are marked 1 and 2, respectively; distances (in Å ) for l-Abu are average values for four molecules. In the L2 sheet, the H1B of molecule B (light grey C atoms) is involved in a three-centered interaction to the carboxylate group of molecule A (dark grey C atoms), with H1BÁ Á ÁO2A as the shorter contact, while H1A participates in a two-centered interaction to O1B (H1AÁ Á ÁO2B in orange is > 2.8 Å ). In the Lx sheet all syn (1) hydrogen bonds are similar, with H1Á Á ÁO1 as the shorter component of a threecentered interaction.
Using the disordered, but well defined 210 K structure as a reference for l-Nle, increasing temperature brings about conformational rearrangements and increasing disorder, corresponding to the relatively high transition entropy of 6.3 J mol À1 K À1 , Table 6. This is labelled as transition 3 in Fig.  1. Numerous ways to refine the side-chain disorder above room temperature were tested, and we settled for two positions at 330 K (Fig. 8b) and three at 380 K (Fig. 8c, Table 5).   Temperature-dependent positions of H atoms interacting with the syn lone pairs of the l-Nva carboxylate group. From their starting positions at 100 K (blue), both H1B and H1A move towards more central positions as the temperature increases through 220 K (green) to 270 K (orange). After transition 2 in Fig. 1, the distinction between molecule A and B (Fig.  5) has disappeared, giving a single type of three-centered interaction (dashed lines) at 293 K (red).

Figure 6
Crystal packing of l-Nva at (a) 100 K, (b) 220 K and (c) 293 K and (d) of l-Val at 293 K (Torii & Iitaka, 1970), all viewed along the a-axis. At the two lowest temperatures, C atoms of molecule A are colored in dark grey, while those of molecule B are light grey. Similar sections of a molecular bilayer of l-Nva are highlighted by blue shading in (a) and (b) to highlight the sliding half a unit-cell length along the vertical 5.2 Å axis during transition 1. Red shades in (c) and (d) cover the hydrophobic regions at room temperature, of width 8.82 Å for l-Nva and 6.45 Å for l-Val (calculated as the distance between planes running through the centers of the C -C bonds).
The space group remains C2, but Table 3 reveals a decrease for the -angle from 97.628 (2) at 210 K to 90.916 (5) at 380 K.
Transition 4 at 395 K in Fig. 1 concerns a 4.01 Å slide along the 9.6 Å a-axis (Figs. 9b and c). The -angle increases to 103.11 (2) without changes to the space group or the hydrogen-bonding pattern. Unlike the displacive transition for l-Nva at 207 K described above, no concomitant slide along the b-axis is seen (Fig. S7). Sliding along a single axis also occurs for the quasiracemate l-Nle:d-Met (Gö rbitz & Karen, 2015), but in a two-step manner.
Our first attempt to solve the 180 K structure was based on a monoclinic C2 unit cell with a = 28.579 (4), b = 5.2472 (8), c = 14.759 (2) Å and = 97.983 (5) , which can be derived from the unit cell at 210 K (Table 3) by tripling the length of a. As Z 0 is then increased from 1 to 3, we initially assumed that the 0.700 (7):0.300 (7) disorder between two side-chain conformations at 210 K had become crystallographically ordered 2:1 at 180 K. Subsequent structure refinement was, however, unsatisfactory, with R > 0.10 and unreasonable thermal displacement ellipsoids (Fig. S8). A closer look at the diffraction pattern (Fig. S9) immediately revealed something out of the ordinary, two types of reflections being identified: the strong ones indexed on the lattice of the 210 K structure and weak satellites defining a vector q = 0.6978a * À 0.1095c * of a modulated structure in the (3 + 1)-dimensional superspace introduced by de Wolff et al. (1981). The new integration of frames was made by CrysAlis software (Agilent, 2014), and the space-group test in JANA2006 (Petříček et al., 2014) proved the superspace group C2(,0,)0. With the 210 K structure as a starting model, molecular modulations as well as site occupancies were refined to an almost perfect spatial separation of the two conformers for either of the alternative modulation functions, harmonic or crenel (Table S3). The harmonic model, which needs just three additional parameters, gives a significantly better fit. The result shows that in the 180 K structure it is the 'order' of the chains that is incommensurably modulated, yet it is an order as manifested by the relatively high entropy of 2.75 J mol K À1 for transition 2 in Fig. 1.
At 100 K yet another structure is obtained. This is also modulated, with vector q = 2/3a * À 1/6c * , i.e. commensurate within experimental accuracy. Hence it has a supercell of six bilayers (Fig. 10b); a 3 Â 1 Â 6 multiple of the C2 unit cell at 210 K. The parameters of the modulated refinement are listed in the Table S4. The difference in refinement fits for the two modulation functions (harmonic and crenel) is not so pronounced as at 180 K. This means that in this commensurate 100 K phase both conformers are fully separated, as the tiny residual disorder of the incommensurate modulation has been removed (assuming that the same incommensurate phase is obtained on cooling as on heating, as indicated by two additional, partial data sets from a less favorable specimen). A comparison of distances, angles and torsion angles for the 210, 180 and 100 K phases with details of the refinement models is in Table S5.
The solution of the 100 K phase provided an opportunity to study how the mutual molecular interactions affect the geometries of both conformers in their independent positions. The relatively large ratio of independent reflections to the number of refined parameters for the commensurate model with the crenel function (9704/186 ' 52) allows a refinement in which the condition of rigidity of molecules is suppressed. To keep the number of refined parameters low, we did constrain the anisotropic thermal-displacement parameters to be the same for the two conformers, and let the atomic coordinates be freely determined by the modulation function. The observed lowering of the R-factor indicates that both conformers are slightly but significantly affected by the interactions of their side chains, violating partially the rigid-body model. (a) Crystal packing of l-Nle at 210 K viewed along the a-axis. C atoms of To model these interactions, the rigid-body condition was applied to three groups of molecules: the molecule pair A + D (the conformer trans, gauche+, trans) and to the molecule pairs B + E and C + F of the other conformer (trans, trans, trans). The result in Table S6 shows that the bond lengths are kept uniform, suggesting that the interactions affect mainly the torsion angles of the conformers.
The 100 K data set can also be refined on a regular 3 Â 1 Â 2 unit cell of two bilayers shown in Fig. 10(a). The space group is then C2 (Table 3) with six molecules in the asymmetric unit (Fig. 11). Further analysis shows that an l-Nle bilayer with a 2:1 distribution between side-chain conformations trans,trans,trans (4 molecules) and trans,gauche+,trans (2 molecules) could occur in three different types 1, 2 and 3 (Fig.  10c). The observed stacking sequence along the c-axis is 1-2-1-2 (Fig. 10b), with no trace of type 3. Only four other aminoacid structures have two types of bilayers in the crystal: The I2 and P2 1 phases of l-Abu discussed above ( Fig. 3a and 3b) as well as form (I) (Ihlefeldt et al., 2014) and form (III) (Mossou et al., 2014) of l-phenylalanine. These four structures have in common not only a Z 0 value of 4, but also that adjacent bilayers are antiparallel. All other structures have identical, parallel bilayers. Considering that hydrogen-bonding patterns are unaffected by the side-chain conformations, it is indeed quite remarkable that l-Nle forms a modulated, but ordered crystalline 1-2-1-2 arrangement at 100 K instead of any of the simpler 1-1-1, 2-2-2 or 3-3-3 alternatives.
Transition 1 is not seen in the DSC scan on cooling, but visible on heating (Fig. 1). Our 180 K data set was collected after first cooling the structure to 100 K, but subsequent testing (with somewhat lower quality crystals) confirmed that both modulation and the apparent C2 unit cell with Z 0 = 3 is observed at 180 K both on cooling and on heating, so the reason why we do not observe the weak transition 1 upon cooling is not clear. The details of the transitions to and between the modulated l-Nle phases will be subject to future, more comprehensive investigations, which will also include monitoring obvious crystal-to-crystal variation. (a) The C2 unit cell with two bilayers for l-Nle at 100 K. H atoms are omitted, hydrogen bonds are dotted. Molecules B (pink), C (light pink), E (light grey) and F (white) have the same side-chain conformation, but B and E are tilted slightly to relieve close contacts (double arrows) with A (purple) and D (blue). The two hydrophobic regions in the unit cell (grey shades) are related by the central twofold rotation axis. (b) Comparison of the 100 K cell (black edges) with the commensurate supercell (orange) and the unit cell at 210 K (purple). (c) The three possible types of bilayers with a 2:1 conformational distribution between trans, trans, trans (light molecules) and trans, gauche+, trans (dark molecules). Type 3 (grey and black molecules) has not been observed experimentally. Red and blue shadings in (b) highlight type 1 and type 2 bilayers and the 1-2-1-2 stacking sequence along the caxis (arrows).

L-Met
No side-chain disorder was described for l-Met at 120 K (Dalhus & Gö rbitz, 1996a), 150 K (Sadler et al., 2005) or at room temperature (Torii & Iitaka, 1973). The present structure refinement reveals, on the other hand, two side-chain conformations for molecule A and four for molecule B at 293 K (Fig. 12a). The two positions for the molecule A side chain both define the same formal trans, trans, trans orientation for N1A-C2A-C3A-C4A, C2A-C3A-C4A-S1A, C3A-C4A-S1A-C5, with small separations between the two alternative positions for each atom. Considering that short intermolecular distances (less than sum of van der Waals radii) to atoms in the side chain of molecule B should be avoided, the major orientation of A [occupancy 0.830 (4)] is associated with the trans, gauche+, gauche+ and trans, trans, gaucheÀ conformations for B [combined occupancy 0.809 (3)]. Conversely, the A side chain adopts the minor orientation when the side chain of B is either gaucheÀ, trans, gauche+ or gaucheÀ, gaucheÀ, gaucheÀ, Table 5. Fig. 1 shows two previously unknown transitions for l-Met above room temperature. Upon heating from room temperature only minor structural changes are apparent above transition 1, despite a rather high value for ÁS of 4.66 J mol À1 K À1 , Table 6. These are associated with increased populations for the minor side-chain conformations ( Fig. 12b and Table 5) as well as a smaller value for the angle and increased interlayer spacing (Table 4 and Figs. 13a and 13b). By comparison, structural changes between the 320 and 405 K forms are much more evident, even though the P2 1 space group is retained. Molecular disorder is very complex for l-Met above transition 2; the high number of electrons for the side-chain sulfur atom allowing detection of atomic positions with low occupancy. The final refinement model displayed in Fig. 12(c) employed no less than four different side-chain positions for molecule A and six for molecule B, but the true number of conformations in the crystal may actually be even larger. More elaborate refinement models did not, however, result in a significant reduction of the R-factor. In addition to the development of multifold disorder above transition 2, there is also a slide along the 9.5 Å axis (Fig. 13c) that closely mimics the slide at transition 4 of l-Nle taking place in the same temperature range. Sliding along the b-axis is similarly absent (Fig. S11). Cell parameters recorded at 430 K (Table S7) deviate primarily from those obtained at 405 K in terms of a smaller angle, 94.13 (10) versus 99. 869 (13) , and what appears to be a reduction in unit-cell volume from 791.3 (5) to 773 (7) Å 3 . Due to the complex disorder at 405 K, no full data collection was carried out to further investigate this matter.
It is noteworthy that the hydrogen-bonding patterns of l- Molecular structures of l-Met at (a) 293 K, (b) 320 K and (c) 405 K; style as in Figs. 5 and 8 except that at 405 K side-chain conformations are colored in a rainbow sequence (red, orange, yellow, light green, light blue, light violet) from highest to lowest occupancy. Only a single set of coordinates was refined for O1, O2, N1 and C1 of each amino acid; these atoms thus occur in regular red, blue and black colors.

Figure 11
The six molecules A to D in the asymmetric unit of the C2 unit cell of l-Nle at 100 K. Atomic numbers are given for molecule A.
Nle and l-Met are different at all temperatures, Lx-Lx versus L2-L2. The change triggered by the associated-C H 2 -to -S-substitution suggests, like the temperature-induced transition 2 for l-Nva discussed above, that these patterns have quite similar energies. This is furthermore substantiated by l-Abu (Gö rbitz, 2010) and the monoclinic polymorph of l-Cys (Gö rbitz & Dalhus, 1996), for which the related CH 3 -to-SH substitution induces a shift from Lx-Lx to L2-L2 hydrogen bonding.

Conclusions
Prior to the present investigation, only a single temperatureinduced phase transition was known for an enantiomeric amino acid, pertaining to orthorhombic l-Cys (Moggach et al., 2005), where a disordered thiol group becomes ordered at 30 K. This picture is changed dramatically by the results presented here for l-methionine (l-Met), l-aminobutyric acid (l-Abu), l-norvaline (l-Nva) and l-norleucine (l-Nle). Together, these four amino acids with linear, hydrophobic side chains display at least 12 phase transitions, which are associated with a surprising variety of physical processes in the crystal. These include concerted side-chain rearrangements (l-Abu), regular symmetry increase due to developing disorder (l-Abu), simultaneous sliding along two crystallographic axes (l-Nva), hydrogen-bond pattern rearrangement (l-Nva), more gradual introduction of complex disorder or change in rotamer composition (l-Nle, l-Met), displacive transition along a single axis (l-Nle, l-Met) and finally transitions to commensurate and incommensurately modulated structures (l-Nle), the first of their kind for amino acids. For the amino acid counterparts with branched side chains, such as l-Val, l-Ile and l-Leu, no comparable transitions have been found, highlighting the remarkable properties of the four compounds studied here.

Figure 13
Crystal packing of l-Met at (a) 293 K, (b) 320 K and (c) 405 K viewed along the b-axis with C atoms of molecule A colored in dark grey and those of molecule B in light grey. As in previous packing diagrams, only the most populated side-chain conformation is shown for each molecule. The length of the gray double arrow at 293 K represents the distance between the centers of neighboring molecular bilayers [calculated as cÁsin()]. Arrows of the same length at 320 and 405 K illustrate the expansion perpendicular to the molecular bilayers as a function of temperature and phase transitions.