# Crystallization Kinetics of an Equimolar Liquid Crystalline Mixture and Its Components
## 3 Results and Discussion
### Dielectric Relaxation Processes  
The dielectric spectra show the complex dielectric permittivity \(\epsilon^{*}\) as a function of the frequency \(f\) of the external electric field. The models used for fitting the experimental \(\epsilon^{*}(f)\) dependences in this study are the [PERSON] [48], [PERSON] [49], and Havriliak-Negami [50] models, together with the contribution of ionic conductivity [48]:  
\[\epsilon^{*}(f)=\epsilon^{\prime}(f)-ie^{\prime\prime}(f)=\varepsilon_{\infty}+ \sum_{j}\frac{\Delta\varepsilon_{j}}{\left(1+\left(2\pi if\tau_{j}\right)^{1 -a_{j}}\right)^{b_{j}}}-\frac{iS}{\left(2\pi f\right)^{n_{S}}}, \tag{3}\]  
where \(\epsilon^{\prime}\) and \(\epsilon^{\prime\prime}\) are the real and complex components of \(\epsilon^{*}\) (corresponding to dielectric dispersion and absorption, respectively), \(\varepsilon_{\infty}\) is the \(\epsilon^{\prime}\) value in the limit of high frequencies, \(\Delta\varepsilon\) is the dielectric increment of each process, \(\tau\) is the relaxation time of each process, and \(S\) and \(n_{S}\) are parameters describing the background in \(\epsilon^{*}\) at low frequencies. If \(n_{S}=1\), then \(S=\sigma/\varepsilon_{0}\), where \(\sigma\) is the ionic conductivity and \(\varepsilon_{0}\) is the vacuum permittivity. The parameters \(a\) and \(b\) describe the shape of the step in \(\epsilon^{\prime}\) and peak in \(\epsilon^{\prime\prime}\) originating from  
Figure 5: XRD patterns of the MIX2 HF6 mixture (**a**), the smectic layer spacing \(d\) in MD2 HF6 and its components (**b**), and the average intermolecular distance \(w\) and correlation length \(\xi\) of the short-range order in MIX2 HF6 (**c**). each relaxation process. For the Debye model, \(a=0\) and \(b=1\). For the Cole-Cole model, \(a\in(0,1)\) and \(b=1\). For the Havriliak-Negami model, \(a\in(0,1)\) and \(b\in(0,1)\). The presence of some relaxation processes facilitates the identification of the smectic phases. The soft mode (SM) is related to collective fluctuations in the tilt angle value, and is observed in the SmA* and SmC* phases. Upon cooling, the \(\tau\) and \(\Delta\varepsilon\) of the SM increase in SmA* and decrease in SmC*, showing the characteristic V-dependence on temperature [51]. The Goldstone mode (GM) is related to collective fluctuations in the tilt azimuth around the tilt cone, and is observed in the SmC* phase. It shows a much larger \(\Delta\varepsilon\) than the SM [51]. In the SmC\({}_{A}\)* phase, there are two GM-like phasons, P\({}_{\rm L}\) and P\({}_{\rm H}\), related to collective fluctuations in the tilt azimuth, which are, respectively, in-phase and anti-phase in the neighboring smectic layers. P\({}_{\rm L}\) has a higher \(\tau\) than P\({}_{\rm H}\), and it can overlap with the molecular s-process (rotations around the short molecular axis) [52; 53]. The representative fits of Equation (3) to the experimental BDS spectra of MIX2 HF6 are shown in Figure 6. The \(\Delta\varepsilon\), \(\tau\), and \(\sigma\) values, determined as a function of temperature, are presented in Figures 7-9 for MHPOBC, 3F2 HPhF6, and MIX2 HF6, respectively. The SM with \(\tau\) and \(\Delta\varepsilon\) increasing upon cooling confirms the SmA* phase in MHPOBC and MIX2 HF6. The GM with high \(\Delta\varepsilon\) values confirms the SmC* phase and the pair of weaker phasons P\({}_{\rm L}\) and P\({}_{\rm H}\) confirm the SmC\({}_{\rm A}\)* phase in MIX2 HF6 and both components. The GM is also observed in the SmC\({}_{\rm H}\)* phase [53], which can be present for MHPOBC. Thus, the strongest value of the GM's \(\Delta\varepsilon\) at 391 K is attributed to SmC*, while the lowered \(\Delta\varepsilon\) values at 389-390 K can be attributed to SmC\({}_{\rm H}\)*. From the high-temperature side, the relatively strong SM may indicate the SmC\({}_{\rm A}\)* phase [53; 54]. The final phase sequence in MHPOBC would be SmA*, SmC\({}_{\rm A}\)*, SmC*, SmC\({}_{\rm H}\)*, and SmC\({}_{\rm A}\)*. On the other hand, the DSC thermograms show only one phase between SmA* and SmC\({}_{\rm A}\)*.