J. Phys. Chem. B 2010, 114, 1745–1750
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Permittivity, Conductivity, Elasticity, and Viscosity Measurements in the Nematic Phase of a Bent-Core Liquid Crystal Pramod Tadapatri, Uma S. Hiremath, C. V. Yelamaggad, and K. S. Krishnamurthy* Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India ReceiVed: June 23, 2009; ReVised Manuscript ReceiVed: NoVember 25, 2009
We report on measurements of dielectric permittivity ε, electrical conductivity σ, elastic moduli kii, and rotational viscosity γ for a bent-core nematic liquid crystal. The static permittivity anisotropy εa ) ε| - ε⊥ is negative; at a given temperature in the interval 107-123 °C, ε| shows two relaxations falling in the frequency bands 20-200 kHz and 0.9-2 MHz; ε⊥ also shows a relaxation between 0.9 and 5 MHz. The conductivity anisotropy σa ) σ| - σ⊥ is negative at low frequencies; it changes sign twice at frequencies f1 and f2 that increase with temperature, in the ranges 6.5-10 and 95-600 kHz, respectively. Surprisingly, the splay modulus k11 is considerably greater than the bend modulus k33 in the entire nematic range. Viscous relaxation is more complex than in calamitic systems involving at least a two-step process. The γ values are an order of magnitude greater compared to calamitics. Introduction The uniaxial nematic is the most liquid-like of the mesophases formed of strongly anisometric molecules that may be rodlike (calamitic), disclike (discotic), or boomerang-shaped (bent-core, BC).1 The orientational order in the nematic renders many of the material properties dependent on the direction relative to the preferred axis (director). These so-called nonscalar properties2 are of both fundamental and technological importance. It is through the anisotropic interactions with external fields that a great variety of interesting orientational and hydrodynamic phenomena are generated.1,3 The vast majority of investigations on physical properties in the nematic phase deal with materials formed of calamitic molecules.4 Thus, structure-property correlations are reasonably well established for calamitics. On the other hand, for bentcore nematics (BCNs), measurements of physical properties are scanty and no general trends in their variation are established. The steric effects will obviously exercise a profound influence on some of the physical properties such as viscosity. Some recent investigations5 on a BCN do reveal the rotational and flow viscosities of the compound to be larger than for straightcore nematics by a factor of 10 and 100, respectively. Similarly, the bend elastic constant in a BCN has been noted as about equal to the splay constant, unlike in conventional nematics.6 There are also reports7 of a giant bend flexoelectric coefficient for a BCN, while normal flexocoefficients are observed8 in some other BCNs. Further, unusual low frequency dielectric relaxations are known to exist in some BCNs.9 It appears that extensive investigations of physical properties of different BC materials are necessary for a general appreciation of the structure-property correlations in these mesogens. An extensive dependence on material parameters is perhaps best seen in anisotropic electroconvection, where as many as 12 physical parameters are found necessary to arrive at the threshold features based on the so-called standard model.10 It is in the course of our analysis of the patterned electroconvective states in the bent-core uniaxial nematic 4-cyanoresorcinol bis[4* Corresponding author. E-mail:
[email protected].
(4-n-dodecyloxybenzoyloxy)benzoate] (CNRbis12OBB) that we undertook a systematic study of the following material param-
eters: the principal conductivities σ| and σ⊥, | and ⊥ denoting the directions relative to the director; the principal permittivities ε| and ε⊥; the splay (k11) and bend (k33) elastic moduli; and rotational viscosity (γ1). We have determined the static and dynamic features of σ|, σ⊥, ε|, and ε⊥ at various temperatures (Ts); k11, k33, and γ1 are also measured as functions of T. It is our purpose here to present the experimental data and discuss their significance. Experimental Section Compound. Kovalenko et al.9a were the first to synthesize CNRbis12OBB and report its phase sequence as with Cr,
SmCPA, SmC, N, and I denoting, respectively, the crystal, antipolar smectic C, smectic C, nematic, and isotropic phases. The nematic phase in virgin samples of CNRbis12OBB synthesized by us had a clearing temperature TNI of 128.5 °C; during continued electric field experiments, it dropped to a minimum of ∼125 °C, while the N range remained about 20 °C. We indicate the temperature here by its reduced value T* ) T/TNI, with T and TNI in K. Electrical Measurements. For dielectric and conductance spectra, a HP4194A Impedance/Gain-phase analyzer was used. The temperature variations of static permittivity ε(T) and conductivity σ(T) at 1 kHz were determined using an Agilent 4284A precision LCR meter. In both dynamic and static measurements, the cell voltage was 0.5 V and the samples were
10.1021/jp905879n 2010 American Chemical Society Published on Web 01/19/2010
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magnetically aligned using a field (B) of about 1.38 T from a Bruker B-MC1 electromagnet. As this B is about 10 times the Freedericksz threshold corresponding to the d values used (∼42-57 µm), we assume the director n to be along B. The sample temperature was maintained by an Instec HS250 hotstage connected to an RTC1 programmable temperature controller with an accuracy of 1 mK. Elastic Constants. For measurement of the elastic constants, we employed both electric and magnetic Freedericksz techniques and monitored the cell capacitance at 1 kHz and 0.5 V to detect the orientational transition, using the LCR meter mentioned above. In these experiments, the sample cells used were of sandwich type, constructed of passivated, indium tin oxide (ITO) coated glass plates from Delta Technologies. Mylar spacers, heat-sealed to the electrodes through cooling from ∼ 250 °C under a uniform pressure, determined the cell gap d; d was measured interferometrically. The permittivity anisotropy of the sample εa ) (ε| - ε⊥) happens to be negative. Hence, we employed homeotropic samples in electric Freedericksz experiments to determine k33 given by the well-known relation VF ) π[k33/(εoεa)]1/2, where VF is the threshold voltage. For securing the homeotropic alignment, the ITO electrodes were first dip-coated with octadecyltriethoxysilane and cured for 90 min at 150 °C prior to fabricating the sample cell. The sample temperature T was maintained to an accuracy of (0.1 °C by an Instec HCS402 hot-stage connected to a STC200 temperature controller. While monitoring the cell capacitance, the Freedericksz transition point was also confirmed optically by examining the sample between crossed polarizers under a Carl-Zeiss Axio Imager.M1m polarizing microscope. We employed the magnetic Freedericksz threshold BF ) (π/ d)(µokii/χa)1/2 for a homeotropic sample with the director transverse to the field to obtain k33/χa, χa being the diamagnetic susceptibility anisotropy. Thus, χa(T) could be retrieved using the k33(T) values obtained from electric Freedericksz experiments. Similarly, k11/χa (and hence k11) at various temperatures was determined from BF using a planarly aligned sample with the magnetic field along the measuring electric field. To obtain the planar sample alignment, the ITO electrodes were, prior to cell construction, spin-coated with polyimide and cured for 3 h at 300 °C; then, the coated surfaces were buffed unidirectionally on velvet cloth. Rotational Viscosity. We used the optical decay response of the sample from a dielectrically reoriented state to estimate γ1.11 For this purpose, a homeotropically aligned sample of 33 µm thickness was first subjected to a field of 1 kHz frequency and voltage amplitude slightly above the threshold VF, and then the field was turned off. The photodiode response to the light transmitted through the sample placed between crossed polarizers of the microscope was recorded on a Tektronix TDS 420A oscilloscope. The voltage source was a Stanford Research Systems DS345 function generator coupled to a FLC Electronics voltage amplifier (model A800). The applied voltage, V, was measured with a Keithley-200 multimeter. The dynamics of the change in phase retardation δ, for small distortions, may be expressed as δt ) δo exp(-2t/τo), with δo denoting the retardation in the field-on state.11 In calculating δt, we used the time dependent normalized intensity of transmitted light It ) sin2(δt/2) and extracted τo from a plot of ln(δo/δt) vs t. The rotational viscosity γ1 was obtained from γ1 ) π2k33τo/ d2. For purposes of calculation, we took retardation by π as δo, and t as 0 at δo. It is pertinent to add that the γ1 given here is the effective rotational viscosity arrived at by ignoring the
Tadapatri et al.
Figure 1. Temperature variation of dielectric permittivity measured at 1 kHz in nematic CNRbis12OBB.
“backflow” induced by director rotation. This value is expected to be lower than the actual rotational viscosity.3,4 Further, at temperatures close to TNI, γ1 itself is lowered due to the lower values of k33, as will be explained in the following section. In discussing the temperature variation of γ1, we have used the sample birefringence which was measured with a planarly aligned sample and a tilt compensator. It may be mentioned in passing that the flexoelectric coefficients of CNRbis12OBB, which have been measured and reported separately,8a are of the usual order of magnitude as in calamitics, i.e., a few pC m-1. Results and Discussion A. Dielectric Behavior. From the low-frequency ε(T*) data presented in Figure 1, it is seen that the static permittivity anisotropy of CNRbis12OBB is negative. Further, the jε(T*) line, jε denoting the average permittivity jε ) (ε| + 2ε⊥)/3, lies slightly below the extrapolated line corresponding to the isotropic permittivity εiso. This is probably indicative of an antiparallel correlation between the longitudinal dipolar components of the neighboring molecules.12 Representative data on the frequency dependent complex dielectric function ε*(ω) ) ε′(ω) - iε′′(ω) are given in Figure 2, for T* ) 0.9749 and the frequency range 0.1 kHz to 10 MHz. In Figure 2a, showing frequency dispersions for the principal components of the in-phase permittivity, ε|′(ω) is characterized by two relaxation modes of which the stronger one lies in the low frequency region and ε⊥′(ω) shows a single strong relaxation. The corresponding spectra of dielectric losses, ε|′′(ω) and ε⊥′′(ω), are presented in parts b and c of Figure 2, respectively. The dielectric response along n is described by eq 2 where εs is the static permittivity, σs the static conductivity, εi the frequency limit of the ith mode, τi the relaxation time of the ith mode, and R the Cole-Cole distribution parameter; a and b are adjustable parameters. Equation 2 also describes ε⊥*(ω) but with a single relaxation function of the Cole-Cole type. The fitted curves, shown by the continuous lines in Figure 2, are based on the analyses of the data only up to 5 MHz. For higher frequencies, an artifact in the form of a rise in permittivity appears. This instrumental limitation renders τ2 rather approximate.
ε* ) ε2 +
ε1 - ε2 εS - ε1 iσS a + + b 1-R 1 + iωτ1 ε ω 1 + (iωτ2) ω o
(2)
Evidently, the first of the longitudinal relaxations is a Debyelike process; it is associated with the end-over-end rotations of the molecules around their short axes, which is severely retarded by the nematic potential. On the other hand, both the longitudinal
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Figure 4. Temperature variation of electrical conductivity σ measured at 1 kHz in the isotropic, nematic, and SmC phases of CNRbis12OBB.
Figure 2. Frequency dependence of the real and imaginary components of complex dielectric permittivities measured along and transverse to the nematic director at T* ) 0.9749. The continuous lines are the fits to eq 2.
Figure 5. Frequency dependence of the principal electrical conductivities σ| and σ⊥ at T* ) 0.9749 showing the σa sign reversals at frequencies f1 and f2. Inset: Temperature dependence of f1 and f2.
Figure 3. Temperature variation of dielectric relaxation times τ in the isotropic and nematic phases for the frequency range 100 Hz to 10 MHz; τ|1 and τ|2 correspond, respectively, to the Debye and Cole-Cole processes; τ⊥ and τiso are for the Cole-Cole process governing the corresponding relaxations in the nematic and isotropic phases.
and transverse relaxations occurring around a few MHz involve a Cole-Cole type mechanism; even in the isotropic phase, a similar relaxation is observed (Figure 3). These relaxations, characterized by a distribution of time constants, may arise due to independent rotations of dipolar groups around the long axis. In calamitics, the corresponding modes usually occur in the GHz region; their large down shift here is ascribable to the increased molecular size and very high viscosity of the medium. Similar features of frequency variation of complex permittivity have been reported for the BC nematics ClRbis12OBB9a and ClPbis10BB.9b B. Electrical Conductivity. In Figure 4, we present the temperature variation of the principal components of conductivity, σ|(T) and σ⊥(T), measured at three different frequencies. The data for 1 kHz are illustrative of the static conductivity features. Significantly, the static anisotropy σa is negative in the entire temperature range of the N phase; the ratio σR ) σ|/ σ⊥ steadily increases from ∼0.53 near the SmC-N point toward 1 as TNI is approached. A similar σa behavior is also found for the static anisotropy in some nematics such as 4,4-diheptyl-
oxyazoxybenzene (HOAB).13 This departure from the usual σR value of 1-2 found in most nematics is indicative of the presence of a short-range SmC-like order in the N phase here; the ion diffusion is thereby rendered slower along the director than across it. It is relevant to recall that the X-ray patterns of oriented nematic CNRbis12OBB samples have shown9a the existence of cybotactic groups in this phase, with the molecules tilted at 28° with respect to the layer normal as in the underlying SmC phase. It is to be noted, however, that the N phase is macroscopically uniaxial. This is evident from our observation8a of the uniaxial figure in homeotropically aligned samples viewed conoscopically. Above a few kHz, the σa(ω) becomes dynamic. At 10 kHz, while cooling from the liquid phase, the conductivity remains almost isotropic well into the N phase and becomes increasingly positive toward the N-SmC transition point; interestingly, the anisotropy begins to decrease only after this transition and changes sign again deep in the SmC phase. The frequency dependence of the principal conductivities, σ|(ω) and σ⊥(ω), at T* ) 0.9749 is shown in Figure 5; it is typical of the dynamic conductivity features observed at various temperatures. As already mentioned, the conductivity relaxation begins to show up beyond a few kHz for both σ| and σ⊥, with σ| starting to rise steeply at a lower frequency. σ|(ω) shows two regions of sharp rise in conductivity corresponding to the two relaxations, separated by a plateau-like region; for σ⊥(ω), in the frequency window examined (0.1 kHz-1 MHz), we see only the conductivity relaxation part but not the plateau. Interestingly, the
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Figure 6. The ratio σR ) σ|/σ⊥ as a function of frequency showing a regular displacement of the peak position with changing temperature.
anisotropy σa changes its sign twice at frequencies f1 and f2. With an increase in T, f1(T) tends to saturate, while f2(T) rises with ever increasing rapidity, as in the inset of Figure 5. The ratio σR measured at various temperatures ranges between 0.2 and 2.7 over the entire frequency span; at a given temperature, σR(f) varies smoothly, reaching its peak at fM between f1 and f2, as depicted in Figure 6; fM shows an Arrhenius-like exponential dependence on temperature. The negative-positive-negative sign sequence of σa(ω) has also been reported for ClPbis10BB.6a Further, qualitatively, several of the relaxation features of σ(ω) are also seen in many
calamitic mesogens.14 However, quantitative agreement with the expressions based on the dispersion of orientational polarization seems marginal. For example, it is expected14 that the conductivity maximum in a plateau region is governed by the equation
σmax ) σS +
εo(ε - 1) τ
(3)
and that, in any relaxation region, the conductivity is a quadratic in frequency according to
σ(ω) ) ε0(ε-1)τω2
(4)
Here, ε is the static permittivity applicable to the measurement direction. For σ|(ω), the plateau conductivity in Figure 5 is ∼10 µS m-1, whereas that expected from eq 3 is ∼19 µS m-1. Similarly, in the double logarithmic plots in Figure 5, the slope of the line corresponding to the first relaxation of σ|(ω) is ∼1.3, and that to the relaxation of σ⊥(ω), ∼1.6. C. Elastic Moduli. In Figure 7, we present the elastic moduli k11 and k33 (inset) as a function of temperature T*. It is remarkable that k11/k33 varies from ∼2 near TNI to ∼6.5 near TNS. By comparison, for ClPbis10BB, the reported values of the two moduli are nearly equal (k11 ) 2.23 pN and k33 ) 2.37 pN for T* ≈ 0.98).6a Further, for some BC systems, it has recently been reported6b that k11/k33 ∼1. In calamitics, k11 is usually smaller than k33,12 but there are examples of nematogens, like some 4,4-dialkylazoxybenzenes with long alkyl chains, for which k11 > k33.4 This apparent anomaly has been interpreted on the basis of molecular models involving the molecular shape
Figure 7. Temperature variation of the splay k11 and bend k33 (inset) elastic constants in nematic CNRbis12OBB showing the unusual feature of k11 being significantly greater than k33 at all temperatures. The red and blue squares refer, respectively, to samples having TNI ) 125 and 126.8 °C.
j 4.15a In fact, k11/k33 is j 2 and P anisotropy and order parameters, P shown to have a direct correlation with the width to length ratio W/L of the molecules. Thus, when paraffinic terminal chains are present in the molecules, their flexibility may impede translation and favor clustering so that the effective width Weff may become larger than L.15b Similarly, banana-shaped molecular conformations may occur in rodlike systems resulting in Weff > L.15c Obviously, these considerations apply even more to BC systems. The natural propensity of BC molecules to promote a local bend of the nematic director may also lower k33 significantly.16 It is necessary to note here that the homeotropic alignment becomes unstable close to the N-SmC point TNS, with the director tilting progressively away from the layer normal as the transition is approached. As this effect was more pronounced in thin samples, we used 40-50 µm thick cells. In these cells, by conoscopic observation, using the shift of the melatope of the uniaxial figure, we estimated the tilt to be ∼3° at 2 °C above TNS; the tilt decreased to a negligible value for (T - TNS) ≈ 5 °C. The values of k33 determined experimentally are, therefore, likely to be lower than the actual values in this temperature range.17 In fact, for a sample with a uniform oblique orientation in the field-off state, the initial tilt plays the role of an external field and the orientational distortion is finite at any finite applied electric field E, disappearing only for E ) 0; although the phase transition is thus removed by the initial tilt, the field-induced tilt displays an apparent transition at VFA < VF.18 Thus, the k33 values corresponding to VFA are lower than the actual values;19 this in turn leads to an underestimation of χa as well as k11 in the way we have estimated these parameters (see the Experimental Section). Thus, k11/k33 is unlikely to be seriously affected. It is relevant to recall here for comparison the findings of Tamba et al.20 relating to elastic coefficients in a twin mesogen comprising BC and rodlike units. They find, by electric Freedericksz experiment on their compound, k11/(εoεa) to be ∼27.5 pN at T* ) 0.9829. In the absence of permittivity data, they simply conclude that either k11 is relatively large or εa is relatively small (
