## Abstract

Thermotropic hydrogen-bonded ferroelectric binary liquid crystal mixtures comprising of *N*-carbamyl-l-glutamic acid (CGA) and p-n-alkyloxy benzoic acids (BAO) are investigated. Variation in the molar proportion of X and Y (where X=CGA+5BAO and Y=CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO) comprising of four series yielded 36 binary mixtures. Optical and thermal properties of these mixtures are meticulously studied in the present article. In addition to the traditional phases, a novel smectic ordering namely smectic X* is observed in all the four series. The aim of the investigation is to obtain abundance occurrence of smectic X* with a large thermal span, and hence, the proportions of the binary mixtures are so chosen that the prelude task is accomplished. Optical tilt angle in smectic X* and smectic C* phases is experimentally determined, and a theoretical fit is performed. Phase diagrams of the four series are constructed from the data obtained from the differential scanning calorimetry and correlated with the phases recorded by the polarising optical microscope studies. Thermal stability factor and thermal equilibrium are also premeditated.

## 1 Introduction

The liquid crystals possessing anisotropy property and with a tilted smectic C phase find wide applications [1]. In recent days, hydrogen-bonded liquid crystals (HBLC) are designed and synthesised based on the molecular reorganisation and self-assembly capability for commercial viability. Hydrogen bond interaction involves at least two functional groups: one acts as the donor of proton, and the other acts as the acceptor of electron, which gives rise to a complementary bond [2]. Formation of intermolecular hydrogen bonding between the two chemical moieties are well resolved using the fundamental Fourier transform infrared spectroscopy (FTIR) spectra recorded. Any chemical substances having covalent bonds, whether organic or inorganic, absorb various frequencies of electromagnetic radiation in the infrared region of the electromagnetic spectrum. The wavelength is inversely proportional to the frequency (ʋ=*c*/*λ*), and the energy is directly proportional to the frequency (*E*=*h*ʋ). Thus, the absorption of infrared gives rise to various energy transactions, and from it, vital information regarding the bond formation and the types of stretching can be deduced. Only the bonds having dipole moment that changes as a function of time are capable of absorption of infrared radiation. Uses of the infrared spectrum lies in identifying the identical molecules and determining the structural information about a molecule.

Paleos and his group [3–7] are the pioneers in investigating various types of HBLC. Many other researcher groups [8–12] also actively contribute by investigating several HBLC systems. Ferroelectricity is a phenomenon exhibited by these materials that possesses permanent spontaneous polarisation even in the absence of an external field, and re-orientation of the molecules takes place whenever an external field is applied [13]. This phenomenon is first observed by Meyer in the chiral liquid crystal systems with the help of symmetry considerations [14]. Such thermotropic ferroelectric liquid crystals also obtained through hydrogen bonding are referred to as the hydrogen-bonded ferroelectric liquid crystals (HBFLC).

One of the methods to obtain the desired physical properties from the mono component systems is to mix various mono component systems that exhibit interesting properties to form binary mixtures of suitable proportions. The advantages of binary mixtures are many compared to the mono component systems. These binary mixtures can be prepared in such a way so as to elevate the desirable thermal span of a specified phase of interest, to increase the magnitude of tilt angle in a desired phase, and so on. In the literature, many such studies on binary mixtures are reported [15–20].

Variation in the molar proportion of X and Y (where X=CGA+5BAO and Y=CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO) yielded 36 binary mixtures, and the properties exhibited by these mixtures are clearly discussed. Further characterising of a new smectic ordering namely smectic X* through binary mixtures and its physical, optical, and thermal properties are also studied in detail. The present work lies in comprehending the properties of various HBFLC binary systems through thermal analysis and scrutinising the thermal span of the individual phases.

## 2 Materials and Methods

The liquid crystalline textures are processed, analysed, and stored with Nikon polarising microscope equipped with Nikon digital CCD camera system (Nikon, Tokyo, Japan) with 5 mega pixels and 2560*1920 pixel resolutions, and the imaging software used is NIS. A temperature resolution of ±0.1 °C is obtained by Instec (Boulder, USA) HCS402-STC 200 temperature controller (Instec, USA). The transition temperatures and corresponding enthalpy values are obtained by the differential scanning calorimetry (DSC) (Shimadzu DSC-60, Kyoto, Japan). Chemicals p-n-alkyloxy benzoic acids (BAO) and *N*-carbamyl-l-glutamic acid (CGA) are supplied by Sigma Aldrich (Steinheim, Germany), and all the solvents used are of high-performance liquid chromatography (HPLC) grade.

### 2.1 Synthesis of Hydrogen-Bonded Ferroelectric Binary Complexes

Alkyloxy benzoic acids referred to as BAO with carbon number pentyloxy (5BAO) and nonyloxy to dodecyloxy (9BAO–12BAO) formed inter-molecular hydrogen bond with a dicarboxylic acid namely *N*-carbamyl-l-glutamic acid referred to as CGA yielding five hydrogen-bonded ferroelectric homologous series represented as CGA+*n*BAO. The reported synthetic procedure [21] is adopted for synthesising the present homologous series. HBFLC binary mixtures are formed by taking nine molar ratios of CGA+5BAO in steps of 0.1–0.9 with the other four HBFLC complexes. The binary mixtures thus formed are thoroughly mixed in isotropic state for obtaining homogeneity. CGA+5BAO and CGA+9BAO yielded nine binary mixtures with varying mole fractions of CGA+5BAO from 0.1 to 0.9. In a similar way, the other three HBFLC namely CGA+10BAO, CGA+11BAO, and CGA+12BAO with CGA+5BAO independently yielded 27 binary mixtures. Thus, in all, 36 binary mixtures comprising of CGA+5BAO with other CGA+*n*BAO HBFLC are prepared. As a representative case, the molecular structures of CGA+5BAO and CGA+9BAO are illustrated in Figure 1a and b, respectively.

## 3 Results and Discussion

The 36 binary mixtures isolated under the present investigation are insoluble in water and sparingly soluble in common organic solvents such as methanol, ethanol, and benzene and dichloro methane. All these 36 binary mixtures melt at specific temperatures below 64.4 °C (Tabs. 1–4). They also show high thermal and chemical stability when subjected to repeated thermal scans performed during the polarising optical microscope (POM) and DSC studies.

X=CGA+5BAO, Y=CGA+9BAO | Phase variance | DSC | Melt | X* | C* | G* | K |
---|---|---|---|---|---|---|---|

X=0.9, Y=0.1 | X* | H | 120.7 (20.54) | 146.4 (0.78) | |||

C | 141.2 (3.14) | 97.3 (15.80) | |||||

POM | 141.7 | 97.5 | |||||

X=0.8, Y=0.2 | X*G* | H | 111.3 (17.66) | 145.2 (5.27) | |||

C | 139.6 (5.93) | 89.3 (merged) | 85.6 (18.68) | ||||

POM | 140.2 | 89.8 | 85.9 | ||||

X=0.7, Y=0.3 | X*G* | H | 74.5 (22.35) | 143.7 (4.73) | |||

C | 140.2 (5.69) | 74.3 (merged) | 58.4 (15.54) | ||||

POM | 140.6 | 74.8 | 58.8 | ||||

X=0.6, Y=0.4 | X*C*G* | H | 75.07 (16.04) | 144.2 (3.76) | |||

C | 139.5 (5.95) | 68.9 (2.08) | 62.2 (merged) | 57.8 (19.54) | |||

POM | 140.2 | 69.4 | 62.7 | 58.4 | |||

X=0.5, Y=0.5 | X*C* | H | 66.1 (13.46) | 141.7 (3.96) | |||

C | 136.9 (5.76) | 84.8 (1.67) | 55.6 (11.7) | ||||

POM | 137.5 | 85.3 | 56.2 | ||||

X=0.4, Y=0.6 | X*C* | H | 83.9 (5.05) | 143.5 (5.27) | |||

C | 138.5 (6.58) | 92.7 (2.32) | 58.0 (10.25) | ||||

POM | 139.1 | 93.2 | 58.4 | ||||

X=0.3, Y=0.7 | X*C* | H | 84.03 (8.22) | 143.4 (4.28) | |||

C | 137.9 (5.32) | 92.1 | 58.2 (8.44) | ||||

POM | 138.4 | 92.5 | 58.5 | ||||

X=0.2, Y=0.8 | X*C* | H | 85.3 (19.17) | 142.1 (4.61) | |||

C | 137.6 (5.55) | 96.3 (2.25) | 59.6 (8.41) | ||||

POM | 138.2 | 96.8 | 60.2 | ||||

X=0.1, Y=0.9 | X*C* | H | 89.40 (25.69) | 142.8 (3.36) | |||

C | 138.4 (4.56) | 105 (2.23) | 52.7 (30.56) | ||||

POM | 138.9 | 105.4 | 53.2 |

H – heating run and C – cooling run observed in the DSC thermogram. POM – transition temperatures observation in the cooling run through POM. Enthalpy values in J/g are given in parentheses.

X=CGA+5BAO, Y=CGA+10BAO | Phase variance | DSC | Melt | Ch | X* | C* | K |
---|---|---|---|---|---|---|---|

X=0.9, Y=0.1 | X* | H | 117.9 (24.38) | 145.2 (6.15) | |||

C | 139.9 (5.82) | 97.1 (22.24) | |||||

POM | 140.5 | 97.6 | |||||

X=0.8, Y=0.2 | Ch | H | 109.2 (7.50) | 144.9 (3.69) | |||

C | 139.6 (6.30) | 78.0 (12.03) | |||||

POM | 140.2 | 78.6 | |||||

X=0.7, Y=0.3 | Ch C* | H | 67.36 (10.66) | 143.8 (2.89) | |||

C | 138.6 (6.54) | 81.3 (4.50) | 55.5 (5.66) | ||||

POM | 139.2 | 81.7 | 55.9 | ||||

X=0.6, Y=0.4 | Ch C* | H | 66.8 (15.08) | 141.9 (5.15) | |||

C | 137.3 (6.93) | 59.7 (merged) | 54.4 (16.97) | ||||

POM | 137.9 | 60.1 | 54.8 | ||||

X=0.5, Y=0.5 | X* | H | 64.5 (24.6) | 141.6 (5.01) | |||

C | 136.3 (6.0) | 53.9 (13.38) | |||||

X=0.4, Y=0.6 | X* | POM | 136.8 | 54.4 | |||

H | 67.5 (22.9) | 140.7 (4.07) | |||||

C | 135.9 (5.41) | 56.6 (11.9) | |||||

X=0.3, Y=0.7 | X*C* | POM | 136.4 | 57.2 | |||

H | 66.5 (20.48) | 143.2 (5.98) | |||||

C | 138.7 (9.25) | 54.8 (12.57) | |||||

X=0.2, Y=0.8 | X*C* | POM | 139.2 | 55.2 | |||

H | 64.4 (8.98) | 142.4 (6.47) | |||||

C | 138.4 (7.71) | 103.0 (2.0) | 52.9 (3.02) | ||||

POM | 138.9 | 103.4 | 73.5 | ||||

X=0.1, Y=0.9 | X*C* | H | 82.14 (21.18) | 140.9 (5.18) | |||

C | 137.3 (2.19) | 135.9 (5.99) | 106.8 (1.79) | 69.1 (8.77) | |||

POM | 136.4 | 107.3 | 69.4 |

H – heating run and C – cooling run observed in the DSC thermogram. POM – transition temperatures observation in the cooling run through POM. Enthalpy values in J/g are given in parentheses.

X=CGA+5 BAO, Y=CGA+11 BAO | Phase variance | DSC | Melt | Ch | X* | C* | K |
---|---|---|---|---|---|---|---|

X=0.9, Y=0.1 | Ch | H | 117.3 (21.07) | 143.0 (5.19) | |||

C | 137.5 (7.46) | 95.6 (20.42) | |||||

POM | 138.1 | 96.1 | |||||

X=0.8, Y=0.2 | X* | H | 111.5 (10.68) | ||||

C | 137.0 (6.01) | 82.3 (13.81) | |||||

POM | 137.5 | 82.6 | |||||

X=0.7, Y=0.3 | X* C* | H | 68.3 (1.94) | 142.6 (4.90) | |||

C | 137.6 (5.63) | 71.5 (24.73) | |||||

POM | 137.9 | 86.3 | 71.9 | ||||

X=0.6, Y=0.4 | X* C* | H | 69.2 (13.23) | 142.4 (4.75) | 84.2 (4.04) | ||

C | 137.9 (7.48) | 63.7 (merged) | 60.4 (20.19) | ||||

POM | 138.4 | 64.1 | 60.9 | ||||

X=0.5, Y=0.5 | X* | H | 70.2 (24.88) | 141.2 (4.1) | |||

C | 136.2 (4.48) | 63.1 (22.65) | |||||

POM | 136.8 | 63.7 | |||||

X=0.4, Y=0.6 | Ch X*C* | H | 68.4 (26.68) | 138.7 (5.60) | 103.9 (1.31) | ||

C | 138.4 (4.3) | 134.6 (6.1) | 100 (1.30) | 60.9 (27.0) | |||

POM | 138.9 | 135.2 | 100.4 | 61.4 | |||

X=0.3, Y=0.7 | X*C* | H | 67.8 (25.3) | 139.3 (4.74) | 110.5 (1.74) | ||

C | 138.5 (8.85) | 106.6 (1.70) | 61.6 (25.62) | ||||

POM | 139.2 | 107.2 | 62.1 | ||||

X=0.2, Y=0.8 | X*C* | H | 94.8 (50.84) | 139.9 (5.33) | 124.4 (2.95) | ||

C | 140.3 (3.45) | 119.4 (3.11) | 69.4 (32.74) | ||||

POM | 140.9 | 119.9 | 69.8 | ||||

X=0.1, Y=0.9 | X*C* | H | 94.8 (46.08) | 139.8 (4.95) | |||

C | 139.0 (3.28) | 135.6 (6.97) | 69.4 (32.92) | ||||

POM | 139.5 | 136.1 | 69.7 |

H – heating run and C – cooling run observed in the DSC thermogram. POM – transition temperatures observation in the cooling run through POM. Enthalpy values in J/g are given in parentheses.

X=CGA+5 BAO, Y=CGA+12BAO | Phase variance | DSC | Melt | Ch | X* | C* | K |
---|---|---|---|---|---|---|---|

X=0.9, Y=0.1 | X* | H | 68.7 (4.42) | 139.6 (6.43) | |||

C | 134.6 (4.09) | 60.1 (10.42) | |||||

POM | 134.9 | 60.5 | |||||

X=0.8, Y=0.2 | Ch C* | H | 67.9 (3.82) | 139.9 (4.93) | 109.2 (4.71) | ||

C | 138.3(1.25) | 134.5 (5.32) | 77.3 (20.32) | ||||

POM | 138.9 | 135.0 | 77.5 | ||||

X=0.7, Y=0.3 | Ch C* | H | 69.5 (16.95) | 138.7 (5.09) | |||

C | 137.8 (3.57) | 134.8 (6.09) | 63.0 (23.5) | ||||

POM | 138.5 | 135.2 | 63.2 | ||||

X=0.6, Y=0.4 | Ch C* | H | 69.9 (16.14) | 139.2 (4.61) | |||

C | 137.0 (1.77) | 134.8 (5.59) | 61.6 (23.32) | ||||

POM | 137.8 | 135.3 | 61.9 | ||||

X=0.5, Y=0.5 | X*C* | H | 75.9 (30.67) | 137.1 (7.56) | 122.4 (1.98) | ||

C | 132.7 (7.48) | 118.8 (2.07) | 66.9 (31.38) | ||||

POM | |||||||

X=0.4, Y=0.6 | Ch X*C* | H | 74.1 (19.35) | 136.4 (4.37) | 116.6 (1.25) | ||

C | 135.0 (1.35) | 132.2 (4.12) | 113.2 (1.24) | 65.7 (19.13) | |||

POM | 135.9 | 132.7 | 113.6 | 65.9 | |||

X=0.3, Y=0.7 | Ch X*C* | H | 73.0 (31.07) | 138.8 (5.53) | 111.0 (1.08) | ||

C | 137.3 (5.76) | 134.2 (6.36) | 107.4 (1.51) | 64.7 (30.0) | |||

POM | 134.4 | 134.8 | 107.8 | 65.0 | |||

X=0.2, Y=0.8 | Ch X*C* | H | 78.2 (24.1) | 138.4 (5.25) | 123.8 (1.97) | ||

C | 136.0 (3.17) | 133.0 (5.58) | 118.9 (1.58) | 68.4 (23.8) | |||

POM | 136.8 | 133.5 | 119.2 | 68.6 | |||

X=0.1, Y=0.9 | Ch X*C* | H | 81.0 (30.97) | 138.0 (5.82) | 128.8 (2.85) | ||

C | 139.0 (4.34) | 133.8 (7.03) | 124.8 (2.74) | 73.2 (30.06) | |||

POM | 139.8 | 134.5 | 125.1 | 73.5 |

### 3.1 Phase Variance and Identification

Four binary mixtures of CGA+5BAO with CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO, respectively, are obtained with mole fractions varying from 0.1 to 0.9 in steps of 0.1. Thus, the formed 36 binary mixtures are optically and thermally investigated. The phases exhibited by the various mole fractions along with their transition temperatures and corresponding enthalpy values are tabulated in Tables 1–4 along with their phase variance. The phases are characterised by POM for textural identification and are compared with the standard ones for textural identification [22]. Furthermore, DSC studies are performed at different scan rates to all the 36 binary mixtures to elucidate the enthalpy, transition temperature data, and order of the transitions.

The 36 binary mixtures exhibit rich phase polymorphism as tabulated in Table 5. In all, four liquid crystalline phases have been identified. The orthogonal phase observed in the binary mixtures is the cholesteric phase (Plate 1), and the tilted phases are smectic X* (partially grown smectic X* as Plate 2 and fully grown smectic X* as Plate 3), smectic C* (Plate 4), and smectic G* (Plate 5). Smectic X* is a new phase that has been identified in 29 of the total 36 binary mixtures. This type of smectic ordering has been characterised by various techniques and reported earlier by us [23–29]. Cholesteric droplets coalescing to four brushes are the identity of the cholesteric phase; the worm-like texture is referred to as smectic X*, while the broken focal conic texture is attributed to the smectic C* phase and the multi-coloured smooth mosaic is the characteristic texture of smectic G*. The general phase sequences of the four binary mixtures in cooling and heating runs are shown as follows.

Mesogen | Various mole fractions of CGA+5BAO | ||||||||
---|---|---|---|---|---|---|---|---|---|

0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | |

CGA+9BAO | X* C* | X* C* | X* C* | X* C* | X* C* | X* C* G* | X* G* | X* G* | X* |

CGA+10BAO | Ch X* C* | X* C* | X* C* | X* C* | X* | Ch C* | Ch C* | Ch | X* |

CGA+11BAO | X* C* | X* C* | X* C* | Ch X* C* | X* | X* C* | X* C* | X* | Ch |

CGA+12BAO | Ch X*C* | Ch X* C* | Ch X* C* | Ch X* C* | X* C* | Ch C* | Ch C* | Ch C* | X* |

Ch – cholesteric, X* – smectic X*, C* – smectic C*, and G* – smectic G*.

In the binary mixtures of CGA+5BAO and CGA+9BAO, the former is referred to as X and the latter as Y. The mole fraction is given in parentheses.

In the binary mixtures of CGA+5BAO and CGA+10BAO, the former is referred to as X and the latter as Y. The mole fraction is given in parentheses.

In the binary mixtures of CGA+5BAO and CGA+11BAO, the former is referred to as X and the latter as Y. The mole fraction is given in parentheses.

In the binary mixtures of CGA+5BAO and CGA+12BAO, the former is referred to as X and the latter as Y. The mole fraction is given in parentheses.

Single arrows indicate the monotropic transitions, while double arrows indicate the enantiotropic transitions.

### 3.2 Fourier Transform Infrared (FTIR) Spectroscopy

FTIR spectra for all the hydrogen-bonded ferroelectric complexes CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO and their respective 36 binary mixtures under the present study are recorded in the solid state (KBr) at room temperature. As a representative case, FTIR spectra in the solid state (KBr) at room temperature of CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO are depicted in Figure 2a–d, respectively. In the precursors, carboxylic acid exists in monomeric form, and the stretching vibration of C=O is observed at 1760 cm^{−1} [30–33]. When a hydrogen bond is formed between carboxylic acids, it results in lowering of the carbonyl frequency of saturated acids that has been detected in the present hydrogen-bonded ferroelectric complexes, CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO at 1682, 1682, 1674, and 1674 cm^{−1}, respectively. The O–H and C=O stretching are clearly observed in all the studied complexes, indicating the formation of hydrogen bond upon complexation.

### 3.3 DSC Studies

DSC thermograms are obtained in heating and cooling runs. The heating and cooling runs are performed with scan rates of 10 and 5 °C/min, respectively, for all the 36 binary mixtures. The respective equilibrium transition temperatures and corresponding enthalpy values of the mesogens of the four series are listed separately in Tables 1–4. POM studies also confirm these DSC transition temperatures. As a representative case, the DSC thermograms in the cooling run of nine binary mixtures corresponding to CGA+5BAO and CGA+10BAO are given in Figure 3a and b, and the corresponding data are tabulated in Table 2. All the phase transition temperatures of the corresponding phases discussed earlier concur reasonably with the data obtained by the POM studies.

### 3.4 Phase Diagram

The phase diagram is constructed from the textural data of the POM studies and correlated to the transition temperatures obtained by the DSC thermograms. The phase variance of precursor BAO is reported [34] as nematic, smectic C, and smectic G. CGA is observed to be non-mesogenic in nature. The homologues CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO exhibit rich phase polymorphism as reported by us earlier [35].

#### 3.4.1 Phase Diagram of CGA+5BAO and CGA+9BAO Binary Mixtures

Nine mole fractions of CGA+5BAO with CGA+9BAO are studied. The studied mole fractions are 0.1–0.9 of CGA+5BAO in CGA+9BAO. The obtained phase diagram is depicted in Figure 4a. The following points are drawn from the figure:

Three phases namely smectic X*, smectic C*, and smectic G* are observed in the present binary mixtures.

An interesting feature is inducement of smectic X* in all the binary mixtures.

The manifestation of abundance of smectic X* as a mono phase in the higher mole fractions of 0.9 with a wide thermal span of ∼44 °C is noticed.

Isotropic transition temperatures for the entire series remain unaltered.

Higher-ordered smectic G* phase induced from 0.6 to 0.8 mol fraction quenches the thermal span of smectic X* observed.

For quantitative analysis, the phase diagram is further examined in terms of area occupied by the mesophase. The area occupied by each of the phase exhibited is mathematically calculated. The percentage of the area for all the three phases namely smectic X*, smectic C*, and smectic G* is 68.60 %, 0.72 %, and 30.67 %, respectively. Thus, the percentage of smectic X* and smectic G* alone accounts for 99.2 % of the total area.

The percentages of the precursor phases along with the binary mixture phases are tabulated in Table 6. It can be noticed that the thermal span of smectic X* increased by 52.7 times compared to its precursor CGA+9BAO. Furthermore, the precursor CGA+9BAO exhibits phases Cholesteric, smectic X*, smectic C*, and smectic G*, and the cholesteric phase has been completely wiped out in the binary mixtures of CGA+5BAO and CGA+9BAO. Thus, the manifestation and stabilisation of smectic X* phase in the binary mixtures are accomplished.

Mesogen | Phase variance | Percentage of individual phases in the entire mesogenic range | ||||
---|---|---|---|---|---|---|

Ch | X* | C* | G* | Total % | ||

CGA+5BAO, CGA+9BAO | X* C* G* | – | 68.6 | 0.72 | 30.67 | 99.99 |

CGA+5BAO, CGA+10BAO | Ch X* C* | 31.92 | 49.48 | 18.59 | – | 99.99 |

CGA+5BAO, CGA+11BAO | Ch X* C* | 3.9 | 64.38 | 31.61 | – | 99.98 |

CGA+5BAO, CGA+12BAO | Ch X* C* | 6.5 | 12.46 | 81.0 | – | 99.97 |

CGA+5BAO | X* | – | 100 | – | – | 100 |

CGA+9BAO | Ch X* C* G* | 41.1 | 1.3 | 15.6 | 41.8 | 99.8 |

CGA+10BAO | Ch X* C* | 31.57 | 1.43 | 35.88 | 31.10 | 99.98 |

CGA+11BAO | Ch X* C* G* | 24.24 | 2.42 | 49.24 | 24.24 | 99.99 |

CGA+12BAO | Ch X* C* | 0.090 | 21.76 | 78.14 | – | 99.99 |

Ch – cholesteric, X* – smectic X*, C* – smectic C*, and G* – smectic G*.

#### 3.4.2 Phase Diagram of CGA+5BAO and CGA+10BAO Binary Mixtures

CGA+5BAO along with CGA+10BAO forms nine binary mixtures with the increment of mole fraction in steps of 0.1 and continues till 0.9. The following conclusions are made from the phase diagram obtained for CGA+5BAO and CGA+10BAO binary mixtures, which is depicted in Figure 4b.

Cholesteric, smectic X*, and smectic C* are the three mesogenic phases observed in the phase diagram.

Clearing point temperatures of the entire binary mixtures remains almost same.

Smectic X* is observed in six binary mixtures with wide thermal span.

Suppression of smectic X* phase takes place in 0.1–0.4 mol fraction of the binary mixtures, and inducement of smectic C* phase is noticed.

Replacing the smectic X* phase, the appearance of cholesteric phase is observed from 0.6 to 0.8 mole fractions, while the smectic C* is evinced from 0.6 to 0.7 mol fractions.

The area occupied by the individual mesogenic phases is calculated mathematically from this phase diagram also. The percentages of cholesteric, smectic X*, and smectic C* are found to be 31.92 %, 49.48 %, and 18.59 %, respectively. The phases of the precursors namely CGA+5BAO and CGA+10BAO are also analysed.

It is interesting to note that the precursor CGA+10BAO also exhibits three mesogenic phases namely cholesteric, smectic X*, and smectic C*, as like as the binary mixtures. However, the percentages of the thermal span of smectic X* in CGA+10BAO and binary mixtures are 1.43 % and 49.43 %, respectively (Tab. 6). Hence, the thermal span of smectic X* has enriched by 34.6 times in the binary mixtures compared to the CGA+10BAO.

#### 3.4.3 Phase Diagram of CGA+5BAO and CGA+11BAO Binary Mixtures

Nine binary mixtures formed between nine mole fractions of CGA+5BAO and CGA+11BAO in steps of 0.1 are studied, and the following observations are made from the phase diagram (Fig. 4c) obtained for these binary mixtures:

Phase diagram comprises of three liquid crystalline phases namely cholesteric, smectic X*, and smectic C*.

Out of nine binary mixtures, eight exhibit smectic X* mesogenic phase with a notable thermal range.

Isotropic transition temperatures for this series also remain unaltered.

Smectic C* phase is observed in 0.1–0.7 mol fractions quenching the thermal span of smectic X*.

Phase diagram is further examined in terms of area occupied by individual mesophases mathematically. The percentages of cholesteric, smectic X*, and smectic C* are found to be 3.9 %, 64.38 %, and 31.61 %, respectively.

CGA+11BAO and its corresponding binary mixtures formed with CGA+5BAO exhibit symmetric mesogenic phases namely cholesteric, smectic X*, and smectic C*. However, the percentages of the thermal span of smectic X* in CGA+11BAO and binary mixtures are 2.42 % and 64.34 %, respectively. Hence, the thermal span of smectic X* has enriched by 26.6 times in the binary mixtures compared to the CGA+11BAO.

#### 3.4.4 Phase Diagram of CGA+5BAO and CGA+12BAO Binary Mixtures

CGA+5BAO with CGA+12BAO forms nine binary mixtures in steps of 0.1 mol fraction. Following deductions can be made from the phase diagram constructed for these binary mixtures, which is depicted in Figure 4d.

This binary mixtures also exhibits three mesogenic phases namely cholesteric, smectic X*, and smectic C*.

Here also, the isotropic transition temperatures for the entire series remain unaltered.

Smectic X* prevails in the six of the binary mixtures formed.

Smectic C* phase is observed in all the mole fractions except 0.9 quenching the thermal span of smectic X*.

The phase diagram of the present binary mixtures is also further examined in terms of area occupied by the mesophase. The percentages of cholesteric, smectic X*, and smectic C* are found to be 6.5 %, 12.46 %, and 81 %, respectively.

Identical phase sequences (cholesteric, smectic X*, and smectic C*) are obtained for CGA+12BAO and its corresponding binary mixtures. However, the percentages of the thermal span of smectic X* in CGA+12BAO and binary mixtures are obtained to be 21.6 % and 12.46 %, respectively. Only in this case, the thermal span of smectic X* has decreased by 1.74 times in the binary mixtures compared to the CGA+12BAO.

### 3.5 Factors Influencing the Abundance Occurrence of Smectic X* in Binary Mixtures

It is observed that 29 out of the 36 binary mixtures exhibit smectic X* phase with wide thermal span. The possible reasons for the rich abundance [36] of this smectic ordering phase are detailed:

Smectic X* phase depends more on molecular structure of the constituent molecules, to be precise, more on the length of the chains of the terminal alkyloxy groups.

Smectic X* phase appears to be exhibited predominantly by the molecules having two alkyloxy terminal chains on either sides of the chemical moieties.

Symmetrical molecular structures existing in the system favours the occurrence of smectic X* phase.

Branching of terminal chain enhances the probability of the existence of smectic X*phase.

In all the four binary series, the chemical composition on either side of the rigid core (CGA) constitutes large terminal alkyloxy chain length (BAO). Thus, the abundance of the smectic X* phase is attributed to the chemical structure of the present mesogens.

#### 3.5.1 Factors Influencing the Abundance Occurrence of Smectic X* in CGA+5BAO and CGA+9BAO Binary Mixtures

The phase variances exhibited by nine binary mixtures that are formed between CGA+5BAO and CGA+9BAO with various mole fractions ranging from 0.1 to 0.9 are tabulated in Table 5, while the percentages of individual mesogenic phase spreaded over the entire mesogenic range of the precursors along with the binary systems are tabulated in Table 6. Reasons for the abundance occurrence of smectic X* phase are discussed as follows:

CGA+5BAO complex exhibits mono phase variance namely smectic X* phase, while CGA+9BAO exhibits four mesogenic phases namely cholesteric, smectic X*, smectic C*, and smectic G*.

Annihilation of cholesteric phase (41.1 %–0 %, Tab. 6) is noticed, which leads to the enhancement of mesogenic thermal range of smectic X* phase in the binary systems formed whose percentage increased from 1.3 % to 68.6 % (Tab. 6). This abundance of the smectic X* phase is attributed to the increased alkyloxy chain length formed between the binary mixtures CGA+5BAO and CGA+9BAO.

The rigid core CGA is grouped with flexible alkyloxy chemical moiety namely benzoic acids (5BAO and 9BAO) on either ends that favours the inducement of smectic X* phase in all the molar proportions prepared due to the increased chain length.

Symmetrical molecular structures namely 5BAO is attached to either ends of the CGA forming CGA+5BAO complex (Fig. 1a). In a similar manner, symmetrical CGA+9BAO complex is also formed (Fig. 1b). As a result, these two complexes form binary mixtures with different molar proportions, which are also symmetrical in nature. Thus, the symmetrical structure triggers the enhancement of smectic X* phase in all the nine binary mixtures.

As CGA+5BAO is a mono phase variant system, 0.9 mol fraction of CGA+5BAO in CGA+9BAO exhibits mono phase variance.

#### 3.5.2 Factors Influencing the Abundance Occurrence of Smectic X* in CGA+5BAO and CGA+10BAO Binary Mixtures

The phase variance exhibited by CGA+5BAO and CGA+10BAO binary mixtures and the corresponding percentage of the individual phases are tabulated in Tables 5 and 6, respectively. Explanations for the abundance occurrence of smectic X* phase is discussed as follows:

CGA+10BAO exhibits three mesogenic phases namely cholesteric, smectic X*, and smectic C*, while CGA+5BAO complex exhibits mono phase variance namely smectic X* phase.

In the binary systems, cholesteric phase prevails in four mole fractions (0.1, 0.6, 0.7, and 0.8), which concludes the inducement to be a discontinuous manner, which may be attributed to the lengthy flexible chains attached to either ends of the CGA.

Enhancement of mesogenic thermal range of smectic X* phase in the binary systems is noticed, which increased from 1.3 % to 49.48 % (Tab. 6). This abundance of the smectic X* phase is attributed again to the increased alkyloxy chain length formed between the binary mixtures CGA+5BAO and CGA+10BAO.

Attachment of alkyloxy groups, i.e. 5BAO and 10BAO, on either ends of the rigid core CGA favours the inducement of smectic X* phase in most of the molar proportions (six out of nine) prepared. In the remaining mixtures, CGA+10BAO phase variance dominates CGA+5BAO, and hence, smectic X* phase is suppressed with cholesteric and smectic C* phases.

Symmetrical molecular structures namely 5BAO and 10BAO trigger the enhancement of smectic X* phase in six of the binary mixtures.

The 0.9 mol fraction of CGA+5BAO in CGA+10BAO exhibits mono phase variance smectic X* as CGA+5BAO is a mono phase variant system.

#### 3.5.3 Factors Influencing the Abundance Occurrence of Smectic X* in CGA+5BAO and CGA+11BAO Binary Mixtures

Tables 5 and 6 give a clear picture regarding the phase variance and the percentage of the individual mesophases exhibited by the nine binary mixtures that are formed between CGA+5BAO and CGA+11BAO. Detailed arguments relating to the abundance occurrence of smectic X* phase is given in the following:

Enhancement in the thermal span of smectic X* phase happens by suppressing the cholesteric phase in eight of the binary mixtures.

Drastic increase in the thermal span of smectic X* phase, i.e. from 2.42 % to 64.38 %, is noticed (Tab. 6), which is attributed to the alkyloxy chain length increment.

Annihilation of other mesogenic phases is noticed in the 0.9 mol fraction of CGA+5BAO and in the 0.1 mol fraction of CGA+11BAO, where the cholesteric phase dominates due to the abundance of its thermal range (24.24 %) observed in the succeeding complex.

Cholesteric phase is observed only in two of the binary mixtures prepared, which are suppressed by smectic X* and smectic C* phases in rest of the mixtures due to the variation in the molar proportion favouring the inducement of smectic orderings.

Alkyloxy chain length increment and the symmetrical structures on either sides of the rigid core favour the enhancement in the thermal range of smectic X* phase.

#### 3.5.4 Factors Influencing the Smectic X* Phase in CGA+5BAO and CGA+12BAO Binary Mixtures

Phase variance and the percentage of the mesogenic phases exhibited by the nine binary mixtures that are formed between CGA+5BAO and CGA+12BAO with various mole fractions ranging from 0.1 to 0.9 are tabulated in Tables 5 and 6, respectively. Favourable points regarding the occurrence of smectic X* phase are discussed as follows:

Surprisingly, the thermal span of the smectic X* phase is decreased from 21.76 % to 12.46 % (Tab. 6) due to the frail stability possessed by the dodecyloxy carbon chain attached.

In four of the binary mixtures, template of the phase variance exhibited by CGA+12BAO is noticed.

Annihilation of smectic X* phase happens, even though the molar fraction of CGA+5BAO exhibiting mono phase variant is increased (0.6, 0.7, and 0.8) with an exemption of 0.9 molar fraction, declaring the supremacy of cholesteric and smectic C* phase prevalence.

Variation in the intensity of CGA+5BAO dominates the phase variance, which is clearly visualised. CGA+5BAO and 0.9 mol fraction of CGA+5BAO in CGA+12BAO exhibit mono phase variant smectic X*.

### 3.6 Odd–Even Effect at Smectic X* Transition

Chemical structure of the mesogens contributes to the odd–even effect observed in transition temperatures and enthalpy values possessed by them. In even carbon number mesogens, the nature of the terminal groups attached is to enhance the molecular anisotropy and hence the molecular order, whereas in the odd carbon number, it has the opposite effect. Increment in carbon chain length is proportional to the flexibility of the structure, which leads to the suppression in the odd–even effect. The results of the odd–even effect observed in the present binary mixtures formed from the hydrogen-bonded complexes are in accordance with the quantitative calculations proposed and reported earlier [37–41].

In the present intermolecular hydrogen-bonded ferroelectric liquid crystalline binary mixture molecules, CGA is considered to be the rigid or core molecule, whereas benzoic acids form the flexible part. The rigid core length varies with an increase in the alkyloxy benzoic acid carbon chain. The rich phase polymorphism and the associated enthalpy values exhibited by these binary mixtures (Tabs. 1–4) with an increment in the alkyloxy carbon chain length are thus attributed to this part of the chemical structure. Moreover, the length (*l*) of the total HBFLC varies with the alkyloxy carbon chain length, while the width (*d*) remains constant. Thus, the altering of *l*/*d* ratio triggers the phase variance in the homologous series in turn influences the phase transition temperatures and the corresponding enthalpy values. Hence, the rigid cores and *l*/*d* ratio play a vital role in establishing the pronounced odd–even effect as evinced in the present binary mixtures.

In two binary mixtures namely CGA+5BAO with CGA+9BAO and CGA+5BAO with CGA+11BAO, the odd–even effect is noticed across the enthalpy values of the smectic X* phase transition, which is represented in Figure 5. Plots are constructed with the corresponding enthalpy values along *y*-axis and the mole fractions along *x*-axis. From Figure 5, it can be observed that the magnitudes of the enthalpy values corresponding to the even homologous mole fraction exhibit one type of behaviour, while their odd counter parts show a different pattern. In the literature, such behaviour has been reported [38] and is referred to as the odd–even effect.

### 3.7 Thermal Equilibrium Analysis

Thermal law of equilibrium is verified in the DSC thermal analysis cycles, i.e. total enthalpy values evolved out of different phases observed in the heating cycle are compared with the enthalpy values obtained for the same phases in the cooling cycle for binary mixtures corresponding to CGA+9BAO, CGA+10BAO, CGA+11BAO, and CGA+12BAO formed with CGA+5BAO. For practical implementation, the summation of the enthalpy values possessed by the different phases in the heating cycle (endothermic reaction) will be slightly higher than the enthalpy value possessed by the same binary mixtures in the cooling cycle (exothermic reaction). As a representative case, the thermal equilibrium of CGA+5BAO and CGA+12BAO binary mixtures is depicted in Figure 6. The amount of heat evolved is equal to the heat absorbed in the binary mixtures. This thermal equilibrium condition prevails when all the transitions are enantiotropic. However, the deviation from the magnitudes in heating to cooling cycles may be attributed to the monotropic transitions observed.

### 3.8 Thermal Stability of Smectic X*

It is reported [42, 43] that when the liquid crystalline molecules have two symmetric end chains, the phase transition temperatures and the temperature ranges are affected. The molecular weights of terminal chain could be considered as the measure of balancing, and if they are nearly equal, the system is balanced. In other words, the system is symmetric about its molecular short axis.

Phase stability is one of the important parameters that govern the utility of the mesogen. In the present case, phase stability of smectic X* is discussed. The term phase stability can be attributed to isotropic to smectic X* transition temperature as well to the temperature range of smectic X* phase. It is reasonable to consider both the above factors and define a parameter called stability factor (*S*). As a representative case, the stability factor for smectic X* (S_{X*}) is given by

where *T*_{mid} is the mid smectic X* temperature, and Δ*T*_{X*} is the smectic X* thermal range. In this manner, the thermal stability of cholesteric, smectic C*, and smectic G* exhibited by CGA+5BAO with CGA+9BAO, CGA+5BAO with CGA+10BAO, CGA+5BAO with CGA+11BAO, and CGA+5BAO with CGA+12BAO binary mixtures are calculated and tabulated in Table 7a–d, respectively, for all the 36 binary mixtures. It can be noticed that the variation in the molar proportion alters the thermal stability of the phases with respect to their thermal span from the data obtained from Tables 7a–d.

X=CGA+5BAO, Y=CGA+9BAO | X* | C* | G* |
---|---|---|---|

X=0.9, Y=0.1 | 4711 | 524.3 | – |

X=0.8, Y=0.2 | 5758 | 323.5 | – |

X=0.7, Y=0.3 | 7060 | – | 1060 |

X=0.6, Y=0.4 | 7362 | 437 | 271 |

X=0.5, Y=0.5 | 5787 | 2049 | – |

X=0.4, Y=0.6 | 5291 | 2612 | – |

X=0.3, Y=0.7 | 5267 | 2546 | – |

X=0.2, Y=0.8 | 4824 | 2864 | – |

X=0.1, Y=0.9 | 4055 | 3130 | – |

X* – smectic X*, C* – smectic C*, and G* – smectic G*.

X=CGA+5BAO, Y=CGA+10BAO | Ch | X* | C* |
---|---|---|---|

X=0.9, Y=0.1 | – | 3173 | 1898 |

X=0.8, Y=0.2 | 6702 | – | – |

X=0.7, Y=0.3 | 6300 | – | 1764 |

X=0.6, Y=0.4 | 7643 | – | 305 |

X=0.5, Y=0.5 | 7831 | – | – |

X=0.4, Y=0.6 | 7619 | – | 254.9 |

X=0.3, Y=0.7 | – | 4262 | 3854 |

X=0.2, Y=0.8 | – | 4272 | 2632 |

X=0.1, Y=0.9 | 191.2 | 3531 | 3315 |

Ch – cholesteric, X* – smectic X*, and C* – smectic C*.

X=CGA+5BAO, Y=CGA+11BAO | Ch | X* | C* |
---|---|---|---|

X=0.9, Y=0.1 | 4883 | – | – |

X=0.8, Y=0.2 | – | 5997 | 1102 |

X=0.7, Y=0.3 | – | 6909 | 4561 |

X=0.6, Y=0.4 | – | 7479 | 186.6 |

X=0.5, Y=0.5 | – | 7136 | 147 |

X=0.4, Y=0.6 | 518 | 4058 | 3145 |

X=0.3, Y=0.7 | 3909 | 3786 | |

X=0.2, Y=0.8 | – | 2713 | 4719 |

X=0.1, Y=0.9 | – | 2506 | 4719 |

Ch – cholesteric, X* – smectic X*, and C* – smectic C*.

X=CGA+5BAO, Y=CGA+12BAO | Ch | X* | C* |
---|---|---|---|

X=0.9, Y=0.1 | – | 6310 | – |

X=0.8, Y=0.2 | 6057 | – | – |

X=0.7, Y=0.3 | 408 | – | 7101 |

X=0.6, Y=0.4 | 298 | 7188 | – |

X=0.5, Y=0.5 | 1749 | – | 4818 |

X=0.4, Y=0.6 | 374 | 2331 | 4248 |

X=0.3, Y=0.7 | 420 | 3237 | 3674 |

X=0.2, Y=0.8 | 403 | 1775 | 4719 |

X=0.1, Y=0.9 | 709 | 1163 | 5108 |

Ch – cholesteric, X* – smectic X*, and C* – smectic C*.

### 3.9 The Cox Ratio

Navard and Cox [44, 45] executed a new experimental method in determining the order of phase transition through a number *N*, where the scan rate of the sample or the weight of the sample can be a varying parameter with respect to the phase transition peak height obtained by the DSC thermograms. Navard and Haudin [44, 45] gave the theoretical derivation for the isothermal and non-isothermal first-order and second-order phase transitions. In the present work, for practical convenience, the variation in the scanning rate, i.e. 5 and 10 °C/min, has been considered. According to the Cox theory, the first- and second-order transitions can be classified based on the ratio (Nc) of the measured phase transition peak heights. The ratio (Nc) is 1<Nc ≥ √2 for an isothermal first-order transition, and when Nc=2, the order of transition is classified as second-order transition.

Tables 8a–d illustrate the Cox ratio of various mesophases corresponding to the CGA+5BAO with CGA+nBAO (*n*=9, 10, 11, and 12) binary mixtures.

Binary mixture X=CGA+5BAO, Y=CGA+9BAO | Phase variance | Ratio | Order of transition |
---|---|---|---|

X=0.9, Y=0.1 | X* | 2.10 | Second |

X=0.8, Y=0.2 | X* | 1.90 | Second |

G* | 0.66 | First | |

X=0.7, Y=0.3 | X* | 1.00 | First |

G* | 1.20 | First | |

X=0.6, Y=0.4 | X* | 1.60 | Second |

C* | 1.40 | First | |

G* | 0.80 | First | |

X=0.5, Y=0.5 | X* | 1.51 | Second |

C* | 1.00 | First | |

X=0.4, Y=0.6 | X* | 1.50 | Second |

C* | 1.20 | First | |

X=0.3, Y=0.7 | X* | 1.50 | Second |

C* | 1.51 | Second | |

X=0.2, Y=0.8 | X* | 1.44 | First |

C* | 1.40 | First | |

X=0.1, Y=0.9 | X* | 1.40 | First |

C* | 1.50 | Second |

X* – smectic X*, C* – smectic C*, and G* – smectic G*.

Binary mixture X=CGA+5BAO, Y=CGA+10BAO | Phase variance | Ratio | Order of transition |
---|---|---|---|

X=0.9, Y=0.1 | X* | 0.66 | First |

X=0.8, Y=0.2 | Ch | 1.19 | First |

X=0.7, Y=0.3 | Ch | 1.70 | Second |

C* | 1.70 | Second | |

X=0.6, Y=0.4 | Ch | 1.85 | Second |

C* | 1.70 | Second | |

X=0.5, Y=0.5 | X* | 1.60 | Second |

X=0.4, Y=0.6 | X* | 1.20 | First |

C* | 0.62 | First | |

X=0.3, Y=0.7 | X* | 1.30 | First |

C* | 1.50 | Second | |

X=0.2, Y=0.8 | X* | 1.30 | First |

C* | 2.70 | Second | |

X* | 1.60 | Second | |

C* | 1.80 | Second |

Ch – cholesteric, X* – smectic X*, and C* – smectic C*.

Binary mixture X=CGA+5BAO, Y=CGA+11BAO | Phase variance | Ratio | Order of transition |
---|---|---|---|

X=0.9, Y=0.1 | Ch | 1.70 | Second |

X=0.8, Y=0.2 | X* | 1.60 | Second |

X=0.7, Y=0.3 | X* | 1.80 | Second |

C* | 1.30 | First | |

X=0.6, Y=0.4 | X* | 1.70 | Second |

C* | 1.00 | First | |

X=0.5, Y=0.5 | X* | 1.30 | First |

X=0.4, Y=0.6 | Ch | 1.50 | Second |

X* | 1.40 | First | |

C* | 2.00 | Second | |

X=0.3, Y=0.7 | X* | 1.40 | First |

C* | 1.60 | Second | |

X=0.2, Y=0.8 | X* | 1.30 | First |

C* | 1.60 | Second | |

X=0.1, Y=0.9 | X* | 1.40 | First |

C* | 1.20 | First |

Ch – cholesteric, X* – smectic X*, and C* – smectic C*.

Binary mixture X=CGA+5BAO, Y=CGA+12BAO | Phase variance | Ratio | Order of transition |
---|---|---|---|

X=0.9, Y=0.1 | X* | 1.20 | First |

X=0.8, Y=0.2 | Ch | 2.10 | Second |

C* | 1.70 | Second | |

X=0.7, Y=0.3 | Ch | 2.00 | Second |

C* | 1.50 | Second | |

X=0.6, Y=0.4 | Ch | 1.80 | Second |

C* | 1.90 | Second | |

X=0.5, Y=0.5 | X* | 1.60 | Second |

C* | 1.50 | Second | |

X=0.4, Y=0.6 | Ch | 1.40 | First |

X* | 2.10 | Second | |

C* | 1.80 | Second | |

X=0.3, Y=0.7 | Ch | 1.80 | Second |

X* | 1.40 | First | |

C* | 1.80 | Second | |

X=0.2, Y=0.8 | Ch | 1.20 | First |

X* | 1.40 | First | |

C* | 1.60 | Second | |

X=0.1, Y=0.9 | Ch | 1.70 | Second |

X* | 1.20 | First | |

C* | 0.70 | First |

Ch – cholesteric, X* – smectic X*, and C* – smectic C*.

### 3.10 Optical Tilt Angle Measurement

#### 3.10.1 Tilt Angle Measurement in Smectic X*

The primary-order parameter, i.e. optical tilt angle, is experimentally measured in smectic X* phase by the optical extinction method [46] in the 29 binary mixtures exhibiting smectic X* phase (Tabs. 1–4). Tilt angle variations in smectic X* of various mole fractions 0.1, 0.2, 0.7, 0.8, and 0.9 pertaining to CGA+5BAO in CGA+9BAO binary mixture is depicted in Figure 7a. Similarly, tilt angle variations in smectic X* of various mole fractions 0.1, 0.2, 0.3, and 0.4 pertaining to CGA+5BAO in CGA+10BAO binary mixture is depicted in Figure 7b. Tilt angle variations in smectic X* of various mole fractions 0.1, 0.5, and 0.6 pertaining to CGA+5BAO in CGA+11BAO binary mixture is depicted in Figure 7c.

In Figure 7a–c, the solid line indicates the theoretical fit obtained from the power law where the critical exponent value of mean field theory is found to be 0.5 as optimum. The symbol indicates the experimental data obtained from the optical extinction technique. In all the three figures, it can be noticed that the tilt angle value measured increases with a decrease in temperature and attains a saturated value thereby indicating the viewing angle possessed by the binary mixtures when implemented for the display device applications. The fair magnitudes of the tilt angle obtained are attributed to the direction of the soft covalent hydrogen bond interaction that spreads along the short molecular long axis with finite inclination [47].

Tilt angle is a primary-order parameter [48], and the temperature variation is estimated by fitting the observed data of *θ* (*T*) to the relation

The critical exponent *β* value estimated by fitting the data of *θ* (*T*) to the preceding equation is found to be 0.50 to agree with the mean field prediction [48, 49]. Furthermore, the agreement of magnitude of *β* (0.5) with mean field value (0.5) infers the long-range interaction of transverse dipole moment for the stabilisation of tilted smectic phases.

The highest magnitude of tilt angle in smectic X* phase is observed to be ∼17° and the lowest to be ∼9°. This fair magnitude of the tilt angle is attributed to the enhanced orientational disorder introduced by the lengthy flexible part of the molecule, contributing to the ordered smectic X* phase.

#### 3.10.2 Tilt Angle in Smectic C*

The same optical extinction method used for measuring the tilt angle value for smectic X* phase is followed for measuring the tilt angle in 24 binary mixtures exhibiting smectic C* phase (Tabs. 1–4). Tilt angle variations in smectic C* of various mole fractions 0.1, 0.2, 0.3, 0.4, 0.6, and 0.7 pertaining to CGA+5BAO in CGA+11BAO binary mixture are depicted in Figure 8a. Similarly, tilt angle variations in smectic C* of various mole fractions 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 pertaining to CGA+5BAO in CGA+12BAO binary mixtures are depicted in Figure 8b and c, respectively.

In Figure 8a–c, the solid line indicates the theoretical fit obtained from the critical exponent value of mean field theory, and the symbols indicate the experimental data obtained from the optical extinction technique. It is observed that the tilt angle increases with decreasing temperature and attains a saturation value.

## 4 Conclusions

The 36 binary mixtures of thermotropic HBFLC comprising of four homologous series are optically and thermally characterised. A new smectic ordering smectic X* has been observed in 29 binary mixtures, and its tilt angle has been experimentally measured and fitted to a theoretical value along with the traditional smectic C*, which is observed in 24 binary mixtures.The hydrogen bonding is established by the FTIR studies.Order of the phase transition is quantitatively examined by the Cox ratio analysis.

## Acknowledgments

The authors acknowledge the financial support rendered by BRNS-DAE, Mumbai, vide 2012/34/35/BRNS. Infrastructural support provided by Bannari Amman Institute of Technology is gratefully acknowledged.

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**Received:**2015-4-7

**Accepted:**2015-6-8

**Published Online:**2015-7-1

**Published in Print:**2015-9-1

©2015 by De Gruyter