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2009, 113, 10077–10080 Published on Web 07/06/2009
Neat Liquid Consisting of Hydrogen-Bonded Tetramers: Dicyclohexylmethanol Yu-ta Suzuki, Yasuhisa Yamamura, Masato Sumita,† Syuma Yasuzuka, and Kazuya Saito* Department of Chemistry, Graduate School of Pure and Applied Sciences, UniVersity of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan ReceiVed: May 25, 2009; ReVised Manuscript ReceiVed: June 23, 2009
Nonmonotonous temperature dependence was detected in the heat capacity and dielectric constant of the title compound in the liquid state. A coherent analysis of FT-IR spectra, heat capacity, and dielectric constants shows that the neat liquid at low temperatures consists of closed (square) tetramers via H-bonds. Molecular association is ubiquitous in hydrogen-bonding (Hbonding) liquids and is believed to play crucial roles in determination of their physical properties as exemplified in the unique properties of water.1 The establishment of adequate descriptions of associating liquids is also an important issue in industry2 for, e.g., designing chemical processes. Although systems consisting of small, simple molecules are generally preferable for detailed studies from the basic point of view, this is not the case here because such molecules possibly form an extending network and/or chains through H-bonds. To proceed with the basic research of associating liquids further, a clean system with a moderate complexity is necessary. Although the introduction of bulky groups is a plausible way to suppress the extending association, it is not always useful for the control of the association. Tricyclohexylmethanol (TCHM) is, for example, monomeric in the liquid state in spite of the formation of H-bonded dimers in the crystal below room temperature.3,4 The formation of an extending network and/or chain via H-bonds is also found widely in crystals. This suggests that the structural information for solids offers a useful guide to identify candidates for the model associating liquids with a moderate complexity. As the dimer is too simple and the trimer is generally hard to fit a crystalline symmetry, the tetramer was chosen as the preferable structural motif. The survey over available structural data suggested that some molecules having moderate steric effects form crystals consisting of H-bonded closed tetramers. A further survey over available literatures suggested that the title compound, dicyclohexylmethanol (DCHM),5 is a plausible candidate for a model associating liquid. In this study, we conducted spectroscopic, energetic, and structural experiments on normal and supercooled liquids of DCHM. A coherent analysis of FT-IR, calorimetric, and dielectric results shows that the neat liquid at low temperatures consists mostly of closed (square) tetramers via H-bonds. DCHM (Aldrich) was purified by fractional sublimation in a vacuum at 300 K. Differential scanning calorimetry (DSC, TA Instruments Q200) was applied for establishment of the lowtemperature limit of stability of the liquid state of DCHM while * To whom correspondence should be addressed. E-mail: kazuya@chem. tsukuba.ac.jp. † Present address: National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan.
10.1021/jp9048764 CCC: $40.75
Figure 1. Measured heat capacities of liquids and liquid quenched glass of DCHM by modulated DSC (circles, left axis) and the excess heat capacity calculated according to the model for association via H-bonds (dotted line, right axis). For the details of the model, see the text.
cooling after the fusion at 337 K. It appears that the liquid is easily brought into a glassy state (liquid quenched glass, LQG) without crystallization. The heat capacity of the liquid DCHM was measured in the modulated DSC mode (ramp rate, -5 K min-1; sinusoidal modulation, (1.0 K; period, 40 s) from 410 to 180 K. The absolute scale of measured heat capacity was adjusted slightly to fit that of the unpublished results of independent adiabatic calorimetry performed with a superior precision in this laboratory.6 The heat capacity determined by modulated-DSC is shown in Figure 1. A glass transition is observed as a sudden decrease in heat capacity around 250 K, above which the DCHM is in the liquid state. The discussion on the glass transition will be published separately together with that in TCHM on the basis of precise heat capacities measured by adiabatic calorimetry. Besides the glass transition, a large hump can be recognized with a maximum around 330 K. A naı¨ve separation of the hump yields a rough estimate of the enthalpy involved as ca. 10 kJ mol-1. This magnitude suggests that the hump is related to the formation/destruction of the weak H-bonds (OH-O). It is emphasized that heat capacities of simple liquids usually depend only weakly on temperature, though it has been recognized that some liquids suffering from steric effects show a hump.8 We will present later the analysis of the hump in heat capacity on the basis with a clearer microscopic view. To see the possible relation between the hump in heat capacity and the association by the H-bonds, the IR spectra were recorded 2009 American Chemical Society
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Figure 3. Relative dielectric permittivity of liquid and liquid quenched glass of DCHM measured at 1 kHz (circles) and calculated according to the model (dotted line).
Figure 2. (a) IR spectra of liquid and liquid quenched glass of DCHM at various temperatures (solid line) and of the crystal at 300 K (broken line). (b) Normalized intensity of the OH stretching band at ca. 3400 cm-1 (circles) and population of OH bonds participating in H-bonds calculated according to the model (dotted line).
for normal and supercooled liquids and LQG while sandwiching the sample between two KBr disks using a JASCO FT/IR-550 instrument between 80 and 360 K. Typical results are shown in Figure 2a together with the spectrum of the crystal at 300 K for the sake of comparison. Since the interest here is the H-bond, we concentrate our attention to the relevant regions (ca. 3500 and 800 cm-1). We can recognize a gradual change in both regions upon temperature variation. It is well-known that the OH stretching frequency is around 3400 cm-1 in the bonded state for weak H-bonds such as OH-O, whereas it is around 3600 cm-1 in the free state.9 The OH stretching band of the crystal is definitely within the former region with the incomplete splitting probably due to the nonequivalence of two H-bonds inside the tetramer. The corresponding band still remains around 3400 cm-1 in the liquid and LQG, though it is broadened by microscopic inhomogeneity of the liquid. This observation clearly indicates that a notable amount of DCHM molecules is in the H-bonded state in the liquid state. Namely, DCHM forms an associating liquid. The temperature dependence of the population of the OH groups participating in H-bonds was estimated from the intensity of the OH stretching band around 3400 cm-1. The ratio of the integrated intensities of the OH stretching band and the CH stretching bands (between 2900 and 3000 cm-1) was normalized to unity at the lowest temperature studied. The resultant temperature dependence is shown in Figure 2b. The population of the OH groups participating in the H-bonds gradually decreases on heating. It is about 0.8 at the glass transition temperature and 0.5 at the melting temperature. Although it becomes clear from the DSC and IR results that a significant portion of DCHM molecules is involved in the H-bonds in the liquid and that the portion continuously decreases upon heating, yielding a hump in heat capacity, the identification of the structure of H-bonded aggregates is not an easy task because of the rather complex structure of the DCHM molecule. Since the closed aggregates are expected to have a negligible dipole moment, the dielectric measurement was conducted. The dielectric constant of the liquid was determined using a capacitor with 10 planar electrodes (ca. 12 pF in dry air). Figure 3 shows the (real) dielectric permittivity measured at 1 kHz. The most prominent feature is a broad maximum around 350 K because
the dielectric permittivity of polar liquids usually shows a monotonous decrease on heating as in n-alkanols.10 Since the maximum remained the same upon the frequency variation (1 kHz-1 MHz), this is not a relaxational but static (equilibrium) property. A detailed discussion on this maximum is given later. Another feature is a slight but sudden decrease around 270 K. This anomaly comes from the main relaxation relevant to the glass transition because its temperature shifts reasonably when the measuring frequency is varied. The most important feature here is, however, the absolute magnitude. It is well-known that polar organic liquids such as acetonitrile (36.6), ethanol (25.3), and cyclohexanol (16.4)11 have a relative dielectric permittivity of 1 order of magnitude larger than the experimental result for the liquid DCHM (2.3 at 200 K). The experimental magnitude is comparable to those of nonpolar liquids such as n-alkanes (1.9 for hexane) and cyclohexane (2.0).11 The dielectric permittivity of the liquid DCHM at low temperature is just comparable with that of the crystalline DCHM observed before melting in this study. It is noted that, the crystal is formed by the closed tetramers with null dipole.5 The smallness of the dielectric permittivity indicates that there are few “particles” having a dipole moment in the liquid DCHM. The increase above 250 K can be interpreted as a symptom of the gradual destruction of the H-bonded closed aggregates and the formation of polar aggregates and/or monomer on heating. It is thus concluded that most DCHM molecules are in H-bonded closed aggregates in the liquid. It is also noted that the addition of a small amount of DCHM to cyclohexane scarcely affected the dielectric permittivity, implying that closed aggregates are also formed in the solution. A simple but reasonable model is to be constructed to analyze the experimental results. The possible formation of the closed H-bonded trimer in addition to the H-bonded tetramer observed in the crystal5 was considered through quantum chemical calculations. The calculations were performed on monomer, dimer, closed trimer, and closed tetramer in the isolated condition while utilizing the Gaussian 03 package7 at the DFT/ B3LYP/6-31G* level. The H-bonded tetramer and closed trimer were successfully optimized without symmetry constraints, as shown in Figure 4. The stabilization energies for the trimer and tetramer are 16.7 and 20.5 kJ (mol of monomer)-1, respectively, after corrections for the basis set superposition error (BSSE) by using the counterpoise method. These stabilization energies are comparable to that of dimer [17.9 kJ (mol of dimer)-1], suggesting their proportionality, though only approximate, to the number of H-bonds. Namely, closed aggregates have superior stability in energy to the open aggregates. It appears that the tetramer is more stable than the dimer and closed trimer.
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Figure 4. Structures of the closed trimer (a) and tetramer (b) of DCHM optimized theoretically in vacuo: red, oxygen; light green, hydrogen in H-bond; black, carbon. The hydrogen atoms attached to carbon atoms are not shown for clarity.
It is noted that the stabilization energy is, roughly speaking, the sum of contributions by H-bonds and van der Waals interaction. The dipole moments were calculated as 1.55, 3.66, 0.41, and 0.38 D for monomer, dimer, closed trimer, and closed tetramer, respectively. Since the contribution to dielectric permittivity is proportional to the squared magnitude of dipole moment, those of the closed trimer and tetramer are smaller than that of the monomer by 1 order of magnitude even if their number densities are the same as one another. Although the hump in heat capacity can be explained within a simple two-state model,8 we construct a physically clearer model, which will coherently explain the experimental results for the liquid DCHM. Here, we consider aggregates consisting of up to four molecules (tetramer). Therefore, the model assumes states for four molecules. In this sense, the present model can be regarded as a kind of cell model of liquids. Since the H-bonded tetramer in the crystal is closed due to the steric effect, we assume that the (OH)4 core of the tetramer be closed and flat without an electric dipole. This is acceptable considering the quantum chemical calculation for an isolated tetramer. The dipole moment of the monomer is denoted as µ. The dimer is expected to have a dipole moment of 2 µ. The trimer may take two structures, closed and open. The former has a negligible dipole, while the latter has a large dipole, which is assumed as 3 µ for simplicity, though this is certainly overestimated. The energies of aggregates are assumed to be proportional to the number of H-bonds. Considering the fact that the closed trimer (triangle) is the most rigid, the degeneracy (possessed by a molecule) is expressed by the ratio with respect to that in the closed trimer (g0). In summary, the states assumed in the present model are (1) four monomers (energy 0 and degeneracy G1 ) g14g0-4), (2) two monomers and a dimer (-E and G2 ) g12g22g0-4), (3) two dimers (-2E and G3 ) g24g0-4), (4) a monomer and an open trimer (-2E and G4 ) g1g33g0-4), (5) a monomer and a closed trimer (-3E and G5 ) g1g0-1), and (6) a closed tetramer (-4E and G6 ) g44g0-4). Following a standard procedure of statistical mechanics, the temperature dependence of population of each state and heat capacity are analytically calculated. As for the dielectric permittivity, the contribution by a dipole moment is proportional to the number density of dipole moments, the squared magnitude of dipole moment, and the inverse temperature (Curie’s law) with a certain background arising from the electronic contribution (optical permittivity). Trial-and-error gave acceptable fits for all experimental results shown in Figures 1-3 for E ≈ 12 kJ mol-1, G1 ) 2.7 × 107, G2 ) 5.2 × 104, G3 ) 100, G4 ) 3.6 × 103, G5 ) 7.2, and G6 ) 1. The magnitude of E is
Figure 5. Temperature dependence of contributions to relative dielectric permittivity by monomer, dimer, and open trimer (a) and population of molecules involved in different aggregates calculated according to the model (b). The structures of aggregates are schematically indicated using bold arrows.
primarily determined by the enthalpy involved in the hump in heat capacity. The degeneracy is decomposed as g1/g0 ≈ 160, g2/g0 ≈ 7, g3/g0 ≈ 8, and g4/g0 ≈ 2. The resultant parameters are acceptable because the magnitude of E is within an acceptable range for the energy of a weak H-bond (OH-O) though slightly smaller than usual (ca. 15-20 kJ mol-1),9 and all degeneracy for monomer, dimer, open trimer, and closed tetramer is larger than that of the closed trimer as expected. The information unavailable directly from the experimental results is shown in Figure 5. Figure 5a shows the contribution of each aggregate and monomer to the dielectric permittivity. It is clear that the decrease in the high temperature region on heating is due not to Curie’s law but to the decrease in the number of the open trimer. The population of molecules in each aggregate is shown in Figure 5b. That of dimer is very small through the whole temperature range. As for trimers, the population is very small for the closed trimer, whereas that of the open trimer is notable around 350 K. This is due to the larger degeneracy (entropy arising from the flexibility) of the latter. The larger population is magnified by the large dipole moment (3 µ), giving the dominant contribution to the dielectric permittivity. The population of the molecule in the tetramer is remarkable. This originates in its superior energetic stability. The population of the molecule involved in the tetramer amounts to ca. 0.95 at the glass transition temperature. In this respect, the glass transition is one within molecular liquid consisting of molecular tetramers. The study on this point is underway in this laboratory. In summary, the coherent analysis of FT-IR, calorimetric, and dielectric results shows that the neat liquid at low temperatures consists of closed (square) tetramers via H-bonds. Since higher aggregates can be safely neglected, the liquid DCHM is an ideal system for the basic research of associating liquids from both experimental and theoretical sides. Acknowledgment. This work was partly supported by a Grant-in-Aid for Scientific Research on Priority Area “NonEquilibrium Soft Matter” (No. 463/19031002) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. Supporting Information Available: Cartesian coordinates of all atoms in optimized monomer, dimer, closed trimer, and
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closed tetramer. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Eisenberg, D.; Kauzmann, W. The structure and properties of water; Oxford University Press: New York, 2005. (2) Mu¨ller, E. I.; Gubbins, K. E. Ind. Eng. Chem. Res. 2001, 40, 2193– 2211. (3) Malarski, Z.; Szostak, R.; Sorriso, S. Lett. NuoVo Cimento 1984, 40, 261–264. (4) Yamamura, Y.; Saitoh, H.; Sumita, M.; Saito, K. J. Phys.: Condens. Matter 2007, 19, 176219 (11pp). (5) Sgarabotto, B. P.; Ugozzoli, F.; Sorriso, S.; Malarski, Z. Acta Crystallogr., Sect. C 1988, 44, 671–673. (6) Yamamura, Y.; Saito, K.; Saitoh, H.; Matsuyama, H.; Kikuchi, K.; Ikemoto, I. J. Phys. Chem. Solids 1995, 56, 107–115. (7) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Letters Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (8) Cerdeirin˜a, C. A.; Gonzalez-Salgado, D.; Romani, L.; Delgado, M. C.; Torres, L. A.; Costas, M. J. Chem. Phys. 2004, 120, 6648–6659. (9) Mare´chal, Y. The hydrogen bond and the water molecule; Elsevier: Amsterdam, 2007. (10) Deruichi, Y.; Magallanes, C.; Giordan, L.; Garis, E.; Catenaccio, A. Mol. Phys. 2001, 99, 77–79. (11) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, 83rd ed.; CRC: Boca Raton, FL, 2002; pp 6-153-6-175.
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