10020
J. Phys. Chem. B 2005, 109, 10020-10024
Molecular Dynamics and Residual Entropy in the Soft Crystal, SmE Phase, of 4-Butyl-4′-isothiocyano-1,1′-biphenyl Shin’ichi Ishimaru,† Kazuya Saito,*,† Satoaki Ikeuchi,†,‡ Maria Massalska-Arodz,§ and Waclaw Witko§ Department of Chemistry, Graduate School of Pure and Applied Sciences, UniVersity of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan, Research Center for Molecular Thermodynamics, Graduate School of Science, Osaka UniVersity, Toyonaka, Osaka 560-0043, Japan, and The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krako´ w, Poland ReceiVed: January 7, 2005; In Final Form: March 22, 2005
Molecular dynamics and resulting disorder in the soft crystal, smectic E (SmE) phase, were studied in detail for the title compound, 4-butyl-4′-isothiocyano-1,1′-biphenyl (4TCB), by 1H NMR spectroscopy and adiabatic calorimetry. The ordered crystal phase of 4TCB was realized for the first time under ambient pressure after long two-step annealing and used as the reference state in the analysis of the experimental results. Four motional modes were identified in the SmE phase through the analysis of the 1H NMR T1. The residual entropy was determined as ca. 6 J K-1 mol-1. This magnitude implies that most of the disorder in the SmE phase at high temperatures is removed on cooling except for the head-to-tail disorder of the rod-shaped 4TCB molecule. Standard thermodynamic functions are tabulated below 375 K.
1. Introduction Although the basic mechanism of appearance of mesophases such as plastic and liquid crystals on the course of melting of the perfect crystal was established long ago,1,2 there are many exotic mesophases beyond the basic understanding. A soft crystalline phase called smectic E (SmE) phase belongs to such a class of mesophases. The SmE phase was historically classified as a liquid crystalline phase, but later identified as a kind of three-dimensional crystal though it is soft. The SmE phase is found in compounds or a mixture consisting of rodlike molecules similarly to liquid crystalline phases such as nematic, SmA, and SmC phases. Several studies on molecular motions in SmE phase have been done by dielectric,3-5 2H NMR,6 and quasielastic neutron scattering7,8 measurements. A very slow motion identified as the molecular reorientation around the molecular short axis, flipping motion of phenyl rings, translational diffusion and libration around the molecular long axis were detected. X-ray diffraction studies have shown that even the molecular rotation around its long axis should be restricted.9,10 Due to the limited temperature range where the SmE phase appears in most systems, details of the molecular dynamics and resulting disorder in the SmE phase still remain unclear. 4-n-Alkyl-4′-isothiocyano-1,1′-biphenyls (CnH2n+1-C6H4C6H4-NCS, abbreviated as nTCB in this paper) show the SmE phase around room temperature for n ) 2-10. The title compound, 4TCB, belongs to this series of compounds having the SmE phase. 4TCB exhibits a different behavior from other members of the series: The SmE phase at room temperature can be cooled to liquid-nitrogen temperature, which is much below the expected transition temperature between the ordered * To whom correspondence should be addressed. Tel: +81-29-853-4239. Fax: +81-29-853-6503. E-mail:
[email protected]. † University of Tsukuba. ‡ Osaka University. § Polish Academy of Sciences.
crystalline phase and the SmE phase. No ordered crystalline phase has been reported under ambient pressure. The ordered crystalline phase was formed only under high pressure above 88.7 MPa.11 This peculiar phase behavior of 4TCB opens the possibility to study the properties of the SmE phase in detail over a wide temperature range. Indeed some studies have been done on 4TCB.3,5 If the ordered crystalline phase is obtained by suitable thermal treatments, the analysis of experimental data on the SmE phase becomes easy and reliable by regarding the ordered crystalline phase as a reference state. Besides, precise calorimetry on both SmE and ordered crystalline phases will give the residual entropy of the SmE phase for the first time. Such information will contribute greatly to the basic understandings of the SmE phase. In this paper, the results of precise calorimetry and 1H NMR measurements on 4TCB are described. The formation of the ordered crystalline phase is reported. Molecular dynamics and resultant disorder in the SmE phase is revealed and discussed. 2. Experimental Section The 4TCB sample was kindly supplied by Prof. R. Dabrowski, the Military University of Technology in Warsaw,12,13 and used as obtained for thermal measurements at first and then recrystallized from toluene to measure 1H NMR. Heat capacity was measured using a laboratory-made adiabatic calorimeter, the details of which were described elsewhere.14 The measurement was performed by the so-called intermittent-heating adiabatic method in a heating direction. The sample was loaded into a gold-plated calorimeter vessel. The vessel was evacuated for 1 h and sealed after introducing a small amount of helium gas (105 Pa at room temperature), which serves as heat conduction gas inside the vessel. The mass of the sample was 1.7999 g (6.7312 mmol) after the buoyancy correction. The sample contributed to the total heat capacity by 22% at 50 K, 17% at 100 K, 20% at 200 K, 25% at 300 K, and 30% at 375 K. The working thermometer was a platinum
10.1021/jp0501244 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/22/2005
Soft Crystal, SmE Phase, of 4TCB
Figure 1. Measured heat capacities of the quenched (open circle) and annealed (plus-sign) SmE phase, and of the ordered crystalline phase (filled circle) of 4TCB.
resistor (MINCO, S1059), the temperature scale of which is based upon the ITS-90. The purity of the calorimetric sample was 99.94 mol % as determined by cryometry. The NMR measurements were conducted on a quenched sample at first and remeasured after annealing the sample. 1H NMR measurements were performed by a Bruker MSL-300 NMR system applying a solid-echo pulse sequence to obtain spectra and a saturation-recovery sequence to determine T1. The experimental error in T1 was estimated to be within 10%. The sample temperature was controlled by the N2 gas flow method using a Bruker BVT-1000 controller with an accuracy of 1 K. 3. Results and Discussion A. Formation of the Ordered Crystalline Phase by Annealing. The SmE phase was quenched first from room temperature to liquid-nitrogen temperature at a cooling rate of -0.5 K min-1 around 250 K. Although a small heat evolution (80 µW or experimentally 0.5 mK min-1) was detected around 225 K, the heat capacity measurement could be performed without serious difficulties up to room temperature. The results are shown in Figure 1. Since the heat evolution was encountered around 225 K, the sample was annealed at 223 K for 23 h, after which the heat evolution ceased completely. The succeeding measurement from liquid-nitrogen temperature to room temperature yielded slightly different heat capacities as shown in Figure 1. Although the difference in heat capacity is definitely beyond the experimental imprecision, the overall temperature dependence closely resembles that of the quenched SmE phase. Besides, the heat evolution was again encountered not around 225 K but around 255 K (250 µW or 1.5 mK min-1). Annealing of the sample was performed at 255 K, accordingly. The heat evolution ceased only after 100 h. The sample shows the smaller heat capacities below 270 K than those of the previous measurements on the quenched and annealed (at 223 K) samples, and undergoes a first-order phase transition around 284 K as in Figure 1. Above this phase transition, the heat capacity coincides with those of the SmE phase. Since the location of the thermal anomaly is reasonably close to the extrapolated one from the high-pressure DTA results,11 it is concluded that the sample after the two-step anneal is in the ordered crystalline phase. The successive ordering phenomenon during the anneal was also detected in the 1H NMR line width. Figure 2 shows a time evolution of the full width at half-maximum (∆ν1/2) of the 1H NMR line observed at the annealing temperatures, 225 and 255 K. The ∆ν1/2 of 1H NMR line, ca. (15 ( 0.1) kHz, observed in
J. Phys. Chem. B, Vol. 109, No. 20, 2005 10021
Figure 2. Time evolution of full width at half-maximum of 1H NMR line in 4TCB at annealing temperatures. t ) 0 corresponds to the time when the sample was quenched from room temperature to 225 K and at t ) 22 h (shown by a broken line) the sample was heated to 255 K.
4TCB quenched from room temperature to 225 K was readily increased and reached a constant value, (26 ( 0.5) kHz. The drastic growth of the ∆ν1/2 implies that molecular motion is damped during this first stage of anneal. During the second anneal at 255 K, the ∆ν1/2 showed further increase to (28 ( 1) kHz. It is noted that the utilization of adiabatic calorimetry is crucial to confirm the completion of annealing because the linewidth changes around the midpoint where the portions of old and new phases are comparable. B. Heat Capacity and Phase Transition. The heat capacity of the quenched SmE phase was measured by cooling down the sample after it melted once around 355 K. The temperature dependence of heat capacity of the quenched SmE phase exhibits a hump between 150 and 250 K. The integration of the hump yields the excess enthalpy and entropy involved as 3 kJ mol-1 and 15 J K-1 mol-1. This anomaly at 250 K seems to correspond to that detected in the differential scanning calorimetry (DSC).15 Since the temperature is close to that where the motional correlation time becomes 103 s as extrapolated from the dielectric results,3,5 the anomaly was previously suggested to be due to a glass transition corresponding to the freezing-in of the head-to-tail disorder.5 It is well-known that, around a glass transition, heat capacity shows a positive jump (larger heat capacity at higher temperature) and characteristic enthalpy relaxation is observed in adiabatic calorimetry.16 In the present experiments, however, both features were not observed. The nature of the hump is open at present even considering the results of 1H NMR described later. Although there is a possibility that the hump corresponds to some phase transition of a higher-order, the quenched sample is assumed to be in the SmE phase. The heat capacity of the ordered crystalline phase was measured from 6 K after suitable sample treatment. Its temperature dependence shown in Figure 3 is typical and shows no anomaly suggesting the occurrence of any phase transitions and glass transitions. Above 270 K, however, the heat capacity is larger than that of the SmE phase, where molecular dynamics is highly excited. This apparent inconsistency can be resolved by taking the following fact into account: The heat capacity of a free rotor is smaller than the limiting heat capacity of an oscillator by the contribution of the potential energy. It is plausible that the motion of a whole molecule or a part of the molecule is restricted in the ordered crystalline phase, whereas it is almost free in the SmE phase. By repeating anneal and measurement cycles, the temperature of the ordered crystal-SmE phase transition was determined to be (284.1 ( 0.2) K. The enthalpy and entropy of transition
10022 J. Phys. Chem. B, Vol. 109, No. 20, 2005
Ishimaru et al. TABLE 1: Standard Thermodynamic Quantities of 4TCB
Figure 3. Measured heat capacities of the quenched SmE phase and isotropic liquid (open circle) and of the ordered crystalline phase (filled circle) of 4TCB.
are 9.567 kJ mol-1 and 33.67 J K-1 mol-1, respectively. The entropy of transition is nearly the same as the entropy of fusion of the SmE phase. This means that a molecular order in the SmE phase is just intermediate between the ordered crystal and isotropic liquid in terms of entropy. The volume of transition is estimated as 9.5 cm3 mol-1 from the high-pressure data [(dTtrs/ dp) ) 0.283 K MPa-1]11 using the Clapeyron formula. C. Fusion and Cryometry. 4TCB melted around 355 K inside the adiabatic calorimeter. By applying the so-called fractional melting method utilizing the melting point depression phenomenon, the temperature of fusion of the pure compound (calorimetric sample) was obtained as 355.37 K (355.32 K) assuming the liquid-soluble and solid-insoluble impurities. From the dependence of equilibrium temperature on the fraction melted, the purity of the calorimetric sample was estimated to be 99.94 mol %. The enthalpy and entropy of fusion was determined as (11.690 ( 0.005) kJ mol-1 and (32.89 ( 0.01) J K-1 mol-1, respectively. D. Thermodynamic Functions and Residual Entropy. The measured heat capacities were smoothed out by least-squares methods and integrated in appropriate ways from low temperatures to yield standard thermodynamic functions. Contributions below the lower temperature limit of the experiment were estimated assuming the Debye model for the lattice vibrations. Resultant thermodynamic functions are tabulated for the equilibrium phase sequence in Table 1 at round temperatures. The SmE phase has a higher Gibbs energy than the ordered crystalline phase below the equilibrium ordered crystal-SmE phase transition temperature (284.1 K). The difference in Gibbs energy amounts to 5.8 kJ mol-1 at T ) 0 K, which is equal to the difference in enthalpy. The residual entropy of the SmE phase is estimated to be 6.2 J K-1 mol-1 while assuming that the ordered crystalline phase obeys the third law of thermodynamics. It is noted that this is the first estimate of the residual entropy for any SmE phase. This estimation stands on the fact that the SmE phase can be supercooled to very low temperatures in 4TCB. For mesogenic substances, this is only a practical way to determine the residual entropy because the statistical calculation of the absolute entropy is impractical due to complex molecular structures. The absence of any phase transition on cooling the SmE phase suggests that the head-to-tail disorder of the molecules remains
[H°(T) H°(0)]/T, J K-1 mol-1
-[G°(T) H°(0)]/T, J K-1 mol-1
T, K
Cp°, J K-1 mol-1
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 284.1
6.46 26.30 46.84 65.19 85.35 95.62 108.47 119.71 130.76 141.68 152.30 162.80 173.37 184.10 195.03 206.1 217.4 228.7 240.3 252.3 265.0 278.3 292.3 307.0 322.6 340.1 361.1 385.8 396
Ordered Crystal 2.18 12.43 27.01 43.06 59.38 75.50 91.21 106.42 121.16 135.51 149.51 163.21 176.66 189.90 203.0 216.0 228.7 241.5 254.2 266.8 279.4 292.0 304.8 317.5 330.4 343.4 356.6 370.4 376.6
1.66 8.79 18.07 27.62 36.78 45.42 53.52 61.08 68.21 75.02 81.56 87.89 94.06 100.11 106.07 111.98 117.85 123.69 129.52 135.36 141.22 147.16 153.20 159.31 165.52 171.90 178.52 185.73 189.14
0.53 3.64 8.93 15.44 22.60 30.08 37.69 45.34 52.95 60.49 67.95 75.32 82.60 89.79 96.90 103.9 110.9 117.8 124.7 131.4 138.2 144.9 151.6 158.2 164.8 171.5 178.1 184.7 187.4
284.1 290 300 310 320 330 340 350 355.37
366.2 371.2 379.8 388.6 397.8 407.2 417.0 427.0 432.4
Smectic E 410.2 417.8 430.5 443.1 455.6 468.0 480.3 492.5 499.0
222.8 225.8 230.8 235.7 240.6 245.5 250.4 255.3 257.9
187.4 192.0 199.8 207.4 215.0 222.4 229.9 237.2 241.0
355.37 360 370 375
471.5 474.4 480.7 483.9
Isotropic liquid 531.9 538.1 551.2 557.6
290.8 293.2 298.2 300.6
241.0 244.9 253.0 257.0
298.15
378.1
Smectic E 428.2
229.8
198.3
S°(T) - S°(0), J K-1 mol-1
at low temperatures. Freezing-in of this head-to-tail disorder contributes to the residual entropy by R ln 2 (≈5.8 J K-1 mol-1) as widely observed in classic examples of simple molecular crystals such as N2O (ref 17) and substituted benzenes.18,19 The comparable magnitude of the residual entropy obtained for the SmE phase of 4TCB implies that most disorder in the SmE phase disappears on cooling. Namely, the 4TCB molecules that are highly excited in reorientation/libration around long and short axes3,5 find on cooling favorable and nearly unique orientations keeping their head-to-tail disorder. The anomalous hump in heat capacity between 150 and 250 K is probably associated with this ordering process. E. 1H NMR Spectra. Having established the condition for the formation of the ordered crystalline phase under ambient pressure, 1H NMR experiments were done on 4TCB samples after suitable treatment. Although the exact phase purity could not be confirmed, the line-width was consistent in each case. The 1H NMR line in 4TCB showed no fine-structure at all temperatures. Figure 4 shows temperature dependences of ∆ν1/2
Soft Crystal, SmE Phase, of 4TCB
J. Phys. Chem. B, Vol. 109, No. 20, 2005 10023
Figure 4. Temperature dependences of full width at half-maximum of 1H NMR line observed upon heating the 4TCB sample in the SmE phase (open triangle) and the ordered crystalline phase (filled circle) of 4TCB.
TABLE 2: 1H NMR Second Moment (M2) Values Calculated for a 4TCB Molecule in Various Motional Statesa motional states
M2/G2
static CH3- reorientation CH3- reorientation + single -C6H4- reorientation CH3- reorientation + two -C6H4- reorientation CH3- reorientation + axial reorientation
12.1 9.52 9.32 9.31 5.69
a The static conformation of the 4TCB molecule was determined by semiempirical method (AM1).21
of the 1H NMR line observed on heating the 4TCB sample in the SmE phase (open triangle) and the ordered crystalline phase (filled circle). The ∆ν1/2 values observed for the ordered crystalline phase were almost constant at ca. (30 ( 2) kHz between 150 and 280 K. A steep decrease in ∆ν1/2 to (13 ( 1) kHz was observed between 280 and 290 K, where the phase transition to the SmE phase occurs. On the other hand, that of the SmE phase decreased gradually from 24 kHz at 140 K to 12 kHz at 330 K with increasing temperature. For discussion of molecular motion, it is better to deal with the second moment (M2) of NMR line
∫-∞∞ω2f(ω) dω M2 ) ∫-∞∞ f(ω) dω
M2 ) γ p 4
2 2
I(I + 1) N
〈
∑ j,k
the optimum molecular geometry reached by the molecular modeling (AM1 method21), one can ascribe it to the methyl reorientation around the C3 axis. The 1H NMR line-width observed in the SmE phase is narrow in comparison with those in the ordered crystalline phase. This indicates that some molecular motions with large amplitude are still active even at 140 K in the SmE phase. Since the NMR line in this phase is not Gaussian, the details of molecular motions are discussed in the following section through the analysis of NMR relaxation. F. 1H NMR Spin-Lattice Relaxation Time (T1). 1H NMR T1 was measured to clarify molecular motions in detail. The nuclear magnetic relaxation rate T1-1 can generally be assumed to be the superposition of respective contributions expressed as
T1total-1 )
∑ T1-1
(2)
In case where the relaxation originates in the fluctuation of magnetic dipole-dipole interactions due to molecular motions, each T1 is given by the BPP-type function20
than with ∆ν1/2, where f(ω) is a shape function of the resonance line. The second moment M2 is directly related to the spin correlation in a crystal by a relation20
3
Figure 5. Temperature dependences of 1H NMR T1 observed upon heating the 4TCB sample in the SmE phase (open circle) and the ordered crystalline phase (filled circle). A solid line shows the best fit represented by a superposition of four BPP curves (each shown by dotted lines) and a vertical broken line shows the melting temperature observed in the NMR measurement.
〉
(1 - 3 cos2 θjk)2 rjk6
(1)
where γ and I are the gyromagnetic ratio and spin quantum number of the proton, N is the number of the proton in the unit cell, rjk is the distance between the jth and kth proton in the system, and θjk is the angle between a vector rjk and an external field. The braket indicates the average. The NMR line shape observed in the ordered crystalline phase of 4TCB was represented well by a Gaussian curve and in this case the ∆ν1/2 is simply related to M2 by ∆ν1/2 ) 2.35xM2. The ∆ν1/2 value (30 kHz) observed in the ordered crystalline phase corresponds to 9.0 G2 in terms of the M2 scale. Comparing the value with those collected in Table 2 calculated by averaging eq 1 over the several motions of a single molecule assuming
{
3 4τ τ + T1-1 ) γ2∆M2 2 1 + ω2τ2 1 + 4ω2τ2
}
(3)
where ∆M2 is the reduction in the second moment M2 caused by the motional mode, ω is the 1H Larmor frequency, and τ is the correlation time of the motion. The motional correlation time τ is reasonably assumed to obey the Arrhenius equation
τ ) τ0 exp(Ea/RT)
(4)
Here τ0 and Ea are the correlation time at infinite temperature and the activation energy of the motion, respectively. Temperature dependences of 1H NMR T1 observed upon heating the 4TCB sample in the SmE phase (open circle) and the ordered crystalline phase (filled circle) are shown in Figure 5. Although the ordered crystalline phase exhibited a simple T1 curve having a single minimum around 160 K, the complicated T1 behavior was observed for the SmE phase. The simple T1 behavior of the ordered crystalline phase can be reproduced well by a single BPP function with the fitting parameters of ∆M2 ) (2.9 ( 0.2) G2 and Ea ) (9.0 ( 1.0) kJ mol-1. The former
10024 J. Phys. Chem. B, Vol. 109, No. 20, 2005
Ishimaru et al.
TABLE 3: Motional Modes and Parameters Obtained by Curve Fitting of 1H NMR T1 on the Sm E Phase of 4TCB mode 1 mode 2 mode 3 mode 4
Ea/kJ mol-1
∆M2/G2
τ0/10-15 s
9.0 ( 0.5 18 ( 2 20 ( 2 95 ( 10
2.9 ( 0.3 1.4 ( 0.2 2.9 ( 0.3
500 ( 50 3.0 ( 0.3 8.0 ( 1.0
value coincides well to the difference in M2, 2.68 G2, calculated as that between motional modes assuming molecules that are rigid or undergoing a methyl reorientation (Table 2). The magnitude of the activation energy, ca. 10 kJ mol-1, is also of a typical magnitude reported for methyl reorientation.22 It is therefore concluded that in the ordered crystalline phase the nuclear magnetic relaxation is dominated by the methyl reorientation. This conversely means that the methyl reorientation is the only dominant molecular motion in this phase. The nuclear magnetic relaxation time, T1, could be measured in a wide temperature range between 140 and 365 K due to the supercooling of the SmE phase. This enables us to analyze the experimental T1 in detail as follows. The temperature dependence of T1 seems to be a superposition of three or more BPP curves and some arbitrariness is unavoidable in the curve fitting. Therefore, we assume that the motional parameters corresponding to the methyl reorientation remain the same in the SmE phase as those in the ordered crystalline phase: Intramolecular motion is considered to be scarcely affected by intermolecular potential, i.e., crystal structures. Under this assumption, the temperature dependence of T1 was decomposed to four BPP curves represented by eqs 3 and 4. Four motional modes are designated 1, 2, 3, and 4 according to the sequence of temperatures at which a corresponding BPP curve shows a minimum (see Figure 5). The motional parameters obtained for each mode by the fitting are listed in Table 3. Mode 3 is attributable to an axial reorientation of a whole molecule, which was implied from a reduced 1H NMR line width as discussed before. For mode 4, only the activation energy, (95 ( 10) kJ mol-1, was estimated because, due to melting at 284 K, only a decrease in T1 at the lower temperature side (i.e., slow motion side) of the BPP curve was observed. This motional mode can be identified as the reorientation of the molecular long axis around the short axes observed in the dielectric studies3,5 at kHz region with a large activation enthalpy, 94 kJ mol-1. It is difficult to ascribe a specific motion to mode 2. Considering a small ∆M2 value, it may be attributed to some local motions, such as flipping of the phenyl rings and tumbling of the alkyl terminal. The T1 results imply that at low enough temperature the methyl reorientation (mode 1) is the only mode present in the SmE phase as in the ordered crystalline phase. 4. Conclusion The ordered crystalline phase of 4TCB was formed under ambient pressure for the first time after two-step long annealing.
The proper annealing is crucial for the formation of the ordered phase. Inadequate annealing is probably the reason until now the formation was never observed under ambient pressure. Assuming the ordered crystalline phase obeys the third law of thermodynamics, the residual entropy of the SmE phase was for the first time estimated as 6.2 J K-1 mol-1, which is larger only slightly than R ln 2 attributable to the head-to-tail disorder. The 1H NMR T1 study in the Sm E phase of 4TCB implies the existence of four motional modes of molecules in this phase: (i) methyl reorientation, (ii) flipping of phenyl rings or tumbling of alkyl group, (iii) reorientation around the long axis, and (iv) head-to-tail reorientation. Relatively low activation energy of the molecular reorientation around the long axis is compatible with the softness of the SmE phase. On the other hand, the fact that only the methyl reorientation was observed in the ordered crystalline phase shows the tight molecular packing in it. The essential difference between the ordered crystalline and SmE phases is the presence/absence of the head-to-tail disorder. Acknowledgment. Support of Polish Committee for Scientific Research (Grant No. 1 PO3 060 28) is kindly acknowledged. References and Notes (1) Pople, J. A.; Karasz, F. E. J. Phys. Chem. Solids 1961, 18, 28. (2) Chandrasekhar, S.; Shashidhar, R.; Tara, N. Mol. Cryst. Liq. Cryst. 1970, 10, 337. (3) Urban, S.; Crzuprynski, K.; Dabrowski, R.; Gestblom, B.; Janik, J.; Kresse, H.; Schmalfuss, H. Liq. Cryst. 2001, 28, 691. (4) Drozd-Rzoska, A.; Rzoska, S.; Czuprynski, K. Phys. ReV. E 2000, 61, 5355. (5) Massalska-Arodz, M.; Schmalfuss, H.; Witko, W.; Kresse, H.; Wu¨rflinger, A. Mol. Cryst. Liq. Cryst. 2001, 366, 221. (6) Vaz, N. A.; Vaz, M. J.; Doane, J. W. Phys. ReV. A 1984, 30, 1008. (7) Richardson, R. M.; Leadbetter, A. J.; Carlile, C. J.; Howells, W. S. Mol. Phys. 1978, 35, 1697. (8) Richardson, R. M.; Leadbetter, A. J.; Frost, J. C. Mol. Phys. 1982, 45, 1163. (9) Doucet, J.; Levelut, A. M.; Lambert, M.; Leibert, L.; Strzelecki, L. J. Phys. (Paris) Colloq. 1975, 36, C1-13. (10) de Vries, A. Liquid Crystals; Saeva, F. D., Ed.; Dekker: New York, 1979; pp 1-71. (11) Massalska-Arodz, M.; Wu¨rflinger, A.; Bu¨sing, D. Z. Naturforsch. A 1999, 54, 675. (12) Czuprynski, K.; Dabrowski, R.; Przedmojski, J. Liq. Cryst. 1989, 4, 429. (13) Czuprynski, K. Mol. Cryst. Liq. Cryst. 1990, 192, 47. (14) Yamamura, Y.; Saito, K.; Saitoh, H.; Matsuyama, H.; Kikuchi, K.; Ikemoto, I. J. Phys. Chem. Solids 1995, 56, 107. (15) Mayer, J. Data unpublished. (16) Suga, H.; Seki, S. J. Non-Cryst. Solids 1974, 16, 171. (17) Atake, T.; Chihara, H. Bull. Chem. Soc. Jpn. 1974, 47, 2126. (18) Tozuka, Y.; Yamamura, Y.; Saito, K.; Sorai, M. J. Chem. Phys. 2000, 112, 2355. (19) Tozuka, Y.; Akutsu, H.; Yamamura, Y.; Saito, K.; Sorai, M. Bull. Chem. Soc. Jpn. 2000, 73, 2279. (20) Abragam, A. The Principle of Nuclear Magnetism; Clarendon Press: Oxford, U.K., 1961. (21) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Eamonn, F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902. (22) For example, Kumar, A.; Johnson, C. J. S. J. Chem. Phys. 1974, 60, 137.
