Non-Isothermal Crystallization Behavior of Poly(vinylidene ﬂuoride) in Dialkyl Phthalate Diluents during Thermally Induced Phase Separation Process

: The non-isothermal crystallization behavior of poly(vinylidene ﬂuoride) (PVDF) in dialkyl phthalate diluents during the thermally induced phase separation (TIPS) process was investigated by di ﬀ erential scanning calorimetry (DSC) at various cooling rates. Dialkyl phthalates with di ﬀ erent alkyl chain-length, namely dimethyl phthalate (DMP), diethyl phthalate (DEP) and dibutyl phthalate (DBP), were used as the diluent. The e ﬀ ects of alkyl chain-length of dialkyl phthalate and cooling rate on the non-isothermal crystallization behavior as implied by the Avrami analysis modiﬁed by Jeziorny and Mo’s analysis were determined. The values of half-time, t 1/2 , and the parameters Z c and F ( t ) , which characterized the kinetics of non-isothermal crystallization, showed that the crystallization rate increased with the increase of the alkyl chain-length of dialkyl phthalate due to the lower compatibility between PVDF and dialkyl phthalate. Moreover, the alkyl chain-length of dialkyl phthalate also has a great impact on the compact spherulitic structure of PVDF membranes prepared from di ﬀ erent PVDF / dialkyl phthalate blends. With the decrease of the alkyl chain-length of dialkyl phthalate, the number of spherulites increased and the size of spherulites became smaller. This research thus not only proves the e ﬀ ects of alkyl chain-length of dialkyl phthalate on the non-isothermal crystallization behavior of PVDF, but also provides a systematic strategy to evaluate a single diluent during the TIPS process.


Introduction
Microporous semi-crystalline polymeric membranes with controlled pore size, shape and distribution can be prepared via the thermally induced phase separation (TIPS) method, which was first introduced by Castro in the late 1970s [1]. In the TIPS process, an appropriate polymer/diluent system is heated to achieve a homogeneous solution. During cooling, both by isothermal or non-isothermal quenching, TIPS can proceed either solid-liquid phase separation or liquid-liquid phase separation. The solid-liquid phase separation usually results from the crystallization of polymer from the homogeneous solution phase [2]. In the real TIPS process, the non-isothermal step occurs much more often than the isothermal step. Thus, the non-isothermal crystallization behavior of the crystalline polymer in the diluted system would predominate the pore structure of the resulted membrane. from 5 to 9 mg. The sample was first heated to 200 • C and maintained there for 10 min to erase thermal history, and then cooled to 40 • C at a rate of 2, 5, 10 and 20 • C/min. The exothermic curves of heat flow with temperature decreasing at various rates were recorded and investigated. The crystallization half-time (t 1/2 ), which is defined as the half-time of crystallization, was used as a characteristic parameter of the crystallization process.
The melting process of PVDF from the PVDF/diluent sample cooled at the different rates mentioned above was detected by maintaining at 40 • C for 2 min, followed by heating to 200 • C at a rate of 10 • C/min. The absolute crystallinity of PVDF (χ c ) is as recorded below [20]: where ∆H f * = 104.5 J/g is the melting enthalpy for a 100% crystalline PVDF, ∆H f is the melting enthalpy of the PVDF/diluent sample measured in DSC and ω is the PVDF weight fraction.

Avrami Analysis Modified by Jeziorny
The Avrami analysis modified by Jeziorny [21] is an extended expression to analyze the non-isothermal crystallization process. The Avrami equation was modified as follows: where n is the Avrami exponent, Z t is the Avrami rate constant involving nucleation and growth parameters and X(t) is the relative degree of crystallinity at the time t, which was obtained from the area of the DSC exothermic peak at time t divided by the total area under the exothermic peak, as shown in Equation (3): where t o and t ∞ represent the onset and end of crystallization temperatures respectively, and dH/dt is the heat flow rate.

Mo's Approach Analysis
By combining the Ozawa analysis [22] and modified Avrami analysis, Mo [23] obtained another kinetic equation for non-isothermal crystallization behavior to relate the crystallinity with the cooling rate, φ, and the crystallization time, t. The relationship between φ and t was defined for a given degree of crystallinity as follows.
where the parameter F(t) refers to the necessary value of the cooling rate to reach a defined crystallinity within unit crystallization time, and b is the ratio between Avrami and Ozawa exponents. From Equation (4), it is followed that, at a given crystallinity, the plot of log φ versus log t should be a straight line with an intercept of log F(t) and a slope of −b.

Membrane Preparation and Sem Observation
The PVDF/dialkyl phthalate sample obtained in the manner mentioned above was re-heated to 200 • C for 5 min, and then quenched into ice-water to induce phase separation and polymer solidification. The diluent that remained in the membrane precursor was extracted by ethanol, and the PVDF membrane was obtained after the volatilization of ethanol. The resulting PVDF membrane was fractured in liquid nitrogen and coated with platinum. A scanning electron microscope (SEM, JSM7401, JEOL Ltd., Akishima, Japan) with the accelerating voltage set to 1.0 kV was used to examine the cross-section of membranes.

Non-Isothermal Crystallization Behavior
No cloud points were found and only the crystallization (solid-liquid phase separation) occurred in these three PVDF/dialkyl phthalate systems because dialkyl phthalates had good compatibility with PVDF. Figure 1 shows the exothermic curves for PVDF/dialkyl phthalate blends at different cooling rates. Table 1 summarizes how the crystallization temperature and the value of enthalpy of crystallization for PVDF/dialkyl phthalate blends depended upon the alkyl chain-length of dialkyl phthalate. The melting data are listed in Table 2, which were obtained from the melting thermograms shown in Figure 2. It clearly shows that an increase of the alkyl chain-length of dialkyl phthalate accelerated the crystallization of PVDF progressively. The onset crystallization temperature, t c o , peak crystallization temperature, t c p , and final crystallization temperature, T c f , all increased with the increase of the alkyl chain-length of dialkyl phthalate. The crystallization behavior of the PVDF/dialkyl phthalate blend was analyzed in terms of the compatibility between PVDF and dialkyl phthalate. The degree of compatibility could be estimated from the different interaction parameter, χ 12 , between polymer and diluent using the following expression [24]: where R is the ideal gas constant (8.314 J/mol/K), T is the environment temperature (298 K), and δ d , δ p and δ h are the Hansen's parameters for dispersion, polar and hydrogen bonding interactions, respectively [25]. V m is the molar volume of the diluent. In general, the larger the interaction parameter, χ 12 , value, the weaker the compatibility between the polymer and diluents.
Crystals 2020, 10, x FOR PEER REVIEW 4 of 11 The resulting PVDF membrane was fractured in liquid nitrogen and coated with platinum. A scanning electron microscope (SEM, JSM7401, JEOL Ltd., Akishima, Japan) with the accelerating voltage set to 1.0 kV was used to examine the cross-section of membranes.

Non-Isothermal Crystallization Behavior
No cloud points were found and only the crystallization (solid-liquid phase separation) occurred in these three PVDF/dialkyl phthalate systems because dialkyl phthalates had good compatibility with PVDF. Figure 1 shows the exothermic curves for PVDF/dialkyl phthalate blends at different cooling rates. Table 1 summarizes how the crystallization temperature and the value of enthalpy of crystallization for PVDF/dialkyl phthalate blends depended upon the alkyl chain-length of dialkyl phthalate. The melting data are listed in Table 2, which were obtained from the melting thermograms shown in Figure 2. It clearly shows that an increase of the alkyl chain-length of dialkyl phthalate accelerated the crystallization of PVDF progressively. The onset crystallization temperature, o c t , peak crystallization temperature, p c t , and final crystallization temperature, f c T , all increased with the increase of the alkyl chain-length of dialkyl phthalate. The crystallization behavior of the PVDF/dialkyl phthalate blend was analyzed in terms of the compatibility between PVDF and dialkyl phthalate. The degree of compatibility could be estimated from the different interaction parameter, 12 χ , between polymer and diluent using the following expression [24]: where R is the ideal gas constant (8.314 J/mol/K), T is the environment temperature (298 K), and d δ , p δ and h δ are the Hansen's parameters for dispersion, polar and hydrogen bonding interactions, respectively [25]. m V is the molar volume of the diluent. In general, the larger the interaction parameter, 12 χ , value, the weaker the compatibility between the polymer and diluents.   Table 2 shows the interaction parameter, 12 χ , value between PVDF and dialkyl phthalate. As a result, with the increase of the alkyl chain-length of dialkyl phthalate, the interaction parameter, 12 χ , value increased, which indicated the decrease of the compatibility between PVDF and the diluent. Favorable compatibility induced full extension of PVDF segments, which led to the required higher supercooling degree for PVDF segments to fold when cooling at the same rate. Namely, the crystallization temperature of PVDF decreased with the decrease of the alkyl chain-length of dialkyl phthalate.    Table 2 shows the interaction parameter, χ 12 , value between PVDF and dialkyl phthalate. As a result, with the increase of the alkyl chain-length of dialkyl phthalate, the interaction parameter, χ 12 , value increased, which indicated the decrease of the compatibility between PVDF and the diluent. Favorable compatibility induced full extension of PVDF segments, which led to the required higher supercooling degree for PVDF segments to fold when cooling at the same rate. Namely, the crystallization temperature of PVDF decreased with the decrease of the alkyl chain-length of dialkyl phthalate.    Relative crystallinity, X(t), as a function of the crystallization time, t, for PVDF/dialkyl phthalate blends is plotted in Figure 3. As would be expected, PVDF at higher cooling rates required a shorter time to complete crystallization. From these curves, it was easy to find that PVDF/dialkyl phthalate blends showed similar development of the crystallization process, and a series of S-shaped curves were obtained due to the spherulitic impingement in the later crystallization stage. The crystallization half-time, t 1/2 , which represents the overall crystallization rate, is defined as the time at which the relative crystallization degree is 50% completed. The shorter the half-time, t 1/2 , the faster the overall crystallization rate. As listed in Table 1, it could be seen that, as expected, t 1/2 decreased with the increase of the cooling rate for all the cases. Moreover, t 1/2 decreased with the increase of the alkyl chain-length of dialkyl phthalate. As stated above, with the increase of the alkyl chain-length of dialkyl phthalate, the compatibility between PVDF and dialkyl phthalate became weaker, which led to a higher growth rate of PVDF crystallization.

Avrami Analysis Modified by Jeziorny
The Avrami plot of log{ ln{1 ( )}} X t − − versus log t for PVDF/dialkyl phthalate is shown in Figure 4. Each curve had a linear portion, most of which was followed by a gentle deviation at longer times. Usually, this deviation is considered to be due to the secondary crystallization, which is caused by the spherulite impingement in the later stage [28].  As listed in Table 1, the melting temperature was decreased with the decrease of the alkyl chain-length of dialkyl phthalate. As reported, depression of melting temperature, due to a decrease in the chemical potential of the crystalline polymer, could provide the information on compatibility between the polymer and diluent. The higher the depth of melting temperature depression that occurred, the better compatibility between the polymer and diluent [26,27]. So, it was also suggested that the compatibility between PVDF and dialkyl phthalate increased with the decrease of the alkyl chain-length of dialkyl phthalate.

Avrami Analysis Modified by Jeziorny
The Avrami plot of log − ln 1 − X(t) versus log t for PVDF/dialkyl phthalate is shown in Figure 4. Each curve had a linear portion, most of which was followed by a gentle deviation at longer times. Usually, this deviation is considered to be due to the secondary crystallization, which is caused by the spherulite impingement in the later stage [28]. The calculated values of n, Z t and Z c for the linear portion are listed in Table 3. The Avrami exponent lies between 2.9 and 3.7. The values of crystallization rate parameter, Z c , were comparable for every sample. At a specific cooling rate, the values of Z c for PVDF decreased with the decreasing alkyl chain-length of dialkyl phthalate. In the case of dialkyl phthalate having a shorter alkyl chain-length, favorable compatibility between PVDF and dialkyl phthalate induced full extension of PVDF segments, which brought resistance for the transport of the 7 of 11 PVDF segment to the growing crystal surface and reduced the rate of crystallization growth. At the same time, the values of Z c increased with the increase of the cooling rate. Increasing the cooling rate could provide the system with more energy to improve the activity of the chain segment, thus resulting in the increase of crystallization rate parameter, Z c . by the spherulite impingement in the later stage [28]. The calculated values of n , t Z and c Z for the linear portion are listed in Table 3. The Avrami exponent lies between 2.9 and 3.7. The values of crystallization rate parameter, c Z , were comparable for every sample. At a specific cooling rate, the values of c Z for PVDF decreased with the decreasing alkyl chain-length of dialkyl phthalate. In the case of dialkyl phthalate having a shorter alkyl chain-length, favorable compatibility between PVDF and dialkyl phthalate induced full extension of PVDF segments, which brought resistance for the transport of the PVDF segment to the growing crystal surface and reduced the rate of crystallization growth. At the same time, the values of c Z increased with the increase of the cooling rate. Increasing the cooling rate could provide the system with more energy to improve the activity of the chain segment, thus resulting in the increase of crystallization rate parameter, c Z .

Mo's Approach
At a given degree of crystallinity, plotting log φ versus log t ( Figure 5) yielded a linear relationship between log φ and log t. The data of the kinetic parameter F(t) and b estimated from the intercept and slope for PVDF/dialkyl phthalate are listed in Table 4. For each sample, with the increase of relative crystallinity, X(t), the values of b changed slightly, while the values of F(t) increased, indicating that at a given crystallization time, a higher cooling rate should be used to obtain a higher degree of crystallinity. However, at the same X(t), the values of F(t) decreased with the increase of the alkyl chain-length of dialkyl phthalate. Namely, the increase of compatibility between PVDF and dialkyl phthalate could reduce the crystallization rate, and this was consistent with the analysis of crystallization half-time and the Avrami analysis modified by Jeziorny. the increase of relative crystallinity, ( ) X t , the values of b changed slightly, while the values of ( ) F t increased, indicating that at a given crystallization time, a higher cooling rate should be used to obtain a higher degree of crystallinity. However, at the same ( ) X t , the values of ( ) F t decreased with the increase of the alkyl chain-length of dialkyl phthalate. Namely, the increase of compatibility between PVDF and dialkyl phthalate could reduce the crystallization rate, and this was consistent with the analysis of crystallization half-time and the Avrami analysis modified by Jeziorny.    Figure 6 shows the cross-section structure of the membranes prepared from PVDF/dialkyl phthalate systems via the TIPS method. Each sample presented spherulitic structure due to only solid-liquid phase separation occurring. With the decrease of the alkyl chain-length of dialkyl phthalate, the number of spherulites increased and the size of spherulites became smaller. As mentioned above, while the alkyl chain-length of dialkyl phthalate decreased, the onset crystallization temperature, t c o , decreased, which resulted in more nuclei formation at the beginning of crystallization. Therefore, these nuclei grew up into smaller spherulites with the same polymer concentration.

Membrane Structure
solid-liquid phase separation occurring. With the decrease of the alkyl chain-length of dialkyl phthalate, the number of spherulites increased and the size of spherulites became smaller. As mentioned above, while the alkyl chain-length of dialkyl phthalate decreased, the onset crystallization temperature, o c t , decreased, which resulted in more nuclei formation at the beginning of crystallization. Therefore, these nuclei grew up into smaller spherulites with the same polymer concentration.

Conclusions
With the DSC data obtained at various cooling rates, the effect of the alkyl chain-length of dialkyl phthalate on the non-isothermal crystallization behavior of PVDF/dialkyl phthalate blends during the TIPS process was investigated through the Avrami analysis modified by Jeziorny and Mo's analysis. DSC exotherms of non-isothermal crystallization showed that all the crystallization temperatures (t c o , t c p and t c f ) increased with the increasing alkyl chain-length of dialkyl phthalate. On the other hand, t 1/2 increased as the alkyl chain-length of dialkyl phthalate and the cooling rate decreased. With the increase of the alkyl chain-length of dialkyl phthalate, the parameter Z c increased and F(t) decreased, which revealed that the crystallization rate increased. SEM results showed that the cross-section of the PVDF membrane prepared from the PVDF/dialkyl phthalate system presented spherulitic structure due to the solid-liquid phase separation occurring. Moreover, the number of spherulites increased and the size of spherulites became smaller with the decrease of the alkyl chain-length of dialkyl phthalate.

Conflicts of Interest:
The authors declare no conflict of interset.