Overall Dielectric Study on the Odd Members of a Highly

Article pubs.acs.org/JPCB

Overall Dielectric Study on the Odd Members of a Highly Nonsymmetric Pyrene-Based Series of Liquid Crystal Dimers N. Sebastián,*,† M.R. de la Fuente,† D.O. López,*,‡ M.A. Pérez-Jubindo,† J. Salud,‡ and M.B. Ros§ †

Departamento de Física Aplicada II, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain ‡ Grup de Propietas Físiques dels Materials (GRPFM), Departament de Física i Enginyeria Nuclear, E.T.S.E.I.B., Universitat Politècnica de Catalunya, Diagonal, 647 08028 Barcelona, Spain § Departamento de Química Orgánica, Facultad de Ciencias, Instituto de Ciencia de Materiales de Aragón, Universidad de Zaragoza-CSIC, 50009 Zaragoza, Spain ABSTRACT: Broadband dielectric spectroscopy (103 Hz−1.8 × 109 Hz) has been performed on the odd nonsymmetric liquid crystal dimers of the series α-(4cyanobiphenyl-4′-oxy)-ω-(1-pyreniminebenzylidene-4′-oxy) alkanes (CBOnO.Py) with n ranging from 3 to 11, as a function of temperature. A previous thermal behavior study through heat capacity measurements has been made. Dielectric measurements enable us to obtain information about the molecular dynamics in the nematic mesophase as well as in the isotropic phase. Two orientations (parallel and perpendicular) of the molecular director with regard to the probe electric field have been investigated. In the nematic mesophase, the dielectric anisotropy is revealed to be positive for all studied compounds. Measurements of the parallel component of the dielectric permittivity are well-explained by means of the molecular theory of dielectric relaxation in nematic dimers (Stocchero, M.; Ferrarini, A.; Moro, G. J.; Dunmur, D. A.; Luckhurst, G. R. J. Chem. Phys., 2004, 121(16), 8079). The dimer is seen as a mixture of cis and trans conformers, and the model allows us to estimate their relative populations at each temperature. The main molecular motions are interpreted by the model as independent end-overend rotations of each terminal semirigid unit of the dimer.

1. INTRODUCTION Liquid crystal dimers are materials in which the constituent molecules are formed by two terminal semirigid groups (mesogenic or not) connected by a flexible chain of variable length. The most widely synthesized dimers are those with calamitic mesogenic rigid groups connected by ether or methylene linkages.1 Other less conventional architectures explore bent-core mesogenic rigid groups2−7 or even nonmesogenic terminal units.8,9 In recent years, liquid crystal dimers have attracted a renewed interest because of the discovery of exciting unusual properties. Among the most recent findings are the identification of a new mesophase, the twist-bend nematics,10−12 and the existence of Blue phases over an unusually wide temperature range in dimers doped with chiral agents.13 Interestingly, at the moment, both findings have been observed in liquid crystal dimers with an odd number of carbons in the flexible chain and is believed to be attributed to the combination of a large value of the flexoelectric coefficient e3 together with a small value of the bend elastic constant K3.14,15 Liquid crystal dimers with an even number of carbons in the flexible chain have been recently used in tunable laser devices.16 The length, parity, and nature of the flexible core strongly affect the properties of liquid crystal dimers. It is welldocumented how liquid crystal dimers exhibit a pronounced © 2013 American Chemical Society

odd−even effect in the transitional properties (transition temperatures and entropy changes).1,17 Even members of a given dimeric series exhibit higher values than odd compounds and this fact, well-explained in some theoretical approaches,18−22 has been attributed to the dependence of the energetically favored molecular shapes (conformers) on the parity of the flexible core. It is known that for each compound, the distribution of conformers between the accessible states is temperature-dependent over the range of the mesophase, but there are no specific studies available in relation to the distribution of conformers exclusively with the temperature and length of the flexible spacer. In order to avoid the odd−even effect, only odd or even compounds of a given series of liquid crystal dimers should be considered. This is just this idea applied to the odd members of the series α-(4-cyanobiphenyl4′-oxy)-ω-(1-pyreniminebenzylidene-4′-oxy)akanes (CBOnO.Py) with n ranging from 3 to 11, which forms the focus of our paper. One of the physical properties sensitive to changes in the molecular shape of polar molecules is the dielectric permittivity. In previous work,3,4,8,9,11,12,23−29 dielectric measurements have Received: June 20, 2013 Revised: October 25, 2013 Published: October 28, 2013 14486

dx.doi.org/10.1021/jp406085r | J. Phys. Chem. B 2013, 117, 14486−14496

The Journal of Physical Chemistry B

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temperature rate and the modulated heat flow). In our work, the experimental conditions (temperature amplitude and oscillation period) were adjusted to only get the real part (the static part) of the complex heat capacity in such a way that the phase lag angle (ϕ) is nearly zero, and consequently, the imaginary part of the complex heat capacity data vanishes. However, when a first-order phase transition takes place at a certain temperature, there exists a region around this temperature (the coexistence region), where the ϕ angle cannot be kept as zero. A more detailed description of the MDSC technique can be found in other studies.9,32−34 The MDSC measurements consisted of heating runs at 1 K· min−1 from room temperature up to the I-phase and cooling runs at 5 K·min−1 (exceptionally at 1 K·min−1) to observe glassy behavior. The parameters of modulation (temperature amplitude and oscillation period) were ±0.5 K and 60 s. The sample masses (chosen between 2 and 3 mg) were selected to ensure a uniform thin layer within the aluminum pans. Measurements of the complex dielectric permittivity ε*(f) = ε′( f) − iε″( f), in the range of 103−1.8 × 109 Hz, were performed using two impedance analysers: the HP 4192A and 4291A. The cell consists of two gold-plated brass electrodes (diameter 5 mm) separated by thick silica spacers of the order of 50 μm. A modified HP16091A coaxial test fixture was used as the sample holder. It was held in a cryostat (Novocontrol), and both temperature and dielectric measurements were computer-controlled. Additional details of the experimental technique can be found elsewhere.9,33,34 Dielectric measurements were performed on heating and on cooling with different temperature steps being stabilized to ±20 mK.

provided information on the temperature dependence of the distribution of conformers in liquid crystalline phases and have allowed researchers to gain insight into the rotational dynamics of the dipolar groups of the dimer. Some of those preliminary dielectric data have prompted the development of a new theory for the dielectric relaxation of mesogenic dimers in a nematic phase.30 The odd and even members of the series of liquid crystal dimers CBOnO.Py, with n ranging from 3 to 11, were first synthesized by Attard and co-workers who, together with the synthesis procedure, released a preliminary study on their thermal behavior.8 Recently, one of the compounds of the series, the n = 11 (CBO11O.Py), has been the subject of a study9 of the dielectric behavior of the nematic and isotropic phases as well as the critical behavior of the nematic−isotropic phase transition. Concerning the latter, a comparative preliminary study for the three odd compounds of the series with longer chains (n = 7, 9, and 11)31 has also recently been published. In the present paper, the main interest consists of performing a complete and comparative dynamic dielectric study for all the odd compounds of the CBOnO.Py series. However, a global and appropriate interpretation of results requires a deeper knowledge of the thermal behavior of the compounds that will be addressed. The structure of the paper is as follows. In section 2, we describe the experimental details. In section 3, we present and discuss results concerning the overall thermal behavior of the odd members of the CBOnO.Py series on the basis of heat capacity data. The presentation and analysis of the dynamic dielectric measurements is addressed in section 4. An overall discussion and the concluding remarks are summarized in sections 5 and 6, respectively.

3. THERMAL BEHAVIOR The work of Attard et al.8 basically dealt with the transitional properties of the CBOnO.Py dimers. As set out in that study, all compounds exhibit a nematic (N) phase and some of them also a smectic A (SmA) phase at lower temperatures. Among the pure nematogenic dimers, the thermal results concerning the CBO11O.Py have been extensively treated elsewhere.9 From this study, it should be remembered that the N-mesophase exhibits an enantiotropic behavior and can be supercooled at cooling rates of 15 K·min−1 or higher, leading to a nematic glassy state. At lower cooling rates, the N-mesophase can only be supercooled down to about 45 K below the N−I phase transition. In this slow cooling regime the N-mesophase crystallizes. There is no evidence of the existence of a SmAmesophase at any temperature. As a guide for the reader, the most characteristic transition temperatures on heating run are listed in Table 1. The thermal behavior of CBO3O.Py deserves a special mention. In the preliminary work of Attard et al.,8 it is mentioned that the propyl homologue shows a monotropic Nmesophase, but this affirmation does not give much information about the complex thermal behavior of such a mesophase. First of all, it should be stressed that Attard and coworkers performed DSC experiments at not less than 10 K· min−1, a cooling or heating rate which is 10 times higher than that used in our heat capacity experiments. Figure 1 shows heat capacity measurements on cooling from the isotropic (I) phase (red symbols) down to 300 K and the subsequent heating (black symbols) up to close to 400 K, both at 1 K·min−1. It is clearly observed how a slow cooling from the I-phase transforms the sample into the N-mesophase, which

2. EXPERIMENTAL METHODS 2.1. Materials. The schematic molecular structure of CBOnO.Py is

It consists of two terminal groups with different shape and size (named A and B in the scheme) attached by a flexible spacer of n-methylene units. The terminal group A has an important dipole moment along its long axis associated with the nitrile group (horizontal arrow in the scheme), while the B group has a smaller and mainly transverse dipole moment (drawn in the scheme as a perpendicular arrow) associated with the imine group. The transverse dipole moment of the ether linkages will be neglected due to its much smaller value. The material has been synthesized according to the previous work of Attard et al.8 2.2. Experimental Techniques. Heat capacity data at normal pressure were obtained by means of a commercial differential scanning calorimeter DSC-Q2000 from TA-Instruments working in modulated mode (MDSC). It is important to realize that similar to an AC calorimeter, the MDSC technique, besides heat capacity data, simultaneously provides phase shift angle data ϕ (the phase lag between the modulated 14487



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Table 1. Temperatures of the Cr−N (TCrN), glass (Tg), SmA−N (TSN), and N−I (TNI) transitions for the odd CBOnO.Py dimers CBOnO.Py (n)

Figure 1. Heat capacity data as a function of temperature for CBO3O.Py (red and black symbols correspond to data collected on cooling and on heating at 1 K·min−1, respectively). The inset shows both the heat capacity (black symbols) and the heat flow (blue line) on heating the sample from the I phase above 400 K.

TCrN (K) a

Tg (K)

TSN (K)

TNI (K)

3

472.2 465.4 ± 0.5a

324.2 323.3

393.2 388.0 ± 0.5

5

425.2 409.0 ± 0.5

314.2 312.6

323.2 324c

427.2 426.0 ± 0.5

7

429.2 428.2 ± 0.5

310.2 310.6

338.2 333.5

437.2 433.4 ± 0.5

9

426.2 427.0 ± 0.5

306.2 306.9

328.2 340c

434.2 432 ± 0.5

11

423.2 421.3 ± 0.5

307.2 305.0

432.0 426.9 ± 0.5

ref 8b this work 8b this work 8b this work 8b this work 8b 9

a

Corresponds to the Cr-to-I phase transition. bTemperatures were obtained from the peak maximum in the DSC traces at 10 K·min‑1. Measurements are performed with a Perkin-Elmer DSC-7. cMDSC measurements on cooling regime at 5 K·min‑1.

remains in the glass transition and leads to a nematic glassy state . The subsequent heating shows how the cooling behavior is exactly reproducible on heating, and the nematic mesophase does not crystallize in this temperature range. Ultimately, the N−I phase transition occurs. This behavior is completely reproducible in the temperature range of 300−400 K. However, if the sample is heated up from 400 K, the N-mesophase crystallizes at about 415 K, and at higher temperatures, the Cr− I phase transition is observed (see the inset of Figure 1). It should be stressed that once the crystal state is formed at temperatures higher than 400 K, either on cooling or on heating, the Cr to mesophase transition is not observed. Thus, once the I phase is formed, operating in the conditions of Figure 1 (300−400 K) or even at higher rates, the N mesophase appears to be so stable as a stable phase, and the CBO3O.Py dimer could be considered as a pseudonematogenic liquid crystal with a pseudoenantiotropic N mesophase. The most characteristic transition temperatures on heating run are listed in Table 1. In the manuscript of Attard et al.,8 it is noted that the central compounds of the series (n = 5, 7, and 9) exhibit monotropic SmA mesophases. Figure 2 shows the heat capacity for the three compounds measured at the same conditions. In all cases, the sample is cooled at 5 K·min−1 (red symbols) from the isotropic phase down to 290 K and heated at 1 K·min−1. There is a relatively small heat capacity peak associated with the N-toSmA phase transition on cooling. For CBO7O.Py, the SmA-toN phase transition is detected on heating, but once the N mesophase is formed, the sample abruptly crystallizes. In all cases, for the sake of clarity, the heat capacity peak corresponding to the melting (Cr-to-N) is not represented in the main figure. However, the top insets in Figure 2A−C show the Cr-to-N and the N-to-I phase transitions. It is clearly observed in the inset of Figure 2C (CBO5O.Py) that the representative heat capacity peak corresponding to the N-to-I phase transition is too small in relation to that of the melting. From Figure 2, it may be observed how all of these compounds show the typical heat capacity jump of a glass transition, in fact, a smectic glass, on cooling and on heating regimes. Lower cooling regimes than that used (5 K·min−1) make difficult the formation of smectic glasses, and, in some

cases, there is a partial crystallization of the sample. The most characteristic transition temperatures on the heating run for all these compounds are listed in Table 1.

4. DYNAMIC DIELECTRIC BEHAVIOR Dielectric results for the odd members of the CBOnO.Py series have been obtained for both the parallel and perpendicular alignments. In metallic cells, the set of CBOnO.Py compounds spontaneously align parallel to the surface, resulting in a perpendicular alignment (ε⊥) of the sample with respect to the probing electric field. The fact that the dielectric anisotropy (Δε = ε|| − ε⊥) of such compounds at low frequencies is positive9,35 enables the use of a dc bias voltage (35 V) to generate parallel (ε||) alignment of the director with respect to the probing electric field. Saturation of the alignment in the nematic phase was confirmed by measuring the capacitance as a function of voltage. The frequency dependence of the complex permittivity has been analyzed using the empirical function Δεk σ ε(ω) = ∑ + ε∞ − i dc αk βk ωε0 (1) k [1 + (iωτk) ] where Δεk is the dielectric strength of each relaxation mode, τk the relaxation time related to the frequency of maximum dielectric loss, αk and βk are parameters which describe the shape (width and symmetry) of the relaxation spectra (αk = βk = 1 corresponds to a simple Debye relaxation), and σdc is the dc conductivity. The summation is extended over all relaxation modes, and each is fitted according to the Havriliak−Negami (H−N) function. An important part of this dielectric study consists in identifying the different molecular motions of the set of CBOnO.Py dimers. In liquid crystal monomers, dielectric results29,33,34,36,37 are satisfactorily interpreted by means of the well-known theories of Maier−Meier38 for the static permittivity and Nordio−Rigatti−Segre39 for the dielectric relaxation. In dimers, the above-mentioned theories are not specifically adapted to interpret the observed results. The theoretical model for nematogenic liquid crystal dimers published by Stocchero et al.30 has been revealed to be very 14488



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Figure 3. Three-dimensional plot of dielectric losses vs temperature and logarithm of the frequency for CBO9O.Py in parallel (A) and perpendicular (B) alignments. Dashed lines are an eye-guide depiction of the relaxation processes.

temperature of CBO9O.Py for both parallel and perpendicular alignments. In the nematic phase, the dielectric spectrum of the parallel component is clearly dominated by two relaxation processes (denoted as m1,L∥ and m1,H∥ in Figure 3A) whose strengths seem to be correlated in the same way as previously interpreted in detail for CBO11O.Py,9 according to the theoretical model of Stocchero et al.30 On the other hand, the dielectric spectrum of the perpendicular component shows a predominant relaxation process (denoted as m2,⊥ in Figure 3B). The other long chain dimer CBO7O.Py exhibits comparable results. For the purposes of illustrating the data analysis followed for the long chain dimers, Figure 4 shows the real and imaginary parts of the permittivity for CBO7O.Py as a function of frequency at one temperature of the isotropic phase (Figure 4A) and at one temperature of the nematic mesophase for both alignments (Figure 4B,C). In the isotropic phase (Figure 4A), the results were fitted, according to eq 1, to a single broad relaxation mode (α = 0.82, β = 0.65) that could be attributed to a concerted rotation of the whole dimer, denoted hereafter as m1-mode. Figure 4B shows a typical result for the parallel component of the permittivity in the N-mesophase (T = 403 K). The fitting procedure, according to eq 1, was identical to the followed for the CBO11O.Py dimer,9 in which three relaxation processes were assumed. The low and intermediate frequency relaxations (both Debye-like), both at lower frequencies than the isotropic m1-mode, have been identified with the modes m1,L∥ and m1,H∥ predicted by the model.30 Thus, m1,L∥ and m1,H∥ modes are attributed to the individual flip-flop reorientations of the mesogenic units A and B via changes in the conformational state of the flexible spacer of the dimer, respectively. The third relaxation process (α = 0.7, β = 1) at higher frequencies,

Figure 2. Heat capacity data as a function of temperature for CBO9O.Py (A), CBO7O.Py (B), and CBO5O.Py (C) in the same conditions: cooling from the I phase at 5 K·min−1 (red symbols) and the subsequent heating from the smectic glassy state at 1 K·min−1 (black symbols). All the heating data are disrupted at the onset of the heat capacity peak corresponding to the Cr−N phase transition. Insets show in a zoom window the heat capacity around both the Cr−N and the N−I phase transitions on heating regime.

useful in interpreting the molecular motions at low frequencies of the parallel component of the permittivity.9,11,12,23,28−30 However, the faster processes that are not contemplated by the model of Stocchero et al. will be tentatively described in the same terms as in liquid crystal monomers, as proposed elsewhere.40 In the exposition of the dielectric results of the odd CBOnO.Py dimers, those compounds with n ranging from 11 to 7 exhibit comparable behaviors in both the isotropic and nematic phases yet different in a certain extent from the shorter chain dimers (n = 5 and 3). On that basis, the obtained results are presented grouped in two distinct parts according to the length of the spacer. 4.1. Long Chain Dimers CBOnO.Py (n = 11, 9, and 7). As a representative example of the dielectric behavior of the long chain dimers, Figure 3 shows the three-dimensional plots of the dielectric absorption as a function of frequency and 14489



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Figure 5. Dielectric strength as a function of [T − TNI] of the different elementary contributions for CBO9O.Py (denoted as 9) and CBO7O.Py (denoted as 7). The data corresponding to the longest chain dimer CBO11O.Py (denoted as 11) are shown for purposes of comparison.

populations of the cis/trans conformers and not on the relative strengths of the dipoles of the terminal groups. Thus, such data indicate that there is a change of the population distribution as the chain becomes shorter. Such an analysis will be presented later in section 5. It can also be seen in Figure 5 how the dielectric strength of the m2∥-mode (Δεm2∥) for the investigated compounds decreases on entering the N-mesophase, stabilizing in a nearly constant value at lower temperatures as previously reported for the longest member of the family, the CBO11O.Py dimer.9 In perpendicular alignment, the dielectric strength of the high frequency relaxation (m2⊥-mode) (Δεm2⊥) behaves similar with temperature to Δεm2∥. Such behavior for both Δεm2∥ and Δεm2⊥ is as expected according to the Nordio−Rigatti−Segre theory39 for the rotation of the molecule around its long axis and for the precessional motions. Figure 6 shows for CBO7O.Py and CBO9O.Py long chain dimers, in an Arrhenius plot, the temperature dependence of the characteristic relaxation frequencies associated with each mode for both the N and I phases. As in Figure 5, CBO11O.Py

Figure 4. Frequency dependence of the dielectric permittivity of CBO7O.Py in the isotropic phase (T = 439 K)(A) and in the nematic phase (T = 403 K) in both the parallel (B) and perpendicular (C) alignments. Black solid and dashed lines are fittings according to eq 1. Symbol lines represent deconvolution into elementary modes.

denoted as m2∥-mode, could be mainly attributed to the rotation around the molecular long axis and then related to the transverse dipole moment as described by the Nordio− Rigattli−Segre theory.39 Figure 4C shows both components, real and imaginary, of the perpendicular dielectric permittivity in the N mesophase. Measurements were fitted, according to eq 1, by assuming two relaxation processes. However, the strength of the low frequency relaxation is extremely small (not drawn in Figure 4C), being indicative of a small amount of misalignment and will be disregarded in the following analysis. The dielectric spectrum of the perpendicular component is dominated by a high frequency relaxation process (α = 0.71, β = 1) that was assigned to the superposition of the precessional motions of the semirigid units and the rotation of the molecule around its long axis, as described by the Nordio−Rigatti−Segre theory.39 Hereafter, this relaxation process will be denoted as m2,⊥-mode. Figure 5 shows the temperature dependence of the dielectric strength data for all the aforementioned relaxation modes in both alignments for CBO7O.Py and CBO9O.Py long chain dimers. For sake of comparison and completeness, the dielectric strength data for the longest member of the family, the CBO11O.Py dimer,9 are also included in Figure 5. For all the compounds that were considered, a clear correlation between the dielectric strengths of the m1,L∥-mode (Δεm1,L∥) and m1,H∥-mode (Δεm1,H∥) can be observed: while Δεm1,L∥ increases with decreasing temperature (order increases), Δεm1,H∥ decreases. One interesting feature arises from the comparison of the relative strengths between these two modes for the three compounds. It can be seen how the shorter the chain, the closer the temperature at which Δεm1,L∥ is equal to Δεm1,H∥ from the isotropic-to-nematic transition temperature (TNI). The model of Stocchero et al.30 establishes that the relative strengths of both relaxations depend on the relative

Figure 6. Arrhenius plot of the relaxation frequencies ( f k) of the different elementary contributions for CBO9O.Py (denoted as 9) and CBO7O.Py (denoted as 7). Data corresponding to the longest chain dimer CBO11O.Py (denoted as 11) are shown for purposes of comparison. 14490



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has been included for the purpose of comparison. It should be stressed that the characteristic relaxation frequencies corresponding to the m2∥-mode are not shown in Figure 6 because they are very close to those corresponding to the m2⊥-mode. Thus, both sets of characteristic frequencies follow a comparable behavior, but among them, those corresponding to the m2⊥-mode have been chosen to be shown because they exhibit higher dielectric strengths. A simple inspection of Figure 6 points out that both the CBO7O.Py and CBO9O.Py dimers exhibit very close characteristic frequencies of the m1,L∥ and m1,H∥ modes and that of the m1 mode (I phase) as well. In that sense, the longest chain dimer CBO11O.Py differs substantially from the other two CBO7O.Py and CBO9O.Py. A more quantitative dissertation focusing on activation energies of such modes, m1,L∥ and m1,H∥, will be presented in Section 5. 4.2. Short Chain Dimers CBOnO.Py (n = 5 and 3). Let us consider the dielectric behavior in the N mesophase of the dimer CBO5O.Py. Figure 7A,B show the real and imaginary Figure 8. Frequency dependence of the dielectric permittivity of CBO5O.Py (A) and CBO3O.Py (B) in the isotropic phase at 433 and 398 K, respectively. Black solid and dashed lines are fittings according to eq 1. Symbol lines represent deconvolution into elementary modes.

temperatures in the I phase for the two dimers, CBO5O.Py (Figure 8A) and CBO3O.Py (Figure 8B). A broad absorption peak is observed which results from the superposition of two relaxation processes, much more evident in the shortest chain dimer CBO3O.Py than in CBO5O.Py. This feature constitutes the most remarkable difference with respect to the results obtained for long chain dimers (see Figure 4A). The explanation of the appearance of both processes is not straightforward and will be discussed in section 5. Subsequently, the low and high frequency relaxations of the isotropic phase will be denoted as m1,L and m1,H, respectively. The fitting procedure, according to eq 1, is difficult because the shape of the lower frequency process m1,L is hidden by the higher strength of the m1,H-mode. Thus, the shape parameters for the m1,L-mode have been set as α = β = 1; however, for the m1,H-mode, distinct values have been obtained for CBO5O.Py (α = 0.9 and β = 0.6) and for CBO3O.Py (α = 0.8 and β = 0.8). According to the thermal behavior observed for the shortest chain dimer CBO3O.Py which has been detailed in section 3, once the I-phase is formed, on slow cooling and in the way the dielectric measurements are performed, the I phase transforms to the N mesophase, remaining as such in a wide temperature range. The dielectric losses as a function of temperature and frequency for such a dimer are shown for both alignments in the three-dimensional plot of Figure 9. It can be observed how the parallel component of the permittivity (Figure 9A) is dominated apparently by two relaxation processes whose strengths seem to be correlated as observed for the other dimers. However, a careful interpretation through the fitting procedure according to eq 1 leads to three processes. The lower frequency relaxation (Debye-like) prevails throughout the temperature range of the N mesophase and is identified with the m1,L∥-mode. At higher frequencies, the broad and highly asymmetric relaxation is tentatively fitted by two modes, the socalled m2∥ and m1,H∥, which are superimposed due to their proximity in frequency. Such a questionable fitting criterion was adopted in accordance with the other related like-dimers. Figure 9B qualitatively shows the perpendicular component of the permittivity observed for the shortest chain dimer

Figure 7. Frequency dependence of the dielectric permittivity of CBO5O.Py in the nematic phase (T = 403 K) in both the parallel (A) and perpendicular (B) alignments. Black solid and dashed lines are fittings according to eq 1. Symbol lines represent deconvolution into elementary modes.

components of the permittivity in both the parallel and perpendicular alignments. It is quite evident from both figures that the dielectric behavior of the N mesophase is qualitatively similar to that observed for long chain dimers (see Figure 4). Thus, the analysis procedure was performed in a smilar way. The parallel component of the permittivity, Figure 7A, was fitted, according to eq 1, to three relaxation processes: the two at lower frequencies associated with the individual flip-flop reorientations of the mesogenic units (m1,L∥ and m1,H∥, both Debye-like) and the other at higher frequencies (m2∥, α = 0.6, β = 1) attributed to the rotation around the molecular long axis. The perpendicular component, Figure 7B, was fitted, according to eq 1, to two relaxation process, but that of the low frequency is due to a misalignment and is not considered in further analyses. Thus, the relaxation at higher frequencies, denoted as the m2⊥-mode (α = 0.7, β = 0.8), is attributed to the superposition of the precessional motions of the semirigid units and the rotation around the molecular long axis. The analysis of the real and imaginary components of the permittivity in the isotropic phase deserves a special mention. Such dielectric results are given in Figure 8 for representative 14491



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Figure 9. Three-dimensional plot of dielectric losses vs temperature and logarithm of the frequency for CBO3O.Py in parallel (A) and perpendicular (B) alignments. Dashed lines are an eye-guide depiction of the relaxation processes.

Figure 10. Dielectric strength as a function of [T − TNI] of the different elementary contributions for CBO5O.Py (A) and CBO3O.Py (B).

CBO3O.Py. The above-mentioned two relaxations in the I phase (m1,L and m1,H) are clearly visible. They remain in the N mesophase because of a certain degree of misalignment (denoted as m1,L⊥), as in the case of CBO5O.Py. The m2,⊥mode, the most prominent at high frequencies, is also clearly visible. The temperature dependence of the dielectric strengths of the relaxation modes for both short dimers is given in Figure 10A,B. The differences with respect to long chain dimers (n = 7, 9, and 11) in Figure 5 are evident. Apart from the appearance of two relaxation peaks in the I phase, in the whole range of the N mesophase, the dielectric strength of the m1,L∥-mode (Δεm1,L∥) is higher than that of the m1,H∥-mode (Δεm1,H∥). However, the dielectric strength of the m2∥-mode (Δεm2∥) and that of the m2⊥-mode (Δεm2⊥) behave similarly with temperature, as in the case of long chain dimers. Figure 11 shows for CBO5O.Py and CBO3O.Py short chain dimers, in an Arrhenius plot, the temperature dependence of the characteristic relaxation frequencies associated with each mode for both the N and I phases. It is noteworthy that the I− N phase transition of CBO3O.Py occurs far below that of the CBO5O.Py. Even so, once the transition of CBO3O.Py takes place, the characteristic frequencies of the m1,L∥ and m1,H∥ modes experience a jump down to nearly the corresponding frequencies of the CBO5O.Py. In Figure 11, for the sake of clarity (as in Figure 6), the characteristic relaxation frequencies corresponding to the m2∥mode are not shown; however, those corresponding to the m2⊥mode are drawn. It can be observed how the characteristic relaxation frequencies of the m2⊥-mode of CBO3O.Py are considerably lower than those of CBO5O.Py. Even so, for both dimers, the frequencies exhibit a slight increase at the I−N transition with respect to the isotropic m1,H-mode. Such behavior is compatible with a mode attributed to the

Figure 11. Arrhenius plot of the relaxation frequencies ( f k) of the different elementary contributions for CBO5O.Py (denoted as 5) and CBO3O.Py (denoted as 3).

superposition of the rotation around the molecular long axis and the precessional motions of the semirigid units.

5. DISCUSSION 5.1. Conformational Distribution. The dielectric data of the odd members of the series of liquid crystal dimers CBOnO.Py allow us to provide a quantitative description of the changes of the conformational distribution in the nematic mesophase with temperature and chain length. The evidence shows that the parallel component of the permittivity of each member of the series is dominated by two relaxation processes (m1,L∥- and m1,H∥-modes) with correlated dielectric strengths. According to the model of Stocchero et al.,30 the ratio of dielectric strengths of both modes (Δεm1,L∥ and Δεm1,H∥) can be 14492



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observed for the two shortest chain length dimers (see Figure 8), but it is not appreciated for the so-called long chain dimers. 5.2. Main Relaxation Processes and Activation Energies. The Arrhenius plots of Figures 6 and 11 show how the characteristic relaxation frequencies of the permittivity associated with the different motions for the odd members of the CBOnO.Py series change with temperature. Let us only consider the main characteristic frequencies associated with the longitudinal component, the so-called f m1,L|| and f m1,H||, along an isotherm (for example 2.5 K−1 scaled as 1000/T). At first glance, it is observed how such motions, that is, the individual flip-flop reorientations of the mesogenic units A (m1,L∥ mode) and B (m1,H∥ mode) are slowing down as the chain length decreases. This fact can be observed whatever the temperature is over the N-mesophase. As it has been observed from Figures 6 and 11, both m1,L∥and-m1,H∥-modes follow an Arrhenius behavior in a certain temperature range (Arrhenius law: f = f 0e−EA/KT, where EA is the activation energy) with the exception of the shortest chain dimer CBO3O.Py, which is clearly non Arrhenius-like and will be excluded from this analysis. The activation energies (EAm1,L∥ and EAm1,H∥) can be obtained by fitting the corresponding frequency data in Figures 6 and 11 and the values are listed in Table 2. It is evident that irrespective of the mode ((EAm1,L∥ or

easily expressed as a function of the equilibrium population of trans conformers (PTeq) (for more details, see ref 9): Δεm1, L || Δεm1, H ||

=

(2PTeq − 1)2 4PTeq(1 − PTeq)

(2)

PTeq

From eq 2, as a function of temperature can be obtained for each member of the dimeric family and is represented in Figure 12. It can be observed for each compound how PTeq

Table 2. Activation Energies (EA)a of the Two Relaxation Processes (m1,L∥- and m1,H∥-Modes) for the Odd Members of the Series of Liquid Crystal Dimers CBOnO.Py with n Ranging from 5 to 11

Figure 12. Equilibrium population of trans conformers (PTeq) as a function of [T − TNI] for the odd members of the series of liquid crystal dimers CBOnO.Py with n ranging from 5 to 11. The inset shows PTeq as a function of the chain length n along the isotherm 384 K and at TNI.

increases as temperature decreases (or in other words, as the orientational order increases). Within the assumptions of the model, for the longest chain dimer CBO11O.Py, the proportion of trans conformers changes from 77% (23% of cis conformers) to 88% (12% of cis conformers) over a wide nematic temperature range ([T − TNI] = −45 K). Over the same nematic range, for CBO5O.Py, PTeq changes from 88 to 94%. We avoided performing this kind of calculation on the shortest chain dimer CBO3O.Py because the interpretation of molecular motions has only a qualitative character. The inset of Figure 12 shows how PTeq changes with the chain length (n) of the dimer, at two different temperatures. In one of these, PTeq is calculated at a common isotherm (384 K) and the other at TNI, which corresponds to a nearly isotherm path for n ranging from 5 to 11, because the TNI are very close each other. It seems clear that the isothermal changes of the trans conformer population with the chain length of the dimer are much more pronounced for low orientational orders. Let us consider the appearance of two relaxation processes (m1,L- and-m1,H-modes) in the isotropic phase of the two short chain dimers CBO5O.Py and CBO3O.Py. It should be remembered that both the RIS model22,41 and the full torsional potential through the Stocchero et al. model30 seem to agree with the fact that the conformational distribution only changes slightly at the N−I phase transition for odd dimers. Thus, in the I phase, the longer chain members are expected to exhibit a lower difference between trans and cis conformers population than the shorter ones. On the other hand, the model30 strictly predicts the absence of the m1,L-mode for the same proportion of trans and cis conformers. Thus, the more asymmetric are both populations, the easier the appearance of both m1,L-andm1,H modes would be expected. This is unambiguously

CBOnO.Py (n)

EAm1,L∥ (kJ·mol−1)

EAm1,H∥ (kJ·mol−1)

EAm1,H∥/EAm1,L∥

5 7 9 11

124.8 114.6 110.2 107.1

104.6 95.2 93.3 88.7

0.84 0.83 0.85 0.83

a

Fittings according to the Arrhenius law have been performed in the data range from 280 to 420 K in Figures 6 and 11.

EAm1,H∥), the activation energy increases as the chain length (n) decreases. In addition, whatever the compound for a given chain length, EAm1,L∥ is always higher than EAm1,H∥. Finally, the ratio EAm1,H∥/ EAm1,L∥ is about 0.8, irrespective of the chain length of the dimer, showing that both activation energies change in the same proportion. On the other hand, it is known that the value of the EAm1,H∥/EAm1,L∥ ratio is about 0.8 for another nonsymmetric dimer, α-(4-cyanobiphenyl-4′-yloxy)-ω(4-decylaniline-benzylidene-4′-oxy) nonane (denoted as CBO9O.10),23 an odd member of a different series of liquid crystal dimers which also has only one polar terminal unit as in the case of the CBOnO.Py series. 5.3. Thermodynamic Glass Transition. The interest in the glassy behavior for members of the CBOnO.Py series dates from the 1990s.8 Among the odd members investigated, two of them, the longest chain dimer (CBO11O.Py) and the shortest one (CBO3O.Py), form nematic glasses, while three others (n from 5 to 9) exhibit smectic glasses. In the bottom inset of Figure 13, the thermodynamic glass transition temperatures (listed in Table 1) are plotted as a function of the n chain length. One of the most characteristic thermodynamic features of a glass transition is the jump in the heat capacity (see Figures 1 and 2). Our results argue for a single glass transition for each member of the family, and among the different molecular 14493



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Many efforts were performed to get a thermodynamic parameter that can be used instead of the m-fragility.52−55 In glass-forming polymers, Huang and McKenna53 introduced the ratio Cp,l/Cp,g, where Cp,l and Cp,g are the heat capacities of the liquid and the corresponding liquid frozen as glassy state at Tg, respectively, as a thermodynamic fragility parameter that correlates quite well with the m-fragility (Cp,l/Cp,g increases when the m-fragility decreases). In our case, liquid crystal dimers are a kind of polymer. In fact, the simplest polymers called oligomers, in which, instead of a liquid, we have a mesophase, either nematic or smectic A, leading to a glassy state. Thus, we propose for glass-forming liquid crystal dimers the ratio of Cp,m/Cp,g in which Cp,m (the heat capacity of the mesophase at Tg) is used instead of Cp,l. In the top inset of Figure 13, the heat capacity jump of the CBO11O.Py is shown as an example of how both Cp,m and Cp,g have been calculated. Figure 13 shows the ratio Cp,m/Cp,g as a function of the chain length of the dimers (n). Among the dimers forming smectic glasses (full symbols), the most fragile dimer (highest mfragility) would be the CBO9O.Py and the less fragile would be CBO5O.Py. It would seem that the shorter the chain length of the dimers, the stronger the dimer is. Let us consider the dimers forming nematic glasses. Both dimers, CBO11O.Py and CBO3O.Py, nearly exhibit the same fragility, very close to that of the smectic glass former CBO7O.Py. For CBO11O.Py, there are frequency data in the nematic phase, but very far from Tg (about 80 K), and as already cited in section 3, the compound crystallizes at low cooling rates to get dynamic dielectric data near Tg. Regarding the CBO3O.Py, there are frequency data in the nematic phase down to about 340 K, only 20 K above Tg. Thus, taking into account the slope at Tg in a plot of log10( f‑1) versus Tg/T, an estimation of the m-fragilty only considering the main m1,L∥and m1,H∥-modes (from data of Figure 11) lead to a tentative mvalue of about 100. Interestingly, the correlation found by Huang and McKenna53 (m = 254−120 Cp,l/Cp,g) gives rise to an m value of 106 (changing Cp,l/Cp,g by Cp,m/Cp,g with a value of 1.23 corresponding to the CBO3O.Py). Despite our pleasure in having such calculations, we do not think, however, that we can draw any firm conclusions without confident dielectric data at temperatures closer to Tg.

Figure 13. Ratio Cp,m/Cp,g as a function of the chain length n of the odd dimers CBOnO.Py with n ranging from 3 to 11. The nematic glassy state and smectic glassy state are represented by red ⊕-symbol and full circles, respectively. Bottom inset shows the evolution of the glass transition temperature (Tg) with the chain length n. Top inset shows the heat capacity jump of the CBO11O.Py around Tg as an example of the methodology of calculation of both Cp,m and Cp,g.

motions identified by dielectric spectroscopy, either one of such motions is frozen at the glass transition temperature (Tg) or all motions are frozen at the same time at Tg. Regarding the former possibility, we only know one case42 where among two different kinds of molecular motions, only one of them seems to be frozen at Tg. On the contrary, very recently we have reported a study on liquid crystal dimers12 in which all the identified molecular motions are responsible for the glass transition. It may be emphasized that it is a common practice in glass-forming materials to consider a single structural dielectric relaxation representative of the overall molecular motion where the deconvolution into different motions is not done. Let us consider the fragility concept43−45 as a very useful tool to compare the five glass-forming liquid crystals of the CBOnO.Py series. Originally, the fragility emerged to account for the manner in which the dynamic properties of the glassforming materials change as long as the glass transition temperature is approached. One of the formalisms most used to quantify fragility was introduced in the earliest years of 1990s by Angell and co-workers,46,47 the so-called m-fragility. Among the kinetic parameters to be taken into account, the m-fragility usually considers the dielectric structural relaxation time (τ) or the equivalent relaxation frequency ( f) at Tg in such a way that if such parameters (τ or f) follow an Arrhenius behavior, m is considered to be 16 (the minimum value and the strongest glass-forming material). The value of m increases with fragility and with the non-Arrhenius behavior of τ or f. The upper fragility limit is controversial. It has been recently suggested an m value of 175, 48 but m may tend toward infinity.49 The mfragility usually depends on the phenomenological equation used to describe the temperature dependence of τ or f.12,50 Alternative metrics to the fragility could be used.51 The problem is so complex that it exceeds the scope of the current study, and additionally, dynamic data (our f-data) corresponding to the mesophase which leads to the glassy state are, at best, very limited (spanning a narrow range of temperature) and far from the glass transition, with the exception of the shortest chain dimer CBO3O.Py. It should be stressed that our comparative study of fragility for the set of compounds is unapproachable from the current dynamic data.

7. CONCLUSIONS The study reported in this paper is a comparative investigation of the dynamic dielectric properties of the odd nonsymmetric dimers (CBOnO.Py; with n ranging from 3 to 11) with high molecular biaxiality induced by the pyrenimine benzylidene unit. So far, our dielectric and heat capacity measurements are the first performed in odd compounds of the CBOnO.Py series. The model of Stocchero et al.30 has allowed us to identify and interpret the molecular processes that are responsible for the two main dielectric relaxations observed at low frequencies for the parallel alignment. It has been clearly shown, at least for those compounds with n > 3, that one of these relaxations, at lower frequencies, is a consequence of the flip-flop motion of the larger terminal group of the dimer, while the other relaxation involves a flip-flop motion of the smaller group. On the basis of the model, a mixture of trans and cis conformers has been evidenced, and their relative populations have been calculated as a function of temperature. In addition, isothermal changes of their relative populations exclusively with the chain length of the dimer have been studied. It is concluded that low orientational orders allow more pronounced changes in the 14494



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(5) Umadevi, S.; Sadashiva, B. K.; Murthy, H. N. S.; Raghunathan, V. A. Mesogenic Dimers Composed of Bent-Core Molecules with Flexible Alkylene Spacer. Soft Matter 2006, 2, 210−214. (6) Srivastava, R. M.; Neves, R. A. W.; Schneider, R.; Vieira, A. A.; Gallardo, H. Synthesis, Optical Properties and Thermal Behaviour of 1,3,4-Oxadiazole-Based Twin Dimers. Liq. Cryst. 2008, 35, 737−742. (7) Vergara, J.; Barberá, J.; Serrano, J. Ll.; Ros, M. B.; Sebastián, N.; de la Fuente, M. R.; López, D. O.; Fernández, G.; Sánchez, L.; Martín, N. Liquid−Crystalline Hybrid Materials Based on [60]Fullerene and Bent-Core Structures. Angew. Chem., Int. Ed. 2011, 50, 12523−12528. (8) Attard, G. S.; Imrie, C. T.; Karasz, F. E. Low Molar Mass LiquidCrystalline GlassesPreparation and Properties of the α-(4-Cyanobiphenyl-4′-oxy)-ω-(1-pyreniminebenzylidene-4′-oxy)alkanes. Chem. Mater. 1992, 4, 1246−1253. (9) Sebastián, N.; de la Fuente, M. R.; López, D. O.; Pérez-Jubindo, M. A.; Salud, J.; Diez-Berart, S.; Ros, M. B. Dielectric and Thermodynamic Study on the Liquid Crystal Dimer α-(4Cyanobiphenyl-4 ′-oxy)-ω-(1-pyreniminebenzylidene-4′-oxy)undecane (CBO11O.Py). J. Phys. Chem. B 2011, 115, 9766−9775. (10) Panov, V. P.; Nagaraj, M.; Vij, J. K.; Panarin, Y. P.; Kholmeier, A.; Tamba, M. G.; Lewis, R. A.; Mehl, G. H. Spontaneous Periodic Deformations in Nonchiral Planar-Aligned Bimesogens with a Nematic-Nematic Transition and a Negative Elastic Constant. Phys. Rev. Lett. 2010, 105, 167801. (11) Cestari, M.; Diez-Berart, S.; Dunmur, D. A.; Ferrarini, A.; de la Fuente, M. R.; Jackson, D. J. B.; López, D. O.; Luckhurst, G. R.; PérezJubindo, M. A.; Richardson, R. M.; et al. Phase Behavior and Properties of the Liquid-Crystal Dimer 1′′,7′′-Bis(4-cyanobiphenyl-4′yl) Heptane: A Twist-Bend Nematic Liquid Crystal. Phys. Rev. E 2011, 84, 031704. (12) López, D. O.; Sebastian, N.; de la Fuente, M. R.; MartínezGarcía, J. C.; Salud, J.; Pérez-Jubindo, M. A.; Diez-Berart, S.; Dunmur, D. A.; Luckhurst, G. R. Disentangling Molecular Motions Involved in the Glass Transition of a Twist-Bend Nematic Liquid Crystal through Dielectric Studies. J. Chem. Phys. 2012, 137, 034502. (13) Coles, H. J.; Pivnenko, M. N. Liquid Crystal ’Blue Phases’ with a Wide Temperature Range. Nature 2005, 436, 997−1000. (14) Cestari, M.; Frezza, E.; Ferrarini, A.; Luckhurst, G. R. Crucial Role of Molecular Curvature for the Bend Elastic and Flexoelectric Properties of Liquid Crystals: Mesogenic Dimers as a Case Study. J. Mater. Chem. 2011, 21, 12303−12308. (15) Atkinson, K. L.; Morris, S. M.; Castles, F.; Qasim, M. M.; Gardiner, D. J.; Coles, H. J. Flexoelectric and Elastic Coefficients of Odd and Even Homologous Bimesogens. Phys. Rev. E 2012, 85, 012701. (16) Coles, H. J.; Coles, M. J.; Broughton, B. J.; Morris, S. M.; Ford, A. D. U.S. Patent No. 0041065A1, 2009 (17) Imrie, C. T.; Henderson, P. A. Liquid Crystal Dimers and Higher Oligomers: Between Monomers and Polymers. Chem. Soc. Rev. 2007, 36, 2096−2124. (18) Emsley, J. W.; Luckhurst, G. R.; Shilstone, G. N. The Orientational Order of Nematogenic Molecules with a Flexible Core: A Dramatic Odd Even Effect. Mol. Phys. 1984, 53, 1023−1028. (19) Ferrarini, A.; Luckhurst, G. R.; Nordio, P. L.; Roskilly, S. J. Prediction of the Transitional Properties of Liquid-Crystal DimersA Molecular-Field Calculation Based on the Surface Tensor Parametrization. J. Chem. Phys. 1994, 100, 1460−1469. (20) Luckhurst, G. R. The Marcelja−Luckhurst Molecular-Field Theory for Uniaxial Nematics Composed of Flexible MoleculesA Variational Derivation. Mol. Phys. 1994, 82, 1063−1073. (21) Luckhurst, G. R.; Romano, S. Computer Simulation Studies of Anisotropic Systems. XXVI. Liquid Crystal Dimers: A Generic Model. J. Chem. Phys. 1997, 107, 2557−2572. (22) Ferrarini, A.; Luckhurst, G. R.; Nordio, P. L.; Roskilly, S. J. Understanding the Unusual Transitional Behavior of Liquid-Crystal Dimers. Chem. Phys. Lett. 1993, 214, 409−417. (23) Dunmur, D. A.; Luckhurst, G. R.; de la Fuente, M. R.; Diez, S.; Pérez-Jubindo, M. A. Dielectric Relaxation in Liquid Crystalline Dimers. J. Chem. Phys. 2001, 115, 8681−8691.

relative populations, with the exception of the shortest chain dimer (CBO3O.Py), which, in many aspects, exhibits a discordant behavior with the other odd members of the family. First, CBO3O.Py is not a stable mesogen but can be treated as such. Its N−I transition temperature (see Table 1) is very different with respect to the other odd members. Even its glassy behavior is singular and the dynamic dielectric behavior, although comparable in some features with that of the CBO5O.Py, is clearly different throughout the nematic phase. In addition, the identification of the different relaxations both in the parallel and the perpendicular components is hard to be done without ambiguity. Regarding the other four compounds of longer chain length, some common facts can be highlighted. Starting with the individual flip-flop reorientations of the mesogenic units A (m1,L∥ mode) and B (m1,H∥ mode) over the N-mesophase, such motions are slowed down as the chain length decreases, regardless of the temperature. The ratio of the activation energies EAm1,H∥/ EAm1,L∥ is found to be about 0.8. As for the mfragility in terms of the Cp,m/Cp,g, with the notable exception of the shortest chain dimer (CBO3O.Py), all odd compounds (n from 5 to 11) seem to follow a trend with the chain length in such a way that m-fragility increases with n. From a physical point of view, the flexibility which increases with the chain length allows the molecules of the dimer to adopt a strongly cooperative dynamic regime as temperature decreases, approaching the glass transition and consequently increasing the fragility of the material.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (D.O.L.). *E-mail: [email protected] (N.S.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are grateful for financial support from the MICINN projects MAT2009-14636-C03-01,02,03, MAT201238538-C03-03,02,01 and from the Gobierno Vasco (GI/IT449-10). The authors also thank the recognition from the Generalitat de Catalunya of GRPFM as Emergent Research Group (2009-SGR-1243). N.S. would like to thank the Universidad del Paiś Vasco for a postdoctoral contract. We ́ are grateful to Dr. U. Martinez-Estibalez, Universidad del Paiś Vasco, for his assistance in the synthesis of the material.

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REFERENCES

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Overall Dielectric Study on the Odd Members of a Highly

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