Glass transitions in the stable crystalline states of dibenzofuran and fluorene

O-570 J. Chem. Thermodynamics 1995, 27, 927–938

Glass transitions in the stable crystalline states of dibenzofuran and fluorene Hiroaki Fujita, Hiroki Fujimori, and Masaharu Oguni a Department of Chemistry, Faculty of Science, Tokyo Institute of Technology, Ookayama-2 , Meguro-ku, Tokyo 152 , Japan

(Received 28 November 1994; in final form 7 March 1995) Heat capacities of dibenzofuran and fluorene were measured with an adiabatic calorimeter in the temperature ranges 245Q(T/K)Q375 and 200Q(T/K)Q419, respectively. Glass transitions were discovered at Tg=316 K for both the compounds in the stable crystalline state due to freezing-in of the reorientational motion of the pseudo-planar molecule. In dibenzofuran, the molar-heat-capacity jump at Tg was estimated to be (6.820.2) J·K−1·mol−1 and the molar activation energy for the reorientation to be (9825) kJ·mol−1 . In fluorene, the molar-heat-capacity jump at Tg was estimated to be (7.020.3) J·K−1·mol−1 , and the enthalpy relaxation as a function of time showed a remarkable non-exponentiality. The latter was interpreted potentially to be related to non-planarity of the molecule. 71995 Academic Press Ltd.

1. Introduction A glass transition takes place as a freezing-in phenomenon of some configurational degree of freedom of molecules.(1) This can be understood on the consideration that the configurational change, namely positional or orientational rearrangement, or both, of molecules proceeds through surmounting some energy barrier, and thus the fluctuational frequency of the rearrangement decreases with decreasing temperature. The glass-transition temperature is then defined as the temperature at which the equilibration time concerning the configurational degree of freedom from the non-equilibrium state crosses the experimental time scale, often taken to be 1 ks. Correspondingly, in the glass-transition-temperature region, the relaxation phenomenon of thermodynamic quantities such as enthalpy and volume is observed as due to the approach from non-equilibrium to equilibrium state with respect to the molecular configuration, and the jump of thermodynamic quantities such as heat capacity and cubic expansion coefficient appears as due to the difference between those in the frozen-in state and in the equilibrium state concerning the relevant configurational degree of freedom. Especially the latter appearance of a glass transition a

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often leads one to the misunderstanding that ‘‘what is happening is a phase transition of the second order’’. The glass transition occurs even in the stable crystalline state as well as in the supercooled liquid state only if an appreciable amount of configurational disorder of molecules remains at the relevant temperature.(1, 2) Dibenzofuran:

and fluorene:

molecules consisting of three rings, were studied calorimetrically by Chirico et al.(3) and Finke et al.,(4) and were reported to show a phase transition accompanying a heat-capacity jump at T1290 K. They added, in the case of dibenzofuran, the statement that, at Tq260 K, the equilibration times increased to 2 h near T=270 K, 5 h near T=280 K, and to greater than 48 h near T=290 K. Meanwhile, Reppart et al.(5) reported from a room-temperature X-ray-diffraction study of dibenzofuran that the molecules were disordered with an alternative orientation only of 9 per cent, and that the two orientations were related to each other by a rotation through p about the axis which passed through the center of mass and was perpendicular to the furan ring. The reorientation proceeds naturally by surmounting a certain energy barrier as a classical process. Therefore, the possibility remains that the heat-capacity anomaly observed at T1290 K originates from a glass transition, and not from a phase transition, associated with the orientational disorder of molecules remaining in only a little of the sample. The enthalpy-relaxation processes observed in the glass-transition-temperature region have been tracked as a function of time and characterized in terms of the following stretched exponential function to derive information about the relaxation processes:(6) DH(t)=DH(0)·exp{−(t/t)b};

0QbE1,

(1)

where t and b denote a characteristic time and a non-exponentiality parameter, respectively. When b=1, the function is exponential, and the deviation of b from 1 is recognized as a measure of non-exponentiality of the process. The b values for the relaxation processes in the crystalline state have been found to be close to 1.(7–9) The reason would be that all the molecules are essentially fixed in their positions and, thus, the activation energy for the reorientation of one molecule is rather independent of the orientations of the other molecules in the crystalline state. If so, bQ1 is understood to be caused by a distribution of activation energies (therefore relaxation times) differing from molecule to molecule, for example, due to the presence of impurities or

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FIGURE 1. Equilibrium temperature of fusion plotted against the inverse melt fraction f −1 of dibenzofuran. ——, The curve fitted by using Mastrangelo’s equation.

many reorientation processes. And, in the case where the relaxation function is of a remarkably non-exponential form, it would be very difficult to analyze the relaxation processes in order to derive the activation parameters.

FIGURE 2. Equilibrium temperature of fusion against the inverse melt fraction f −1 of fluorene. ——, The curve fitted by using Mastrangelo’s equation.

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In the present study, heat capacities of the above two compounds were remeasured for the purpose of examining whether the anomalies at T1290 K were accompanied simultaneously by the enthalpy-relaxation effects characteristic of a glass transition. The enthalpy-relaxation process observed in reality was tracked for a long time so as to examine the distribution of relaxation times. This is attractive, since Gerkin et al.(10) have reported that the molecule is not exactly planar, but pseudo-planar, with an angle of 0.023·p between the two planes of the benzene rings and the situation would be considered to bring some distribution into the activation parameters for the molecular reorientation.

2. Experimental Commercial-reagent dibenzofuran, purchased from Tokyo Chemical Ind. Co., Ltd., was purified by recrystallization from C2 H5OH three times, and from CH3(CH2 )4CH3 once, and by subsequent vacuum sublimation at T1323 K. The purified sample was loaded into a calorimeter cell under helium gas. The powdered sample was melted under helium gas at pressure p185 kPa, resulting in dense packing of the sample in the cell, and another powdered sample was added to the cell after cooling to room temperature. This process was repeated three times and finally the cell was sealed vacuum-tight under helium gas with p=0.1 MPa. The mass of the sample was 16.639 g (X98.928 mmol), and the volume of unoccupied space within the cell was evaluated to be 4.417 cm3 at room temperature. Heat capacities were measured in the temperature

TABLE 1. Molar heat capacities Cs, m of dibenzofuran; R=8.31451 J·K−1·mol−1 T K

Cs, m R

Crystal First series 245.12 18.61 248.08 18.85 251.05 19.08 254.02 19.31 256.99 19.55 259.96 19.78 262.94 20.03 265.92 20.24 268.90 20.48 271.89 20.73 274.88 20.97 277.87 21.22 280.87 21.46 283.87 21.71 286.88 21.95 289.90 22.20 292.92 22.44 295.96 22.67 299.00 22.90

T K

Cs, m R

T K

Cs, m R

T K

Cs, m R

301.60 303.31 304.62 306.18 308.53 311.43 314.32 317.22 320.13 323.04 325.95 328.87 331.79 334.71 337.63 338.01 340.00 341.99 343.99 345.98 347.97

23.11 23.25 23.36 23.55 23.87 24.31 24.71 25.12 25.51 25.82 26.05 26.27 26.49 26.74 26.99 27.02 27.19 27.38 27.57 27.77 27.97

349.96

28.21

297.90 301.42 304.90 308.33 311.74 315.16 318.59 322.02 325.45 328.88 332.31 335.73 339.14

22.83 23.14 23.51 23.95 24.40 24.85 25.32 25.74 26.02 26.26 26.54 26.84 27.16

Second series 233.03 17.65 236.70 17.94 240.36 18.23 244.01 18.51 247.65 18.80 251.28 19.08 254.91 19.37 258.53 19.65 262.14 19.94 265.75 20.23 269.35 20.51 272.94 20.81 276.53 21.09 280.11 21.39 283.68 21.68 287.25 21.96 290.81 22.26 294.36 22.54

Liquid Third series 361.11 31.88 364.73 32.07 368.37 32.28 372.01 32.47 375.66 32.68

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931

range T=245 K to T=375 K by an intermittent-heating method with an adiabatic calorimeter described previously.(8) Fluorene, commercially available from Tokyo Chemical Ind. Co., Ltd., was purified and loaded into the calorimeter cell in the same way as dibenzofuran. The mass of the sample was 17.014 g (X102.356 mmol), and the unoccupied volume of the cell was found to be 5.518 cm3 at room temperature. Heat capacities were measured in the temperature range T=200 K to T=419 K by the same method and with the same calorimeter as used for dibenzofuran. A platinum resistance thermometer (Minco Products S1059, U.S.A.) was used after the temperature scale was transferred from another thermometer calibrated on ITS-90. The imprecision and the inaccuracy of the heat capacity obtained were estimated previously to be better than 20.06 per cent and 20.3 per cent, respectively.(8)

3. Results and discussion Purities of the samples were determined by a fractional-melting experiments. The temperature of the calorimeter cell during fusion was followed for 60 min

FIGURE 3. Molar heat capacities Cs, m of dibenzofuran: w, present work; r, Chirico et al.(3) The upper and lower lines indicate the assumed molar-heat-capacity curves in the equilibrium and the frozen-in states, respectively, with respect to the reorientational degree of freedom of the molecule relevant to a glass transition.

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after each energy supply, and the equilibrium temperature was determined by extrapolating the temperature-against-time relation to infinite time with an exponential function. Figures 1 and 2 show the equilibrium temperatures of fusion against the inverse f −1 of the fractions melted of dibenzofuran and fluorene, respectively. Since the plots of temperature against f −1 exhibited curvature, indicating the presence of solid-soluble impurities, Mastrangelo’s equation(11) was used to derive the mole-fraction purities and the triple-point temperatures. The absolute value of fusion enthalpy was determined from a combination of the below-mentioned heat-capacity measurements and of the experiment of heating the calorimeter cell at a stretch; in the latter experiment, the temperature was increased from 342.27 K to 359.56 K for dibenzofuran, and from 383.50 K to 391.01 K for fluorene. The baseline for the molar heat capacities in the crystalline state is expressed in the equation: Cs, m /(J·K−1·mol−1 )=2.694·10−3·(T/K)2−1.132·(T/K)+2.991·102,

(2)

for dibenzofuran, and Cs, m /(J·K−1·mol−1 )=8.238·10−4·(T/K)2+4.647·10−1·(T/K)+1.005·10,

(3)

FIGURE 4. Spontaneous temperature drift rates observed during the series of heat-capacity measurements of dibenzofuran in the crystalline state: w, sample precooled rapidly at 0.165 K·s−1; W, sample precooled slowly at 1.07 mK·s−1 .

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for fluorene. For dibenzofuran, the molar enthalpy of fusion was determined to be (19.3420.02) kJ·mol−1 , the mole-fraction purity to be 0.9993, and the triple-point temperature to be Ttr=355.24 K which was 50 mK lower than the literature value (after conversion to the ITS-90).(3) For fluorene, the molar enthalpy of fusion was determined to be (19.4020.02) kJ·mol−1 as an average of two measurements (19.39 and 19.40) kJ·mol−1 , the mole-fraction purity to be 0.9971, and the triple-point temperature to be Ttr=387.78 K which was lower by 0.13 K than the literature value (after conversion to the ITS-90).(4) The experimental molar heat capacities Cs, m at saturated vapor pressure of dibenzofuran are tabulated in table 1 and shown in figure 3 together with the results of Chirico et al.(3) The correction for vaporization was made using the vapor pressure.(3, 12–14) The temperature dependence of the vapor pressures was expressed by the Antoine equation: lg(p/p°)=3.31−1340/{(T/K)−149},

(4)

where p°=101.325 kPa. The correction was negligible; only 0.004 per cent even at T=375 K. The heat capacities reported by Chirico et al. are larger by 1.6 per cent at T1340 K and by 0.60 per cent at T1370 K than the present values. Anomalous spontaneous temperature drifts due to enthalpy evolution or absorption by the sample were observed in the temperature-rating periods of series of measurements on the intermittent heating in the temperature range 260 K to 320 K. The drifts were followed in the rating periods for 8 min after each energy input of 30 min duration, while the equilibration of the calorimeter cell was achieved in 13 min.(8) Figure 4 shows the temperature dependence of the observed drift rates. The

FIGURE 5. Enthalpy relaxation process at T1303.7 K of dibenzofuran, tracked for a long time after a sudden temperature decrease. – – –, A ‘‘natural’’ drift due to the inevitable heat leak between the calorimeter cell and its surroundings even under adiabatic conditions.

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sample precooled rapidly at 0.165 K·s−1 exhibited an exothermic effect starting at T1260 K, showing its maximum at T=297 K, and subsequently an endothermic effect starting at T=305 K showing its maximum at T1313 K. The sample precooled slowly at 1.07 mK·s−1 , on the other hand, exhibited an exothermic effect considerably smaller than the sample precooled rapidly, and a rather large endothermic effect starting at T=295 K and showing its maximum at T=310 K. The anomalous drifts turned back to the normal ones at T1330 K in both samples. A heat-capacity jump associated with the anomaly could be recognized clearly at T1320 K. Such behavior is typical of a glass transition. The transition is reasonably interpreted as originating from freezing-in of the molecular reorientation, since this is only a configurational degree of freedom in the disordered state in the relevant temperature range as described above.(5) The molar-heat-capacity jump associated with the transition was estimated to be (6.820.2) J·K−1·mol−1 at T=316 K. Figure 5 shows the result of the spontaneous endothermic temperature drift tracked under the adiabatic conditions for 10 h at T1303.7 K after a sudden temperature

FIGURE 6. Arrhenius plots of relaxation times t associated with the glass transition in the crystalline state of dibenzofuran. ——, The straight line fitted by using an Arrhenius equation.

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935

decrease. The results were fitted by the stretched exponential function, equation (1), with addition of a term of ‘‘natural temperature drift’’ due to some inevitable heat leak remaining. The t and b values were obtained as 4.5 ks and 0.97, respectively, with the resulting standard deviation of 1.38·10−4 K. The b value is quite close to 1.0, indicating that the relaxation is almost of the exponential form and that there is only a small distribution of the relaxation times. Based on the result that the relaxation is essentially characterized to be of the exponential function, the characteristic times t of the enthalpy relaxations were calculated, according to the method described previously in detail,(15) by using the following equation, the above-obtained heat-capacity jump, and the spontaneous drift rates given in figure 4: dDHc /dt=−DHc /t.

(5)

The temperature dependence of the derived relaxation times, plotted in figure 6, is well expressed by an Arrhenius equation t=t0·exp{Doa /RT} with t0=6.31·10−14 s and Doa=(9825) kJ·mol−1 . The glass-transition temperature, at which the relaxation time became 103 s, was estimated from the dependence to be Tg=(31621) K. The experimental molar heat capacities Cs, m at saturated vapor pressure of fluorene are shown in figure 7 together with the result by Finke et al. and the numerical values

FIGURE 7. Molar heat capacities Cs, m of fluorene: w, present work; r, Finke et al.(4) The upper and lower lines indicate the assumed molar-heat-capacity curves in the equilibrium and the frozen-in states, respectively, with respect to the reorientational degree of freedom of the molecule relevant to a glass transition.

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H. Fujita, H. Fujimori, and M. Oguni TABLE 2. Molar heat capacities Cs, m of fluorene; R=8.31451 J·K−1·mol−1

T K

Cs, m R

Crystal First series 200.20 15.68 202.14 15.83 205.43 16.08 208.72 16.33 212.00 16.59 215.27 16.84 218.55 17.10 221.82 17.36 225.09 17.63 228.36 17.89 231.63 18.18 234.89 18.46 238.15 18.70 241.41 18.97 244.67 19.24 247.93 19.50 251.19 19.77 254.45 20.04 257.71 20.31 260.96 20.59 264.22 20.87 267.47 21.16 270.72 21.43 273.98 21.71 277.23 21.98 280.48 22.26 283.73 22.54

T K

Cs, m R

T K

Cs, m R

T K

Cs, m R

286.99 290.25 293.51 296.76 300.01 303.24 306.44 309.62 312.77 315.91 319.04 322.17 325.30 328.42 331.54 334.65 337.76 340.86 342.97 346.14 349.29 352.90 356.26 359.61 362.95 366.27 369.58 372.88 376.17 379.45

22.82 23.11 23.39 23.67 23.97 24.29 24.63 25.01 25.44 25.92 26.42 26.92 27.41 27.85 28.25 28.62 29.00 29.37 29.62 30.02 30.41 30.88 31.31 31.73 32.17 32.59 33.00 33.34 33.65 34.00

382.71

34.48

284.87 288.16 291.45 294.75 298.04 301.32 304.57 307.79 310.98 314.14 317.29 320.43 323.58 326.72 329.85 332.98

22.64 22.93 23.21 23.49 23.79 24.09 24.42 24.80 25.22 25.65 26.12 26.62 27.14 27.61 28.03 28.42

Second series 196.04 15.36 199.37 15.62 202.69 15.87 206.01 16.12 209.32 16.38 212.63 16.64 215.94 16.90 219.24 17.15 222.54 17.42 225.83 17.68 229.13 17.96 232.42 18.26 235.70 18.50 238.98 18.76 242.27 19.04 245.55 19.31 248.83 19.57 252.11 19.84 255.39 20.11 258.66 20.39 261.94 20.67 265.21 20.96 268.48 21.24 271.76 21.52 275.03 21.79 278.31 22.07 281.59 22.35

Liquid Third series 391.88 35.64 394.89 35.82 397.91 36.00 400.92 36.18 403.94 36.36 406.97 36.54 409.99 36.73 413.02 36.90 416.05 37.09 419.09 37.27

are collected in table 2. The correction for vaporization was made using vapor pressures:(13, 16, 17) lg(p/p°)=3.61−1530/{(T/K)−142}

(6)

where p°=101.325 kPa. The correction was evaluated to be negligible: only 0.008 per cent even at T=400 K. Good agreement was obtained between the present and literature results. The molar heat-capacity jump was observed definitely and estimated to be (7.020.3) J·K−1·mol−1 at T=316 K. Figure 8 shows the rates of spontaneous temperature drifts observed in the temperature-rating periods during two series of measurements at T1300 K. The drifts were followed in the rating periods for 8 min after each energy input of 30 min. The sample precooled rapidly exhibited, in the subsequent intermittent heating process, a larger exothermic effect in the low-temperature region and a smaller endothermic one in the high-temperature region, than the sample precooled slowly. These results definitely indicate the presence of a glass transition in crystalline fluorene. The glass transition was recognized to take place at almost the same temperature as for dibenzofuran from the fact that the temperature

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937

FIGURE 8. Spontaneous temperature drift rates dT/dt observed during the series of heat-capacity measurements of fluorene in the crystalline state. w, Sample precooled at 0.155 K·s−1; W, sample precooled at 0.132 K·s−1 .

dependences of spontaneous temperature drift rates were almost same for both samples of fluorene and dibenzofuran precooled rapidly at 10.16 K·s−1 . Figure 9 shows the spontaneous temperature drift for fluorene tracked under adiabatic conditions at T1300 K just after a sudden temperature decrease. The results were fitted in terms of the stretched exponential function, equation (1), with a term

FIGURE 9. Enthalpy relaxation process at T1300 K of fluorene, tracked for a long time after a sudden temperature decrease. – – –, A ‘‘natural’’ drift due to the inevitable heat leak between the calorimeter cell and its surroundings even under adiabatic conditions.

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for the inevitable heat leak. The fitting was very good with the standard deviation of 1.06·10−4 K. The b value was derived to be 0.77, considerably different from 1, suggesting the presence of a certain distribution of relaxation times in the process tracked. Since the procedure for deriving the relaxation times based on equation (5) could be taken only in the case where the relaxation process was characterized essentially by a single relaxation time, no effort was made to derive relaxation times of the process. It is noted that the b values are quite different between dibenzofuran and fluorene. In view of the large deviation of b from 1, the non-exponentiality of the relaxation function in fluorene should not be considered as due to the impurities of mole fraction 0.0029, but to the non-planarity of the molecule.(10) The presence of head and tail for the molecular plane gives rise to many potential curves for the reorientational process of the molecule even in the crystalline state. Why this effect hardly appears in dibenzofuran is quite open to question. Somehow, such characterization of enthalpy-relaxation process as that using the stretched exponential function is expected to have the possibility of giving rise to new detailed information about the motion of molecules in the crystalline state. This work was supported partly by the Grant-in-Aid for Scientific Research No. 6453017 from the Ministry of Education, Science and Culture, Japan. REFERENCES 1. Suga, H.; Seki, S. J. Non-Cryst. Solids 1974, 16, 171. 2. Suga, H. Ann. NY. Acad. Sci. 1986, 484, 248. 3. Chirico, R. D.; Gammon, B. E.; Knipmeyer, S. E.; Nguyen, A.; Strube, M. M.; Tsonopoulos, C.; Steele, W. V. J. Chem. Thermodynamics 1990, 22, 1075. 4. Finke, H. L.; Messerly, J. F.; Lee, S. H.; Osborn, A. G.; Douslin, D. R. J. Chem. Thermodynamics 1977, 9, 937. 5. Reppart, W. J.; Gallucci, J. C.; Lundstedt, A. P.; Gerkin, R. E. Acta Cryst. 1984, C40, 1572. 6. Williams, G.; Watts, D. C. Trans. Faraday Soc. 1970, 66, 80. 7. Okamoto, N.; Oguni, M.; Suga, H. J. Phys. Chem. Solids 1989, 50, 1285. 8. Fujimori, H.; Oguni, M. J. Phys. Chem. Solids 1993, 54, 271. 9. Matsuo, T.; Suga, H.; David, W. I. F.; Ibberson, R. M.; Bernier, P.; Zahab, A.; Fabre, C.; Rassat, A.; Dworkin, A. Solid State Commun. 1992, 83, 711. 10. Gerkin, R. E.; Lundstedt, A. P.; Reppart, W. J. Acta Crystallogr. 1984, C40, 1892. 11. Mastrangelo, S. V. R.; Dornte, R. W. J. Am. Chem. Soc. 1955, 77, 6200. 12. Hansen, P. C.; Eckert, C. A. J. Chem. Eng. Data 1986, 31, 1. 13. Sivaraman, A.; Kobayashi, R. J. Chem. Eng. Data 1982, 27, 264. 14. Nasir, P.; Sivaraman, A.; Kobayashi, R. J. Chem. Thermodynamics 1984, 16, 199. 15. Matsuo, T.; Oguni, M.; Suga, H.; Seki, S.; Nagle, J. F. Bull. Chem. Soc. Jpn. 1974, 47, 57. 16. Osborn, A. G.; Douslin, D. R. J. Chem. Eng. Data 1975, 20, 229. 17. Bradly, R. S.; Cleasby, T. G. J. Chem. Soc. 1953, 1690.