Isothermal and Nonisothermal Crystallization Kinetics of Poly(ε-caprolactone) Blended with a Novel Ionic Liquid, 1-Ethyl-3-propylimidazolium Bis(trifluoromethanesulfonyl)imide

Recently, ionic liquids (ILs) and biodegradable polymers have become crucial functional materials in green sustainable science and technology. In this study, we investigated the influence of a novel IL, 1-ethyl-3-propylimidazolium bis(trifluoromethanesulfonyl)imide ([EPrI][TFSI]), on the crystallization kinetics of a widely studied biodegradable polymer, poly(ε-caprolactone) (PCL). To obtain a comprehensive understanding, both the isothermal and nonisothermal crystallization kinetics of the PCL blends were studied. Incorporating [EPrI][TFSI] reduced the isothermal and nonisothermal crystallization rates of PCL. Regarding isothermal crystallization, the small k and 1/t0.5 values of the blend, estimated using the Avrami equation, indicated that [EPrI][TFSI] decreased the rate of isothermal crystallization of PCL. The Mo model adequately described the nonisothermal crystallization kinetics of the blends. Increasing the [EPrI][TFSI] content caused the rate-related parameter F(T) to increase. This indicated that the crystallization rate of PCL decreased when [EPrI][TFSI] was incorporated. The spherulite appearance temperature of the blending sample was found to be lower than that of neat PCL under a constant cooling rate. The analysis of the effective activation energy proposed that the nonisothermal crystallization of PCL would not be favorited when the [EPrI][TFSI] was incorporated into the blends. The addition of [EPrI][TFSI] would not change the crystal structures of PCL according to the results of wide angle X-ray diffraction. Fourier transform infrared spectroscopy suggested that interactions occurred between [EPrI][TFSI] and PCL. The crystallization kinetics of PCL were inhibited when [EPrI][TFSI] was incorporated.


Isothermal Crystallization Kinetics
The Avrami equation [1,2] was used to evaluate the isothermal crystallization kinetics of the [EPrI][TFSI]/PCL blends. The following equation presents the original form of the Avrami equation.
In equation (1), it should note the relative degree of crystallinity at time t is denoted by Xt. The value n is a constant relating to the crystallization mechanism. In addition, the rate constant is denoted by k in equation (1). The Avrami equation can be further converted into the log-log representation, and this representation can be applied to evaluate the relevant kinetic parameters. Equation (2) shows the Avrami equation in the log-log form.
According to equation (2), it can estimate the values of n and k from the slope and intercept, respectively, of the log[−ln(1−Xt)] versus log(t) plot with a linear relationship. Moreover, it can also determine the crystallization half-time (t0.5) according to the form shown in equation (3). It should note that the t0.5 is the time at which the extent of crystallization is 50%

Non-isothermal Crystallization Kinetics
The non-isothermal crystallization kinetics of the blends comprising [EPrI][TFSI] and PCL was also discussed in this study. The influence of [EPrI][TFSI] on the non-isothermal crystallization of PCL can be further identified with relevant discussions. We applied several conventional models such as the modified Avrami equation [3], Ozawa equation [4], and Mo model [5] for our analysis. Equation (4) shows the modified Avrami equation [3] for the nonisothermal crystallization, and it can be correlated to the overall rate of non-isothermal crystallization.
In the modified Avrami equation [3] for the non-isothermal crystallization, it assumes that a series of infinitesimally small isothermal crystallization steps are involved in the crystallization process when the cooling rate is fixed. The exponent n' is related to the nucleation type and the dimension of the crystal growth. Furthermore, Zt is a rate constant and can be correlated to the parameters of nucleation and growth. The time (t) and temperature (T) relationship of the non-isothermal crystallization can be further derived as the following equation.
In equation (5), the rate of cooling is denoted by Φ. The modified Avrami equation in the logarithmic form for analyzing non-isothermal crystallization kinetics is presented as the equation (6).
Ozawa [4] further modified the Avrami equation. Ozawa suggested that numerous infinitesimal steps of isothermal crystallization are included in the crystallization process proceeding non-isothermally. The Ozawa equation for analyzing non-isothermal crystallization is shown as the equation (7).
In equation (7), the relative crystallinity (at temperature T) and the cooling function related to the overall rate of crystallization are denoted by XT and K(T), respectively. The cooling rate and the Ozawa exponent are denoted by Φ and m, respectively, in equation (7). The crystal growth dimension is associated with the Ozawa exponent. By taking the logarithm of both sides of equation (7), the Ozawa equation can be rearranged, and the logarithmic form of the Ozawa equation can be presented. The Ozawa equation in the logarithmic form is shown as equation (8).
The Mo model derived by Mo and his coworkers [5] were also applied for analyzing the non-isothermal crystallization in this study. The Mo equation is shown as the following equation.
In equation (9), the correlation between the cooling rate and crystallization time is demonstrated. The Mo index is denoted by a in equation (9), and this index is equal to the ratio of Avrami exponent (n)/Ozawa exponent (m). In addition, the logF(T) in equation (9) is equal to the value of [K(T)/k] 1/m . At a certain temperature in unit crystallization time, it can associate the value of F(T) with the cooling rate needed to reach a defined degree of crystallinity. The parameter F(T) can be estimated from the intercept of the logΦ versus log(t) plot at a defined relative crystallinity. In addition in the same plot of logΦ versus log(t), it can determine the value of a by the slop of logΦ versus log(t) plot.

Effective Activation Energy of Non-isothermal Crystallization
The effective activation energy were also estimated for the neat PCL and the [EPrI][TFSI]/PCL blend. We used the isoconversion method proposed by Friedman [6,7] for relevant estimations. According to the Friedman method, the equation relating to the effective activation energy can be shown as equation 10, In equation 10, at a specific conversion X, dX/dt represents the instantaneous crystallization rate as a function of time. ΔEX is the effective activation energy at a specific conversion X and TX,i represents the temperatures correlated with a specific X at different cooling rates. The subscript i means each cooling rate used in the non-isothermal crystallization experiment. To estimate the effective activation energy, the X as a function of t can be obtained from the non-isothermal crystallization results. The value of dX/dt at a given X can be calculated by differentiating the obtained X(t) function. The specific TX value related to a given X can be further found according to the relationship among X, t, and T. By plotting the specific value of ln(dX/dt) to 1/TX, the slope with a straight line plot can be used to estimate the effective activation energy ΔEX. More detail descriptions on the estimation of the effective activation energy by the Friedman method can be found in the literatures [7].