Correlation between nucleation, phase transition and dynamic melt-crystallization kinetics in PAni/PVDF blends

Abstract

In this study, polyaniline (PAni)/poly(vinylidene fluoride) (PVDF) blends of different compositions were prepared by in situ chemical polymerization of aniline in a mixture of PVDF and dimethylformamide (DMF). Fourier transform infrared spectroscopy (FT-IR), thermo-gravimetry (TG) and differential scanning calorimetry (DSC) were utilized to understand the effect of different amounts of in situ PAni loading on the crystalline structure, phase transition and dynamic melt-crystallization kinetics of PVDF. The images for morphology obtained using scanning electron microscopy and polarizing optical microscopy also provided the confirming evidences. FT-IR studies revealed that the transition of the crystalline structure (from β- to α-phase) of pure PVDF during recrystallization is hindered by the incorporation of PAni within the matrix. The dynamic crystallization kinetics data were analysed with different macroscopic models to describe the polymer crystallization, and the parameters obtained from the analyses were correlated with the structural evidence to verify their applicability for the systems under investigation. Values for the effective activation energy (E_X) of the crystallization process of PVDF and its blends were calculated by the differential isoconversional methods of Friedman. It was observed that, although PAni acted as an effective nucleating agent to induce a great number of heterogeneous nuclei within the blends, it actually delayed the overall crystallization process. The increased values of the crystal growth parameters obtained from the analysis of the temperature-dependent E_X by the modified Hoffman–Lauritzen theory also support the above mentioned interpretations.

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1. Introduction

Poly(vinylidene fluoride) (PVDF) is an important chemically stable, semi-crystalline material with extraordinary properties, including good toughness, flexibility, and predominantly outstanding electrical properties such as ferro-, piezo-, and pyro-electricity.^1,2 PVDF is well-known for its polymorphism, and can display five different polymorphs depending on its processing conditions.² The α-phase is the most common and stable polymorph of PVDF, which is generally produced from the melt crystallization of PVDF at atmospheric pressure.¹ However, from an application perspective, β-PVDF is the most important polymorph because it possesses the largest spontaneous polarization per unit cell and thus exhibits superior ferroelectric and piezoelectric properties. Therefore, the enhancement of the polar β-phase and simultaneous suppression of the nonpolar α-phase in PVDF materials are of great importance for their widespread application, and have been studied extensively in the recent years.^2–6

For a crystallizable polymeric system, crystallization is considered to occur from two successive events, first homogeneous or heterogeneous nucleation (caused by impurities, external additives or other effects), followed by growth of the crystals with increasing crystallization time.⁷ In these procedures, nucleation is the key parameter that can control the structure and phase transition of the polymer.⁷ Nucleation agents assist secondary nucleation by providing a surface on which the melt crystallizes. During crystallization, they either influence the crystallization kinetics, the crystallite size, or the crystalline phase.⁸ The overall free energy associated with nucleation combines the favorable term arising from chain aggregation and the unfavorable term associated with the interface formation.⁸ Thus, the efficiency of nucleation agents depends on increase in the surface area and decrease in the nucleation barrier required to enhance the heterogeneous nucleation process.

Consequently, control of the spherulite size or crystalline phase by the addition of nucleation agents is an attractive method to modify and improve the physical properties of bulk crystalline polymers for specific end uses. From earlier reports, it was observed that the heterogeneous nucleation processes and phase transition of PVDF can be influenced either by blending it with different organic compounds such as poly(methyl methacrylate),^9–11 poly(vinyl acetate),¹² nylon-6,¹³ poly(butylene adipate),¹⁴ poly(ethylene terephthalate)¹⁵ or by incorporating nanoparticles,¹⁶ nanoclay,^17,18 or carbon nanotubes (CNTs)¹⁹ within its matrix. It was observed that in the blended polymeric systems, due to the restriction effect of the additive component on the nucleation and growth of the crystalline component, the crystallization of PVDF is sometimes hindered and the melting temperature of the blends is decreased, as compared with the pure crystalline component. It was also reported⁸ that the nucleation and phase transition of the miscible polymer blends can be influenced by the surface charge of the organic nucleation agent and that nucleation agents with positively charged surfaces are most effective to induce more extended PVDF chain conformers in the polar β-phase.⁸

Conducting organic materials such as polyaniline (PAni) have found widespread application in recent times. These materials, doped with bulky organic acids and being very organic in nature, offer excellent compatibility with semi-crystalline polymer matrices such as PVDF.^20,21 Therefore, it is highly expected that blending doped polyaniline (PAni) with PVDF may influence the overall phase transition and nucleation of PVDF due to the presence of radical cations on the doped polyaniline chain. Recently, several blends^20–24 of PVDF with PAni or its derivatives²⁵ have been prepared using different methods to study their electrical and other properties^21–23,26 due to their numerous application potentials. However, to the best of our knowledge, exploration of the heterogeneous nucleation ability of conducting PAni in semi-crystalline PVDF polymer, which is of great research interest, has not been addressed until this present study.

Based on the above considerations, an attempt has been made in the present study to investigate the influence of camphorsulfonic acid (CSA)-doped PAni on the nucleation, phase transition and growth of PVDF crystals by studying the melt-crystallization kinetics of different PAni/PVDF blends using differential scanning calorimetry (DSC). To improve the miscibility between PAni and PVDF, the blends were processed by in situ chemical polymerization of aniline in a mixture of PVDF and dimethylformamide (DMF).²⁰ To study the crystallization kinetics of these blended polymeric systems, a constantly changing environment (non-isothermal) rather than an isothermal one was implemented, because this is the usual environment in the melt processing of polymers for industrial applications. The experimentally obtained kinetic data were analysed by several existing theoretical models. An isoconversional technique was used to evaluate the variation of the effective activation energy of the blends during the crystallization process. Thermo-gravimetric analysis, infrared spectroscopy, scanning electron microscopy (SEM) and polarizing optical microscopy (POM) were also used to support the results and to obtain direct evidence for the crystalline morphologies and phase transition of the blends.

2. Experimental

2.1 Materials

Aniline monomer (Merck) was distilled under vacuum before the polymerization reactions. PVDF (M_w 534 000) (Sigma Aldrich), ammonium persulfate ((NH₄)₂S₂O₈) (APS) [98%, Sigma Aldrich], N,N-dimethylformamide (DMF) (Sigma Aldrich), camphorsulfonic acid (CSA) (Sigma Aldrich) and chloroform (Merck) were used as received.

2.2 Synthesis of PVDF/PAni blends

In a typical synthesis, 1.0 g of PVDF was dissolved in 10 ml of DMF at 70 °C. The solution was then cooled at room temperature. Pre-distilled aniline monomer was then added with stirring. Stoichiometric amounts of CSA and APS were dissolved in 20 ml DMF at room temperature. To initiate the polymerization of aniline, the solution containing CSA + APS was slowly added to the An/PVDF/DMF solution with a subsequent addition of 50 ml chloroform into the reaction solution under vigorous stirring. The polymerization reaction was allowed to proceed for 5 hours under stirring at room temperature to obtain a dark green miscible blend of PAni and PVDF, which remained as a kinetically stable dispersion within the solution. At the end of the polymerization, de-ionized water was added into the system to precipitate the blend. No separated PAni was found in the aqueous part, confirming the entire confinement of in situ synthesized PAni within the hydrophobic PVDF matrix. The precipitated blends were filtered and washed several times with de-ionized water and dried under a dynamic vacuum for 24 hours at 70 °C to obtain its final form. Two different PAni/PVDF blends with different concentrations of aniline (Table 1) were prepared, and are referred as sample PP1 and sample PP3. The ratio of CSA : An and APS : An were maintained fixed (1 : 1) for each blend. A pure PVDF film was also obtained after processing 1.0 g PVDF through DMF accordingly. Pure polyaniline was also synthesized for comparison, with the same stoichiometric ratio between An, CSA and APS as used for PP3 and DMF as the solvent without PVDF (Table 1).

Table 1 Preparation of different samples using different molar concentrations of An, CSA and APS

PVDF (gm)	An [M]	CSA [M]	APS [M]	Sample
1	0	0	0	PVDF
1	0.1	0.1	0.1	PP1
1	0.3	0.3	0.3	PP3
0	0.3	0.3	0.3	PAni

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2.3 Differential scanning calorimetry (DSC) and thermo-gravimetric analysis (TGA)

The non-isothermal crystallization experiments were carried out using a Netzsch DSC 214 Polyma instrument under a nitrogen atmosphere with temperature calibrated with indium. In practice, ∼10 mg of polymer films was encapsulated in concavus aluminium crucibles covered by lids. The samples were heated to 200 °C at 10 K min⁻¹ and kept for 10 min at this temperature to eliminate the thermal history, and then cooled to room temperature at various cooling rates of 2, 5, 10, 15, 20, 25 and 30 K min⁻¹. The percentage of PAni within the PVDF matrix was evaluated by thermo-gravimetric analysis (TGA). TGA was performed with a Netzsch TG 209 F3 Tarsus system at a heating rate of 10 K min⁻¹ under a nitrogen environment, and the samples were scanned from room temperature to 700 °C.

2.4 Scanning electron microscopy and optical microscopy

The dispersion of conducting PAni in PVDF matrix was characterized with EVO LS 10 (Zeiss) SEM at an accelerating voltage of 20 kV. The surface of the sample was gold coated before SEM observation. The surface morphology for all the samples was evaluated before and after the crystallization experiments.

The morphology of spherulitic growth during the crystallization of PVDF and its composites was observed by polarizing optical microscopic investigation using an Olympus BX41 microscope attached with a DP11 digital camera system (Olympus). The temperature variation of the samples was controlled by a Mettler Toledo FP90 Central processor. The samples were pre-heated to 200 °C, held for 5 min and then cooled.

2.5 Fourier transform infrared (FT-IR) spectroscopy

Fourier transform infrared (FT-IR) spectra of the samples were obtained on a Shimadzu IR affinity 1S FT-IR spectrometer, equipped with a single-reflection diamond attenuated total reflection Fourier transform infrared (ATR-FTIR) sampling module. The spectra were acquired using 64 scans and 4 cm⁻¹ resolution within a spectral range of 4000–400 cm⁻¹. The ATR-FTIR spectra for all the samples were obtained before and after melt crystallization.

3. Results and discussion

3.1 Thermal stability

The thermo-gravimetric behaviours of pure PVDF, PAni/PVDF blends and pure PAni have been compared in Fig. 1. The onset degradation temperature of the pure PVDF chain²⁷ is observed around 400 °C. A similar pattern of weight loss can be observed for the blends as well; however, they exhibit a considerable weight loss at considerably lower temperatures. The weight loss detected within the temperature range from 200 °C to 300 °C can be ascribed to the loss of bonded water and the dopant CSA of synthesized PAni within the PVDF matrix,^25,28 as also observed for pure PAni. The TGA curve of PP3 shows a considerably higher weight loss because the amount of dopant in the blend is higher. From TGA, the percentage of in situ polymerized CSA-doped PAni within the PVDF matrix was estimated to be ∼4.3% and ∼9.67% for PP1 and PP3, respectively.

Fig. 1 Thermo-gravimetric analysis of pure PVDF, PAni/PVDF blends and pure PAni.

3.2 Molecular structure and crystalline phase content

By comparing the FTIR spectra of PVDF and PAni/PVDF blends before and after the melt-crystallization process, as shown in Fig. 2(a) and (b), respectively, it can be observed that the in situ synthesized PAni within the PVDF matrix considerably influences the PVDF molecular structure and phase content. Fig. 2a depicts the spectra of solvent-casted pure PVDF and its blends. The spectrum of pure CSA-doped PAni is also included in the figure for comparison. It is well documented^23,24,29 that the absorption bands observed near 1072 and 876 cm⁻¹ (γCH₂ of PVDF⁴) are sensitive to the crystallinity of PVDF. The bands situated near 488, 532, 615, 764, 795, 974 and 1149 cm⁻¹ are attributed to the α-PVDF phase, while those obtained near 511, 840 and 1275 cm⁻¹ are assigned to β-PVDF phase.²³ For the spectrum of pure PAni, the overwhelming presence of the characteristic stretching vibrations at 1582 cm⁻¹ (γC=C for quinoid rings), 1484 cm⁻¹ (γC=C for benzenoid rings), 1297 cm⁻¹ (γC–N for the secondary aromatic amine), 1125 and 798 cm⁻¹ (γC–H aromatic in-plane and out-of-plane deformation for the 1,4-disubstituted benzene) support the formation of PAni. It is important to note that the intensity of the quinoid band of the PAni chain is higher than the benzenoid band, indicating that the PAni is in the conducting emeraldine salt state due to CSA doping. In the PAni/PVDF blends, although most of the bands associated with PAni coincide with the dominating absorption bands of PVDF, the feeble presence of the bands near 1582 cm⁻¹ and 1484 cm⁻¹ in both the blends (higher intensity for PP3) with an identical intensity as observed for pure PAni confirms the presence of PAni in the blend. This is also confirmed from Fig. 2a, where both pure PVDF and its blends possess a β-crystalline phase, as manifested by the noticeable peak near 840 cm⁻¹ in all the spectra. The feeble presence of the α-phase in PVDF almost totally diminishes with the increase of PAni content within the matrix.

Fig. 2 FTIR spectra of PVDF and its blends obtained at different conditions: (a) as-casted and (b) recrystallized. Spectrum of pure PAni is also shown with the as-casted spectra for comparison.

The FTIR spectra for the samples obtained after the melt-crystallization are demonstrated in Fig. 2b within the wave number range from 1400 to 450 cm⁻¹. As observed, the area of both the bands at 1072 and 876 cm⁻¹ remain almost the same, indicating that the degree of crystallinity of the recrystallized samples remains almost unchanged. It is also worth noting that there is a transition of the crystalline structure (from β- to α-phase) during the melt crystallization of PVDF (noticeable band near 764 cm⁻¹), while the trace of the β-phase is almost absent (Fig. 2b). However, the incorporation of PAni within the PVDF matrix prevents the complete transformation of the β- to α-phase in the blends, as manifested by the presence of the band at 840 cm⁻¹ in the spectra, whose intensity increases with higher PAni content within the matrix. Simultaneously, the band intensity corresponding to the α-phase diminishes with the increase of PAni within the matrix, as compared to pure PVDF. The role of PAni in the phase transformation can be revealed more conveniently by evaluating the relative fraction of the β-phase within the samples. The ratio of the absorption areas of the major bands corresponding to the α- and β-phases, denoted as A₇₆₄ and A₈₄₀, respectively, to that of the band at 876 cm⁻¹ (A₈₇₆) are compared in Fig. 3a. Considering that the infrared absorption follows the Lambert–Beer law for a system containing α- and β-phases, the fraction of the β-phases, F(β), can be calculated as follows:^6,29

where K_α and K_β are the absorption coefficients^4,23 of the bands (K_α = 6.1 × 10⁴ and K_β = 7.7 × 10⁴) corresponding to the α- and β-phases, respectively, where X_α and X_β are the % of crystallinity of the respective phases. Using the above mentioned equations, F(β) for different samples have been calculated and are shown in Fig. 3b.

Fig. 3 (a) Absorbance ratios and (b) F(β) obtained from the FT-IR spectra for neat PVDF and its blends under different conditions.

It can be observed from Fig. 3a that the ratios corresponding to A₈₄₀/A₈₇₅ and A₇₆₄/A₈₇₅ for pure PVDF decrease and increase, respectively, upon recrystallization, which leads to a lower value of F(β) (Fig. 3b). For the blend obtained with in situ synthesized PAni within the PVDF network, it can be observed that the α-phase is continuously diminished (decreasing value of A₇₆₄/A₈₇₅) with a simultaneous rise in the β-phase (higher values of A₈₄₀/A₈₇₅), which demonstrates a significant increase in F(β). Thus, the above mentioned study clearly reveals that the presence of in situ synthesized PAni significantly influences the crystal structure and phase transformation of the PVDF and, moreover, it hinders the transformation of β-PVDF to its α-phase during recrystallization.

3.3 SEM observations

The SEM micrographs of the as-casted films of PVDF and the PAni/PVDF blends are shown in Fig. 4a, c and e. As observed, pure PVDF contains uniform spherical particles, which indicate the formation of perfect spherulites with fewer nucleation sites, which produces larger crystallites. With the incorporation of PAni, the spheres overlap with each other and their size gradually decreases, which is attributed to the strong mutual interaction between the blend components and the increase in the nucleation sites and the formation of imperfect crystallites. Moreover, it can be clearly observed that in the blend with a higher PAni concentration (PP3) (Fig. 4e), the PAni phase is uniformly dispersed within the PVDF matrix in the form of small conductive islands.

Fig. 4 Scanning electron micrographs of as-casted and recrystallized PVDF (a) and (b); PP1 (c) and (d) and PP3 (e) and (f), respectively.

Fig. 4b, d and f show the SEM micrographs of the recrystallized PVDF and its blends.

As shown, the PVDF sample displays a rough surface morphology consisting of large spherulites, while both PP1 and PP3 exhibit a comparatively smooth surface. It can also be observed that both the blended samples have notable crystalline particles compared to that of pure PVDF, whose size decreases and numbers increase with increasing PAni content. From the above mentioned observation, it can be inferred that, with the insertion of PAni, the entanglement of PVDF chains may occur, resulting in large numbers of nucleation sites. However, at high PAni content, PVDF is surrounded by large numbers of conducting islands, which hinder the larger growth of crystals, and thus smaller, imperfect and non-spherical crystallites are formed.

3.4 Polarizing optical microscopy observations

The impact of PAni on the crystallization of PVDF was also demonstrated by POM images of PVDF and PAni/PVDF blends, as seen in Fig. 5. For the pure PVDF, the POM image exhibits a normal spherulitic structure with perfect Maltese extinction crosses, and the spherulitic size is around 100 μm. The spherulitic size decreases and their number increases significantly due to the incorporation of PAni into PVDF. This suggests that the crystallization of PVDF is greatly affected by the presence of PAni within the PVDF matrix. Herein, PAni acts as an effective nucleating agent to induce a great number of heterogeneous nuclei and to simultaneously generate large numbers of small spherulites within a limited space.

Fig. 5 Polarized light microscopy micrographs of (a) pure PVDF and (b) and (c) PAni/PVDF blends.

Moreover, with a higher PAni content, the spherulitic size of the blend becomes even smaller and difficult to be evaluated, which further confirms the greater heterogeneous nucleation effect of the PAni within this blend. However, it is worth noting that the growth of smaller spherulites, as illustrated by both the SEM and POM micrographs, often causes more crystal defects, leading to a lower degree of crystallinity.

Thus, to achieve more insight into the effect of the in situ incorporation of PAni within the PVDF matrix, a detailed study regarding the dynamic melt-crystallization kinetics of PVDF and its blends was performed.

3.5 Effect of cooling rate and in situ PAni loading on the non-isothermal melt-crystallization behavior of PVDF

The typical dynamic melt-crystallization thermo-grams measured at various cooling rates for pure PVDF and its blends are shown in Fig. 6. Table 2 shows the data of the non-isothermal crystallization peak temperature corresponding to the maximum crystallization rate (T_C) and crystallization enthalpy (ΔH_C) obtained at different cooling rates for pure PVDF and its blends. ΔH_C was calculated using the sample mass. It can be observed that for both PVDF and PAni/PVDF blends, as the cooling rate increases, T_C considerably shifts to a lower temperature with a simultaneous substantial increase in ΔH_C. The observed difference in ΔH_C at different cooling rates is analogous to the previously observed reports for different polymeric systems.^30–32 Because the crystallization process is time dependent, lower cooling rates provide macromolecular chains enough time to change their conformation, i.e., availability of a longer time for nucleation and crystallization. Therefore, the lower cooling rate facilitates the crystallization. Because the crystallization is an exothermic process and can be accelerated at a lower temperature, at higher cooling rates, high crystallization enthalpy (Table 2), i.e. a broader exothermic crystallization peak, arises (Fig. 6).

Fig. 6 Non-isothermal crystallization patterns (exothermic curves) of PVDF (a) and PAni/PVDF blends (b) and (c) at different cooling rates.

Table 2 DSC data for pure PVDF and PAni/PVDF blends at different cooling rates (φ)

Sample	φ (K min^−1)	T^*m (°C)	XC (%)	TC (°C)	ΔHC (J g^−1)	t1/2 (min)
PVDF	2	174	48.7	151.6	38.61	1.97
	5			148.2	45.75	1.11
	10			145.0	47.96	0.73
	15			142.9	48.87	0.58
	20			141.2	50.85	0.49
	25			139.8	51.41	0.40
	30			138.3	53.24	0.36
PP1	2	165	41.9	144.5	37.72	3.18
	5			140.7	42.09	2.44
	10			137.6	43.32	1.24
	15			135.4	43.69	1.08
	20			133.8	44.08	0.76
	25			132.2	45.39	0.64
	30			131.0	45.50	0.50
PP3	2	161	31.1	142.1	24.09	4.12
	5			138.6	27.95	2.84
	10			134.8	29.28	1.52
	15			132.1	30.02	1.16
	20			129.9	29.42	0.95
	25			128.2	29.23	0.77
	30			126.7	28.54	0.62

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However, the most relevant observation is the influence of PAni concentration on the crystallization temperature of PVDF for a particular cooling rate. There is a decrease in both T_C and ΔH_C when PVDF is blended with PAni. The decrease in T_C for the blends with increasing PAni content, irrespective of the cooling rate, can be attributed to the steric dipole/dipole interactions between the (=N–H)⁺ group of PAni and the (–[CH₂–CF₂]_n–) group of PVDF, hindering the α-phase and favoring the trans-conformation of the highly polar β-phase during melt crystallization,²⁹ as evidenced from the FTIR observation.

The absolute crystallinity fraction X_C was estimated (Table 2) from the enthalpy evolved during crystallization using the following equation:³⁰

where ΔH₀ refers to the extrapolated enthalpy corresponding to the melting of 100% crystalline PVDF [104.7 J g⁻¹]³³ and x is the weight fraction of PAni in the blend. It can be observed that, although PAni significantly enhances the heterogeneous nucleation within the blends, it actually diminishes the overall crystallinity of the blends, as compared to pure PVDF.

In the dynamic crystallization mechanism, it is generally considered that the development of crystallinity is linearly proportional to the evolution of heat released during the crystallization. Based on the above consideration, the relative degree of crystallinity (X_t) is defined as the ratio of crystallinity at any time t to the crystallinity as time approaches infinity, and can be expressed as a function of the crystallization temperature as follows:³⁴

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 the time approaches infinity. T₀, T and T_∞ denote the initial (t = 0), arbitrary and final (t = ∞) crystallization temperatures, respectively, and are related to the cooling rate φ as follows:

t = (T₀ − T)/φ (4)

Fig. 7 shows the relative crystallinity (X_t) with respect to temperature for the non-isothermal crystallization kinetics process. All the curves have the same sigmoid shape, indicating that only the retardation effect of the cooling rate separates them from each other. The transformation from temperature to time is performed using eqn (4) for different constant cooling rates and is shown in Fig. 8 for the different samples. All the X_t vs. time curves at various cooling rates have the same characteristic sigmoid shape. Each of the curves can be divided into four segments. First, a nonlinear part, characteristic of the initiation of nucleation, followed by a linear part associated with primary crystallization, and a subsequent second nonlinear part with slight deviation, which is a signature of secondary crystallization. The formation of a plateau in the final part of all these curves is perhaps due to spherulite impingement or the approach of saturation in the crystallization process. The lower plateau is the cooling rate, whereas the larger is the temperature (time) range at which the crystallization occurs, which indicates that the transformation is controlled by nucleation.

Fig. 7 Temperature variation of relative degree of crystallinity during crystallization process of (a) PVDF and (b) and (c) PAni/PVDF blends.

Fig. 8 Time variation of relative degree of crystallinity during the crystallization process of (a) PVDF and (b) and (c) PAni/PVDF blends.

The half non-isothermal crystallization time (t_1/2), defined as the time taken to reach the relative crystallinity at a value of 50%, can be obtained from the X_t vs. time curve, as summarized in Table 2 for PVDF and PAni/PVDF blends at different cooling rates. The t_1/2 value gradually decreases with increasing cooling rate, as the crystallization proceeds faster. Moreover, at a given cooling rate, the values of t_1/2 for the PAni/PVDF blends increase significantly more than those for neat PVDF, indicating that the addition of PAni may decelerate the overall crystallization process. Such a prolonged crystallization due to in situ incorporation of PAni within the PVDF matrix suggests that the PAni likely plays a role in retarding the transformation of β-PVDF to its α-phase during recrystallization, as already confirmed from the FT-IR analysis, or it acts as the nucleating agent of β-PVDF.

Because the half-crystallization time is only a single reference of the non-isothermal crystallization process, additional important kinetics parameters, such as nucleation rate and activation energy, were also determined from the analysis of the temperature and time-dependent X_t using different existing models.

3.6 Analysis of dynamic crystallization kinetics using different models

The isothermal crystallization of crystalline polymers can be simulated using the well-known Avrami equation.³⁵ The Avrami equation considers that the nucleation rate and the increase in volume of lamellar crystals are the main processes in crystallization and therefore it relates the time and the volume fraction of transformed material (X_t) as follows:

X_t = 1 − exp(−Z_ttⁿ) (5)

where n is the Avrami constant, associated with the nucleation mechanism and the geometry of crystal growth, and Z_t is the overall (macroscopic) rate constant involving both nucleation and growth rate parameters.

Because the Avrami equation deals with an isothermal process, it is not suitable to qualitatively describe the progress of crystallinity in a constantly changing environment. Owing to this inadequacy, a number of models, such as those of Jeziorny,³⁶ Ozawa,³⁷ and Liu and coworkers,³⁸ have been adopted to revise the Avrami equation and describe the non-isothermal crystallization process, which has been used here to determine different kinetic parameters.

3.6.1 Avrami–Jeziorny model. Jeziorny extended³⁶ the Avrami model by considering the dependence of the rate parameter Z_t upon the cooling rate (φ) and replaced it with the rate constant at a unit cooling rate Z_c as

log Z_c = log Z_t/φ (6)

where Z_c is the Jeziorny constant. From eqn (5) and (6), the modified Avrami equation becomes

log[−ln(1 − X_t)] = log Z_t + n log t (7)

The values of n and Z_c as well as the rate constant Z_t can be simultaneously obtained (Table 3) from the slopes and intercepts of the linear plots of log [−ln(1 − X_t)] versus log t, as shown in Fig. 9 for the different samples. As depicted in Fig. 9, the crystallization of PVDF and its blends appeared to occur through two main stages involving primary and secondary crystallization processes. Moreover, the primary crystallization, also comprising two different segments, suggests that multifaceted developments are involved in the crystallization. This type of complex crystallization was also evidenced earlier for other polymeric systems.^30,39 For a particular sample, the fitting lines for each segment are approximately parallel to each other, indicating a similar nucleation mechanism and crystal growth geometries at different cooling rates for the samples.

Table 3 Non-isothermal crystallization kinetic parameters calculated for PVDF and PAni/PVDF blends from the Avrami and Jeziorny model

Sample	φ (K min^−1)	Primary crystallization				Secondary crystallization
		First stage		Second stage
		ZcP1	nP1	Zcp2	nP2	Zcs2	nS2
PVDF	2	0.004	2.32	0.02	4.38	0.21	1.98
	5	0.011	2.12	0.27	4.44	0.72	2.04
	10	0.005	1.98	2.63	5.36	1.41	1.89
	15	0.006	1.92	7.58	5.09	1.99	1.57
	20	0.075	1.98	28.1	5.39	2.95	2.17
	25	—	—	16.9	4.09	4.16	2.14
	30	—	—	26.3	3.84	4.36	1.91
PP1	2	0.009	2.31	0.005	4.64	0.17	2.41
	5	0.012	2.06	0.019	5.16	0.51	1.51
	10	0.018	2.16	0.101	6.23	1.11	1.58
	15	0.019	2.23	0.211	7.85	1.23	1.65
	20	0.025	2.44	0.794	7.99	1.77	1.73
	25	0.028	2.21	1.047	6.98	2.51	2.01
	30	0.058	2.13	1.148	6.23	2.59	1.75
PP3	2	8.7 × 10^−4	1.56	1.4 × 10^−4	5.93	0.16	1.65
	5	0.004	2.17	0.001	6.96	0.40	1.58
	10	0.001	1.83	0.014	7.51	0.82	1.52
	15	0.006	1.99	0.121	7.73	1.14	1.61
	20	0.006	1.96	0.588	7.31	1.31	1.71
	25	0.022	2.18	1.910	7.56	1.63	1.82
	30	0.025	2.31	2.38	7.23	2.11	1.76

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Fig. 9 Avrami–Jeziorny plots of (a) PVDF and (b) and (c) PAni/PVDF blends calculated for different cooling rates.

During the first stage of the primary crystallization, the values of n for all the samples lie within 1.8 < n < 2.5 (Table 3), which indicates the two-dimensional growth of particles with a constant nucleation rate.⁴⁰ The first stage region becomes narrower with the increase in cooling rate (absent for PVDF at a higher cooling rate) but is gradually extended with increasing PAni extent within the PVDF matrix, indicating that PAni loading regulates the nucleation and crystal growth manner of the PVDF crystals within the blend.

During the second stage, the value of n reaches more than 3 for pure PVDF and even higher than 4 for PAni/PVDF blends, which may correspond to either a very complex crystallization process or to the growth of smaller crystallites.^39,40 During the secondary crystallization process, all the n values remain within 2, which again indicates that the crystallization process concludes with a two-dimensional growth of particles at a constant nucleation rate. Furthermore, it can be observed from Table 3 that, at the same cooling rate, the Z_c values for PAni/PVDF blends are considerably lower than that of neat PVDF. Considering the relation between the half-crystallization time t_0.5 and the crystallization rate Z_c, a lower t_0.5 value should be accompanied with a fast crystallization rate, i.e. a higher Z_c value. Thus, this again indicates that the inclusion of PAni could hinder the crystallization, although it offers a more specific area to crystallize under the non-isothermal scans. As a consequence, there are more sites available to nucleate, but the crystal growth proceeds at a slower rate. The net effects are the observed smaller grain size and lower crystallinity in the blends, as evidence in the aforementioned SEM and POM results.

3.6.2 Ozawa model and combined Avrami–Ozawa model. Ozawa³⁷ extended the Avrami equation assuming that the crystallization in non-isothermal conditions is the result of an infinite number of isothermal steps. According to this model, the relative degree of crystallinity (X_t) at any temperature T can be calculated as

This can be simplified as

log[−ln(1 − X_t)] = log K(T) − m log φ (9)

where K(T) is a function of temperature, which relates to the nucleation style, nucleation rate, and crystal growth rate, and m is the Ozawa exponent, which depends on the dimensions of the crystal growth. However, it was observed in the previous studies^18,30,41,42 that the Ozawa model is inadequate to explain the dynamic crystallization kinetics of the polymeric systems because the secondary crystallization and the impingement of spherulites are neglected in this model.³⁷

Liu et al.³⁸ combined the Avrami and Ozawa equations to give a relationship between X_t and t as

where the kinetic parameter F(T) = [K(T)/Z_t]^1/m represents the necessary value of the cooling rate per unit crystallization time to reach the systems at a distinct degree of crystallinity, i.e. the parameter that specifies the polymer crystallization rate, and λ is the ratio of the Avrami exponent (n) to the Ozawa exponent (m). The plots of log φ vs. log t are illustrated in Fig. 10 for different samples at different degrees of crystallinity (20%, 40%, 60% and 80%), which are found to be linear for all the samples according to the theory.

Fig. 10 Liu plots of the dynamic crystallization of (a) PVDF and (b) and (c) PAni/PVDF blends.

The slope λ and F(T) obtained from the straight line fits are presented in Table 4, from which it is worth noting that the values of F(T) for a particular sample increase steadily with increasing relative crystallinity, indicating that, at a particular crystallization time, to achieve a higher degree of crystallinity, a higher cooling rate is necessary. The values of the parameter λ are almost constant for a particular sample. Moreover, it can be seen that, for an identical degree of crystalline transformation, the F(T) value is significantly higher for PAni/PVDF blends as compared to neat PVDF. Thus, to achieve the same X_t, a higher cooling rate is required for PAni/PVDF blends than for neat PVDF. This means that the crystallization rate of PAni/PVDF blends gradually become slower with increasing extent of PAni within the PVDF. These results are in accordance with those obtained from Jeziorny's model.

Table 4 Dynamic crystallization kinetic parameters at different degrees of crystallinities by Liu's method

Sample	Parameter	Xt (%)
		20	40	60	80
PVDF	F(T)	4.5	6.1	8.1	11.4
	λ	1.50	1.53	1.60	1.67
PP1	F(T)	10.0	13.0	15.8	20.4
	λ	1.48	1.53	1.55	1.62
PP3	F(T)	13.8	16.9	20.4	25.0
	λ	1.46	1.49	1.53	1.57

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Table 5 Different growth parameters obtained from the analysis of the modified Lauritzen–Hoffman equation (eqn (18)) for the different samples

Sample	Regime I			Regime II
	Kg (10^5) (K^2)	U (kJ mol^−1)	Range (T)	Kg (10^5) (K^2)	U (kJ mol^−1)	Range (T)
PVDF	0.21	0.53	407–412	0.36	4.89	413–418
PP1	0.42	3.86	398–406	0.95	6.48	407–412
PP3	0.87	8.39	400–410	—	—	—

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3.6.3 Nucleation ability. Though the process of melt-crystallization involves a simultaneous nucleation and growth of crystals during the initial stage, but at the vicinity of the crystallization peak temperature, the process is mainly dominated by the growth of crystallites, and the process becomes isokinetic. Therefore, the effect of a foreign agent on the overall crystallization of a polymer is mainly associated with its nucleation ability at the initial stage. According to Dobreva and Gutzow,⁴³ the nucleation activity of foreign substrates in polymer melts can be calculated from the ratio ψ = B*/B, where B* stands for the parameter during heterogeneous nucleation, while B stands for the homogeneous nucleation parameter. B and B* can be experimentally determined from the slope of the linear plots corresponding to the following heating rate equation

log φ = A − B/ΔT_C² (11)

where A is a constant and ΔT_C = T_m − T_C is the difference between the melting temperature and the temperature corresponding to the peak temperature of the DSC exothermal curves. The values of B and B* are obtained from the linear fitting using eqn (11), as shown in Fig. 11, from which the values of ψ were calculated, as shown in the inset of Fig. 11. If the foreign substrate is extremely active, ψ approaches 0, while for inert particles, ψ approaches 1. It can be seen that ψ decreases significantly with the wt% of PAni within the PVDF matrix, again confirming that PAni is effectively acting as a nucleation agent in the PVDF matrix.

Fig. 11 Linear plots following the eqn (10) for different homogeneously or heterogeneously nucleated samples with corresponding values of ψ.

3.7 Effective activation energy of non-isothermal crystallization

To characterize the non-isothermal crystallization of melt polymers, the determination of the effective activation energy (E_X) is essential. In this regard, the reaction model-independent isoconversional methods are advantageous as compared to the other methods. The isoconversional methods also enable to evaluate the dependence of E_X on the conversion and temperature, which is considerably helpful in detecting and elucidating complex kinetics and the crystal growth mechanism in polymeric systems. Among the different existing isoconversional methods, the differential method of Friedman⁴⁴ and the advanced integral method of Vyazovkin⁴⁵ are the most appropriate to use, and thus, in the current investigation, the Friedman's method was used to evaluate E_X for different samples.

Usually, kinetic methods used in thermal analysis consider the process rates (dX_t/dt) to be a function of only two variables: the temperature (T) and the extent of conversion (X_t) as⁴⁶

where K(T) is the rate constant whose variation can be described as

K(T) = A exp(−E_X/RT) (13)

In all the isoconversional methods, the reaction rate at constant extent of conversion is only a function of temperature.⁴⁶ Considering this, by taking the logarithmic derivative of the reaction rate at constant X_t, for constant f(X_t), the expression for E_X from eqn (12) becomes

According to Friedman's differential isoconversional method,⁴⁴ using eqn (12) and (13), different effective activation energies (E_X) can be determined for every degree of crystallinity from

where the subscripts i and X denote the ordinal number of a non-isothermal experiment conducted at the cooling rate α_i and the quantities evaluated at a specific conversion degree X_t, respectively, whereas, T_X,i is the set of temperatures related to a given conversion X at different cooling rates, α_i.

By selecting appropriate degrees of crystallinity (from 2% to 98%), the values of dX_t/dt at a specific X_t for different cooling rates are correlated to the corresponding crystallization temperature at this X_t, i.e., T_X for each sample. Straight line plots of the left-hand side of eqn (15) with respect to 1/T_X for PVDF and its blends at three different conversions are depicted in Fig. S1.† The values of E_X obtained from the slopes of the as-shown straight lines achieved for each conversion and for different cooling rates were plotted as a function of X_t for each samples, as shown in Fig. 12. Negative values for E_X were observed always, which increased with the advance of the crystallization process. Moreover, the E_X values of the PAni/PVDF blends are closer to zero than the pre-PVDF, indicating that they are crystallizing at temperatures closer to their maximum crystallization rate.⁴⁷

Fig. 12 Variation of the effective activation energy with the relative extent of crystallization for PVDF and PAni/PVDF blends, obtained by the Friedman's method. The dotted lines represent the variation of the temperature with the relative crystallinity for the respective samples.

The resultant E_X dependencies can be utilized^45,46 for estimating the parameters related to crystal growth by correlating the isoconversional principle with the Hoffman–Lauritzen theory.⁴⁸ According to the Hoffman–Lauritzen theory,⁴⁸ the temperature dependence of the linear growth rate, G, can be described as follows:

where G₀ is the pre-exponential factor and U* is the activation energy of the segmental jump. The first exponential term contains the contribution of the diffusion process to the growth rate, while the second exponential term is the contribution of the nucleation process. T_∞ is the temperature below which motion associated with viscous flow ceases.⁴⁸ K_g is a nucleation constant and ΔT denotes the degree of under cooling (ΔT = T_m − T), whereas f is a correction factor that is close to unity at high temperatures.^45,48,49 Extensive experimental measurements by Toda et al.⁵⁰ established that the logarithmic derivative of the microscopic growth rate is equivalent to the logarithmic derivative of the overall crystallization rate, (dX_t/dt), according to the following equation:where (dX_t/dt) = ΔhSG with Δh as the volumetric heat of crystallization and S as the total area of the growth surface.⁵⁰ It was demonstrated⁴³ that the left-hand side of eqn (17) can be considered as the effective activation energy of the overall crystallization rate, as estimated from eqn (15).

Using eqn (16) and (17), Vyazovkin and Sbirrazzuoli⁴⁵ derived the temperature dependence of the effective activation energy of the growth rate as

Fig. 13 displays the variation of E_X with the average temperature for a particular X_t for different cooling rates (T_avg). The value of E_X for all the samples increases with diminution of the average temperature, as can be found in a variety of polymer systems,^47,51 which clearly indicates that the crystallization rate increases with decreasing temperature.⁴⁷

Fig. 13 The dependence of the effective activation energy on average temperatures for PVDF and PAni/PVDF blends obtained by the Friedman's method. The solid lines represent the best fits to the eqn (18).

As observed from Fig. 13, the E_X (T_avg) dependence demonstrates discontinuities at 414 K (i.e., 141 °C) and 407 K (i.e., 134 °C) for PVDF and for the blend with low PAni content (PP1), respectively. However, no such discontinuous variation can be found for the higher PAni incorporated blend (PP3). The observed discontinuity may be attributed to a change in the crystallization mechanism. Different parameters related to the mechanism of crystal growth have been obtained from the fitting of E_X (T_avg) data with eqn (18), as shown in Table 5. To incorporate any possible change in the crystallization mechanism, the parameterization of the higher temperature (T > 414; 407 K) and lower temperature (T < 414; 407 K) ranges of the E_X (T_avg) for PVDF and PP1, respectively, were performed (solid lines in Fig. 13). It can be observed from Table 5 that the values of both K_g and U significantly increase at the higher temperature range, clearly ascribing to the change in the crystallization mechanism from regime I to regime II. Moreover, both K_g and U significantly increase with in situ PAni integration within PVDF. In the high temperature regime, the PVDF chains have a lower mobility for nucleation and growth than in the low temperature regime, and the mobility decreases further with the incorporation of PAni within the matrix and thus requires a higher energy for the growth of crystallites. This conclusion is parallel to that obtained from the aforementioned other analysis.

4. Conclusions

Results and analysis based on structural, morphological and non-isothermal crystallization kinetics investigations of PVDF and different PAni/PVDF blends clearly confirm that the nucleation and phase transition of PVDF macromolecules are significantly controlled by PAni in the non-isothermal crystallization process of the blends. During the melt-crystallization process, PAni serves as an efficient heterogeneous nucleation agent, and on the other hand it defends the β-phase to α-phase transition of PVDF, thereby increasing the percentage of the β-phase within the blend. From the analysis, it can also be concluded that PAni actually delays the crystal growth process, leading to a decrease in both T_C and overall crystallinity of the blends. The higher values of the effective activation energy for the blends as compared to neat PVDF and the higher values of growth parameters obtained from the analysis of the average temperature variation of the effective activation energy by the modified Hoffman–Lauritzen theory also accomplish the same.

Acknowledgements

The authors acknowledge the DST-FIST scheme of the Department of Physics, University of Kalyani and DST-PURSE program, University of Kalyani for providing the instrumental facilities. The authors also acknowledge Prof. P. K. Mandal, University of North Bengal, for providing POM facility.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra15989j

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