Calorimetric and Dielectric Studies on an Order−Disorder Transition in

18546

J. Phys. Chem. 1996, 100, 18546-18549

Calorimetric and Dielectric Studies on an Order-Disorder Transition in the Hydrogen-Bond System Formed by Water Molecules in the [H31O14][CdCu2(CN)7] Crystal† Kenji Okishiro, Osamu Yamamuro,* and Takasuke Matsuo Department of Chemistry and Microcalorimetry Research Center, Graduate School of Science, Osaka UniVersity, Toyonaka, Osaka 560, Japan

Shin-ichi Nishikiori and Toschitake Iwamoto Department of Chemistry, College of Arts and Sciences, The UniVersity of Tokyo, Komaba, Meguro, Tokyo 153, Japan ReceiVed: June 12, 1996; In Final Form: August 30, 1996X

The heat capacity of [H31O14][CdCu2(CN)7] has been measured in the temperature range between 14 and 340 K with an adiabatic calorimeter. A first-order phase transition appeared at 217.5 ( 0.2 K involving an entropy change of 37.5 ( 1.5 J K-1 mol-1 corresponding to 2.68 ( 0.11 J K-1 (mol of H2O)-1 ()R ln 1.38). Dielectric permittivity has been measured at 10 kHz at temperatures between 130 and 280 K. An abrupt increase of the real part (∆′ ≈ 100) appeared at around 215 K. The most likely mechanism of the phase transition is the orientational ordering of the water molecules forming a hydrogen-bonded network in the crystal. The orientation of the water molecules is constrained by the ice rules as in the various ice polymorphs and clathrate hydrates. 1. Introduction The proton ordering process in the hydrogen-bonded lattice of water molecules has been one of the important subjects in condensed matter physics and physical chemistry.1 Our group has studied this subject from the thermodynamic point of view. According to previous heat capacity measurements, the protons become either ordered through a phase transition or frozen-in at a glass transition on cooling in various ice polymorphs,2-6 clathrate hydrates,7-14 SnCl2‚2H2O,15 and Cu(HCO2)2‚4H2O;16 the former two (ice polymorphs and clathrate hydrates) have three-dimensional hydrogen-bonded systems while the latter two have two-dimensional networks. In the case of ice Ih2-5 and the structure II hydrates of tetrahydrofuran (THF),7,8 acetone,9 and trimethylene oxide (TMO),10 the ordering transitions were observed only when the sample was doped with a small amount (ca. mole fraction of 10-4) of potassium hydroxide (KOH) to accelerate the reorientational motion of the water molecules. It was of interest that the nature of the transitions and the waterreorientational motion are strongly dependent on the dimensional and topological properties of the networks. Recently, Nishikiori and Iwamoto17 synthesized [H31O14][CdCu2(CN)7] and found by single-crystal X-ray diffraction that its structure involves an interesting three-dimensional hydrogenbonded network. This crystal belongs to the space group Pa3 (a ) 12.94 Å, Z ) 4). A pyrite-like framework is built of Cd2+ and pyrosilicate-like [Cu2(CN)7]5- ions linked to one another by the terminal CN groups. The C and N atoms between Cu and Cu atoms (not between Cu and Cd atoms) are positionally disordered; one-seventh of the C-N groups are disordered. This disorder is probably static because the Cu-C-N-Cu covalent bond is too rigid to be broken by thermal agitation at room temperature even though there is no experimental evidence for this. Actually, the C and N atoms in a related compound Cd(CN)2 are statically disordered according to a 113Cd NMR * Corresponding author. Phone: +81-6-850-5399. FAX: +81-6-8505397. E-mail: [email protected]. † Contribution No. 122 from the Microcalorimetry Research Center. X Abstract published in AdVance ACS Abstracts, October 1, 1996.

S0022-3654(96)01729-7 CCC: $12.00

study.18 Twelve water molecules form a hydrogen-bonded ring around the linear Cu-(CN)-Cu bond which is parallel to the crystallographic C3 axis. The rings of the water molecules are interconnected by two other water molecules, forming a novel three-dimensional hydrogen-bonded network. The frameworks of the cyanometalate and of the hydrogen-bonded water molecules, partly protonated by the excess three protons, are mutually interpenetrating without direct chemical bonds. The positions of the 31 protons, which could not be determined by the X-ray, are likely to be disordered as in other threedimensional hydrogen-bonded networks studied so far. In the present study, the heat capacity of the [H31O14][CdCu2(CN)7] crystal has been measured in the temperature range between 14 and 340 K. The aim of the study was to investigate the ordering process of the protons from the thermodynamic point of view. The dielectric permittivity has also been measured at 10 kHz at temperatures between 130 and 280 K. This measurement allows one to investigate the dipole fluctuation of the water molecules and its ordering at low temperature. 2. Experimental Section [H31O14][CdCu2(CN)7] was prepared by the method described elsewhere.17 The powder sample was packed into a bag made of poly(ethylene terephthalate) (PET) to avoid reaction with the sample cell made of copper. This bag was then loaded into the sample cell. The dead spaces of the PET bag and the sample cell were filled with helium gas to enhance thermal equilibration at low temperatures. The masses of the sample and PET were 2.8692 g (0.004 239 0 mol) and 0.0285 g, respectively. The heat capacity of [H31O14][CdCu2(CN)7] was measured using an adiabatic calorimeter described elsewhere19 in the temperature range between 14 and 340 K. The heat capacity measurement was carried out by a standard intermittent heating method, i.e., repetition of equilibration and energizing intervals. The temperature increment for each measurement was between 1 and 2.5 K. It took about 1 min for the sample and cell to reach thermal equilibrium after each energy input around 14 K and about 5 min around 300 K. Single-step heating experiments © 1996 American Chemical Society

H-Bond System Formed in [H31O14][CdCu2(CN)7] Crystal

J. Phys. Chem., Vol. 100, No. 47, 1996 18547

TABLE 1: Experimental Molar Heat Capacities of the [H31O14][CdCu2(CN)7] Crystal (M ) 676.86 g mol-1, R ) 8.314 51 J K-1 mol-1) T/K

Cp,m/R

T/K

Cp,m/R

T/K

Cp,m/R

T/K

Cp,m/R

T/K

Cp,m/R

T/K

Cp,m/R

15.06 15.68 16.23 16.76 17.28 17.81 18.36 18.96 19.59 20.24 20.98 21.77 22.62 23.51 24.42 25.37 26.44 27.65 28.94 30.25 31.53 32.75 33.93 35.12 36.33 37.55 38.82

3.785 4.122 4.409 4.681 4.958 5.224 5.540 5.878 6.242 6.623 7.059 7.500 8.005 8.520 9.076 9.616 10.27 10.99 11.84 12.60 13.39 14.15 14.87 15.63 16.36 17.10 17.86

40.08 41.38 42.71 44.02 45.34 46.69 48.00 49.34 50.68 52.00 53.34 54.69 56.00 57.42 58.94 60.42 61.88 63.38 64.91 66.42 67.90 69.32 70.74 72.29 73.89 75.47 77.00

18.60 19.37 20.16 20.92 21.68 22.45 23.21 23.97 24.73 25.49 26.23 27.00 27.73 28.51 29.34 30.13 30.86 31.63 32.40 33.15 33.84 34.53 35.25 35.97 36.71 37.46 38.16

78.54 80.28 82.13 83.95 85.76 87.63 89.56 91.47 93.35 95.30 97.31 99.30 101.27 103.29 105.37 107.43 109.48 111.58 113.73 115.87 117.99 120.17 122.39 124.61 126.81 129.06 131.36

38.84 39.60 40.41 41.20 41.97 42.76 43.60 44.36 45.13 45.91 46.67 47.46 48.22 48.96 49.73 50.45 51.22 51.59 52.74 53.46 54.19 54.95 55.67 56.40 57.09 57.80 58.54

133.65 135.93 138.26 140.63 143.07 145.58 148.13 150.74 153.33 155.90 158.53 161.21 163.88 166.53 169.24 171.99 174.23 176.99 177.84 180.58 183.30 186.08 188.92 191.75 194.57 197.45 200.38

59.27 59.97 60.67 61.33 62.10 62.81 63.52 64.27 65.06 65.68 66.39 67.09 67.76 68.49 69.19 69.88 70.42 71.12 71.27 71.91 72.63 73.27 73.96 74.62 75.29 75.99 76.73

202.80 204.71 206.61 208.59 210.62 212.31 213.63 214.92 216.07 216.94 217.51 218.07 219.01 220.30 221.93 223.89 225.91 228.39 231.26 234.19 237.17 239.64 242.82 246.46 249.33 252.25 255.23

77.29 77.70 78.23 78.85 80.47 83.90 88.18 100.8 149.8 317.4 502.6 348.0 96.32 88.67 87.51 87.84 88.18 88.78 89.42 90.01 90.63 91.28 91.85 92.46 93.05 93.63 94.24

258.21 261.19 264.22 267.30 270.38 273.45 276.51 279.57 282.62 285.72 288.87 292.00 295.14 298.26 301.38 304.50 307.61 310.77 313.98 317.18 320.37 323.56 326.73 329.90 333.06 336.20 339.39

94.82 95.41 96.03 96.57 97.11 97.64 98.13 98.71 99.22 99.82 100.5 101.0 101.4 101.9 102.4 102.9 103.4 103.8 104.3 104.9 105.3 105.9 106.4 107.1 107.7 108.5 109.2

were performed separately to determine the transition enthalpy precisely. The accuracy of the heat capacity measurement was better than 1% at T < 20 K, 0.3% at 20 < T < 30 K, and 0.1% at T > 30 K. In the calorimetric measurement, the temperature was measured using a Rh-Fe resistance thermometer (27 Ω at 273 K, purchased from Oxford Instruments Co.) calibrated on the temperature scale EPT76 (T < 30 K) and IPTS68 (T > 30 K). The heat capacity difference caused by the conversion to the new temperature scale ITS9020 was estimated to be smaller than 0.05% over the 14-300 K temperature range. For dielectric measurement, the powder sample of [H31O14][CdCu2(CN)7] was further ground on a mortar and shaped into a disk with the diameter of 13.00 mm and the thickness of 0.888 mm by applying pressure of ca. 300 MPa. The mass density of the disk was 1.86 g cm-3, which is 89.9% of the density determined by the single-crystal X-ray diffraction (2.07 g cm-3). For electrodes, circular pieces of gold foil with diameters of 10.09 mm were attached with a thin layer of Apiezon N-grease on both sides of the sample disk. The disk was mounted in a double-thermostated environment in a cryostat. The sample temperature was stabilized to (0.03 K with an accuracy of (0.1 K. The capacitance was measured with an LCR meter (HP4284A, Hewlett-Packard) at the frequency of 10 kHz and in the temperature range of 130-280 K. The measurement was performed in the heating direction as in the case of the heat capacity measurement. 3. Results and Discussion A. Heat Capacity. The molar heat capacities of [H31O14][CdCu2(CN)7] are collected in Table 1 and also plotted in Figure 1. A first-order transition appeared at 217.5 ( 0.2 K, accompanied by a substantial excess heat capacity in the hightemperature phase. The temperature dependence of the excess heat capacity characterized by a strong latent heat and a gradual part in the high-temperature phase is similar to those of the transitions in other three-dimensional hydrogen-bonded systems, e.g., ice Ih2-5 and clathrate hydrates.7-10 In these systems, the

Figure 1. Molar heat capacity of the [H31O14][CdCu2(CN)7] crystal.

gradual parts are known to be due to the short-range ordering of the water molecule relative to each other as well as to the crystal lattice. B. Transition Entropy. To separate the excess heat capacity ∆Cp due to the phase transition from the vibrational heat capacity, the latter (baseline) was determined by the leastsquares fitting. A second-order polynomial function fitted well with the data between 174 and 207 K and those between 330 and 339 K. With this function as the baseline, the excess entropy due to the transition ∆S was calculated by integrating ∆Cp/T. It is plotted as a function of temperature in Figure 2. The total entropy change was 37.5 ( 1.5 J K-1 mol-1, 70% of which was gained as the first-order component and 30% in the gradual part at higher temperature. The transition entropy corresponds to 2.68 ( 0.11 J K-1 (mol of H2O)-1. The transition entropies of KOH-doped ice Ih2-5 and the KOH-doped structure II clathrate hydrates7-10 are about 2.5 J K-1 (mol of H2O)-1. The orientational entropy of the water systems obeying ice rules21 is theoretically calculated to be R ln(3/2), corresponding to 3.4 J K-1 (mol of H2O)-1.22 The present observed value lies between these two values (2.5 and 3.4 J K-1 (mol of H2O)-1).

18548 J. Phys. Chem., Vol. 100, No. 47, 1996

Okishiro et al. TABLE 2: Molar Thermodynamic Functions of the [H31O14][CdCu2(CN)7] Crystal (M ) 676.86 g mol-1, R ) 8.314 51 J K-1 mol-1, Φ°m ) ∆0TS °m - ∆0TH °m/T) T/K

Figure 2. Excess entropy due to the transition of the [H31O14][CdCu2(CN)7] crystal.

Figure 3. Real part of dielectric permittivity of the [H31O14][CdCu2(CN)7] crystal measured at 10 kHz.

C. Dielectric Permittivity. Figure 3 shows the real part of the dielectric permittivity of [H31O14][CdCu2(CN)7] measured at 10 kHz on heating. ′ steeply increased at the transition point determined by the calorimetry. The magnitude of the increase ∆′ was about 100, which is comparable with ∆′ observed at the water-ordering transitions of ice Ih (∆′ ≈ 100)23,24 and clathrate hydrates (∆′ ≈ 70).25,26 The ′ curve was reproducible in the cooling run and also in the runs after several cycles of heating and cooling. This indicates that the transition is not accompanied by a large volume change which would shatter the shaped powder sample. D. Mechanism of the Transition. Both calorimetric and dielectric measurements indicate that the phase transition of the [H31O14][CdCu2(CN)7] crystal is due to the orientational ordering of the water molecules in the H31O14 hydrogen-bonded system. The transition entropy also suggests that the orientational disorder of the water molecules in the high-temperature phase is constrained by the ice rules.21 The transition mechanism of the [H31O14][CdCu2(CN)7] crystal is thus similar to those in other three-dimensional hydrogen-bonded systems such as ice polymorphs and clathrate hydrates. It is noteworthy that the transition temperature of the[H31O14][CdCu2(CN)7] crystal is much higher than that of other systems (cf. 72 K in KOH-doped ice Ih and 62 K in KOH-doped THF hydrate). This may be the reason the ordering transition occurs without any impurity doping, which has been necessary to accelerate the waterreorientational motions for the low-lying transitions in other ice forms and clathrate hydrates. This property may further be associated with the fact that the crystal is perprotonated by three protons. It is plausible that the low-temperature ordered phase

10 15 20 25 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 230 240 250 260 270 273.15 280 290 298.15 300 310 320 330 340

C°p,m/R

∆T0 H°m/TR

∆T0 S°m/R

1.460 0.3930 0.5319 3.761 1.112 1.535 6.475 2.107 2.981 9.411 3.273 4.740 12.45 4.547 6.722 18.56 7.293 11.15 24.36 10.13 15.92 29.88 12.97 20.85 34.89 15.75 25.84 39.48 18.43 30.80 43.75 21.01 35.70 47.73 23.48 40.52 51.41 25.86 45.24 54.86 28.13 49.87 58.12 30.32 54.39 61.19 32.41 58.81 64.06 34.43 63.13 66.78 36.37 67.35 69.37 38.23 71.48 71.77 40.03 75.51 74.21 41.77 79.46 76.63 43.45 83.33 79.98 45.09 87.60 phase transition at 217.5 K 89.14 51.41 97.87 91.25 53.03 101.7 93.22 54.60 105.5 95.16 56.12 109.2 97.03 57.60 112.8 97.60 58.06 113.9 98.83 59.04 116.4 100.6 60.44 119.9 101.9 61.56 122.7 102.2 61.81 123.3 103.7 63.14 126.7 105.3 64.43 130.0 107.1 65.69 133.3 109.4 66.94 136.5

Φ°m/R 0.1389 0.4224 0.8737 1.467 2.175 3.854 5.786 7.884 10.09 12.37 14.69 17.03 19.39 21.73 24.07 26.40 28.70 30.99 33.25 35.48 37.69 39.88 42.51 46.46 48.68 50.88 53.05 55.20 55.87 57.32 59.41 61.10 61.49 63.53 65.56 67.56 69.54

is more stabilized than the high-temperature phase by the excess protons making some chemical bonds between the H31O14 and CdCu2(CN)7 sublattices. The positionally disordered C and N atoms do not play a role in the transition mechanism if they are static in the hightemperature phase as we assume here. Even if they are dynamically disordered at T > Tc and become ordered at the transition, the contribution to ∆trsS is small ((1/14)R ln 2 ) 0.41 J K-1 mol-1). The contribution to ∆′ should also be small because the dipole moment of the CN ion (0.22 D) is much smaller than that of the water molecule (1.94 D). The number density of the disordered CN ions is also small, probably making their contribution to ′ insignificant. Structural studies in the low-temperature phase are obviously desirable for a clearer description of the ordering process. Multinuclear NMR studies (e.g., 1H, 2H, 13C, 113Cd) could also provide important information on dynamics of the molecules and the nature of the phase transition. Appendix Standard Thermodynamic Functions. The molar heat capacity, enthalpy, entropy, and Giauque function of the [H31O14][CdCu2(CN)7] crystal were calculated from the smoothed heat capacity data and summarized in Table 2. Extrapolation of the heat capacity down to 0 K was performed by using the following odd-order polynomial function:

Cp/(J K-1 mol-1) ) 1.51 × 10-2(T/K)3 - 3.22 × 10-5(T/K)5 + 2.84 × 10-8(T/K)7

H-Bond System Formed in [H31O14][CdCu2(CN)7] Crystal References and Notes (1) Personage, N. G.; Staveley, L. A. K. Disorder in Crystals; Clarendon Press: Oxford, U.K., 1978; Chapter 8. (2) Haida, O.; Matsuo, T.; Suga, H.; Seki, S. J. Chem. Thermodyn. 1974, 6, 815. (3) Tajima, Y.; Matsuo, T.; Suga, H. Nature 1982, 299, 810. (4) Tajima, Y.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1984, 45, 1135. (5) Matsuo, T.; Tajima, Y.; Suga, H. J. Phys. Chem. Solids 1986, 47 165. (6) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1987, 48, 935. (7) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. Solid State Commun. 1987, 62, 289. (8) Yamamuro, O.; Oguni, M.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1988, 49, 425. (9) Yamamuro, O.; Kuratomi, N.; Matsuo, T.; Suga, H. Solid State Commun. 1990, 73, 317. (10) Kuratomi, N.; Yamamuro, O.; Matsuo, T.; Suga, H. J. Therm. Anal. 1992, 38, 1921. (11) Yamamuro, O.; Handa, Y. P.; Oguni, M.; Suga, H. J. Inclusion Phenom. 1990, 8, 45. (12) Kuratomi, N.; Yamamuro, O.; Matsuo, T.; Suga, H. J. Chem. Thermodyn. 1991, 23, 485.

J. Phys. Chem., Vol. 100, No. 47, 1996 18549 (13) Yonekura, T.; Yamamuro, O.; Matsuo, T.; Suga, H. Thermochim. Acta 1995, 266, 65. (14) Yamamuro, O.; Suga, H. J. Therm. Anal. 1989, 35, 2025. (15) Matsuo, T.; Oguni, M.; Suga, H.; Seki, S.; Nagle, J. F. Bull. Chem. Soc. Jpn. 1972, 47, 57. (16) Matsuo, T.; Kume, Y.; Suga, H.; Seki, S. J. Phys. Chem. Solids 1976, 37, 499. (17) Nishikiori, S.; Iwamoto, T. J. Chem. Soc., Chem. Commun. 1993, 20, 1555. (18) Nishikiori, S.; Ratcliffe, C. I.; Ripmeester, J. A. Can. J. Chem. 1990, 68, 2270. (19) Tatsumi, M.; Matsuo, T.; Suga, H.; Seki, S. Bull. Chem. Soc. Jpn. 1975, 48, 3060. (20) Goldberg, R. N.; Weir, R. D. Pure Appl. Chem. 1992, 64, 1545. (21) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 525. (22) Pauling, L. J. Am. Chem. Soc. 1935, 57, 2680. (23) Fletcher, N. H. The Chemical Physics of Ice; Cambridge University Press: Cambridge, U.K., 1970. (24) Kawada, S.; Dohata, H. J. Phys. Soc. Jpn. 1985, 54, 477. (25) Yamamuro, O.; Matsuo, T.; Suga, H. J. Inclusion Phenom. 1990, 8, 33. (26) Yamamuro, O.; Kuratomi, N.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1993, 54, 229.

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