# Crystallization Kinetics of an Equimolar Liquid Crystalline Mixture and Its Components
## 3 Results and Discussion
### Isothermal Crystallization  
Isothermal crystallization was investigated by the DSC method. Each sample was heated to isotropic liquid and cooled at 20 K/min to the crystallization temperature \(T_{cr}\). The ranges of \(T_{cr}\) were selected based on the DSC results from Figures 2-4. The isothermal DSC thermograms as a function of time are presented in Figure 14a-c. The crystallization degree vs. time was obtained using Equation (7), but the integration was performed over time, not over temperature. The \(x(t)\) dependences were fitted by the Avrami model [73; 74], commonly used to analyze isothermal crystallization [74; 75; 22; 76; 77]:  
\[x(t)=1-\exp\biggl{(}\biggl{(}\frac{t-t_{0}}{\tau_{cr}}\biggr{)}^{n}\biggr{)}, \tag{9}\]  
where \(t_{0}\) is the initialization time, \(\tau_{cr}\) is the characteristic crystallization time, and \(n\) depends on the type of nucleation (constant number of nuclei or constant nucleation rate) and dimensionality of the crystal growth (shape of crystallites). For a constant number of nuclei, \(n=\) 1, 2, 3 indicates 1D, 2D, and 3D crystal growth. For a constant nucleation rate, the respective \(n\) values are 2, 3, 4 [73; 74; 75]. Higher \(n\) can be interpreted as the sheaf-like growth of crystallites [75]. The results for 3F2 HPhF6 (Figure 14d) can be fitted with Equation (9). For MHPOBC, two overlapping crystallization processes are observed (Figure 14e), which requires the fitting of two Avrami models, where \(A\) is the fraction of the crystal developed in the first stage of crystallization [78]:  
\[x(t)=\left\{ \begin{array}{c}A\left[1-\exp\biggl{(}-\left(\frac{t-t_{01}}{ \tau_{1}}\right)^{n_{1}}\biggr{)}\right]\text{ for }t_{01}\leq t\leq t_{02}\\ A\left[1-\exp\biggl{(}-\left(\frac{t-t_{01}}{\tau_{1}}\right)^{n_{1}}\biggr{)} \right]+\left(1-A\right)\left[1-\exp\biggl{(}-\left(\frac{t-t_{02}}{\tau_{2}} \right)^{n_{2}}\biggr{)}\right]\text{ for }t\geq t_{02}\end{array} \right., \tag{10}\]  
The crystallization of MIX2 HF6 occurs in two stages, but the second stage starts after the completion of the first stage (Figure 14f). Therefore, it is also possible to fit their \(x(t)\) dependences separately with Equation (9). The isothermal crystallization of MHPOBC results in a mixture of Cr2 and Cr1 phases, with the fraction of the Cr2 phase increasing with increasing \(T_{cr}\) (Figure 14g). The 3F2 HPhF6 sample consists mostly of the Cr2 phase, which transforms into the Cr1 phase shortly before melting. Only for \(T_{cr}\) = 308 K, the Cr2 \(\rightarrow\) Cr1 transition is not visible at the slope of the melting anomaly; therefore, the isothermal crystallization at this temperature results in the Cr1 phase (Figure 14h). The structural differences between Cr2 and Cr1 are presumed to be small, as the Cr2 \(\rightarrow\) Cr1 transition shows a small anomaly in the DSC thermograms. The melting temperature of MIX2 HF6 is 303-308 K, and increases with increasing \(T_{cr}\) (Figure 14i). It is comparable with the melting temperature of the Cr1 phase formed upon heating from the Cr2 or Cr3 phase (Figure 4d). After the isothermal crystallization of MIX2 HF6, two closely overlapping melting anomalies are observed, which indicates two crystal phases with slightly different structures or fractions of the components. The parameters of the Avrami model obtained for MIX2 HF6 and its components are presented in Figure 15. The initialization time is shown in the time-temperature-transition (TTT) diagram [19] (Figure 15a). In the idealized TTT diagram, \(t_{0}\) is expected to have a minimum at a certain \(T_{cr}\). Above and below this temperature, the crystallization kinetics are controlled by the nucleation and diffusion rates. Therefore, \(t_{0}\) decreases and increases with decreasing \(T_{cr}\), respectively.