#
Study of Liquid Crystals Showing Two Isotropic Phases by ^{1}H NMR Diffusometry and ^{1}H NMR Relaxometry

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

**9/2 RS/RS**, and a bimesogenic liquid crystal labelled

**L1**, show a direct transition between two isotropic phases followed, at lower temperatures, by the optically isotropic, 3D structured, cubic phase. These systems have been investigated by means of

^{1}H NMR diffusometry and

^{1}H NMR relaxometry in order to characterize their isotropic–isotropic’–cubic mesophase behavior, mainly on the dynamic point of view. In particular, the temperature trend of the self-diffusion coefficients measured for both samples allowed us to significantly distinguish between the two isotropic phases, while the temperature dependence of the

^{1}H spin-lattice relaxation time (T

_{1}) did not show significant discontinuities at the isotropic–isotropic’ phase transition. A preliminary analysis of the frequency-dependence of

^{1}H T

_{1}at different temperatures gives information about the main motional processes active in the isotropic mesophases.

^{1}H NMR

## 1. Introduction

_{1}32 symmetry, a double gyroid structure with Ia3d symmetry, the tricontinuous cubic phase with Im3m symmetry, and a multicontinuous type Pm3m structure [1,2,3,8,14,15,16,17,18,19,20].

^{2}H and

^{13}C have been widely used to get information about the average molecular conformations, supramolecular organization, and orientational properties of LC mesophases [36,37,38,39]. Multinuclear NMR approaches demonstrated to be of help in understanding the short-range orientational properties and the peculiar dynamics in the isotropic phase formed by bent-core LCs [40,41,42].

^{1}H NMR spectroscopic techniques have also been used to investigate different dynamic processes active in the different liquid crystalline phases, such as single molecular motions (i.e., self-diffusion and reorientational motions) and collective processes (i.e., order director fluctuations and layer undulations). Different NMR techniques can be used to explore different dynamic processes having characteristic correlation times, τ

_{c}. For instance, exchange diffusion processes can be investigated by means of

^{2}H 2D NMR or

^{2}H NMR line-shape analysis [30,31,32,33]; their characteristic time being in the range of 10

^{−5}–10

^{−4}s. Self-diffusion molecular processes, either isotropic or anisotropic ones, are better studied by means of

^{1}H NMR diffusometry, where the signals are averaged over characteristic times in the range of 10

^{−1}–10

^{−3}s [43,44,45,46,47,48,49,50].

^{2}H NMR spin-lattice relaxation times, T

_{1}, typically measured at high Larmor frequencies (hundreds of MHz), are sensitive to fast motions, such as overall molecular motions having 10

^{−11}< τ

_{c}< 10

^{−7}s, while

^{2}H NMR spin-spin relaxation times, T

_{2}, can be used to investigate collective and other slow motions, with τ

_{c}ranging from 10

^{−6}s up to 10s [31,40,41,42,49,50]. Another important NMR technique is represented by

^{1}H NMR relaxometry, based on the experimental measurement of

^{1}H spin-lattice relaxation times, T

_{1}, at different

^{1}H Larmor frequencies, typically from few KHz to several tens of MHz [49,50,51,52]. The analyses of the frequency-dependence of

^{1}H NMR T

_{1}can be done invoking different dynamic contributions by means of suitable theoretical models [51,52,53,54,55,56,57,58,59].

^{1}H NMR diffusometry [29,60,61,62,63], and

^{1}H NMR relaxometry [64,65] of 3D ordered optically isotropic phases.

**9/2 RS/RS**, has a highly anisotropic molecular shape and it shows a sponge-type cubic phase with Im3m symmetry [8], the second mesogen, labelled

**L1**, is an asymmetric dimer, having a double gyroid cubic phase with Ia3d symmetry [14]. The dynamic properties of these two LC systems will be discussed based on

^{1}H NMR diffusometry and

^{1}H NMR relaxometry data.

## 2. Materials and Methods

#### 2.1. Liquid Crystalline Samples

**9/2 RS/RS**; it is a symmetric molecule, having a 4,4′-bis(4″-carboxybenzyloxy) biphenyl mesogenic core, belonging to the series of compounds whose synthesis and mesomorphic characterization are reported in Ref. [8]. The second mesogen is the 4′-{5-pentylenate-[phenyloxycarbonyl-(4′-decyloxy)]}-4-[(E)-2-(4-methoxyphenyl)ethenyl]benzoate, labelled

**L1**; it belongs to a series of asymmetric dimeric compounds [14] formed by two rigid cores: a trans-stilbene moiety connected by an ester bond to a biphenyl fragment (first rigid part) and a benzoate derivative (second rigid part) linked by a flexible chain of five carbons length.

**9/2 RS/RS**and an Ia3d symmetry for compound

**L1**. In the case of the mesogen

**9/2 RS/RS**, a metastable columnar phase having a 2D hexagonal symmetry appears by cooling the sample from the isotropic phases [8,29]. This columnar phase converts into the cubic phase with relatively fast kinetics (as detected by NMR spectroscopy [29]). In the case of

**L1**, a metastable columnar phase is only detectable by POM [14]. The symmetric mesogen

**9/2 RS/RS**has been previously investigated by means of a multinuclear NMR approach, including

^{13}C and

^{2}H NMR spectroscopy to study its ordering properties, and

^{1}H NMR diffusion measurements [29].

#### 2.2. ^{1}H NMR Diffusometry

**9/2 RS/RS**were previously reported in Ref. [29].

#### 2.3. ^{1}H NMR Relaxometry

## 3. Results and Discussion

#### 3.1. ^{1}H NMR Diffusometry

_{A}is the activation energy. In the

**L1**sample, the values of 67 kJ/mol and 152 kJ/mol were obtained for the isotropic and isotropic’ phases, respectively. In the case of

**9/2 RS/RS**sample, the values of 65.4 kJ/mol and 124 kJ/mol were obtained [29]. As already noted for the sample

**9/2 RS/RS**[29], the increase in activation energy moving from the isotropic to the isotropic’ phases could be ascribed to the formation of a so-called “spongy” cubic phase, the precursor of the lower-temperature cubic phase. In this second isotropic phase, molecules move partially free or aggregated in metastable very flexible LC “cybotactic” clusters that are supposed to increase in dimensions/stability as temperature decreases, until the formation of the LC phase with total disappearance of isotropic local residue. It should be noticed that, on the self-diffusion time-scale, differences among molecules experiencing a free environment and those experiencing a locally oriented environment are completely averaged out, as can be deduced from the fact that a single isotropic self-diffusion coefficient, D, could be measured in the whole mesophasic range. As observed in Figure 3, the isotropic’–cubic phase transition is identified by a first-order change, namely a sudden decrease of D as molecules assemble completely in the 3D long-range pattern of the cubic phase. Here, the temperature dependence of D is associated with the activation energy of 68 kJ/mol and 74.6 kJ/mol for sample

**L1**and

**9/2 RS/RS**, respectively.

**9/2 RS/RS [29]**, in order to test possible effects of the supra-molecular phase structure on translational diffusion,

^{1}H NMR diffusion measurements were performed both changing the gradient directions, as well as varying the diffusion time, ranging from 70 ms to 700 ms, by changing the gradient delay accordingly from 1 ms to 3 ms to preserve the same decay rate in all the STE-PG experiments. As shown in Figure 3 (for cubic

**L1**), change in the time diffusion does not affect the results, as well as varying the direction on the measurement. For instance, the diffusion coefficient D measured at T = 380 K and T = 373 K (in the cubic phase), resulted in a diffusion coefficient D = 9.6 × 10

^{−13}m

^{2}/s and D = 6.4 × 10

^{−13}m

^{2}/s within a 5% experimental error, independently from the diffusion time Δ and the gradient direction. According to these measurements, we can state that also in the case of

**L1**sample the cubic phase assembles in the magnetic field with a completely isotropic distribution of domains that averages molecular translational diffusion to a scalar value. In particular, considering a diffusion length scale, ℓ, calculated as:

**L1**sample at T = 373 K, the diffusion coefficient measured, D = 6.4 × 10

^{−13}m

^{2}/s, with Δ = 70 ms indicates that the averaging occurs within 300 nm, while, in the case of the

**9/2 RS/RS**sample, the limit was even smaller; about 170 nm at T = 346 K, with a diffusion coefficient D = 2.3 × 10

^{−13}m

^{2}/s [29]. Consequently, we can also estimate, in the cubic phase, the average domain dimension to be smaller than 300 nm and 170 nm in the

**L1**and

**9/2 RS/RS**samples respectively. The difference between the two investigated samples could also be explained with the different structural features of the two cubic phases (Ia3d and Im3m in the case of

**L1**and

**9/2 RS/RS**, respectively), but this aspect would need further investigations. An important aspect, from the self-diffusion measurement point of view, is that no differences in terms of diffusion motion among different directions can be detected in the whole investigated temperature range.

#### 3.2. ^{1}H NMR Relaxometry

**L1**and

**9/2 RS/RS**, respectively, at chosen Larmor frequencies. Here, we should note that the magnetization decay/recovery curves for T

_{1}measurements could be clearly described by a single-exponent function, corresponding to a single spin-lattice relaxation time for all protons in the molecule, only at higher fields. At lower fields (4 MHz and below), slight deviations from a single exponent model could be observed, hinting that spin-lattice relaxation can instead be interpreted using two components. An example of two-exponential and single-exponential fittings of the magnetization recorded at high and low fields for the sample

**L1**in the isotropic phase reported Figure S1 (Supplementary Materials). Similar phenomena have been observed before, for example in HZL 7/* [56] and 10BBL [57] liquid crystals, where multi-exponential functions gave better fitting of the magnetization than a single-exponential function. In such cases [56,57], the different components were attributed to the relaxation of methyl, methylene, and aromatic protons in the LC molecule. In the present case, despite the fact that a bi-exponential function gives a better fitting than a single-exponential one at low fields, in order to consistently present the spin-lattice relaxation results, we have shown the total relaxation rate—i.e., using only a single exponential function to describe the magnetization decay/recovery curves.

_{1}when crossing the phase transitions are strong indicators of the onset of additional dynamic processes in the system mainly due to changes in local order. Looking at Figure 4 and Figure 5, in both LC systems, T

_{1}temperature dependencies at higher frequencies are flat throughout both isotropic–isotropic’ and isotropic’–cubic phase transitions, indicating that there is no change in fast dynamic processes. The same can be observed when crossing the isotropic–isotropic’ phase transition at lower frequencies: there is no discontinuity and not even a change of the slope, in agreement with what already seen from the NMR diffusion measurements. However, we can spot a clear jump in T

_{1}when crossing from isotropic’ to cubic phase at the lowest frequencies, which represents an indication of the onset of collective motions, which are expected in the locally ordered cubic phase. Additional low-frequency contribution in ordered liquids are commonly attributed to collective molecular dynamics. However some other mechanisms—such as cross-relaxation—cannot be excluded [71].

_{1}trend could be related to the fact that the dominating dynamic contributions are the fast reorientations, namely the overall molecular spinning and internal reorientations. This interpretation agrees with previous

^{1}H NMR relaxometry studies on rod-like LC systems having a relatively similar molecular structure [56,57]. To confirm such a hypothesis, a more detailed study about the frequency dependent T

_{1}trends can be done. In Figure 6 and Figure 7, a selection of T

_{1}-dispersions recorded at different temperatures is reported for

**L1**and

**9/2 RS/RS**, respectively.

**L1**sample, we can see a significant difference between the T

_{1}-dispersions in the high-temperature isotropic phase (T = 405 K and T = 396 K) with respect to those obtained in the lower temperature isotropic phase (T = 389 K) and in the cubic phase (T = 379 K and T = 371 K). These last T

_{1}-dispersions are, indeed, quite similar, as shown in Figure 6. In the case of

**9/2 RS/RS**sample, on the contrary, the T

_{1}-dispersion recorded in the lower temperature isotropic phase (T = 369 K) presented intermediate features between the higher temperature isotropic phase (T = 386 K and T = 377 K) and the cubic phase (T = 360 K and T = 351 K), as seen in Figure 7.

_{1}-dispersions [51]. In a first approximation, in the isotropic phases, the relaxation rates, R

_{1}(1/T

_{1}), can be modelled as the sum of independent contributions due to reorientational motions and to self-diffusion [40,43,70], as reported here:

**L1**, a good reproduction of the experimental R

_{1}-dispersion curves is obtained by assuming two relevant reorientational motions, modelled according to the BPP model, active in the range between 10 MHz and 5 KHz, and the self-diffusion process, modelled by using Equation (6), active in the MHz regime. Here, we are reporting, as an example, the fitting curves (i.e., the total relaxation rate and the single motion contributions to the relaxation rate) obtained for the

**L1**sample at 396 K (Figure 8).

**9/2 RS/RS**sample, the three motional processes, namely two reorientational motions modelled according to Equation (5) and the molecular self-diffusion process described as reported in Equation (6), give a good reproduction of the total proton spin-lattice relaxation rate, R

_{1}, in both isotropic phases. For example, the fitting obtained in the high-temperature isotropic phase at T = 377 K is reported in Figure 9, and relevant fitting parameters are reported in Table 1. As in the case of the

**L1**system, these three motional processes are not able to reproduce the R

_{1}-dispersions in the cubic phase, indicating the need to include additional dynamic contributions.

^{1}H NMR relaxation curves of the two samples in the isotropic phase indicates that three motional processes can be used to reproduce in a satisfying way the experimental data. By comparing the characteristic correlation times of the two reorientational motions, modelled according to the BPP model [72], namely τ

_{ROT1}and τ

_{ROT2}, with the average time of the diffusion displacement length, τ

_{D}, [73], we can see that they differ by one order of magnitude in both samples (see Table 1). In particular, the self-diffusion process is faster than the other two motions, which can be ascribed to the overall molecular spinning (ROT2) and molecular tumbling or other internal reorientations (ROT1). Further investigations, however, are needed in order to extend this preliminary analysis to lower temperature phases by including the temperature dependence of relevant parameters and additional motional and/or relaxation mechanisms in low-temperature phases.

## 4. Conclusions

^{1}H NMR diffusometry and

^{1}H NMR relaxometry.

^{1}H NMR diffusometry allowed us to distinguish among the different phases. The temperature dependence of the self-diffusion coefficient, D, which is isotropic in all the mesophases, show a clear slope variation at the isotropic–isotropic’ transition and a first-order jump at the isotropic’–cubic phase transition. Based on previous works and on the observed change in the diffusion slope at the isotropic–isotropic’ transition, a plausible explanation is that in the lower temperature isotropic phase local “sponge-like” cubic domains start growing until the cubic phase is reached. On the NMR diffusion time-scale, the measured diffusion coefficient is isotropic, and it results from the time-average between a completely free environment and a locally ordered cluster one.

^{1}H NMR relaxometry added information on the active dynamic processes in the two samples.

^{1}H NMR spin-lattice relaxation times recorded at high frequency do not show any evident discontinuity among the mesophase transitions. However, slightly different behavior was observed between the two samples when moving to frequencies below 1 MHz. A preliminary analysis of the frequency T

_{1}-dispersions in the isotropic phase of the two samples allowed us to have a good reproduction of the experimental data by assuming three main motional processes responsible for the proton relaxation rates. These motions were the molecular self-diffusion, active in the MHz regime, and two slower reorientational motions, which were described according to the BPP model, ascribable to overall molecular spinning or internal reorientations (faster processes) and to flipping around the short axis or overall molecular tumbling motion (slower process). However, a more detailed analysis is required in order to better characterize the dynamic motional profiles as a function of temperature and to describe the isotropic’–cubic phase transition and the cubic phases by considering additional relaxation mechanisms.

## Supplementary Materials

**L1**sample at 396K at high field (

**a**) and at low field (

**b**), by using a single- and two-exponential function.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Tschierske, C. Liquid crystalline materials with complex mesophase morphologies. Curr. Opin. Colloid Interface Sci.
**2002**, 7, 69–80. [Google Scholar] [CrossRef] - Tschierske, C. Development of Structural Complexity by Liquid-Crystal Self-assembly. Angew. Chem. Int. Ed.
**2013**, 52, 8828–8878. [Google Scholar] [CrossRef] [PubMed] - Diele, S. On thermotropic cubic mesophases. Curr. Opin. Colloid Interface Sci.
**2002**, 7, 333–342. [Google Scholar] [CrossRef] - Zeng, X.; Ungar, G.; Imperor-Clerc, M. A triple-network tricontinuous cubic liquid crystal. Nat. Mater.
**2005**, 4, 562–567. [Google Scholar] [CrossRef] - Zeng, X.; Cseh, L.; Mehl, G.H.; Ungar, G. Testing the triple network structure of the cubic Imm (I) phase by isomorphous replacement and model refinement. J. Mater. Chem.
**2008**, 18, 2953–2961. [Google Scholar] [CrossRef] - Ozawa, K.; Yamamura, Y.; Yasuzuka, S.; Mori, H.; Kutsumizu, S.; Saito, K. Coexistence of Two Aggregation Modes in Exotic Liquid-Crystalline Superstructure: Systematic Maximum Entropy Analysis for Cubic Mesogen, 1,2-Bis(4′-n-alkoxybenzoyl)hydrazine [BABH(n)]. J. Phys. Chem. B
**2008**, 112, 12179–12181. [Google Scholar] [CrossRef] - Zeng, X.; Prehm, M.; Ungar, G.; Tschierske, C.; Liu, F. Formation of a Double Diamond Cubic Phase by Thermotropic Liquid Crystalline Self-Assembly of Bundled Bolaamphiphiles. Angew. Chem. Int. Ed.
**2016**, 55, 8324–8327. [Google Scholar] [CrossRef] - Vogrin, M.; Vaupotic, N.; Wojcik, M.M.; Mieczkowski, J.; Madrak, K.; Pociecha, D.; Gorecka, E. Thermotropic cubic and tetragonal phases made of rod-like molecules. Phys. Chem. Chem. Phys.
**2014**, 16, 16067–16074. [Google Scholar] [CrossRef] - Luzzati, V.; Spegt, P.A. Polymorphism of lipids. Nature
**1967**, 215, 701–704. [Google Scholar] [CrossRef] - Baalbaki, N.H.; Kasting, G.B. A pseudo-quantitative ternary surfactant ion mixing plane phase diagram for a cationic hydroxyethyl cellulose with dodecyl sulfate counterion complex salt. Colloids Surf. A Physicochem. Eng. Asp.
**2017**, 522, 361–367. [Google Scholar] [CrossRef] - Serrano, L.A.; Fornerod, M.J.; Yang, Y.; Gaisford, S.; Stellacci, F.; Guldin, S. Phase behaviour and applications of a binary liquid mixture of methanol and a thermotropic liquid crystal. Soft Matter
**2018**, 14, 4615–4620. [Google Scholar] [CrossRef] [Green Version] - Matraszek, J.; Zapala, J.; Mieczkowski, J.; Pociecha, D.; Gorecka, E. 1D, 2D and 3D liquid crystalline phases formed by bent-core mesogens. Chem. Commun.
**2015**, 51, 5048–5051. [Google Scholar] [CrossRef] - Jasinski, M.; Pociecha, D.; Monobe, H.; Szczytko, J.; Kaszynski, P. Tetragonal Phase of 6 Oxoverdazyl Bent-Core Derivatives with Photoinduced Ambipolar Charge Transport and Electro-optical Effects. J. Am. Chem. Soc.
**2014**, 136, 14658–14661. [Google Scholar] [CrossRef] - Wolska, J.M.; Pociecha, D.; Mieczkowski, J.; Gorecka, E. Double gyroid structures made of asymmetric dimers. Liq. Cryst.
**2016**, 43, 235–240. [Google Scholar] [CrossRef] - Archbold, C.T.; Davis, E.J.; Mandle, R.J.; Cowling, S.J.; Goodby, J.W. Chiral dopants and the twist-bend nematic phase--induction of novel mesomorphic behaviour in an apolar bimesogen. Soft Matter
**2015**, 11, 7547–7557. [Google Scholar] [CrossRef] [PubMed] - Demurtas, D.; Guichard, P.; Martiel, I.; Mezzenga, R.; Hebert, C.; Sagalowicz, L. Direct visualization of dispersed lipid bicontinuous cubic phases by cryo-electron tomography. Nat. Commun.
**2015**, 6, 8915. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Park, C.; La, Y.; An, T.H.; Jeong, H.Y.; Kang, S.; Joo, S.H.; Ahn, H.; Shin, T.J.; Kim, K.T. Mesoporous monoliths of inverse bicontinuous cubic phases of block copolymer bilayers. Nat. Commun.
**2015**, 6, 6392. [Google Scholar] [CrossRef] [Green Version] - Kutsumizu, S. Recent progress in the synthesis and structural clarification of thermotropic cubic phases. Isr. J. Chem.
**2012**, 52, 844–853. [Google Scholar] [CrossRef] - Mori, A.; Yamamoto, E.; Kubo, K.; Ujiie, S.; Baumeister, U.; Tschierske, C. Bicontinuous cubic phase with the Pn3m space group formed by N,N,N-tris(5-alkoxytroponyl)-1,5,9-triazacyclododecanes. Liq. Cryst.
**2010**, 37, 1059–1065. [Google Scholar] [CrossRef] - Liu, F.; Prehm, M.; Zeng, X.; Tschierske, C.; Ungar, G. Skeletal Cubic, Lamellar, and Ribbon Phases of Bundled Thermotropic Bolapolyphiles. J. Am. Chem. Soc.
**2014**, 136, 6846–6849. [Google Scholar] [CrossRef] [PubMed] - Kitzerow, H.S. Blue phases at work! ChemPhysChem
**2006**, 7, 63–66. [Google Scholar] [CrossRef] - Kikuchi, H. Liquid crystalline blue phases. In Liquid Crystalline Functional Assemblies and their Supramolecular Structures, 1st ed.; Kato, T., Ed.; Springer: Berlin, Germany, 2008; pp. 99–117. ISBN 978-3-540-77866-0. [Google Scholar]
- He, W.L.; Wang, L.; Wang, L.; Cui, X.P.; Xie, M.W.; Yang, H. Wide Temperature Range Blue Phase Liquid Crystalline Materials. Prog. Chem.
**2012**, 24, 182–192. [Google Scholar] - Yamamoto, J.; Nishiyama, I.; Inoue, M.; Yokoyama, H. Optical isotropy and iridescence in a smectic ‘blue phase’. Nature
**2015**, 437, 525–528. [Google Scholar] [CrossRef] - Oton, E.; Netter, E.; Nakano, T.; Katayama, Y.D.; Inoue, F. Monodomain Blue Phase Liquid Crystal Layers for Phase Modulation. Sci. Rep.
**2017**, 7, 44575. [Google Scholar] [CrossRef] [Green Version] - Yamamoto, T.; Nishiyama, I.; Yoneya, M.; Yokoyama, H. Novel Chiral Effect That Produces the Anisotropy in 3D Structured Soft Material: Chirality-Driven Cubic−Tetragonal Liquid Crystal Phase Transition. J. Phys. Chem. B
**2009**, 113, 11564–11567. [Google Scholar] [CrossRef] [PubMed] - Nishiyama, I.; Yamamoto, J.; Goodby, J.W.; Yokoyama, H. A symmetric chiral liquid-crystalline twin exhibiting stable ferrielectric and antiferroelectric phases and a chirality-induced isotropic-isotropic liquid transition. J. Mater. Chem.
**2001**, 11, 2690. [Google Scholar] [CrossRef] - Nishiyama, I.; Yamamoto, J.; Goodby, J.W.; Yokoyama, H. Ferrielectric and antiferroelectric chiral twin liquid crystals showing a stable chiral nematic phase. Liq. Cryst.
**2002**, 29, 1409. [Google Scholar] [CrossRef] - Cifelli, M.; Domenici, V.; Gorecka, E.; Wojcik, M.; Dvinskikh, S.V. NMR investigation of a thermotropic liquid crystal showing isotropic-isotropic’-(columnar)-cubic phase transitions. Mol. Cryst. Liq. Cryst.
**2017**, 649, 20–30. [Google Scholar] [CrossRef] - Dong, R.Y. Nuclear Magnetic Resonance of Liquid Crystals, 2nd ed.; Springer: New York, NY, USA, 1997; ISBN 978-1-4612-7354-7. [Google Scholar]
- Domenici, V. The role of NMR in the study of partially ordered materials: Perspectives and challenges. Pure Appl. Chem.
**2011**, 83, 67. [Google Scholar] [CrossRef] - Domenici, V. Nuclear magnetic resonance: A powerful tool to study liquid crystals. Liq. Cryst. Today
**2017**, 46, 2–10. [Google Scholar] [CrossRef] - Dong, R.Y. Recent NMR Studies of Thermotropic Liquid Crystals. In Annual Reports on NMR Spectroscopy; Webb, G.A., Ed.; Elsevier Academic Press Inc.: San Diego, CA, USA, 2016; pp. 41–174. ISBN 978-0-12-804711-8. [Google Scholar]
- Cifelli, M.; Domenici, V.; Veracini, C.A. Recent advancements in understanding thermotropic liquid crystal structure and dynamics by means of NMR spectroscopy. Curr. Opin. Colloid Interface Sci.
**2013**, 18, 190–200. [Google Scholar] [CrossRef] - Cifelli, M.; Domenici, V.; Marini, A.; Veracini, C.A. NMR studies of the ferroelectric SmC* phase. Liq. Cryst.
**2010**, 37, 935. [Google Scholar] [CrossRef] - Marini, A.; Domenici, V. H-2, C-13 NMR and Ab Initio Calculations Applied to the SmC* Phase: Methodology and Case Studies. Ferroelectrics
**2010**, 395, 46. [Google Scholar] [CrossRef] - Domenici, V.; Marini, A.; Veracini, C.A.; Zhang, J.; Dong, R.Y. Effect of the magnetic field on the supramolecular structure of chiral smectic C phases: H-2 NMR studies. ChemPhysChem
**2007**, 8, 2575. [Google Scholar] [CrossRef] - Domenici, V.; Lelli, M.; Cifelli, M.; Hamplova, V.; Marchetti, A.; Veracini, C.A. Conformational Properties and Orientational Order of a de Vries Liquid Crystal Investigated through NMR Spectroscopy. ChemPhysChem
**2014**, 15, 1485. [Google Scholar] [CrossRef] - Domenici, V.; Veracini, C.A.; Novotna, V.; Dong, R.Y. Twist grain boundary liquid-crystalline phases under the effect of the magnetic field: A complete H-2 and C-13 NMR study. ChemPhysChem
**2008**, 9, 556. [Google Scholar] [CrossRef] - Domenici, V. Dynamics in the isotropic and nematic phases of bent-core liquid crystals: NMR perspectives. Soft Matter
**2011**, 7, 1589. [Google Scholar] [CrossRef] - Domenici, V.; Geppi, M.; Veracini, C.A.; Blinc, R.; Lebar, A.; Zalar, B. Unusual Dynamic Behavior in the Isotropic Phase of Banana Mesogens Detected by
^{2}H NMR Line Width and T_{2}Measurements. J. Phys. Chem. B.**2005**, 109, 769. [Google Scholar] [CrossRef] [PubMed] - Cifelli, M.; Domenici, V. NMR investigation of the dynamics of banana shaped molecules in the isotropic phase: A comparison with calamitic mesogens behaviour. Phys. Chem. Chem. Phys.
**2007**, 9, 1202. [Google Scholar] [CrossRef] [PubMed] - Furo, I.; Dvinskikh, S.V. NMR methods applied to anisotropic diffusion. Magn. Reson. Chem.
**2002**, 40, S3–S14. [Google Scholar] [CrossRef] - Cifelli, M.; Domenici, V.; Dvinskikh, S.V.; Veracini, C.A.; Zimmermann, H. Translational self-diffusion in the smectic phases of ferroelectric liquid crystals: An overview. Phase Trans.
**2012**, 85, 861. [Google Scholar] [CrossRef] - Dvinskikh, S.V.; Furó, I. Nuclear magnetic resonance studies of translational diffusion in thermotropic liquid crystals. Russ. Chem. Rev.
**2006**, 75, 497. [Google Scholar] [CrossRef] - Cifelli, M.; Domenici, V.; Dvinskikh, S.V.; Glogarova, M.; Veracini, C.A. Translational self-diffusion in the synclinic to anticlinic phases of a ferroelectric liquid crystal. Soft Matter
**2010**, 6, 5999. [Google Scholar] [CrossRef] - Cifelli, M.; Domenici, V.; Veracini, C.A. From the synclinic to the anticlinic smectic phases: A deuterium NMR and diffusion NMR study. Mol. Cryst. Liq. Cryst.
**2005**, 429, 167–179. [Google Scholar] [CrossRef] - Cifelli, M.; Domenici, V.; Dvinskikh, S.V.; Luckhurst, G.R.; Timimi, B.A. The twist-bend nematic phase: Translational self-diffusion and biaxiality studied by H-1 nuclear magnetic resonance diffusometry. Liq. Cryst.
**2017**, 44, 204–218. [Google Scholar] [CrossRef] - Domenici, V. Rod-like and Banana-Shaped Liquid Crystals by Means of Deuterium NMR; Lambert Academic Publishing: Saarbrucken, Germany, 2010; pp. 15–54. [Google Scholar]
- Hoatson, G.L.; Levine, Y.K. A comparative survey of the physical techniques used in studies of molecular dynamics. In The Molecular Dynamics of Liquid Crystals; Luckhurst, R.G., Veracini, C.A., Eds.; Nato ASI Series; NATO Publisher: London, UK, 1989. [Google Scholar]
- Sebastiao, P.J.; Cruz, C.; Ribeiro, A.C. Advances in Proton NMR Relaxometry in Thermotropic Liquid Crystals. In Nuclear Magnetic Resonance Spectroscopy of Liquid Crystals; Dong, R.Y., Ed.; World Scientific Co.: Oxford, UK, 2009; pp. 129–167. [Google Scholar]
- Noack, F. NMR field-cycling spectroscopy: Principles and applications. Prog. Nucl. Magn. Reson. Spectrosc.
**1986**, 18, 171–276. [Google Scholar] [CrossRef] - Carvalho, A.; Sebastião, P.J.; Ribeiro, A.C.; Nguyen, H.T.; Vilfan, M. Molecular Dynamics in Tilted Bilayer Smectic Phases: A Proton Nuclear Magnetic Resonance Relaxometry Study. J. Chem. Phys.
**2001**, 115, 10484–10492. [Google Scholar] [CrossRef] - Sebastião, P.J.; Ribeiro, A.C.; Nguyen, H.T.; Noack, F. Proton NMR Relaxation Study of Molecular Motions in a Liquid Crystal with a Strong Polar Terminal Group. Z. Naturforsch. A Phys. Sci.
**1993**, 48, 851–860. [Google Scholar] [CrossRef] - Sebastião, P.J.; Gradišek, A.; Pinto, L.F.V.; Apih, T.; Godinho, M.H.; Vilfan, M. Fast Field-Cycling NMR Relaxometry Study of Chiral and Nonchiral Nematic Liquid Crystals. J. Phys. Chem. B
**2011**, 115, 14348–14358. [Google Scholar] [CrossRef] - Apih, T.; Domenici, V.; Gradišek, A.; Hamplová, V.; Kaspar, M.; Sebastião, P.J.; Vilfan, M.
^{1}H NMR Relaxometry Study of a Rod-Like Chiral Liquid Crystal in Its Isotropic, Cholesteric, TGBA*, and TGBC* Phases. J. Phys. Chem. B**2010**, 114, 11993–12001. [Google Scholar] [CrossRef] - Gradišek, A.; Apih, T.; Domenici, V.; Novotná, V.; Sebastião, P.J. Molecular Dynamics in a Blue Phase Liquid Crystal: A 1 H Fast Field-Cycling NMR Relaxometry Study. Soft Matter
**2013**, 9, 10746–10753. [Google Scholar] [CrossRef] - Domenici, V.; Gradišek, A.; Apih, T.; Hamplová, V.; Novotná, V.; Sebastião, P.J.
^{1}H NMR Relaxometry in the TGBA* and TGBC* Phases. Ferroelectrics**2016**, 495, 17–27. [Google Scholar] [CrossRef] - Gradišek, A.; Domenici, V.; Apih, T.; Novotná, V.; Sebastião, P.J.
^{1}H NMR Relaxometric Study of Molecular Dynamics in a “de Vries” Liquid Crystal. J. Phys. Chem. B**2016**, 120, 4706–4714. [Google Scholar] [CrossRef] - Frise, A.E.; Ichikawa, T.; Yoshio, M.; Ohno, H.; Dvinskikh, S.V.; Kato, T.; Furó, I. Ion conductive behaviour in a confined nanostructure: NMR observation of self-diffusion in a liquid-crystalline bicontinuous cubic phase. Chem. Commun.
**2010**, 46, 728. [Google Scholar] [CrossRef] [PubMed] - Pampel, A.; Strandberg, E.; Lindblom, G.; Volke, F. High-resolution NMR on cubic lyotropic liquid crystalline phases. Chem. Phys. Lett.
**1998**, 287, 468. [Google Scholar] [CrossRef] - Momot, K.I.; Takegoshi, K.; Kuchel, P.W.; Larkin, T.J. Inhomogeneous NMR line shape as a probe of microscopic organization of bicontinuous cubic phases. J. Phys. Chem. B
**2008**, 112, 6636. [Google Scholar] [CrossRef] - Hendrikx, Y.; Sotta, P.; Seddon, J.M.; Dutheillet, Y.; Bartle, E.A. NMR Self-diffusion measurements in inverse micellar cubic phases. Liq. Cryst.
**1994**, 16, 893. [Google Scholar] [CrossRef] - Burnell, E.E.; Capitani, D.; Casieri, C.; Segre, A.L. A proton nuclear magnetic resonance relaxation study of C12E6/D2O. J. Phys. Chem. B
**2000**, 104, 8782–8791. [Google Scholar] [CrossRef] - Schlienger, S.; Ducrot-Boisgontier, C.; Delmotte, L.; Guth, J.L.; Parmentier, J. History of the Micelles: A Key Parameter for the Formation Mechanism of Ordered Mesoporous Carbons via a Polymerized Mesophase. J. Phys. Chem. C
**2014**, 118, 11919–11927. [Google Scholar] [CrossRef] - Jerschow, A.; Müller, N. Suppression of convection artifacts in stimulated-echo diffusion experiments. Double-stimulated-echo experiments. J. Magn. Reson.
**1997**, 125, 372. [Google Scholar] [CrossRef] - Burstein, D. Stimulated echoes: Description, applications, practical hints. Concepts Magn. Reson.
**1996**, 8, 269. [Google Scholar] [CrossRef] - Stejskal, E.O.; Tanner, J.E. Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient. J. Chem. Phys.
**1965**, 42, 288. [Google Scholar] [CrossRef] - Gibbs, S.J.; Johnson, C.S. A PFG NMR experiment for accurate diffusion and flow studies in the presence of eddy currents. J. Magn. Reson.
**1991**, 93, 395. [Google Scholar] [CrossRef] - Domenici, V.; Apih, T.; Veracini, C.A. Molecular motions of banana-shaped liquid crystals studied by NMR spectroscopy. Thin Solid Films
**2008**, 517, 1402–1406. [Google Scholar] [CrossRef] - Canet, D. Introduction to Nuclear Spin Cross-relaxation and Cross-correlation Phenomena in Liquids. In New Developments in NMR; book n. 12, Chapter 1; Canet, D., Ed.; Royal Society of Chemistry: London, UK, 2017; ISBN 1849739137. [Google Scholar]
- Bloembergen, N.; Purcell, E.M.; Pound, R.V. Relaxation Effects in Nuclear Magnetic Resonance Absorption. Phys. Rev.
**1948**, 73, 679. [Google Scholar] [CrossRef] - Vilfan, M.; Rutar, V.; Zumer, S.; Lahajnar, G.; Blinc, R.; Doane, J.W.; Golemme, A. Proton spin-lattice relaxation in nematic microdroplets. J. Chem. Phys.
**1988**, 89, 597. [Google Scholar] [CrossRef]

**Figure 1.**Molecular structure of the two rod-like liquid crystals: (

**a**) the symmetric mesogen,

**9/2 RS/RS**; (

**b**) the asymmetric dimer,

**L1**.

**Figure 2.**Pulsed field gradient Stimulated echo with LED for suppression of eddy currents before echo acquisition. Spoil gradient during diffusion time is used to remove spin echo forming after the second radio frequency (r.f.) pulse.

**Figure 3.**Diffusion coefficients measured in the three mesophases (isotropic, isotropic’ and cubic phases) of the two samples on cooling from the isotropic phase. (On the

**right**) Data for

**9/2 RS/RS**are reproduced from Ref. [29] by permission of the publisher Taylor & Francis Ltd. (On the

**left**) In the

**L1**sample, diffusion coefficients measured varying the diffusion time and gradient directions, as discussed in the text, are also shown as black triangles.

**Scheme 1.**Representation of the self-diffusion motion of samples

**L1**and

**9/2 RS/RS**in their cubic phase, where the upper limit of the diffusion time scale length, ℓ, is evidenced. The sphere of radius ℓ indicates that, on the diffusion time scale, the motion of single molecules is isotropic within the cubic mesophase structure.

**Figure 4.**Temperature dependence of proton spin-lattice relaxation time of

**L1**at some chosen Larmor frequencies. Vertical dashed lines indicate the phase transition temperatures.

**Figure 5.**Temperature dependence of proton spin-lattice relaxation time of

**9/2 RS/RS**at some chosen Larmor frequencies. Vertical dashed lines indicate the phase transition temperatures.

**Figure 6.**Frequency (MHz) dependence of proton spin-lattice relaxation time T

_{1}(s) of

**L1**at some chosen temperatures in the three mesophases: isotropic, isotropic’, and cubic phases.

**Figure 7.**Frequency (MHz) dependence of proton spin-lattice relaxation time T

_{1}(s) of

**9/2 RS/RS**at some chosen temperatures in the three mesophases: isotropic, isotropic’, and cubic phases.

**Figure 8.**Frequency (MHz) dependence of proton spin-lattice relaxation rate, R

_{1}(s

^{−1}) of

**L1**at T = 396 K, in a Logarithmic scale, recorded in the high-temperature isotropic phase. The black curve represents the best fitting curve of the R

_{1}-dispersion by using Equation (4) with two rotational processes (ROT1 and ROT2) described by the BBP model (Equation (5)) and the self-diffusion (SD) process (Equation (6)). Fitting data are reported in Table 2.

**Figure 9.**Frequency (MHz) dependence of proton spin-lattice relaxation rate, R

_{1}(s

^{−1}) of

**9/2 RS/RS**at T = 377 K, on a Logarithmic scale, in the high-temperature isotropic phase. The black curve represents the best fitting curve of the R

_{1}-dispersion by using Equation (4) with two rotational processes (ROT1 and ROT2) described by the BBP model (Equation (5)) and the self-diffusion (SD) process (Equation (6)). Fitting data are reported in Table 2.

**Table 1.**Mesophase sequences and temperature transitions observed for the two rod-like mesogens from DSC on cooling the samples.

Sample Label | Phase Sequence |
---|---|

9/2 RS/RS [8] | Isotropic 372.4 K Isotropic’ 365.6 K Columnar ^{1}/Cubic ^{2} |

L1 [14]
| Isotropic 391.3 °C Isotropic’ 386.4 °C Cubic ^{3} 347.7 °C Crystal |

^{1}Columnar phase with hexagonal symmetry (Col

_{h}).

^{2}Cubic phase with Im3m symmetry.

^{3}Cubic phase with Ia3d symmetry.

**Table 2.**Values of T

_{1}(s) at different frequencies (B

_{RLX}) and relevant best fitting parameters of the

^{1}H NMR R

_{1}—dispersions for the two samples

**L1**and

**9/2 RS/RS**in the isotropic phase, as obtained by using Equations (4)–(6).

Samples | T_{1} (s) at B_{RLX} = 100 MHz | T_{1} (s) at B_{RLX} = 10 MHz | T_{1} (s) at B_{RLX} = 5 KHz | A_{ROT1}/A_{ROT2} | τ_{ROT1}(10 ^{−8} s) | τ_{ROT2}(10 ^{−8} s) | τ_{D}(10 ^{−9} s) |
---|---|---|---|---|---|---|---|

L1 (T = 396 K) | 0.52 | 0.038 | 0.015 | 3.2 | 14 | 1.5 | 0.3 |

9/2 RS/RS(T = 377 K) | 0.41 | 0.059 | 0.047 | 1.4 | 10 | 1.3 | 0.5 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gradišek, A.; Cifelli, M.; Wojcik, M.; Apih, T.; Dvinskikh, S.V.; Gorecka, E.; Domenici, V.
Study of Liquid Crystals Showing Two Isotropic Phases by ^{1}H NMR Diffusometry and ^{1}H NMR Relaxometry. *Crystals* **2019**, *9*, 178.
https://doi.org/10.3390/cryst9030178

**AMA Style**

Gradišek A, Cifelli M, Wojcik M, Apih T, Dvinskikh SV, Gorecka E, Domenici V.
Study of Liquid Crystals Showing Two Isotropic Phases by ^{1}H NMR Diffusometry and ^{1}H NMR Relaxometry. *Crystals*. 2019; 9(3):178.
https://doi.org/10.3390/cryst9030178

**Chicago/Turabian Style**

Gradišek, Anton, Mario Cifelli, Michal Wojcik, Tomaž Apih, Sergey V. Dvinskikh, Ewa Gorecka, and Valentina Domenici.
2019. "Study of Liquid Crystals Showing Two Isotropic Phases by ^{1}H NMR Diffusometry and ^{1}H NMR Relaxometry" *Crystals* 9, no. 3: 178.
https://doi.org/10.3390/cryst9030178