Orientational Order, Molecular Organization, and Dynamics in

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Orientational Order, Molecular Organization, and Dynamics in Mixtures of Bent-Core and Rod-Shaped Mesogens: A 2H NMR Study Lucia Calucci,† Katalin Fodor-Csorba,‡ Claudia Forte,*,† and Marco Geppi§ Istituto di Chimica dei Composti OrganoMetallici, CNR-Consiglio Nazionale delle Ricerche, Area della Ricerca di Pisa, Via G. Moruzzi 1, 56124, Pisa, Italy; Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences, 1525, P.O. Box 49, Budapest, Hungary; and Dipartimento di Chimica e Chimica Industriale, UniVersita` di Pisa, Via Risorgimento 35, 56126, Pisa, Italy ReceiVed: September 27, 2010; ReVised Manuscript ReceiVed: NoVember 30, 2010

Mixtures of a bent-core mesogen (ClPbis10BB) and a calamitic mesogen (6OO8), showing a nematic phase over the entire compositional range and one or two smectic phases (namely, SmA, SmC, or SmCA) below the nematic one over a wide concentration range, were investigated by means of 2H NMR spectroscopy, exploiting selectively deuterated isotopomers of both mesogens. The analysis of 2H NMR spectra recorded in the liquid crystalline phases on several representative mixtures gave information on the orientational order properties and the molecular organization within the phases as well as on the alignment properties upon application of a magnetic field. On the other hand, the analysis of 2H longitudinal relaxation times (T1Z and T1Q) in 6OO8d2/ClPbis10BB mixtures and pure 6OO8-d2 allowed the influence of the bent-core mesogen on the dynamics of the calamitic one to be highlighted. Introduction Since the pioneering results by Niori et al. in 1996,1 bentcore (BC) or banana-shaped mesogens have become a major topic of research in different fields, such as liquid crystals, soft condensed matter, and supramolecular chemistry. The occurrence of novel and intriguing polar mesophases (the so-called banana or B phases), the induction of supramolecular chirality using achiral molecules, and the noticeable optical, ferroelectric, and antiferroelectric responses are aspects that render these materials particularly interesting from both the applicative and the academic point of view.2-8 Moreover, the bent molecular structure may lead to extraordinary properties even in the conventional nematic (N) and smectic (Sm) mesophases; e.g., BC nematics are regarded as candidates for exhibiting a longsearched biaxial N phase, and unusual physical properties,9-11 including very high rotational and flow viscosity, giant flexoelectricity, and nonstandard electroconvection, have been found for the N phase of BC mesogens. However, the practical applications of BC liquid crystals are limited because their mesophases appear at relatively high temperatures (>70 °C), and most of the few BC materials which do not crystallize are glassy at room temperature and, therefore, cannot be switched. Another important aspect that still limits the use of BC mesogens concerns the difficulty in obtaining bulk phase alignment.8 To overcome these problems and regulate the temperature range and some material parameters of the liquid crystalline phases, it has been suggested to mix BC and calamitic compounds. As a matter of fact, in recent years the polymorphism of binary systems composed of a BC and a rodlike mesogen has been extensively studied with the aim of investigating the effect of mixing these two types of compounds on mesophase formation, * Corresponding author: phone +39-050-3152462; Fax +39-0503152442; e-mail [email protected]. † Istituto di Chimica dei Composti OrganoMetallici, CNR. ‡ Hungarian Academy of Sciences. § Universita` di Pisa.

including the induction of new mesophases.12-23 These systems have shown interesting properties such as the induction of anticlinic order (SmCA or SmCA*) over synclinic order (SmC or SmC*) in smectics,12,15,16,18,22 the induction of banana phases,13,14,17,21,23 and a complete miscibility of smectic bentcore and nematic rod-shaped substances.22 These mixtures have been mainly characterized by optical microscopy, DSC, and X-ray diffraction measurements, and the induction of anticlinic (SmCA) ordering in an untilted smectic (SmA) phase has also been proven by Monte Carlo simulations.24 However, to the best of our knowledge, only a few studies are reported in the literature concerning the investigation of orientational ordering14,17 and dynamics25 of these systems, despite the fundamental importance of understanding these molecular level properties for both the comprehension of the macroscopic behavior and for suggesting possible applications of liquid crystalline phases. In this work, we present a detailed 2H NMR study of a recently reported binary system22 composed of the calamitic compound 4-n-octyloxyphenyl-4-n-hexyloxybenzoate (6OO8),26 exhibiting a nematic and a SmC mesophase, and the nematic BC mesogen 4-chloro-1,3-phenylenebis[4-(10-decenyloxy)benzoyloxy]benzoate (ClPbis10BB);27 6OO8 has been selected as the calamitic compound because its chemical structure is similar to that of the ClPbis10BB arms (Figure 1). These mesogens show complete miscibility and form liquid crystals near room temperature that change their birefringence color by applying an electric field, thus opening up a path toward possible practical applications. All mixtures have a nematic phase and, in some concentration ranges, one or two smectic phases below the nematic one (see phase diagram in Figure 2). The smectic phase induced over a wide concentration range is an anticlinic smectic C (SmCA) phase, as determined by textural and miscibility observations and by X-ray diffraction measurements.22 In particular, the latter experiments showed that the layer spacing in the SmCA phase decreases with decreasing the 6OO8 content in the mixtures, the director tilt angle (i.e., the angle between the normal to the smectic layers and the long axis of the

10.1021/jp109224w  2011 American Chemical Society Published on Web 12/15/2010

2H

NMR on Rodlike and Bent-Core Mesogen Mixtures

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Figure 1. Molecular structure of 6OO8 and ClPbis10BB and their deuterated isotopomers with reference frames for orientational order analysis.

Figure 2. Left: phase diagram of 6OO8/ClPbis10BB mixtures adapted from ref 22. Right: schematic representation of the arrangement of calamitic and bent-core molecules in the N, SmA, SmC, and SmCA phases.

molecules) increasing from ∼15° to ∼30° as the rodlike component decreases from 85 wt % to 30 wt %. Simultaneously, the height of the diffraction peak decreases, indicating frustration of the smectic ordering imposed by the BC molecules. Very recently, the electroconvection28 and dielectric properties25 of 6OO8/ClPbis10BB binary mixtures were studied in comparison with those of the pure mesogens; however, a detailed interpretation of the data was prevented by the difficulty in separating the contributions ascribable to the single components. In our study, the use of selectively deuterated isotopomers of 6OO8 and ClPbis10BB (namely, 6OO8-d2 and ClPbis10BB-d2 in Figure 1) allowed site-specific information on structure and dynamics of the liquid crystalline phases to be obtained by 2H NMR spectroscopy and relaxation measurements, respectively.29-32 These methods, which have been extensively used for the characterization of calamitic and, to a minor extent, of BC liquid crystals, are here applied for the first time to mixtures of BC and rodlike mesogens. Experimental Section Materials. ClPbis10BB and ClPbis10BB-d2 were prepared following the procedure reported in ref 33. 6OO8 and 6OO8d2 were synthesized according to ref 26; in the case of 6OO8d2 4-hydroxybenzoic acid-d2, prepared following ref 34, was used. The deuteration level, estimated from 1H NMR spectra

in acetone-d6, was 92% and 15% for 6OO8-d2 and ClPbis10BBd2, respectively. Samples for NMR measurements were prepared by weighing suitable amounts of 6OO8-d2 and ClPbis10BB and of 6OO8 and ClPbis10BB-d2 directly in the NMR tube, heating above the clearing temperature, mixing for a few minutes in the isotropic phase, and keeping them at 10 °C above the highest clearing point for 24 h. Mixtures of 6OO8-d2 and ClPbis10BB containing 5, 30, 50, 64, 72, 80, 82, 86, and 90 wt % of 6OO8d2 and mixtures of 6OO8 and ClPbis10BB-d2 containing 30, 50, 64, 72, 84, and 90 wt % of 6OO8 were prepared. NMR Measurements. 2H NMR spectra were recorded at different temperatures within the mesomorphic range of neat 6OO8-d2 and of all 6OO8-d2/ClPbis10BB and 6OO8/ClPbis10BBd2 mixtures on a Bruker AMX-300 WB spectrometer operating at the deuterium frequency of 46.04 MHz, equipped with a 5 mm probehead. The samples were uniformly aligned by slow cooling from the isotropic to the nematic phase in the spectrometer magnetic field (7.05 T). The spectra were acquired by using the quadrupolar echo pulse sequence with a 90° pulse of 9.5 µs, an echo delay of 40 µs, a recycle delay of 1 s, and a number of scans ranging from 400 to 80 000 depending on the sample. Spectra were recorded on cooling, letting the temperature equilibrate for at least 15 min before measurement. 2 H T1Z and T1Q relaxation times at 46.04 MHz were measured on selected 6OO8-d2/ClPbis10BB mixtures at different temper-

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atures using the same equipment and experimental setup, employing the broadband version35 of the Jeener-Broekaert pulse sequence.36 A 90° pulse of 9.5 µs, a recycle delay of 1 s, and 400 scans were used. 2 H NMR spectra at several temperatures within the mesophases were recorded on the 6OO8-d2/ClPbis10BB mixture containing 64 wt % of 6OO8-d2 also using a Varian Infinity Plus 400 spectrometer working at 61.38 MHz for deuterium, equipped with a 5 mm goniometric probe. The sample was uniformly aligned with the molecular director parallel to the magnetic field by slow cooling from the isotropic into the N phase in the spectrometer field (9.4 T). Spectra were recorded on cooling letting the temperature equilibrate for at least 15 min before measurement. On the same sample, angular dependent 2H NMR spectra were recorded at 313 K (i.e., in the SmCA phase) by rotating the aligned sample at different angles around an axis perpendicular to the magnetic field. All the spectra were acquired by using the quadrupolar echo pulse sequence with a 90° pulse of 4.5 µs, an echo delay of 30 µs, a recycle delay of 2 s, and 400 scans. In all the experiments the temperature was stabilized within (0.2 K. Results and Discussion 2

H NMR Spectra Interpretation. 2H NMR spectra were recorded at different temperatures in the mesophases of neat 6OO8-d2 and of all the 6OO8-d2/ClPbis10BB and 6OO8/ ClPbis10BB-d2 mixtures uniformly aligned by slowly cooling from the isotropic to the N phase in the spectrometer magnetic field (7.05 T). A uniformly aligned sample could not be obtained for the N phase of neat ClPbis10BB-d2. All the spectra were dominated by the quadrupolar interaction, each deuterium giving a doublet and the two deuteria of 6OO8d2 being equivalent because of fast ring flips. Moreover, for deuteria with protons in the ortho position each peak of the doublet was further split by the 2H-1H dipolar interaction. Therefore, as exemplified in Figure 3, the spectra of samples containing 6OO8-d2 showed a double doublet, whereas those of samples containing ClPbis10BB-d2 displayed in most cases a doublet and a double doublet for deuteria D2 and D1, respectively, similarly to what reported for the homologous ClPbis11BB-d2 in nematic solvents.33 For samples containing less than 20 wt % of ClPbis10BB-d2, the low deuteration level prevented the detection of the D1 signals in a reasonable experimental time at all the temperatures; at higher concentrations the D1 signals were not observable at the lower temperatures where the quadrupolar splitting is too large with respect to the available radiation power of the 90° pulse. The quadrupolar splittings measured in the spectra recorded at different concentrations and temperatures are reported in Figures 4 and 5 for ClPbis10BB-d2 and 6OO8-d2, respectively. As far as the dipolar splittings are concerned, they could be measured accurately for all mixtures containing 6OO8-d2 at all temperatures, whereas due to the poor resolution, they could not be determined at some temperatures for mixtures containing ClPbis10BB-d2 (data not shown). Given that the principal axis of the quadrupolar interaction tensor nearly coincides with the CD bond direction, the observed quadrupolar splittings give direct information on the molecular orientation in the different liquid crystalline phases. Therefore, trends of quadrupolar splittings as a function of the temperature can be exploited to follow the mixtures’ polymorphism, to determine phase transitions, and to investigate orientational order, tilt angle, and sample alignment in the magnetic field.

Figure 3. (a) 2H NMR spectrum recorded at 336 K on a 6OO8-d2/ ClPbis10BB mixture containing 72 wt % 6OO8-d2. (b) 2H NMR spectrum recorded at 336 K on a 6OO8/ClPbis10BB-d2 mixture containing 72 wt % 6OO8.

For all the mixtures and in all mesophases, ClPbis10BB molecules showed the typical behavior of calamitic mesogens with positive magnetic susceptibility anisotropy which align with their long axes along the magnetic field direction. In fact, for all the samples containing ClPbis10BB-d2 we observed deuterium quadrupolar (and dipolar) splittings regularly increasing by lowering the temperature within both N and Sm phases, with discontinuities at the N-SmC, SmA-SmCA, and N-SmCA phase transitions, but not at the N-SmA transition (Figure 4). Similar splittings were observed in the N phase of all mixtures containing up to 36 wt % of ClPbis10BB-d2 at the same TNI-T, TNI being the clearing temperature; the splittings progressively decreased at the same TNI-T by further increasing the ClPbis10BBd2 content. On the other hand, 6OO8 molecules showed different alignment properties with respect to the magnetic field depending on the mesophase. In particular, in the N phase all the samples containing 6OO8-d2 showed a regular increase in the quadrupolar and dipolar splittings by lowering the temperature, as expected for calamitic nematogens with positive magnetic susceptibility anisotropy (Figure 5). Very similar splittings were determined at the same TNI-T in the N phase for neat 6OO8-d2 and 6OO8-d2/ClPbis10BB mixtures containing up to 20 wt % of BC compound, whereas progressively smaller splittings were found at the same TNI-T for mixtures with further increasing the banana mesogen content. Peculiar behaviors were observed on entering the Sm phases depending on the composition of the mixture. In particular, for the mixture containing 90 wt % of 6OO8-d2, showing a N and a SmC phase, a jump was observed at the N to SmC first-order phase transition, analogously to what observed for neat 6OO8-d2; then a further increase of the splitting was found upon lowering the temperature within the SmC phase (Figure 5a). This trend is typically observed when a calamitic sample is cooled from the N into the SmC phase within the magnetic field, where the molecules remain aligned with the long axes in the direction of the field,

2H



Figure 4. Quadrupolar splittings for deuterium D1 (left) and D2 (right) measured from 2H NMR spectra recorded at different temperatures within the mesophases of 6OO8/ClPbis10BB-d2 mixtures. TNI is equal to 354, 359, 360, 360, 360, and 360 K for mixtures containing 30, 50, 64, 72, 84, and 90 wt % 6OO8, respectively.

Figure 5. Quadrupolar splittings measured from 2H NMR spectra recorded at different temperatures within the mesophases of 6OO8-d2/ClPbis10BB mixtures displaying N and SmC phases (a), N, SmA, and SmCA phases (b), and N and SmCA phases (c).

while the SmC planes are inclined with respect to the field direction.37,38 For mixtures containing 72-86 wt % of 6OO8d2, showing a N, a SmA, and a SmCA phase,59 the quadrupolar splitting increased on cooling within the SmA phase, with a slight slope change at the N-SmA phase transition, and then decreased by further lowering the temperature within the SmCA phase, showing no discontinuity at the SmA to SmCA phase transition (Figure 5b). The trend of the quadrupolar splittings indicated that in the N and SmA phases the 6OO8-d2 long molecular axes align, as usual, parallel to the magnetic field, but they progressively tilt with decreasing the temperature in the SmCA phase. A completely different behavior was observed for mixtures containing from 30 to 64 wt % of 6OO8-d2, which do not show the SmA phase; in this case, the 6OO8-d2 deuteria quadrupolar splitting showed a jump at the N to SmCA firstorder phase transition and remained almost constant within the SmCA phase, as expected for phases with a temperatureindependent tilt angle. It is worthy of note that the behavior

observed for the tilt angle with the temperature in the SmCA phase is analogous to that reported by Wise et al. for the SmC one,39 where the tilt angle was found temperature dependent only in the case of the occurrence of a SmA phase above the SmC one, being fixed otherwise.40 2 H NMR spectra acquired on the mixture containing 64 wt % of 6OO8-d2 within the N and SmCA mesophases at a stronger magnetic field (9.4 T) were essentially identical to those recorded at 7.05 T, indicating that, even in a stronger magnetic field, the 6OO8 molecules do not remain aligned along the field direction on cooling from the N to the SmCA phase. This is evidence that the alignment of the long molecular axis of ClPbis10BB parallel to the magnetic field is the determinant factor for whole mixture alignment, therefore imposing a suitable tilt of the 6OO8 molecules. For the mixture containing 64 wt % of 6OO8-d2, 2H NMR spectra were recorded in the SmCA phase (313 K) at several orientations with respect to the magnetic field; the spectra

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Calucci et al. BC molecules in the different mesophases as well as to evaluate the tilt angle in the SmCA phase. The general expressions relating the experimental quadrupolar (∆νq) and dipolar (∆νdip) splittings to the local orientational order parameters SCD and SDH relative to the CD bond and the D-H internuclear vector are given by eqs 1 and 2, respectively:

(

3 cos2 θ - 1 3 ∆νq ) qSCD 2 2 ∆νdip ) -2KDH

Figure 6. Bottom: 2H NMR spectra recorded on a 6OO8-d2/ ClPbis10BB mixture containing 64 wt % of 6OO8-d2 in the SmCA phase (313 K) at several orientations in a 9.4 T magnetic field. Top: quadrupolar splitting values (circles) measured from the spectra as a function of rotation angle and fitting curve to eq 5 (line).

obtained for a number of angles of rotation between 0° and 90° and the corresponding quadrupolar splittings are shown in Figure 6. The same spectra, but in reverse order, were obtained on going from 90° to 180°. The spectral variations highlight the absence of any observable field-induced reorientation. Moreover, the spectra were exactly reproduced on returning to a given sample orientation after rotation, indicating that the structure was not distorted during the experiments. Furthermore, the maximum quadrupolar splitting was observed at 0° rotation, which means that, notwithstanding the relatively rigid layered structure, there is a rapid and essentially isotropic rotation of the whole molecule and/or of the individual aromatic rings about the molecular long axes.38 The observation of a single quadrupolar doublet at all orientations is instead an indication of fast interlayer molecular exchange, which can be described as a twosite chemical exchange.41-43 Orientational Order and Molecular Organization in the Mesophases. The quadrupolar and dipolar splittings measured from the 2H NMR spectra were analyzed to determine the orientational order parameters for both the calamitic and the

(

)

SDH 3 cos2 θ - 1 3 2 rDH

(1)

)

(2)

In eq 1 the quadrupolar coupling tensor was considered to be cylindrically symmetric, with the major axis along the CD bond, as commonly assumed; q is the quadrupolar coupling constant, here taken equal to the typical value of 185 kHz.29 In eq 2 rDH is the distance between the D and H nuclei in ortho position and KDH ) γHγDh/4π2 ) 18 434.4 Hz Å3. θ is the angle between the liquid crystal phase director and the magnetic field; here θ is equal to zero for ClPbis10BB in all the mesophases and for 6OO8 in the N, SmA, and SmC phases, as discussed above. The local order parameters can in turn be related to the molecular ones by quite complicated expressions containing a large number of geometrical and orientational order parameters, which, however, may be reduced on the basis of known structural properties and of molecule and phase symmetry.29 In the present case, due to the small number of independent experimental data, some assumptions had to be made in order to extract molecular order parameters from the experimental splittings, as explained in the following. The ClPbis10BB molecule has a Cs symmetry, thus requiring five elements of the Saupe matrix for the description of the molecular orientational order. However, the experimental data for ClPbis10BB-d2, comprising at most two quadrupolar and one dipolar splittings at each temperature, refer to the sole central ring so that only orientational order parameters relative to this fragment can be obtained from their analysis. This considered, two principal orientational order parameters (Szz and Sxx - Syy) relative to a frame where the Saupe matrix is diagonal are sufficient to describe the local order; the location of this frame on the central phenyl ring is described by the angle (to be determined) between the z axis and the φ-OCO bond in para to the chlorine atom (Figure 1). The local order parameters Si in eqs 1 and 2 are expressed in terms of Szz and Sxx - Syy by the following equation:

Si ) Szz

(

)

sin2 φi 3 cos2 φi - 1 + (Sxx - Syy) 2 2

(3)

where the angles φi between the principal axis for the interaction and the z axis are a function of and bond angles determined by geometry optimization performed using density functional theory (DFT) calculations33 (φi is equal to 235.2° + , 115.4° + , and 355.6° + for C-D1, C-D2, and D2-H, respectively). A global fitting procedure was applied for the mixtures where both quadrupolar splittings for D1 and D2 and the dipolar splitting for D1 were available for several temperatures within each phase, obtaining values of Szz, Sxx - Syy, and . In the fitting, the order parameters were considered temperature dependent, whereas was assumed constant; on the basis of previous

2H



Figure 7. Principal order parameter (Szz) determined from 2H NMR spectra analysis for ClPbis10BB in all mesophases (a) and for 6OO8 in the N, SmA, and SmC phases (b). For the Szz values relative to 6OO8 in the SmCA phase, see text.

studies,33 ∆νq(D1) was taken positive, while ∆νq(D2) and ∆νdip(D1) were taken negative, and rDH, obtained from geometry optimization, was 2.49 Å. Whereas the best fit values of Szz varied with the temperature and mixture composition, Sxx - Syy was found to remain essentially constant within each phase independently of mixture composition; in particular, Sxx - Syy was 0.070 ( 0.003 and 0.120 ( 0.005 in the N and Sm phases, respectively. The angle was determined equal to 31.5 ( 0.5° for all mixtures. These values of Sxx - Syy and were used to calculate Szz for the cases where only one or two quadrupolar splittings were available. The Szz values obtained for the various mixtures in the different mesophases are reported in Figure 7a. Very similar values of Szz were found in the N phase for all the mixtures at the same TNI-T; on the other hand, Szz showed a progressive decrease in the SmCA phase with increasing ClPbis10BB content. In the analysis of the quadrupolar and dipolar splittings of 6OO8-d2, deriving from deuteria on a para-disubstituted aromatic ring with a C2V symmetry, we assumed that two order parameters (Szz and Sxx - Syy) relative to the principal reference frame for the order matrix, fixed on the aromatic ring with the z axis along the para axis direction (Figure 1), are sufficient to describe the orientational order. In this frame SDH coincides with Szz; this given, and considering that the ratio between the quadrupolar and dipolar splittings was in all cases practically constant, the order biaxiality Sxx - Syy was neglected in the calculations. Therefore, the following equation was used for SCD:

(

SCD ) Szz

3 cos2 φ - 1 2

)

(4)

with φ the angle between the CD bond and the z axis; this angle could be determined from the ∆νq/∆νdip ratio and, taking rDH ) 2.49 Å, was found equal to 57.8 ( 0.2° for all mixtures at all temperatures. For the N, SmA, and SmC phases, where the long molecular axes are aligned along the magnetic field, the order parameter Szz was determined from the quadrupolar splittings using eqs 1

and 4 with θ ) 0° and φ ) 57.8°; the results are reported in Figure 7b. It must be pointed out that, considering that the local z axis is nearly aligned along the long molecular axis, in the calculations dipolar and quadrupolar splittings were taken negative. Upon comparison of the trends in Figures 7a and 7b, it can be observed that in the N, SmA, and SmC phases the principal order parameters for the deuterated 6OO8 and ClPbis10BB rings were essentially identical in the case of mixtures with 6OO8 content g64 wt %, whereas for the N phase of the other mixtures the ClPbis10BB Szz values were appreciably higher than those of 6OO8. This is clearly a consequence of a progressive decrease of the orientational order of 6OO8 in the N phase with increasing the content of BC mesogen in the mixtures. For measurements in the SmCA phase, the quadrupolar and dipolar splittings of 6OO8-d2 depend on both Szz and the tilt angle, which coincides with θ of eqs 1 and 2 assuming that the layer normals are aligned along the magnetic field. Therefore, an independent determination of Szz and θ is prevented, also considering that θ varies with the temperature for mixtures containing 72-86 wt % of 6OO8-d2 while it is almost fixed for those with 6OO8-d2 content between 30 and 64 wt %. Comforted by the fact that the same Szz values were observed for 6OO8 and ClPbis10BB in the N phase (Figure 7), for the mixtures containing at least 64 wt % of 6OO8 we decided to use the Szz values determined for ClPbis10BB in the SmCA phase to evaluate the tilt angle for 6OO8 from the quadrupolar splittings using eqs 1 and 4. Upon entering the SmCA phase, θ values ranging from 11.0 ( 0.5° to 21.0 ( 0.5° with decreasing the 6OO8 content (from 86 to 64 wt %) were calculated; in all cases θ reached a maximum value of 25.0 ( 0.5° at the lowest temperature. For the 6OO8-d2/ClPbis10BB mixture containing 64 wt % 6OO8-d2, the tilt angle was also independently determined from the quadrupolar splittings obtained in the angular dependent 2H NMR measurements at 313 K (Figure 6) using the equation

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|(

)

3 cos2 φ - 1 3 ∆νq(∆, θ) ) qSzz × 2 2 2 3 cos2 η- - 1 1 3 cos η+ - 1 + 2 2 2

(

Calucci et al.

)|

(5)

with

η( ) cos θ cos ∆ ( sin θ sin ∆ cos γ

(6)

where θ is the tilt angle, ∆ is the rotation angle, and the other parameters are as in eqs 1 and 4. The sum in eq 5 derives from the assumption of fast interlayer exchange, η( accounting for the anticlinic arrangement of the molecules in adjacent layers, having azimuthal angles of γ and γ + π. It must be noticed that eq 5 is similar to those used by Zalar et al.41 and by Carvalho et al.44 for SmCA* phases. In the present case γ ) 0° as a consequence of the magnetic free energy minimization as the sample is rotated around an axis perpendicular to the magnetic field. In fact, since for ClPbis10BB the components of the magnetic susceptibility tensor are in the order χ11 > χ22 > χ33 (with 1 being along the long molecular axis, 2 parallel to the bend direction, and 3 perpendicular to 1 and 2),45 the minimum energy is realized when axis 3 is parallel to the rotation axis (Figure 8). By fitting the trend of the quadrupolar splittings with the rotation angle to eq 5 with φ ) 57.8° a good reproduction of the experimental data was obtained (Figure 6, top) with values of 25.0 ( 0.3° and 0.91 ( 0.01 for θ (in the following indicated as θ64) and Szz, respectively. The good agreement between θ64 and the tilt angle values calculated above for the mixture containing 64 wt % of 6OO8 indicates that the assumption of the same Szz parameters for both ClPbis10BB and 6OO8 in the SmCA phase is reasonable. The tilt angle (θx) of the mixtures containing 50 and 30 wt % of 6OO8 were calculated from the quadrupolar splittings, assuming the same Szz value as that of the 64 wt % sample, using eq 7:

∆νq(x) 3 cos2 θx - 1 ) ∆νq(64) 3 cos2 θ64 - 1

(7)

Average tilt angles of 25.5 ( 0.5° and 26.0 ( 0.5° were found for θ50 and θ30, respectively. Considering all the assumptions made, the tilt angles here determined for the different mixtures in the SmCA phase well agree with those previously reported on the basis of X-ray diffraction measurements.22 Dynamics of the Rod-Shaped Mesogen in the Mesophases. In order to investigate the influence of the BC mesogen on the dynamics of the calamitic one in the different mesophases, the relaxation times for the Zeeman (T1Z) and the quadrupolar (T1Q) order of the aromatic deuteria of 6OO8-d2 were measured at various temperatures on 6OO8-d2/ClPbis10BB mixtures containing 30, 50, and 86 wt % 6OO8-d2 and on neat 6OO8-d2. These relaxation times are related to the spectral densities of motion J1(ω0) and J2(2ω0), which are the Fourier transform of the autocorrelation functions, by the following equations:30,31

J1(ω0) )

1 3T1Q

(8)

Figure 8. (a-c) Schematic representation of the arrangement of the SmCA layers with respect to the magnetic field in the angular dependent 2 H NMR measurements. (d) Principal axis frame for the diamagnetic susceptibility tensor of ClPbis10BB.

Figure 9. Experimental (symbols) and calculated (lines) spectral densities J1(ω0) (full symbols and solid lines) and J2(2ω0) (empty symbols and dashed lines) for aromatic deuteria of neat 6OO8-d2 (a) and of 6OO8-d2/ClPbis10BB mixtures containing 86 (b), 50 (c), and 30 (d) wt % 6OO8-d2.

J2(2ω0) )

(

1 1 1 4 T1Z 3T1Q

)

(9)

where ω0 is the Larmor frequency, here equal to 2.89 × 108 rad s-1. The spectral densities obtained from the experimental relaxation times are reported as a function of the temperature in Figure 9. For neat 6OO8-d2 and for the mixture containing 86 wt % 6OO8-d2 both J1(ω0) and J2(2ω0) regularly increased with decreasing the temperature in all mesophases, indicating a motional narrowing regime for the motions contributing to relaxation at the Larmor frequency, as usually found for low molecular weight calamitic liquid crystals. Higher J1(ω0) and J2(2ω0) values were found for the mixture with respect to the neat 6OO8-d2 at each temperature, suggesting a slightly more hindered dynamics. On the other hand, for the mixtures containing 30 and 50 wt % 6OO8-d2, different trends were

2H



observed in the N and SmCA phase. In particular, in the N phase J1(ω0) and J2(2ω0) increased with decreasing the temperature, with higher values for higher BC mesogen content at the same temperature; in the SmCA phase J1(ω0) and J2(2ω0) tended to flatten out as the temperature decreased. In order to obtain quantitative information on the dynamics, spectral densities must be analyzed in terms of models for molecular motions. In liquid crystalline phases, different dynamic processes, usually assumed independent on the basis of time scale arguments, have been found to contribute to deuterium relaxation; these processes have been classified as internal, “overall molecule”, and collective, in order of increasing time scales.30,31 Several models have been devised to describe reorientations of the whole molecule, the most used being the anisotropic Viscosity model proposed by Nordio et al.46,47 and by Freed et al.,48,49 which considers these motions as small step diffusional rotations in a Maier-Saupe meanfield potential, and the extension of this model by Vold and Vold, named the third rate anisotropic Viscosity model.50 As far as the internal motion of interest here, i.e., phenyl ring rotation, is concerned, it has been mainly described in an isotropic potential by means of either small step diffusion51 or strong collision52 models. Collective motions, which can be essentially identified with order director fluctuations, have been usually modeled on the basis of the theories proposed by Pincus53 and by Blinc et al.54 In the present work, the relaxation data were analyzed considering the Nordio model for the overall motions with superimposed internal rotation of the phenyl ring expressed in terms of the small step diffusion model. To this end the CAGE software55 as modified for tilted Sm phases56 was used. A global target approach, in which an Arrhenius temperature dependence is considered for the diffusional coefficients, was applied to J1(ω0) and J2(2ω0) data sets obtained at different temperatures within each mesophase for each sample. However, it was not possible to independently determine the values of the overall diffusion coefficients (D| and D⊥ for molecular spinning and tumbling, respectively) and of the diffusion coefficient DR for the phenyl ring rotational diffusion. In particular, the data were not sensitive to D⊥, so that it could not be determined in the analysis; in addition, a strong correlation was found between D| and DR, which, when the long molecular axis and the phenyl para axis are parallel, as here assumed, refer to rotations about the same axis. The observed indeterminacy of the diffusional coefficients, already highlighted in previous 2H relaxation data analyses,55 arises from the fact that the data refer to only one kind of deuterium at a single Larmor frequency. The spectral density analysis was therefore carried out considering only the motions about the long molecular axis, described by an effective diffusion coefficient DE, using eq 10: JmL(mLω0) ) 3π2 2 q 2

2

∑

mR)-2

cmLmR[dm2 R0(βi,Qi)]2

∑ j

am(j)LmR

m2RDE (mLω0)2 + (m2RDE)2

(10) where βi,Qi is the angle (here 57.8°) between the C-D bond and the phenyl para axis, here coinciding with the long molecular axis, and the coefficients a(j) mLmR and cmLmR are calculated from the principal orientational order parameter as in ref 50. The global fitting procedure applied on the spectral densities relative to neat 6OO8-d2 gave a good reproduction of the data (Figure 9a) with the values of DE shown in Figure 10 and the

Figure 10. Diffusion coefficient DE and jump rate kj vs 1000/T.

orientational order and geometric parameters reported in the orientational order analysis. For the 6OO8-d2/ClPbis10BB mixture containing 86 wt % 6OO8-d2 the data were analyzed in the same way, but taking into account the tilt of the long molecular axis with respect to the magnetic field direction in the SmCA phase; the data were well reproduced (Figure 9b) using the same Arrhenius equation for DE in all mesophases as shown in Figure 10. For mixtures containing 30 and 50 wt % 6OO8-d2 the global analysis satisfactorily fitted the experimental data in the N phase (Figure 9c,d) but failed to reproduce the spectral densities in the SmCA one, giving in particular too small J1/J2 ratios. These results suggested that another type of motion, here tentatively identified with interlayer diffusion, contributes to deuterium relaxation in the SmCA phase. Indeed, whereas in synclinic smectic phases interlayer diffusion does not affect 2H relaxation due to the intramolecular nature of the quadrupolar interaction, in the SmCA phase interlayer diffusion inevitably involves a reorientation of the CD bonds41-43 that can modulate the quadrupolar interaction. This motion was invoked above to reproduce the trend of the quadrupolar splittings with the rotation angle ∆ in measurements performed at different orientation of the sample with respect to the magnetic field (Figure 6). The observation of an average quadrupolar splitting at all ∆ values indicates that the interlayer diffusion is fast with respect to the difference in quadrupolar splitting between two adjacent layers, that is, its rate should be g107 s-1, therefore matching the frequency scale suitable for 2H relaxation. Although interlayer diffusion has been found to affect both deuterium spectral line shapes41,42 and proton relaxation,57 no suitable models for the analysis of 2H relaxation including this motion have been proposed. This considered, the experimental spectral densities in the SmCA phase were analyzed using a model in which the rotational diffusion about the long molecular axis, governed by DE, is superimposed to interlayer diffusion described as a twosite jump motion of the long molecular axis between two equally populated positions with a rate constant kj, adapting the expressions of the motional correlation functions given by Torchia and Szabo for deuterium longitudinal relaxation in solids58 to the case of liquid crystalline phases. Equation 11 was therefore used to express the spectral densities:

448


JmL(mLω0) )

3π2 2 2 q Szz 2

Calucci et al.

∫0∞ Cm (t) cos(mLω0t) dt L

(11) where Szz is the principal order parameter and CmL is the motional correlation function given by 2

CmL(t) ) ΓmL(t)

∑

mR)-2

[dm2 RmL(θ)]2[dm2 R0(βi,Qi)]2ΓmR(t)

(12) where

1 1 ΓmL(t) ) [1 + (-1)mL]2 + exp(-2kjt)[1 - (-1)mL]2 4 4 (13) and

ΓmR(t) ) exp(-mR2DEt)

(14)

ΓmL(t) describes the jump motion of the long molecular axis between two sites defined by the polar angles (θ, 0) and (-θ, 0), respectively, with respect to the laboratory frame having z parallel to the magnetic field direction; θ here is thus the tilt angle determined above. ΓmR(t) describes the rotational diffusion motion with effective coefficient DE, similarly to what used in the N and SmA phases. This model allowed a satisfactory reproduction of the experimental spectral densities of the 30 and 50 wt % 6OO8-d2/ClPbis10BB mixtures to be obtained (Figure 9c,d) with values of DE and kj shown in Figure 10. It must be pointed out that, due to the strong correlation found in the fitting between DE and kj, the same kj values were assumed for the two mixtures; hence, the numerical values determined for DE and kj should be considered only as a rough estimate. Nonetheless, the good reproduction of the data with this model is clear evidence that interlayer translational diffusion contributes to 2H relaxation in the SmCA phase. Lower values of DE were determined in the mixtures with respect to the neat 6OO8, with a progressive decrease with increasing the BC mesogen content, indicating that the rotational diffusion of the calamitic mesogen about its long molecular axis becomes slower in environments richer in banana molecules. In the N phase, the decrease in DE values can be associated with the viscosity increase observed on passing from neat 6OO8 to 6OO8/ClPbis10BB mixtures due to the quite high viscosity of ClPbis10BB.9 In the SmCA phase DE resulted smaller than in the N one, as expected for a layered structure, although remaining on the order of 109 s-1. The relatively low or negligible temperature dependence of DE in the SmCA phase of the 50 and 30 wt % mixtures, respectively, should not be taken as an indication of a decrease in activation energy for rotational diffusion, but rather of the onset of a deviation from an Arrhenius-type behavior in BC mesogen-rich mixtures, possibly due again to the high phase viscosity. Values of kj on the order of 107-108 s-1 were found, confirming that interlayer diffusion is fast as assumed above. Conclusions 2

H NMR spectroscopy was here applied for the first time to obtain information on the structural and dynamic properties of

the liquid crystalline phases (N, SmA, SmC, and SmCA) formed by mixtures of a bent-core (ClPbis10BB) and a rodlike (6OO8) mesogen. The analysis of 2H NMR spectra of selectively deuterated isotopomers of the two mesogens allowed the molecular arrangement within the different mesophases to be described quite in detail. In particular, ClPbis10BB was found to behave like an usual calamitic mesogen, with its long axis aligning parallel to the magnetic field direction in all phases at all temperatures, therefore lying along the axis perpendicular to the layers in the SmCA phase. On the other hand, 6OO8 molecules changed their arrangement to accommodate the bentcore mesogen by forming a SmCA phase instead of a SmC one for ClPbis10BB contents larger than 10 wt %, with a tilt angle slightly increasing with increasing the ClPbis10BB content. The principal order parameter values relative to the two mesogens were similar and fell in ranges typical for the different mesophases, while a significant order biaxiality was determined only for ClPbis10BB, as expected for bent-core molecules. The analysis of 2H NMR longitudinal relaxation indicated that 6OO8 molecules undergo quite fast rotational diffusion in all the mesophases at all temperatures. The increase in viscosity upon increasing the amount of ClPbis10BB in the mixtures caused a progressive slowing down of the 6OO8 rotational motions in all the mesophases accompanied by a progressive change in the temperature dependence of the rotational diffusion coefficient in the SmCA phase. In addition, fast interlayer diffusion of the calamitic mesogen was found to occur in the SmCA phase, which required a suitable model for 2H relaxation to be devised. We believe that the detailed description here obtained of the dependence of structural and dynamic properties of calamitic and bent-core mesogen mixtures on temperature and composition is fundamental for understanding the mutual influence of these two kinds of mesogens and, therefore, may be of aid in the formulation of liquid crystalline binary systems with specific properties. Acknowledgment. This work was supported by the CNRMTA Joint Project 2007/2009 on “Novel polymers and monomers from banana-shaped molecules for electrooptics”. References and Notes (1) Niori, T.; Sekine, T.; Watanabe, J.; Furukawa, T.; Takezoe, H. J. Mater. Chem. 1996, 6, 1231–1233. (2) Pelzl, G.; Diele, S.; Weissflog, W. AdV. Mater. 1999, 11, 707– 724. (3) Tschierske, C.; Dantlgraber, G. Pramana 2003, 61, 455–481. (4) Ros, M. B.; Serrano, J. L.; De la Fuente, M. R.; Folcia, C. L. J. Mater. Chem. 2005, 15, 5093–5098. (5) Amaranta Reddy, R.; Tschierske, C. J. Mater. Chem. 2006, 16, 907–961. (6) Takezoe, H.; Takanishi, Y. Jpn. J. Appl. Phys. 2006, 45, 597–625. (7) Weissflog, W.; Sheenivasa Murthy, H. N.; Diele, S.; Pelzl, G. Philos. Trans. R. Soc. London, Ser. A 2006, 364, 2657–2679. (8) Etxebarria, J.; Ros, M. B. J. Mater. Chem. 2008, 18, 2919–2926. (9) Wiant, D.; Gleeson, J. T.; E´ber, N.; Fodor-Csorba, K.; Ja´kli, A.; To´th-Katona, T. Phys. ReV. E 2005, 72, 041712-1-12. (10) Dorjgotov, E.; Fodor-Csorba, K.; Gleeson, J. T.; Sprunt, S.; Ja´kli, A. Liq. Cryst. 2008, 35, 149–155. (11) Harden, J.; Mbanga, B.; Fodor-Csorba, K.; Sprunt, S.; Gleeson, J. T.; Ja´kli, A. Phys. ReV. Lett. 2006, 97, 157802-1-4. (12) Gorecka, E.; Nakata, M.; Mieczkowski, J.; Takanishi, Y.; Ishikawa, K.; Watanabe, J.; Takezoe, H.; Eichorn, S. H.; Swager, T. M. Phys. ReV. Lett. 2000, 85, 2526–2529. (13) Pratibha, R.; Madhusudana, N. V.; Sadashiva, B. K. Science 2000, 288, 2184–2187. (14) Pratibha, R.; Madhusudana, N. V.; Sadashiva, B. K. Pramana 2003, 61, 405–415. (15) Kishikawa, K.; Muramatsu, N.; Kohmoto, S.; Yamaguchi, K.; Yamamoto, M. Chem. Mater. 2003, 15, 3443–3449. (16) Zhu, M. H.; Dodge, M. R.; Shioda, T.; Rosenblatt, C.; Parker, D. D.; Kim, J. M.; Neubert, M. E. Liq. Cryst. 2004, 31, 1381–1386.

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Orientational Order, Molecular Organization, and Dynamics in

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