Entropic Contribution of Flexible Terminals to Mesophase Formation

Mar 18, 2010 - To understand the role of intramolecular degrees of freedom in forming mesophases, thermodynamic analysis was performed for ...
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Entropic Contribution of Flexible Terminals to Mesophase Formation Revealed by Thermodynamic Analysis of 4-Alkyl-4′-isothiocyanatobiphenyl (nTCB) Katsuya Horiuchi,† Yasuhisa Yamamura,† Robert Pełka,†,‡ Masato Sumita,†,§ Syuma Yasuzuka,† Maria Massalska-Arodz,‡ and Kazuya Saito*,† Department of Chemistry, Graduate School of Pure and Applied Sciences, UniVersity of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan, and The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Krakow 31-342, Poland ReceiVed: January 12, 2010; ReVised Manuscript ReceiVed: March 4, 2010

To understand the role of intramolecular degrees of freedom in forming mesophases, thermodynamic analysis was performed for 4-n-alkyl-4′-isothiocyanatobiphenyl (nTCB, n is the number of carbon atoms in the alkyl group), which exhibits the crystal E (CrE) phase as a mesophase. The heat capacities of 2TCB and 5TCB were measured by adiabatic calorimetry. Their entropies of transition (∆trsS) were compared with those of other nTCBs (n e 10). ∆trsS of the phase transition from the ordered crystal to CrE phase increased with their alkyl chain length, whereas that of fusion of the CrE phase remained essentially constant. These behaviors clearly show that the alkyl chain of nTCB is fully disordered even in the CrE phase. Through the comparison of ∆trsS among 5TCB, 4-pentyl-4′-cyanobiphenyl (5CB), and pentylbiphenyl, the role of the alkyl chain for the formation of mesophases is discussed. I. Introduction In molecular crystals, molecules are arranged with orders involving not only their positions but also orientations and intramolecular degrees of freedom. These forms of order are lost in a melting process from an ordered crystal to isotropic liquid (IL). When the compounds possess some stable mesophases between an ordered crystal and IL, the order is lost step by step.1 The partial loss of the orders yields, for example, soft crystal, smectic, and nematic phases as mesophases in a case of calamitic (rodlike) mesogens.1 Soft crystal phases such as crystal E, B, and H have positional (translational) order, and show no fluidity in contrast to nematic and smectic phases, accordingly. All of the soft crystal phases have a layered structure with two-dimensional order. The smectic phases, smectic A, C, etc., also have a layered structure and show a periodic order along, at least, one direction with some orientational order of long molecular axes. The nematic liquidcrystalline phase is the closest in nature to IL and possesses only a long-range orientational order. Although the calamitic mesogens can, in principle, pass many of these mesophases with gradual decrease in the long-range order, most mesogens exhibit a limited number of mesophases.1 The mesophases exhibited by calamitic mesogens can be classified according to partial disorder of molecular position and/or orientation.1 Traditional classification does not take into account the intramolecular degrees of freedom. This is validated by results of many simulations2–6 for systems consisting of rigid anisotropic particles, which display phase diagrams including smectic and nematic phases between an ordered crystal and IL. Many actual mesogens have intramolecular degrees of freedom besides those of rigid particles. Most mesogens certainly possess a fairly rigid core moiety such as biphenyl, * Corresponding author. E-mail: [email protected]. † University of Tsukuba. ‡ Polish Academy of Sciences. § Present address: National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan.

which plays a central role in the formation of mesophases. In addition, the mesogens have a variety of terminal groups,7,8 such as cyano (-CN) and nitro (-NO2) groups, alkyl chain, and so on. In calamitic mesogens, various combinations of the core and the terminal parts yield a variety of mesophases. One of the typical terminal groups of mesogens is a linear alkyl chain, which enables us to control the mesophases by changing its length. The alkyl chain has conformational degrees of freedom (gauche and trans conformations). The molecular conformation is ordered in an ordered crystal, whereas the order is lost in IL. That is, the intramolecular order must be lost at some step(s) from an ordered crystal to IL. To specify the step where and the way how the intramolecular order is lost, therefore, is very important for understanding the roles of conformational degrees of freedom in the formation of mesophases. However, the collapse of the intramolecular order and the contribution of intramolecular degrees of freedom to the formation of mesophases have not been understood fully, though some computer simulations assuming molecular flexibility were reported recently.9–12 To clarify these issues, it is important to investigate the intramolecular disorder and dynamics in a mesophase resembling closely the ordered crystalline phase. The crystal E (CrE) phase is the closest to an ordered crystal among orthogonal mesophases exhibited by calamitic mesogens.1 The CrE phase has a layered structure but has no fluidity. That is, the CrE phase has the periodic positional order. The molecules are arranged in layers with orthorhombic symmetry and herringbone array.1 The vertical orientational order (head-to-tail order) of the molecules is lost due to reorientational motion around short axes. Rotation of the molecule around the molecular long axis perpendicular to the layer is restricted in the CrE phase. Accordingly, the orientational order of molecules around that axis is lost only partially. One of the mesogenic series showing the CrE phase is 4-alkyl4′-isothiocyanatobiphenyl (abbreviated as nTCB or nTB, with n being the number of carbon atoms in the alkyl chain, Scheme

10.1021/jp100301r  2010 American Chemical Society Published on Web 03/18/2010

Entropic Role of Flexible Terminals of Mesogens

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SCHEME 1: 4-Alkyl-4′-isothiocyanatobiphenyl (nTCB) (a) and 4-alkyl-4′-cyanobiphenyl (nCB) (b)

1a). The molecules of nTCB have simple structures composed of biphenyl core, isothiocyanato group (-NCS), and alkyl chain. The phase diagram of nTCB (n ) 2-12)13,14 has already been reported. The nTCB (2 e n e 10) compounds show only the CrE phase as a mesophase below fusion, while the compounds with n ) 11 and 12 show CrE and SmA phases between the ordered crystal and IL.13,14 The molecular structure of nTCB is similar to that of 4-alkyl-4′-cyanobiphenyl (nCB, Scheme 1b), one of the most famous mesogens showing simple liquid crystalline phases (nematic and smectic phases).1,7 These molecules are only different in polar groups. In spite of the similarity of the molecular structure, however, nTCB exhibits not a nematic but a CrE phase as a mesophase.13 Dielectric13,15–18 and NMR19 investigations on the CrE phase of nTCB have been reported. Although these methods yield information on the motion of a molecule as a whole in the CrE phase, these are difficult to assess the (intramolecular) order of the nTCB molecules, such as the conformational order. To see the degree of order, we utilize entropy in this study. The (absolute) entropy as a thermodynamic function is a measure of the disorder of molecules because the entropy is related to the number of microscopic states by Boltzmann’s principle. In addition, the entropy of transition corresponds to the difference in the order of molecules between the two adjacent phases. The heat capacity measurement of nTCB has been limited to 3TCB20,21 and 4TCB19 so far. In this study, we measured the heat capacities of 2TCB and 5TCB and analyzed the order of molecules in the CrE phase while paying special attention to the intramolecular degrees of freedom through a thermodynamic approach. II. Experimental Section 2TCB and 5TCB were kindly supplied by Prof. R. Dabrowski, the Military University of Technology in Warsaw, and used as obtained for thermal measurements. The chemical purities of the samples were determined as 99.91 mol % (2TCB) and 99.88 mol % (5TCB) by using the fractional melting method, which utilizes the melting point depression. Heat capacity measurements for nTCB (n ) 2, 5) were performed using a laboratory-made adiabatic calorimeter, the details of which are described elsewhere.22 The measurement was carried out 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 sealed after introducing a small amount of helium gas (105 Pa at room temperature), which serves as heat conduction gas inside the vessel. The thermal equilibrium inside the vessel was attained within the normal time (1-30 min depending on temperature). The masses of the samples were 1.52134 g (6.35650 mmol) for 2TCB and 1.36481 g (4.84981 mmol) for 5TCB after the buoyancy correction. The sample contributed to the total heat capacity by 14% at 100 K, 20% at 200 K, and 27% at 300 K in the case of 2TCB, and 13% at 100 K, 16% at 200 K, and 20% at 300 K for 5TCB. The working thermometer was the

Figure 1. Molar heat capacity of 4-pentyl-4′-isothiocyanatobiphenyl (5TCB). Filled circles, as grown; open circles, after long annealing at 255 K.

platinum resistance thermometer (MINCO, S1059), the temperature scale of which is based upon the ITS-90. DSC measurements of 7TCB (supplied by Prof. R. Dabrowski), pentylbiphenyl (Wako Chemical), and methylbiphenyl (Wako Chemical) were carried out using a DSC apparatus (TA Instruments Q200). Quantum chemical calculations were performed on nTCB (2 e n e 5) in isolated condition by utilizing the Gaussian 03 package23 at the DFT/B3LYP/6-31G* level. The optimized atomic coordinates of molecules and molecular vibrational frequencies were listed in the Supporting Information. III. Results and Discussion 1. Heat Capacities and Phase Transitions of 5TCB and 2TCB. Two series of the heat capacity measurements of 5TCB were carried out from 6 K, as shown in Figure 1. In the first run, the heat capacity of the sample was measured after cooling down to 6 K from room temperature at ca. -1 K min-1 around 250 K. The obtained heat capacities are plotted by filled circles in Figure 1. A large hump was observed around 175 K. A similar large hump has also been seen in 3TCB.20 Since a strong heat evolution was encountered around 255 K with increasing temperature, the sample was annealed at 255 K for about 2 weeks until the heat evolution ceased completely. Such a heat evolution was also observed in the as-cooled sample of 3TCB.20 After the long annealing, the heat capacity of 5TCB was measured from 6 to 360 K (second run), as shown in Figure 1 (open circles). No heat evolution was detected in this run of measurements. The heat capacities of the annealed sample are smaller than those of the as-cooled one in the first run. Since no hump was observed around 175 K, the annealed sample is probably in the most stable crystalline phase. In the result of the second run, there are three anomalies accompanied by latent heat at 285, 326, and 347 K, where supercooling phenomena were observed in separate runs. The observed supercooling phenomena and latent heats indicate that the three anomalies are due to first-order phase transitions. Considering the reported phase diagram of nTCB,13 the anomalies at 347 and 326 K are attributed to fusion from the CrE phase to IL and the phase transition from an ordered crystalline phase (CrII) to the CrE phase, respectively. The other anomaly at 285 K seems to be a phase transition between two crystalline phases, CrII and CrIII, the latter of which has not been identified previously. The temperatures (Ttrs), enthalpies (∆trsH), and entropies (∆trsS) associated with the three anomalies were determined and

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Horiuchi et al.

TABLE 1: Thermodynamic Quantities Associated with the Phase Transitions of 5TCB and 2TCB phase transition

Ttrs/K

5TCB CrE-IL 347.53 ( 0.01a CrII-CrE 326.0 ( 0.1 CrIII-CrII 285.7 ( 0.1 2TCB CrE-IL 358.22 ( 0.01a Cr-CrE 328.2 ( 0.2

∆trsH/kJ mol-1 ∆trsS/J K-1 mol-1 10.85 ( 0.01 11.92 ( 0.01 5.516 ( 0.003 11.90 ( 0.01 8.180 ( 0.005

31.22 ( 0.01 36.58 ( 0.02 19.31 ( 0.01 33.21 ( 0.02 24.92 ( 0.02

a The temperatures are the temperature of fusion of the pure compounds determined by the fractional melting method utilizing the melting point depression phenomenon.

Figure 3. Alkyl chain length dependence of combined entropies of transition (Σ∆trsS ) ∆CrES + ∆fusS) of 4-alkyl-4′-isothiocyanatobiphenyl (nTCB, 2 e n e 10).13,19,20 ∆CrES, from the adjacent ordered crystal to the CrE phase (white bars); ∆fusS, from the CrE phase to IL (shaded bars). The dotted line is a guide for the eyes with a slope of 10 J K-1 (mol of -CH2-)-1.

Figure 2. Molar heat capacity of 4-ethyl-4′-isothiocyanatobiphenyl (2TCB).

summarized in Table 1, where ∆trsS was calculated as ∆trsH/ Ttrs. The thermodynamic quantities of CrII-CrE and CrE-IL phase transitions are consistent with the reported DSC result.13 The heat capacity of 2TCB was measured from 6 to 370 K, as shown in Figure 2. There are two large anomalies at 328 and 358 K. Since no anomalous behavior was observed below 328 K, we assume that the most stable low-temperature crystalline phase appears without any annealing process. Considering the reported phase diagram of nTCB,13 the anomalies at 328 and 358 K are attributed to the phase transition from the ordered crystal to the CrE phase and the fusion from the CrE phase to IL, respectively. The temperature, enthalpy, and entropy of transition were determined as summarized in Table 1. Those values are consistent with the reported DSC result.13 The heat capacity of 2TCB increases rather rapidly with increasing temperature below the phase transition temperature from the crystal to the CrE phase (328 K). The heat capacity of the CrE phase is smaller than that of the ordered crystal, though the CrE phase is a higher temperature phase than the ordered crystal. A similar temperature dependence of heat capacity was observed for 4TCB.19 On the other hand, 3TCB20 and 5TCB do not show such a trend. The difference probably arises from a kind of the so-called odd-even effect. The heat capacities of the most stable phases of 2TCB and 5TCB were smoothed out by the least-squares method 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 in the Supporting Information. 2. Alkyl Chain Length Dependence of Entropy of Transition. Although Boltzmann’s principle is very clear, it is generally quite difficult to analyze the absolute entropy on a microscopic

level of molecule. The degree of the disorder of an alkyl chain can, however, be deduced from the chain length dependence of entropy by virtue of the extensive nature of entropy. The slope in the entropy of transition against the chain length directly indicates the contribution from a methylene group to the entropy of transition.24–26 Since the entropy of transition reflects the ratio of numbers of microscopic states between the two adjacent phases, the slope is related to the degree of disorder in a specific phase if an appropriate reference state can be assumed.24–27 In neat nalkanes, the reference state can be either ordered crystals or IL.28 The following analysis also adopts the IL as the reference state. The entropies of transition of nTCB (∆CrES and ∆fusS) were collected first. The data of nTCB (n ) 2-5) were taken from our data obtained by adiabatic calorimetry. Those of nTCB (n ) 6-10) can be calculated (∆trsS ) ∆trsH/Ttrs) from the reported DSC results,13 though that of 7TCB is not acceptable in comparison with those of other compounds. We redetermined ∆CrES and ∆fusS of 7TCB to be 64.0 J K-1 mol-1 (Ttrs ) 322.5 K) and 32.2 J K-1 mol-1 (Tfus ) 344.3 K), respectively, by using DSC in this study. Figure 3 shows ∆CrES, ∆fusS and their sum (Σ∆trsS ) ∆CrES + ∆fusS) against the length of alkyl chain n. Here, Σ∆trsS virtually corresponds to the entropy of transition from the ordered crystals to IL. Σ∆trsS is roughly linear against n above n ) 4 with a slope of ca. 10 J K-1 (mol of -CH2-)-1, the broken line in Figure 3. This slope is essentially equal to that of the entropy of fusion of n-alkane against the number of methylene groups.24,28 This magnitude corresponds to the entropy associated with the conformational disordering of the methylene group (∼R ln 3 ≈ 9.1 J K-1 mol-1; R, gas constant) because the methylene group has three available conformations (two gauche and one trans forms). The accordance, therefore, shows that the alkyl chain of nTCB is conformationally disordered fully in the IL phase above n ) 4 at least.24–26 The IL phase could be used as the reference state in the following analysis. In contrast to Σ∆trsS, ∆fusS is almost constant against n, as seen in Figure 3. This indicates that the conformational disorder of the alkyl chain of nTCB is effectively equal between the CrE phase and IL. This means that the alkyl chain of nTCB (n g 4) becomes conformationally disordered fully at the phase transition from the ordered crystal to the CrE phase. Indeed, the entropy of transition (∆CrES) linearly increases with increasing n above n ) 4, though the linearity shows a small irregularity due to the so-called even-odd effect of alkyl chain as in the case of Σ∆trsS. The slope of ∆CrES against n is equal to ca. 10 K-1 (mol of -CH2-)-1, which is again equal to the slope of entropy of fusion of the n-alkane against alkyl chain length.24,28 Thus, it is concluded that the alkyl chain of nTCB above n )

Entropic Role of Flexible Terminals of Mesogens

Figure 4. Molar entropies of 4-alkyl-4′-isothiocyanatobiphenyl (nTCB, n ) 2, 3,20 4,19 5) as a function of temperature above 310 K.

4 becomes fully disordered at the phase transition from the ordered crystal to the CrE phase and that the conformational disorder in the CrE phase is nearly the same as that in IL. Such an alkyl chain length dependence of entropy of transition is also seen in another compound showing the CrE phase. 4-Alkoxy-4′-acetylbiphenyl [AAn (4 e n e 12); n being the number of carbon atoms in an alkoxy group],29,30 for example, shows the CrE phase between ordered crystals and IL. Their entropies of transition, calculated from their reported transition temperatures and enthalpies, indicate a chain length dependence similar to that of nTCB. This strongly suggests that a terminal alkyl chain of calamitic mesogens is fully disordered in the CrE phase. ∆CrES of 2TCB is nearly the same as that of 3TCB, as shown in Figure 3. The linearity of ∆CrES in n g 4 turns off between n ) 3 and 4, and the chain length dependence is lost below n ) 3. The deviation implies that the behaviors of the alkyl chain of 2TCB and 3TCB are significantly different from those of nTCB (n g 4) in the CrE phase. The trend also applies to the IL phase, i.e., the constant ∆fusS is kept even below n ) 3. For nTCB with n g 4, the entropy associated with the conformational disordering of methylene groups increases with increasing n, whereas the contribution of the conformational disorder seems missing in 2TCB and 3TCB. This is rationalized if we assume that the disorder is suppressed for one or two methylene groups close to the biphenyl core. When the alkyl chain length becomes longer than three methylene groups, the third or further methylene group(s) from the core can be conformationally disordered fully in the CrE phase and IL. The difference of the entropy of transition between 4TCB and 3TCB (or 2TCB) therefore corresponds to the contribution of a methylene upon the conformational disordering of the butyl chain in 4TCB. The difference is smaller than the expected conformational entropy, ca. 10 J K-1 mol-1 (∼R ln 3) for full disorder, considering the even-odd effect of the alkyl chain. This reflects that the conformational disordering of the methylene groups close to the core part is suppressed in part. Only methylene groups far from the core part show sufficient disorder. The situation agrees well with the results observed in the nematic phase of nCB (n ) 5-8) by 2H NMR.31–33 The suppressed disordering in 2TCB and 3TCB can be recognized also in absolute entropy. The experimental entropies of 2TCB and 5TCB as a function of temperature are shown in Figure 4 together with those of 3TCB and 4TCB reported previously.19,20 The entropies increase on increasing temperature with some discontinuities at phase transition temperatures. The

J. Phys. Chem. B, Vol. 114, No. 14, 2010 4873 increase is due to thermal excitation and disordering associated with translational, rotational, and intramolecular degrees of freedom. It is expected that the absolute entropy uniformly increases with increasing alkyl chain length in the IL phase, if the alkyl chains presumably have the identical state because the vibrational entropy of a methylene group scarcely depends on the chain length n. Indeed, the quantum chemical calculation shows that the vibrational entropy increases uniformly by ca. 32 J K-1 mol-1 at 365 K against the chain length. The entropy difference between 2TCB and 3TCB and that between 4TCB and 5TCB at 365 K are consistent with this increment in vibrational entropy per methylene group. On the other hand, that between 3TCB and 4TCB (48 J K-1 mol-1) is larger by ca. 16 J K-1 mol-1. This is consistent with the alkyl chain length dependence of ∆CrES shown in Figure 3. 3. Disordering Process from Ordered Crystal to Isotropic Liquid in 5CB and Pentylbiphenyl. The alkyl chain length dependence of the entropy of transition revealed the degree of the conformational disorder of the alkyl chain in the CrE phase. Most of the conformational order is lost at the phase transition from the ordered crystal to the CrE phase. To clarify the disordering process of nTCB from the ordered crystal to IL through the CrE phase, we attempted to divide the entropy of transition into contributions arising from specific degrees of freedom of nTCB. To this end, the entropies of transition of 5TCB are compared with those of 5CB34 and pentylbiphenyl. The three molecules have common parts, a biphenyl core and a pentyl chain. The common structure implies that they have almost the same intramolecular degrees of freedom, except for their terminal polar groups. It is, therefore, expected that the total entropy change attributed to the intramolecular degrees of freedom in the disordering process from the ordered crystal to IL is common to the three compounds. In this section, 5CB and pentylbiphenyl are analyzed to put a basis for the analysis of 5TCB in the next section. 5CB undergoes two phase transitions: one from the ordered crystal to the nematic phase at 297 K and the other from the nematic phase to IL at 309 K.34 Their reported entropies of transition are ca. 55 J K-1 mol-1 and ca. 3 J K-1 mol-1, respectively.34 The sum of the entropies is ca. 58 J K-1 mol-1. On the other hand, pentylbiphenyl has no mesophase and directly melts at the temperature of fusion, Tfus ) 281 K. We determined its entropy of fusion to be 56 J K-1 mol-1 by using DSC. The value is almost equal to the combined entropy of transition of 5CB. That is, 5CB and pentylbiphenyl change from the ordered crystalline phase and IL with almost the same amount of configurational entropy. This is reasonable if we notice the fact that the cyano group is linear and rigid. The entropy of fusion of pentylbiphenyl probably consists of contributions arising from positional (translational), conformational, and orientational degrees of freedom. The contribution from the disordering of positional degrees of freedom (positional melting) is expected to be ca. 14 J K-1 mol-1,35 because it is probably comparable to the entropy of fusion of rare gases, which involves just the positional degrees of freedom. The second contribution is that of the conformational disordering of the alkyl chain. Considering 5TCB, the entropic contribution of methylene groups is estimated to be ca. 12 J K-1 mol-1 from the difference of ∆CrES between 5TCB and 2TCB. The entropic contribution of conformational disordering of the terminal methyl group was estimated as ca. 3 J K-1 mol-1 from entropies of fusion of n-alkane.28 The contribution of the alkyl chain is thus estimated as ca. 15 J K-1 mol-1. The last contribution is the entropy arising from the disordering of the molecular

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Figure 5. Contents of the entropies of transition for pentylbiphenyl, 4-pentyl-4′-cyanobiphenyl (5CB), and 4-pentyl-4′-isocthioyanatobiphenyl (5TCB) from an ordered crystal to IL.

orientation. This contribution is thus assumed as the rest of the entropy of fusion of pentylbiphenyl, ca. 27 J K-1 mol-1. This magnitude is consistent with that of methylbiphenyl, for which the sum of the orientational and positional entropies is ca. 40 J K-1 mol-1 estimated from its entropy of fusion (43 J K-1 mol-1 at Tfus ) 320 K) by subtracting the contribution of a methyl group. The three contributions for pentylbiphenyl are summarized as an entropy diagram in Figure 5. Considering 5CB in the same manner as pentylbiphenyl, the contributions of the disordering of the positional35 and conformational degrees of freedom are ca. 14 and 15 J K-1 mol-1, respectively. These magnitudes suggest that the two disordering processes are completed within ∆Cr-NS ) 55 J K-1 mol-1 below the phase transition from the nematic phase to IL, because its entropy of transition (∆N-ILS) is only ca. 3 J K-1 mol-1. In the nematic phase, the calamitic molecules are free to rotate about their long axes and to some extent about their short axes, concurrently.1 Since the molecules have a disordered head-totail arrangement at least, the corresponding entropy with respect to orientational disorder about the short axis is R ln 2 (≈5.8 J K-1 mol-1). Consequently, the rest of the entropy, (55 - 14 15 - 6) J K-1 mol-1 ≈ 20 J K-1 mol-1, is attributed to the orientational disordering about the long molecular axis. Finally, the entropy of transition from the nematic phase to IL, ca. 3 J K-1 mol-1, reflects the collapse of the nematic order.36 4. Disordering Process from Ordered Crystal to Isotropic Liquid in 5TCB. On the basis of the analyses on 5CB and pentylbiphenyl, the behavior of 5TCB is analyzed in this section. The entropy of transition of 5TCB from the CrII to CrE phases (∆CrES) is ca. 36 J K-1 mol-1, and that from the CrE phase to IL (∆fusS), ca. 31 J K-1 mol-1 (see Figure 5). The sum of the entropy of transition from the CrII phase to IL is, thus, ca. 67 J K-1 mol-1, which is larger than that of 5CB by ca. 9 J K-1 mol-1. Since the molecules in the CrE phase have the positional (translational) order, the entropy change associated with the translational disordering, 14 J K-1 mol-1, is included in ∆fusS. Consequently, the entropy of ca. 17 J K-1 mol-1 in ∆fusS is left. It means that the orientational order of the molecules is partially lost in the CrE phase. The head-to-tail orientations of the molecules are disordered, as they are arranged in a herringbone array in the layered planes and flip-flop.13,17,18,37 The molecules also flap about their long axes and have no distinction between front and rear faces. Consequently, the orientational order corresponding to the entropy contribution of (2 × R ln 2) is lost at the phase transition from the ordered crystal to the CrE phase. Subtracting 2R ln 2 from the entropy by the full orientational disordering (ca. 27 J K-1 mol-1) estimated through the analyses of 5CB and pentylbiphenyl, the

Horiuchi et al. result is ca. 15 J K-1 mol-1, which is reasonably close to the rest of the entropy of transition, ca. 17 J K-1 mol-1. The magnitude ca. 17 J K-1 mol-1, therefore, is attributed to the orientational disordering from the CrE phase to IL. Subtracting 2R ln 2 from ∆CrES, 36 J K-1 mol-1, gives ca. 24 J K-1 mol-1. Since the entropy contribution from the pentyl chain is ca. 15 J K-1 mol-1, an entropy of ca. 9 J K-1 mol-1 is left. This value is identical to the difference of the total entropy of transition from the ordered crystal to IL between 5TCB (ca. 67 J K-1 mol-1) and 5CB (ca. 58 J K-1 mol-1). Because the entropic contributions by position, orientation, and conformation of alkyl chain have already been taken into account, it is reasonable to consider that this difference results from the different terminal polar groups between 5TCB and 5CB. 5CB has a cyano terminal (-CN), which is very rigid and has no conformational degree of freedom. On the other hand, 5TCB has an isothiocyanato terminal (-NCS), which bends at its N atom. We estimated the entropic contribution of isothiocyanato terminal associated with the conformational disordering in a following manner. The entropy of 5CB in the IL phase was estimated to be ca. 542 J K-1 mol-1 at 350 K by extrapolating the reported heat capacity.34,38 Because the entropy of 5TCB is 557 J K-1 mol-1 at 350 K from Figure 4, the difference between 5CB and 5TCB is ca. 15 J K-1 mol-1. This value includes the difference of entropy of intramolecular vibration between the two mesogens, which can be calculated to be 6.6 J K-1 mol-1 from intramolecular frequencies of HCN39 and HNCS.40 Consequently, the entropic contribution from the conformational disordering of the isothiocyanato group is calculated to be ca. 8.4 J K-1 mol-1. This is comparable to the rest of the entropy of transition, ca. 9 J K-1 mol-1. The above entropic consideration is schematically summarized together with 5CB and pentylbiphenyl in Figure 5. The analysis of entropy of transition revealed that nTCB gains partially orientational disorder of the molecules and conformational disorder of isothiocyanato and alkyl terminals at the phase transition from the ordered crystal to the CrE phase and that the remaining orientational and positional orders are lost simultaneously at the phase transition from the CrE phase to IL. That is, the conformation of the alkyl chain is disordered even in the CrE phase, which is the mesophase closest to the ordered crystalline phase. The intramolecular degrees of freedom of the molecules in the CrE phase are disordered as highly as those in the other mesophases having lower degrees of order. This conclusion implies that the conformational disordering of the alkyl chain plays an important role upon forming mesophases. Usually, the roles of the alkyl terminal of mesogens in the formation of a mesophase are assumed to be the promotion of the so-called excluded volume effect and the extension of molecular length leading to stabilization of layered structure.8 These effects, however, do not need an alkyl chain as the terminal group. Indeed, there are some mesogens that have no alkyl terminal, such as long polyphenyls.41 A methylene group can supply the conformational entropy of ca. 10 J K-1 mol-1. This entropic contribution is comparable to the entropy gain upon positional melting and surmounts to one-third of the entropy due to orientational melting. The larger entropy stabilizes the highertemperature phase through the entropy term in the Gibbs energy (G ) H - TS). It is therefore concluded that the main contribution from alkyl chains to the formation of mesophases is a source of large entropy. 5. Different Behavior of nTCB and nCB Caused by Conformational Disorder of the NCS Group. Along the above scenario, the entropic promotion becomes poor in the case of mesogens having a short alkyl terminal. Indeed, the mesogens having a few carbon atoms in the alkyl terminal often exhibit relatively high melting temperatures (Tfus) and directly undergo

Entropic Role of Flexible Terminals of Mesogens the fusion of an ordered crystal. This is the case in nCB and AAn. nCB (n e 4) show monotropically a nematic phase only on cooling from IL.7 The CrE phases of AAn (n e 3) are also monotropic.29 In contrast to these mesogens, nTCB even with n ) 2 or 3 undergoes a phase transition from an ordered crystal to the CrE phase, though the conformational entropy of the alkyl chain is only 3 J K-1 mol-1. The apparent contradiction is solved by the entropic contribution of the terminal isothiocyanato group. The analysis given in the previous section revealed that the isothiocyanato group contributes to the configurational entropy by ca. 9 J K-1 mol-1, which is comparable to that of one methylene group. The large entropy is able to compensate the insufficient entropic contribution of the short alkyl chain. Besides, the isothiocyanato group is similar in length to the propyl chain of 3TCB. Therefore, the isothiocyanato group of nTCB (n < 4) substitutes for the alkyl chain as a source of conformational entropy, whereas the short alkyl chains serve to elongate the core part of nTCB. Conclusion A comparison of entropies among nTCB and its analogues revealed the conformational disordering of the alkyl chain terminal in mesophases and its entropic contribution to formation of mesophases. The large supply of the conformational entropy of the alkyl chain relatively enhances an entropy term of the Gibbs energy, which prefers higher temperature phases. In addition, the mesogenic molecules can preserve their densely packed structure, because the alkyl terminal can retain its rodlike shape even in disordered conformation on average. Therefore, the alkyl chain is superior to other terminal groups for the formation of mesophases of the calamitic mesogens. The vital role of the excellent capacity to supply conformational entropy is not limited to the calamitic mesogens. The alkyl chain length dependence of entropy of transition has also been observed in discotic mesogens28 and ionic liquids.27 The conformational entropy supplied by disordering of the alkyl chains contributes to the formation of their high-temperature phases. Although the alkyl chain has been frequently used for molecular design of mesogens,7,8 the present study reveals clearly one of the important roles played by the alkyl chains. Supporting Information Available: Standard thermodynamic functions of 2TCB and 5TCB and optimized Cartesian coordinates of all atoms and molecular vibrational frequencies of nTCB (n ) 2-5). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Demus, D.; Goodby, J.; Gray, G. W.; Spiess, H. W.; Vill, V. Handbook of Liquid Crystals; Wiley-VCH: Weinheim, Germany, 1998; Vol. 2A. (2) Veerman, J. A. C.; Frenkel, D. Phys. ReV. A 1990, 41, 3237–3244. (3) Veerman, J. A. C.; Frenkel, D. Phys. ReV. A 1991, 43, 4334–4343. (4) McGrother, S. C.; Williamson, D. C.; Jackson, G. J. Chem. Phys. 1996, 104, 6755–6771. (5) Bolhuis, P.; Frenkel, D. J. Chem. Phys. 1997, 106, 666–687. (6) Capita´n, J. A.; Martı´nez-Rato´n, Y.; Cuesta, J. A. J. Chem. Phys. 2008, 128, 194901-1–194901-8. (7) Luckhurst, G. R.; Gray, G W. The Molecular Physics of Liquid Crystals; Academic Press: London, 1979. (8) Demus, D.; Goodby, J.; Gray, G. W.; Spiess, H. W.; Vill, V. Handbook of Liquid Crystals; Wiley-VCH: Weinheim, Germany, 1998; Vol. 1. (9) Duijneveldt, J. S.; Gil-Villegas, A.; Jackson, G.; Allen, M. P. J. Chem. Phys. 2000, 112, 9092–9104.

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