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Phase Transition and Abnormal Behavior of a Nematic Liquid Crystal in Benzene Shyamal Kumar Kundu,§ Shun Okudaira, Masanori Kosuge, Naoki Shinyashiki, and Shin Yagihara* Department of Physics, School of Science, Tokai UniVersity, 1117 Kitakaname, Hiratsuka, Kanagawa 259-1292, Japan ReceiVed: April 13, 2009; ReVised Manuscript ReceiVed: July 2, 2009
Differential scanning calorimetry and broadband dielectric spectroscopy measurements were performed to investigate the phase transitions in nematic liquid crystal (LC)/benzene mixtures. Noticeable changes of the crystal-isotropic phase transition and the phase transition enthalpy were observed. We also estimated the number of unfreezable benzene molecules from the LC/benzene mixtures. The crystal-isotropic phase transition temperature was described very accurately from the temperature-dependent relaxation strength, the relaxation time, and the symmetric shape parameter obtained from the fitting procedure. Surprisingly, the abnormal behavior of the isotropic phase was observed in LC/benzene mixtures that suggested the presence of local structure in the mixture, which set off the dipole moments along the long axis. The interaction between the LC molecules was also discussed from the τ-β diagram. 1. Introduction Phase transitions in liquid crystals (LCs) in an external field have been studied with great interest for a long time. The behavior of a nematic bulk liquid crystal (NLC) in the presence of an external field is of importance for many technical applications as well as basic physical research.1-9 The most fundamental problems of predicting physical properties of liquid crystalline compounds are based upon information on the molecular shape and intermolecular interactions. A study of the dynamic microstructure of liquid crystals is very essential to solve recent problems about properties of matter of liquid crystals. This is so because the properties of matter of liquid crystals reflect not only chemical structure of one molecule but also various molecular arrangements and structure of a domain. There are many different types of LC phases distinguished by the different optical properties. When viewed under a microscope using a polarized light source, different liquid crystal phases appear to have distinct textures. The contrasting areas in the textures correspond to domains where the LC molecules are oriented in different directions. Within a domain, however, the molecules are well ordered. The dielectric anisotropy of NLCs plays an important role in the applications of the electrical effect, display devices, spatial modulators, etc.10 Jady˙n et al.11 showed a pretransitional criticallike behavior of dielectric permittivity in the mixtures of mesomorphic and nonmesomorphic compounds. Usol’tseva et al.12 showed that dissolving a thermotropic liquid crystal compound into nonpolar organic solvent could produce ferroelectric liquid crystals with remarkable properties. The electrooptic switching properties of the solutions are, to some extent, better than those of the pure liquid crystals.13 It turned out that the liquid crystals in nonaqueous solvents can be used in electrooptic devices. However, the fundamental properties of liquid crystals at a molecular level have not been clarified yet. * To whom correspondence should be addressed. E-mail: yagihara@ keyaki.cc.u-tokai.ac.jp. § Present address: Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, Japan.
The objective of the present study is to investigate the phase transitions of a nematic liquid crystal in nonpolar solvent, benzene. Broadband dielectric spectroscopy (BDS) and differential scanning calorimetry (DSC) techniques are used to investigate the dynamics and phase transitions of these mixtures. 2. Experimental Section 2.1. Sample. Because of the simple structure and for simplicity of the present discussion, we used 4′pentyl-4-biphenylcarbonitrile (5CB) as the standard liquid crystalline material. The liquid crystalline material, 5CB, was purchased from SIGMAAldrich, Japan. Benzene with pure grade was purchased from WAKO Pure Chemical Industries, Japan. These were used without further purification. 5CB/benzene mixtures with different concentrations of 5CB (e.g., 10, 20, ..., 100 wt %) were used for DSC and BDS measurements. 2.2. Differential Scanning Calorimetry. The DSC measurements were made with differential scanning calorimeter (Seiko SSC/5200H DSC-120). The DSC measurements were performed by heating process from -20 to 70 °C at a scanning rate of 1 °C/min. The sample was kept at -20 °C for about 2 h to ensure the equilibrium before starting data acquisition. 2.3. Broadband Dielectric Spectroscopy. BDS measurements were carried out by two subsystems, time domain reflectometer (TDR) (Hewlett-Packard 54210B) having a frequency range of 100 MHz to 30 GHz and impedance analyzer (Agilent Technology HP4294A) having a frequency range of 40 Hz to 110 MHz. During the dielectric measurements, the sample temperature was varied between -10 to 40 °C. A coaxial-cylindrical cell with the inner conductor diameter (made by platinum) of 2 mm and the outer conductor (gold plated stainless still) inner diameter of 3.5 mm was used for both TDR and impedance analyzer systems of dielectric measurements. The lengths of the inner and outer conductor were 5 mm and 23.7 mm, respectively, and the electric cell length was approximately 6.65 mm. 3. Result and Discussion The BDS and DSC were used to study the nematic liquid crystal molecules (5CB) in solution and in the frozen state. The
10.1021/jp903391z CCC: $40.75 2009 American Chemical Society Published on Web 07/21/2009
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Figure 2. Phase transition enthalpy-concentration phase diagram of 5CB/benzene mixtures: O represents K-Iso phase transitions, 0 represents K-N phase transitions, and 4 represents N-Iso phase transitions. The error bar shows standard deviation. The solid lines are drawn as a guide for the eye along the plots. The regions I, II, and III were defined according to the concentration dependences of the phase transition enthalpies.
Figure 1. Heating DSC curves of benzene solutions at different concentrations of 5CB. K, N, and Iso indicate the crystal, nematic, and isotropic phases, respectively. The vertical lines indicate the onset temperatures of the phase transitions from K to N, from N to Iso, and from K to Iso.
intermolecular interaction between 5CB and benzene molecules could determine the dielectric behavior in the freezing process. Pure 5CB takes a nematic liquid crystalline phase at room temperature (∼22.4 °C) because of the anisotropic shape of the rigid molecule. 3.1. Differential Scanning Calorimetry. It is well known that the DSC is a very useful tool to investigate the phase transitions in liquid crystals. The DSC curves obtained for 5CB/ benzene mixtures for some different concentrations of 5CB are shown in Figure 1. It is seen from this figure that the crystalline (K)-isotropic (Iso) phase transition temperature decreases very slowly with increasing concentration of 5CB14 but at 70 wt % of 5CB, the heat of fusion is extremely large and the phase transition temperature is much higher than that of pure 5CB. It is clear from Figure 1 and also Figure 1 in ref 14 that not only 5CB molecules but also benzene molecules participate the phase transition at around 28 °C. Therefore at 70 wt % of 5CB, most of the molecules (benzene and LC) are crystallized at 27.2 °C. A small amount of benzene remained in the liquid state and these were crystallized at 0.2 °C. So, one can say that 70 wt % of 5CB is the critical concentration, where phase behavior is strongly correlated with the composition of LC and benzene molecules, thus the molecules have strong tendency to form antiparallel correlated pairs.14 Therefore, in the range of 70-96 wt % of 5CB, the LC molecules form antiparallel correlated pairs, hence, the antiparallel dimers of the LC molecules are built-up.15-20 Such dimers are viewed as being formed by the bonding of two “monomers”, each monomer consisting of a
mesogenic core and an end-chain of half the spacer length. These pairs are formed more easily in the nematic phase. So that the molecular alignments are easily produced above 96 wt % of 5CB to form a nematic (N) phase.14 It is seen from Figure 1 that the peak height changes remarkably with increasing concentration of 5CB. The phase transition enthalpy (∆H) obtained from Figure 1 for K-Iso, K-N and N-Iso phase transitions is shown in Figure 2. It is naively anticipated that the value of ∆H obtained from K-Iso and K-N phase transition points for all the 5CB/benzene mixtures should lie on the line connecting between pure benzene and 5CB. But Figure 2 clearly shows the three types of K-Iso phase transitions which are indicated by the region I [0 e C < 70 wt % of 5CB], region II [70 wt % of 5CB e C e 96 wt % of 5CB], and region III [96 wt % of 5CB < C e 100 wt % of 5CB]. In the region I, ∆H decreased with increasing concentration of 5CB [from benzene ()132.8 J/g) to 67.5 wt % of 5CB ()8.1 J/g)] and the K-Iso phase transition temperature decreased from 5 to 0.2 °C. In this region, the interactions between LC and benzene molecules are weak14 and the K-Iso phase transition is mainly attributed by benzene. It is seen from this figure that between 0 to 30 wt % 5CB, the transition enthalpy, ∆H, appeared to be along the dashed line within an experimental error. It indicates that all the benzene molecules are crystallized completely. Then below 70 wt % 5CB, observed value of ∆H deviated from the dashed line, which is due to existence of some benzene molecules being uncrystallized in the frozen state, and these molecules in liquid state increases with LC concentration. In the region II, ∆H increased suddenly and also phase transition temperature increased (27.2 °C for 70 wt % 5CB) and then decreased for both. In this region, both LC and benzene attribute to the K-Iso phase transition. The interactions between LC and benzene molecules14 are stronger than that in the region I. All of the molecules (benzene and LC) are crystallized in this region, and the sudden increase of ∆H and the K-Iso phase transition temperature might be due to supersolidification21 where phase behavior is strongly correlated with the composition of LC and benzene molecules. Thus, the molecules have a strong tendency to form antiparallel correlated pairs, and due to eutectic type crystal formation,22,23 which is composed of LC and benzene molecules, the melting of the crystal including not only LC but also benzene shows large ∆H. In the region 3, nenatic
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Figure 3. Concentration dependence of the number of unfreezable benzene molecules/1LC molecules for the 5CB/benzene mixtures. The error bar shows standard deviation. The solid curves are drawn as a guide for the eye.
phase appeared in between K and Iso phases. In this region, the interactions between LC molecules14 are very strong and the K-N-Iso phase transitions are mainly attributed by LC. Here, ∆H decreased a little from the region II where the phase transition appeared to be K-N. On the other hand, the ∆H obtained from the N-Iso phase transition of the 5CB/benzene mixtures was very small (∼2.5 J/g within an experimental error). Such a behavior of the K-Iso phase transition obtained from 5CB/Benzene mixtures is quite surprising. On the basis of the results obtained from Figure 2 mainly on the K-Iso phase transition, in the regions I and II we can calculate the number of unfreezable benzene molecules in the frozen state. We assume that the transition enthalpy is kept in the mixtures. Then one can estimate the number of unfreezable benzene molecules per one liquid crystal molecule (nnfB) by the following equation:
nnfB )
∆HCal - ∆HMeas 100 - CLC MLC ∆HCal MBen CLC
(1)
where ∆HCal ) [1 - (CLC/100)] ∆HBen. CLC is the concentration of LC in wt %, ∆HBen (J/g) is the transition enthalpy of benzene, ∆HLC (J/g) is the transition enthalpy of LC, ∆HMeas (J/g) is the measured transition enthalpy of LC/benzene mixture, MLC is the molecular weight of LC, and MBen is the molecular weight of benzene. From eq 1, we see that nnfB mainly depends on ∆HMeas. On the basis of Figure 2 using eq 1, the concentration dependence of the number of unfreezable benzene molecules (nnfB) is presented in Figure 3. The estimated number of unfreezable molecules depends on ∆HMeas. The value of ∆HMeas for all the mixtures should lie on the line connecting between CLC ) 0 wt %; ∆HBen ) 132.55 J/g (pure benzene) and CLC ) 100 wt %; ∆HBen ) 0 J/g (pure 5CB). It is seen from this figure that in the region I, the number of unfreezing benzene molecules increases, but in the region II, number of unfreezing benzene molecules shows negative value. It is expected because in the region II, the ∆HMeas is higher than ∆HCal (Figure 2). The negative value observed in this region suggests two possible mechanisms, (i) ∆HMeas could be higher than ∆HCal due to supersolidification21 or (ii) ∆HMeas could be higher than ∆HCal due to eutectic crystal formation22,23 of LC and benzene.
Figure 4. Temperature variation of (a) real and (b) imaginary parts of the dielectric functions with frequency for 60 wt % (left Figure) and 90 wt % (right Figure) of 5CB/benzene mixtures.
3.2. Broadband Dielectric Spectroscopy. We performed the BDS measurements to examine the temperature dependent LC phase transitions at different concentrations and observed the similar nature of the phase transitions obtained from DSC study. As for example, we have shown the two different concentrations (e.g., 60 wt % of 5CB from the region I and 90 wt % of 5CB from the region II) of 5CB/benzene mixtures. The temperature variations of the real and imaginary parts of the complex dielectric permittivity (ε* ) ε′ - iε′′, where ε′ and ε′′ are, respectively, the real and imaginary parts of the complex dielectric permittivity) measured for two different concentrations of 5CB (e.g., 60 and 90 wt % 5CB) are shown in Figure 4. The K-Iso phase transition is well observed from this figure. In the K phase, the ε′ and ε′′ are almost flat whereas in the Iso phase, ε′ and ε′′ increases. It is very interesting that even in the Iso-phase, the loss peak changes to be smaller with decreasing temperature, since the relaxation strength increases with decreasing temperature for molecular liquid in isotropic liquid phase generally. It is seen from this figure that for 60 wt % 5CB, the relaxation peak is shifted toward lower frequency, whereas for 90 wt % 5CB the relaxation peak is shifted toward higher frequency by increasing temperature. This behavior of the relaxation spectrum is also surprising. To characterize the dielectric relaxation spectrum, curve fitting procedures were carried out. The dielectric constant and loss for the liquid crystalline materials were described from the fitting of the complex dielectric permittivity using 2
ε*(ω) - ε∞ )
∆ε
k ∑ 1 + (iωτ )β
k)1
k
+ k
σdc iωε0
(2)
where ∆εk is the dielectric strength, σdc for the dc conductivity, ε0 is the dielectric constant in vacuum and ε∞ is the highfrequency permittivity, τk ()1/2πνk) is the relaxation time, νk is the characteristic frequency, and βk is the symmetric shape parameter. β ) 1 gives the Debye function and 0 < β < 1 gives the Cole-Cole function. All the dielectric spectra shown in Figure 4 were described well by considering two relaxation processes and dc conductivity. The fitting curves obtained from eq 2 are shown in Figure 5 at an arbitrary temperature, 18 °C. Two relaxation processes are clearly observed from this figure, where the low frequency process with larger relaxation time is
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Figure 5. Frequency dependences of (a) real and (b) imaginary parts of the dielectric functions for 90 wt % of 5CB/benzene mixture at 18 °C. Solid and dashed curves are the fitting curves using eq 2.
Figure 7. Temperature dependences of (a) relaxation strength, (b) relaxation time and (c) shape parameter for 90 wt % of 5CB/benzene mixture. K and Iso correspond to the crystallization and isotropic phases, respectively. The solid curves are drawn as a guide for the eye.
Figure 6. Temperature dependences of (a) relaxation strength and (b) relaxation time for 60 wt % of 5CB/benzene mixture. K and Iso correspond to the crystallization and isotropic phases, respectively. The solid lines are drawn as a guide for the eye.
due to the rotational motion along the short axis (process 1) and the high frequency process with small relaxation time is due to the motion along the long axis (process 2).24-28 Figure 5 also shows the contribution from the dc conductivity which is generally observed in the low-frequency side of the dielectric spectrum for the liquid crystalline materials. It is well known that liquid crystals are not absolutely free from impurities. Figures 6 and 7 show that the temperature dependence of the relaxation parameters (dielectric relaxation strength, ∆ε; relaxation time, τ; and the symmetric shape parameter, β) for two different concentrations of 5CB [e.g., 60 wt % (Figure 6)
and 90 wt % (Figure 7)]. One can see from these figures that the relaxation parameters are strongly temperature dependent. Note that two relaxation processes (processes 1 and 2) were observed for 60 wt % of 5CB and followed the Debye function where β ) 1, but for 90 wt % of 5CB these two processes were also observed (see Figure 5) and followed the Cole-Cole function where 0 < β < 1. However, K-Iso phase transitions for 60 and 90 wt % of 5CB are described very accurately from the discontinuous nature of each relaxation parameters obtained from each relaxation processes. In the Iso phase, two relaxation processes (processes 1 and 2) are observed but in the K phase, the process 1 disappeared and the relaxation time that is similar with the process 1 but even larger than that of the process 1 showed a discontinuity at the crystallization temperature. The relaxation time is larger than those obtained in the Iso phase because of the large restrictions in the crystalline phase. This is because the molecular motion of 5CB takes a different mode of dynamics below the freezing point and indicates a characteristic feature of large relaxation time where the anisotropic shape brings a large excluded volume effect in the molecular rotation along the short axis. The rotational motion along the short axis is strongly restricted and disappeared at the freezing temperature at which benzene and/or 5CB molecules are partially crystallized. On the other hand, the motion along the longer axis is also affected partially by surrounding medium because it takes a quite smaller excluded volume. Therefore, this motion is still active even below the freezing temperature. This unfreezable 5CB and benzene molecules are restricted by partially crystallized 5CB and benzene molecules. A discontinuous behavior of the relaxation time for 5CB dynamics at the
Nematic Liquid Crystal in Benzene
Figure 8. Variations of the real and imaginary parts of the complex dielectric permittivity with frequency for different concentrations of 5CB/benzene mixture at 20 °C. Solid curves represent the fitting curves using eq 2.
crystallization temperature results from the abrupt decrease in the volume by one 5CB molecule in the noncrystalline phase, comparing with that required as the excluded volume effect.29 It is seen from Figure 6 that the dielectric relaxation strength, ∆ε, and relaxation time, τ, for the process 1 in the Iso phase behave abnormal. The increase of ∆ε and τ with increase of temperature for the process 1 implies that the Iso-phase is not so-called isotropic phase. If it is isotropic in molecular scale, ∆ε for the process 2 would be increased and also the relaxation time, τ, for the process 1 would be increased with decreasing temperature. Although, the solutions appeared to be transparent macroscopically, they were not homogeneous at the molecular level. Depending on the kind of intermolecular interactions among the component molecules, a local structure30,31 is expected to form in the Iso-phase. Figure 7 also shows that in the Iso phase around 17-20 °C, dielectric relaxation strength, ∆ε, for the process 1 and the shape parameter, β, of the two processes decrease with decreasing temperature where the LC molecules are strongly correlated with the benzene molecules. The concentration dependences of the real, ε′, and imaginary, ε′′, parts of the complex dielectric permittivity were measured at different fixed temperatures (see Figure 8 for example). Figure 8 represents the concentration dependences of ε′ and ε′′ for 5CB/ benzene mixtures at 20 °C. Solid curves represent the fitting curves using eq 2. The relaxation processes 1 and 2 (the same as above) are observed for all the concentrations. The variations of the relaxation parameters obtained from the process 1 (∆ε1, τ1, and β1) and from the process 2 (∆ε2, τ2, and β2) with concentration of 5CB/benzene mixture for three different fixed temperatures are shown in Figure 9. It is seen from Figure 9a,b that ∆ε1, ∆ε2, τ1, and τ2 are strongly concentration dependent as well as temperature dependent and show abnormal behavior. When the temperature is low (e.g., 10 °C), both the relaxation processes are observed in the region I only. For the temperatures of 20 and 30 °C, both the relaxation processes are observed in the regions I and II. However, in the region I the dielectric strength, ∆ε1, and the relaxation time, τ1, increased monotonically (e.g., 20 and 30 °C) with increasing
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Figure 9. Concentration dependence of (a) relaxation strength (b) relaxation time and (c) distribution parameter for 5CB/benzene mixture at three different temperatures.
LC molecules and no significant differences were observed, which came from the change of the local structure.30,31 Figure 9a shows that in the region I, ∆ε1 increases with increasing concentration of 5CB because the number density of dipoles increases by increasing concentration. But in the region II, ∆ε1 decreases because the molecules are more ordered and restricted than those in the lower concentrated region and the effective dipole moment of the LC molecules decreases. For the process 2, ∆ε2 increases gently below 70 wt % of 5CB and then ∆ε2 increases a little. This is because at even higher concentrations, the dynamics is not restricted by the small excluded volume effect that is much more effective for the process 1. Figure 9b shows that both τ1 and τ2 increases with increasing concentration of 5CB. This is because when the concentration is low, the liquid crystal molecules are freely rotating around their own axis. By increasing the concentration, the interaction between the LC molecules increases and the viscosity of the solutions increases which reduces the rate of the rotation of dipoles around their own axis. Figure 9c shows that in the region I, the relaxation processes 1 and 2 are the Debye type (β ) 0) whereas in the region II, the both the relaxation processes are Cole-Cole type (0 < β < 1). The intermolecular interactions between liquid crystal molecules can be described by the τ-β diagram. Figure 10 shows that the τ-β diagram of the processes 1 and 2 for 5CB/benzene mixture for three different temperatures in the regions I and II. It is seen from this figure that in the region I, the interaction between the liquid crystal molecules is not very large because it is treated as an increasing viscosity of surrounding medium so that no downward nature of the curves are seen. But characteristic changes with decreasing β values appear for both processes in the region II. The plots obtained at different temperatures (Figure 10) for each process seem to follow the same trajectory. In this region, the interaction between the liquid crystal molecules is very strong so that downward curves indicate the change in the relaxation time distribution due to the variation of local structure with decreasing β values. The
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Kundu et al. and the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research on Priority Areas “Water and Biomolecules” (No. 18031034). References and Notes
Figure 10. τ-β diagram of the processes 1 and 2 for 5CB/benzene mixture at three different temperatures. Dashed (for process 1) and solid (for process 2) curves are drawn as a guide for the eye. Region I indicates no deviation of β with τ, and region II indicates deviation of β with τ.
process 2 is accompanied with intermolecular interactions in more structured order than those for the process 1. 4. Conclusion DSC measurements were used to study the K-Iso and K-N-Iso phase transitions of the 5CB/benzene mixtures. The phase transition temperatures and the phase transition enthalpy were successfully obtained from the DSC curves. The phase transition enthalpy was obtained at the K-Iso, K-N and N-Iso phase transition points of the 5CB/benzene mixtures. Below 70 wt % of 5CB, there exist mobile unfreezable molecules in the frozen state. We estimated the amount of unfreezable benzene from the 5CB/benzene mixtures. BDS measurements were performed to study the K-Iso phase transitions in 5CB/benzene mixtures. For all concentrations, two relaxation processes were observed in the isotropic phase due to the overall rotation of the molecules along the short and long molecular axes. In the crystalline phase, only the molecular rotation along the long axis was observed. K-Iso phase transition temperature was discontinuous as found from the temperature dependence of the relaxation time, relaxation strength, and also from the shape parameters obtained from the fitting procedure of eq 2. The phase transition temperatures obtained from DSC and BDS study were almost the same within an experimental error. Isotropic phase in LC/benzene mixtures in the region I showed abnormal behavior, which suggested the presence of local structure in the mixture. In the region II, the liquid crystal molecules are strongly correlated with the benzene molecules. Acknowledgment. This work was supported by the Japan Society for the promotion of Science (JSPS) (No. 17-05061)
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