III. RESULTS AND DISCUSSION

Figure 1 shows the heat-flow curve obtained in a 10 °C/min heating standard DSC from a PLLA sample, which underwent a 40 °C/min cooling from the melt. It is well known that PLLA is a thermoplastic with a slow crystallization kinetics and, thus, in this case the original crystallinity is expected to be not more than 10%. Typical thermal events of PLLA can be observed on the heat-flow curve. The inset shows how the glass transition is overlapping with enthalpy relaxation in the 40–60 °C range. The enthalpy relaxation is due to the different cooling and heating rates to which the sample was subjected and to the period of time where the sample was below the glass transition temperature (T _g), evolving to a lower energy content state. The cold crystallization results from the fact that the sample was not allowed to completely crystallize during the relatively fast cooling preceding the heating experiment. The double melting peak was largely reported and will be discussed later.

FIG. 1.

Heat-flow curve obtained in a 10 °C/min heating standard differential scanning calorimetry from a poly(l-lactic acid) sample, which underwent a 40 °C/min cooling from the melt.

A first TMDSC trial is done with the aim to separate the glass transition from enthalpy relaxation, as well as to find out how the heat capacity changes along the cold crystallization process. That change of heat capacity is expected to be linked to the crystallization since the heat capacity of crystals is lower than the heat capacity of the corresponding glasses. To meet the heat only requirements, the following conditions were chosen for this experiment: heating rate of 2 °C/min, period of 60 s, and amplitude of 0.32 °C. The results are shown in Fig. 2.

FIG. 2.

Reversing C_p, nonreversing heat flow and, modulated heat flow obtained with heating rate of 2 °C/min, period of 60 s, and amplitude of 0.32 °C.

A perfect separation of the glass transition and the enthalpy relaxation can be observed in Fig. 2. The glass transition is visible as a step change on the reversing heat capacity (C_{p rev}) signal while the enthalpy relaxation appears on the nonreversing heat-flow curve. Nevertheless, the C_{p rev} curve shows unexpectedly peaks at the cold crystallization that should not be taken as a realistic expression of the material heat capacity. Looking at the modulated heat-flow curve, one can realize that there is not enough number of cycles along the transition (minimum is four) to perform a good separation according to the TMDSC method. Thus, the number of cycles is increased by lowering the heating rate to 0.5 °C, keeping the same period of 120 s and an amplitude of 0.16 °C. The heat only conditions are also satisfied.

It can be observed in Fig. 3 how, with these new experimental conditions, the change of heat capacity is tracked along the cold crystallization process. A decrease of C_{p rev} is observed along the crystallization, which is related to a decrease of molecular movement. Then, after the cold crystallization, an increase of C_{p rev} is observed. This increase seems to be accelerated in the range above 100 °C suggesting the beginning of the forthcoming melting process. A new experiment was performed to investigate the melting process. In this case, the range under study was increased up to 190 °C, and heating rate and period conditions were chosen in accordance to other reports: heating rate of 2 °C/min and period of 60 s. An amplitude of 0.32 °C was chosen to meet the heat only requirements. The results are shown in Fig. 4. The two classical melting peaks of this material can be observed on the reversing heat-flow curve.Reference Yasuniwa, Tsubakihara, Ohoshita and Tokudome^10–Reference Gunaratne and Shanks¹⁵ The nonreversing heat-flow curve shows two exotherms with a bigger endotherm in the middle, as reported in other works.Reference Orozco, Brostow, Chonkaew and López¹⁶ This is an unexpected result and deserves further analysis. Crystallization is a kinetic process with characteristic time higher than tenths of seconds. Conceptually, since the observation time used here is only 60 s, crystallization should be π/2 degrees out of phase with respect to the heating rate. Thus, crystallization should appear as exotherm, but not as endotherm, on the nonreversing curve. On the other hand, the characteristic time of melting is usually much lower and may be about tenths of seconds. With observation time of 60 s, a part of the melting is observed on the reversing signal and the other part on the nonreversing one. This is what happens in this case and in other cases where the period was not specified.Reference Orozco, Brostow, Chonkaew and López¹⁶ If we want to send all the melting to the reversing signal, the observation time has to be increased. Thus, the period was increased to 120 s. The heating rate was lowered to 1 °C/min to have a sufficient number of cycles along the transition. An amplitude of 0.32 °C was kept since it allows for heat only conditions. Figure 5 shows the results obtained with these new conditions. The double melting peak is observed on the reversing heat-flow curve. But now the nonreversing signal shows only two endotherms, whose peaks appear approximately at the same temperature than the corresponding ones on the reversing signal.

FIG. 3.

Reversing C_p, nonreversing heat flow, and modulated heat flow obtained with heating rate of 0.5 °C/min, period of 120 s, and amplitude of 0.16 °C.

FIG. 4.

Reversing heat flow and nonreversing heat flow obtained with a 2 °C/min heating rate, a period of 60 s and, an amplitude of 0.32 °C.

FIG. 5.

Reversing heat flow and nonreversing heat flow obtained with a 1 °C/min heating rate, a period of 120 s, and an amplitude of 0.32 °C.

Two theories were proposed for the double melting peak: the lamellar thickness modelReference Cebe and Hong^17, Reference Bassett, Olley and Raheil¹⁸ and the melting–recrystallization model.Reference Lee, Porter and Lin^19, Reference Jonas, Russell and Yoon²⁰ The double lamellar thickness model considers that the double endothermic behavior is due to the existence of two kinds of crystal lamellae with different thicknesses. So, the melting of the thinner lamellae would be related to the lower temperature endotherm, and the melting of the thicker lamellae to the higher temperature endotherm. On the other side, the melting–recrystallization model proposes that the lower temperature endotherm is produced by the melting of the lamellae initially present. The partially melted amorphous material would recrystallize into a more perfect lamellae, which would melt at higher temperatures. Nevertheless, in view of Fig. 5, obtained under suitable modulation conditions, a different explanation can be given. The existence of two exotherms at practically the same temperatures than the endotherms is an indication of two simultaneous melting–crystallization processes. As the cold crystallized material melts, the molecules arrange in more perfect lamellae, which again melt and recrystallize in an even more perfect lamellae. This model implies the existence of three crystalline forms: the one corresponding to the cold crystallization and the two corresponding to the nonreversing exotherms. The melting of those three crystalline structures is reflected in only two strongly overlapping peaks as their melting processes are strongly overlapped. To estimate the heat involved in each of the overlapping melting and crystallization peaks, a convolution method based on a previous work was applied.Reference Artiaga, Lopez-Beceiro, Tarrio-Saavedra, Gracia-Fernandez, Naya and Mier^21, Reference López-Beceiro, Gracia-Fernández, Gómez-Barreiro, Castro-García, Sánchez-Andújar and Artiaga²² Accordingly, each peak is assumed as a time derivative of a generalized logistic function, and the baseline changes proportionally to the conversion at each point. The estimated peaks are shown in Fig. 5. Table I shows the measured and estimated enthalpy values of the observed crystallization and melting processes.

TABLE I.

Measured and estimated enthalpy values (in J/g) of the observed crystallization and melting processes

It can be observed that the total heat of melting is higher than the sum of all the observed heats of crystallization. The difference is about 11.8% with respect to the total melting area. This means that the sample developed an important degree of crystallization during the 40 °C/min cooling ramp, which preceded the measuring heating ramp. In view of these results, it is not possible to establish a relation between the amounts of sample involved in each of the single processes. Nevertheless, considering the peak areas, it is clear that the first melting peak represents a different fraction of the sample than the one involved in the first overlapping crystallization process and that the second endotherm corresponds to most of the crystalline structures, including those formed in both overlapping exotherms.