Role of ionic liquid [BMIMPF₆] in modifying the crystallization kinetics behavior of the polymer electrolyte PEO-LiClO₄

Abstract

We report on the modification in crystallization kinetics behavior of PEO + 10 wt% LiClO₄ polymer electrolyte by the addition of an ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (BMIMPF₆). Three techniques have been used for studying crystallization kinetics, viz., (i) isothermal crystallization technique using DSC, (ii) non-isothermal crystallization technique using DSC, and (iii) by monitoring the growth of spherulites with time in the polymer electrolyte films using a polarizing optical microscope (POM). Results from all the three techniques show that the presence of ionic liquid BMIMPF₆ suppresses the crystallization rate due to its plasticization effect. Isothermal crystallization data was well described by the Avrami equation, and Avrami exponent n lies in the range of 1 to 2, which signifies 2D crystal growth geometry occurring in these polymer electrolytes under the investigated temperature range. However, the Avrami crystallization rate constant ‘K’ increases exponentially with crystallization temperature and ionic liquid content as well. However, the non-isothermal crystallization kinetics of these polymer electrolytes is discussed in terms of three different models (Jeziorny's, Ozawa's and Mo's method), and it is found that Mo's method better explains the non-isothermal crystallization data. In addition, crystalline morphology and spherulite growth were studied by POM, which shows the suppression in crystallization in the presence of ionic liquid, as confirmed by spherulite growth rate (G_s) analysis.

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Introduction

The development of ion-conducting materials (such as polymers, gels, and glasses) has recently attracted global interest in developing a variety of electrochemical devices including rechargeable batteries, fuel cells, supercapacitors, solar cells, and actuators.^1–5 A straightforward strategy adopted for this purpose is to integrate mobile ionic species into different solid/polymeric soft matrices. Polymers have advantages over other ion conducting materials because they exhibit various favorable properties such as ease of fabrication in thin film form, and they are mechanically, thermally and electrochemically more stable.⁶ One of the necessary conditions, in addition to thermal/mechanical/chemical stability, is to make a polymer backbone conducive for providing high ionic mobility for ionic movement. Earlier, many ion conducting polymer matrices or polymer electrolytes were formed by complexing ionic salts (such as Li⁺, Na⁺, Mg²⁺, and Zn²⁺) with polar polymers (such as PEO, PMMA, PVA, and PVdF) and were much studied, but their room temperature ionic conductivity is very low (∼10⁻⁶ to 10⁻⁷ S cm⁻¹) because of its high degree of crystallinity, which hinders the motion of the ions in the polymer network.^7–11 Therefore, various approaches have been adopted to improve their ionic conductivity, which includes (a) addition of low molecular weight plasticizers/organic carbonates,^12,13 such as ethylene carbonate (EC), propylene carbonate (PC), diethyl carbonate (DEC), and (b) use of inorganic fillers^14–16 such as SiO₂, Al₂O₃, CNT, TiO₂. The use of conventional plasticizers in polymer electrolytes can enhance the ionic conductivity by lowering their glass transition temperature (T_g), which further increases the amorphous phase of the polymer matrix but also cause poor mechanical and thermal stability and a narrower electrochemical potential window due to their volatile nature, which limits their application in devices.¹⁷ Recently, a new approach has been adopted to enhance the ionic conductivity of the polymer electrolyte membranes by incorporating ionic liquids (ILs) into the polymer matrix.^18–20 ILs have attracted considerable attention as an excellent alternative to the conventional plasticizers due to their distinct properties such as wide liquidus range, non-volatility, non-flammability, negligible vapour pressure, wide electrochemical stability window, high ionic conductivity and excellent thermal and chemical stability.^21–23 ILs are entirely composed of bulky and asymmetric organic cations and inorganic anions. Due to the unique properties of ILs, polymer electrolytes based on ionic liquid offer high conductivity along with improved thermal and mechanical properties. In polymer electrolytes, ionic liquid plays the role of a plasticizer as well as a supplier of free charge carriers for ion conduction.²⁴

In most of the polymer electrolytes, the amorphous phase is found to be more conducting than the crystalline phase. Accordingly, it is very important to learn about the crystallization kinetics behavior of polymer as well as polymer electrolytes.^25–28 Crystallization is a process of phase transformation that involves the transformation of a disordered amorphous phase into a single or multi ordered phase. Polymer crystallization is a complex process that affects the final properties of the materials.²⁹ It has also been observed that some polymers can crystallize, while some cannot. Among the polymers that crystallize, the degree of crystallization, the structure of crystal and crystal size depend upon a number of parameters, such as temperature, time, concentration of solution, and stress present during the crystallization.³⁰ Some studies are available on the modification in crystallization behaviour of polymers on the addition of complexing salts³¹ or by changing its molecular weight,³² using inorganic fillers,³³ carbon nanotubes,³⁴ and also in confined geometries.³⁵ The polymer PEO is known to be a “semicrystalline” polymer that consists of both crystalline and amorphous phases, and its high capability in forming complexes with many salts, as well as its high chemical stability, led to its emergence as a promising host matrix for the preparation of polymer electrolytes. However, PEO tends to crystallize due to its highly ordered chain structure, which impedes the ion transport in the polymeric matrix. This is a general observation for semicrystalline polymer electrolytes and is well documented in literature.^36,37 Therefore, it would be interesting to study the crystallization kinetics behavior of such a semicrystalline polymer PEO including its crystal structure and crystalline morphology. The degree of crystallinity is of particular interest for the better understanding of the structure–property relationship to significantly improve the performances of the solid state devices containing PEO-based polymer electrolytes.

This paper reports the crystallization kinetics behavior of the polymer electrolyte (PEO + 10 wt% LiClO₄) with different amounts of added ionic liquid (BMIMPF₆). Crystallization kinetics was studied by isothermal and non-isothermal crystallization methods using DSC, and the affirmative confirmation of the crystallization behavior was obtained by examining the expansion of spherulites by polarizing optical microscope (POM). It has been found that the addition of BMIMPF₆ into PEO + 10 wt% LiClO₄ slows the crystallization rate due to the plasticization effect of the ionic liquid BMIMPF₆.

Experimental section

Materials and method

The starting materials used for the preparation of polymer electrolyte films are poly(ethylene oxide), PEO of average mol. wt 6 × 10⁵ g mol⁻¹, lithium salt LiClO₄ and ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate BMIMPF₆, obtained from Sigma Aldrich. The ionic liquid BMIMPF₆ was vacuum dried at 10⁻⁶ torr for 24 h before use.

Polymer electrolyte films of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ (for x = 0, 5, 10, 15 and 20) were prepared by a solution casting method. The particular weight ratio of 10 wt% LiClO₄ in PEO was chosen for incorporating varying amounts of ionic liquid BMIMPF₆ to prepare PEO + 10 wt% LiClO₄ +x wt% BMIMPF₆ polymer electrolyte films because of its excellent mechanical stability as well as reasonable ionic conductivity compared to other high lithium salt-containing samples. Though the high conducting films containing higher loading of lithium salt LiClO₄ could be prepared without BMIMPF₆, on loading of ionic liquid BMIMPF₆ these films tend to become unstable. In the solution casting method, polymer PEO was dissolved in methanol with stirring at 40 °C and then requisite amount of LiClO₄ was added and stirred until it appeared as a homogeneous solution. Subsequently, the required amount of BMIMPF₆ was added to the abovementioned solution and stirred again for 2–4 h until a viscous solution was obtained. The viscous solution so obtained was poured into polypropylene Petri dishes. After the complete evaporation of the solvent, PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ polymer electrolyte films containing different amounts of BMIMPF₆ were obtained. These films were vacuum dried before further use.

Three methods, viz., isothermal, non-isothermal and optical microscopic study, were used for studying the crystallization kinetics. The isothermal and non-isothermal crystallization kinetics of the prepared samples were studied using a differential scanning calorimeter (Mettler Toledo DSC1 system). All the DSC measurements were conducted under a nitrogen atmosphere. The detailed procedures of the isothermal and non-isothermal method are given in their respective sections where results are discussed.

For studying the crystalline morphology and spherulite growth rate, a Lietz DMR polarizing microscope was used. All polarizing optical microscopy (POM) studies were done at a magnification of 50×. For carrying out the POM-studies, the samples were first heated above the melting temperature (T_m) of the polymer electrolyte films and held there for some time until a completely isotropic amorphous phase was observed in POM. Then, the polymer films were quickly quenched to the desired temperature of crystallization (these temperature are less than T_m of the polymer electrolytes). The size of spherulites as a function of time elapsed after their initial appearance was monitored by POM for crystallization study.

Crystallization kinetics by isothermal method

For carrying out the actual experiment, the samples were heated to ∼75 °C (above the melting temperature of polymer T_m) and held there for 5 min to erase the thermal history, and then quickly cooled to the temperature at which crystallization was desired to be studied (note that these temperatures are less than (T_m)_onset as determined by DSC thermograms). The samples were maintained at desired crystallization temperatures, viz., T_c = 44, 46, 48 and 50 °C, to crystallize, and DSC exothermic curves for heat flow vs. time were recorded. These DSC isothermal curves obtained for different samples were used for studying the crystallization kinetics by an isothermal method. The heat flow vs. time plot for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films (for x = 0, 10 and 20) are shown in Fig. 1. It can be seen that with increasing crystallization temperature, the crystallization exothermic peak flattens, possibly due to increase in the flexibility of polymer PEO backbone, which suggests that the samples take relatively longer time to crystallize as they approach their (T_m)_onset.

Fig. 1 Heat Flow vs. time plots for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ for (a) x = 0, (b) x = 5 and (c) x = 10 during isothermal crystallization at different T_c.

The crystallization kinetics of polymers under isothermal conditions is described by the well-known Avrami equation³⁸ in terms of the dependence of relative crystallinity (X_t) on the crystallization time (t) as follows:

X_t = 1 − exp(−Ktⁿ) (1)

where X_t is the relative crystallinity generated at any time t, n is the Avrami exponent dependent on the nucleation and growth geometry of the crystal, and K is the overall crystallization rate constant associated with nucleation as well as growth contributions.

The relative crystallinity (X_t) generated at any time (t) can be obtained using the DSC exothermic isothermal curves, as illustrated in Fig. 1. The relative crystallinity (X_t), is defined as the ratio of crystallinity generated at any time t to the crystallinity when time approaches infinity. X_t has been evaluated using the following relation:

where dH/dt is the rate of heat evolution, ΔH_t is the total heat evolved at any time t and ΔH_∞ is the heat evolved when time approaches infinity (∞).

Obviously, the values of X_t at a given crystallization time t can be obtained by integrating the area of exothermic DSC isothermal curves between time t = 0 to t, divided by the entire area of the exothermic peaks.

Using eqn (2), the conversion curves of X_t (the crystallized fraction) versus t for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films (for x = 0, 5 and 10) at various crystallization temperatures (T_c = 44, 46, 48 and 50 °C) are shown in Fig. 2. All the curves show sigmoid characteristics with time and shift towards a higher time regime as the crystallization temperature (T_c) increases. These features indicate that at higher T_c, the crystallization rates become slow and samples take more time to crystallize because the system approaches (T_m)_onset. Further, a comparison of the results of polymer electrolyte PEO + 10 wt% LiClO₄ (see Fig. 2, curve ‘a’) with those polymer electrolyte films doped with ionic liquid, BMIMPF₆ (see Fig. 2, curves b and c) showed that BMIMPF₆-containing samples take a longer time to crystallize in comparison to pristine polymer electrolyte due to the increase in amorphicity of the samples.³⁹ For example, we can see that the pristine polymer electrolyte PEO + 10 wt% LiClO₄ took nearly 1.8 min to obtain complete crystallization at T_c = 44 °C, and the time required to finish crystallization for 5 wt% BMIMPF₆-containing polymer electrolyte slightly increased. It was found to be ∼2 min at the same crystallization temperature, whereas at higher T_c (e.g. 50 °C), it takes ∼15 min to complete crystallization (for detail see Fig. 2c).

Fig. 2 The X_t vs. t plot for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ for (a) x = 0 (b) x = 5 and (c) x = 10 at different T_c, viz., 44, 46, 48, 50 °C.

These observations clearly indicate that with increasing crystallization temperature or ionic liquid concentration, the samples take longer time to crystallize because of the plasticization effect of ionic liquid.^40–42 In our previous studies^43,44 on the crystallization kinetics of polymer PEO upon the inclusion of ionic liquid as well as lithium salt, it has been shown that the crystallization rate of PEO changes more on addition of BMIMPF₆ alone rather than for (PEO + LiClO₄) because the plasticization effect of ionic liquid is less experienced by the latter, which has already been amorphosized by the addition of LiClO₄. This effect will become clearer while discussing the results of crystallization half time (t_1/2) in the subsequent section.

The crystallization half time (t_1/2), which is defined as the time necessary to attain 50% of the final crystallinity of the samples, is an important parameter for discussing the crystallization kinetics.⁴⁵ The values of t_1/2 are directly obtained from Fig. 2, from which the rate of crystallization (G = 1/t_1/2) can be calculated. The greater the value of t_1/2, the lower is the rate of crystallization. Fig. 3 shows the variation of G for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ at various crystallization temperatures (T_c). As illustrated in Fig. 3, the values of G decrease with increasing T_c for all the samples, indicating that the overall crystallization rate becomes slow at higher T_c because the nucleation process is more difficult at higher crystallization temperatures.⁴⁶ Furthermore, it may be noted here that the values of G (=1/t_1/2) obtained for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films are lower in comparison to that of pristine polymer electrolyte PEO + 10 wt% LiClO₄ at a given T_c, as shown in Fig. 3, which clearly indicates the slowing of the crystallization rate by the incorporation of BMIMPF₆. In addition, the reduction in overall crystallization rate G of polymer electrolytes with increasing BMIMPF₆ concentration is attributed to the fact that the presence of ionic liquid BMIMPF₆ exerts a dilution effect for the crystallizable polymer PEO due to the plasticization effect of the ionic liquid. Our previous studies^47–49 also showed of the similar situation in which the effects of ionic liquid on the properties of polymers and polymer electrolytes were studied and it was found that the ionic liquid acts as an efficient plasticizer.

Fig. 3 The rate of crystallization (G = 1/t_1/2) vs. crystallization temperature plots for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ for (a) x = 0 (b) x = 5 and (c) x = 10 at different crystallization temperatures 44, 46, 48, 50 °C.

Avrami plots (i.e., double logarithmic graphic representations of crystallization data) are generally used to calculate the values of n and K. They can be obtained by taking the double logarithmic of eqn (1) and can be written as follows:

log[−ln(1 − X_t)] = log K + n log t (3)

According to eqn (3), the plot of log[−ln(1 − X_t)] vs. log t should be a straight line. In the present study, the Avrami plots for PEO + 10 wt% LiClO₄ films containing different amounts of BMIMPF₆ give rise to a series of parallel straight lines at different crystallization temperatures (viz., T_c = 44, 46, 48 and 50 °C), as shown in Fig. 4. After linear fitting of these plots by a straight line at different T_c, both the Avrami exponent ‘n’ and crystallization rate constant ‘K’ can be obtained by the slope and intercept of the straight line, respectively. The various Avrami parameters obtained from isothermal crystallization method for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ at various crystallization temperatures are given in Table 1.

Fig. 4 Avrami plots using isothermal method for (a) PEO + 10 wt% LiClO₄ (b) PEO + 10 wt% LiClO₄ + 5 wt% BMIMPF₆ and (c) PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ at different crystallization temperatures (viz., T_c = 44, 46, 48, 50 °C).

Table 1 Different crystallization parameters of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films obtained by Avrami plots using the isothermal crystallization method

PEO + 10 wt% LiClO4 + x wt% BMIMPF6	Tc (°C)	n	K (min^−n)	t1/2 (min)
(a) x = 0	44	1.48	0.70	0.94
	46	1.40	0.39	1.45
	48	1.65	0.07	3.85
	50	1.86	0.02	3.95
(b) x = 5	44	1.55	0.66	1.02
	46	1.53	0.40	1.35
	48	1.63	0.10	4.09
	50	1.76	0.06	7.09
(c) x = 10	44	1.34	0.33	1.57
	46	1.31	0.11	3.49
	48	1.70	0.02	10.69
	50	1.74	0.01	15.08

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It is known that the values of Avrami exponent are the consequences of the geometry of specific crystal dimension and have been used to specify the dimension of growing crystals. The value of Avrami exponent n is assumed to lie in the range between 1 and 4 and is related to the geometry characteristics of the growing crystals: n = 1 is ascribed to the 1D structure, 2 is ascribed to the 2D structure, and 3 or 4 ascribed to the 3D structure.⁵⁰ In the present study, the values of ‘n’ for all the polymer electrolyte PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films lie between 1 and 2 at all crystallization temperatures studied. This indicates that the 2D crystal growth morphology dominates at all temperatures at which crystallization has been studied.

The effect of the incorporation of ionic liquid into the polymer membrane, apart from decreasing the rate of crystallization, is also expected to reflect the values of activation energy for crystallization. To check this, we determined this activation energy for PEO + 10 wt% LiClO₄ polymer electrolyte with BMIMPF₆. The Avrami crystallization rate constant K can be assumed to be a consequence of a thermally activated process and has been used to determine the activation energy for crystallization.⁵¹ The crystallization rate constant K can be expressed by the Arrhenius equation as follows:

K^1/n = K_o exp(−ΔE/RT_c) (4)

Eqn (4) can also be written as

ln K^1/n = ln K_o − ΔE/RT_c (5)

where K_o is the pre-exponential factor independent of temperature, ΔE is the isothermal crystallization activation energy, R is the gas constant and T_c is the crystallization temperature.

By plotting the ln K^1/n versus 1/T_c, ΔE can be obtained by the slope of these curves. Typical plots for PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ are shown in Fig. 5. The slope of this curve gives the value of ΔE/R, from which the isothermal crystallization activation energy ΔE can be directly calculated. The value of isothermal crystallization activation energy ΔE for PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ polymer electrolyte was found to be 97 kJ mol⁻¹.

Fig. 5 ln K^1/n vs. 1/T_c plot for PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ during isothermal crystallization.

Crystallization kinetics by a non-isothermal method

Non-isothermal crystallization method using DSC is also one of the most convenient methods for studying the crystallization kinetic behavior of polymers. In this method, samples were heated above the melting temperature of the polymer PEO (∼75 °C), kept there for 5 min to erase the thermal history, and then cooled at different cooling rates (viz., 5, 10, 15 and 20 °C min⁻¹). DSC exothermic curves for heat flow versus temperature were recorded to analyze the non-isothermal crystallization data. Samples used for non-isothermal crystallization were the same for which isothermal crystallization kinetic studies were carried out. The DSC exothermal curves for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films at different cooling rates 5, 10, 15 and 20 °C min⁻¹ are shown in Fig. 6. It can be seen that the exothermic crystallization peaks were shifted to lower temperature side, which became broader with increasing cooling rates. To find the non-isothermal crystallization kinetics, relative crystallinity (X_t) versus temperature plots for these polymer electrolyte films were obtained using eqn (2) and are shown in Fig. 7 (the procedure is similar to that used for the isothermal crystallization method described earlier). Fig. 7 shows the plots of X_t versus temperature (T), which illustrate an anti-S-shaped characteristic. In non-isothermal crystallization process, temperature scale of X_t versus T plots could be converted into X_t versus t using the following relation:⁵²where t is the crystallization time, T_o is the onset temperature of crystallization (t = 0), T is the crystallization temperature and ϕ is the cooling rate. Using eqn (6), the plot of relative crystallinity versus temperature (X_t vs. T) can be easily transformed to the plot of relative crystallinity versus time (X_t vs. t). The X_t vs. t plots for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films (for x = 0, 5, 10, 15 and 20) are given in Fig. 8, showing that higher the cooling rate, shorter is the time required to complete crystallization and vice versa.

Fig. 6 Heat flow vs. temperature plot for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films during non-isothermal crystallization for (a) x = 0 (b) x = 5 (c) x = 10 (d) x = 15 and (e) x = 20 at different cooling rates by DSC.

Fig. 7 X_t vs. temperature plot during non-isothermal crystallization process of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ for (a) x = 0 (b) x = 5 (c) x = 10 (d) x = 15 and (e) x = 20 at different cooling rates (viz., 5, 10, 15, 20 °C min⁻¹).

Fig. 8 X_t vs. time plot during non-isothermal crystallization process of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ for (a) x = 0 (b) x = 5 (c) x = 10 (d) x = 15 and (e) x = 20 at different cooling rates (viz., 5, 10, 15, 20 °C min⁻¹).

Several approaches have been used for describing the crystallization process involved in the non-isothermal crystallization kinetics, which are based on various models, including the modified Avrami equation by Jeziorny,⁵³ Ozawa analysis⁵⁴ and Mo's method.⁵⁵ These approaches are discussed in the subsequent sections.

Modified Avrami equation. The modified Avrami⁵³ equation is frequently used to analyze the non-isothermal crystallization process. Considering the non-isothermal crystallization character of the process, the Avrami equation can be written as follows:

X_t = 1 − exp(−Z_tt^n′) (7)

where n′ is a constant depending on the type of nucleation and crystal growth dimension, also known as non-isothermal Avrami exponent, and Z_t is the non-isothermal crystallization rate constant and depends on nucleation and growth parameters. The values of n′ and Z_t were obtained from the slope and intercept of straight regime of plots drawn between log[−ln(1 − X_t)] and log t. The log[−ln(1 − X_t)] vs. log t plots for PEO +10 wt% LiClO₄ + x wt% BMIMPF₆ (for x = 0, 5, 10, 15 and 20) at different cooling rates (viz., 5, 10, 15 and 20 °C min⁻¹) are shown in Fig. 9. From these plots, we can see that at initial stages, these curves are fitted well by eqn (7) but deviate from the linear relation on higher crystallization. Therefore, the Avrami equation cannot be accurately used for describing the entire non-isothermal crystallization kinetics process.

Fig. 9 Avrami plots using non-isothermal method of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films for (a) x = 0 (b) x = 5 (c) x = 10 (d) x = 15 and (e) x = 20 at different cooling rates.

Jeziorny⁵³ modified the Avrami equation for non-isothermal crystallization processes; it assumes that curves with a fixed cooling rate represent a series of isothermal crystallization processes, and it gave a modified non-isothermal crystallization rate (Z_c) in which the effect of cooling rate ‘ϕ’ on the value of Z_t was included as follows:

The values of the Avrami constants n′ and Z_c obtained by the modified Avrami equation in a non-isothermal crystallization method are given in Table 2. It may be noted here that the values of n′ and Z_c obtained in non-isothermal crystallization do not have the same magnitude as in the isothermal method due to different experimental conditions used in these two methods.

Table 2 Different crystallization parameters of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films obtained by Avrami plots using non-isothermal crystallization method

PEO + 10 wt% LiClO4 + x wt% BMIMPF6	Cooling rate ϕ (°C min^−1)	n′	Zt (min^−n′)	Zc	t^′1/2 (min)
(a) x = 0	5	2.29	0.139	0.674	1.96
	10	2.27	0.516	0.936	1.13
	15	2.01	0.651	0.971	1.02
	20	2.05	0.717	0.986	0.88
(b) x = 5	5	2.539	0.096	0.626	2.16
	10	2.225	0.067	0.961	1.04
	15	2.215	0.839	0.988	1.14
	20	1.742	0.900	0.994	0.85
(c) x = 10	5	2.260	0.138	0.673	1.96
	10	2.242	0.516	0.936	1.13
	15	2.017	0.662	0.972	1.00
	20	1.893	0.751	0.985	0.91
(d) x = 15	5	2.374	0.106	0.638	2.17
	10	2.107	0.311	0.889	1.42
	15	1.387	0.439	0.946	1.07
	20	1.642	0.608	0.975	0.84
(e) x = 20	5	2.199	0.095	0.625	2.47
	10	1.913	0.289	0.883	1.57
	15	1.844	0.398	0.940	1.38
	20	1.503	0.599	0974	1.13

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Ozawa analysis. Ozawa⁵⁴ extended the Avrami equation by considering that the non-isothermal crystallization process consists of a large number of infinitesimal isothermal crystallization steps. According to the Ozawa theory, the non-isothermal crystallization process can be described by the following equation:where X^′_T is the relative crystallinity at temperature T, ϕ is the cooling rate, K*(T) is the cooling function related to the overall crystallization rate, m is the Ozawa exponent, which depends on the dimension of the crystal growth. eqn (9) can also be expressed as follows:

log[−ln(1 − X^′_T)] = log K^*(T) − m log ϕ (10)

If the Ozawa theory is fully applicable for describing the non-isothermal crystallization process, then the plot of log[−ln(1 − X^′_T)] vs. log ϕ should be a straight line, which was not the case for our samples, as shown in Fig. 10. Therefore, the Ozawa equation is not be fully applicable for describing the non-isothermal crystallization process of PEO + 10 wt% LiClO₄ polymer electrolytes as well as PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ containing different amounts of BMIMPF₆.

Fig. 10 Ozawa plots of log[−ln(1 − X_T)] vs. log ϕ during the non-isothermal crystallization of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films for (a) x = 0 (b) x = 5 (c) x = 10 (d) x = 15 and (e) x = 20.

Mo's method. The kinetic equation proposed by Mo and coworkers⁵⁵ based on the combination of the Ozawa and Avrami equations has frequently been used for describing the non-isothermal crystallization process. This method has been successfully applied for describing the non-isothermal crystallization behavior of many polymeric systems.^56,57 The general form of this equation can be written as follows:

log ϕ = log F(T) − b log t (11)

where log F(T) = [K*(T)/Z_t]^1/m and b is the ratio between the Avrami and Ozawa exponents n and m. Here, the function F(T) refers to the value of cooling rate required to reach a defined degree of crystallinity at a certain temperature in unit crystallization time.⁵⁸ The higher value of F(T) gives lower crystallization rate. The plot between log ϕ and log t for PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films at different cooling rates and various crystallinity gives a straight line as shown in Fig. 11. The values of log F(T) and b can be obtained for the samples for different values of ‘x’ from the intercept and slope, respectively. These values are listed in Table 3. From this, we can see that for a given degree of crystallinity (e.g., 10%), the value of log F(T) for PEO + 10 wt% LiClO₄ polymer electrolyte is 0.607, which increases to 0.629, 0.634, 0.688 and 0.714, respectively, for the polymer electrolyte containing 5, 10, 15 and 20 wt% BMIMPF₆. In general, the value of F(T) for all the polymeric films is found to increase with the increasing amount of BMIMPF₆ in PEO + 10 wt% LiClO₄. The abovementioned observation clearly indicates that the incorporation of ionic liquid into PEO + 10 wt% LiClO₄ polymer electrolyte decreases the crystallization rate due to the plasticization effect of an ionic liquid.^59–61 The addition of ionic liquid BMIMPF₆ into PEO + LiClO₄ polymer electrolyte hinders the crystallization of polymer and leads to slowing of the crystal growth rate, as confirmed by the morphological studies.

Fig. 11 log ϕ vs. log t plot of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ films for (a) x = 0 (b) x = 5 (c) x = 10 (d) x = 15 and (e) x = 20 at different crystallinities using the non-isothermal crystallization method.

Table 3 Non-isothermal crystallization parameters of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ at different degrees of crystallinities obtained by the Li and Mo method

PEO + 10 wt% LiClO4 + x wt% BMIMPF6	X^′T in %	F(T)	b
(a) x = 0	10	0.607	1.563
	20	0.840	1.579
	30	0.983	1.662
	40	1.086	1.677
	50	1.171	1.671
	60	1.311	1.784
	70	1.504	1.504
	80	1.727	1.786
(b) x = 5	10	0.629	1.263
	20	0.864	1.180
	30	0.957	1.245
	40	1.059	1.356
	50	1.172	1.172
	60	1.331	1.331
	70	1.570	1.570
	80	1.753	1.583
(c) x = 10	10	0.634	1.485
	20	0.842	1.573
	30	0.973	1.635
	40	1.086	1.695
	50	1.204	1.774
	60	1.343	1.850
	70	1.529	1.529
	80	1.713	1.713
(d) x = 15	10	0.688	1.420
	20	0.932	1.594
	30	1.078	1.714
	40	1.208	1.815
	50	1.334	1.936
	60	1.485	2.060
	70	1.672	2.149
	80	1.820	1.997
(d) x = 20	10	0.714	1.075
	20	0.952	1.267
	30	1.113	1.473
	40	1.254	1.635
	50	1.397	1.818
	60	1.546	1.967
	70	1.722	2.121
	80	1.866	2.126

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Kissinger analysis. It has been already shown by the isothermal crystallization kinetics study that the incorporation of BMIMPF₆ in PEO + 10 wt% LiClO₄ polymer electrolyte changes the activation energy of the crystallization. We have also re-confirmed this assertion from the non-isothermal kinetic study. The crystallization activation energy for a non-isothermal crystallization process can be obtained by the Kissinger method.⁶² In this method, the effect of various cooling rates (ϕ) on the crystallization peak temperature (T_p) has been studied. The crystallization activation energy (ΔE′) for a non-isothermal process using Kissinger method can be expressed as follows:where R is the gas constant and ϕ is the cooling rate. The slope of the plot ln(ϕ/T_p²) vs. 1/T_p gives a straight line, from which by knowing the value of ΔE′/R, ΔE′ can directly be calculated. Typical Kissinger plots for PEO + 10 wt% LiClO₄) + 10 wt% BMIMPF₆ polymer electrolyte are shown in Fig. 12. The value of ΔE′ obtained for PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ polymer electrolyte was found to be 37 kJ mol⁻¹. This value is somewhat lower than those obtained for the isothermal crystallization method previously found because different experimental conditions were used in the two methods. In the non-isothermal crystallization method, the temperature changes constantly, which affects the rate of nuclei formation as well as spherulite growth.

Fig. 12 Kissinger plot of ln(ϕ/T_p²) vs. 1/T_p for PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆.

Crystalline morphology and spherulite growth by polarized optical microscopy

When polymers are crystallized from the melt, the most commonly observed structures are the spherulites. These spherulites are in the form of spherical aggregates of lamellae, characteristics of polymers crystallized isothermally in the absence of pronounced stress or flow.^63–65 The typical dimensions of spherulites are of the order of microns, and sometimes even millimeters. Therefore, they can be easily viewed under a polarizing optical microscope. The spherulites continue to grow radially until they impinge upon one another. A measure of their growth until the time of impingement provides abundant information regarding the mechanism of crystallization in the polymer, and has been the focus of several investigations.^66–68

The number and size of spherulites growing in the polymer matrix controls the overall crystallinity of the polymer. Therefore, measuring the size of spherulites as a function of time can provide an estimate of the rate of crystallization. We used this technique for measuring the rate of crystallization of our polymer electrolyte membranes. The size of spherulites was measured by a polarizing optical microscope (POM). Typical growth of such spherulites appearing in PEO + 10 wt% LiClO₄ and PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ polymer electrolyte films at different times, crystallized at 50 °C, are shown in Fig. 13. We can see that spherulite growth was very rapid for PEO + 10 wt% LiClO₄ polymer electrolyte: within 10 seconds it acquired ∼100 μm diameter, and then its size increased to 310 μm at the elapsed time of 120 s, as shown in Fig. 13 curve a (i) and (v). As BMIMPF₆ was added to PEO +10 wt% LiClO₄ polymer electrolyte, the spherulite size was reduced and the number of nucleating sites increased. This is evident when we compare Fig. 13 curves a (i–v) with b (i–v).

Fig. 13 Image of spherulite growth of (a) PEO + 10 wt% LiClO₄ and (b) PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ films crystallized at 50 °C at different crystallization times (i) 10 s, (ii) 30 s, (iii) 60 s, (iv) 90 s and (v) 120 s.

In the present case, we can also see that the size of one particular spherulite at any particular snap increased with time, as indicated in rectangle of Fig. 13. Therefore, it is important to determine the spherulitic growth rate (and therefore crystallization rate) for deciding the effect of BMIMPF₆ on the crystallization behavior of polymer electrolytes with and without ionic liquid. The spherulite size vs. time plot for PEO + 10 wt% LiClO₄ polymer electrolyte and with added 10 wt% BMIMPF₆ is shown in Fig. 14, whose slope gives the spherulites growth rate (G_s). The value of G_s for pure PEO + 10 wt% LiClO₄ is found to be 1.77 μm s⁻¹, which decreases to 0.675 μm s⁻¹ for PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆. The abovementioned observation clearly indicates that the incorporation of BMIMPF₆ in PEO +10 wt% LiClO₄ polymer electrolyte hinders the spherulites growth rate of polymer PEO. This supports our previous results obtained from isothermal and non-isothermal DSC technique, which indicate the suppression in the crystallization rate of polymer PEO due to the incorporation of an ionic liquid (BMIMPF₆) owing to its plasticization effect, as discussed earlier in this paper.

Fig. 14 Spherulite diameter vs. crystallization time plot for (a) PEO + 10 wt% LiClO₄ (b) PEO + 10 wt% LiClO₄ + 10 wt% BMIMPF₆ films crystallized at 50 °C at different crystallization times.

Conclusions

The crystallization kinetics behavior of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ polymer electrolytes has been studied using three techniques, viz., isothermal and non-isothermal crystallization methods using DSC as well as by monitoring spherulite growth using a polarizing optical microscope. The well-known Avrami equation has been used to describe the isothermal crystallization process. The obtained crystallization parameters for isothermal crystallization, such as Avrami exponent (n), crystallization rate constant (K), crystallization half time (t_1/2), crystallization rate (G) and isothermal crystallization activation energy (ΔE) suggested that the incorporation of the ionic liquid BMIMPF₆ into PEO + 10 wt% LiClO₄ polymer electrolyte hinders the crystallization of polymer PEO due to the plasticization effect. The value of Avrami exponent ‘n’ obtained for the isothermal crystallization process of PEO + 10 wt% LiClO₄ + x wt% BMIMPF₆ (for x = 0, 5 and 10) was found to be less than 2, indicating the 2D crystal growth geometry. It was also found that the non-isothermal crystallization data cannot be fully described by the modified Avrami equation (Jeziorny method) and Ozawa analysis. The method proposed by Mo and coworkers was employed to accurately analyze the non-isothermal crystallization process. The POM study shows that the incorporation of BMIMPF₆ in PEO + 10 wt% LiClO₄ polymer electrolyte slows down the spherulite growth rate, as observed by spherulite size vs. time plots. All the three techniques used by us to study the effect of ionic liquid BMIMPF₆ on the crystallization behavior of polymer electrolytes have led to the conclusion that the presence of BMIMPF₆ suppresses the crystallization rate. This will have an effect in decreasing the absolute crystallinity of PEO with increasing BMIMPF₆ content.

Acknowledgements

One of us (RKS) is grateful to BRNS-DAE Mumbai and DST New Delhi, India, for financial assistance for carrying out this work and SKC is thankful to UGC New Delhi, India, for providing the Dr D. S. Kothari Postdoctoral research fellowship.

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