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J. Phys. Chem. B 2009, 113, 640–646
Smectic C to Cubic Phase Transition of 4′-n-Docosyloxy-3′-nitrobiphenyl-4-carboxylic Acid (ANBC-22) and Alternating-Current Electric Field Effect Shoichi Kutsumizu,*,† Kouhei Hosoyama,† Makoto Yamada,† Katsufumi Tanaka,‡ Ryuichi Akiyama,‡ Shinichi Sakurai,‡ and Eiji Funai‡ Department of Chemistry, Faculty of Engineering, Gifu UniVersity, 1-1 Yanagido, Gifu 501-1193, Japan, and Department of Macromolecular Science and Engineering, Graduate School of Science and Technology, Kyoto Institute of Technology, Matsugasaki, Sakyo, Kyoto 606-8585, Japan ReceiVed: August 5, 2008; ReVised Manuscript ReceiVed: NoVember 11, 2008
Smectic C (SmC) to cubic (Cub) phase transition behavior of 4′-n-docosyloxy-3′-nitrobiphenyl-4-carboxylic acid (ANBC-22) and alternating-current (AC) electric field effect on the SmC phase were examined. The most important and unexpected finding is that even at a temperature 8 K below the zero-field SmC to Cub phase transition temperature (TSmC-Cub ≈ 408 K) determined previously for the compound and without field, the Cub phase growth occurs, after a very long induction period of several hours. The X-ray diffraction measurements revealed the formation of an Im3m-type Cub phase at the temperature. It is suggested that the “true” transition temperature, which is difficult to determine precisely, exists around 396 K. The time-dependence of the Cub phase growth both without field and under field was analyzed using the wellknown Avrami equation, implying the nucleation and growth mechanism mainly operating in the SmC to Cub phase transformation. The fact uncovered is that between 408 and 396 K, the SmC to Cub transformation is virtually prohibited by the strongly limited nucleation. It is concluded that the effect of the electric field on the transition is to promote the nucleation of the Cub phase in the temperature region where the Cub phase is potentially more stable than the precursory SmC phase. 1. Introduction The cubic (Cub) mesophases have attracted great attention because of their self-organization of simple rodlike molecules into a complex aggregation structure with cubic symmetry.1 4′n-Docosyloxy-3′-nitrobiphenyl-4-carboxylic acid (ANBC-22, where “22” represents the number of carbon atoms in the alkoxy group) is such a Cub phase-forming compound.1d,2–7 It exhibits the following phase sequence upon heating: Smectic C (SmC) f Im3m-Cub f Ia3d-Cub f isotropic liquid.2 The lowtemperature three phases are considered to be basically made up by layered aggregates of the ANBC-22 molecules, but having different degrees of dimensionality; the SmC phase is a onedimensionally ordered phase, whereas the two Cub phases are three-dimensionally ordered ones. The Ia3d-Cub phase is widely seen in thermotropic and lyotropic liquid crystals (LCs) and block copolymers,1 often called gyroid, but the Im3m-Cub phase is at present limited in the thermotropic LCs.1d,e,g The phase transition behavior has been investigated by several techniques such as differential scanning calorimetry (DSC),3 adiabatic calorimetry,4 polarizing optical microscopy (POM),3 dynamic viscoelasticity (DVE),5,6 and X-ray diffraction (XRD).2 Nevertheless, like other soft materials, little is understood about the transition kinetics and detailed mechanisms of the transformation from the SmC to Cub phases and from one Cub phase to another. The chemical structure of this compound is very simple, composed of a nitrobiphenyl-carboxylic acid core and a long alkyl tail. The carboxylic acid group is hydrogen-bonded, and * To whom correspondence should be addressed. E-mail: kutsu@ gifu-u.ac.jp. † Gifu University. ‡ Kyoto Institute of Technology.
thus, the dimerized ANBC-22 is the minimum building unit.7 The packing in each phase is governed by several factors; repulsive interaction between the aromatic core and alkyl chain parts, and dipole-dipole interaction through the lateral nitro group, and hydrogen bonding by the carboxylic acid group. Temperature is also crucial, affecting the above three factors; elevating temperature, for example, expands the alkyl part more and enhances a mismatch between the two incompatible parts, destabilizing the SmC layer structure and favoring the Cub phase. The lateral dipole-dipole interaction, on the other hand, contributes to stabilize side-by-side packing of the molecules as in the layered structure, and weakening or breaking of the hydrogen bonding gives a profound influence on all three aggregation structures. Thus, the phase realized at a given temperature is under a delicate balance between those interactions. Thus, like other soft materials, the aggregation structure of ANBC-22 is also expected to change sensitively in response to physical external stimuli such as electric field, shear deformation, etc.8,9 Such information is important not only for practical application reasons but also for basic understanding of those factors governing the phase stability. Recently, we examined the effect of an alternating-current (AC) electric field application on the SmC phase and found that the AC electric field application at temperatures 4-10 K below the zero-field SmC to Cub phase transition temperature (TSmC-Cub ≈ 408 K) induces the SmC to Cub phase transition; the higher frequency accelerated the Cub phase growth more effectively, and from this observation we considered no possibility of the Joule heating effect due to ionic impurities.10,11 The origin of this field effect was tentatively assigned to the lateral nitro group with a large dipole moment (4.2 D; 1 D ) 3.33 × 10-30 C m); the AC electric field would probably enhance the undulation of
10.1021/jp806972x CCC: $40.75 2009 American Chemical Society Published on Web 12/31/2008
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the SmC layered structure of dielectric anisotropy, leading to a disruption of the structure and stabilizing the Cub phase structure. To clarify the origin of the field-induced transition mentioned above, in the present paper, we investigated the Cub phase growth behavior from the SmC phase, both without field and under field, by using POM, DVE, and XRD. The investigation, unexpectedly, has uncovered the real transition behavior between the SmC and Cub phases of this compound. 2. Experimental Section Materials. ANBC-22 was prepared according to the method of Gray et al.12,13 but with a slight modification.14 The starting material, 4′-hydroxybiphenyl-4-carboxylic acid, was esterified into ethyl 4′-hydroxybiphenyl-4-carboxylate, which was then reacted with 1-bromodocosane to produce ethyl 4′-n-docosyloxybiphenyl-4-carboxylate. The hydrolysis of this ethyl ester was the next step, followed by nitration, giving the final product of ANBC-22. The sample was purified by repeated recrystallizations from ethanol and confirmed to be fully pure by 1H NMR (JEOL JMN-R400 spectrometer), thin layer chromatography, differential scanning calorimetry (DSC: Seiko Denshi SSC 5000 system), and elemental analysis (see the Supporting Information for the details). Instrumentation. The phase transitions were examined using DSC at a scanning rate of 2.5 K min-1 under a dry nitrogen flow of ca. 40 mL min-1. The texture of each mesophase was observed by a polarizing optical microscope (POM: Nikon Optiphot-pol XTP-11) equipped with a Mettler FP82 hot stage and a Mettler FP80 central processor at a heating/cooling rate of 5 K min-1 or at a constant temperature. The influence of AC electric field application was examined by both POM observations and DVE measurements. For POM observations, 4 µm thick transparent sandwich-type cells consisting of two indium-tin-oxide (ITO) coated glass plates were used, into which the samples were inserted in the isotropic liquid state. The cell was then placed in the hot stage, to which a triangular-wave field of 40-120 V (field strength E ) 100-300 kV cm-1) and frequencies 1-100 kHz was applied. The DVE measurements were performed with a rotational rheometer (Rheology MR-300V2E) with a fixture of parallel plates. The angular frequency of the oscillatory shear strain was fixed to be 9.42 rad s-1, and the preset amplitude of the strain was 0.024. The gap distance between the parallel plates was 65 µm. Sufficient care was taken that the temperature of the parallel plates was kept below 394 K during the sample insertion. After the sample was completely sandwiched, the temperature was raised carefully to the preset temperature (400 K) and was kept constant for more than 1 h prior to the measurements. For one measurement, the sinusoidal electric field with an amplitude of 200 kV cm-1 and a frequency of 10 kHz was applied to the sample between the parallel plates acting as electrodes and then removed during the measurement. The details of the electro-rheological measurements were reported elsewhere.15,16 XRD patterns at elevated temperatures were obtained for powder samples sandwiched between two Kapton windows. The sample was placed in a heated cell and the temperature was controlled within ( 0.1 K. Synchrotron radiation was used as the X-ray source at the Photon Factory (PF) beamline BL-10C of the high energy accelerator research organization (KEK), Tsukuba, Japan, and at the RIKEN structural biology beamline I (BL45XU) at the SPring-8, Hyogo, Japan. The wavelength (λ) was 0.1488 nm for PF-KEK and 0.1015 nm for BL45XU-
Figure 1. Optical microphotographs under crossed polarizers for ANBC-22 at 397.3 K under E (E ) 100 000 V cm-1 at 10 kHz): (a) before application of the field E, and (b) 8 min, (c) 15 min, and (d) 60 min, after application of the field.
SPring-8. The incident beam intensity was monitored by an ionization chamber to correct a minor decrease in intensity during the measurements. The geometry was further checked with chicken tendon collagen, which gives a set of sharp diffractions corresponding to a spacing of 65.3 nm. Details of the optics and instrumentation of the BL-10C-PF-KEK17 and of the BL45XU-SPring-818 are described elsewhere. When a two-dimensional (2D) detector (an X-ray image intensifier with a cooled charge coupled device (CCD)) was used, the obtained 2D pattern was isotropic, and so it was converted to the corresponding one-dimensional SAXS profile, that is, the scattering intensity I(q) versus q curve, by circularly averaging. Here, q is the magnitude of the scattering vector, defined as q ) (4π/λ)sin θ with 2θ being the scattering angle. Subtraction of the air scattering was further conducted by taking the absorption of X-rays by the sample into consideration. 3. Results Polarizing Optical Microscopy (POM). We first investigated how the SmC phase of the ANBC-22 changes in response to AC electric field application using POM. Figure 1 shows the optical microphotographs taken at 397.3 K under crossed polarizers. Figure 1a is a photo before application of the electric field, which is characterized by a fine smectic C schlieren texture. In this experiment, the inner surfaces of the ITO glasses were treated for aligning the molecules homeotropically with respect to the substrate, but the treatment was not successful and, as is easily seen, the sample showed a polydomain nature. To the sample in this state was applied an AC electric field with a strength (E) of 100 000 V cm-1 and a frequency of 10 kHz, and after 8 min, a small black spot was observed, as indicated by a circle in panel b. The spot grew larger with time under the field, and in panel c, in a photo taken after 15 min, the growth of the spot is easily recognized, with similar black areas at other sites as well. After 60 min, in panel d, these black areas occupied more than half of the whole area. The black areas are either a pseudoisotropic domain in homeotropic alignment or an optically isotropic Cub domain. As displayed later in Figure 6, the growth of these black areas was followed by an increase of the storage modulus G′, and thus, assigned to the formation of the Cub phase. In some cases,
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Figure 2. Evolution behavior of the Cub phase regions at 397.1-397.3 K as a function of time (t in min) under E (E ) 100 000 V cm-1 at 10 kHz): E was applied during the observation (filled triangles), or E was applied for 0 e t e 23 and then removed for 23 e t (open triangles). For the former case, a broken curve is the best-fit based on the Avrami equation (t0 ) 10 min, τ ) 68 min, and n ) 1.1), and for the latter, the solid curve is a guide for the eye.
as shown in Figure 1 of ref 10, for example, at 396.5 K under an electric field of E ) 100 000 V cm-1 and a frequency of 10 kHz, the black areas were of polygonal shapes, characteristic of the Cub phase growth.19,20 From the POM images as shown in Figure 1, the area fraction of the Cub phase in the system can be estimated and plotted as a function of time (t). An example is shown in Figure 2. Filled triangles represent the time dependence of the Cub phase evolution where an electric field (the strength E ) 100 000 V cm-1 and the frequency is 10 kHz) was applied at t ) 0 and kept during the whole experiment at 397.3 K. The growth of the Cub phase became evident around t ) 10 min, and after that the fraction steeply increased with t. The broken curve is the best-fit based on the Avrami equation, which will be discussed later. The same figure includes another plot denoted as open triangles for comparison. In this experiment, the field was removed at a time of t ) 23 min, as shown by an arrow, and the response after that was also monitored. After t ) 23 min, the evolution seemed to become slightly slow compared with the filled triangle data mentioned above, but the Cub phase growth never stopped. Our preceding paper10 considered a reason for this as follows: the field-induced Cub phase can remain as a metastable phase at that temperature because the field-induced evolution was limited within the temperature region where a supercooled Cub phase is observed on cooling. However, more striking results were obtained, which are shown in Figure 3. Figure 3 shows the optical microphotographs taken at 400.5 K under crossed polarizers with no electric field. Here, the cover glasses were used without any surface treatment prior to the experiment. The temperature was assumed to be about 8 K below the zero-field SmC to Cub phase transition temperature (TSmC-Cub ≈ 408 K), which was determined by adiabatic calorimetry.4 As seen in panel a, a fine schlieren texture was seen and presumed to be kept forever. After 265 min, however, faint changes were recognized, as seen within two circles in panel b, and these two regions and another were changed into completely black areas in panel c after 300 min, that is, 5 h. After waiting for a very long time of 10 h, the black areas exceed more than half of the whole area, as shown in panel d. This is a very shocking observation, because the transition temperature determined by adiabatic calorimetry, which is usually recognized as the thermal equilibrium value, is not so. The same kinds of POM observations were also made at 396.5 and 398.5 K for 10 h. The triplicate results at the two temperatures showed no Cub phase formation. Figure 4 presents the evolution behaviors of the Cub phase regions at two temperatures as a function of time (t). For each
Figure 3. Optical microphotographs under crossed polarizers for ANBC-22 at 400.5 K without E: (a) initial state, (b) after 265 min, (c) after 300 min, and (d) after 600 min.
Figure 4. Growth behavior of the Cub phase regions of ANBC-22 at (a) 400.5 and (b) 402.5 K as a function of time (t in min). Triplicate data are shown, and broken curves are best fits based on the Avrami equation: (a) t0 ) 248 min, τ ) 230 min, and n ) 2.0 in the range t e 400 min for Run No. 1; t0 ) 349 min, τ ) 312 min, and n ) 2.2 in the range t e 540 min for Run No. 2; and t0 ) ∞ (>600 min) for Run No. 3. (b) t0 ) 9.2 min, τ ) 55 min, and n ) 0.99 for Run No. 1; t0 ) 14 min, τ ) 100 min, and n ) 0.92 for Run No. 2; and t0 ) 35 min, τ ) 60 min, and n ) 1.1 for Run No. 3.
temperature, the same kind of experiments were made in triplicate. At 402.5 K, in panel b, three experiments gave essentially the same results: after 10-40 min, the growth became evident and the evolution was almost completed after 4 h. On the other hand, in panel a at 400.5 K, the results were scattered: one experiment reported no Cub phase formation until 10 h, whereas in the other two the growth was recognized after 5 or 6 h but the accomplishment of the conversion was at most 50% even after 10 h and almost leveled off. Broken curves are bestfits for their initial growth up to ∼30%, based on the Avrami equation discussed later in detail. Differential Scanning Calorimetry (DSC). We checked the sample degradation during the long-time measurements. Figure 5 shows the comparison of DSC heating thermograms recorded at a scanning rate of 2.5 K min-1 before and after annealing at 402.4 K for 5 h. The second heating scan after the annealing
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Figure 5. DSC heating thermograms of ANBC-22 recorded at 2.5 K min-1 before (solid curve) and after annealing at 402.4 K for 5 h (broken curve). Inset enlarges the region 400-420 K.
Figure 7. Time evolution of XRD patterns of ANBC-22 about 7 K below TSmC-Cub under E ) 0: (a) initial state, (b) after 5 h, and (c) after 9 h. Figure 6. Time evolution of the storage modulus (G′) at 400 K, under no electric field (E ) 0, open circles, O, and open squares, 0) or under electric field only in part in the interval designated by Eon and Eoff (open triangles, 4). In the three cases, the frequency and preset amplitude of the shear strain were 9.42 rad s-1 and 0.024, respectively, and the gap between the two plates (electrodes) was 65 µm.
showed two recrystallization peaks at 340 and 358 K, but the phase behavior above the melting temperature (376 K) is almost identical with the first heating before the annealing. The onset temperature of the SmC to Cub phase transition was 408.7 K on the first heating scan, and that of the second heating scan was 408.1 K, 0.6 K lower than the former. The same kinds of experiments were performed for two other annealing temperatures, 404.2 and 399.5 K, one is slightly higher and the other lower than 402.4 K. The obtained difference in the SmC to Cub phase transition temperature between the two scans before and after those 5 h annealings were -0.4 and -0.3 K, respectively. Thus, these experiments verified that the lowering of the transition temperature owing to the sample degradation at high temperatures is, if occurred, less than 1 K, almost negligible. Because the Cub phase formation does occur about 8 K below the previously determined SmC to Cub phase transition temperature without field, we have to conclude that the true SmC to Cub phase transition temperature is at least as low as 400 K. Moreover, comparing Figure 3 with Figure 1, it is also certain that the evolution behavior is accelerated by the electric field application. Dynamic Viscoelasticity (DVE). What is the role of the electric field application? Figure 6 shows the time evolution of the storage modulus (G′) at 400 K. The frequency and preset amplitude of the shear strain for three cases were 9.42 rad s-1 and 0.024, respectively, and the sample was kept for 1 h after the temperature reached the objective one; for one experiment, represented by open triangles, an AC electric field of a strength E ) 200 000 V cm-1 and a frequency of 10 kHz was applied to the sample in the limited time period between the two arrows designated by Eon and Eoff. Under no electric field (E ) 0), as represented by open circles, the G′ value increased very slowly with time t for the initial 80 min (which corresponds to a duration time of 140 min after the temperature reached 400 K), and after that rapidly increased. After 6 h, the value became more than 100 times the initial value. Another case, represented
by open squares, however, showed no time dependence except for fluctuations observed at around t ) 30-140 and 240-260 min. Although the two results are completely different, this situation is quite similar to the result of Figure 4a. In contrast with this, scattering of the results under an electric field was less pronounced; in the case under electric field only in part, the G′ value jumped slightly at the time of the field application (Eon) and started increasing rapidly. This result indicates that the field application acts as a trigger for the transition. Even when the field was removed at the time designated as Eoff, the increase was not influenced so much, consistent with the result of Figure 2. X-ray Diffraction (XRD). Since ANBC-22 exhibits two types of Cub phases, Im3m-type and Ia3d-type phases, upon heating,2 a question arises as to which type appears during prolonged annealing in the SmC phase. Figure 7 shows the X-ray diffraction patterns about 7 K below the zero-field SmC to Cub phase transition temperature. The initial state was the SmC phase with a strong reflection at a scattering vector q of 1.2 nm-1 and a small second-order peak at q ) 2.4 nm-1. In addition to these two peaks, after 5 h in panel b, three other peaks were barely detected. They are assigned to the Im3mCub (321), (400), and (420) reflections, respectively, which developed and became predominant after 9 h; 14 reflections are seen in panel c. If we could estimate the volume fraction of the Cub phase on the basis of the intensities of the SmC (001) and Im3m-Cub (321) reflections, which are the most intense peak of each phase, the fraction was 0.17 in panel b and 0.86 in panel c. From Figure 7 we can conclude that the Cub phase formed after a prolonged annealing at the SmC phase temperature is of Im3m type, which is the low-temperature Cub phase observed upon heating; the formation of the Im3m-Cub phase is suppressed at temperatures several Kelvin below the previously determined SmC to Cub phase transition temperature and emerges after a prolonged annealing at the temperature. Evolution Behavior of Im3m-Cub Phase in SmC Phase. To estimate the effect of electric field application on the Cub phase evolution, the time dependence of the fraction of the Cub phase regions (f, in %) was analyzed using the Avrami equation,21–23
f ) 100 × (1 - exp(-[(t - t0)/τ]n))
(1)
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Figure 8. Avrami parameters as a function of temperature (T) for the Cub phase evolution under E * 0 (open symbols) and E ) 0 (filled symbols): (a) time constant (τ), which corresponds to the time for 63.2% accomplishment of the transition; (b) the early stage period (t0, in min); and (c) the Avrami index (n). Upward arrows in panel b indicate that the transition was not observed for the indicated t0 value under each experimental condition.
where t is time, and in case of field application experiments, elapsed time after the application of the electric field (in min), t0 is the early stage period, τ is the time constant (which corresponds to the time for 63.2% accomplishment), and n is the Avrami index. Several examples of this analysis for the transition under no electric field (E ) 0) are already shown in Figure 4, and that under electric field (E * 0) is presented in Figure 2 (and more in Figure 1 of ref 10). The good applicability of the equation implies that the transformation proceeds via a nucleation and growth process. A similar observation was observed for both the hexagonal to Cub and the Cub to lamellar phase transitions in a hexaethylene glycol mono-n-dodecyl ether (C12EO6)/water mixture.24 In Figure 4a, however, the evolution at 400.5 K under E ) 0 seems to show a tendency to become equilibrated at about half of the transformation after several hours. Similar observations were obtained for the evolutions at 396.5 K under E * 0; the application of an electric field with a high strength of E ) 300 000 V cm-1 and frequencies of 1-100 kHz at the same temperature did accelerate the evolution, but the accomplishment of the conversion was almost leveled off and 50-60% after 1 h for the three frequencies (see Figure S1 of the Supporting Information). According to thermodynamics, two phases can coexist at the phase boundary between the two. Thus, these two results suggest the location of the true zero-field SmC to Cub phase transition temperature at around 400.5-396.5 K. How does the electric field application affect the evolution of the Cub phase in the vicinity of the SmC to Cub phase transition temperature? Figure 8 summarizes three Avrami parameters for the evolution under E * 0 (open symbols) and E ) 0 (filled symbols) as a function of temperature (T) (The respective values of those parameters are compiled in Table S1 of the Supporting Information). Panels a and b in Figure 8 are the plots of τ and t0, respectively. The data points of both parameters for E ) 0 are shifted toward higher temperatures compared with those for E * 0. This clearly implies that the
Kutsumizu et al. SmC to Cub phase transition is more kinetically restricted when the electric field is not employed. The finite value of t0 implies that the transformation is never completely hindered, although we did not conduct the experiments beyond 10 h. Thus, the data points for E ) 0 represent the boundary between the Cub and SmC phases without any external fields, suggesting that the true zero-field SmC to Cub phase transition temperature is down to at least around 400 K. It is more likely that the true transition temperature is as low as 396 K, if we assume that the electric field only affects the potential barrier between the two phases and not the free energies of the two. This will be discussed later again. Figure 8c includes the Avrami index n obtained. The values for E * 0 are around 1 for all three frequencies used, but those for E ) 0 are scattered between 1 and 2.5, with the mean value being ∼1.7. Under the POM observation, the Cub phase region cannot be recognized until the region chains between the two glass plates. Therefore, after the presence of the Cub phase is recognized, the growth is hindered along the direction perpendicular to, and only allowed parallel to, the glass plates. Besides, if assuming heterogeneous nucleation or homogeneous nucleation with diffusion-controlled growth, the n value is not beyond 2.23 However, some data showed values beyond 2. 4. Discussion The adiabatic calorimetry is widely accepted to provide the most precise determination of the thermal equilibrium values of phase transition temperatures. The SmC to Im3m-Cub phase transition temperature of ANBC-22 previously determined by this method was 408 K,4 but the present investigation has unexpectedly revealed that this temperature is not the true transition temperature. It is very likely that the true transition temperature exists around 396 K, although it is very difficult to determine precisely. A byproduct of the present investigation is that the transformation from the SmC to Im3m-Cub phase structures undergoes mainly via a nucleation and growth process as described by the Avrami equation; scattering of the values of the Avrami index n obtained under E ) 0 was never small, which seems to reflect that, not a single but some, mechanisms operate to hinder the transformation. In the temperature region from 396 K to about 10 K above this temperature, the SmC to Im3m-Cub phase transition of this compound is virtually prohibited by the strongly restricted nucleation and very low growth rate. As already pointed out by Demus et al.,19,20 such features of the transformation sometimes result in the appearance and growth of regular polygonal Cub phase domains as observed by POM. The restricted nucleation and very low growth rate of the SmC to Im3m-Cub phase transformation is considered to reflect the restricted mobility of constituent molecules and demand of too much time for reconstruction of the Im3m-Cub phase structure from the precursory SmC phase. In the C12EO6/water mixture,24 the time scale of the transformation process from the Ia3d-Cub to lamellar phases is on the order of 0.1 s (the τ ranges between 0.02 and 0.57 s). In contrast, in the present compound, the process is very slow and the τ value at a temperature 4 K above the true transition temperature (i.e., 400.5 K) is on the order of several hundreds of minutes (Figure 8a). Two different points between the two systems are: (i) the symmetry of the Cub phase structure in the present compound is Im3m, and this type of bicontinuous Cub phase is limited in the thermotropic LCs at this stage;1d,e,g and (ii) the aggregation structures in the present compound are built up by one kind of molecules, about 6000 molecules per unit lattice.6 In connection with the second
Phase Transition of ANBC-22 and AC Electric Field Effect point, in the above lyotropic systems, it is most probable that mobile water molecules would assist a much faster completion of the process than in the present case. Regarding the first point, on the other hand, whether the highly restricted nucleation uncovered in the present work is really characteristic of the formation of the Im3m-Cub phase from the SmC phase remains to be clarified. This question is certainly an issue that attracts further attention because such clarification will also contribute to understand factors determining the equilibrated structure of the Im3m-Cub phase.25 If we accept that the true transition temperature from the SmC to Im3m-Cub phases is around 396 K, the free energy of the Im3m-Cub phase is lower than that of the SmC phase when temperature T is higher than 396 K. In the region from 396 K to about 10 K above this temperature, the potential barrier between the two phases is crucial in prohibiting the actual transition severely. Thus, the recorded transition temperature of this compound under E ) 0 may be some temperature that derives from a mix of thermodynamic and kinetic factors. In other words, it may be said that the applied field lowers the kinetic barrier to the transition and uncovers the true transition temperature inhibited under the normal condition. Let us consider the effect of the electric field on the transition in more detail. As described in the preceding paper,10 the formation of the field-induced Cub phase was dependent on the frequency of the applied field, and as seen from Figure 8, the higher frequency induces the evolution more effectively. On the basis of this fact, the paper suggested no possibility of the Joule heating effect due to ionic impurities. Very recently, a similar field-application experiment was conducted on a binary mixture of 1,2-bis(4′-n-decyloxybenzoyl)hydrazine (BABH-10) with 9.37 mol% benzhydrazide in the SmC phase; the BABH10 and their homologues having different alkyl chains are another interesting Cub-phase-forming system,26 and an important point for this system and the mixtures is that the SmC phase is a high-temperature phase of the Cub phase. The result showed the evolution of the Cub phase (of Ia3d-type in this case), which ensures that the field-induced Cub phase formation is not due to the Joule heating effect. For the proper effects of the electric field on the transition, one of the effects considered is the shift of the transition temperature; the electric field E (E ) |E|) changes the free energies of both phases with different dielectric constants.8,27 Although the SmC phase has a dielectric anisotropy, we use here the directionally averaged value εSmC [) (ε|SmC + 2ε⊥SmC)/ 3] because of its polydomain nature in the real sample. Here, ε|SmC and ε⊥SmC are the dielectric constants measured parallel and perpendicular to the long axis of the molecule, respectively. The dielectric constant of the Cub phase is denoted as εCub. T* (∼396 K as mentioned above) and T are the thermodynamic transition temperatures under E ) 0 and E * 0, respectively. From the equivalence of the two free energies µSmC(T,E) and µCub(T,E) at the phase boundary,28 the magnitude of the temperature shift ∆T () T - T*) under the field is expressed as:
∆T ) -[T*M/(2F∆SmC-CubHm)][(εCub - εSmC)ε0E2] (2) Here, M is the molar mass of ANBC-22 () 567 g mol-1), F is the density () 0.990 g cm-3),6 ∆SmC-CubHm is the molar transition enthalpy () 2 kJ mol-1),2,4 and ε0 is the vacuum permittivity () 8.854 × 10-12 C2 m-2 N-1). From our preliminary dielectric studies,11 it was shown that |εCub - εSmC|
J. Phys. Chem. B, Vol. 113, No. 3, 2009 645 e 0.1 at 10-100 kHz (see Figure S2 of the Supporting Information), and thus, we can roughly estimate |∆T| e 0.005 K for E ) 100 000 V cm-1. This implies that the electric field effect on the transition temperature is almost negligible. Another possibility is the reorientation effect. For ANBC22, we can reasonably assume the dielectric anisotropy ∆εSmC () ε|SmC - ε⊥SmC) is negative because the main origin of the anisotropy is the nitro group of a large dipole moment (4.2 D) attached as a side group. In this case, the SmC slabs receive a torque from the electric field E and is most stabilized when the normal vector of the SmC layer is perpendicular to E. This effect is usually coupled with the elastic properties of the SmC phase, and is called the Frederiks transition. Pelzl et al. investigated the Frederiks transition of several SmC mesogens using an AC electric field with a frequency of 1-2 kHz and with a strength E up to 100 000 V cm-1.29–31 For ANBC-22, one plausible mechanism is that the same type of rearrangement might be a trigger for the transition; the nucleation of the Cub phase is produced by the rearrangement of the SmC slabs, which is normally activated thermally and in this case would be assisted by the application of the electric field. If the application of the electric field prominently promoted the nucleation and increased the number of the nucleus proportionally with elapsed time, without changing the growth mechanism, then the value of the Avrami index n for E * 0 would be by unity larger than the value for E ) 0. The experimental result is, however, rather opposite, which may suggest that the value for E * 0 is smaller than the value for E ) 0 by ∼0.7. This contradiction may be explained as follows. Since the growth rate under E * 0 is much higher than that under E ) 0 as seen from Figure 8a, it is easily expected that the growth mechanism itself change from a process with a constant velocity under E ) 0 to a diffusion-controlled one under E * 0. Besides, it is reasonable to consider that the nucleation process under E ) 0 would be heterogeneous. In that case, the Avrami theory23 predicts that the index n would change from 2 for E ) 0 to 1 for E * 0, as far as both the nucleation process (heterogeneous) and the dimensionality of the growth (disk-like growth) are identical. The experimental result might be the case. In other words, the application of the field seems to affect the nucleation just at the beginning, consistent with the result of Figure 6. In the orientation effect, the magnitude of the ∆εSmC is important. Unfortunately, we were unable to prepare the oriented samples necessary to get the precise value of ∆εSmC,32 but it is reasonably assumed that the magnitude of ∆εSmC is small, most probably on the order of 1 at most, due to the dimerization of two ANBC-22 molecules with the antiparallel fashion. Moreover, the frequencies used were much higher in our case compared to the work by Pelzl et al. Thus, the real mechanism would be more complicated than discussed here. As already mentioned, some growth behaviors both under E ) 0 and for E * 0 cannot be fully described by the Avrami relation and/or the obtained values of the Avrami index are scattered under E ) 0. It is probable that two or more processes may simultaneously operate. Further investigation is of course demanded. 5. Conclusions The SmC to Im3m-Cub phase transition behavior of ANBC22 and AC electric field effect on the SmC phase were examined using POM, DSC, DVE, and XRD techniques. One of the very shocking results is that the transition temperature previously determined by adiabatic calorimetry (408 K)4 is not the true transition temperature. All the results obtained can be understood if we admit that the true transition temperature, which is very
646 J. Phys. Chem. B, Vol. 113, No. 3, 2009 difficult to determine precisely, exists around 396 K. A byproduct of the present studies is that the transformation from the SmC to Im3m-Cub phase structures undergoes mainly via a nucleation and growth process as described by the Avrami equation. In the temperature region from this 396 K to about 10 K above this temperature, the SmC to Im3m-Cub phase transition of this compound is kinetically prohibited by strongly restricted nucleation and very low growth rate. This is probably due to the dramatic change in dimensionality of the ordered structures between the two phases and is also due to the ordered structures being constructed of only one kind of molecules. In that temperature region, the recorded transition temperature from the SmC to Im3m-Cub phases of this compound under E ) 0 may be regarded as some temperature that derives from a mix of thermodynamic and kinetic factors. From this viewpoint, it is noted that the present investigation has uncovered the true transition behavior inhibited under the normal condition by applying the electric field and lowering the kinetic barrier between the two phases. Acknowledgment. We first thank Professor Hirotsugu Kikuchi at Kyushu University and Professor Keiichi Moriya and Dr. Koichi Sakajiri at Gifu University for their valuable discussions. We also thank Mr. Hiroyuki Mori and Mr. Yutaro Taguchi at Gifu University for their experimental aid. This work was partly supported by Grant-in-Aid for Scientific Research on Priority Areas (A), “Dynamic Control of Strongly Correlated Soft Materials” (No. 413/14045232) and “Super-Hierarchical Structures” (No. 446/19022012) from the Ministry of Education, Science, Sports, Culture, and Technology, Japan, and by Grantin-Aid for Scientific Research (C) 14550846 and 18550121 from Japan Society for the Promotion of Science. Beamtimes at PFKEK (2004G297 and 2006G342) and at BL45XU-SPring-8 (2003B0417-NL2b-np, 2004A0392-NL2b-np and 2004B0144NL2b-np) are also acknowledged. Supporting Information Available: Synthesis and characterization of ANBC-22, supplementary figure and table concerning cubic phase evolution behavior and temperature dependence of dielectric constant (PDF). This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Hyde, S.; Andersson, S.; Larsson, K.; Blum, Z.; Landh, T.; Lidin, S.; Ninham, B. W. The Language of Shape, The Role of CurVature in Condensed Matter: Physics, Chemistry and Biology; Elsevier: Amsterdam, 1997. (b) Tschierske, C. Annu. Rep. Prog. Chem., Sect. C 2001, 97, 191267, and references therein. (c) Diele, S. Curr. Opin. Colloid Interface Sci. 2002, 7, 333–342. (d) Kutsumizu, S. Curr. Opin. Solid State Mater. Sci. 2002, 6, 537–543. (e) Impe´ror-Clerc, M. Curr. Opin. Colloid Interface Sci. 2005, 9, 370–376. (f) Bicontinuous Liquid Crystals; Lynch, M. L., Spicer, P. T., Eds.; Surfactant Science Series, Vol. 127; CRC Press, Taylor & Francis Group: Boca Raton, 2005. (g) Zeng, X.; Ungar, G.; Impe´rorClerc, M. Nat. Mater. 2005, 4, 562–567. (2) Kutsumizu, S.; Morita, K.; Ichikawa, T.; Yano, S.; Nojima, S.; Yamaguchi, T. Liq. Cryst. 2002, 29, 1447–1458. (3) Kutsumizu, S.; Yamada, M.; Yano, S. Liq. Cryst. 1994, 16, 1109– 1113.
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