New Rod-Like H-Bonded Assembly Systems: Mesomorphic and Geometrical Aspects

Experimental and geometrical approaches of new systems of mesomorphic 1:1 supramolecular H-bonded complexes (SMHBCs) of five rings are discussed. The H-bonding between 4-alkoxyphenylimino benzoic acids (An, as proton acceptor) and 4-(4′–pyridylazophenyl) 4′′-alkoxybenzoates (Bm, as proton donor) were investigated. Mesomorphic behaviors were analyzed by differential scanning calorimetry (DSC) and mesophase textures were identified by polarized light microscopy (POM). H-bonded assembly was established by FT-IR spectroscopic measurements via Fermi band discussion. Thermal and theoretical factors were predicted for all synthesized complexes by density functional theory (DFT) predictions. The results revealed that all prepared complexes were monomorphic, with a broad range of smectic A phases with a high thermal stability of enantiotropic mesophase. Furthermore, DFT stimulations illustrated the experimental results in terms of the influence of the chain length either of the acid or the base component. Many parameters, such as the calculated stability, the dipole moment and the polarizability of the H-bonded complexes, illustrate how these parameters work together to enhance the smectic mesophases with the obtained stability and range.


Introduction
Supramolecular hydrogen-bonding liquid crystal complexes (SMHBLCs) were first made in the 20th century [1]. The first reported SMHBLC dimers were made between 4-n-alkoxycinnamic acids and 4-n-alkoxybenzoic acids that showed stable smectic and nematic mesophases [2][3][4]. A huge number of liquid crystalline materials have been investigated using different synthetic methods, however, the design of SMHBLCs through intermolecular interactions between complementary components are of great interest. The types of interactions might be H-bonding [5][6][7] or halogen bonding [8][9][10][11][12][13] and both have the advantage of easy accessibility compared to covalently bonding liquid crystals.
Thermotropic LCs based on intermolecular hydrogen bond interactions are mostly used in display devices and sensor applications [14][15][16][17][18]. Molecular geometry in LC H-bonded complexes can be assembled between different conformations depending on the investigated hydrogen bond donors and acceptors. Recently, several SMHBLCs were formed using different types of H-donors and donors and acceptors. Recently, several SMHBLCs were formed using different types of H-donors and H-acceptors to afford varied varieties of structural geometries, such as rod-like complexes [19,20], angular complexes [21][22][23][24] polymeric architectures [25], modular hierarchical complexes [26] and non-symmetric dimers possessing nematic mesophases [27] or showing the heliconical twist-bend nematic phase [28] or supramolecular polycatenars of chiral cubic phases [29]. Modification of efficient materials to be in a novel architecture is an attractive area of interest [30][31][32].
Azo and azomethine-functionalized LC linkers are of great interest for the technology of light-responsive compounds [33][34][35]. Later, more types of azobenzene and azomethine-based LCs were reported [36][37][38][39][40][41][42]. Azopyridines are of research interest since they possess the ability of assembly by intermolecular H-bonding and the unique property of trans-cis photo-isomerization and thermal isomerization because of the existence of the azo linkage. In addition, calamitic Schiff base liquid crystals possess a unique mesomorphic character [43].
Recently, many researchers [5,31,[44][45][46][47][48][49][50][51][52][53][54] have reported the mesophase characteristics of new supramolecular H-bonded complexes (SMHBCs) between acids and pyridines as base one [55,56]. In order to better understand the structural effect relationship of SMHBC-based azopyridines, two groups of H-bonded complexes (1:2) based on pyridine as the H-acceptor were investigated [55,57,58]. In another study, the 1:1 SMHBCs prepared between the nitrogen atom of the azomethine derivative and 4-alkoxybenzoic acids [59] has been reported and characterized. In recent research, it has been described [60] that the mesomorphic properties and geometrical expectations can be impacted in a different way by exchanging the azo core group in the base part with an azomethine one [59]. These findings have encouraged us to study the preparation and analysis of another SMHBC based on the azo and azomethine calamitic derivatives. Furthermore, the mixing of computational simulations of geometrical calculations with experimental findings is also interesting [55,[61][62][63] and, in our studies concerning SMHBCs, new calamitic SMHBCs based on the H-bonding interaction between the proton donor, 4-alkoxyphenylimino benzoic acids [45] (An), and the proton acceptor, 4-(4′-pyridylazophenyl) 4′′-alkoxybenzoates [19] (Bm), were prepared. The study aims to examine their mesomorphic characteristics and their geometrical parameters by density functional theory (DFT) simulation. Moreover, this study aims to correlate the experimental outcomes of the mesomorphic properties with their estimated thermal and geometrical outcome values.

Experimental
The acid An and the base Bm and their complexes An/Bm were prepared according to the following Scheme 1: An/Bm; n = 6, 8 and 16; m = 10, 12 and 14.

Experimental
The acid An and the base Bm and their complexes An/Bm were prepared according to the following Scheme 1:

Preparation of Complexes An/Bm:
The acid An and the base Bm were prepared according to the previous reported methods in [64] and [19], respectively. Supramolecular complexes An/Bm were synthesized by mixing 1:1 molar ratios of alkoxy Schiff acids (An) with different chain lengths of n = 6, 8 and 16 and the azo base (B) with alkoxy chain lengths m = 10, 12 and 14. The mix was melted with stirring till the intimate blend, then allowed to cool, as shown in Scheme 1. The characteristics of the prepared supramolecular complexes (An/Bm) were studied by differential scanning calorimetry (DSC) measurements, as well as FT-IR spectroscopy (see Supplementary Materials).
As shown in Figure 1, the peak at 1678 cm −1 was attributed to C=O groups of the dimeric the alkoxy Schiff acid A6. On the other hand, the ester linkage C=O group of the base B12 appeared at 1735 cm −1 . The replacement of the dimeric H-bond between the alkoxy acid A6 and the nitrogen atom of the base (B12) affects the strength of the C=O of either the acid or the base, and consequently, their stretching vibration is affected. This information could be proved by the FT-IR spectral data. The new H-bonding decreases the C=O stretching vibration of the ester linkage of the base B12 to

Preparation of Complexes An/Bm
The acid An and the base Bm were prepared according to the previous reported methods in [64] and [19], respectively. Supramolecular complexes An/Bm were synthesized by mixing 1:1 molar ratios of alkoxy Schiff acids (An) with different chain lengths of n = 6, 8 and 16 and the azo base (B) with alkoxy chain lengths m = 10, 12 and 14. The mix was melted with stirring till the intimate blend, then allowed to cool, as shown in Scheme 1. The characteristics of the prepared supramolecular complexes (An/Bm) were studied by differential scanning calorimetry (DSC) measurements, as well as FT-IR spectroscopy (see Supplementary Materials).

FT-IR Characterizations
The formation of the supramolecular complexes An/Bm was proved via FT-IR, X-ray and NMR spectral analysis [65][66][67][68][69]. However, FT-IR measurements proved to be an effective tool for such confirmation [40,60,[69][70][71]. The spectral data were measured for the individual compounds A6, B12 and their complex A6/B12 and are given in Figure 1. stretching vibration peaks, A-, B-and C-type, of the H-bonded OH functional group is a proof for the formed SMHB complex. The Fermi peak of the A-type of the complex A6/B12 was below the C-H vibrational frequency at 2922 to 2852 cm −1 . Moreover, the band at 2504 cm −1 (A6/B12) is attributed to the B-type of the in-plane bending stretching vibration of the O-H. On the other hand, the 1919 cm −1 peak of the C-type Fermi band is due to the interaction between the overtone of the torsional influence and the essential influence of the OH stretching vibration.

Mesomorphic and Optical Studies
Mesomorphic behaviors for the present 1:1 SMHBCs (An/Bm) were investigated. Phase transition temperatures (T), associated enthalpy (∆H) and their normalized entropy (∆S/R), as well as the mesomorphic range based on DSC measurements for all prepared SMHBCs, An/Bm, are summarized in Table 1. Examples of DSC cycles upon second heating and cooling scans are depicted in Figure 2. In addition, a textural observation example under polarized light microscopy (POM) is represented in Figure 3. A graphical representation of the chain length/transition temperature dependences of the characterized complexes is illustrated in Figure 4, in order to study the effect of the length of alkoxy acid and base chains on the mesomorphic characteristics. As shown in Figure 1, the peak at 1678 cm −1 was attributed to C=O groups of the dimeric the alkoxy Schiff acid A6. On the other hand, the ester linkage C=O group of the base B12 appeared at 1735 cm −1 . The replacement of the dimeric H-bond between the alkoxy acid A6 and the nitrogen atom of the base (B12) affects the strength of the C=O of either the acid or the base, and consequently, their stretching vibration is affected. This information could be proved by the FT-IR spectral data. The new H-bonding decreases the C=O stretching vibration of the ester linkage of the base B12 to 1728 cm −1 , however, it increases that of the C=O of the COOH group of the alkoxy acid A6 to 1737 cm −1 .
One of the important reported proofs of the SMHBC formation is the OH Fermi vibrational stretching bands [28,[69][70][71][72][73][74]. It has been reported that the existence of the three Fermi resonance stretching vibration peaks, A-, B-and C-type, of the H-bonded OH functional group is a proof for the formed SMHB complex. The Fermi peak of the A-type of the complex A6/B12 was below the C-H vibrational frequency at 2922 to 2852 cm −1 . Moreover, the band at 2504 cm −1 (A6/B12) is attributed to the B-type of the in-plane bending stretching vibration of the O-H. On the other hand, the 1919 cm −1 peak of the C-type Fermi band is due to the interaction between the overtone of the torsional influence and the essential influence of the OH stretching vibration.

Mesomorphic and Optical Studies
Mesomorphic behaviors for the present 1:1 SMHBCs (An/Bm) were investigated. Phase transition temperatures (T), associated enthalpy (∆H) and their normalized entropy (∆S/R), as well as the mesomorphic range based on DSC measurements for all prepared SMHBCs, An/Bm, are summarized in Table 1. Examples of DSC cycles upon second heating and cooling scans are depicted in Figure 2. In addition, a textural observation example under polarized light microscopy (POM) is represented in Figure 3. A graphical representation of the chain length/transition temperature dependences of the characterized complexes is illustrated in Figure 4, in order to study the effect of the length of alkoxy acid and base chains on the mesomorphic characteristics.        The azomethine benzoic acids (An) used to prepare the present SMHBCs form smectic A and narrow nematic (N) phases depending on the length of their alkoxy chain terminals [64]. The azopyridine derivatives (Bm) are mesomorphic, exhibiting only SmA mesophases [19]. As can be seen from Table 1 and Figure 4, all formed calamitic SMHBCs (An/Bm) exhibit a broad enantiotropic range of SmA phases and the N phase is not observed for any prepared mixture. In addition, the melting temperatures of complexes have irregular values. Furthermore, the thermal stabilities of the SmA phase are decreased with increments in the length of the terminal chain. Generally, the mesogenic core and the length of the terminal chain of the H-donor molecule influence the stability of the formed mesophase. In addition, the polarity difference between H-donors and H-acceptors affects the strength of H-bonding interactions and enhances the molecular anisotropy, as well as promotes a broadening of the mesomorphic range [75]. However, the length of the terminal alkoxy chain of the mixture does not affect the polarity of each component.
In order to study the structural relationship in liquid crystalline materials further, theoretical calculations were performed by the DFT method (see Supplementary Materials) at B3LYP 6-31G (d, p) for selected series of the SMHBCs An/Bm to show the chain length effect of the acid and the base moieties. Evidence for the geometrical stability of all SMHBCs is the absence of imaginary frequencies. Although these calculations offer an expectation of the favored molecular structure in the gas phase, the existence of these derivatives in a liquid crystalline condensed phase means that the least energy might be changed and the more lengthened species with the longer chain length will be preferred [76]. Figure 5 shows the most favorable geometries of the H-bonded complexes An/Bm. The azomethine benzoic acids (An) used to prepare the present SMHBCs form smectic A and narrow nematic (N) phases depending on the length of their alkoxy chain terminals [64]. The azopyridine derivatives (Bm) are mesomorphic, exhibiting only SmA mesophases [19]. As can be seen from Table 1 and Figure 4, all formed calamitic SMHBCs (An/Bm) exhibit a broad enantiotropic range of SmA phases and the N phase is not observed for any prepared mixture. In addition, the melting temperatures of complexes have irregular values. Furthermore, the thermal stabilities of the SmA phase are decreased with increments in the length of the terminal chain. Generally, the mesogenic core and the length of the terminal chain of the H-donor molecule influence the stability of the formed mesophase. In addition, the polarity difference between H-donors and H-acceptors affects the strength of H-bonding interactions and enhances the molecular anisotropy, as well as promotes a broadening of the mesomorphic range [75]. However, the length of the terminal alkoxy chain of the mixture does not affect the polarity of each component.
In order to study the structural relationship in liquid crystalline materials further, theoretical calculations were performed by the DFT method (see Supplementary Materials) at B3LYP 6-31G (d, p) for selected series of the SMHBCs An/Bm to show the chain length effect of the acid and the base moieties. Evidence for the geometrical stability of all SMHBCs is the absence of imaginary frequencies.
Although these calculations offer an expectation of the favored molecular structure in the gas phase, the existence of these derivatives in a liquid crystalline condensed phase means that the least energy might be changed and the more lengthened species with the longer chain length will be preferred [76]. Figure 5 shows the most favorable geometries of the H-bonded complexes An/Bm. Since both components of the hydrogen-bonded complex are completely in its planar geometry, their SMHBCs are also linear with very little bending. Figure 5 emphasizes that the length of the chains does not significantly affect their structural geometries. However, this small structure change could affect the mesomorphic behavior of liquid crystal complexes, which is highly dependent on the terminal length of wings [31]. SmA transition peaks (Figure 2) are affected by increasing the order parameter coupling during liquid crystal mixing that leads to broadening their peak transition in some cases [77]. Mesomorphic stability of the prepared 1:1 supramolecular complexes An/Bm decreases in the order An/B10 > An/B12 > An/B14, while the mesophase ranges change with the length of the terminal alkoxy chains. The A6/Bm series showed an SmA phase with a wide range for the complex A6/B10 (~120.2 °C) and a narrow range for A6/B14 (~96.5 °C). For series A8/Bm, the highest range was observed for the complex A8/B14 (~101.7 °C) while the lowest value was observed for A8/B12 (~86.5 °C). Finally, the A16/Bm set exhibit a higher mesomorphic range for A16/B10 (~100.0 °C) and a lower one for the A6/B14 (~89.8 °C) mixture.

Thermal Parameters
The projected thermal factors were predicted by DFT by using the same method and base set for both chain lengths of the acid and the base component of the prepared H-bonded complexes An/Bm, and the results are presented in Table 2. The results of the calculated thermal parameters revealed that there is no significant effect of the chain length of the acid or the base component on the Since both components of the hydrogen-bonded complex are completely in its planar geometry, their SMHBCs are also linear with very little bending. Figure 5 emphasizes that the length of the chains does not significantly affect their structural geometries. However, this small structure change could affect the mesomorphic behavior of liquid crystal complexes, which is highly dependent on the terminal length of wings [31]. SmA transition peaks ( Figure 2) are affected by increasing the order parameter coupling during liquid crystal mixing that leads to broadening their peak transition in some cases [77]. Mesomorphic stability of the prepared 1:1 supramolecular complexes An/Bm decreases in the order An/B10 > An/B12 > An/B14, while the mesophase ranges change with the length of the terminal alkoxy chains. The A6/Bm series showed an SmA phase with a wide range for the complex A6/B10 (~120.2 • C) and a narrow range for A6/B14 (~96.5 • C). For series A8/Bm, the highest range was observed for the complex A8/B14 (~101.7 • C) while the lowest value was observed for A8/B12 (~86.5 • C). Finally, the A16/Bm set exhibit a higher mesomorphic range for A16/B10 (~100.0 • C) and a lower one for the A6/B14 (~89.8 • C) mixture.

Thermal Parameters
The projected thermal factors were predicted by DFT by using the same method and base set for both chain lengths of the acid and the base component of the prepared H-bonded complexes An/Bm, and the results are presented in Table 2. The results of the calculated thermal parameters revealed that there is no significant effect of the chain length of the acid or the base component on the estimated theoretical thermal stability, compare A6/B12 and A8/B10. These complexes are of the same length, with different lengths with respect to the acid and the base and they showed the same energy with ∆E = 0.0082 kcal/mole. However, as could be expected, the longer chain length affords highly stable molecules. The extra stability could be explained in terms of a high degree of packing with longer chain lengths. The increase in the length of the alkoxy chains of individuals enhances the calculated stability of the mixtures. The longer terminal length increases the Van der Waals interactions of the flexible chains and thus lowers the estimated energy of the complexes. The alteration of the mesophase behavior and temperature ranges (∆T) for the stable SMHBCs An/Bm for alkoxy chain length are summarized in Table 3. It is obvious from Table 3 that the total smectic mesophase range and stability are decreased with alkoxy chain length either of the acid or the base. Moreover, the high dipole moment of the H-bonded complex could be an illustration of the formation of the smectic mesophase. The high dipole moment of the compounds enhances the molecular packing of the compounds in a highly ordered smectic mesophase. The lateral molecular interaction enhancement that is facilitated by the high dipole moment permits the smectic mesophase to be predominant. As shown in Figures 6 and 7, the predicted polarizability of the H-bonded supramolecular complexes An/Bm is significantly affected by the length of the alkoxy chain on the acid and base components. Increments in the alkoxy chain length increases the H-donor impact on the polarizability successively. The increment in the alkoxy chains resulted in higher space filling and so increased the polarizability. Alternatively, the dependence of the mesophase thermal stability on the polarizability is shown in Figures 6 and 7. The increments in the polarizability accordingly decreases the mesophase stability and its range. The smectic mesophase range and stability decrease with longer chain lengths, where, with the elongation of the chain lengths, the enhanced mesophase gradually became unstable due to the steric aspect. Moreover, that abnormal trend proposes that the geometrical structure alterations play a significant role. This behavior could be attributed to the dual role of increments in the length of the terminal alkoxy chain that led to an enhancement of the shape anisotropy of the complex, thus diluting the intermolecular interaction between the mesogenic parts [78,79]. Furthermore, the steric effect impacts the stability and the range of the mesophase rather than the polarizability, which has a different trend. It is clear that we could control the characteristics of the H-bonding, which could improve the properties of the individual components, by changing the parameters that are needed for special applications, such as the polarizability of the liquid crystalline material to be suitable for electro-optical applications [80][81][82].
Crystals 2020, 10, x 9 of 16 mesogenic parts [78,79]. Furthermore, the steric effect impacts the stability and the range of the mesophase rather than the polarizability, which has a different trend. It is clear that we could control the characteristics of the H-bonding, which could improve the properties of the individual components, by changing the parameters that are needed for special applications, such as the polarizability of the liquid crystalline material to be suitable for electro-optical applications [80][81][82].

Frontier Molecular Orbitals (FMOs) and Polarizability
Figures 8 and 9 demonstrate the predictable plots of the FMOs' highest occupied molecular orbital (HOMO) and the lowest unoccupied one (LUMO of the prepared SMHBCs An/Bm. As shown from the figures, it is obvious that the electron densities in the sites that participate in the formation of the HOMOs of the prepared SMHBCs showed sharing of the phenyl ring of the alkoxy acid in the formation of their HOMOs with the predominance of the pyridyl base in the formation of their LUMOs. Moreover, there was no obvious effect of the length of the alkoxy group of either the base or the acid on the location of the electron density of the FMOs. The energy difference between Figure 6. The relationship between the polarizability of the SMHBCs (An/Bm) and the total mesophase stability.
Crystals 2020, 10, x 9 of 16 mesogenic parts [78,79]. Furthermore, the steric effect impacts the stability and the range of the mesophase rather than the polarizability, which has a different trend. It is clear that we could control the characteristics of the H-bonding, which could improve the properties of the individual components, by changing the parameters that are needed for special applications, such as the polarizability of the liquid crystalline material to be suitable for electro-optical applications [80][81][82].

Frontier Molecular Orbitals (FMOs) and Polarizability
Figures 8 and 9 demonstrate the predictable plots of the FMOs' highest occupied molecular orbital (HOMO) and the lowest unoccupied one (LUMO of the prepared SMHBCs An/Bm. As shown from the figures, it is obvious that the electron densities in the sites that participate in the formation of the HOMOs of the prepared SMHBCs showed sharing of the phenyl ring of the alkoxy acid in the formation of their HOMOs with the predominance of the pyridyl base in the formation of their LUMOs. Moreover, there was no obvious effect of the length of the alkoxy group of either the base or the acid on the location of the electron density of the FMOs. The energy difference between  Figures 8 and 9 demonstrate the predictable plots of the FMOs' highest occupied molecular orbital (HOMO) and the lowest unoccupied one (LUMO of the prepared SMHBCs An/Bm. As shown from the figures, it is obvious that the electron densities in the sites that participate in the formation of the HOMOs of the prepared SMHBCs showed sharing of the phenyl ring of the alkoxy acid in the formation of their HOMOs with the predominance of the pyridyl base in the formation of their LUMOs. Moreover, there was no obvious effect of the length of the alkoxy group of either the base or the acid on the location of the electron density of the FMOs. The energy difference between the FMOs could be used in the prediction of the ability of electron transformation from HOMO to LUMO during any electronic excitation process. It is clear from Table 4 that there is no significant impact of the alkoxy chain on the energy difference between the frontier orbitals. The global softness (S) = 1/∆E is the parameter that predicts the polarizability and the sensitivity of materials for the photoelectric property. Crystals 2020, 10

Molecular Electrostatic Potential (MEP)
The simulation of the distribution of charges in molecular electrostatic potential (MEP) of the structure of the SMHBCs An/Bm was done by the same method and with the same basis sets (Figure 10). The red region is considered the negatively charged atomic center and was estimated to be localized on the ester linkage of the H-bonds of the alkoxy acid carboxylate. On the other hand, part of the base and the electron donor alkoxy chains of the acid were expected to be blue regions and show atomic sites of the lowest negative charge. As shown in Figure 10, the length of the alkoxy group of the acid, as well as the base, does not affect the distribution of the charge mapping for An/Bm.

Conclusions
New five-membered rings of 1:1 SMHBLC complexes were reported. Mesomorphic and geometrical aspects were investigated. Optical measurements were carried out by DSC and POM, whereas the geometrical characterizations were performed by the DFT method. Mesomorphic investigations revealed that the mesogenic core (azomethine group) of the acid molecule has a role in the formation of enantiotropic SmA mesophase with wide smectogenic range and high thermal stability. DFT results revealed that the geometrical shapes of the present complexes are rod-like (calamitic structural shape). Moreover, the theatrical investigations revealed that the high dipole moment of the H-bonded complex illustrates the enhancement of the smectic mesophases. On the other hand, increasing the alkoxy chain length enhances the acid component and affects the polarizability successively. Finally, there was no obvious effect of the length of alkoxy group of either the base or the acid, the position of the electron density of the FMOs nor their energy gap.

Entropy Changes
The transition entropy changes (∆S/R) of all prepared 1:1 SMHBCs were estimated from DSC measurements and are collected in Table 1. Small magnitudes of entropy changes for an SmA-I transition are observed in addition to an irregular trend for all series with the length of the terminal flexible alkoxy groups. According to previous reports [83][84][85][86], the lower values of estimated entropy changes for conventional mesogens of low molar mass are due to the thermal cis/trans isomerization of the linkage. Furthermore, the enhanced shape anisotropy of molecules to pack more closely in the liquid crystal phase will result in higher transition temperatures and affect the change of the entropy [87].

Conclusions
New five-membered rings of 1:1 SMHBLC complexes were reported. Mesomorphic and geometrical aspects were investigated. Optical measurements were carried out by DSC and POM, whereas the geometrical characterizations were performed by the DFT method. Mesomorphic investigations revealed that the mesogenic core (azomethine group) of the acid molecule has a role in the formation of enantiotropic SmA mesophase with wide smectogenic range and high thermal stability. DFT results revealed that the geometrical shapes of the present complexes are rod-like (calamitic structural shape). Moreover, the theatrical investigations revealed that the high dipole moment of the H-bonded complex illustrates the enhancement of the smectic mesophases. On the other hand, increasing the alkoxy chain length enhances the acid component and affects the polarizability successively. Finally, there was no obvious effect of the length of alkoxy group of either the base or the acid, the position of the electron density of the FMOs nor their energy gap.