DOI: 10.1021/cg900507w
Pressure Effect on the Solid I-Liquid and Solid III-Solid I Equilibrium Forms of Cyclohexane
2009, Vol. 9 4674–4679
Koji Shigematsu,*,† Hironori Honda,† Takanori Kumagai,† and Yoshinori Takahashi‡ †
Faculty of Education, Iwate University, Morioka 020-8550, Japan, and ‡Department of Agriculture, Forestry and Fisheries, Iwate Prefectural Government, Morioka 020-8570, Japan Received May 11, 2009; Revised Manuscript Received September 28, 2009
ABSTRACT: This paper describes the changes in equilibrium forms of cyclohexane as functions of temperature and pressure. The crystals were grown by increasing pressure using a diamond anvil cell (DAC). After single crystals were prepared in the DAC under high pressure, the crystals were maintained for a long period under constant pressure and temperature. During the changes in the shape of the single crystal, both cubic and orthorhombic shapes appeared. The cubic crystals (the solid phase I of cyclohexane) were grown from the liquid and the orthorhombic crystals (the solid phase III) were grown from the solid phase I. These crystal shape variations, depending on pressure and temperature, were consistent for the anisotropies of the cubic and orthorhombic unit cells predicted from the molecular arrangements in the unit cells. We may be able to control the morphology of the organic ring compounds strongly bound by the interaction between their ring components using pressure variation.
Introduction Cyclohexane is only one ring-strain-free cycloalkane, as its angles between C-C and C-H bonds are nearly the same as those of the tetrahedral geometry of the sp3 hybridized carbon atoms. This ring-strain-free molecule brings cyclohexane conformational stability. Owing to the stability, solid cyclohexane exhibits a highly developed polymorphism under a wide range of pressure and temperature.1 Intensive research has been carried out on the solid structures of cyclohexane using various methods under high pressure. Cyclohexane can be easily solidified to the solid phase I by a slight cooling below 280 K under atmospheric pressure or a slight compression above a few 10 MPa, and it can be transformed to the solid phase II, which has a monoclinic lattice, by a cooling below 186 K under atmospheric pressure.2-5 The solid phase I has a face-centered-cubic lattice with free rotation of the molecules around the lattice points (Figure 1). The free rotation brings cyclohexane a very rapid molecular reorientation.6 Cyclohexane transforms to the solid phase III with compression above 0.5 GPa under room temperature.7-10 The solid phase III has an orthorhombic lattice (Figure 2).11 Cyclohexane, moreover, transforms to the solid phase IV with compression above 0.8 GPa under room temperature.12 The solid phase IV has a monoclinic lattice.13 The solid phase V was first found12 and verified14 under compression around 3.2 GPa. Moreover, the presences of the solid phases VI and VII have been suggested up to 40 GPa,15 and the phases were verified14 and further verified in detail.16 We investigated the equilibrium forms of cyclohexane along the liquid-solid I and solid I-solid III equilibrium lines by varying both pressure and temperature. These lines are located in the pressure range (∼1 GPa) of our diamond anvil cell (DAC), which was optimized for high-definition microscopy around room temperature (Figure 3).17 We thus adopted the pressure-induced crystal growth method using the DAC, which can provide a uniform pressure *To whom correspondence should be addressed. E-mail: sigematu@ iwate-u.ac.jp. Fax: þ81 19 621 6560. Telephone: þ81 19 621 6548. pubs.acs.org/crystal
Published on Web 10/08/2009
distribution in a growth cell and very fast variation of pressure with sound velocity. Since DACs generally have a very small compression volume, the DAC, of which the compression volume is 0.6 mm in diameter and less than 0.5 mm in height, cannot provide a constant growth condition with continuously increasing pressure. On the contrary, this small compression volume, instead of a very short growing interval just after compression, brings a long period of equilibration under constant pressure and temperature. The DAC is unsuitable to observe the growth form brought about by the anisotropy in growth rate, which is affected by many factors such as crystal structural static factor, energetic factor on growing interface, and time and space distribution of growth condition.18-20 Even when hydrostatic conditions are satisfied in the DAC, the above factors may affect the crystal growth. If there were nonhydrostatic conditions in the DAC, where, for example, the medium of the crystal growth was a solid phase which has naturally various anisotropies of its physical properties, the crystal growth would also be affected by the anisotropies. Fortunately, cyclohexane I, which is the crystal growth medium of cyclohexane III, is expected to have very small anisotropies of its physical properties due to the highest symmetry in the crystal structures and the free rotation of the molecule around the lattice point. As cyclohexane III can be crystallized under low pressures less than 1 GPa, even though there may be small anisotropies of cyclohexane I, the effects of the anisotropies of cyclohexane I on the crystal growth of cyclohexane III would be very small. We can thus expect the observed shapes of cyclohexane III, which passed through their growth forms, to portray their intrinsic shapes. However, we cannot expect small nonhydrostatic conditions during the growth of cyclohexane IV, V, VI, and VII surrounded with cyclohexane III, IV, V, and VI, respectively, in a pressure vessel. This is because these surrounding solids must have strong anisotropies of their physical properties arising from their crystal structures of low symmetry. Inversely, the complicated conditions may be able to allow the creation of interesting crystal forms which appear as different r 2009 American Chemical Society
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Figure 3. Temperature dependence of the solid I-liquid (indicated by open circles25,26) and solid III-I (indicated by closed circles) equilibrium pressures for cyclohexane. The reference lines of equilibrium pressure p (GPa) as a function of temperature T (°C) obtained by the method of least-squares are as follows: solid I-liquid, p = 0.001913T - 0.012814; solid III-I, p = 0.0055459T þ 0.34297. The correlation coefficients of the lines are 0.99993 (solid I-liquid) and 0.88206 (solid III-I). Figure 1. Instantaneous view of the unit cell of the solid phase I of cyclohexane. The unit cell has a face-centered-cubic lattice of cell parameter a = 0.861 nm.4 The molecule of cyclohexane is denoted by only a carbon atom ring. The next instant, the view will be changed by the free rotation of the molecules around the lattice points.6
It is suitable to observe the equilibrium form, which is only brought about by the anisotropy in interfacial energy. Unfortunately, the crystal size in the DAC is 0.1 mm in representative length. The crystal in the DAC will require a long interval to reach the equilibrium form, as the equilibrium form can appear on the very small crystal grown from vapor less than 0.01 mm in diameter after 70 h from the deposition.21 However, we can say the form which appears in the DAC after long equilibration is very near the equilibrium form, because the crystal in the DAC completes its growth within 15 min and the crystal form stabilizes within 4 h; in other words, it already reaches stabilized equilibrium in the crystal size. These crystal form variations, which could be explained by the anisotropy of the pressure and temperature on the interfacial energy, will provide the possibility of controlling the morphology of the organic ring compounds bound by the van der Waals’ force between their ring components. Experimental Apparatus and Procedure
Figure 2. Orthorhombic unit cell of the solid phase III of cyclohexane with unit cell parameters a = 0.6587 nm, b = 0.7844 nm, c = 0.5295 nm.11 (a) Three-dimensional view of the unit cell with cyclohexane molecules indicated by C-C and C-H bond sticks only. (b) Perpendicular view of the molecular arrangement in the unit cell onto the a-b plane of the cell. The indicated molecules are drawn with an electron cloud. Two pairs of tangents in contact with the electron clouds of the corner molecules and the angles determined by the pairs are also indicated. (c) View perpendicular to the b-c plane. (d) View perpendicular to the a-c plane.
forms simultaneously during a process of pressure variation in the vessel. The possibility to control crystal morphology throughout pressure variation under the nonhydrostatic conditions is an issue to research further.
Cyclohexane (C6H12) of analytical grade (purity>99%) made by Merck Schuchardt OHG was used as it is supplied (without further purification). This liquid was directly drawn from the sample bottle using a disposable microsyringe to prevent unnecessary contamination. We confined a small amount of cyclohexane in the hole (diameter: 0.6 mm) of a gasket (thickness: 0.5 mm), interposed between the upper and lower diamond faces (diameter: 1.6 mm) of the DAC. The gasket was made of Pt-5% Au alloy, which was selected to avoid contamination of cyclohexane. We directly observed the specimen in the DAC using an inverted optical microscope.22 After solidification of the entire liquid by initial compression, a single crystal of the solid phase I survived after several pressure adjustments and was used for our observation. After a single crystal of the solid phase I filled the compression volume of the DAC by small compression, some single crystals of the solid phase III appeared on the inner surface of the gasket by subsequently large compression and were used for our observation. Pressure was measured by the ruby fluorescence technique with a precision of (0.01 GPa.23,24 Thus, a ruby ball was enclosed together with cyclohexane in the gasket hole. We used a monochromator (Japan Spectroscopic Co.; type, CT-50C) with a grating of 1800 line/ mm, a scanning controller (Japan Spectroscopic Co.; type, SMD50C), and a two-branch light-guide. The resolution in wavelength of the monochromator, according to the industry standard, is officially 0.02 nm. This value is a modest one, because we could measure the temperature dependence of the solid-liquid equilibrium pressure of
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Figure 4. Temperature dependence of the solid-liquid equilibrium pressure of n-tetradecane. The fitting line of the equilibrium pressure p (MPa) as a function of temperature T (°C) obtained by the method of least-squares is as follows: p = 2.5656T - 25.833. The correlation coefficient of the line is 0.97452. Note that the melting temperature of n-tetradecane is 5.86 °C under atmospheric pressure.32,33 n-tetradecane (6-37 °C). The pressure was less than 0.1 GPa. As the measured pressures showed a good linear temperature dependence, we could know that the pressures were measured with a precision of less than (0.01 GPa (Figure 4). Accordingly, the actual resolution in wavelength of our pressure measurement system could be calculated as 0.004 nm from the wavelength shift of the ruby fluorescence by compression (0.00365 nm shift per 0.01 GPa pressure variation). Both ruby fluorescence and the Ne spectrum were introduced into the monochromator through the light-guide. We precisely measured the wavelength of the second peak of the ruby fluorescence (∼692.9 nm) in comparison with a very sharp Ne peak (692.947 nm) as a reference light on a chart paper. The paper had an enlarged wavelength scale (0.01 nm/mm) and was drawn with a very slow scanning speed (0.15 nm/min). In our measurements, the ruby fluorescence spectra of 692.0-694.5 nm, which included the first peak of ruby fluorescence (∼694.3 nm), were drawn on the papers, except for the Ne peak wavelength. The Ne peak was drawn only in the narrow wavelength width of 0.05 nm (5 mm width on the paper) for 20 s by a switching technique of shutters, which was comprised of coordinating two postcard-size covers held by two persons with a call for synchronization and was located in front of the entrances of the light-guide branches for the ruby fluorescence and the Ne spectrum, respectively. We could thus precisely measure the very small wavelength shift of the ruby fluorescence by compression from the distance measurement between the peaks of ruby fluorescence and the Ne spectrum with a precision of 0.3 mm on the paper. Temperature was measured by a copper-constantan thermocouple of thin wires (diameter, 0.1 mm) tightly inserted between the diamond side and the gasket of the DAC using a digital thermometer (Advantest Corp.; type, TR2114H) and a 0 °C reference contact device (Coper Electronics Co.; type, ZC-114; temperature stability, (0.02 K). Temperature was regulated with a precision of (0.1 K by using a water jacket made of copper in which temperature-regulating water was flowing. The temperature-regulating water was circulated with a low-temperature water bath with a circulating pump (As One Corp.; type, LTB-125; temperature regulating range, -30-80 °C). The water jacket had a flat-box shape and could be divided into lower (body) and upper (lid) parts. As the DAC had a hingelike shape, the DAC also had lower and upper parts. We measured the temperatures of the lower and upper parts of the DAC put in the water jacket in which the temperature-regulating water of 40 °C was flowing.22 The temperature of the lower part was 0.1 K higher than that of the upper part. The temperature difference between the diamond anvils should be far smaller than that between the lower and upper parts of the DAC.
Results Figure 3 shows the temperature dependence (10-50 °C) of the solid I-liquid25,26 and solid I-solid III equilibrium pressures for cyclohexane. The solid I-solid III equilibrium pressure coincided with that previously reported.10,11 We
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Figure 5. Sequential images of the selection process of several single crystals of cyclohexane of the solid phase I in the gasket hole of the DAC. The sphere at the right part of the hole is a ruby ball (diameter, 0.134 mm) for pressure measurement by the ruby fluorescence technique. Intervals between adjacent steps were indicated between the panels of the steps. The scale bar indicates 0.1 mm.
Figure 6. Images of the equilibrium forms of cyclohexane of the solid phase I grown in the DAC. (a) Temperature, T = 9.9 °C; pressure, p = 0.006 GPa; (b) T = 39.0 °C; p = 0.061 GPa. An edge of the equilibrium form (image-enhanced) is attached to each panel. The squares drawn by broken lines surrounding the imageenhanced equilibrium forms denote the edges of the growth forms that appeared in a very short time just after the compression for the next stage. The sphere in the gasket hole of the DAC is a ruby ball (diameter, 0.134 mm) used for pressure measurement. All the scale bars indicate 0.1 mm.
could not measure the solid I-liquid equilibrium pressure by the ruby fluorescence technique, although we could measure the solid-liquid equilibrium pressures of n-tetradecane, which were less than 0.1 GPa in a temperature range of 637 °C (Figure 4). For example, measurements were taken of 0.013 GPa at 15 °C and 0.038 GPa at 25 °C. The solid I-liquid equilibrium pressure would be smaller than the previously reported value,25,26 samples of which are 0.017 GPa at 15 °C and 0.035 GPa at 25 °C. Figure 5 shows a very fast selection process of several single crystals of the solid phase I as six steps. They combined to form a single component within 2 min due to the rapid molecular reorientation of cyclohexane.6 The fast selection process made the compression volume of the DAC easily filled with a single crystal of the solid phase I for the growth of the solid phase III. Figure 6 shows the equilibrium shapes of the solid phase I at two temperatures. Both the shapes that formed at the
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Figure 7. Images of the equilibrium forms of cyclohexane of the solid phase III grown in a single crystal of the solid phase I in the DAC. (a) Temperature, T = 12.1 °C; pressure, p = 0.408 GPa; (b) T = 21.4 °C; p = 0.425 GPa; (c) T = 30.4 °C; p = 0.510 GPa; (d) T = 40.4 °C; p = 0.544 GPa. The enlarged equilibrium form (image-enhanced) with a solid line, and the growth form that appeared just after the compression a with broken line, are attached below each upper panel. The directions of the crystal lattice axes are also attached to each lower panel. The regions of the aberrant surface appearing between the a- and b-planes are indicated by two-headed arrows in parts a, b, and c. The line-drawn crystals in the lower panel of part d represent those in the white-line circle in the upper panel. The sphere in the gasket hole of the DAC is a ruby ball (diameter: 0.134 mm) used for pressure measurement. All the scale bars indicate 0.1 mm.
terminals of our temperature variation range are clear disks. The growth forms appeared within a very short interval just after the compression of the DAC in a sequence of the pressure variation for the transfer to the next observation stage. They showed a square shape with sharp edges. The growth forms had rapidly changed to the shapes with round corners after compression. Figure 7 shows the equilibrium shapes of the solid phase III grown in a single crystal of the solid phase I at four temperatures in the range from 10 to 40 °C. As these shapes lacked clear edges due to the transformation between solid phases, the enlarged and image-enhanced equilibrium forms with the directions of the crystal lattice axes are added to the equilibrium shapes shown in Figure 7. The image-enhanced shapes varied from the plate of long edges along the b-axis and thin thickness along the c-axis to the rectangular solid of slightly long edges along the b-axis and mostly equal length edges along the a- and c-axes with increasing temperature and pressure. The aberrant surface between the a- and b-planes with an obtuse angle, which is roughly in agreement with the obtuse angle shown in Figure 2b, gradually disappeared with increasing temperature and pressure. The forms shown in Figures 6 and 7 are those attained from the previous forms after more than 4 h following the pressure adjustments. The attained forms did not change after 480 h following the adjustments. We thus took the images of the crystals shown in Figures 6 and 7 as the equilibrium formed. Discussion As the cyclohexane molecule in the solid phase I has a stable conformation and free rotation around its fixed lattice point on its face-centered-cubic lattice, which has the highest symmetry in all crystal lattices, it behaves like a sphere in the crystal lattice. Therefore, the anisotropy of the phase is very weak. As a result, the equilibrium shapes of the phase shown
in Figure 5 had clear disks with beveled side surfaces throughout a wide temperature range. Unless the compression volume in the DAC was a thin disk shape, the equilibrium shapes would be spheres. Pressure-increase stops the free rotation of the cyclohexane molecule and transforms the solid phase I into the solid phase III. If the rings of an organic compound faced each other in a small area, the anisotropy of the compound would not be strong. For example, benzene I, which has an orthorhombic cell, identical to cyclohexane III with lattice parameters a = 0.717 nm, b = 0.928 nm, and c = 0.665 nm, stacks up partially the hexagonal ring planes of its molecule along the c-axis onto the a-b plane.27 The equilibrium shape of benzene I with the liquid in a DAC shows a thin beveled disk of the c-plane, identical to cyclohexane I.28,29 Thus, we can say inversely that the solid phase III of cyclohexane is mainly bound by the van der Waals’ force between the stable ring of the cyclohexane molecule. This is because the crystal shape of the solid phase III basically has not a thin beveled disk, but a rectangular solid shape of long length along the b-axis where the ring of the cyclohexane molecule faces the adjacent one head-on. The shape variation of cyclohexane III from the thin plate of the c-plane and of the long length along the b-axis to the rectangular solid of slightly long length along the b-axis and with mostly equal length along the a- and c-axes and with the disappearance of the aberrant surface between the a- and bplanes, with increasing temperature and pressure, was brought about by the decrease of the anisotropy of the solid phase III. The question to consider here is why does the anisotropy of the interfacial energy of the solid phase III decrease with increasing temperature and pressure simultaneously along the solid phases I and III equilibrium lines. Generally speaking, temperature-increase decreases interaction between the crystal surface molecule and the adjacent molecule in the environmental phase, as temperature-increase
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increases the conformational instability of the molecule in the environmental phase. As a result, the decrease of interaction between the crystal surface molecule and the adjacent molecule in the environmental phase brings about a uniformity on the entire crystal surface according to the anisotropy of the interface. Thus, temperature-increase decreases the anisotropy of interfacial energy. A typical example of the decrease of the anisotropy of interfacial energy can be seen in the equilibrium shapes of small even n-alkane crystals (n = 8, 10, 12; n = carbon number) in the liquids.30 Temperature-increase increases the randomness of the C-C bond chain in the n-alkanes. The random carbon chain decreases the interactions not only between the liquid molecules but also between the solid and liquid molecules. The decrease of the interaction between the crystal surface molecule and the adjacent liquid molecule is not uniform across the entire interface where the c-plane is the regular arrangement of the terminals of carbon chains and the a- and b-planes of the even n-alkanes are the parallel arrangements of the long sides of carbon chains. The interaction between the surface molecule on the c-plane and the adjacent liquid molecule of the random carbon chain slightly decreases with increasing temperature. This is because the interaction weakly depends on the randomness of the carbon chain due to the pointlike interaction between a terminal of the carbon chain on the c-plane and a small part of the random carbon chain in the liquid. On the other hand, the interactions between the surface molecules on the a- and b-planes and the adjacent liquid molecules of the random carbon chain rapidly decrease with increasing temperature. This is because the interactions strongly depend on the randomness of the carbon chain due to the linelike interaction between the sides of the carbon chain on the a- and b-planes and a part of the random carbon chain in the liquid molecule of which the length rapidly decreases with increasing temperature. Thus, although most of the equilibrium shapes of the even n-alkane crystals showed very thin plates of the c-plane bounded by beveled side faces, those of n-octane at 30 °C, n-decane at 20 °C, and n-dodecane at 10 °C were relatively thick plates of the c-plane bounded by a- and b-planes with sharp edges. The shape-change to thick plates in the narrow temperature regions was caused by the decreases of the anisotropy of interfacial energy arising from temperatureincrease. However, temperature-increase cannot decrease the anisotropy of the interfacial energy of cyclohexane III in a wide temperature range, because the cyclohexane molecule has a strong conformational stability and behaves like a sphere due to the free rotation in the environmental phase (the solid phase I). Pressure-increase decreases intermolecule distance. As the decrease in crystal lattice parameters with increasing pressure increases the density of interaction at the crystal-environmental phase interface, pressure increases the interfacial energy between the crystal molecule and the adjacent molecule in the environmental phase. Pressure, furthermore, decreases the anisotropy of the interfacial energy, because the decrease in crystal lattice parameters with increasing pressure is not uniform across the entire interface of the crystal. In other words, the interfacial energy between the crystal molecule and the adjacent molecule in the environmental phase generally has anisotropy. The anisotropy of the interfacial energy has an influential effect on changes of crystal shapes.
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For example, the equilibrium shapes of small odd n-alkane crystals (n = 9, 11, 13; n = carbon number) of the hightemperature/low-pressure phase, which has a hexagonal cell and a disorder phase called a “rotator phase”, showed in the liquids the hexagonal pillar shape of a long c-axis (n = 9) and the thinner disk of the c-plane (n = 11, 13) with increasing n.31 The molecule arrangements on the crystal surface of the odd n-alkanes are mostly the same as those of the a-, b-, and c-planes of the even n-alkanes. The larger n, the denser the interfacial energy on the a- and b-planes, where the long sides of carbon chains are arranged in parallel. As a result, the anisotropy of the interfacial energy of the small odd n-alkane crystals was weakened by increasing n. The interfacial energy can be increased not only by the distance-increase between the carbon-chain lengths of the crystal surface molecule and the adjacent molecule of the environmental phase brought about by the carbon-number-increase, as in the case of the odd n-alkanes, but also by the distance-decrease between them brought about by the pressure-increase. As this distance-decrease is inversely proportional to the compressibility of the crystal surface, the anisotropy of the distance-decrease is inversely proportional to the anisotropy of the compressibility. From the variation of the electron cloud occupancy on the a-, b-, and c-planes of cyclohexane shown in Figure 2 (b > a > c), the compressibility normal to the b-plane is the largest of the three planes, and that of the a-plane is larger than that of the c-plane. The distance-decrease on the b-plane is thus the smallest of the three planes, and that of the a-plane is slightly larger than that of the c-plane (b < a < c). The increase of the interfacial energy on the b-plane is the smallest of the three planes, and that of the a-plane is slightly larger than that of the c-plane (b < a < c). As the original interfacial energy on the bplane is the largest of the three planes, and that of the a-plane is larger than that of the c-plane, the anisotropy of the interfacial energy after a pressure-increase is thus weakened (b g a g c). Therefore, the anisotropy of the interfacial energy of the solid phase III of cyclohexane decreases with increasing pressure. The relatively small increase of the interfacial energy on the b-plane, compared with the a- and c-planes, extinguished the aberrant surface between the a- and b-planes, which had a specific obtuse angle to the a-plane, with increasing pressure. Pressure-increase increases the interfacial energy and the isotropy of the interfacial energy of the solid phase III of cyclohexane. We could therefore observe the bulky crystal of the solid phase III with increasing temperature and pressure. Conclusions As the solid phase III of cyclohexane has strong interaction of the van der Waals’ force between the stable rings of the molecule stacked up along the b-axis, it basically has a rectangular solid shape of long length along the b-axis. The crystal shape of the phase changed from the thin plate of the c-plane with long edges along the b-axis to the rectangular solid of slightly long length along the b-axis, and with mostly equal length along the a- and c-axes. These occurred with the disappearance of the aberrant surface between the a- and b- planes with increasing temperature and pressure. The shape change can be attributed to the pressure-increase, which decreases the anisotropy of the interfacial energy of the phase.
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We may be able to control the morphology of the organic ring compounds strongly bound by the interaction between their ring components using pressure variation.
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