# Crystallization Kinetics of an Equimolar Liquid Crystalline Mixture and Its Components
## 3 Results and Discussion
### Structure of Smectic Phases  
The XRD patterns of the smectic phases (Figure 5a) are characterized by sharp diffraction peak or peaks located at low 20 angles. The peak position is related to the smectic layer spacing by the Bragg equation [31]:  
\[n\lambda=2d\sin\theta, \tag{1}\]  
where \(n\) is the order of the peak (\(n=1\), \(2\), \(3\)...--the number of visible peaks of the order \(n>1\) varies between the compounds and smectic phases), \(\lambda=1.540562\) A is the wavelength characteristic of CuK\(\alpha_{1}\) radiation [40], \(d\) is the layer spacing, and \(\theta\) is the peak position corrected for the systematic shift (in this study, results for the SRM 675 reference material were used for this correction). The XRD patterns at higher 20 angles depend on the intra-layer order in the smectic phase [31]. For smectics A and C, the intra-layer positional order \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Sample** & **SmX\({}_{\text{A}}\)* & \multicolumn{2}{c}{**SmC\({}_{\text{A}}\)***} & \multicolumn{2}{c}{**SmC\({}^{\text{*}}\)**} & \multicolumn{2}{c}{**SmA\({}^{\text{*}}\)**} & \multicolumn{2}{c}{**Iso**} \\ \hline \multicolumn{8}{c}{cooling} \\ \hline \multirow{3}{*}{MHPOBC} & \multirow{3}{*}{\(\bullet\)} & 339 & 394 \({}^{\text{a}}\) & \multirow{3}{*}{\(\bullet\)} & 394 \({}^{\text{a}}\) & \multirow{3}{*}{\(\bullet\)} & 424 & \multirow{3}{*}{\(\bullet\)} \\  & & **337.3** & & **386.6** & & **388.3** & & **418.2** & \\  & & 1.5 & & \textgreater{}0.1 & & \textgreater{}0.1 & & _6.0_ & \\ \hline \multirow{3}{*}{3F2 HPhF6} & \multirow{3}{*}{-} & 366 & 365.1 & \multirow{3}{*}{\(\bullet\)} & & 380 & \multirow{3}{*}{\(\bullet\)} \\  & & & **365.1** & & & & **377.6** & \\  & & & \textgreater{}0.1 & & & & _6.8_ & \\ \hline \multirow{3}{*}{MIX2 HF6} & \multirow{3}{*}{-} & 377 & 388 & \multirow{3}{*}{\(\bullet\)} & 394 & \multirow{3}{*}{\(\bullet\)} \\  & & & **373.6** & & **386.9** & & **395.9** & \\  & & & \textgreater{}0.1 & & 1.1 & & _4.6_ & \\ \hline \multicolumn{8}{c}{heating} \\ \hline \multirow{3}{*}{MHPOBC} & \multirow{3}{*}{-} & 394 \({}^{\text{a}}\) & 394 \({}^{\text{a}}\) & 394 \({}^{\text{a}}\) & & 424 & \multirow{3}{*}{\(\bullet\)} \\  & & & **385.0** & & **389.3** & & **416.6** & \\  & & & \textgreater{}0.1 & & \textgreater{}0.1 & & _5.9_ & \\ \hline \multirow{3}{*}{3F2 HPhF6} & \multirow{3}{*}{-} & 371 & 369.2 & \multirow{3}{*}{\(\bullet\)} & & 380 & \multirow{3}{*}{\(\bullet\)} \\  & & & **369.2** & & & & _6.8_ & \\ \hline \multirow{3}{*}{MIX2 HF6} & \multirow{3}{*}{-} & 377 & 388 & \multirow{3}{*}{\(\bullet\)} & 394 & \multirow{3}{*}{\(\bullet\)} \\  & & & **375.6** & & **386.2** & & 394 & \\  & & & \textgreater{}0.1 & & _0.9_ & & _4.8_ & \\ \hline \hline \end{tabular}  
\({}^{\text{a}}\) only the textures collected at 394 K during cooling and heating were attributed to SmC\({}^{\text{*}}\).  
\end{table} 
Table 1: Polymorphism of the smectic phases of MIX2 HF6 and its components. The presence and absence of a smectic phase are indicated by \(\bullet\) and -, respectively. The first row (normal font) contains the transition temperatures, in K, obtained by POM (5 K/min), the second row (**bold**) contains the transition temperatures, in K, obtained by DSC (extrapolated to 0 K/min), and the third row (_italics_) contains the enthalpy changes, in kJ/mol, determined by DSC. is short-range, described by the average intermolecular distance \(w\) and correlation length \(\xi\). It corresponds to the wide maximum in the XRD patterns located around \(2\theta\approx 18\)-\(20^{\circ}\), defined by the Lorentz peak function [47]:  
\[I(q)\propto\frac{1}{1+\xi^{2}(q-q_{0})^{2}}, \tag{2}\]  
where \(q=4\pi/\sin\theta\) is the scattering vector and \(q_{0}=2\pi/w\) is the peak position. Upon transition to the hexatic phase, the diffuse maximum becomes narrower and has a sharper peak [31]. For MIX2 HF6, sharpening of the peak at \(2\theta\approx 19^{\circ}\) is observed at 298 K (full-width at half-height equal to \(1.0^{\circ}\), compared to \(4.9^{\circ}\) at 303 K).