Crystallization kinetics in the chiral compound showing the vitrification of the smectic CA* phase for moderate cooling rates

ABSTRACT The crystallization of the 3F5FPhF6 compound from the liquid crystalline antiferroelectric smectic CA* phase is investigated in various conditions using differential scanning calorimetry and polarizing optical microscopy. The kinetics of isothermal melt and cold crystallization is studied on the basis of the Avrami model. The kinetics of non-isothermal cold crystallization is analysed using the Ozawa model and the activation energy is determined by the Augis-Bennett, Friedman’s differential isoconversional and Matusita methods. The border temperature between the diffusion-controlled crystallization and thermodynamically-controlled crystallization is estimated. The high fragility index of 105 is determined from the α-process in the smectic CA* phase by the broadband dielectric spectroscopy. The metastable, conformationally disordered crystal phase, forming only via cold crystallization, is reported.


Introduction
Liquid crystals are phases where the long-range orientational order is present while the positional order is lowered in comparison with the solid crystals. In a nematic phase, the positional order is only short-range, as in liquids. In the smectic phases, molecules form layers, which is a quasi-longrange order in one dimension, and within the smectic layers the positional order is short-range [1,2]. There are also smectic phases with a long-range positional order within layers, where the molecules have still a possibility to reorient around their long and short axes. Such ordered smectic phases are closer to plastic crystal phases than to liquid crystals [1,3,4]. The intermediate properties of liquid crystals between these isotropic liquid and a solid crystal, and their sensitivity to an electric field and temperature enable various applications, e.g. in liquid crystal displays, in thermometers or for preparation of glasses with anisotropic properties [5,6].
The liquid crystalline 3FmX 1 PhX 2 r compounds show the antiferroelectric smectic C A * (SmC A *) phase in a broad temperature range [7][8][9]. The variations in their molecular structure ( Figure 1) are related to the length of the non-chiral, partially fluorinated chain (m = 2-7), the length of the chiral chain (r = 4-7) and fluorosubstitution of the benzene ring in the molecular core (X 1 , X 2 = H or F). The most widely investigated 3FmX 1 PhX 2 r compounds are these with r = 6. The high tilt angle of 40-45°in the SmC A * phase enabled the preparation of several orthoconic antiferroelectric mixtures for possible application in displays [8,10]. Another property of the 3FmX 1 PhX 2 r compounds is that many of them show the vitrified SmC A * or hexatic SmX A * phases, which can be observed even for cooling with low 0.5-5 K/min rates, depending on the compound [11][12][13][14][15][16].
This paper contributes to the ongoing systematic investigation of correlation between the molecular structure of the 3FmX 1 PhX 2 r compounds and their tendency to form the glass of the SmC A * phase. The studied compound is 3F5FPhF6, with m = 5, r = 6 and the fluorine atoms at X 1 and X 2 positions, tested already as a component of liquid crystalline mixtures [8,17]. 3F5FPhF6 has a rich polymorphism of the chiral smectic phases. The phase sequence on heating is Cr (325.6 K) SmC A * (380.3 K) SmC* (380.7 K) SmC α * (381.5 K) SmA* (382.3 K) Iso [18], where Cr stands for a crystal and Iso for isotropic liquid. 3F5FPhF6 forms the crystal phase on very slow cooling, however, the differential scanning calorimetry results obtained during cooling at 5-20 K/min imply that in such conditions the crystallization can be partially or even completely hindered [18]. The aim of this investigation is to determine the cooling rate necessary to avoid crystallization and observe the glass transition of the SmC A * phase, and to determine the mechanism of the melt crystallization (on cooling) and cold crystallization (on heating) of 3F5FPhF6. The experimental methods used in this study are polarizing optical microscopy (POM), differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (BDS).

POM measurements
POM observations were performed for the unaligned sample between two glass slides with Leica DM2700 P polarizing microscope equipped with Linkam temperature controller.
(1) In order to investigate the kinetics of isothermal melt crystallization, the sample was heated to 393 K and then cooled down at 20 K/min to a selected temperature T mc . The sample was kept in T mc until the whole observed area was occupied by the crystal phase. The measurements were done for T mc = 277, 278, 279, 280, 281, 282, 283, 284, 285 K. (2) The vitrification of the SmC A * phase and cold crystallization were investigated by cooling the sample at 20 K/min from isotropic liquid to 190 K and heating back to isotropic liquid at 10 K/min.
The POM textures were analysed with ImageJ program [19]. The degree X(t) of melt crystallization was calculated as the fraction of the area of the POM texture occupied by the crystal phase [20].

DSC measurements
DSC measurements were performed for the 5.490 mg sample in an aluminium pan with DSC 2500 (TA Instruments) calorimeter. In DSC the quantities that have to be calibrated are the temperature Figure 1. General formula of compounds from the 3FmX 1 PhX 2 r family. For the compound studied in this paper, m = 5, X 1 = F, X 2 = F, r = 6. and heat flow. These two quantities are usually calibrated by evaluating melting or/and solid-solid transitions of chosen reference materials with well-known transition enthalpies and temperatures. For calibration equipment were used indium (T m = 429.7 K, DH m 28.71 J/g [21]) and adamantane (T t = 207.6 K, DH t = 20.57 J/g [22]).
The crystallization was investigated by application of four distinct protocols: (1) Isothermal melt crystallizationthe sample was heated to 403 K (isotropic liquid phase), cooled down at 20 K/min to a selected temperature T mc and kept in this temperature until crystallization was completed. After crystallization, the sample was heated up at 10 K/min back to the isotropic liquid phase. The DSC data were analysed with TRIOS software. The crystallization degree of isothermal crystallization was calculated by integration of the exothermic anomaly over time in the heat flow F(t) curve, normalized by the enthalpy change upon crystallization DH cr [23]: where t 0 is the initialization time and t end is the time of complete crystallization. For non-isothermal crystallization, the integration was done over temperature.

BDS measurement
BDS experiment was performed using the Novocontrol Technologies spectrometer, The sample of 90 μm thickness between two gold electrodes was heated to 403 K and cooled down directly to 173 K. After this preparation, the BDS spectra were collected on heating up to 353 K in the frequency range of 0.1-10 7 Hz.

Kinetics of isothermal melt crystallization
POM textures registered during crystallization in isothermal conditions (Figure 2(a)) show that the nucleation occurs simultaneously with the crystal growth. The number of growing crystallites N(t) increases with time and decreases with increasing crystallization temperature T mc (Figure 2(b)). The nucleation rate calculated as dN(t)/dt is a function descending with time, however, the simple differentiation does not include the decreasing fraction of the SmC A * phase, described by the formula 1 − X(t). If one includes the ongoing crystallization, the number of crystallites can be calculated as: where J(t) is the nucleation rate. When the nucleation rate is constant, it can be moved before the integral and this assumption was used in further calculations. The numerical integration of 1 − X(t) over time was applied. The nucleation rates J calculated from Equation (2) using the experimental N(t) and X(t) values ( Figure 2(c)) are indeed approximately constant for each T mc , except the very beginning of crystallization ( Figure 2(d)). The nucleation rate changes with T mc according to the Arrhenius formula and the activation energy is equal to (343 ± 23) kJ/mol (average J for each T mc was used, excluding a few points at the beginning of crystallization), which is interpreted as the energy barrier for nucleation. Similar energy barrier, (306 ± 17) kJ/mol, can be determined straight from the Arrhenius plot of the total number of observed crystallites N total (inset in Figure 2(d)). In the DSC sample, where the sample/container interface is smaller, the energy barrier for nucleation can be higher due to a smaller contribution of heterogeneous nucleation [24]. DSC investigations of isothermal melt crystallization were carried out for T mc = 278-293 K. The exothermic anomaly, indicating crystallization, was present in the DSC curves registered in isothermal conditions. On subsequent heating at 10 K/min, the endothermic anomaly indicating the crystal → SmC A * transition was observed (Figure 3(a)). The onset of the latter anomaly shifts towards higher temperatures with increasing T mc , which is caused by less defected crystals forming at higher T mc . The crystallization time increases with increasing T mc . While for T mc = 278-290 K the initialization time is small, compared to the total crystallization time, for T mc = 292 K the beginning of crystallization is observed about 1600 s after cooling down the sample to T mc .
The isothermal crystallization was analysed using the Avrami model, which involves three parameters: initialization time t 0 , characteristic crystallization time t cr (denoted herein as t mc for melt crystallization and t cc for cold crystallization) and the Avrami parameter n, which depends on the dimensionality of the crystal growth [25][26][27]: The analysis was done only for the POM results for T mc = 277-283 K and the DSC results for T mc = 278-288 K. For higher T mc , the proper fitting of Equation (3) could not be performed because the X(t) curve became more complicated, probably due to small number of growing crystallites. The determined parameters of the Avrami model are collected in Table 1. In most of cases, the initialization time is shorter for the sample studied by POM, which is caused by the heterogeneous nucleation, as mentioned earlier. At the same time, the t mc values are shorter for the sample studied by the DSC method. It can be explained by hindrance of the crystal growth in the very thin sample used in the POM measurements. The Avrami parameter determined by POM is around 3 in almost all cases. Since it has been previously determined that the nucleation rate is constant, n ≈ 3 means the two-dimensional crystal growth [27]. In the DSC results, the Avrami exponents are larger, n ≥ 3 in most of cases, indicating that the hindrance of crystal growth in the third dimension is smaller than in the POM sample. Both the POM and DSC results show that the melt crystallization is restricted by nucleation [28], as the nucleation rate decreases with decreasing thermodynamic  driving force of crystallization, which is approximately proportional to undercooling [29]. Consequently, the melt crystallization occurs slower for higher T mc .

DSC measurements
The DSC curves collected during cooling from isotropic liquid ( Figure 4) show that at 10 K/min and higher cooling rates, melt crystallization does not occur and the SmC A * glass is obtained. The glass transition temperature T g , determined at the middle-height of the step in the DSC curve, is equal to 237-238 K for 15-30 K/min and 233 K for the 10 K/min cooling rate. When 3F5FPhF6 is cooled at 5 K/min, the partial crystallization is visible as a small anomaly with the onset at 279 K and the remaining SmC A * phase is vitrified at 236 K (inset in Figure 4). On subsequent heating at 10 K/ min, the glass softening is observed as a step at 241-242 K. The large exothermic anomaly observed on further heating indicates cold crystallization to the crystal phase denoted herein as Cr2. The onset temperature of cold crystallization decreases with the decreasing cooling rate in the preceding measurement stage from 257.5 to 259.7 K for 5 and 30 K/min, respectively. That shift is caused by nuclei which are formed during cooling and their number increases with the decreasing cooling rate, which enables faster crystallization upon subsequent heating [30,31]. While cooling at 5 K/ min, not only nucleation, but also growth of crystallites begins, therefore the decrease of the cold crystallization temperature on heating is more prominent than for higher applied cooling rates. Cold crystallization is followed by another transition visible in the DSC curves as a smaller exothermic anomaly with the onset at 293.2-294.0 K (without monotonic dependence on the rate of previous cooling). It is interpreted as the transition between two crystal phases, low-temperature Cr2 and high-temperature Cr1. The endothermic anomaly at 324.4-324.6 K indicates the melting of the Cr1 phase. The Cr2 phase is metastable, as the melt crystallization leads directly to the Cr1 phase.

Polarizing optical microscopy observations
The POM textures registered on cooling at 20 K/min and subsequent heating at 10 K/min are shown in Figure S1 in the Electronic Supplementary Information (ESI) file. The numerical analysis of textures was done by two methods. The first one is the fractal count box method, which enables the calculation of the fractal dimension of structures present in the photograph after converting the image into a black-and-white one [32,33]. Another parameter which can be obtained by numerical analysis is the modal luminance, which takes values from the 0 to 255 range and carries information of the brightness of the image ( Figure 5). During fast cooling, crystallization is not observed, in agreement with the DSC results. However, the gradual darkening of some regions of textures with decreasing temperature is evident in the 270-320 K range (Figure S1a-d, Figure 5(a)). It cannot be attributed to the vitrification of the SmC A * phase because it occurs below 240 K. The DSC curves do not indicate any phase transitions in the temperature range where the darkening of texture is observed, therefore it is caused by some changes in the structure of the SmC A * phase, most likely the helix pitch [34]. The vitrification of the SmC A * phase is not clearly visible in the POM textures even after the application of numerical analysis. Meanwhile, the softening of the SmC A * glass on heating can be related to the local wide maximum in the fractal dimension around 220-230 K ( Figure 5(b)). The SmC A * → Cr2 transition begins at ca. 260 K and is visible as darkening of the texture in the whole observed area (Figure S1e-h). In contrast to melt crystallization, where crystallites were easily distinguished and counted, during cold crystallization the number of nuclei is much larger and the boundaries between the SmC A * and Cr2 phases cannot be noticed. Because of that, the degree of cold crystallization cannot be determined based on the POM Figure 5. Results of the numerical analysis of the POM textures registered during cooling at 20 K/min (a) and heating at 10 K/min (b). Between the SmC A * phase and isotropic liquid, there are three other smectic phases (SmC*, SmC α * and SmA*) in a narrow temperature range [18]. These phase transitions are not indicated in the plots. 5.
observations. Above 296 K, the growing fraction of the Cr1 phase is visible ( Figure S1i-k). The number of nuclei is also larger than during melt crystallization. The melting of Cr1 is observed at 328 K.

Analysis of dielectric spectra
The dielectric spectra collected on heating after fast cooling to 173 K are shown in Figure S2 in ESI and the representative dielectric absorption vs. frequency at selected temperatures is shown in Figure 6. Fitting of the Cole-Cole [35] or Havriliak-Negami [36] formulas was done to determine the relaxation time t j and dielectric strength D1 j of each relaxation process: The shape parameters a j , b j describe the width and asymmetry of the distribution of the relaxation time in the ln f domain (b j = 1 for the Cole-Cole model, 0 < b j < 1 for the Havriliak-Negami model, 0 < a j < 1 for both models). The 1 1 parameter is the dielectric dispersion at high frequencies and the last term describes the ionic conductivity at low frequencies with S as a fitting parameter. The fitted t j , D1 j values are presented in Figure 7. The fitting of Equation (4) was not possible for all temperatures, however, all phase transitions and the glass transition are visible in the temperature dependence of the dielectric dispersion at 0.1 Hz (the lowest investigated frequency), shown in Figure 7(a). Below the beginning of cold crystallization at 249 K, two relaxation processes are observed in the supercooled SmC A * phase: α-process and the secondary β-process ( Figure 6(a)). The α-process is usually described by the Havriliak-Negami model [11,12,[14][15][16][36][37][38][39][40]. However, the fitting result for 247 K, where the shape of the absorption peak is well visible and the shape parameters a j , b j obtained from fitting are the most reliable, implies that the α-process for 3F5FPhF6 can be described by the Cole-Cole model, and this model was applied also for other temperatures. The relaxation time of the α-process follows the Vogel-Fulcher-Tammann (VFT) formula, where t 0 is the pre-exponential constant, B is the fitting parameter and T V is the Vogel temperature [37,41]. The fitted parameters of the VFT formula for the t a (T) values of 3F5FPhF6 (including two points above the melting temperature, Figure 7(b)) are T V = (208 ± 1) K, log 10 (t 0 /s) = −11.0 ± 0.2 and B = (883 ± 50) K. The glass transition temperature T g is the temperature where t a = 100 s [41]. Based on the fitted VFT parameters, T g = (238.0 ± 0.3) K, slightly lower than 241-242 K from the DSC results. Another parameter which can be obtained from the VFT formula is the fragility index m f = d log 10 t a /d(T g /T)| T=T g = BT g / ln 10(T g − T V ) [41]. If the relaxation time of the α-process changes with temperature according to the Arrhenius behaviour, m f = 16 and a material is referred to as a strong glassformer [41]. The stronger glassformers are expected to show smaller tendency to crystallization, which, according to Tanaka [42], is related to the larger degree of a short-range order within supercooled liquid, which hinders crystallization (although this interpretation was based on the results for metallic glasses). The more the t a (T) dependence deviates from the Arrhenius formula (i.e. if extrapolated t a diverges at T V > 0), the larger the fragility parameter and for the most fragile glassformers (usually polymers) it can take values of 100-200 [41]. 3F5FPhF6 is a fragile glassformer, as its fragility index m f = 105 ± 4.
The secondary β-process is also described by the Cole-Cole model (Figure 6(a)). The relaxation time of this process is expected to change with temperature according to the Arrhenius formula, t b (T) = t 0 exp(E a /T) [43,44]. The Arrhenius plot of t b shows different slope in the 193-205 K and 205-233 K range (Figure 7(b)), with the corresponding activation energies of (93 ± 2) and (71.7 ± 0.7) kJ/mol. The significant deviation from the Arrhenius dependence is visible upon approaching T g and above it. The relaxation time of the β-process does not follow the Arrhenius formula above T g also for other glassformers [44]. The DFT calculations for other 3FmX 1 PhX 2 r compounds [15,16,45] imply that the β-process in their vitrified SmC A * phase is not a Johari-Goldstein process, involving movements of rigid molecules [43,44], but instead it is related probably to rotations of the benzene ring and biphenyl.
Two weak relaxation processes, denoted as cr-I and cr-II, are observed in the Cr2 phase ( Figure 6  (b)). The cr-I process, at a lower frequency, is described by the Cole-Cole model and the cr-II process, at a higher frequency, is described by the Havriliak-Negami model. The relaxation times of both processes change according to the Arrhenius formula and their activation energies, (46 ± 5) kJ/mol for cr-I and (45.4 ± 0.7) kJ/mol for cr-II, are equal within the uncertainties (Figure 7(b)). The DFT results for other 3FmX 1 PhX 2 r compounds [15,16,45] indicate that the conformational energy barrier for rotation of the benzene ring is equal to 35-53 kJ/mol, therefore the cr-I and cr-II processes arise likely from this intra-molecular rotation. It implies that Cr2 is a conformationally-disordered (CONDIS) phase. Other two relaxation processes are observed in the Cr1 phase ( Figure 6(c)). The low-frequency process arises from electrode polarization or interfacial polarization [46] and it is not attributed to molecular movements in the Cr1 phase. The relaxation time of the higher-frequency cr-III process follows the Arrhenius dependence with the activation energy of (113 ± 3) kJ/mol. The cr-III process is described by the Havriliak-Negami formula with a large asymmetry, which means that there may be more than one overlapping processes that cannot be resolved.
Above the melting temperature, in the SmC A * phase, three relaxation processes are present (Figure 6(d)): the α-process and the anti-phase P H and in-phase P L phasons [47]. The detailed investigation of the P H , P L processes as well as of the relaxation processes in the SmC*, SmC α * and SmA* phases of 3F5FPhF6 is described in [18] and was not repeated here.

Kinetics of isothermal cold crystallization
Cold crystallization in isothermal conditions was investigated for temperatures T cc from the 248-253 K range (Figure 8(a)). The crystallization degree X(t) for each T cc was calculated using Equation (1) and the parameters of the Avrami model, collected in Table 2, were determined by fitting Equation (3), as presented in Figure 8(b). The Avrami exponent increases with increasing T cc from 2 to above 3, which indicates the increasing dimensionality of a crystal growth from platelike crystallites to isotropic ones [27]. The characteristic crystallization time t cc decreases with increasing T cc in agreement with the Arrhenius equation (Figure 8(c)), therefore the rate of isothermal cold crystallization is dependent mainly on diffusion rate [28]. The activation energy of isothermal cold crystallization is equal to E cc = (76 ± 5) kJ/mol. During heating at the 10 K/min rate after completion of isothermal cold crystallization (Figure 8(d)), the Cr2 → Cr1 transition is observed, with the onset temperature increasing with increasing T cc from 291.0 K to 295.2-295.3 K (inset in Figure 8(d)).
The dependence of the Avrami parameter n on the crystallization degree can be determined directly from the formula [48]: where dX/dt is the crystallization rate. The n values calculated for X = 0.1-0.9 are shown in Figure  S3a in ESI. For T cc = 251-253 K, n is constant within uncertainties during the crystallization process. For T cc = 248-250 K, n takes lower values in the beginning and finishing stage of crystallization. Generally, the approximately constant n values for given T cc confirm that the isothermal cold crystallization of 3F5FPhF6 can be described by the single-step Avrami model. The effective activation energy vs. crystallization degree can be obtained using two formulas [48]: where t and dX/dt correspond to a given crystallization degree and C t , C X are fitting parameters. For 3F5FPhF6, the linear dependences are obtained both for the Arrhenius plot of t − t 0 ( Figure  S3b) and of dX/dt ( Figure S3c), enabling determination of E eff from the linear fits. The effective activation energy determined both from Equations (6) and (7) increases during crystallization ( Figure S3d). However, the E eff values obtained using Equation (6), based on time necessary to reach a certain X value, are visibly smaller than these obtained from Equation (7), based on the rates of crystallization at selected X. According to calculations presented in ESI, both Equations (6) and (7) give the E eff value independent on X and equal to the overall activation energy E cc when n does not change with temperature. For 3F5FPhF6, it is not fulfilled because n increases with increasing T cc , which causes difference between E eff and E cc . As it is further shown in ESI, even if n depends on temperature, Equation (6) always gives E eff values consistent with E cc because for X ≈ 0.63, E eff = E cc , while Equation (7) may give the E eff values shifted in respect with E cc in the whole X range. Because of that, Equation (6) is supposed to describe better the changes of the effective activation energy during crystallization. The cold crystallization kinetics is controlled by the rate of diffusion of molecules from the SmC A * phase to the growing crystallites, which occurs more easily in the beginning of crystallization than in the later stages. It leads to increase of E eff with increasing X. It is reverse dependence of that observed for the melt crystallization of a similar compound, where E eff decreases with increasing X because of larger contribution of nucleation rate to the crystallization kinetics [49].

Kinetics of non-isothermal cold crystallization
The investigation of non-isothermal cold crystallization at various heating rates was carried out by cooling the sample from isotropic liquid to the vitrified SmC A * phase at the 30 K/min rate and subsequent heating at rates from the 1-20 K/min range. The DSC curves collected during heating (Figure 9(a)) show the previously observed sequence: SmC A * glass → supercooled SmC A * → Cr2 → Cr1 → SmC A *. The increasing heating rate leads to a slight increase in the glass softening temperature (from 238 K to 242 K), strong increase in the onset temperature of cold crystallization (from 249.8 to 263.8 K) and of the Cr2 → Cr1 transition (from 281.2 to 295.5 K), and to a slight decrease of the temperature of melting (from 326.9 to 324.7 K). The degree of cold crystallization, calculated by integration of the exothermic anomaly over temperature (Equation (1)), is presented in Figure 9 (b). The kinetics of non-isothermal cold crystallization was studied using the Ozawa model [50]: where z is the crystallization rate and n O is the Ozawa exponent. The parameters of the Ozawa model at particular temperature can be determined if the plot of ln (− ln (1 − X)) vs. ln f is linear, which is obtained for 3F5FPhF6 (Figure 9(c)). The slope and intercept of the fitted line for each temperature are equal respectively to −n O and ln z. The determined parameters of the Ozawa model are shown in Figure 9(d). The Ozawa exponent n O = 2.6 ± 0.1-3.4 ± 0.1, on average 3.1 ± 0.2, indicates the three-dimensional crystal growth [27] under the assumption that most of the nuclei are formed at lower temperatures, before the beginning of cold crystallization [31,39]. The ln z values increase linearly with increasing temperature in the 257-266 K range, which means that the crystallization rate is dependent mainly on diffusion rate [51,52]. In the 266-270 K range, ln z is constant within uncertainties, which indicates that the diffusion and nucleation rate have comparable influence on the crystallization kinetics [51,53]. The activation energies E cc for the cold crystallization and Cr2 → Cr1 transition were determined from the onset temperatures T o and peak temperatures T p of respective exothermic anomalies in the DSC curves using the Augis-Bennet formula [54]: where f is the heating rate and C AB is a fitting parameter. The slope of the ln (f/(T p − T o )) vs. 1/T p plot is equal to the E cc /R value. In the results for 3F5FPhF6 (Figure 10(a)), two distinct linear dependences are visible for the slow (1-8 K/min) and fast (8-20 K/min) heating. The activation energy of the SmC A * → Cr2 transition for slow heating, (95 ± 2) kJ/mol, is larger than for fast heating, (64 ± 3) kJ/mol. The activation energy values of the Cr2 → Cr1 transition are much higher: (247 ± 11) and (365 ± 28) kJ/mol for slow and fast heating, respectively. The activation energy of the Cr2 → Cr1 transition is lower for slow heating, which is the opposite of the relationship obtained for the SmC A * → Cr2 transition. The Augis-Bennett method enables determination of the activation energy of the whole crystallization process. Meanwhile, during complex processes, the effective activation energy E eff takes different values for different degree of conversion X(T), which can be determined by Friedman's differential isoconversional method using the formula [55,56]: In this formula, (dX/dt) X,f is the crystallization rate for a given heating rate f when a certain crystallization degree X(T) is reached, T X is the temperature when this X(T) value is reached, A X is a constant and f (X) is the reaction model. If the ln (dX/dt) X,f vs. 1/T X plot is linear, the line's slope is equal to −E eff . For 3F5FPhF6, the linear dependence is obtained separately for slow and fast heating (Figure 10(b)). The border heating rate between two regimes is 5 K/min, lower than 8 K/min determined by the Augis-Bennett method. The activation energy E eff decreases with increasing crystallization degree from (121 ± 4) to (96 ± 2) kJ/mol for slow heating and from (70 ± 1) to (48 ± 2) kJ/ mol for fast heating. The E eff values for slow heating approach the activation energy obtained by the Augis-Bennett method in the finishing stage of crystallization, while for fast heating the Augis-Bennet activation energy is in agreement with E eff for X(T) = 0.3-0.5. The third method applied to determine the activation energy of non-isothermal cold crystallization is the one presented by Matusita et al. [57]: where C M is a fitting parameter. The m M parameter is equal to 1, 2, 3, respectively, for the one-, twoand three-dimensional crystal growth. The n M parameter is a slope of the ln (− ln (1 − X)) vs. ln f plot, identically as n O in the Ozawa model, and it is equal to m M for the constant number of nuclei and to m M + 1 for the constant rate of nucleation. The activation energy for a particular crystallization degree can be determined from the plot of the logarithm of the heating rate vs. the temperature T X where the given crystallization degree is reached. The slope of this plot is equal to 1.052m M E eff /n X R. The linear fits had to be performed separately for slow and fast heating ( Figure  10(c)), with the border heating rate of 5 K/min, identically as in the isoconversional method. The constant number of nuclei and isotropic crystal growth were assumed, i.e. n M = m M ≈ 3. The activation energies determined by the Matusita method for slow heating, (105 ± 2)-(118 ± 2) kJ/mol, are comparable with values obtained by the isoconversional method, (96 ± 2)-(121 ± 4) kJ/mol, but they exceed the activation energy obtained by the Augis-Bennett method (Figure 10(d)). For fast heating, the E X values determined by the Matusita method, (72 ± 2)-(93 ± 2) kJ/mol, are significantly higher for both than the results of the isoconversional method, (48 ± 2)-(70 ± 1) kJ/mol and of the Augis-Bennett method. On the other hand, both the Matusita method and the isoconversional method indicate the decreasing E eff (X) dependence, and for all used methods the activation energy of the nonisothermal cold crystallization is larger for slow heating than for fast heating. Decrease of E eff with the increasing degree of non-isothermal cold crystallization is consistent with the E eff (X) dependence of the isothermal cold crystallization of 3F5FPhF6, and also with the results for the non-isothermal cold crystallization of other glassformers [51,56,58]. Different values of activation energy for slow and fast heating were observed for the cold crystallization of several compounds [13,15,20,58,59], among which the activation energy was larger for high heating rates only in [20].

Comparison of the crystallization kinetics in various conditions
The relationship between the characteristic time of crystallization and the relaxation time of the αprocess (which is proportional to viscosity) is described by the coupling coefficient z, determined as a slope of the ln t cr vs. ln t a plot ( Figure 11). If z ≈ 1, it means the strong coupling between the crystallization kinetics and molecular dynamics, while z < 0 indicates a more prominent contribution of the thermodynamic factor [29,38,39,60]. For 3F5FPhF6, the coupling coefficient was studied only for cold crystallization, as the melt crystallization of this compound is controlled mainly by the nucleation rate. The characteristic time t cc of isothermal cold crystallization was previously obtained by fitting the Avrami model ( Figure 8). For non-isothermal cold crystallization, the same method as for the 3F5HPhH6 compound was applied [15]. The characteristic time t cc for each heating rate was obtained by fitting the Avrami model to the X(t) dependence, therefore both for isothermal and nonisothermal conditions it is defined as X(t cc − t 0 ) ≈ 0.63. Then, the t cc values of non-isothermal cold crystallization were attributed to the corresponding peak temperatures T p of the exothermic anomaly related to the SmC A * → Cr2 transition. The crystallization rate has a maximum at T p , therefore it can be assumed that considerable part of crystallization occurs around this temperature. The t a values in the 248-269 K range were calculated from the fitted results of the VFT formula (Figure 7(b)). As Figure 11 shows, the linear dependence of the ln t cc vs. ln t a plot is obtained both for the isothermal and non-isothermal cold crystallization of 3F5FPhF6. Only two points, corresponding to cold crystallization at 1 and 2 K/min rates, deviate from the linear dependence and also the uncertainty of t cc is the largest in their case. The coupling coefficient z = (0.47 ± 0.2) for non-isothermal cold crystallization is larger than z = (0.30 ± 0.2) for isothermal cold crystallization. The z coefficient is expected to decrease with increasing fragility with the approximate formula z ≈ 1.1 − 0.005m f (determined from linear fit to the experimental results for numerous compounds) with the uncertainty of ∼0.05 [29], which for 3F5FPhF6 leads to z ≈ 0.58, larger than obtained from the ln t cc vs. ln t a plot. The overall results indicate that the coupling between t cc and t a is only partial. Finally, the temperature of maximal crystallization rate of 3F5FPhF6 is determined. In Figure 12 (a), the effective activation energy E eff is plotted against the crystallization degree X(T). When one  takes the average temperature at which a given X(T) is reached, then it is possible to obtain the E eff (T) plot [51,56]. The temperature range of non-isothermal cold crystallization shifts considerably with increasing heating rate, therefore the average is taken over a temperature range which is almost 10 degree wide, as indicated by the horizontal bars in Figure 12(a). Nevertheless, the E eff (T) points for slow and fast heating are located roughly on the common line, which can be used to determine by extrapolation the border temperature where E eff = 0 and crystallization rate is maximal. Below this temperature, E eff (T) > 0, the crystallization is controlled by diffusion and the crystallization rate increases with increasing temperature. Above this temperature E eff (T) < 0, crystallization is controlled by nucleation and the crystallization rate decreases with increasing temperature [51,56]. The linear extrapolation gives the border temperature of 276 K for the Friedmann's isoconversional method and 286 K for the Matusita method. The border temperature can be also estimated from the Arrhenius plots of the characteristic times t mc of melt crystallization and t cc of cold crystallization (Figure 12(b)). The t mc values follow roughly the Arrhenius dependence with the effective activation energy -(90 ± 8) kJ/mol for the DSC results and -(70 ± 15) kJ/mol for the POM results. The ln t cc values determined by DSC for isothermal and non-isothermal crystallization (the latter plotted against 1000/T p ) can be fitted by a common linear function with the corresponding activation energy of (76 ± 3) kJ/mol. By extrapolation of the linear fit to the Arrhenius plots of t mc and t cc from the DSC results, the border temperature is obtained as the intersection at (270.8 ± 0.7) K, which is much closer to the border temperature estimated by the Friedmann's isoconversional method than to the one obtained by the Matusita method. When one includes t mc determined by POM, the border temperature is slightly lower, 267 K. To recall, the Ozawa method (Figure 9(c)) implied that the border temperature was above 266 K. Taking into account all results, the border temperature of maximal crystallization rate is estimated as 266-276 K. The results of the Matusita method are excluded, as for this compound they give seemingly overestimated border temperature. In Figure 7(b) one can see that the relaxation times of the cr-II and α-process (the latter calculated from the VFT formula) intersect at 270 K. In our previous publication about 3F5HPhH6 [15] it was suggested that the crystallization was facilitated when the relaxation process in a crystal phase and the α-process in the SmC A * phase had similar frequencies. For 3F5FPhF6, this statement is even stronger, as the intersection temperature of these relaxation times is close to the temperature of maximal crystallization rate.

Summary and conclusions
The 3F5FPhF6 compound forms the glass of the SmC A * phase for the cooling rate of 10 K/min and more. During cooling at 5 K/min, the partial melt crystallization SmC A * → Cr1 is observed. 3F5FPhF6 undergoes the complete melt crystallization to the Cr1 phase in isothermal conditions, with the total crystallization time not exceeding one hour in the temperature range of 277-293 K. The melt crystallization kinetics is controlled mainly by thermodynamic driving force. The growth of crystallites is 2-dimensional for a sample between two glass plates studied by POM or either 2-or 3-dimensional for a sample in an aluminium pan investigated by DSC, as determined using the Avrami model. The microscopic observations imply the constant rate of nucleation.
Cold crystallization is more complicated, as it includes the phase sequence SmC A * → Cr2 → Cr1. The cold crystallization kinetics, investigated by DSC only, is controlled mainly by diffusion rate of molecules from the SmC A * phase to the Cr2 phase. The growth of crystallites is 3-dimensional in non-isothermal conditions (according to the Ozawa model), while in isothermal conditions the dimensionality of crystallites increases with increasing temperature of crystallization from 2 to 3 in the 248-253 K range (according to the Avrami model). For cold crystallization, the numerous nuclei are formed mainly below the temperature where crystal growth occurs, therefore their number is assumed to be approximately constant during crystallization. The Cr2 phase, not reported before, is observed only after cold crystallization. The BDS results indicate that Cr2 is a conformationally disordered crystal phase (CONDIS crystal).
The temperature dependence of the α-process in the SmC A * phase gives the fragility parameter of 105 ± 4. The corresponding predicted coupling coefficient between the relaxation time of the αprocess and the characteristic time of cold crystallization equals 0.58 ± 0.5. The actual coupling coefficients are lower, 0.47 ± 0.2 and 0.30 ± 0.2 for cold crystallization in non-isothermal and isothermal conditions, respectively. The coupling between the crystallization kinetics and molecular dynamics is therefore stronger for non-isothermal cold crystallization. It is in accord with presumption that in non-isothermal conditions, when temperature increases constantly, the cold crystallization rate is dependent on diffusion rate (increasing with increasing temperature) to a larger extent than the isothermal cold crystallization rate.
The effective activation energy of the crystallization process was determined using various methods. The Arrhenius plots of the characteristic crystallization time give the effective activation energy of -(70 ± 15) kJ/mol and -(90 ± 8) kJ/mol for isothermal melt crystallization investigated by POM and DSC, respectively, and (76 ± 5) kJ/mol for isothermal cold crystallization investigated by DSC. Interestingly, the characteristic time of non-isothermal cold crystallization plotted against the inverse peak temperature of the DSC anomalies follows the same dependence in the Arrhenius plot as the results for isothermal cold crystallization. By intersection of linear slopes in the Arrhenius plot (DSC results), the border temperature corresponding to the maximal crystallization rate is determined to be (270.8 ± 0.7) K. More complex analysis by the Augis-Bennett, Friedmann's isoconversional and Matusita methods shows that non-isothermal cold crystallization is characterized by a smaller activation energy for fast heating than for slow heating. Additionally, two last methods indicate that the effective activation energy increases with increasing crystallization degree. The results of the Friedmann's method are more consistent with the results of the Augis-Bennett method and the temperature of the maximal crystallization rate estimated by the Friedmann's method is in better agreement with the one obtained from the Arrhenius plot than the results of the Matusita method. For cold crystallization in isothermal conditions, the increase of the effective activation energy with an increasing crystallization degree is also reported and it is explained by gradual hindrance of diffusion of molecules between the SmC A * and Cr2 phases.
To sum up, the main conclusions from this study are: . 3F5FPhF6 shows intermediate glassforming properties because the vitrification of the SmC A * phase of this compound and complete avoidance of crystallization does not require very high cooling rate (10 K/min). For comparison, some of the previously studied 3FmX 1 PhX 2 6 homologues undergo vitrification for much slower cooling (0.5-5 K/min) [11][12][13][14][15][16] and some crystallize at much faster cooling (20 K/min) [12]. . 3F5FPhF6 is a fragile glassformer (m f = 105) and easily crystallizes during heating from the SmC A * glass. Because of that, it is not applicable as a pure compound but it can serve as a component of glassforming mixtures. The cold crystallization kinetics is controlled by diffusion, while the melt crystallization kinetics is controlled by the thermodynamic driving force. . The newly reported metastable Cr2 phase of 3F5FPhF6 is formed only during cold crystallization and it is identified as the CONDIS phase. The Cr2 phase is to be characterized further in another publication.
The results presented in this paper confirm the strong influence of position and number of fluorine atoms substituted to the benzene ring in the 3FmX 1 PhX 2 6 compounds on the crystallization process. Considering only compounds with m = 5, one can see that 3F5HPhF6 has the highest glassforming properties [12], as it exhibits the SmC A * glass with no signs of partial crystallization on slow cooling with 3 K/min rate. Total avoidance of crystallization in 3F5HPhH6 [15] and 3F5FPhF6 (this paper) requires cooling rate of 5 and 10 K/min, respectively. Finally, the SmC A * glass of 3F5FPhH6 [61] was not obtained, as its crystallization is observed even for cooling at 30 K/min. It can be concluded that for m = 5, the F atom at X 1 position facilitates vitrification of the smectic phase, while the F atom at X 2 position supports crystallization. At the same time, the length of the C m H 2m chain is known also to contribute, as tendency to form the smectic glass increases with increasing chain length and is higher for odd than for even homologues [12,15,62]. It is therefore important to investigate in detail the behaviour of as much 3FmX 1 PhX 2 6 homologues as available, in order to find patterns in the correlations between their molecular structure and tendency to either vitrification or crystallization. It will enable easier choice of compounds to the liquid crystalline mixtures for application in LCDs, as well as designing new chiral smectogenic compounds for this purpose.

Disclosure statement
No potential conflict of interest was reported by the author(s).