Phase Sequence, Kinetics of Crystallization and Molecular Dynamics of the Chiral Liquid Crystalline Compound Forming a Hexatic Smectic Glass

Abstract

The vitrification of the antiferroelectric hexatic smectic X_A* phase and cold crystallization are reported for (S)-4′-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[5-(2,2,3,3,4,4,4-heptafluorobutoxy) heptyl-1-oxy]benzoate. The kinetics of isothermal cold crystallization and melt crystallization are investigated, revealing that both are controlled mainly by diffusion, as indicated by decrease in the characteristic crystallization time with increasing temperature of crystallization, with an activation energy of 114 kJ/mol. A weak relaxation process is detected in a crystal phase, with an activation energy of 38 kJ/mol, implying the conformationally disordered crystal phase. The estimated fragility parameter of the investigated glass former is equal to 94.5, which indicates rather high fragility.

1. Introduction

Tilted smectic liquid crystalline phases formed by chiral molecules and exhibiting ferro- or antiferroelectric properties are investigated in relation to their potential use in liquid crystal displays, as they show bistable or tristable switching in the external electric field, respectively [1,2,3,4,5,6,7,8,9]. The most promising is the orthoconic smectic C_A* phase (SmC_A*), which shows the tristable switching and where the tilt angle of molecules is close or equal to 45°. Because of the high tilt angle, the perfect dark state of the display based on the orthoconic SmC_A* phase can be obtained despite some defect in the sample alignment, which would lead to a non-zero transmission of light for a lower tilt angle [4]. The SmC_A* phase, with a high tilt angle and with a wide temperature range of stability, is formed, e.g., by the compounds from the 3FmX₁PhX₂6 family [10,11], denoted in this paper as mX₁X₂6 (Figure 1). The molecular structure of mX₁X₂6 is based on the MHPOBC compound, which is the first liquid crystalline substance for which the antiferroelectric properties were reported [3]. The mX₁X₂6 molecule consists of a rigid core built of three aromatic rings and two terminal chains. The single benzene ring may be substituted with one or two fluorine atoms, which was shown to shift the phase transition temperatures [10,11]. The non-terminal chain is partially fluorinated, which is considered to be the cause of the high tilt angle [5]. For some compounds, the SmC_A* phase undergoes the transition to the hexatic smectic phase, either SmI_A* or SmF_A* on cooling, where the bond-orientational order appears in the smectic layers [12]. The SmI_A* or SmF_A* phases differ only by direction of the tilt of molecules in relation to the direction of the bond-orientational order within the smectic layers; therefore, it is difficult to distinguish them, and herein they are both denoted here as SmX_A*. The transition to the hexatic SmX_A* phase was observed for MHPOBC [3] and for some MHPOBC-based compounds with a partially fluorinated terminal chain, namely for 1F7 [13,14], 3F6Bi [15], 4H6 [16], 4HH6 [17], 5HH6 [18] and 5HH7 [19]. It is worth noting that most of these compounds (except 1F7) are not fluorosubstituted at the benzene ring. The vitrification of the SmC_A* and SmX_A* phases results in a glass with a partial positional order and anisotropic properties, which can be applied, e.g., in optical devices [20,21,22,23,24]. In this paper, we present the results for the 7HH6 compound (from the mX₁X₂6 family, see Figure 1), the phase sequence of which on heating is Cr (331.0 K) SmC_A* (389.5 K) SmC* (393.6 K) SmA* (396.2 K) Iso. Differential scanning calorimetry (DSC) is able to detect the SmC_A* → SmX_A* transition during cooling and the subsequent vitrification of the hexatic smectic phase. The observation of the phase transitions is supported by polarizing optical microscopy (POM). The broadband dielectric spectroscopy (BDS) is applied to investigate the molecular dynamics in the supercooled and vitrified sample. Finally, the kinetics of melt and cold crystallization in isothermal conditions is studied by the DSC method.

2. Materials and Methods

The polycrystalline (S)-4′-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[5-(2,2,3,3,4,4,4 -heptafluorobutoxy)heptyl-1-oxy]benzoate, denoted as 7HH6, was synthesized according to the general route for the mX₁X₂6 compounds, described elsewhere [10,11].

DSC measurements were performed with a DSC 2500 (TA Instruments) calorimeter for the 11.24 mg sample of 7HH6 in an aluminum pan. The DSC curves were registered according to three temperature programs:

(1)

Determination of the phase sequence—the sample was heated to the isotropic liquid phase, then cooled and subsequently heated at the temperature change rate 2, 5, 10, 15, 20 K/min in the 153–413 K temperature range;

(2)

Investigation of kinetics of melt crystallization—the sample was heated above the melting temperature and cooled at 2 K/min to the crystallization temperature from the 263–269 K range;

(3)

Investigation of kinetics of cold crystallization—the sample was heated above the melting temperature, cooled down at 10 K/min below the glass transition temperature and heated at 10 K/min to the crystallization temperature from the 259–265 K range.

In procedures (2) and (3), the sample was kept in isothermal conditions during crystallization and heated at 10 K/min above the melting temperature afterwards. The DSC results were analyzed with TRIOS software.

POM observations were carried out using Leica DM2700 P microscope with Linkam temperature attachment for a sample between two glass slides during slow cooling (2 K/min) in the 383–403 K range and during fast cooling and heating (15 K/min) in the 183–408 K range.

BDS measurements were performed with Novocontrol Technologies spectrometer for the sample with 50 μm thickness between gold electrodes in the 1–10⁷ Hz frequency range. The BDS spectra were collected in the 173–403 K range (1) on cooling from the isotropic liquid and subsequent heating and (2) on heating after fast cooling. The measurements in the bias field of 0.8 V/μm were performed on cooling in the 283–403 K range. The analysis of the BDS data was performed with OriginPro.

3. Results and Discussion

3.1. Phase Sequence

The DSC results (Figure 2,

Table 1. Transitions between the smectic phases of 7HH6 investigated by DSC: onset temperature and peak temperature of anomalies, enthalpy change and entropy change obtained on heating and (cooling). Results are for 2 K/min, except the last row, which is for 20 K/min.

Transition	${\mathit{T}}_{\mathit{o}}$ [K]	${\mathit{T}}_{\mathit{p}}$ [K]	$\mathbf{\Delta }\mathit{H}$ [kJ/mol]	$\mathbf{\Delta }\mathit{S}$ [kJ/mol]
Iso/SmA*	396.4 (396.4)	396.7 (396.1)	4.72 (4.68)	7.05 (6.99)
SmA*/SmC*	393.8 (393.7)	394.0 (393.6)	1.59 (1.68)	2.39 (2.52)
SmC*/SmCA*	389.5 (387.5)	389.6 (387.4)	0.21 (0.16)	0.32 (0.23)
SmCA*/SmXA*	(263.5)	(260.0)	(0.34)	(0.65)

) confirm the sequence of the smectic phases SmA* → SmC* → SmC_A* with a decreasing temperature known from the previous measurements [11]. However, on further cooling there is another transition at 263.4–265.1 K, depending on the cooling rate, visible as a small exothermic anomaly and interpreted as the SmC_A* → SmX_A* transition. For 2 and 5 K/min cooling rates, partial crystallization to the phase denoted here as Cr2 is observed just below the transition to the SmX_A* phase. The hexatic SmX_A* phase undergoes vitrification, indicated by a wide, step-like anomaly with a middle at 230–233 K. Another anomaly is visible at 188–201 K, which means the two-step vitrification of 7HH6. On subsequent heating, the glass softening is indicated by two anomalies at 225–229 K and 233–237 K. At higher temperatures, 7HH6 undergoes cold crystallization. For the 2 K/min heating rate, cold crystallization begins at 252 K. The exothermic anomaly, interpreted as the SmX_A* → Cr2 transition, is very weak and it is followed by a larger anomaly with the onset at 271.4 K. The second anomaly indicates cold crystallization to the high-temperature Cr1 phase. For 5–20 K/min heating rates, between exothermic anomalies arising from cold crystallization, there is visible an endothermic anomaly with the onset at 273–277 K, related to the melting of the Cr2 phase. For 2 K/min, this anomaly is not visible, probably because it overlaps with the stronger anomaly from the SmC_A* → Cr1 transition. The melting temperature of the Cr1 phase is 329.2–329.4 K and the enthalpy and entropy changes at melting are $\mathsf{\Delta }H$ = 30.8 kJ/mol and $\mathsf{\Delta }S$ = 51.0 J/(mol∙K), respectively.

In the POM textures collected during slow cooling from the isotropic liquid phase (Figure 3a), one can distinguish three smectic phases. To obtain the vitrified SmX_A* phase and to observe the subsequent cold crystallization, the POM measurement was performed during fast cooling and heating (Figure 3b,c). The textures of the SmC_A* and SmX_A* phases are very similar, as the SmC_A*/SmX_A* transition is not connected with a significant rearrangement of molecules—only the correlation length of the short-range order within the smectic layers increases and the bond-orientational order appears in the SmX_A* phase [12]. The glass of the SmX_A* also shows a similar texture. The clearly visible transition is cold crystallization which occurs during heating. The cold crystallization begins at ca. 273 K, meaning that it leads rather directly to the Cr1 phase. The Cr2 phase was not observed in the POM measurement.

The fluorosubstitution of the benzene ring (Figure 1) has a significant influence on the behavior of 7 X ₁ X ₂6 compounds. Two 7 X ₁ X ₂6 homologues with a single F atom in the molecular core, 7HF6 [25] and 7FH6 [26,27], vitrify during cooling and form the SmC_A* glass. Meanwhile, the double-fluorinated 7FF6 compound is not a glass former, and forms a crystal phase during cooling, as reported for rates up to 20 K/min [28]. Taking into account the previously reported results, the formation of the hexatic phase in the mX₁X₂6 series seems to be present only in the compounds without the F atoms in the molecular core, as it was observed also for 4HH6 [17] and 5HH6 [18]. The tendency to create the glass of the smectic phase (SmX_A* or, more often, SmC_A*) is observed for various types of fluorosubstitution, although the presence of the F atom at X₂ position only is observed to facilitate to the most vitrification during cooling [25,29]. The parity of the C_mH_2m chain also has a significant influence, because the glass of the smectic phase is more often observed for the odd mX₁X₂6 homologues [18,25,29,30].

3.2. Molecular Dynamics

Each dielectric relaxation process is characterized by the dielectric strength $\mathsf{\Delta }\epsilon$, relaxation time $\tau$ and shape parameters $a$, $b$, describing the distribution of the relaxation time ($a$ = 0, $b$ = 1—Debye model, 0 < $a$ < 1, $b$ = 1—Cole-Cole model, 0 < $a$ < 1, 0 < $b$ < 1—Havriliak-Negami model). The complex function fitted to the dielectric spectra has a form [31,32,33]:

$${\epsilon }^{*}\left(f\right)={\epsilon }_{\infty }+{{\displaystyle \sum }}_j\frac{\mathsf{\Delta }{\epsilon }_j}{{\left(1+{\left(2\pi if{\tau }_j\right)}^{1-a_j}\right)}^{b_j}}-\frac{iS}{f},$$

(1)

where ${\epsilon }_{\infty }$ stands for the dielectric permittivity at $f\to \infty$ and $S$ describes the contribution from the ionic conductivity. There are seven relaxation processes observed for the 7HH6 sample (Figure 4 and Figure 5). In the SmA* phase, there is the soft mode, related to the fluctuations of the magnitude of the tilt angle [34,35] and described by the Debye model. The dielectric strength and relaxation time of the soft mode increase with decreasing temperature in the SmA* phase, in accordance with theoretical predictions [34,35]. In the SmC* phase, there is the Goldstone mode, which originates from the fluctuations around the tilt cone [34,35] and which has the largest dielectric strength. In the SmC_A* phase, there are two characteristic phasons, the in-phase P_L process and anti-phase P_H process at lower and higher frequency, respectively [36]. The Goldstone mode, as well as the P_L and P_H processes, are described by the Cole-Cole model. During the measurement performed on slow cooling, 7HH6 crystallizes at 289 K. In two last spectra of SmC_A* collected before crystallization (291–293 K), the third relaxation process is visible. This process is identified as the α-process, which appears at the high-frequency neighborhood of the P_H process for other glass forming mX₁X₂6 compounds [18,25,26,27]. In the crystal phase, there is a relaxation process with a small dielectric strength, described by the Havriliak-Negami model, and named here the cr-process. If the 7HH6 sample is cooled down quickly, the vitrified SmX_A* phase is obtained. The relaxation processes observed on subsequent heating are the α-process and the secondary β-process, which has a smaller dielectric strength and higher frequency than the α-process. The α-process is described by the Havriliak-Negami model (although for fitting in 291, 293 K, the Cole-Cole model was assumed because the absorption peak was not fully visible), while the β-process was fitted with the Cole-Cole model. The relaxation times of three processes, P_L, cr and β, follow the Arrhenius dependence on temperature (Figure 5b). The activation energy of P_L is 106.9(4) kJ/mol. The P_L process is known to overlap with a molecular process, namely the rotation around the short molecular axis (s-process), as it was proven in [36], which can explain the Arrhenius dependence of the relaxation time and large activation energy. The cr-process has an activation energy of 38.0(2) kJ/mol, suggesting that it arises from an intra-molecular rotation. The possible candidate is the rotation of biphenyl in the molecular core. The energy barrier of this rotation, calculated by DFT method for the 5HH6 homologue with the identical structure of the aromatic core, is 35 kJ/mol [18], close to the experimental activation energy. It indicates that 7HH6 forms a conformationally disordered (CONDIS) phase. The activation energy of the β-process is 86.2(5) kJ/mol. The interpretation of this process for the mX₁X₂6 compounds, based on DFT calculations, is the intra-molecular coupled rotation of the benzene ring and biphenyl [26,27,37] (the summed energy barrier for these two rotations obtained for 5HH6 is 81 kJ/mol [18]). The β-process in the mX₁X₂6 compounds is rather a pseudo-Johari-Goldstein relaxation instead of the genuine JG-relaxation, as the latter involves movements of the rigid molecules [38]. The relaxation time of the α-process changes with temperature according to the Vogel-Fulcher-Tammann formula, ${\tau }_{\alpha }\left(T\right)={\tau }_0\exp \left(B/\left(T-T_V\right)\right)$, where $B$ is a fitting parameter and $T_V$ is the Vogel temperature [33]. Using the fitted VFT formula, one can determine the fragility parameter of a glass former, equal to $m_f=B{T}_g/{\left(T_g-T_V\right)}^2\ln 10$, where $T_g$ is the temperature and where ${\tau }_{\alpha }$ = 100 s [25,33]. For 7HH6, $T_g$ = 229(1) K, in accordance with the glass transition temperature determined from the DSC results, and the fragility parameter $m_f$ = 94.5(9). The $m_f$ values of various glass formers are in the range of 16–200 [39]. High fragility parameter indicates that 7HH6 should easily undergo cold crystallization after heating above the glass softening temperature [40], as it is observed experimentally.

3.3. Kinetics of Crystallization

The melt crystallization (Figure 6a) and cold crystallization (Figure 6b) of 7HH6 was investigated in isothermal conditions in various $T_{cr}$ temperatures using the DSC method. The degree of crystallization $X\left(t\right)$ was determined by integration of the exothermic anomalies arising from the crystallization process, after subtraction of a baseline:

$$X\left(t\right)=\frac{{{\displaystyle \int }}_{t_{start}}^t\Phi \left(t\right)dt}{{{\displaystyle \int }}_{t_{start}}^{t_{end}}\Phi \left(t\right)dt},$$

(2)

where $\Phi \left(t\right)$ is the heat flow and $t_{start}$, $t_{end}$ are points in time between which the exothermic anomaly is observed. The isothermal crystallization is described by the Avrami model [41,42,43]:

$$X\left(t\right)=1-\exp \left(-{\left(\frac{t-t_0}{{\tau }_{cr}}\right)}^n\right),$$

(3)

with the fitting parameters $t_0$—the initialization time, ${\tau }_{cr}$—characteristic time of crystallization and $n$—the Avrami parameter dependent on the nucleation rate and dimensionality of crystal growth. The experimental $X\left(t\right)$ values were fitted with Equation (3), except the results for melt crystallization in 263 K, where a two-step Avrami model was fitted [44]:

$$X\left(t\right)=A\left[1-\exp \left(-{\left(\frac{t-t_0}{{\tau }_{cr1}}\right)}^{n_1}\right)\right]+\left(1-A\right)\left[1-\exp \left(-{\left(\frac{t-t_0}{{\tau }_{cr2}}\right)}^{n_2}\right)\right].$$

(4)

The initialization time $t_0$ was assumed to be equal for both crystallization processes and fixed to zero, otherwise the fitting gave unphysical values. The fraction of the sample crystallizing in a process described by the ${\tau }_{cr1}$, $n_1$ parameters is equal to $A$ = 0.544(1). The double exothermic anomaly related to melt crystallization in 263 K is caused probably by the ongoing SmC_A* → SmX_A* transition on cooling (Table 1). The $t_0$, ${\tau }_{cr}$ and $n$ values for all $T_{cr}$ are collected in

Table 2. Parameters of the Avrami model describing the kinetics of crystallization of 7HH6.

${\mathit{T}}_{\mathit{c}\mathit{r}}$ [K]	${\mathit{t}}_0$ [s]	${\mathit{\tau }}_{\mathit{c}\mathit{r}}$ [s]	$\mathit{n}$
melt crystallization
263	0, 0 (fixed)	2050(1), 863(1)	3.55(1), 2.61(1)
265	99(1)	1049(1)	3.61(1)
267	259(2)	738(2)	2.86(2)
269	328(2)	571(2)	2.51(1)
cold crystallization
259	492(4)	3384(4)	2.78(1)
260	219(2)	2899(2)	2.80(1)
262	211(2)	1794(2)	2.86(1)
263	118(2)	1540(2)	2.82(1)
264	52(2)	1224(2)	2.90(1)
265	36(2)	1037(3)	3.00(1)

. The initialization time of melt crystallization increases with increasing $T_{cr}$, while for cold crystallization there is an opposite relationship. The characteristic crystallization time shows similar dependence on $T_{cr}$, as presented in the Arrhenius plot (Figure 7a). The results for melt crystallization in 263 K were excluded from the linear fit. The activation energy obtained from the slope of the Arrhenius plot of ${\tau }_{cr}$ is equal to 114(3) kJ/mol. This result indicates that the kinetics of crystallization is controlled mainly by the rate of diffusion of molecules [45]. It is confirmed by strong coupling between ${\tau }_{cr}$ and the relaxation time of the α-process [45], with the coupling constant $\xi$ = 0.80(2), close to 1 (Figure 7b). One can see that the ${\tau }_{cr}$ value of melt crystallization in 269 K and the highest investigated $T_{cr}$, is longer than obtained from the linear fit. It implies that for this temperature, the thermodynamic factor has a noticeable impact on the kinetics of crystallization. The influence of the thermodynamic factor, i.e., the thermodynamic driving force of crystallization decreasing with increasing $T_{cr}$ [45], also causes the increase of $t_0$ of a melt crystallization with increasing $T_{cr}$. During cold crystallization, the nucleation process occurs mainly below $T_{cr}$,; therefore, the rate of crystal growth has a decisive role in the resultant crystallization time. The Avrami parameter $n$ = 2.8–3.0 for cold crystallization can be interpreted as mainly three-dimensional (isotropic) crystal growth with a constant number of nuclei [43,46], as most of the nuclei are likely formed below $T_{cr}$. For melt crystallization, which occurs after the sample is cooled down from higher temperatures, the more probable situation is the formation of nuclei in $T_{cr}$. With this assumption, $n$ = 2.5–2.9 for $T_{cr}$ = 263, 267, 269 K indicates two-dimensional crystal growth and $n$ = 3.6 for $T_{cr}$ = 263, 265 K means that three-dimensional crystal growth [43,46]. It is worth noting that for 263 K, two different $n$ values are obtained for simultaneous crystallization processes. However, it has to be underlined that these values were obtained with the fixed $t_0$, and their actual uncertainty may be larger than obtained from the fitting of Equation (4). The crystal phase formed both during isothermal melt crystallization and cold crystallization is the Cr1 phase, as it melts at 328.5–328.9 K.

4. Summary and Conclusions

The phase transitions of smectogenic (S)-4′-(1-methylheptylcarbonyl)biphenyl-4-yl 4-[5-(2,2,3,3,4,4,4-heptafluorobutoxy)heptyl-1-oxy]benzoate (7HH6) in the 153–413 K range were investigated by DSC, POM and BDS methods. Along with the confirmation of the previously known sequence of the smectic phases, SmC_A* → SmC* → SmA*, an additional transition to the hexatic SmX_A* phase was detected at 263 K as a small anomaly in the DSC curve. After comparison with the previous results for the mX₁X₂6 family [17,18,25,26,27,28], there is an assumption that fluorination of the benzene ring prevents the formation of the hexatic smectic phase because, up to now, SmX_A* has been observed only for the mHH6 homologues, which are not fluorinated in the molecular core.

The vitrification of SmX_A* is observed for cooling rates of 2–20 K/min, although for 2 and 5 K/min, and partial crystallization of the sample also occurs. The molecular dynamics in the supercooled SmX_A* phase involves the α-process with the relaxation time described by the Vogel-Fulcher-Tammann formula, and the secondary, pseudo-Johari-Goldstein β-process with the relaxation time followed the Arrhenius formula with an activation energy of 86 kJ/mol. The DFT calculations [18] imply that the intra-molecular rotations related to the β-process are rotations of the benzene ring and biphenyl in the aromatic molecular core. The fragility parameter of 7HH6, obtained from the parameters of the VFT equation, is $m_f$ = 94.5. The $m_f$ values for other mX₁X₂6 compounds, which form the SmC_A* glass, are in the 72–129 range [18,25,26,27,29]. This suggests that the fragility does not depend on whether the vitrification occurs in the SmC_A* or SmX_A* phase, at least for the mX₁X₂6 family.

The isothermal crystallization kinetics studies performed by DSC reveal that both melt crystallization and cold crystallization are controlled by diffusion, as their characteristic times in most of investigated temperatures change according to the Arrhenius equation with the same activation energy of 114 kJ/mol, and the coupling constant between the characteristic crystallization time and relaxation time of the α-process (being the determinant of the molecular mobility) is equal to 0.8, indicating a strong coupling. Isothermal crystallization leads to a high-temperature crystal phase, denoted as Cr1. The low-temperature Cr2 phase was formed only in non-isothermal conditions. The phase transition temperatures obtained by DSC vs. cooling/heating rate, as well as the DSC results from isothermal conditions imply that on very slow cooling or heating (e.g., during BDS measurement), the Cr2 phase is not formed, or it is present only in very small amounts. The phase identified as the CONDIS phase (formed often by liquid crystalline compounds [18,19,47]) in the BDS spectra is therefore Cr1. However, Cr2 is expected to be less ordered than Cr1; thus, it is also very likely the CONDIS phase. The absence of Cr2 in POM measurements, despite a high applied rate of 15 K/min, may be explained by hindrance of the Cr2 formation in a very thin sample.

One of the next tasks in the investigation of the mX₁X₂6 compounds is explanation of how the presence of fluorine atoms in the molecular core actually affects the ability of these compounds to form the hexatic smectic phase. It will require the extended study of inter-molecular interactions, which will involve, e.g., DFT calculations for molecular dimers.