Crystallization Kinetics of Phosphonium Ionic Liquids: Effect of Cation Alkyl Chain Length and Thermal History

The effects of alkyl chain length on the crystallization kinetics and ion mobility of tetraalkylphosphonium, [P666,n][TFSI], (n = 2, 6, 8, and 12) ionic liquids were studied by differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (BDS) over a wide temperature range. The liquid–glass transition temperature (Tg) and ion dynamics examined over a broad T range were almost insensitive to structural modifications of the phosphonium cation. In contrast, the crystallization kinetics were strongly affected by the length of the fourth alkyl chain. Furthermore, the thermal history of the sample (cold vs melt crystallization) significantly impacted the crystallization rate. It has been found that the nature of crystallization phenomena is the same across the homologous series, while the kinetic aspect differs. Finally, electric conductivity in supercooled liquid and crystalline solid phases was measured for all samples, revealing significant ionic conductivity, largely independent of the cation structure.


■ INTRODUCTION
Ionic liquids (ILs), salts that melt below 100 °C, have been of interest to chemists for decades, although their applications have changed over time.Recently, ILs have been gaining interest as functional materials equipped with fascinating physicochemical properties that arise from strong Coulombic interactions between ions in the liquid phase.Ionic conductivity enables efficient charge transport and facilitates various electrochemical applications. 1The notable chemical and thermal stability, together with negligible vapor pressure and a wide liquidus range, make them attractive candidates across applications in physics and material science. 2 In order to expand the liquidus range of ILs, their ions have been designed to disrupt crystallization (viz., low symmetry and low and dispersed charges).This resulted in the unique phase behavior of ILs, fueling fundamental studies and inspiring new applications.
In applications of ILs as electrolytes in energy storage devices, it is crucial to maintain their liquid state under various thermodynamic conditions, including elevated pressure.Therefore, ILs that do not crystallize over a wide temperature and pressure range are valuable in this context. 3,4In contrast, ILs that crystallize reproducibly on cooling or reheating are desired for purification strategies and as phase change materials in energy storage and thermal management applications. 5,6urthermore, a subclass of partially ordered ILs, called organic ionic plastic crystals (OIPCs), serve as relatively conductive solid-state electrolytes, which provide better contact with electrodes during volume change than brittle solid electrolytes while preventing the leakage problems associated with liquid electrolytes. 7,8he wealth of applications reliant on phase control motivates fundamental studies into liquid−glass transitions 9 and the crystallization of ILs.−22 Studies on the crystallization kinetics and charge transport mechanisms of quaternary phosphonium ILs have not been reported to date. 23−31 In this work, we investigate the crystallization tendency and ion dynamics of phosphonium ILs with a trihexyl(alkyl)phosphonium cation, [P 666,n ][TFSI], altering the length of a single side chain (n = 2, 6, 8, and 12).To examine the crystallization ability of these materials, a series of isothermal time-dependent measurements have been performed using differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (BDS).This approach enables us to determine the crystallization rate at various temperatures and establish the link between the length of the alkyl chain in the cation and the ordering tendency at different thermodynamic conditions.The effect of the sample's thermal history on the crystallization rate has also been investigated.
■ EXPERIMENTAL METHOD Materials.The synthetic procedure for trihexyl(alkyl)phosphonium bis(trifluoromethylsulfonyl)imide, [P 666,n ] - [TFSI] (n = 2, 6, 8, and 12), is reported in our earlier paper. 32A generalized structure of the homologue series studied here is shown in Figure 1, and the physiochemical properties of each homologue are collected in Table 1.The water content was determined using a coulometric Karl Fischer titration (899 Coulometer, Metrohm).
DSC. Calorimetric measurements were performed using a Mettler-Toledo DSC1STAR instrument with a liquid nitrogen cooling accessory and an HSS8 ceramic sensor with 120 thermocouples.The nitrogen flow was maintained at 60 mL min −1 .Indium and zinc standards were used to calibrate the temperature and enthalpy.The samples were measured in aluminum crucibles having a capacity of 40 μL shut with a punctured cover.To ensure repeatability and precision, a fresh sample was prepared for each experiment and cycled at least three times.
BDS.The conductivity measurements at ambient pressure were performed using a Novo-Control GMBH Alpha dielectric spectrometer over a wide temperature and frequency range (10 −1 to 10 7 Hz).The Quattro system controlled the temperature with an accuracy of 0.1 K.During the measurement, the sample was held between two stainless steel electrodes with a 15 mm diameter and a 0.2 mm quartz ring to maintain a stable separation between the electrodes.
The isothermal conductivity studies were carried out at 223, 218, 213, 208, and 203 K in the supercooled liquid state.The ILs were first cooled to a glassy state for cold crystallization studies.Immediately after amorphization, the temperature was increased to the given T c , and the real part of complex electric conductivity σ′( f) was recorded under isothermal conditions, at specified time intervals throughout the crystallization process.For melt crystallization, the liquid sample was supercooled to the crystallization temperature, and then σ′( f) spectra were recorded at the same predetermined time intervals during the crystallization process.

■ RESULTS AND DISCUSSION
Glass-Forming Study by Differential Scanning Calorimetry.Thermal analysis allows for an understanding of the material properties as a function of temperature.In this work, DSC was used to characterize the thermal properties of a homologous series of [P 666,n ][TFSI] ILs, investigating their glass-forming ability and crystallization tendency.Two different temperature ramping rates were used: a standard rate of 10 K/min and a slower rate of 1 K/min.It has been discovered that all the studied ILs could be vitrified on cooling, even at the slow cooling rate of 1 K/min (see Supporting Information, Figure S1).Consequently, in all cases, the subsequent heating curve featured a step-like increase in heat capacity identified with the glass transition (Figure 2).Glass transition temperatures (T g ) were found to decrease slightly with elongating cationic alkyl chains and decrease with decreasing ramp rates, but all remained within a narrow range of T g = 180−186 K (Table 1).In other words, decreasing the alkyl chain length in [P 666,n ][TFSI] systems has not resulted in observable changes in the thermal characteristics.This contradicts the behavior of imidazolium-based ILs, which showed a decrease in T g for materials with a shorter alkyl substituent. 17,20None of the ILs

The Journal of Physical Chemistry B
showed a crystallization tendency when a 10 K/min heating rate was applied.At a scan rate of 1 K/min, T g values were lower, which agrees with the kinetic nature of the vitrification process, and cold crystallization exotherms were recorded for [P 666,2 ][TFSI] (T m = 224.1 K) and [P 666,6 ][TFSI] (T m = 233.7 K).Cold crystallization of the n = 2 homologue took place at a temperature 10 K lower than for n = 6 homologue, and no cold crystallization was observed for the n = 8 or 12, which indicated an increased tendency toward cold crystallization in ILs with short alkyl chain lengths.
Controlling the degree of crystallinity and crystallization rate on cooling and heating is crucial for applications of ILs, which inspired subsequent kinetic studies.

Kinetics of Isothermal Crystallization of [P 666,2 ]
[TFSI] by DSC.The kinetics of crystallization of [P 666,2 ][TFSI] were studied under both isothermal cold crystallization and isothermal melt crystallization conditions.For this purpose, time-dependent DSC measurements were performed at five different temperatures: 223, 218, 213, 208, and 203 K. To monitor the cold crystallization, the sample was first cooled at 5 K/min from RT (303 K) to the temperature below T g (168 K) and then heated at the same rate to the desired temperature (T c ).The sample was kept at T c until the crystallization process was finished and subsequently heated to the melting point (see the inset of Figure 3a).The isothermal melt crystallization was studied by cooling the sample from room temperature (RT) to T c (see the inset of Figure 3b) and holding it at this temperature until the crystallization process was finished, followed by heating above the melting point (see the inset of Figure 3b).The heating scans performed after each isothermal step are presented in Figure S2.Since the T m and the enthalpy of the melting process (ΔH m = 25.4J/g) are the same for all scans, it can be assumed that a single polymorphic form is obtained in both cold and melt crystallization.Furthermore, the lack of liquid−glass transitions indicates complete crystallization.The only exceptions to these rules are the cold crystallization at 203 K, where ΔH m = 14.6 J/g suggests that 57% of the sample has crystallized, and the melt crystallization at 220 K, where ΔH m = 23.75J/g suggests that 93.5% of the sample has crystallized (Table S1).
The exothermic peaks of isothermal crystallization measured in two different procedures are presented in Figure 3a,b.The cold crystallization maxima shift toward short time scales as T c increases, demonstrating that temperature is a major factor controlling cold crystallization.In contrast, for [P 666,2 ][TFSI] crystallization monitored right after cooling from RT, there was a maximum in crystallization time scale recorded as a function of temperature: the shortest crystallization was recorded at 218 and 213 K (nearly identical exotherms, see Figure 3b), then at 208, and finally at 220 K.The melt crystallization at 223 K was too slow to be monitored in an available experimental time frame.
By integrating exothermic peaks obtained during the crystallization process, the relative degrees of isothermal crystallization, α DSC , at different temperatures could be determined by eq 1 where t 0 and t ∞ are the times at which crystallization begins and ends, respectively, dH/dt represents the rate of heat evolution, and A t and A ∞ denote the areas under the normalized DSC curves for partially and fully crystalline samples.
The time evolutions of isothermal cold and melt crystallization α DSC are presented in Figure 3c,d, respectively.All α DSC (t) curves, irrespective of the type and temperature of crystallization, had a sigmoidal shape and reached unity when crystallization was completed.To gain a generalized understanding of the crystallization kinetics of [P 666,2 ][TFSI], it has been attempted to fit the experimental data with two theoretical models.First, the Avrami equation (eq 2) 33,34 has been applied 35 where K = k n is a crystallization rate constant, which relies on the crystallization temperature and geometry of the material, n denotes the Avrami exponent that is connected to the time dependence of the nucleation rate and crystallization dimensionality, and ideally n would be between 1 and 4. 36,37 Typically, when n values approach 2, it suggests a twodimensional growth of crystals, whereas n values closer to 3 or higher, as observed in the case of composites, are indicative of heterogeneous nucleation followed by three-dimensional growth. 38,39The fitting of the Avrami function to the DSC experimental results is displayed as lines in Figure 3c,d.The Avrami model does not describe the experimental data satisfactorily over the entire time range, which is not surprising and has been many times documented in the literature. 40To determine the values of the Avrami parameters, the log form of eq 2 was used for preparing the so-called Avrami plot (eq 3) According to this equation, log[-ln(1-α DSC (t))] should depend linearly on log(t).Using a simple linear regression allows us to estimate the values of n and log K as the slope and intersect of the linear dependence at each crystallization temperature.The characteristic time of crystallization τ cr = 1/k can be determined for log[−ln(1 − α DSC (t))] = 0.The socalled Avrami plot of [P 666,2 ][TFSI] determined from DSC measurements is shown in the inset of Figure 3c,d.Against theoretical prediction, the Avrami plot of [P 666,2 ][TFSI] does not hold a linear nature across the time frame of the experiment.
As the second model, a method proposed by Avramov et al. 41 has been used (eq 4) in which the parameter n has the same meaning as in the Avrami model (eq 2).
The key advantage of this approach is the possibility of avoiding measurement errors induced by the thermal instability of the sample at the beginning of the experiment and accurately estimating the crystallization induction time t 0 .Furthermore, the characteristic time for the isothermal crystallization, τ cr , can be easily determined from the maximum of the first derivate of normalized crystallization degree, dα(t)/d(ln(t)), plotted versus ln(t) (Figure 4a,b).The parameter n can be estimated as n = (α(t))' max /0.368.Substituting t − t 0 by τ cr in eq 4 gives α(τ cr ) = 1−1/e ≈ 0.63.Consequently, to estimate t 0 , t can be found from the condition α(t)' = 0.63 and t 0 is then calculated as t− τ cr .

The Journal of Physical Chemistry B
A comparison of Avrami and Avramov characteristic parameters determined from DSC results recorded for [P 666,2 ][TFSI] is given in Table 2.
For isothermal cold crystallization, the crystallization rate k, defined as 1/τ cr , increased with increasing temperature.Consequently, from fitting the Arrhenius law (eq 5) to log k vs 1000/T dependence, the activation energy of cold crystallization for [P 666,2 ][TFSI] could be determined as E a = 51 kJ/mol (see Figure 5a) where R is the gas constant and k 0 and E a are fitting parameters.In contrast, the rate of melt crystallization increased first and then decreased as the temperature increased, with the dependence log k vs 1000/T revealing a maximum of around 213 K.
These findings can now be related to the molecular structure of [P 666,2 ][TFSI], with three relatively long hexyl chains on the cation and a flexible anion that can adopt a cis or trans conformation.It is generally known that the crystallization process involves two stages: (i) nucleation, N, and (ii) crystal growth, CG (Figure 5b), 12,42,43 with each process reaching a maximum rate at a temperature somewhere between the glasstransition temperature and the melting point.While nucleation controls the crystallization at lower temperatures close to T g , CG dominates at higher temperatures close to T m (Figure 5b).Avrami exponent n assumes the value of 4 for threedimensional CG with a constant nucleation rate.A decrease to n = 3 informs of the existence of preformed nuclei or   The Journal of Physical Chemistry B restricted dimensionality of crystallization (such as crystallization on the surface).Lower numbers may also be attributed to a decreasing nucleation rate, as crystallization releases heat, which causes a local temperature increase and suppresses crystallization. 14or cold crystallization, the parameters n (Avrami exponent connected to the time dependence of the nucleation rate and crystallization dimensionality), k (crystallization rate), log k, and τ cr (characteristic time for the isothermal crystallization) were essentially independent of the chosen model.By supercooling to the glassy state and subsequent heating to T c cold > T g , the IL has been passed through the nucleation maximum twice, creating a number of preformed nuclei for cold crystallization.For T c = 213−223 K (higher temperature, close to T m ), the Avrami exponent is n = ca.2.35, suggesting preformed nuclei of crystallization and a decreasing nucleation rate.In this thermal range, CG is faster than N because there is enough kinetic energy for molecular diffusion to grow the lattice; combined with pre-existing nuclei, it results in high crystallization rates.Arguably, thermal energy from this fast crystallization could result in local heating of the IL, eliminating some nucleation sites and further contributing to low n values.For T c < 213 K (closer to T g ), the Avrami exponent increased with decreasing T c , reaching n = 2.6 at 208 K and n = ca.3.35 at 203 K, corroborating with increasing nucleation rates in this region, dominating over molecular diffusion.It could be speculated that, at these lower temperatures, molecular diffusion is very slow, and the energy supplied by the ramped heating was used for subtle rearrangements of alkyl chains in cations and/or cis/trans switching in anions, leading to an increase in local ordering of [P 666,2 ][TFSI] and thus -nucleation.This explains the longer time frame for such nucleation-driven crystallization to complete (Figure 3a).
For melt crystallization, there were significant discrepancies between the Avrami and Avramov models: the former predicted lower values of n at extreme temperatures (n = 1.91 at 220 K and n = 3.18 at 208 K), whereas the latter gave n = 2.46 at 220 K and n = 3.38 at 208 K (see Table 2 for a full comparison).Still, both models propose the same trend of increasing n with decreasing T c , analogous to cold crystallization.The core difference in melt crystallization is the absence of preformed nucleation sites.At T > 213 K, although the CG was fast in both melt and cold crystallization, the melt crystallization rate was lower due to the much smaller number of nuclei present.At T c < 213 K, CG was very slow in both melt and cold crystallization, and crystallization was reliant on nucleation, N. Since some nuclei were precreated during cold crystallization (due to the crossing through the maximum of nucleation) in one sample but not in the other, log k cold assumed higher values than log k melt .
Finally, the sample thermal history was not important for T c at which N and CG rates were the same, i.e., 213 K for [P 666,2 ][TFSI], as shown in Figure 5a.The cold and melt crystallization rates were equal, indicating the same contribution of nucleation and CG to the overall crystallization process.
To verify these results, gain better insight into the process dynamics, and determine how crystallization affects the conducting properties of [P 666,2 ][TFSI], isothermal cold and melt crystallization experiments were subsequently monitored by BDS.

Kinetics of Isothermal Crystallization of [P 666,2 ]
[TFSI] by Dielectric Spectroscopy.BDS is a valuable tool for monitoring the crystallization process.Usually, the progress of crystallization is monitored by a decrease in relaxation strength that reflects a reduced number of mobile dipoles.However, in the case of ionic systems, the translational motions of charge carriers dominate both the imaginary and real parts of the dielectric function, ε″(f) and ε′(f).Therefore, the complex The Journal of Physical Chemistry B dielectric conductivity, σ* = ε 0 (Z*(f)•C 0 ) −1 , is commonly employed to express the properties of ILs. 44,45This representation was also selected to investigate the crystallization progress of [P 666,2 ][TFSI].The same experimental protocol was used for BDS measurements to compare the dielectric and calorimetric results quantitatively.
The representative frequency dependence of the real part of complex conductivity, σ′( f), measured during the melt crystallization at 223 K, is presented in Figure 6a.Each recorded curve, except the last one, showed three well-defined regions: (i) the low-frequency region; the area where the polarization effect takes place, (ii) the midfrequency plateau, also called dc-conductivity σ dc , and (iii) an approximate powerlaw increase at higher frequencies.A substantial drop in σ dc , observed in time-dependent measurement, is typical for crystallizing ionic systems because a rise in solid-state fraction reduces ions' mobility, decreasing the number of species contributing to the σ dc .The time evolution of dc-conductivity recorded at various temperatures, with and without annealing in the glassy state, is presented in Figure 6b,c, respectively.In accordance with DSC studies, the cold crystallization time elongated as the temperature decreased for cold crystallization (Figure 6b), but not for melt crystallization (Figure 6c).
To characterize the crystallization kinetics of [P 666,2 ][TFSI] in more detail, the time evolution of dc-conductivity (σ dc norm ) behavior was normalized using the following formula where σ dc (0) and σ dc (∞) are the values of dc-conductivity at which crystallization begins and ends, respectively, whereas σ dc (t) denotes the value of σ dc at a given crystallization time.
The Avramov model was then selected to quantify the data.A representative Avrami-Avramov plot for melt crystallization kinetics at T c = 223 K is shown in Figure 6d, while the parameters describing both cold and melt crystallization are summarized in Table 3.While it would be possible to compare and contrast numerical values of n and τ cr derived from both methods, comparing these in graphic form has been found to be more effective.Thus, the temperature dependence of log k BDS and log k DSC obtained from the Avramov model has been plotted against 1000/T in Figure 7.
Aligned with the DSC results, log k BDS depended linearly on T −1 for cold crystallization, and there was a maximum of log k BDS (T −1 ) at around 213 K found for melt crystallization.However, at each examined T, and irrespective of thermal history, the crystallization rate measured by BDS was faster than that determined from DSC measurements.Furthermore, the value of E a BDS found for cold crystallization was 10 kJ/mol lower than that of E a DSC .The difference in E a and crystallization rate between DSC and BDS has been frequently observed in the literature 46 and can be attributed to different sample thicknesses, such as that in the former technique, which was 0.2 mm -much bigger than that in the DSC measurement.Furthermore, during the dielectric studies, the sample was placed between stainless-steel electrodes, inhibiting contact with air.Compared with DSC, the easier crystallization in the BDS system can be explained by the significant contribution of nucleation on the sample interface in BDS cells.However, the difference in E a is within the experimental error and can be neglected.
A far more interesting aspect of the BDS study was the comparison between the homologous series [P 666,n ][TFSI] (n = 2, 6, and 8), as summarized in Table 3 and analyzed in-depth in the next section.

Effect of Alkyl Chain Length on Isothermal Cold Crystallization and dc-Conductivity of Phosphonium
ILs.To examine the effect of alkyl chain length on the crystallization tendency of phosphonium ILs, isothermal crystallization measurements using the BDS setup were performed on the homologous series [P 666,n ][TFSI] (n = 6 and 8).Neither cold nor melt crystallization was observed for   which gives a 3-fold increase with an increase of alkyl chain length from 6 to 8 carbons.Completing this trend, the inclusion of the dodecyl carbon chain in [P 666,12 ][TFSI] is so disruptive that no crystallization occurred.This is an interesting quantitative insight into ordering within longchained phosphonium ILs.Literature reports on other properties being significantly affected by altering one chain on the phosphonium cation, for example, molar conductivity and ionicity in the [P 444,n ][TFSI] homologue series. 47Here, despite three hexyl chains, elongation of the fourth chain has a marked, disruptive effect on crystallization, significantly hindering the process's kinetics, which has now been quantified for the first time.
To enable further comparison, the temperature dependence of log k BDS for the homologous series, [P 666,n ][TFSI] (n = 2, 6, Qualitative observations and numerical data recorded for the entire homologous series, [P 666,n ][TFSI] (n = 2, 6, 8, and 12) have led these authors to the speculative conclusion that crystallizations of phosphonium ILs differentiated by the length of one alkyl chain may differ in terms of rate but are the same in nature.That is, the entire series is thermodynamically capable of crystallization, and in each case, there is an expected maximum in log k vs 1000/T.However, the detection of the said maximum for n = 2 and 6 lies outside the examined temperature range.
Initially, it was assumed that the difference in the kinetics of crystallization might be related to ionic mobility, as with an increased alkyl chain, the cations would be larger in volume and, therefore, less mobile.The temperature dependences of dc-conductivity have been examined to examine the mobility of the ions under given T c conditions.As shown in Figure 10, in a supercooled liquid state, the σ dc values at any given temperature were nearly identical for all ILs, in particular close to T g .This gives the fact that the difference in alkyl chain length for homologous ILs, [P 666,n ][TFSI] has no effect on ionic mobility.Thus, it has been established that the isoconductivity conditions have been maintained during the isothermal crystallization studies.In consequence, in contrast to the original hypothesis, the crystallization of [P 666,n ] + ILs is not governed by ion diffusion but by thermodynamic factors.
Finally, analysis of plots in Figures 6 and 8 revealed an interesting observation that at the end of the crystallization process, σ dc was larger than 10 −14 −10 −15 S/cm for all examined ILs, almost at every studied T c .To visualize this effect, we compared the σ dc of crystalline materials to the σ dc of supercooled ILs (Figure 11).For [P 666,n ][TFSI] (n = 2, 6, and 8), the temperature dependences of σ dc recorded on cooling (squares) and heating (stars) scans have also been included.The σ dc values of the crystalline phases obtained during heating and isothermal crystallization are pretty close and, except for a few points, larger than 10 −14 −10 −15 S/cm.This indicates that some ion diffusion still exists in the crystalline state of the phosphonium ILs.In our earlier work, 31 we identified a transient supercooled liquid state in some phosphonium ILs, comprising a "frozen" network of alkyl chains, forming corridors where the anions could move rapidly, resulting in high electrical conductivity.It seems plausible to suggest an analogous scenario in the crystalline phase of the [P 666,n ][TFSI] series, whereby immobile cations with interlocking alkyl chains form a matrix allowing for some anion mobility through the lattice, potentially enabled by the conformational flexibility of [TFSI] − .Indeed, in a study of a large family of phosphonium ILs by Hempelmann et al., 47,48 the [TFSI] − anion has shown the highest self-diffusion coefficient despite being the largest (by volume) studied anion.Here, it has been demonstrated that the conductivity of the crystalline phase, like that of the supercooled liquid, had little dependence on the nature of the cation.

■ CONCLUSIONS
Cold and melt crystallization of a series of phosphonium ILs, [P 666,n ][TFSI], have been investigated.Preliminary DSC studies showed all ILs to be relatively good glass formers, with similar T g values and a decreasing cold crystallization tendency as the alkyl chain length increased.■ ASSOCIATED CONTENT * sı Supporting Information purpose of Open Access, the author has applied a CC-BY public copyright license to any Author Accepted Manuscript (AAM) version arising from this submission.The studies was implemented as part of strategy of the University of Silesia� Inicjatywa Doskonałosći (POB 1�Priorytetowy Obszar Badawczy 1: Harmonijny rozwój człowieka�troska o ochronę zdrowia i jakosć́zẏcia.

Figure 3 .
Figure 3. Isothermal crystallization data of [P 666,2 ][TFSI] measured by DSC.Heat flow as a function of time during isothermal cold crystallization (a) and melt crystallization (b).Relative crystallinity α DSC versus crystallization time for cold crystallization (c) and melt crystallization (d).Solid lines in panels (c,d) are Avrami fits in terms of eq 2. Insets are Avrami plots of the dependence log[−ln(1 − α DSC (t))] versus log(t) for each isothermal crystallization.

Figure 4 .
Figure 4. Avrami-Avramov plot of [P 666,2 ][TFSI] obtained from the DSC measurements.Time evolution of the normalized degree of crystallization α DSC and its first derivative with respect to the natural logarithm of the time at T c = 218 K that was obtained from glass (a) and RT (b).Dashed arrows denote the characteristic crystallization time τ cr .

Figure 5 .
Figure 5. Panel (a) presents the temperature dependence of the crystallization rate obtained during cold and melt crystallization.Solid line represents the Arrhenius fit to the cold crystallization data.Panel (b) presents the schematic position of nucleation and crystal growth (CG) curves for [P 666,2 ][TFSI].

Figure 7 .
Figure 7.Comparison between the temperature dependence of log k obtained from the BDS and DSC methods for [P 666,2 ][TFSI].

a
(τ cr error within ±80s, log k error within ±0.018, n error within ±0.015, and t 0 error within ±50 s).The Journal of Physical Chemistry B [P 666,12 ][TFSI] during the heating/cooling scans or in isothermal studies.Since the annealing in the glassy state was found to speed up the crystallization process substantially, only the kinetics of cold crystallization were examined for [P 666,6 ][TFSI] and [P 666,8 ][TFSI].After vitrification in a dielectric cell, the ILs were heated to T c and maintained at this temperature until the end of the crystallization process.Representative spectra obtained during the time-dependent isothermal measurements at 223 K, for [P 666,6 ][TFSI] and [P 666,8 ][TFSI] are presented in Figure 8a,b.The Avramov model quantifies the results obtained under different temperature conditions (Figure 8c,d).The characteristic cold crystallization time τ cr was determined from the Avrami-Avramov plot (see Figure 8e,f) at each examined T c and collected with the other crystallization parameters in Table 3. Comparator plots for [P 666,2 ][TFSI] are shown in Figure 6.The cold crystallization time at 213 K increased from τ cr = 220 min for [P 666,6 ][TFSI] to τ cr = 700 min for [P 666,8 ][TFSI],

Figure 10 .
Figure 10.Temperature dependences of the dc-conductivity measured on cooling for [P 666,n ] + ILs.

Table 1 .
Molecular Weight (M), Water Content (wt), Purity, and Characteristic Temperatures (Glass Transition Temperature T g , Crystallization Temperature T c , and Melting Point T m ) of Studied ILs

Table 3 .
Kinetic Parameters of Isothermal Crystallization [P 666,n ][TFSI] (n = 2, 6, and 8) Were Determined from Isothermal BDS Measurements Analyzed in Terms of the Avramov Model a