Epitaxial Growth of n-Tridecane Low-Pressure Phase Filmy Crystal on

Sep 26, 2014 - (SI) solids coexist, and the SI and liquid coexist. The equilibrium lines of n-tridecane nearly overlap above 40 °C and separate from ...
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Epitaxial Growth of n‑Tridecane Low-Pressure Phase Filmy Crystal on Its High-Pressure Phase Koji Shigematsu,*,† Seiji Sawamura,‡ Wataru Chiba,† and Yoshinori Takahashi†,§ †

Faculty of Education, Iwate University, Morioka 020-8550, Japan Department of Applied Chemistry, Faculty of Life Science, Ritsumeikan University, Kusatsu 525-8577, Japan

‡

ABSTRACT: We measured the p−T diagrams of four odd normal alkanes including ntridecane, which have two equilibrium lines on which the orthorhombic (SII) and hexagonal (SI) solids coexist, and the SI and liquid coexist. The equilibrium lines of n-tridecane nearly overlap above 40 °C and separate from each other with temperatures decreasing less than 40 °C. We also show that the metastable area of SII of n-tridecane widely spreads below the SII−SI coexistence line. We focused on the reason why the metastable region of the SII crystal spreads, based on the transformational relationship between SI and SII and the unisotropies among the SI and SII singular interfaces. The SII crystal first appears from the liquid above 40 °C just after compression, due to the narrow stable region of the liquid−SI crystal system. When the temperature and pressure of the liquid−SII crystal system vary compared with those of the wide stable region of the liquid−SI crystal system, the filmy SI crystal can grow on its SII crystal in the liquid. Therefore, the arrangement and the wide area cause the epitaxial growth of SI filmy crystal on SII crystal.

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INTRODUCTION We can grow crystals using not only temperature control but also pressure control. However, a few difficulties exist in equipment for pressure control, such as providing sufficient pressure generation, strong pressure vessel, and precise pressure measurement. If these difficulties can be overcome, pressure control would be a promising method for research in crystal growth. This is because pressure varies quickly with sound velocity and distributes uniformly in fluids. However, a few molecular crystals show highly developed polymorphisms under wide ranges of pressure and temperature. Anisotropic crystal shapes and crystal structure variations are brought about by variously symmetric/asymmetric molecular shapes. As the molecular crystals can grow and transform between their two solid phases under pressure control, pressure control is also promising in the crystal growth research of molecular crystals. Two of the authors have successively carried out growth research of crystals, such as odd normal alkanes,1 cyclohexane,2 and carbon tetrachloride3 under pressure control. All of these crystals have particular solid phases, including a disordered phase as a low-pressure and high-temperature solid phase. Odd normal alkanes do not have symmetry along the carbon chain axis due to the odd carbon numbers. In order to cancel the asymmetry, a few odd normal alkanes have double-layered structures. As membranes of living cells also have doublelayered structures, we have considered that odd normal alkanes can be a very simple model of membranes of living cells.1 A few odd normal alkanes have two solid phases of doublelayered structure, as described above, which are the lowpressure and high-temperature solid phase SI (disordered, hexagonal), and the high-pressure and low-temperature solid phase SII (ordered, orthorhombic).4−6 © XXXX American Chemical Society

We previously reported the epitaxial growth of the ntridecane filmy SI crystal along the edge of its thick-pillar-like SII crystal in the liquid.1 In order to determine the reason why the SI crystal can grow on the SII crystal in the liquid, we measured the phase relationships in the p−T diagram of ntridecane. The coexistence lines between liquid−SI and between SI−SII are not parallel. Although these nearly overlap above 40 °C, they separate from each other with temperatures decreasing less than 40 °C. The neighboring normal odd alkanes (undecane, pentadecane, and heptadecane) have no such an unparallel relationship. Moreover, the SII crystal of n-tridecane can coexist metastably with the liquid below the coexistence line between liquid−SI. We discussed the reason why the metastable region of the SII crystal spreads even below the coexistence line between liquid− SI, based on the transformational relationship between SI and SII crystal structures and the unisotropies among the SI and SII crystal singular interfaces. As a result, we could elucidate the reason why the filmy SI crystal can grow on its SII crystal in the liquid.

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EXPERIMENTAL APPARATUS AND PROCEDURES

We measured the phase transition pressures and temperatures of ntridecane by the cylinder−piston method.7 A cylinder (outer diameter, 80 mm; inner diameter, 9 mm; height, 82 mm) made of 17-4PH stainless steel (HRC42), thermally regulated by using a water jacket, and stuffed with two mushroom-shaped plugs (diameter, 9 mm; height, 9.3 mm) with polytetrafluoroethylene (PTFE) collars and polyetheretherketone (PEEK) gaskets, was filled with n-tridecane. One Received: May 28, 2014 Revised: September 25, 2014

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plug was fixed at the bottom of the cylinder by a piston tail of 9.1 mm in height, and another plug was inserted into the cylinder by a piston rod of 38.2 mm in length. In the cylinder, n-tridecane was compressed beyond the freezing pressure by the plug pushed with an advance of 0.5 mm of a onedirection motion in 10 min intervals by the piston rod, driven by an oil press. We then decompressed the solidified n-tridecane with the plug retreat of 0.5 mm at 10 min intervals. We needed the 10 min intervals between the 0.5 mm piston rod movements for the dissipation of the latent heat with crystallization or dissolution and the compression heat. In this retreat procedure, we made the plug position, which was measured by a precise dial gauge with a precision of 1 μm, carefully coincide with the corresponding plug position in the advance procedure within 5 μm in a one-direction motion. The compression force on the piston was measured using a strain-gauge load cell interposed between the oil press head and the piston rod. We could easily determine the liquid freezing and the transformation from the SI to SII solids. As the liquid and the SI solid coexist in the cylinder during freezing and the SI and SII solids coexist during the transformation, the pressures measured by the load cell were kept at a constant value during freezing and transformation. Owing to the coincidence with the plug positions in the compressing and decompressing procedures, the plug resistance was in an equally opposite direction at each plug position. We could thus easily calibrate the sample pressure from the average of the compression forces in the compressing and decompressing procedures because the average canceled the plug resistance working in the equally opposite direction. The sample volume was calculated from the plug position measured by the dial gauge. The sample density was 753.0 kg/m3 at 24 °C, the temperature when the sample completely filled the cylinder.8,9 We could simultaneously measure the pressure dependence of both the liquid and solid SI and SII of the n-tridecane densities. The sample of n-tridecane was of analytical grade (purity >99%) made by Merck Schuchardt OHG. It was used as-supplied without further purification and was directly drawn from the sample bottle using a disposable microsyringe to prevent unnecessary contamination. We used a diamond anvil cell (DAC) for pressure generation and optical observation of the crystal growth.10 We confined a small amount of the n-tridecane in the hole (diameter: 0.6 mm) of a Pt-5% Au gasket (thickness: 0.5 mm), interposed between the upper and lower diamond faces of the DAC. A ruby ball (diameter: 0.134 mm) was enclosed together with n-tridecane for pressure measurement by the ruby fluorescence technique.11,12 We improved the pressure measurement with a precision of less than ±0.01 GPa using a reference light of a Ne spectrum peak.2 We directly observed the specimen in the DAC using an inverted optical microscope.13 After solidification of the entire liquid by compression, a single crystal survived after several pressure adjustments, which was used for our observation.

Figure 1. Temperature dependences of the solid−liquid equilibrium pressures for four odd n-alkanes. (a) The dependences of SII−SI and SI−liquid equilibrium pressures for n-undecane, n-tridecane, npentadecane, and n-heptadecane. All the pressures were measured by the piston−cylinder method. (b) The dependences of SII−SI, SI− liquid, and SII−liquid equilibrium pressures for n-tridecane. The equilibrium pressures between SII−SI and SI−liquid phases were the same as those of n-tridecane shown in panel a. The equilibrium pressures between SII−liquid phases were newly added and were measured by the ruby fluorescence technique.

and rarely the SII crystals, due to the parallel separated lines. The liquid of n-heptadecane will crystallize only the SI crystals. As the lines of n-tridecane are very close to each other in the temperature range above 40 °C, the liquid of the temperature above 40 °C first crystallized nearly all the SII crystals. Inversely, the liquid of the temperature below 40 °C first crystallized nearly all the SI crystals. Figure 1b shows the temperature dependences of the SII−SI and SI−liquid equilibrium pressures for n-tridecane measured by the piston−cylinder method and the SII−liquid metastable equilibrium pressures for n-tridecane measured by the ruby fluorescence technique. The SII metastable region overspreads the SI stable region.

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RESULTS Figure 1a shows the temperature dependences (20−45 °C) of the SII−SI and SI−liquid equilibrium pressures for n-undecane, n-tridecane, n-pentadecane, and n-heptadecane measured by the piston−cylinder method. The dependence lines of n-undecane are nearly overlapped. In our preliminary experiment of pressure-induced crystal growth of n-undecane, the liquid first crystallized nearly all the SII crystals due to the very close lines. It should be pointed out here that the pressure-induced crystal growth from the liquid generally needs more than 20% excess pressure on the freezing pressure at the experiment temperature. The large excess pressure directly brought about n-undecane SII crystals. The lines of n-pentadecane and n-heptadecane are parallel and apart from each other. In our preliminary experiment of npentadecane, the liquid first crystallized nearly all the SI crystals

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DISCUSSION Figure 2a shows a perspective of the orthorhombic unit cell of n-tridecane SII crystal, in which the zigzag lines denote the fixed C−C bond chains. As n-tridecane does not have symmetry along the C−C bond chain, it has a double-layered structure. Figure 2b shows a perspective of the hexagonal unit cell of ntridecane SI crystal, in which the cylinders are regarded as the volume of the partially hindered rotation of the C−C bond chains. There is a slight difference between the unit cells. The C−C bond chains, which partially hindered rotation in the cylinders of the hexagonal unit cell, are slightly displaced normal to the chain axes. This slight displacement ceases the rotations and brings a dense-packing to the orthorhombic unit cell. This B

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We could observe both orthorhombic and hexagonal ntridecane crystals in the DAC. As pressure-induced crystal growth requires large excess pressure (usually 20% of equilibrium pressure) for initial crystallization, initially grown crystals just after compression belong to high-pressure phase (orthorhombic). The SII crystals could remain as a metastable phase in the liquid even below the coexistence line of the SI crystal and the liquid (Figure 1b). There are two reasons why the SII crystals have such an unyielding nature. Both the reasons connect the difficulty of the transformation from SII to SI on the a-plane of SII crystal, on which the transformation should start with large displacement along a-axis. First, the a-plane of SII crystal has the interface of the smallest area among those of three singular interfaces of SII crystal. Second, the interfacial free energy on the a-plane of SII crystal, which has the largest value among those of three singular interfaces of SII crystal, has a small difference from those of the a-, b-planes and the mixture of the a- and b-planes of SI crystal. The embryo of the SI crystal on the a-plane of SII crystal, thus, is difficult to generate and to grow. However, the interfacial free energy on the b-plane of SII crystal is expected to have a value close to those of the a-, bplanes and the mixture of the a- and b-planes of SI crystal. Therefore, on the b-plane of SII crystal near the edges between the b- and c-planes of an SII thick-pillar-like crystal, we can grow hexagonal SI crystals of thin films with a parallel arrangement (Figure 2c). This is because the edges of the cplane of the SII crystal have an advantage for the dissipation of the latent heat with crystallization. After heating the temperature of 36.6 to 37.6 °C at the pressure of 0.23 GPa, where the SII crystal is metastable and the SI crystal is stable (Figure 1b), the SI filmy crystal quickly grew on the b-plane of SII crystal near the edge between the band c-planes of an SII crystal (Figure 3). As the sample volume of the DAC is very tiny and the upper diamond anvil face is 0.1 K cooler than the lower face,13 the SI filmy crystal can grow only on the upper edge of the SII crystal, as shown in Figure 3. Compared with the SII crystal shown in Figure 3, which grew a single SI filmy crystal, the SII crystal, shown in Figure 4, grew a pair of SI filmy crystals on the b-plane of SII crystal near the edges between the b- and c-planes after compression of 0.01 GPa at the temperature of 23.0 °C. Pressure was measured after 5 min from photographing Figure 4c. The pressure was 0.12 GPa, which would be slightly lower than that during the growth of SI filmy crystals, shown in Figure 4a,b. If the parallel-arranged pair of SI filmy crystals, which interposed the SII thick-pillar-like crystal resembling a backbone, could grow further, the filmy crystals would attach their peripheries together and thus resemble a dora-yaki, which is a pair of thin round pancakes of 70−100 mm in diameter, with a bulging center part with interposing sweet bean paste between them. It goes without saying that the pair of pancakes corresponds to that of SI filmy crystals. The n-tridecane crystal may be able to create a capsule-like form bounded by a pair of the SI filmy crystals. The transformation from SII to SI on the a-plane of SII crystal rarely occurred (Figure 5). However, the rare transformation infrequently occurs in the low temperature region where the pressure width of the stable region of the SI crystal is large. The transformation started on the upper a-plane and cooperatively propagated downward along a-axis in the figure

Figure 2. Orthorhombic and hexagonal unit cells of n-tridecane.1−3 (a) A perspective of the orthorhombic unit cell (SII phase). (b) A perspective of the hexagonal unit cell (SI phase). The C−C bond chains in both panels a and b have an alternated arrangement between the upper and lower layers. (c) Epitaxial relationships between the orthorhombic and hexagonal unit cells on the edge of c-plane of the orthorhombic unit cell (SII phase).

displacement can be expected to have a large unisotropy during the transformation from SII to SI. Moreover, we can expect that the displacement along a-axis is larger than that of the b-axis and that along the c-axis is a very slight one. We could observe both orthorhombic and hexagonal crystals of n-tridecane in the DAC. Although the structural difference is very slight, we can easily distinguish the difference between their crystal shapes. This large difference can be elucidated by the anisotropies of the intermolecular bonds along the c-axis in these structures. We can expect that the fixed carbon chain axis of the orthorhombic unit cell has the anisotropy of a large value in difference between the parallel and normal directions to the C−C bond chain, compared to that of the partially rotating carbon chain axis of the hexagonal unit cell. We can thus expect as follows: in the orthorhombic shape, the interaction between the parallel-arranged adjacent fixed carbon chain axes is large; in the hexagonal shape, the interaction between the free rotating carbon chain axes is large and isotropic within the c-plane, and the interaction along the c-axis is small. The dominant shape of the orthorhombic crystal is thus a pillar-like shape, of which the axial direction of the pillar is aligned with the a-axis, which is the direction of the largest interaction. That of the hexagonal crystal is thus a hexagonal thin plate with very round corners. We can also elucidate these differences between the orthorhombic and hexagonal shapes using the unisotropies of the interfacial free energies of both the shapes, as follows. In the orthorhombic shape, the interfacial free energy of the a-plane has the largest value among those of the singular planes. Therefore, the normal growth rate of the a-plane has also the largest value. As a result, the rapid growth keeps the area of the a-plane the smallest in those of a-, b-, and c- planes. From the orthorhombic shape, we can arrange the order of the interfacial free energy values of the singular planes as a > b ≫ c. In the hexagonal shape, the interfacial free energies of a- and b-planes have very large values compared with that of the cplane. From the hexagonal shape, we can arrange the order of the interfacial free energy values of the singular planes as a ≈ b ≫c. Moreover, we can speculate on the comparison between the interfacial free energy values from the valuation among the areas of the singular planes as a (orthorhombic) > a (hexagonal), b (ortho) ≈ a, b (hexa), and c (ortho) > c (hexa) from these shapes. C

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Figure 3. Sequential images of the crystal forms of n-tridecane growing in the DAC. Left column pictures are real crystal forms. Right column pictures are schematically drawn crystal forms. In the left column, a thick-pillar-like plate in the center of the gasket hole is a part of SII ntridecane crystal, which has a large c-plane of a parallelogram. Obscure black circle in the lower-left part of the gasket hole in each panel of left column is a ruby ball enclosed for the pressure measurement. In the right column, the edges of an SII n-tridecane crystal are shown by orange solid lines (however, a hidden edge is shown by an orange broken line), an n-tridecane SI filmy crystal is shown by a blue curved solid line, and the ruby ball is shown by a black broken circle. Pressure was kept at 0.23 GPa. (a) Part of the SII n-tridecane crystal just before growth of SI filmy crystal: temperature T = 37.5 °C just before reaching 37.6 °C. (b) Rapidly growing thin film of n-tridecane SI crystal from the upper edge on the c-plane of the SII crystal: T = 37.6 °C which is a slightly lower temperature than the SI−liquid equilibrium temperature, 21 s later than panel a. (c) Slow growing thin film of n-tridecane SI crystal on the SII crystal: T = 37.6 °C, 60 s later than panel b. Growing fronts of the thin film can be seen in the lower-left and lower-right parts in the gasket holes shown in panels b and c. The growth velocity gradually decreased due to the pressure decrease arising from the crystal growth. The scale bars indicate 0.1 mm.

Figure 4. Sequential images of the other crystal forms of n-tridecane growing in the DAC. A vertically arranged thick-pillar-like crystal in the left of the gasket hole is a part of SII n-tridecane crystal. A pair of n-tridecane SI filmy crystals grew from the right edges of the ntridecane SII crystal after a compression of 0.01 GPa. Pressure measured after 5 min from photographing panel c was 0.12 GPa. Temperature was kept at 23.0 °C. The black circle in the upper part of the gasket hole in each panel is a ruby ball enclosed for the pressure measurement. The scale bars indicate 0.1 mm. (a) Part of the SII ntridecane crystal just before growth of SI filmy crystal. (b) Rapidly growing a pair of SI thin films from the right edges near the c-plane of the SII crystal, 40 s later than panel a. (c) Slow growing SI thin films on the SII crystal, 60 s later than panel b.

panels at the pressure of 0.12 GPa and the temperature of 18.6 °C. Finally, the SII thick-pillar-like crystal transformed to the SI thin-disk-like crystal with no destruction due to the expansion from SII to SI crystals.14

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When SII crystals enter the stable region of SI crystal with liquid after the small adjustment in temperature or pressure, SI filmy crystal grows on the b-plane of SII crystal, of which the interfacial free energy is expected to be close to those of the aplane, b-plane, and the mixture of a- and b-planes of SI crystal. Moreover, the filmy crystal grows on the edge of the b-plane near the c-plane due to an advantage for the dissipation of the latent heat with crystallization. Coexistence of the SII and SI crystals of n-tridecane in the region, where the SII crystal is metastable and the SI crystal is stable, generates a new combination of crystals of different

CONCLUSIONS The difficulty of the transformation from SII to SI keeps stable SII thick-pillar-like crystals as a metastable phase in the liquid even below the coexistence line of the SI crystal and the liquid. The difficulty arose from the small a-plane of SII crystal, where the transformation starts with large and cooperative molecular displacements along the a-axis and a small difference between the interfacial free energy of the a-plane of SII crystal and those of the a-plane, b-plane, and the combination of a-plane and bplane of SI crystal. D

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(3) Shigematsu, K.; Sugawara, S.; Takahashi, Y. Cryst. Growth Des. 2012, 12, 3402−3406. (4) Broadhurst, M. G. J. Res. Natl. Bur. Stand. 1962, A66, 241−249. (5) Smith, A. E. J. Chem. Phys. 1953, 21, 2229−2231. (6) Müller, A. Proc. R. Soc. 1930, A127, 417−430. (7) Bridgman, P. W. Proc. Am. Acad. Arts Sci. 1931, 66, 255−271. (8) Hust, J. G.; Schraman, R. E. J. Chem. Eng. Data 1976, 21, 7−11. (9) Doolittle, A. K. J. Chem. Eng. Data 1964, 9, 275−279. (10) Takemura, K.; Shimomura, O.; Sawada, T. Rev. Sci. Instrum. 1989, 60, 3783−3788. (11) Mao, H. K.; Bell, P. M.; Shaner, J. W.; Steinberg, D. J. J. Appl. Phys. 1978, 49, 3276−3283. (12) Barnett, J. D.; Block, S.; Piermarini, G. J. Rev. Sci. Instrum. 1973, 44, 1−9. (13) Shigematsu, K.; Sawada, T.; Takahashi, Y.; Gomi, S. Jpn. J. Appl. Phys. 1999, 38, L1124−L1127. (14) Shigematsu, K.; Takahashi, Y.; Sawada, T.; Takemura, K.; Tanigchi, Y.; Sawamura, S.; Tomobe, T.; Kawasaki, K.; Koyama, M. Jpn. J. Appl. Phys. 1997, 36, L142−L145; Jpn. J. Appl. Phys. 1997, 36, L524−L525 erratum.

Figure 5. Sequential images of the transformation from an n-tridecane SII crystal to an SI crystal in the DAC. Left column pictures are real crystal forms. Right column pictures are schematically drawn crystal forms. Temperature was kept at 18.4 °C. Pressure measured after 26 min from photographing panel c was 0.12 GPa. The scale bars indicate 0.1 mm. In the left column, the black circle in the upper part of the gasket hole in each panel is a ruby ball enclosed for the pressure measurement. (a) A vertically arranged fine thick-pillar-like crystal in the gasket hole center, which is a part of an SII n-tridecane crystal before the transformation. (b) The n-tridecane SI crystal just after the transformation, which started from the a-plane of the upper-side. (c) The n-tridecane SI crystal, which had been changing to a hexagonal thin plate with very round corners, 40 s later than panel b. In the right column, the edges of an SII n-tridecane crystal are shown by orange solid lines in panel a, an n-tridecane crystal transforming from SII to SI is shown by a green curved line in panel b, an SI filmy n-tridecane crystal is shown in a blue curved solid line in panel c, and the ruby ball is shown by a black broken circle in all panels.

structures, which will eventually grow to a dora-yaki-like structure bounded by a pair of SI filmy crystals interposing a backbone of the SII thick-pillar-like crystal.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +81 19 621 6560. Telephone: +81 19 621 6548. Present Address §

Department of Agriculture, Forestry and Fisheries, Iwate Prefecture Government, Morioka 020-8570, Japan. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Shigematsu, K.; Saito, Y.; Saito, K.; Takahashi, Y. J. Cryst. Growth 2008, 310, 4681−4684. (2) Shigematsu, K.; Honda, H.; Kumagai, T.; Takahashi, Y. Cryst. Growth Des. 2009, 9, 4674−4679. E

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