# Crystallization Kinetics of an Equimolar Liquid Crystalline Mixture and Its Components
## 3 Results and Discussion
### Non-Isothermal Crystallization  
The melt crystallization of MIX2 HF6 and its components were investigated by DSC for cooling rates in the 2-40 K/min range (Figures 2-4). The relative crystallization degree \(x\) was determined as an integral of the heat flow \(\Phi\) between temperatures \(T_{start}\) and \(T_{end}\), indicating the temperature range of the exothermic anomaly related to crystallization [65]:  
\[x(T)=\frac{\int_{T_{start}}^{T}\Phi(T)dT}{\int_{T_{start}}^{T_{end}}\Phi(T)dT}, \tag{7}\]  
There are various models for the analysis of non-isothermal crystallization kinetics, including the [PERSON] [66], [PERSON] [67], [PERSON] [68], and Augis-Bennett [69] models, and the isoconversional method [70; 71; 72; 73]. In the [PERSON], [PERSON], and [PERSON] models, the rate of temperature change appears under logarithm, and it is not certain whether it can be applied for cooling, where the rate is negative. In the Augis-Bennett model, the value under logarithm is positive both for cooling and heating. However, it is based on the peak and onset temperatures. Some of the results in this study include overlapped crystallization processes, in which the determination of these temperatures could be vague. Thus, the data were analyzed with the isoconversional method (Figures 11-13), which enables the determination of the effective activation energy \(E_{eff}\) as a function of \(x\) and \(T\)[65; 70; 71]. This method is based on the following formula [70; 71]:  
\[\frac{dx(t)}{dt}=f(x)A\exp\left(-\frac{E_{eff}}{RT}\right), \tag{8}\]  
where \(f(x)\) is the transition model and \(A\) is a pre-exponential factor. The logarithm of the crystallization rate \(dx/dt\) is plotted against the inverted temperature \(T_{x}\) for a selected \(x\), for all cooling rates. The slope of such an activation plot is equal to \(-E_{eff}/R\). The obtained \(E_{eff}\) can be plotted against temperature if the average temperature for each range of the linear fit is used [65; 71]. Figure 11: Crystallization degree vs. temperature of MHPOBC (**a**), activation plot based on isoconversional method (**b**), effective activation energy vs. crystallization degree (**c**), and temperature (**d**). The isoconversional analysis for MHPOBC reveals three crystallization regimes (Figure 11). The effective activation energies \(E_{eff1}\) and \(E_{eff2}\), which correspond mainly to a melt crystallization above the room temperature, are negative and equal to \(-\)(382-329 kJ/mol and \(-\)(171-84 kJ/mol, respectively. The negative values mean that the crystallization kinetics depend mainly on nucleation, i.e., the thermodynamic driving force controls it. Below the room temperature, the effective activation energy \(E_{eff3}\) takes values between \(-\)121 kJ/mol and 37 kJ/mol. Positive \(E_{eff3}\) values, obtained for the intermediate degree of crystallization, mean that at lower temperatures, the diffusion rate has a bigger impact on the crystallization kinetics than at above the room temperature, when the impact of the nucleation rate was the most significant. The results for 3F2 HPhF6 (Figure 12) show four regimes of crystallization. Above the room temperature, \(E_{eff1}=-\)(66-11) kJ/mol, around 290 K, \(E_{eff2}=-\)(170-134) kJ/mol, and  
Figure 12: Crystallization degree vs. temperature of 3F2 HPhF6 (**a**), activation plot based on isoconversional method (**b**), effective activation energy vs. crystallization degree (**c**), and temperature (**d**). Figure 13: Crystallization degree vs. temperature of MIX2 HF6 (**a**), activation plot based on isoconversional method (**b**), effective activation energy vs. crystallization degree (**c**), and temperature (**d**). below 285 K, \(E_{eff3}\) changes between \(-\)81 kJ/mol and 22 kJ/mol. Thus, the crystallization kinetics above the room temperature is controlled by nucleation; the influence of the nucleation rate increases down to 290 K, and at lower temperatures, the diffusion rate has a gradually growing impact.