# Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

_{TB}) phase has emerged as a fascinating phenomenon in the field of supramolecular chemistry, based on complex intermolecular interactions. Through a careful analysis of molecular structures and dynamics, we elucidate how these intermolecular interactions drive the complex twist-bend modulation observed in the N

_{TB}. The study employs broadband dielectric spectroscopy spanning frequencies from 10 to 2 × 10

^{9}Hz to investigate the molecular orientational dynamics within the glass-forming thioether-linked cyanobiphenyl liquid crystal dimers, namely, CBSC7SCB and CBSC7OCB. The experimental findings align with theoretical expectations, revealing the presence of two distinct relaxation processes contributing to the dielectric permittivity of these dimers. The low-frequency relaxation mode is attributed to an “end-over-end rotation” of the dipolar groups parallel to the director. The high-frequency relaxation mode is associated with precessional motions of the dipolar groups about the director. Various models are employed to describe the temperature-dependent behavior of the relaxation times for both modes. Particularly, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics in accordance with findings from infrared (IR) spectroscopy. Here, as the longitudinal correlations of dipoles intensify, the

**m**

_{1}mode experiences a sudden upsurge in enthalpy, while the

**m**

_{2}mode undergoes continuous changes, displaying critical mode coupling behavior. Interestingly, both types of molecular motion exhibit a strong cooperative interplay within the lower temperature range of the N

_{TB}phase, evolving in tandem as the material’s temperature approaches the glass transition point. Consequently, both molecular motions converge to determine the glassy dynamics, characterized by a shared glass transition temperature, T

_{g}.

## 1. Introduction

_{TB}) phase is present in an equal number of degenerate domains with opposite twist directions and the director is tilted relative to the helical axis. This new nematic-type phase is distinguished by unusual periodic patterns observed with polarizing microscopy and very fast electro-optic switching in the microsecond regime [3,4]. However, an unambiguous determination of the phase structure appears to be very difficult, since it exhibits no electron density modulation. Extensive studies [5,6,7] suggested that this structure corresponds to a phase with a spontaneous conical twist-bend director distortion, which was theoretically predicted to be driven by an elastic instability with the sign inversion of the bend elastic constant K

_{33}for bent-shaped molecules [2].The N

_{TB}phase was first discovered for 1,7-bis-4-(4′-cyanobiphenyl)heptane, CB7CB, which consists of two mesogenic units connected with a flexible spacer [5,6,7,8]. Other dimeric mesogen [9,10,11,12,13,14,15,16,17] bent-core species [18,19,20] have been reported to manifest the N

_{TB}phase. Despite the significant number of materials investigated, a general structure–property relationship for the N

_{TB}phase remains elusive; however, it is found that a spatially uniform curvature of the molecule is necessary to form the N

_{TB}phase regardless of the underlying chemical groups [21,22].

_{TB}formed with the polar symmetric dimers CBSC7SCB and the similar asymmetric dimers CBSC7OCB. Dielectric relaxation measurements were carried out for both samples in the entire temperature range up to the glass transition. The observed relaxation processes, as in earlier dielectric relaxation studies [5,20,23,24], were interpreted using different molecular motions defined with theoretical models of dielectric relaxation [25,26,27]. In both nematic phases, the rotation of dipolar groups associated with the terminal cyanobiphenyl groups lead to two relaxation modes related to the rotational dynamics of the molecules. The low-frequency mode, denoted

**m**

_{1}, is caused by “end-to-end” motion of dipolar groups, which are parallel to the mesogen axis. The high-frequency mode, denoted

**m**

_{2}, is the result of the precessional rotation of the dipolar groups around the director. These modes contribute to the complex dielectric permittivity differently depending on the orientation of the dielectric relative to the measured electric field.

_{TB}transition. The glass transition can be characterized by the temperature T

_{g}and the rate at which various properties of the material change with temperature as the liquid phase approaches the glass transition. For systems exhibiting a certain number of structural relaxations, it is possible to identify dielectric glass transitions corresponding to each of the two types of molecular motion independently. It is interesting whether changes in molecular interactions observed in previous spectroscopic studies [28,29] can be related to the observed glass transitions. The results for the CBSC7SCB and CBSC7OCB dimers presented here are discussed for information on which molecular movements are frozen during glass formation. The results for the symmetric and asymmetric liquid crystal dimers presented here are discussed to provide information on how the changes in molecular interactions observed near the N-N

_{TB}transition and below affect the aggregation process and how they are frozen during glass formation.

## 2. Results

#### 2.1. Dielectric Relaxation

_{a}for the reorientation of a molecular dipole in a dielectric environment.

_{0}, some theories are based on the VFT equation such as the Adam–Gibbs entropy model (AG) [31] and some more recent theoretical models [32,33,34]. The basic idea behind these theories is that glass formation is associated with highly cooperative movements in a structurally fluctuating sample, with cooperativity growing as T

_{g}is approached. Combining the above ideas of glass formation with a mean-field description of the virtual phase transition, the dynamic scaling (DS) model [35,36] has been proposed such that

_{0}is defined as the relaxation time at 2T

_{c}; the temperature T

_{c}is the temperature of the virtual phase transition (the critical temperature), usually located slightly below T

_{g}. For the high-temperature dynamic domain, well above the glass transition where the coupling mechanisms can be disregarded, Mode Coupling Theory (MCT) provides a power law function similar to the above eq. but with fitting parameters of the different physical meanings to those reported by the DS model. In that case, T

_{c}accounts for the crossover temperature from the ergodic to the non-ergodic domain. The critical temperature T

_{c}seems to correlate with the caging temperature T

_{A}[37].

_{0}has the same meaning as in the VFT equation; K and C parameters are related with effective activation barriers, being both defined as thermal activation fitting parameters.

**m**

_{1}detected in the parallel component of the permittivity, which is classified as τ

_{00}in terms of the spherical harmonics. Relaxation of the longitudinal component of the molecular dipole with precession about the director axis contributes to a high-frequency mode,

**m**

_{2}, detected in the perpendicular component of the permittivity and is classified as τ

_{10}in terms of the spherical harmonics. This is for a nematic potential assumed to be of the form

**n**direction.

**is that for rotational diffusion in the isotropic phase. Longitudinal, μ**

_{D}_{l}, and transverse, μ

_{t}, components of the molecular dipole moment, μ, contribute to the dielectric permittivity differently and they relax at different frequencies of the probe field. In solving the rotational diffusion equation, a uniaxial nematic potential has been assumed. An inconsistency arises here, since molecules that have a dipole inclined to the long molecular axis are intrinsically biaxial.

#### 2.2. Molecular Modes in the Nematic Phase

**m**

_{1}), according to the theoretical model of dielectric relaxation in nematic dimers [25,26], and the precessional movement of dipolar groups around the director for the high-frequency branch of the spectrum (

**m**

_{2}).

**m**

_{1}and

**m**

_{2}of the symmetric CBSCnSCB and asymmetric CBSCnOCB dimers, as also made for CBCnCB by Cestari et al. [5], Merkel et al. [24], and López et al. [41]. We analyzed the two observed processes, in the N phase, and we were enabled to describe them unequivocally using an orientational order, S, and so-called Debye relaxation time, which corresponds to the relative relaxation in the absence of orientational order. This can be simply interpreted as an extension of the isotropic relaxation time into the temperature range of the nematic phase. Following Equation (4), the contribution to the perpendicular component of permittivity originates from the precession rotation of the transverse component of the dipole moment, i.e., rotation of the bow axis of the bent-core conformation contributes significantly to the perpendicular component.

**m**

_{2}. The higher frequency relaxation process,

**m**

_{2}, can arise from the rotations of a segment of the molecule, i.e., the internal rotation of each monomer with the spacer anchored involves the fluctuations of the cyanobiphenyl dipolar moment. As the length of the spacer in between the two mesogenes in the dimer is large enough, such an independent internal rotation of each monomer of the dimer is highly feasible. The temperature dependencies of δε and of the relaxation time ${\tau}_{10}$ are suggestive of the precessional rotation of the longitudinal component of each tio-cyanobiphenyl (SCB) dipole moment around the director in a planar-aligned cell.

_{00}and τ

_{10}, for mode 1 and 2, respectively, were well fitted using Equations (6)–(8), assuming S and τ

**as unknown values. Results are shown in Figure 1a,b. Temperature dependences of the orientational parameters correspond quite well to the results obtained with infrared spectroscopy [29], but their values are slightly smaller than referenced because dielectric ones are related to the S-CB or (O-CB) dipole moments but IR ones correspond to the molecular axis.**

_{D}_{TB}phase, the temperature dependences of the τ

_{10}of the

**m**

_{2}mode keep their trends without any step at the transition temperature, irrespective of if the director becomes tilted with respect to the symmetry axis. It seems this process is exclusively determined with the local orientational order (relative to the local director), which is continuously growing on decreasing temperature. This is not the case for end-over-end relaxation time, τ

_{00}, of the mode

**m**

_{1}. First of all, relaxation time dependence clearly shows a kink at the transition temperature, which indicates an increased relaxation rate at the transition temperature. This is more likely due to critical fluctuations of the director in the vicinity of transition [42]. Then, in the N

_{TB}phase, the temperature trend of the τ

_{00}relaxation time suddenly increases, with respect to the trend in the nematic phase. We can simply interpret this fact as an apparent growth of the potential barrier, q, separating two minima along the

**n**direction, upon entering the N

_{TB}phase [26,38]. This finding corresponds well with an orientational correlation effect of the longitudinal dipoles (${g}_{\left|\right|}\ne 1$), which was revealed with IR spectroscopy [28,29].

^{−9}s to 10

^{−10}s in isotropic, nematic, and disordered smectic phases. Thus, interpretation of dielectric relaxation processes at MHz or even kHz frequencies in terms of single molecule rotation is not likely to be correct. The low-frequency relaxations observed in liquid crystals are the result of collective molecular motion, although the models outlined above are useful in analyzing results and comparing materials.

## 3. Discussion

#### Dynamic Characterization on Glass Forming

_{TB}. Only two longer dimers, with seven carbons in the link (i.e., CBSC7SCB and CBSC7OCB), show typical glass-forming behavior on cooling [40]. We used phenomenological equations and the Vogel–Fulcher–Tammann formula, Equation (2), to describe the temperature dependence of relaxation time data (τ). The results of fitting are shown in Figure 1a,b as dashed lines. VFT parameters obtained for Equation (2) are listed in Table 1. It should be stressed, as can be observed in Table 1, that two different dielectric glass transition temperatures are obtained, though rather close to one another, within about 1 K. It is also interesting to note that the pre-factor τ

_{0}for the

**m**

_{2}mode is of the order of 10

^{−11}s.

_{A}is denoted as the apparent enthalpy of activation. In terms of the applicability of the VFT equation,${\left[{H}_{A}\left(T\right)/R\right]}^{-1/2}$ is predicted to have a linear dependence on inverse temperature. The results of applying this equation to both modes are shown in Figure 2a for CBSC7SCB and Figure 2b for CBSC7OCB.

**m**

_{2}, the activation enthalpy (almost constant in N phase, H

_{A}= 42 kJ/mol) begins to increase in the N

_{TB}phase showing a region of linearity (of ${\left[{H}_{A}\left(T\right)/R\right]}^{-1/2}$) down to 325 K (1000/T ≅ 3.08 K

^{−1}). On the contrary, the activation enthalpy of the mode

**m**

_{1}jumps at transition N-N

_{TB}(from 54 kJ/mol to 113 kJ/mol) then increases, but less rapidly, to join

**m**

_{2}below 325 K, and from this temperature, both modes have the same enthalpy of activation, probably due to cooperative behavior. Similarly, mode

**m**

_{2}for CBSC7OCB gradually increases activation enthalpy in the N

_{TB}phase (from 53 kJ/mol at transition temperature up to 116 kJ/mol, additionally showing linear region (${\left[{H}_{A}\left(T\right)/R\right]}^{-1/2}$) down to 330 K (1000/T ≅ 3.03 K

^{−1})). In this case, mode

**m**

_{2}shows two linear domains: first from the transition temperature down to 330 K and the second below it. This coincides with the temperature when lateral interaction begins to be important [29].

**m**

_{1}, again jumps at transition N-N

_{TB}(from 53 kJ/mol to 101 kJ/mol) then grows but less rapidly to join the

**m**

_{2}mode at about 320 K and since then, both mode have the same activation enthalpy (~116 kJ/mol) due to the cooperative behavior. Continuous lines in both figures are linear fits according to Equation (9).

_{C}in the above MCT critical-like equation accounts for the crossover temperature from the ergodic to the non-ergodic domain. The critical temperature Tc seems to correlate with the caging temperature T

_{A}. Experimental data for both modes are shown in Figure 3 as a plot of [T

^{2}R/H

_{A}(T)] vs. temperature. It should be stressed that for both dimers, the data of the

**m**

_{1}mode exhibit a linear behavior (i.e., follow the DS model) over the entire temperature range of the N

_{TB}mesophase. The temperature T

_{C}is the temperature of the virtual phase transition (the critical temperature), usually located slightly below T

_{g}. The exponent Φ ≈ 6–15 was suggested as universal for glass-forming polymers. In contrast,

**m**

_{2}data in the N

_{TB}mesophase clearly show two linear domains, one at low temperatures (DS model) from T

_{g}up to about 320–324 K (denoted as T

_{A}in the figures); for both modes, they seem to be indistinguishable from behavior of the

**m**

_{1}mode and another domain at high temperatures (MCT-like description) from T

_{A}up to the vicinity of the N

_{TB}-N phase transition. The crossover temperature coincides well with IR spectroscopy observation for the temperature when lateral interaction increases their strength [29]. Below that temperature, it seems, both modes become coupled and can be described in the same way.

_{C}and the exponent Φ. The final fitting of the relaxation data according to Equation (3) is focused on the pre-factor

**τ**

_{0}. All these derived parameters are listed in Table 3 and results of the fittings are drawn in Figure 3.

_{C}and T

_{A}temperatures corresponding to the

**m**

_{1}and

**m**

_{2}modes. It seems that a common critical temperature (≈273 K) for the virtual phase transition and also the same glass transition temperature of about 276 K are obtained for both modes. As for the exponent, in the DS domain, Φ is 7.0 (

**m**

_{1}mode) and 7.4 (

**m**

_{2}mode), typical values usually reported for spin-glass-like systems. In the MCT domain for the m

_{2}mode, Φ is within the usual range of values.

_{A}(T)/R] exhibits a nearly linear dependence with the inverse of temperature. As suggested recently [44], to proceed further with a linearized expression, Equation (11) can be written as

_{2}data and another at about 330 K for m

_{1}data, can be observed. The former has not been appreciated for VFT or critical-like analyses of m

_{2}data. However, the latter has already been observed in the VFT analysis of m

_{1}data and apparently coincides with the estimation of the caging temperature, T

_{A}, shown with the m

_{2}data. The final fitting of the relaxation time data according to Equation (4) leads to the pre-factor τ

_{0}. All the (WM)-fitting parameters, C, K, and τ

_{0}, for each dynamic domain and relaxation mode are listed in Table 4. The final fits are also drawn in Figure 4. If we focus on the results for τ

_{0}and T

_{g}(see Table 4), a strong parallelism with the VFT results can be observed. Again, τ

_{0}for the m

_{2}mode is of the order of 10

^{−10}s (high-temperature dynamic domain), far from 10

^{−14}s. As for the glass transition temperature, two different values are obtained, but less than ca. 3K apart.

## 4. Materials and Methods

_{j}, τ

_{j}, α

_{j}are the fitting parameters of the equation of the derivative of ε′. Figure 7 shows the fitting examples of the dε′/d(lnf) at two temperatures (370 K, 350 K) and how they reproduce the experimental curve. The errors are less than 5% for frequency and 7% for strength of the mode. The shape parameters were found to be quite small (α < 0.08).

## 5. Conclusions

_{1}and m

_{2}, as predicted with the rotational diffusion model. The high-frequency relaxation process originates from the precession rotation of the longitudinal component of the monomer dipole moment of each thiocyanobiphenyl (SCB) dipole moment around the director. The relaxation rate is accelerated with respect to the isotropic relaxation because ${\tau}_{10}$ is shorter as compared to ${\tau}_{D}$. The low-frequency relaxation corresponds from the “end-over-end” rotation of the monomer dipole moment. The relaxation rate of that mode is retarded with respect to the isotropic one. It is clear that dynamics of the two relaxation process modes m

_{1}and m

_{2}are quite different in the two temperature regions of the N

_{TB}mesophase. In the first region, which is extended almost 30 K from N-N

_{TB}transition, for mode m

_{1}assigned to “end-over-end” rotation, activation enthalpy initially jumps almost twice on entering N

_{TB}then increases continuously over almost 30 K. This turns out to be well associated with the appearance of longitudinal dipole correlations discovered in IR studies. In the same region, the activation enthalpy of mode m

_{2}(assigned to precession of dipoles) grows continuously but much faster than m

_{1}and finally they meet at the same value of H

_{A}(T). This meeting temperature corresponds well to the appearance of transverse interactions as seen in IR measurements. The description of the critical behavior of dynamic domains related to cooperative molecular motions is quite sufficient to adequately describe the dynamics associated with the two main molecular motions in the N

_{TB}mesophase of the symmetric and asymmetric dimer. Both types of molecular motion appear to strongly cooperate at low temperatures, changing in a coordinated manner as the temperature of the material approaches the glass transition point. As expected, it turns out that both molecular motions determine glassy dynamics with the same glass transition temperature T

_{g}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Meyer, R.B. In Les Houches Summer School in Theoretical Physics; Balian, R.G., Weil, G., Eds.; Gordon and Breach: New York, NY, USA, 1976; pp. 273–373. [Google Scholar]
- Dozov, I. On the Spontaneous Symmetry Breaking in the Mesophases of Achiral Banana-Shaped Molecules. Europhys. Lett.
**2001**, 56, 247–253. [Google Scholar] [CrossRef] - Panov, V.P.; Balachandran, R.; Nagaraj, M.; Vij, J.K.; Tamba, M.G.; Kohlmeier, A.; Mehl, G.H. Microsecond Linear Optical Response in the Unusual Nematic Phase of Achiral Bimesogens. Appl. Phys. Lett.
**2011**, 99, 261903-3. [Google Scholar] [CrossRef] - Panov, V.; Balachandran, R.; Vij, J.K.; Tamba, M.G.; Kohlmeier, A.; Mehl, G.H. Field-Induced Periodic Chiral Pattern in the Nx Phase of Achiral Bimesogens. Appl. Phys. Lett.
**2012**, 101, 234106-4. [Google Scholar] [CrossRef] - Cestari, M.; Diez-Berart, S.; Dunmur, D.A.; Ferrarini, A.; de la Fuente, M.R.; Jackson, D.J.B.; Lopez, D.O.; Luckhurst, G.R.; Perez-Jubindo, M.A.; Richardson, R.M.; et al. Phase Behavior and Properties of the Liquid Crystal Dimer 1″,7″-bis(4-cyanobiphenyl-4′-yl) heptane: A Twist-Bend Nematic Liquid Crystal. Phys. Rev. E
**2011**, 84, 031704-20. [Google Scholar] [CrossRef] [PubMed] - Chen, D.; Porada, J.H.; Hooper, J.B.; Klittnick, A.; Shen, Y.; Tuchband, M.R.; Korblova, E.; Bedrov, D.; Walba, D.M.; Glaser, M.A.; et al. Chiral Heliconical Ground State of Nanoscale Pitch in a Nematic Liquid Crystal of Achiral Molecular Dimers. Proc. Natl. Acad. Sci. USA
**2013**, 110, 15931–15936. [Google Scholar] [CrossRef] - Borshch, V.; Kim, Y.K.; Xiang, J.; Gao, M.; Jákli, A.; Panov, V.P.; Vij, J.K.; Imrie, C.T.; Tamba, M.G.; Mehl, G.H.; et al. Nematic Twist-Bend Phase with Nanoscale Modulation of Molecular Orientation. Nat. Commun.
**2013**, 4, 2635–2638. [Google Scholar] [CrossRef] - Meyer, C.; Luckhurst, G.; Dozov, I. Flexoelectrically Driven Electroclinic Effect in the Twist-Bend Nematic Phase of Achiral Molecules with Bent Shapes. Phys. Rev. Lett.
**2013**, 111, 067801-5. [Google Scholar] [CrossRef] - Panov, V.P.; Nagaraj, M.; Vij, J.K.; Panarin, Y.P.; Kohlmeier, A.; Tamba, M.G.; Lewis, R.A.; Mehl, G.H. Spontaneous Periodic Deformations in Nonchiral Planar-Aligned Bimesogens With a Nematic-Nematic Transition and a Negative Elastic Constant. Phys. Rev. Lett.
**2010**, 105, 167801-4. [Google Scholar] [CrossRef] - Henderson, P.A.; Imrie, C.T. Methylene Linked Liquid Crystal Dimers and the Twist-Bend Nematic Phase. Liq. Cryst.
**2011**, 38, 1407–1414. [Google Scholar] [CrossRef] - Adlem, K.; Čopič, M.; Luckhurst, G.R.; Mertelj, A.; Parri, O.; Richardson, R.M.; Snow, B.D.; Timimi, B.A.; Tuffin, R.P.; Wilkes, D. Chemically Induced Twist-Bend Nematic Liquid Crystals, Liquid Crystal Dimers, and Negative Elastic Constants. Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
**2013**, 88, 022503-8. [Google Scholar] [CrossRef] - Mandle, R.J.; Davis, E.J.; Lobato, S.A.; Vol, C.-C.A.; Cowling, S.J.; Goodby, W.J. Synthesis and Characterisation of an Unsymmetrical, Ether-Linked, Fluorinated Bimesogen Exhibiting a New Polymorphism Containing the N
_{TB}or ‘twist-bend’ Phase. Phys. Chem. Chem. Phys.**2014**, 16, 6907–6915. [Google Scholar] [CrossRef] [PubMed] - Mandle, R.J.; Davis, E.J.; Archbold, C.T.; Cowling, S.J.; Goodby, W.J. Microscopy Studies of the Nematic N
_{TB}Phase of 1,11-di-(1″-cyanobiphenyl-4-yl)undecane. J. Mater. Chem. C**2014**, 2, 556–566. [Google Scholar] [CrossRef] - Mandle, R.J.; Davis, E.J.; Archbold, C.T.; Vol, C.-C.A.; Andrews, J.L.; Cowling, S.J.; Goodby, W.J. Apolar Bimesogens and the Incidence of the Twist–Bend Nematic Phase. Chem. Eur. J.
**2015**, 21, 8158–8167. [Google Scholar] [CrossRef] [PubMed] - Gorecka, E.; Vaupotic, N.; Zep, A.; Pociecha, D.; Yoshioka, J.; Yamamoto, J.; Takezoe, H. A Twist-Bend Nematic (N
_{TB}) Phase of Chiral Materials. Angew. Chem. Int. Ed.**2015**, 54, 10155–10159. [Google Scholar] [CrossRef] [PubMed] - Paterson, D.A.; Gao, M.; Kim, Y.-K.; Jamali, A.; Finley, K.L.; Robles-Hernández, B.; Diez-Berart, S.; Salud, J.; de la Fuente, M.R.; Timimi, B.A.; et al. Understanding the Twist-Bend Nematic Phase: The Characterisation of 1-(4-cyanobiphenyl-4′-yloxy)-6-(4-cyanobiphenyl-4′-yl)hexane (CB6OCB) and Comparison with CB7CB. Soft Matter
**2016**, 12, 6827–6840. [Google Scholar] [CrossRef] - Paterson, D.A.; Abberley, J.P.; Harrison, W.T.A.; Storey, M.D.J.; Imrie, C.T. Cyanobiphenyl-Based Liquid Crystal Dimers and the Twist-Bend Nematic Phase. Liq. Cryst.
**2017**, 44, 127–146. [Google Scholar] [CrossRef] - Chen, D.; Nakata, M.; Shao, R.; Tuchband, M.R.; Shuai, M.; Baumeister, U.; Weissflog, W.; Walba, D.M.; Glaser, M.A.; Maclennan, J.E.; et al. Twist-Bend Heliconical Chiral Nematic Liquid Crystal Phase of an Achiral Rigid Bent-Core Mesogen. Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
**2014**, 89, 022506-5. [Google Scholar] [CrossRef] - Sreenilayam, S.P.; Panov, V.P.; Vij, J.K.; Shanker, G. The N
_{TB}Phase in an Achiral Asymmetrical Bent-Core Liquid Crystal Terminated with Symmetric Alkyl Chains. Liq. Cryst.**2017**, 44, 244–253. [Google Scholar] [CrossRef] - Merkel, K.; Kocot, A.; Vij, J.K.; Shanker, G. Distortions in Structures of the Twist Bend Nematic Phase of a Bent-Core Liquid Crystal by the Electric Field. Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
**2018**, 98, 022704-8. [Google Scholar] [CrossRef] - Walker, R.; Pociecha, D.; Salamończyk, M.; Storey, J.M.D.; Gorecka, E.; Imrie, C.T. Supramolecular Liquid Crystals Exhibiting a Chiral Twist-Bend Nematic Phase. Mater. Adv.
**2020**, 1, 1622–1630. [Google Scholar] [CrossRef] - Mandle, R.J. The Dependency of Twist-Bend Nematic Liquid Crystals on Molecular Structure: A Progression from Dimers to Trimers, Oligomers and Polymers. Soft Matter
**2016**, 12, 7883–7901. [Google Scholar] [CrossRef] [PubMed] - Merkel, K.; Welch, C.; Ahmed, Z.; Piecek, W.; Mehl, G.H. Dielectric Response of Electric-Field Distortions of the Twist-Bend Nematic Phase for LC Dimers. J. Chem. Phys.
**2019**, 151, 114908–114920. [Google Scholar] [CrossRef] [PubMed] - Merkel, K.; Kocot, A.; Welch, C.; Mehl, G.H. Soft Modes of the Dielectric Response in the Twist–Bend Nematic Phase and Identification of the Transition to a Nematic Splay Bend Phase in the CBC7CB Dimer. Phys. Chem. Chem. Phys.
**2019**, 21, 22839–22848. [Google Scholar] [CrossRef] [PubMed] - Nordio, P.L.; Rigatti, G.; Segre, U. Dielectric Relaxation Theory in Nematic Liquids. Mol. Phys.
**1973**, 25, 129–136. [Google Scholar] [CrossRef] - Coffey, W.T.; Kalmykov, Y.P. Rotational Diffusion and Dielectric Relaxation in Nematic Liquid Crystals. Adv. Chem. Phys.
**2000**, 113, 487–551. [Google Scholar] - Stocchero, M.; Ferrarini, A.; Moro, G.J.; Dunmur, D.A.; Luckhurst, G.R. Molecular Theory of Dielectric Relaxation in Nematic Dimers. J. Chem. Phys.
**2004**, 121, 8079–8097. [Google Scholar] [CrossRef] - Kocot, A.; Loska, B.; Arakawa, Y.; Merkel, K. Structure of the Twist-Bend Nematic Phase with Respect to the Orientational Molecular Order of the Thioether-Linked Dimers. Phys. Rev. E
**2022**, 105, 044701-10. [Google Scholar] [CrossRef] - Merkel, K.; Loska, B.; Arakawa, Y.; Mehl, G.H.; Karcz, J.; Kocot, A. How Do Intermolecular Interactions Evolve at the Nematic to Twist–Bent Phase Transition? Int. J. Mol. Sci.
**2022**, 23, 11018. [Google Scholar] [CrossRef] - García Colin, L.S.; del Castillo, L.F.; Goldstein, P. Theoretical Basis for the Vogel-Fulcher-Tammann Equation. Phys. Rev. B
**1989**, 40, 7040–7044, Erratum in Phys. Rev. B**1990**, 41, 4785. [Google Scholar] [CrossRef] - Adams, G.; Gibbs, J.H. On the Temperature Dependence of Cooperative Relaxation Properties in GlassForming Liquids. J. Chem. Phys.
**1965**, 43, 139–146. [Google Scholar] [CrossRef] - Cohen, M.H.; Grest, G.S. Liquid-glass transition, a free-volume approach. Phys. Rev. B
**1979**, 20, 1077–1098. [Google Scholar] [CrossRef] - Bouchaud, G.P.; Biroli, G. On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes Scenario for the Viscosity Increase in Glasses. J. Chem. Phys.
**2004**, 121, 7347–7354. [Google Scholar] [CrossRef] [PubMed] - Lubchenko, V.; Wolynes, P.G. Theory of Structural Glasses and Supercooled Liquids. Ann. Rev. Phys. Chem.
**2007**, 58, 235–266. [Google Scholar] [CrossRef] [PubMed] - Colby, R.H. Dynamic Scaling Approach to Glass Formation. Phys. Rev. E
**2000**, 61, 1783–1792. [Google Scholar] [CrossRef] [PubMed] - Erwin, B.M.; Colby, R.H. Temperature Dependence of Relaxation Times and the Length Scale of Cooperative Motion for Glass-Forming Liquids. J. Non-Cryst. Solids
**2002**, 307–310, 225–231. [Google Scholar] [CrossRef] - Drozd-Rzoska, A.; Rzoska, S.J.; Pawlus, S.; Martínez-García, J.C.; Tamarit, J.-L. Evidence for Critical-Like Behavior in Ultraslowing Glass Forming Systems. Phys. Rev. E
**2010**, 82, 031501-8. [Google Scholar] [CrossRef] - Waterton, S.C. The Viscosity-Temperature Relationship and Some Inferences on the Nature of Molten and of Plastic. J. Soc. Glass. Technol.
**1932**, 16, 244–249. [Google Scholar] - Mauro, J.C.; Yue, Y.; Ellison, A.J.; Gupta, P.K.; Allan, D.C. Viscosity of Glass-Forming Liquids. Proc. Natl. Acad. Sci. USA
**2009**, 106, 19780–19784. [Google Scholar] [CrossRef] - Kocot, A.; Czarnecka, M.; Arakawa, Y.; Merkel, K. Dielectric Study of Liquid Crystal Dimers: Probing the Orientational Order and Molecular Interactions in Nematic and Twist-Bend Nematic Phases. Phys. Chem. B
**2023**, 127, 7082–7090. [Google Scholar] [CrossRef] - López, D.O.; Sebastian, N.; de la Fuente, M.R.; Martínez-García, J.C.; Salud, J.; Pérez-Jubindo, M.A.; Diez-Berart, S.; Dunmur, D.A.; Luckhurst, G.R. Disentangling Molecular Motions Involved in the Glass Transition of a Twist-Bend Nematic Liquid Crystal Through Dielectric Studies. J. Chem. Phys.
**2012**, 137, 034502-10. [Google Scholar] [CrossRef] - Pociecha, D.; Crawford, C.A.; Paterson, D.A.; Storey, J.M.D.; Imrie, C.T.; Vaupotič, N.; Gorecka, E. Critical Behavior of the Optical Birefringence at the Nematic to Twist-Bend Nematic Phase Transition. Phys. Rev. E
**2018**, 98, 052706-5. [Google Scholar] [CrossRef] - Stickel, F.; Fischer, E.W.; Richert, R. Dynamics of Glass-Forming Liquids. I. Temperature-Derivative Analysis of Dielectric Relaxation Data. J. Chem. Phys.
**1995**, 102, 6251–6257. [Google Scholar] [CrossRef] - Martínez-García, J.C.; Tamarit, J.L.; Rzoska, S.J. Enthalpy Space Analysis of the Evolution of the Primary Relaxation Time in Ultraslowing Systems. J. Chem. Phys.
**2011**, 134, 024512-7. [Google Scholar] [CrossRef] - Arakawa, Y.; Komatsu, K.; Tsuji, H. Twist-Bend Nematic Liquid Crystals Based on Thioether Linkage. New J. Chem.
**2019**, 43, 6786–6793. [Google Scholar] [CrossRef] - Arakawa, Y.; Ishida, Y.; Tsuji, H. Ether- and Thioether-Linked Naphthalene-Based Liquid-Crystal Dimers: Influence of Chalcogen Linkage and Mesogenic-Arm Symmetry on the Incidence and Stability of the Twist–Bend Nematic Phase. Chem. Eur. J.
**2020**, 26, 3767–3775. [Google Scholar] [CrossRef]

**Figure 1.**Plots of relaxation times for modes

**m**

_{1}and

**m**

_{2}(5 μm planar cell): (

**a**) symmetric dimer (CBSC7SCB), (

**b**) asymmetric dimer (CBSC7OCB). Symbols: red circles (

**○**)—

**m**

_{1}mode, dark blue squares (

**□**)—

**m**

_{2}mode, rotational diffusion model fitting: black solid line—

**m**

_{1}mode, dash blue line—τ

_{D}relaxation time, solid blue line—VFT model [30], solid red line—fitting of experimental data by Equation (2), purple/burgundy triangles (

**∇**,

**∇**)—order parameter, S (as an insert).

**Figure 2.**Plots show a linear dependence ${\left[{H}_{A}\left(T\right)/R\right]}^{-1/2}$ on the inverse temperature in N

_{TB}phase. (

**a**)—CBSC7SCB dimer, (

**b**)—CBSC7OCB. The red arrows show the jump of the H

_{A}that omits the critical fluctuation at the N-N

_{TB}transition, where H

_{A}is denoted as the apparent enthalpy of the activation. Symbols: red circles (

**○**)—

**m**

_{1}mode, dark blue squares (

**□**)—

**m**

_{2}mode, solid line: model fitting according to Equation (9). The fitting parameters are listed in Table 2.

**Figure 3.**Results of the temperature-derivative analysis (Equation (10)) in N

_{TB}phase applied to both

**m**

_{1}and

**m**

_{2}modes in which linear dependences indicate domains of validity of the critical-like description; (

**a**) symmetric dimer (CBSC7SCB), (

**b**) asymmetric dimer (CBSC7OCB). Symbols: red circles (

**○**)—

**m**

_{1}mode, dark blue squares (

**□**)—

**m**

_{2}mode, solid lines: model fitting according to Equation (10). The fitting parameters are listed in Table 3.

**Figure 4.**Results of the temperature-derivative analysis (Equation (11)) in N

_{TB}phase applied to both

**m**

_{1}and

**m**

_{2}modes of (

**a**) CBSC7SCB and (

**b**) CBSC7OCB. Dashed lines (red and black) indicate dynamic domains of validity of the critical-like description. Symbols: red circles (

**○**)—

**m**

_{1}mode, black squares (

**□**)—

**m**

_{2}mode.

**Figure 5.**(

**a**) Molecular structure of symmetric (CBSCnSCB) and asymmetric (CBSCnOCB) dimers. (

**b**) POM textures of the 5 μm planar cell for the CBSC7OCB sample in the N phase (375 K) and the N

_{TB}phase (355 K) (cooling rate of 5 °C/min). The scale bar equals 50 μm.

**Figure 6.**Laboratory and molecular frame of reference. Planar (top) and homeotropic cell (bottom) (

**a**) in the N phase, (

**b**) in the N

_{TB}phase, where k is the helical axis, (

**c**) molecular frame of reference.

**Figure 7.**Fitting of the derivative of permittivity vs. ln(f) showing the deconvolution of the molecular modes:

**m**

_{1}and

**m**

_{2}.

**Table 1.**Fitting parameters according to Equation (2) for the different dimers and the calculated glass transition temperature for the

**m**

_{1}and

**m**

_{2}modes.

Sample | Mode | log_{10} [τ(s)] | T_{0} (K) | B (K) | T_{gl} (K) |
---|---|---|---|---|---|

CBSC7SCB | m_{1} | −10.1 | 266.6 | 682.6 | 289.8 |

m_{2} | −11.9 | 265.6 | 631.9 | 286.3 | |

CBSC7OCB | m_{1} | −9.2 | 261.3 | 596.0 | 284.3 |

m_{2} | −11.5 | 260.5 | 621.7 | 280.5 |

Sample | log_{10} [τ(s)] | Equation (2) | Equation (9) | Range [1000/T(K ^{−1})] |
---|---|---|---|---|

CBSC7SCB | −10.3 | 269 | 289 | 2.96–3.3 |

−11.6 | 264 | 289 | 3.15–3.3 | |

CBSC7OCB | −8.9 | 265 | 266 | 3.08–3.3 |

−11.5 | 261 | 270 | 3.08–3.3 |

Sample | T_{A} | Φ (T < T_{A}) | Tc | Φ | Range (K) | Description |
---|---|---|---|---|---|---|

CBSC7SCB | 324 K | 287.4 7.3 | 293 | 7.3 | 305–347 | DS |

321 | 1.3 | 330–351 | MCT | |||

CBSC7OCB | 320 K | 282.5 7.0 | 287.4 | 7.0 | 295–350 | DS |

303.5 | 1.3 | 320–365 | MCT |

Sample | log_{10} [τ(s)] | K (K) | C (K) | T_{gl} (K) | Range (1000/T (K ^{−1})) |
---|---|---|---|---|---|

CBSC7SCB | −7.78 | 0.0789 | 3016 | 268.2 | 2.97–3.28 |

−9.08 | 0.0082 | 3653 | 267.9 | 3.02–3.22 | |

CBSC7OCB | −7.15 | 0.058 | 3028 | 263.9 | 3.03–3.30 |

−9.05 | 0.031 | 3198 | 260.6 | 2.98–3.35 |

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**MDPI and ACS Style**

Kocot, A.; Czarnecka, M.; Arakawa, Y.; Merkel, K.
Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies. *Molecules* **2023**, *28*, 7441.
https://doi.org/10.3390/molecules28217441

**AMA Style**

Kocot A, Czarnecka M, Arakawa Y, Merkel K.
Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies. *Molecules*. 2023; 28(21):7441.
https://doi.org/10.3390/molecules28217441

**Chicago/Turabian Style**

Kocot, Antoni, Małgorzata Czarnecka, Yuki Arakawa, and Katarzyna Merkel.
2023. "Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies" *Molecules* 28, no. 21: 7441.
https://doi.org/10.3390/molecules28217441