Molecular and Segmental Orientational Order in a Smectic Mesophase of a Thermotropic Ionic Liquid Crystal

We investigate conformational dynamics in the smectic A phase formed by the mesogenic ionic liquid 1-tetradecyl-3-methylimidazolium nitrate. Solid-state high-resolution 13C nuclear magnetic resonance (NMR) spectra are recorded in the sample with the mesophase director aligned in the magnetic field of the NMR spectrometer. The applied NMR method, proton encoded local field spectroscopy, delivers heteronuclear dipolar couplings of each 13C spin to its 1H neighbours. From the analysis of the dipolar couplings, orientational order parameters of the C–H bonds along the hydrocarbon chain were determined. The estimated value of the molecular order parameter S is significantly lower compared to that in smectic phases of conventional non-ionic liquid crystals.


Introduction
Ionic liquids that form ordered mesophases in temperature ranges between solid and isotropic liquid phases belong to a class of ionic liquid crystal (ILC) materials [1].Molecules and ions in liquid crystals (LC) exhibit a high molecular translational and rotational mobility combined with orientational and positional order.The unique synergy of ionic conductivity and anisotropic nanoscale structure makes ILC materials in high demand in the development of low-dimensional charge transport technology and other applications [2].
Nuclear magnetic resonance (NMR) spectroscopy is widely used to study molecular conformational and rotational dynamics and orientational order in LC [3,4].Site-specific information at the atomic level can be obtained by high resolution 13 C NMR combined with selective suppression of spin interactions.Structural and order parameters are obtained through the measurements of orientation-and distance-dependent dipole couplings.Due to the orientational ordering, the dipolar coupling in mesophase is not averaged to zero, in contrast to isotropic phase. 13C-1 H heteronuclear dipolar couplings in LC are measured by two-dimensional (2D) separated local field spectroscopy technique [5].
The local bond order parameter S CH characterizes the average orientation of the C-H bond to the LC director.The ratio of the residual dipolar coupling averaged by the anisotropic motion, to its unaveraged value provides the S CH .For molecules with long hydrocarbon chains one can study a C-H bond order parameter profile, a variation of S CH along the chain, which characterizes the average molecular structure in the mesophase [6][7][8].
Here we investigate conformation and molecular order of organic cations in the smectic A phase of the mesogenic ionic liquid 1-tetradecyl-3-methylimidazolium nitrate (C 14 mimNO 3 ) [9].The sample forms interdigitated bilayer structures where the molecules, consisting of non-ionic and ionic non-miscible parts, phase-separate at the nanoscale.Relatively low transition temperatures between meso-and isotropic phases and a wide temperature range of the mesophase existence make this sample particularly suitable for preparing it both in un-aligned state and with director aligned with respect to external magnetic field.In the latter case, the sample is suitable for studies by high-resolution solid-state NMR at stationary condition (without sample spinning).We apply 2D 13 C-1 H dipolar NMR spectroscopy to the Smectic A phase of the C 14 mimNO 3 to quantitatively characterize the molecular dynamics.Based on the profiles of the order parameters obtained, we put forward a model for the motion of the organic cations in the bilayer of the smectic A phase.

Materials and Methods
The sample of C 14 mimNO 3 (1-tetradecyl-3-methylimidazolium nitrate, CAS 799246-94-9) was obtained from Angene International and used as received.Water content in the sample was estimated to ≈1.0 wt.% from 1 H NMR spectrum recorded in the isotropic phase.No other significant impurity signals were observed.The sample exhibited the following phase transition temperatures: Isotropic as observed by recording proton NMR spectra.Transition temperature to the smectic phase is in agreement with reported phase diagram [9].Slightly higher crystallization temperature compared to that determined by differential scanning calorimetry in [9] is presumably due to much slower cooling rate applied in our NMR experiments.Upon slow cooling from the isotropic phase in the presence of the strong external magnetic field, director of the smectic phase is aligned perpendicular to the magnetic field vector.Most of our experiments were performed in such an oriented sample.To produce random director orientation in the smectic phase, the sample was cooled from the isotropic phase while out of the magnet.Due to the high viscosity of the smectic phase, the domains of different orientations do not reorient when the sample in the smectic phase is placed in magnetic field.
Experiments were performed using Bruker 500 Avance III spectrometer at Larmor frequencies of 500.1 and 125.7 for 1 H and 13 C, respectively.About 0.5 g of the sample was loaded in a standard 5 mm NMR tube.NMR spectra were recorded using solution state multinuclear 5 mm probe-head.The 1 H and 13 C 90 • -pulse lengths were 8 and 13 µs, respectively.For heteronuclear proton decoupling in the mesophase, Spinal64 sequence [10] with the 1 H nutation frequency of 23 kHz was used during acquisition time of 120 ms.To enhance the intensity of the 13 C signal, proton-to-carbon cross polarization (CP) with adiabatic demagnetization in the rotating frame (ADRF) [11] was applied with nutation frequencies up to 16 kHz and contact time in the range 10-20 ms.
Dipolar 1 H- 13 C spectra were recorded using proton detected/encoded local field (PDLF) NMR spectroscopy [12].The PDLF spectrum is governed by a two-spin interaction and thus cross sections in the indirect dimension present superposition of dipolar doublets.The actual PDLF pulse sequence is shown in the Supplementary Materials, Figure S2.The evolution time in indirect time domain was incremented with 384 µs in 256 steps, at each with four collected transients.Proton homonuclear decoupling during the evolution time was achieved by the BLEW-48 multiple-pulse sequence [13] with a nutation frequency of 31.2 kHz.
The temperature was regulated with an accuracy of 0.1 • C. The temperature shift and temperature gradient within the sample, caused by the decoupling irradiation, were calibrated by observing the change in the 13 C spectral line widths and positions.Decoupling power, irradiation time, and repetition delay were adjusted to limit heating effects to <0.5 • C.

Carbon-13 Nuclear Magnetic Resonance (NMR) Spectra
Representative 13 C NMR spectra of the C 14 mim ions in different phases are displayed in Figure 1.All carbons, except carbons 5 and 6 with overlapped signals, were resolved.The assignment of the carbon signals in the isotropic and mesophase was verified, respectively, by the INADEQUATE (incredible natural-abundance double-quantum transfer) experiment [14] and by dipolar INADEQUATE experiment as described in Supplementary Materials.The chemical shifts of the corresponding signals in the spectra in Figure 1a,b reflect different parts of residual chemical shift anisotropy (CSA) tensor.The signal positions in the isotropic phase are given by the isotropic averages δ i of the respective CSA tensors.In the spectrum in the aligned mesophase, (Figure 1b), the chemical shift corresponds to one of the principal values δ αα (α = x, y, z) of the residual CSA tensor.In uniaxial liquid crystals, the chemical shift tensor is described by the components along and orthogonal to the phase director, LC || δ and LC ⊥ δ , respectively.In our sample, which exhibits a negative anisotropy of the diamagnetic susceptibility, the director aligns in the plane perpendicular to the magnetic field of the spectrometer.Hence, the observed chemical shifts are determined by the LC ⊥ δ values.This is verified comparing the spectrum of the aligned sample in Figure 1b to the spectrum of the sample prepared with random director distribution, Figure 1c.The random director alignment was achieved by cooling the sample from the isotropic phase outside the NMR magnet.The chemical shifts corresponding to the edges of the axially symmetric CSA patterns observed in un-aligned sample, match those of the respective lines in the aligned mesophase.In uniaxial liquid crystals, the chemical shift tensor is described by the components along and orthogonal to the phase director, δ LC || and δ LC ⊥ , respectively.In our sample, which exhibits a negative anisotropy of the diamagnetic susceptibility, the director aligns in the plane perpendicular to the magnetic field of the spectrometer.Hence, the observed chemical shifts are determined by the δ LC ⊥ values.This is verified comparing the spectrum of the aligned sample in Figure 1b to the spectrum of the sample prepared with random director distribution, Figure 1c.The random director alignment was achieved by cooling the sample from the isotropic phase outside the NMR magnet.The chemical shifts corresponding to the edges of the axially symmetric CSA patterns observed in un-aligned sample, match those of the respective lines in the aligned mesophase.

1 H-13 C Dipolar Spectra
The 2D PDLF spectrum at 66 • C is shown in Figure 2a.The cross sections in the dipolar direction for different carbons are shown in Figure 2b.The dipolar splittings between directly bound 13 C and 1 H spins are well resolved and can be directly measured in the spectrum for each carbon in the molecule.Additional low intensity doublets observed for some of the dipolar cross-sections, e.g., in the spectrum of the chain carbon 2, are due to partial overlap with nearby signals in the 2D spectrum.The inner multiplets with small splittings resolved for some carbon sites arise from couplings to remote protons in neighbouring groups.
Crystals 2019, 9 FOR PEER REVIEW 4 The 2D PDLF spectrum at 66 °C is shown in Figure 2a.The cross sections in the dipolar direction for different carbons are shown in Figure 2b.The dipolar splittings between directly bound 13 C and 1 H spins are well resolved and can be directly measured in the spectrum for each carbon in the molecule.Additional low intensity doublets observed for some of the dipolar cross-sections, e.g. in the spectrum of the chain carbon 2, are due to partial overlap with nearby signals in the 2D spectrum.The inner multiplets with small splittings resolved for some carbon sites arise from couplings to remote protons in neighbouring groups.The dipole-dipole spin couplings are orientation-and interatomic distances dependent.Anisotropic molecular motion results in partial averaging of the intramolecular dipolar interactions over the conformational dynamics, molecular reorientations, and the molecular axis fluctuations about the mesophase director.Intermolecular spin couplings are averaged to zero by translational dynamics [15].Different motional modes can often be considered uncorrelated and their effects on spin interactions can be separated.A simplified description of orientational ordering can be applied considering an approximately cylindrical symmetry due to fast uniaxial rotations of elongated mesogenic molecules [16].For a 1 H- 13 C spin pair in a molecule in an anisotropic phase the dipolar coupling is: The dipole-dipole spin couplings are orientation-and interatomic distances dependent.Anisotropic molecular motion results in partial averaging of the intramolecular dipolar interactions over the conformational dynamics, molecular reorientations, and the molecular axis fluctuations about the mesophase director.Intermolecular spin couplings are averaged to zero by translational dynamics [15].Different motional modes can often be considered uncorrelated and their effects on spin interactions can be separated.A simplified description of orientational ordering can be applied considering an approximately cylindrical symmetry due to fast uniaxial rotations of elongated mesogenic molecules [16].For a 1 H- 13 C spin pair in a molecule in an anisotropic phase the dipolar coupling is: with P 2 (cos θ PL ) = (3 cos 2 θ PL − 1)/2, where θ PL is the angle between the C-H vector, which defines a principal frame axis P of the dipolar interaction, and the magnetic field B 0 (defines the laboratory frame axis L).The dipolar coupling constant in the principal frame b CH = −(µ 0 /8π 2 )(γ H γ C /r 3 CH ) can be estimated from the atomic distances r CH and the gyromagnetic ratios γ H , γ C .For a single C-H bond with account for vibration effects we accept b CH values of −21.5 kHz and −22 kHz for aliphatic and aromatic sites, respectively [17,18].
Anisotropic molecular mobility leads to a partial averaging of the angular term P 2 (cos θ PL ) .Dynamic molecular disorder in LC is measured by the molecular orientational order parameter S = P 2 (cos θ MN ) , where θ MN is the instantaneous angle between the long molecular axis M and the director N. Similarly, the orientational averaging of the local C-H bond direction with the respect to director is described by the bond order parameter S CH = P 2 (cos θ PN ) , where θ PN is the angle between the inter-nuclear vector P and the director N. Thus, where θ NL is the angle between director and magnetic field vector.Hence, local bond order parameters S CH can be estimated directly from the NMR dipolar spectra.Assuming statistical independence and large time-scale separation of molecular reorientation and conformational dynamics, the bond order parameters S CH can be related to the molecular order parameter S by the expression: where θ PM defines the angle between the bond vector and molecular axis.Thus, Equation (2) can be expanded: For non-rigid molecules, the separation of the terms P 2 (cos θ PM ) and S requires some model assumptions of molecular conformational dynamics.
The splitting ∆ν observed in the PDLF experiment is contributed by residual dipolar coupling d CH and isotropic indirect spin coupling J CH : (anisotropic part of indirect coupling ∆J CH is neglected compared with dipolar coupling [16]).Upon application of homonuclear decoupling both these interactions are scaled down.For the pulse sequence BLEW48 [13], the scaling factor was experimentally calibrated to k = 0.418 ± 0.02.The magnitudes of the isotropic coupling J CH were measured in the isotropic phase by recording 13 C NMR spectrum without proton decoupling.The sign of J CH is known to be positive.Note that the sign of the splitting ∆ν is not obtained in the PDLF experiment.However, the sign of the dipolar coupling d CH can be determined from Equation (4) considering average orientation of molecular axis in the magnetic field and C-H bond angles with respect to molecular axis.The dipolar coupling constant in the principal frame b CH is negative for a proton-carbon pair.The molecular order parameter S is positive.The term P 2 (cos θ NL ) = −0.5 for the director aligned perpendicular to the magnetic field.The sign of the angular term P 2 (cos θ PM ) can be deduced by considering molecular geometry as discussed below.

Order Parameters
With dipolar couplings d CH obtained from Equation ( 5), local bond order parameters S CH are directly calculated using Equation (2).With some assumptions about the direction of the molecular axis, as discussed below, molecular order parameter S can as well be estimated from Equation (3).Thus, the analysis on the PDLF spectra provides quantitative information on the local and molecular order parameters, S CH and S.
The variations of S CH along the alkyl chain, or order parameter profiles, are plotted in Figure 3 for selected temperatures in the smectic A phase.The S CH values are negative assuming the average orientation of the C-H bond perpendicular to the direction of long molecular axis.As expected, the methylene groups close to the imidazolium core are less disordered and segmental mobility increases gradually towards the chain terminal methyl.While this average character of the chain dynamics persists in the whole temperature range of the smectic phase, the alkyl chains become more ordered at lower temperatures.
Crystals 2019, 9 FOR PEER REVIEW 6 perpendicular to the magnetic field.The sign of the angular term 2 (cos ) PM P θ can be deduced by considering molecular geometry as discussed below.

Order Parameters
With dipolar couplings CH d obtained from Equation ( 5), local bond order parameters CH S are directly calculated using Equation (2).With some assumptions about the direction of the molecular axis, as discussed below, molecular order parameter S can as well be estimated from Equation (3).Thus, the analysis on the PDLF spectra provides quantitative information on the local and molecular order parameters, CH S and S .
The variations of CH S along the alkyl chain, or order parameter profiles, are plotted in Figure 3 for selected temperatures in the smectic A phase.The CH S values are negative assuming the average orientation of the C-H bond perpendicular to the direction of long molecular axis.As expected, the methylene groups close to the imidazolium core are less disordered and segmental mobility increases gradually towards the chain terminal methyl.While this average character of the chain dynamics persists in the whole temperature range of the smectic phase, the alkyl chains become more ordered at lower temperatures.The CH S magnitudes are small and similar to those typically found in lyotropic lamellar phases [8].It is interesting that CH S values obtained by MD simulation for C16mimNO3 homologue were also found to be similarly small [19].The low values of CH S , on one hand, may indicate a significant conformational dynamics by trans-gauche isomerisation.The fast decrease of CH S towards chain terminal suggests a gradual intensification of the conformational mobility with increasingly significant population of gauche conformers.On the other hand, limited variation of the order parameters for the first few methylene groups close to the imidazolium core suggests a restricted conformation dynamics for this part of the chain with predominant trans conformation.In this case, relatively small observed values of CH S parameters for the carbons in vicinity of the head group can be due to either a low value of the molecular order parameter S (cf.Equation ( 3)) or a significant tilt angle of this part of the chain with respect to main molecular axis oriented along the director.Based on this observation, we consider the following model of average molecular conformation in the further analysis: the part of the chain in vicinity of the head group is The S CH magnitudes are small and similar to those typically found in lyotropic lamellar phases [8].It is interesting that S CH values obtained by MD simulation for C 16 mimNO 3 homologue were also found to be similarly small [19].The low values of S CH , on one hand, may indicate a significant conformational dynamics by trans-gauche isomerisation.The fast decrease of S CH towards chain terminal suggests a gradual intensification of the conformational mobility with increasingly significant population of gauche conformers.On the other hand, limited variation of the order parameters for the first few methylene groups close to the imidazolium core suggests a restricted conformation dynamics for this part of the chain with predominant trans conformation.In this case, relatively small observed values of S CH parameters for the carbons in vicinity of the head group can be due to either a low value of the molecular order parameter S (cf.Equation ( 3)) or a significant tilt angle of this part of the chain with respect to main molecular axis oriented along the director.Based on this observation, we consider the following model of average molecular conformation in the further analysis: the part of the chain in vicinity of the head group is predominantly in the trans conformation and the symmetry axis of this chain fragment does not significantly deviate from the long molecular axis.The latter assumption is, in fact, supported by the values of S CC order parameters, estimated from the 13 C n -13 C n+2 dipolar couplings for the chain carbons separated by two bonds.The coupling constants were obtained from the dipolar INADEQUATE experiment described in the Supplementary Materials.The estimated magnitude of the order parameters S CC ≈ 0.31 at 66 • C (averaged value over methylene segments 1 to 5) is a factor of two larger than the corresponding value S CH ≈ −0.16.The ratio S CC /S CH ≈ −2 is indeed expected for C n -C n+2 and C-H vectors, respectively, along and perpendicular to the molecular axis, and thus the model assumption is corroborated.
Within this approach, for the methylenes close to the head group the angular term is P 2 (cos θ PM ) ≈ −0.5.The molecular order parameter S is, thus, estimated using Equation (4).Temperature dependence S(T) is displayed in Figure 4b, while temperature dependencies of the local bond order parameters for the imidazolium core and for the selected carbons in the chain are shown in Figure 4a.We conclude that the ionic smectic A phase is formed (counter-intuitively) with significantly lower value of the molecular order parameter S when comparing to non-ionic smectic mesogens [20][21][22].Theoretical and computational studies suggest that, in contrast to neutral mesogens, the orientational ordering is less important for the stabilization of the smectic layers in ILC where dominant stabilizing effect is due to a "charge-ordered" nanoscale segregation induced by ionic interactions [1,19,23,24].
significantly deviate from the long molecular axis.The latter assumption is, in fact, supported by the values of SCC order parameters, estimated from the 13  Temperature dependence S(T) is displayed in Figure 4b, while temperature dependencies of the local bond order parameters for the imidazolium core and for the selected carbons in the chain are shown in Figure 4a.We conclude that the ionic smectic A phase is formed (counter-intuitively) with significantly lower value of the molecular order parameter S when comparing to non-ionic smectic mesogens [20][21][22].Theoretical and computational studies suggest that, in contrast to neutral mesogens, the orientational ordering is less important for the stabilization of the smectic layers in ILC where dominant stabilizing effect is due to a "charge-ordered" nanoscale segregation induced by ionic interactions [1,19,23,24].In order to analyse the dipolar couplings and local bond order parameters in the imidazolium core (Figure 4a), the molecular axis alignment to imidazolium ring plane has to be correctly accounted for.The planar molecular structure as displayed in Figure 1 is not consistent with the observed couplings in the imidazolium core.In fact, it has been shown by density functional theory (DFT) analysis of similar compounds that in the energy optimized equilibrium structure of Cnmim cations there is a significant angle between the core plane and the symmetry axis of the all-trans aliphatic chain [25].Non-planar molecular structure is also consistent with recent molecular dynamics (MD) simulation data [19].A rotation/flip of the imidazolium core around N-C bond can In order to analyse the dipolar couplings and local bond order parameters in the imidazolium core (Figure 4a), the molecular axis alignment to imidazolium ring plane has to be correctly accounted for.The planar molecular structure as displayed in Figure 1 is not consistent with the observed couplings in the imidazolium core.In fact, it has been shown by density functional theory (DFT) analysis of similar compounds that in the energy optimized equilibrium structure of C n mim cations there is a significant angle between the core plane and the symmetry axis of the all-trans aliphatic chain [25].Non-planar molecular structure is also consistent with recent molecular dynamics (MD) simulation data [19].A rotation/flip of the imidazolium core around N-C bond can also be accompanied by the chain re-alignment.The correlation of motion by ion-pairing, as has been observed in isotropic phase of ionic liquids, may impose additional restriction on the core dynamics [26][27][28][29].On the other hand, diffusion and conductivity studies have indicated (partial) dissociation of cations and anions in mesophases [28][29][30].With reservations for the complexity of the processes controlling the core alignment and dynamics, it is still possible make rough estimates of the order parameters using DFT structure analysis as presented in [19].Application of Equation (3) using the direction angles given

Crystals 2019, 9 FOR PEER REVIEW 3 Representative 13 C
NMR spectra of the C14mim ions in different phases are displayed in Figure 1.All carbons, except carbons 5 and 6 with overlapped signals, were resolved.The assignment of the carbon signals in the isotropic and mesophase was verified, respectively, by the INADEQUATE (incredible natural-abundance double-quantum transfer) experiment [14] and by dipolar INADEQUATE experiment as described in Supplementary Materials.The chemical shifts of the corresponding signals in the spectra in Figure 1a,b reflect different parts of residual chemical shift anisotropy (CSA) tensor.The signal positions in the isotropic phase are given by the isotropic averages i δ of the respective CSA tensors.In the spectrum in the aligned mesophase, (Figure 1b), the chemical shift corresponds to one of the principal values(

Figure 1 .
Figure 1. 13 C nuclear magnetic resonance (NMR) spectra of C14mimNO3 in the isotropic (a) and smectic A phase (b and c) at indicated temperatures.The spectrum (c) was recorded in the un-aligned smectic A phase.

Figure 1 .
Figure 1. 13 C nuclear magnetic resonance (NMR) spectra of C 14 mimNO 3 in the isotropic (a) and smectic A phase (b,c) at indicated temperatures.The spectrum (c) was recorded in the un-aligned smectic A phase.

Figure 2 .
Figure 2. (a) Part of 2D proton detected/encoded local field (PDLF) spectrum in C14mimNO3 smectic A phase at 66 °C.(b) Cross-sections along dipolar dimension are shown for all carbons.For spectral assignment, see molecular structure in Figure 1.

Figure 2 .
Figure 2. (a) Part of 2D proton detected/encoded local field (PDLF) spectrum in C 14 mimNO 3 smectic A phase at 66 • C. (b) Cross-sections along dipolar dimension are shown for all carbons.For spectral assignment, see molecular structure in Figure 1.

Figure 3 .
Figure 3. C-H bond order parameter SCH profiles for the alkyl chain of the cation in the smectic A phase of C14mimNO3.

Figure 3 .
Figure 3. C-H bond order parameter S CH profiles for the alkyl chain of the cation in the smectic A phase of C 14 mimNO 3 .

Figure 4 .
Figure 4. (a) Temperature dependencies of the local bond order parameters CH S for the imidazolium core and selected carbons in the chain in the smectic A phase of C14mimNO3.(b) Temperature dependence of the molecular order parameter S.

Figure 4 .
Figure 4. (a) Temperature dependencies of the local bond order parameters S CH for the imidazolium core and selected carbons in the chain in the smectic A phase of C 14 mimNO 3 .(b) Temperature dependence of the molecular order parameter S.
Cn-13Cn+2 dipolar couplings for the chain carbons separated by two bonds.The coupling constants were obtained from the dipolar INADEQUATE experiment described in the Supplementary Materials.The estimated magnitude of Cn+2 and C-H vectors, respectively, along and perpendicular to the molecular axis, and thus the model assumption is corroborated.Within this approach, for the methylenes close to the head group the angular term is .The molecular order parameter S is, thus, estimated using Equation (4).