Article pubs.acs.org/JPCC
Why Propane? Marcin Podsiadło, Anna Olejniczak, and Andrzej Katrusiak* Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland S Supporting Information *
ABSTRACT: According to our survey, of all organic compounds propane has the lowest melting point. This exceptional property of propane has been rationalized by the coincidence of light molecular mass, low electrostatic potential, low molecular symmetry as well as a loose arrangement of molecules, unable to match opposite electrostatic potentials on their surface and efficiently fill the space. The main structural features of molecular arrangement persist at least to 6 GPa in propane and n-butane, which we have isothermally and isochorically crystallized in a diamond-anvil cell. structure can be classified as a loose crystal,10,11 where all intermolecular contacts are longer than the sums of the van der Waals (vdW) radii.12 The shortest intermolecular distances can be correlated with density and electrostatic potential in the structure. The melting point also depends on the molecular symmetry, as described by empirical Carnelley’s rule formulated for isomers.13 The extension of Carnelley’s rule to the series of analogous compounds and interdependence of molecular symmetry, the mp, and molecular mass successfully applied to halomethanes and haloethanes14 has now been applied to alkanes. In our present study, we have determined the structure of propane at high pressure to directly measure the compression of its intermolecular contacts. We have also performed high-pressure experiments for the adjacent analogue of propane, n-butane, for which the melting-point increase is the largest in the series of all n-alkanes studied here. In this article, the term melting point has been generally used, although the term f reezing temperature is often preferred for substances liquid and gaseous under normal conditions. Both of these terms are associated with the thermodynamic stability of phases. However, the freezing and melting points often exhibit a substantial hysteresis, particularly large when the supercooling effect occurs, and the melting more accurately represents the phase boundary.
1. INTRODUCTION The lowest melting temperature (mp) of all known organic compounds is at 85.45 K, a feature of propane, C3H8, according to our survey of all accessible databases, mainly Reaxys. Owing to its lowest mp out of the largest class of compounds known in nature, propane is an ideal model for exploring the structuremelting relations. Along with methane and ethane (CiH2i+2, i = 1, 2), propane (i = 3) constitutes the largest natural organic deposit on Earth and is one of the most common fuels. Most intriguingly, even lighter than propane hydrocarbons, ethane (C2H6, mp = 89.85 K) and methane (CH4, 90.65 K), as well as any freons, melt at higher temperature. Furthermore, there is only a handful of any known chemical substances, in general, that melt lower than propane. They include molecular gases H2, N2, O2, O3, F2, CO, and noble elements He (He requires increased pressure of 2.5 MPa to freeze at 0.95 K), Ne, Ar, as well as quite exotic compounds like NF3 and OF2.1 The melting-point prediction, first attempted by Lindemann in 1910,2 is still intensely developed for traditional and new technologies, including structural biology,3,4 pharmacology,5 and nanotechnology.6 Its significance is often exemplified by the usage of UF6 (hex) in both main uranium enrichment by gaseous diffusion and gas centrifuge methods. The sublimation point of UF6 is 329 K and triple point is 337 K, compared with mp 1300 K of UF4, 1405 K of U, and 3138 K of UO2. The systematically lower melting points of n-alkanes with odd i numbers compared with those with i even, noted by Baeyer in 1877,7 were explained over 120 years later by the molecular shape unsuitable for packing in crystal.8,9 The shape of the propane molecule was approximated by an irregular pentagon inadaptable to dense packing, whereas the n-hydrocarbons of even i were approximated by parallelograms more efficiently filling the space. However, the molecular shape incompatible for crystal packing would generate some short intermolecular contacts, apart from longer ones across gaps between mismatched molecules. Here we show that no such short contacts are present in the solid propane. The solid propane © 2013 American Chemical Society
2. EXPERIMENTAL SECTION Propane and n-butane, 99.5% pure, from Linde Gaz Polska were used. For high-pressure studies they were compressed and loaded into a modified Merrill-Bassett15 diamond-anvil cell (DAC) at cryogenic conditions and in situ crystallized. At 295 K, propane froze at 3.2 GPa and n-butane froze at 1.6 GPa in the form of polycrystalline mass filling the whole volume of the high-pressure chamber. Single-crystals of propane and n-butane Received: November 29, 2012 Revised: February 7, 2013 Published: February 7, 2013 4759
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(Figure 1) were obtained under isochoric conditions: the DAC with the polycrystalline mass was heated with a hot-air gun until
Figure 1. Crystal samples in the diamond-anvil cell: single crystals of propane in three different orientations at 3.30 GPa/332 K (a), 3.69 GPa/348 K (b), and 5.93 GPa/387 K (c); n-butane at: 2.60 GPa/381 K (d), 3.44 GPa/443 K (e), and 5.79 GPa/468 K (f).
Figure 2. Contact parameter δ (Å; red dots) and melting points (K; blue dots) as a function of C-atoms number in n-alkanes. The δ parameters have been calculated for the C−H bonds normalized to the length of 1.092 Å.
all but one grain melted. Then, the DAC was slowly cooled to room temperature and the single crystal grew and eventually filled the entire volume of the chamber. Both propane and n-butane showed exceptionally beautiful intense colors in the polarized light, owing to high optical anisotropy of their crystals. The experimental details and progress in growing the single crystals of propane and n-butane are shown in Figures S1−S7 and Figures S8−S12, respectively, in the Supporting Information. Diffraction data were collected at 295 K by using a KUMA KM4-CCD diffractometer with the graphite-monochromated Mo Kα radiation.16 The CrysAlisCCD and CrysAlisRED programs17 were used for the data collection, determination of the UB matrix, and for the initial data reduction and Lorentz polarization (Lp) corrections for both compounds. The intensity of reflections has been accounted for the absorption of X-rays by the DAC, shadowing of the beams by the gasket edges, and absorption of the sample crystal itself.18,19 The crystal structures of propane and n-butane were solved by direct methods, and the H atoms were located from molecular geometry.20 Details of experiments, structure refinements, and crystal data are given in the Supporting Information. Voids in the propane structure have been calculated by using a probing sphere and the contact surface (Mercury CSD package).21 Program CrystalExplorer22 was used for calculating the electrostatic potential;23 it was mapped onto the molecular surfaces defined as 0.0022 au electron-density envelope.24
positive (i.e., the shortest contacts are longer than the sums of vdW radii), except for n-nonane, where the δ parameter is −0.023 Å. Thus all light n-alkanes can be classified as the socalled loosely packed crystals,10,11 where all interatomic distances are longer than the sums of vdW radii.12 Propane has the strikingly highest δ, of +0.087 Å, which coincides with its lowest melting point. This result suggests that the most loose packing of molecules in propane is connected to its low mp. The main trends in δ changes and melting temperatures are opposite, except the odd/even small alternations in δ and mp values, consistently increasing for i even and decreasing for i odd for all n-alkanes with i = 1, 2, 4, ...9. The main trend in δ changes shows that the tightness of packing is significant for the melting points, which is an expected result. However, the small alternations indicate that there are other factors affecting the melting temperature. Analogous odd/even alternations of melting points in a considerably higher temperature range were also observed for diols, diamines,1,25 and carboxylic acids, where much stronger intermolecular interactions of hydrogen bonds are present. The loose packing in n-alkanes can be explained by very weak intermolecular forces in their crystals. H and C atoms as well as single covalent bonds are weakly polarizable, and the dispersion forces in alkanes are weak. Net atomic charges and electrostatic potential in these molecules are also very low (Figure 3). Moreover, the molecules of propane are arranged in this way that molecular-surface regions with electrostatic potential of the same sign are located close to each other in the structure. Thus weak dispersion attraction is counteracted by electrostatic repulsion. It appears that the molecular shape of propane is most inappropriate for matching electrostatic potentials of opposite signs. The electrostatic matching achieved in n-butane is much better (Figure 3). Soon after Baeyer made his observation about n-alkanes, Carnelley formulated a rule connecting molecular symmetry of isomers with their melting points: the more symmetric isomers, the higher mp they have. Carnelley understood the symmetry of a molecule as its compactness and regular distribution of substituents. His concept of symmetry agrees well with the point-group symmetry of pentane isomers: isopentane (2-
3. RESULTS AND DISCUSSION In n-alkanes, the dependence of melting point on molecular mass holds only for n-butane and heavier alkanes. The plot in Figure 2 shows that methane would match the mass versus mp correlation of heavier alkanes, but propane and ethane are clearly below the correlation line. Intermolecular contacts and aggregation of n-alkanes can be characterized by a contact parameter δ, defined as the shortest of all intermolecular distances relative to the sums of vdW radii of interacting atoms.11 The δ parameters calculated for the ambient-pressure structures of n-alkanes (Figure 2) are all 4760
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orientational disorder leads to the time-averaged spherical symmetry of the space occupied by each molecule in the crystal. This increased average symmetry coincides with relatively high melting points of plastic crystals and that of n-butane. The lightest of alkanes, CH4 and C2H6, both have very high molecular symmetry in Carnelley's sense as well as the pointgroup symmetry, 4̅3m and 3̅m, respectively. Moreover, both methane and ethane molecules become orientationally disordered in the crystalline state,26,27 which compensates for their low-mass effect and increases their melting points to a higher temperature in comparison with propane. The crystal structures of propane and n-butane frozen at low temperature were determined at ambient pressure. Propane crystallizes exclusively in space group P21/n, Z = 4.8 Three lowtemperature polymorphs of n-butane are known: disordered phase I between the mp at 134.55 and 108 K, when it transforms either to metastable phase II or to stable phase III (these two phases may coexist).28 All three phases crystallize in space group P21/c, Z = 2, but their crystal packing is very different.8,28 The single solid phase of propane determined so far can suggest that this molecular arrangement is quite stable, despite postulated molecular shape incompatible with the close packing in crystal. We have experimentally explored the polymorphic behavior of propane and n-butane in the highpressure region of their phase diagrams. We found that at high pressure propane crystallizes in the same phase up to 5.93 GPa at least. High-pressure significantly compresses the unit cell (Table S1 of the Supporting Information) and intermolecular distances (Figure S13 of the Supporting Information). The crystal packing becomes very compact; however, no anomalies indicative of a phase transition have been observed. Voids in the propane structure at 30 K (Figure S15 of the Supporting Information) occupy 29.4% of the unit-cell volume, and at 5.93 GPa they occupy only 4.9%. The propane structure can be considered to be built of layers of molecules in successive (1̅01) planes (Figure 3). The distance between these layers changes from 3.60 Å (at 30 K/0.1 MPa)9 to 3.18 Å (at 295 K/5.93 GPa). At low temperature and ambient pressure all intermolecular distances H···H, H···C, and C···C are longer than the sum of corresponding vdW radii12 (Figure S13 and Table S5 of the Supporting Information). Pressure squeezes these distances, and at 5.79 GPa the shortest of H···H, H···C, and C···C is shorter than the vdW radii sums by −0.18, −0.24, and −0.15 Å, respectively. All of our high-pressure crystallizations of n-butane up to 5.79 GPa resulted in the structure of phase II. Like propane, the structure of n-butane is significantly compressed: the unit-cell dimensions (Table S2 of the Supporting Information) and intermolecular distances (Figure S14 of the Supporting Information) are most affected. The voids volume21 in all three n-butane phases is different. In phase I at 115 K the void space is 34.3% of the structure (see Supporting Information, Figure S16); in phase II at 65 K it is 20.6%; and in phase III at 90 K it is 22.1% and at 5 K it is 20.2%. In the highest pressure structure of phase II at 5.76 GPa/295 K the voids (Figure S16 of the Supporting Information) constitute 2.3% of the structure volume. Like propane, n-butane forms layers in phase II (Figure 3), and the interlayer distance changes from 3.94 Å at 65 K/0.1 MPa to 3.46 Å at 5.79 GPa/295 K. In the n-butane phase II structure at 65 K/0.1 MPa, all intermolecular distances are longer than the sums of vdW radii12 (Figure S14 of the Supporting Information). At 295 K/5.79 GPa, the shortest of H···H and H···C distances are compressed to −0.19 and −0.26
Figure 3. Space-filling drawings of molecular sheets in (a) propane and (b) n-butane phase II, both at 0.1 MPa. The vdW radii of 1.2 Å for H and 1.7 Å for C have been applied.12 Electrostatic potential23 has been mapped onto the molecular surfaces defined as 0.0022 au electron-density envelope;24 a common electrostatic-potential scale from −0.005 (red) to 0.016 au (blue) has been applied.
methylbutane, of the lowest point-group symmetry 1), melting at 113.1 K; n-pentane, of point-group mm, melting at 143.2 K; and neopentane (2,2-dimethylpropane, of the highest symmetry 4̅3m), having the highest melting point of 256.8 K. Butane is an exception to the rule, as Carnelley’s symmetry of isobutene (mp 114 K) and its point group 3m are both higher than those of n-butane (point group mm, mp 135 K). This anomalous behavior of the butane isomers may be a consequence of the phase transition in n-butane at 108 K: in phase I, molecules are orientationally disordered. In fact, the orientational disorder of molecules is one of characteristic features of liquids. Moreover, the heat of transition between ordered and plastic phases often much exceeds the heat of melting, and despite rotations of molecules the plastic phases melt at exceptionally high temperature. This is due to the molecules capable of assuming highly energetical rotational states while preserving average sites in the crystal lattice. Hence n-butane melts at unexpectedly high temperature of 135 K. It is noteworthy that the 4761
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freons, the interplay of molecular mass, symmetry, vibrations, and interactions is least favorable for the melting of propane.
Å below the sums of vdW radii, respectively (Table S6 of the Supporting Information). The shortest of C···C distances at 5.79 GPa is still +0.06 Å over the vdW radii sum (Table S6 of the Supporting Information). The phase diagrams outlined for propane and n-butane in our study (Figure 4) have similar melting and boiling boundaries, but they are lower for propane by 50 K.
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ASSOCIATED CONTENT
S Supporting Information *
Detailed experiment and structures description. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This study was supported by the TEAM grant no. 2009-4/6 from the Polish National Science Foundation. A.O. acknowledges the reception of scholarship START from the Foundation for Polish Science in 2012.
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REFERENCES
(1) Lide, D. R.; Kehiaian, H. V. CRC Handbook of Thermophysical and Thermochemical Data; CRC Press: Boca Raton, FL, 1994. (2) Lindemann, F. A. The Calculation of Molecular Vibration Frequencies. Phys. Z 1910, 11, 609−612. (3) Franzosa, E. A.; Lynagh, K. J.; Xia, Y. Structural Correlates of Protein Melting Temperature. In Proceedings of the 4th ESCEC Symposium, Sept 13−16, 2009, Rüdesheim/Rhein, Germany; Hicks, M. G., Kettner, C., Eds.; Belstein-Institut: Frankfurt, Germany, 2010; pp 99−106. (4) Ku, T.; Lu, P.; Chan, C.; Wang, T.; Lai, S.; Lyu, P.; Hsiao, N. Predicting Melting Temperature Directly from Protein Sequences. Comput. Biol. Chem. 2009, 33, 445−450. (5) Abramowitz, R.; Yalkowsky, S. H. Melting Point, Boiling Point, and Symmetry. Pharm. Res. 1990, 7, 942−947. (6) Zhang, K.; Stocks, G. M.; Zhong, J. Melting and Premelting of Carbon Nanotubes. Nanotechnology 2007, 18, 285703. (7) Baeyer, A. Ueber Regelmäs sigkeiten im Schmelzpunkt Homologer Verbindungen. Ber. Chem. Ges. 1877, 10, 1286−1288. (8) Boese, R.; Weiss, H.-C.; Bläser, D. The Melting Point Alternation in the Short-Chain n-Alkanes: Single-Crystal X-ray Analyses of Propane at 30 K and of n-Butane to n-Nonane at 90 K. Angew. Chem., Int. Ed. 1999, 38, 988−992. (9) Thalladi, V. R.; Boese, R. Why Is the Melting Point of Propane the Lowest Among n-Alkanes? New J. Chem. 2000, 24, 579−581. (10) Bujak, M.; Podsiadło, M.; Katrusiak, A. Crystalline gas of 1,1,1Trichloroethane. CrystEngComm. 2011, 13, 396−398. (11) Kaźmierczak, M.; Katrusiak, A. The Most Loose Crystals of Organic Compounds. J. Phys. Chem. C 2013, 117, 1441−1446. (12) Bondi, A. van der Waals Volumes and Radii. J. Phys. Chem. 1964, 68, 441−451. (13) Carnelley, T. Chemical Symmetry, or the Influence of Atomic Arrangement on the Physical Properties of Compounds. Philos. Mag. 1882, 13, 112−130; ibidium 180−193. (14) Podsiadło, M.; Bujak, M.; Katrusiak, A. Chemistry of Density: Extension and Structural Origin of Carnelley’s Rule in Chloroethanes. CrystEngComm. 2012, 14, 4496−4500. (15) Bassett, W. A. Diamond Anvil Cell, 50th Birthday. High Press. Res. 2009, 29, 163−186. (16) Budzianowski, A.; Katrusiak, A. In High-Pressure Crystallography, Katrusiak, A., McMillan, P. F., Eds.; Kluwer Academic Publisher: Dordrecht, The Netherlands, 2004; pp 101−112. (17) Xcalibur CCD System, CrysAlis Software System, version 1.171; Oxford Diffraction, Ltd.: Oxfordshire, U.K., 2004.
Figure 4. Phase diagrams of propane and n-butane (red and blue color, respectively): the boiling points at 0.1 MPa (231 and 273 K; b.p.), melting points at 0.1 MPa (86 and 135 K; mp), and the critical points (c.p. 4.25 MPa/369.8 K and 3.79 MPa/425.1 K) are from refs 1, 29 and 30; the freezing points (f.p.) at 295 K from the DAC experiment; the freezing lines obtained from the mp at 0.1 MPa, f.p. at 3.20 GPa/295 K, and 1.60 GPa/295 K and from melting points at 3.30, 3.69, and 3.96 GPa and 2.50, 2.60, and 3.44 GPa (optical observation of propane and n-butane melting in the DAC − spectroscopic pressure calibration and a thermocouple temperature measurement − red and blue squares); diffractometric determination of propane (red circles) and of n-butane phase I (blue diamonds), phase II (blue circles), and phase III (blue hexagons). The enhanced gas−liquid region is shown in the inset: the experimental vaporpressure data (red and blue circles)1 and the gas−liquid boundary extrapolation (red and blue lines).
4. CONCLUSIONS It can be concluded that the lowest melting point of propane results from the coincidence of several factors. Because of the unfavorable shape, low electrostatic potential on molecular surface, and electrostatic mismatch between loosely packed molecules, the overall cohesion forces are weaker, and thermal vibrations break them more easily. The melting temperature of light methane and ethane is counteracted by the high symmetry of the molecules, in accordance with the Carnelley’s rule, and additionally by their rotavibrational states and orientational disordering, efficiently absorbing thermal vibrations in the crystal without melting. In other organic compounds either the molecular mass considerably increases or the substituents lead to high polarity of molecules and hence significantly increase electrostatic interactions. For all organic compounds, including 4762
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(18) Katrusiak, A. REDSHABS − Program for Correcting Reflections Intensities for DAC Absorption, Gasket Shadowing and Sample Crystal Absorption; Adam Mickiewicz University, Poznań, Poland, 2003. (19) Katrusiak, A. Shadowing and Absorption Corrections of SingleCrystal High-Pressure Data. Z. Kristallogr. 2004, 219, 461−467. (20) Sheldrick, G. M. A Short History of SHELX. Acta Crystallogr., Sect. A 2008, 64, 112−122. (21) Macrae, C. F.; Bruno, I. J.; Chisholm, J. A.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Rodriguez-Monge, L.; Taylor, R.; van de Streek, J.; Wood, P. A. Mercury CSD 2.0 - New Features for the Visualization and Investigation of Crystal Structures. J. Appl. Crystallogr. 2008, 41, 466−470. (22) Grimwood, D. J.; Jayatilaka, D.; McKinnon, J. J.; Spackman, M. A.; Wolff, S. K. CrystalExplorer, version 2.1; University of Western Australia: Crowley, 2008. (23) Murray, J. N.; Sen, K. D. Molecular Electrostatic Potential: Concepts and Applications; Elsevier: New York, 1996. (24) Bader, R. F. W.; Carroll, M. T.; Cheeseman, J. R.; Chang, C. Properties of Atoms in Molecules: Atomic Volumes. J. Am. Chem. Soc. 1987, 109, 7968−7979. (25) Thalladi, V. R.; Boese, R.; Weiss, H. Ch. The Melting Point Alternation in α,ω-alkanediols and α,ω-Alkanediamines: Interplay between Hydrogen Bonding and Hydrophobic Interactions. Angew. Chem., Int. Ed. 2000, 39, 918−922. (26) Press, W. Structure and Phase Transitions of Solid Heavy Methane (CD4). J. Chem. Phys. 1972, 56, 2597−2609. (27) van Nes, G. J. H.; Vos, A. Single-Crystal Structures and Electron Density Distributions of Ethane, Ethylene and Acetylene. I. SingleCrystal X-ray Structure Determinations of Two Modifications of Ethane. Acta Crystallogr., Sect. B 1978, 34, 1947−1956. (28) Refson, K.; Pawley, G. S. The Structure and Orientational Disorder in Solid n-Butane by Neutron Powder Diffraction. Acta Crystallogr., Sect. B 1986, 42, 402−410. (29) Ambrose, D.; Tsonopoulos, C. Vapor-Liquid Critical Properties of Elements and Compounds. 2. Normal Alkanes. J. Chem. Eng. Data 1995, 40, 531−546. (30) Yasumoto, M.; Uchida, Y.; Ochi, K.; Furuya, T.; Otake, K. Critical Properties of Three Dimethyl Ether binary Systems: Dimethyl Ether (RE-170) + Propane (HC-290), Butane (HC-600), and 2Methyl Propane (HC-600A). J. Chem. Eng. Data 2005, 50, 596−602.
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