In-Situ Isothermal Crystallization of Poly(l-lactide)

The isothermal crystallization of poly(l-lactide) (PLLA) has been investigated by in-situ wide angle X-ray diffraction (WAXD) and polarized optical microscopes (POM) equipped with a hot-stage accessory. Results showed that the spherulites of PLLA were formed at high temperature, whereas irregular morphology was observed under a low temperature. This can be attributed to the varying rates of crystallization of PLLA at different temperatures. At low temperatures, the nucleation rate is fast and hence the chains diffuse very slow, resulting in the formation of imperfect crystals. On the other hand, at high temperatures, the nucleation rate is slow and the chains diffuse fast, leading to the formation of perfect crystals. The change in the value of the Avrami exponent with temperature further verifies the varying trend in the morphological feature of the crystals.


Introduction
Poly(L-lactide) (PLLA) is widely used in almost every aspect of modern technologies, including food packaging [1,2], agriculture, biomedicine, etc., [3] owing to its biodegradability and compostability resulting from the readily hydrolyzable ester bonds. Typically, PLLA is a semi-crystalline polymer, and consists of both amorphous regions and crystalline domains. Generally, upon degradation, the chains in the amorphous region start to degrade initially, followed by those in crystalline part [4][5][6]. Therefore, the degradation behavior of PLLA is closely dependent on the morphology and structure of the polymer matrix, which is in turn determined by the crystallization process leading to the formation of the material [7,8]. To gain better control of the crystalline structure and morphology closely related to the nucleation and growth process of PLLA. Therefore, it is highly desirable to understand the crystallization history of the material under isothermal conditions, as this influences the nucleation and growth of the morphological features of ordered regions of the base substance.
Isothermal crystallization behavior of PLLA has been broadly investigated and reported over the past 20 years [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Typically, PLLA can form different crystal structures through different processing routes. For example, an ordered α-phase is produced at high crystallization temperatures [14], while a conformationally disordered α'-phase is developed at low temperatures under Quiescent melt, or cold crystallization conditions [23]. Although these two structures have different melting temperatures, they have essentially the same crystal structure with a very minor difference in chain conformation and packing density. Other crystal structures such as β-crystals and γ-crystals can also be developed, both under the mechanical stretching [12] or solution-spinning [24], and by epitaxial crystallization in hexamethylbenzene [25]. Additionally, the crystallization kinetics of PLLA have also been explored. It is recognized that the growth rate of PLLA crystals decreases as its molecular weight increases [26,27]. Moreover, the regime transition was observed Recently, the same equilibrium melting temperature of both α-phase and α'-phase has been confirmed through nonlinear extrapolative methods [7], further verifying their identity in crystal structure. Even though some degree of insight into nucleation and growth of PLLA is already established, further studies are definitely warranted in this research area.
In this article, we systematically studied the morphology, structure and isothermal crystallization kinetics of PLLA through in-situ wide angle X-ray diffraction (WAXD) and polarized optical microscope (POM) with a CSS450 hot stage. The nucleation and growth processes were analyzed according to the Avrami theory. Furthermore, the nucleation and growth rates of PLLA can be fine-tuned by adjusting the isothermal crystallization temperature.

Materials and Sample Preparation
Poly(L-lactide) with an average molecular weight (Mw) of 150,000 g/mol supplied by Nature Works LLC, NE, USA, was used as received. Methylene chloride was obtained from Huamei Co., Nanchang, China. The solution casting method was used to fabricate the PLLA films. The pellets of PLLA were first dissolved into methylene chloride to prepare 10 wt.% solution. The solution was then casted onto a glass plate, and then kept at room temperature for 24 h until the solvent was completely evaporated. The PLLA films thus obtained were further dried in vacuum at ca. 50 °C overnight for crystalline morphological observation.
The thickness and elements analysis of films measured by scanning electronic microscope (SEM, HitachiHigh-Technologies Corporation, Tokyo, Japan) are shown in Figure  1. The film shows about 155 um thickness (Figure 1a), and contains a small amounts of the metals such as Cr, Ni and Pt et al. (Figure 1b). The atomic contents of elements are described in Table 1.

DSC and TGA Analysis
The cooling and heating run of PLLA was carried out in a nitrogen atmosphere by using a TA Q100 DSC instrument. The curves were obtained when the samples (ca. 7 mg) were heated to 200 • C at 10 • C/min, held at that temperature for 3 min to ensure complete melting of the polymer, cooled at a rate of 10 • C/min to the 40 • C, and then heated at a rate of 10 • C/min to the melting temperature for further thermal analysis. The TGA analysis of PLLA was performed under a nitrogen atmosphere through a NETZSCH STA 449F5 instrument with a heating rate of 10 • C/min.

In-Situ Isothermal XRD Measurements
The in-situ isothermal crystallization of PLLA was carried out in a nitrogen atmosphere by using a D8 ADVANCE X-ray diffractometer (Bruker Inc., Germany) with Cu Kα radiation. The isothermal crystallization was performed as follows: the samples were heated to 200 • C, held at that temperature for 3 min to ensure complete melting of the polymer, and then cooled at a rate of 30 • C/min to the 100, 110 and 120 • C, respectively, for inducing isothermal crystallization. During the isothermal crystallization, the samples were scattered by XRD at intervals of 1 or 2 min. The data acquisition time was 30 s for each scattering pattern. The X-ray source was set at a voltage of 40 kV. The scattered intensities were registered in the range of scattering angles 2θ from 10 • to 40 • .
The intensity was plotted as a function of the scattering angle, 2θ, then through deconvoluting the peaks of linear WAXD profiles, the fraction of material crystallized after a certain period of time was calculated by where A cryst and A amorph are the fitted areas of crystal and amorphous, respectively. By plotting log [−ln (1 − X(t))] against log t, the crystallization half-time, t 1/2 , defined as the time taken for half of the crystallinity to develop, was obtained [28].

In Situ Observation of PLLA Crystalline Morphology
The crystalline morphologies of PLLA isothermally crystallized from melt were observed in situ by a polarized optical microscope (POM) equipped with a CSS450 hot-stage accessory. The films of the samples were heated from 20 • C to 200 • C at 20 • C/min, and kept at that temperature for 3 min to allow the completion of the melt, then cooled down to the crystallization temperature at 80 • C/min for inducing isothermal crystallization.
The diameter of the spherulites was recorded as a function of the crystallization time using a calibrated video caliper. The increase of spherulite radius is linearly dependent on the crystallization time until impingement. Under isothermal conditions, the spherulitic growth rate is calculated from the slope of the spherulite diameter vs. time plot. Figure 2a represents the typical cooling and heating DSC curves of PLLA with a cooling/heating rate of 10 • C/min, respectively. The Tg is about 61.7 • C, the crystallization temperature is about 115 • C and its melting temperature is about 164.5 • C. The TGA and DTG of PLLA samples are shown in Figure 2b. It can be observed that the PLLA starts to degrade at 365 • C, which shows that the PLLA is stable at 200 • C.

Crystalline Morphologies of PLLA
With a view to getting a fundamental understanding regarding the type of nucleation and morphology of PLLA, the in situ growing process of spherulite was followed by using POM with a hot stage provision. In Figure 3, the optical microscope photographs of PLLA isothermally crystallized at 100 °C are presented. During the initial stages, PLLA starts to nucleate, and the resulting structures are too small to be observed. As the time elapses, the nuclei grow to form the small spherulites that can be observed under POM ( Figure  3b). The small spherulites first formed will further grow in a three-dimensional way, as the melted phase provides enough space for their proliferation. However, as time progresses, the spherulites will start to impinge on each other, thus leaving only a relatively small space for the newly formed nuclei to grow. Therefore, they can only grow in only one-and/or two-dimensional way in the available space. Although the Maltese cross of some spherulites can be observed, most crystals exhibit irregular shapes at the end of crystallization. According to the regime transition theory, at low crystallization temperature the nucleation rate is very fast, while the chains diffuse slowly, resulting in the formation of imperfect crystals.

Crystalline Morphologies of PLLA
With a view to getting a fundamental understanding regarding the type of nucleation and morphology of PLLA, the in situ growing process of spherulite was followed by using POM with a hot stage provision. In Figure 3, the optical microscope photographs of PLLA isothermally crystallized at 100 • C are presented. During the initial stages, PLLA starts to nucleate, and the resulting structures are too small to be observed. As the time elapses, the nuclei grow to form the small spherulites that can be observed under POM (Figure 3b). The small spherulites first formed will further grow in a three-dimensional way, as the melted phase provides enough space for their proliferation. However, as time progresses, the spherulites will start to impinge on each other, thus leaving only a relatively small space for the newly formed nuclei to grow. Therefore, they can only grow in only one-and/or two-dimensional way in the available space. Although the Maltese cross of some spherulites can be observed, most crystals exhibit irregular shapes at the end of crystallization. According to the regime transition theory, at low crystallization temperature the nucleation rate is very fast, while the chains diffuse slowly, resulting in the formation of imperfect crystals.

Crystalline Morphologies of PLLA
With a view to getting a fundamental understanding regarding the type of nucleation and morphology of PLLA, the in situ growing process of spherulite was followed by using POM with a hot stage provision. In Figure 3, the optical microscope photographs of PLLA isothermally crystallized at 100 °C are presented. During the initial stages, PLLA starts to nucleate, and the resulting structures are too small to be observed. As the time elapses, the nuclei grow to form the small spherulites that can be observed under POM ( Figure  3b). The small spherulites first formed will further grow in a three-dimensional way, as the melted phase provides enough space for their proliferation. However, as time progresses, the spherulites will start to impinge on each other, thus leaving only a relatively small space for the newly formed nuclei to grow. Therefore, they can only grow in only one-and/or two-dimensional way in the available space. Although the Maltese cross of some spherulites can be observed, most crystals exhibit irregular shapes at the end of crystallization. According to the regime transition theory, at low crystallization temperature the nucleation rate is very fast, while the chains diffuse slowly, resulting in the formation of imperfect crystals.   Figure 4 represents the POM of PLLA crystallized isothermally at 120 • C for different periods. Typically, the crystalline morphologies of PLLA are spherulites; the Maltese cross can be observed clearly. As the time increases, the diameter of spherulites increases. Compared to the sample crystallized at 100 • C, the number of nuclei is greatly reduced. This result is due to the fact that the chains diffuse very fast, while the nucleation rate is very slow when crystallization takes place at a higher temperature [29][30][31].
R PEER REVIEW 5 of 11 Figure 4 represents the POM of PLLA crystallized isothermally at 120 °C for different periods. Typically, the crystalline morphologies of PLLA are spherulites; the Maltese cross can be observed clearly. As the time increases, the diameter of spherulites increases. Compared to the sample crystallized at 100 °C, the number of nuclei is greatly reduced. This result is due to the fact that the chains diffuse very fast, while the nucleation rate is very slow when crystallization takes place at a higher temperature [29][30][31].

Crystal Structure of PLLA
The X-ray diffraction patterns of PLLA samples crystallized at 100 °C and 120 °C are shown in Figure 5. All the diffraction patterns are normalized using the strongest

Isothermal Crystallization Kinetics of PLLA
The isothermal crystallization kinetics of PLLA was an rami equation [32][33][34] 1 − ( ) = − where X(t) is the volume fraction of crystals at time, t; K is th the temperature dependent terms, and also contains informa nucleation rates; n is the Avrami exponent which depends o occur during nucleation and growth.
However, Lorenzo et al. [35] suggested that direct use encountered many practical problems due to that there exists or the induction time, t0, for the beginning of the crystalliza the absolute time, t. Therefore, they believed that time coun to t0, and a minor modification has to be introduced into the A taking into consideration the experimental induction time t0 then rewritten as:

Isothermal Crystallization Kinetics of PLLA
The isothermal crystallization kinetics of PLLA was analyzed according to the Avrami equation [32][33][34] 1 − X(t) = e −Kt n where X(t) is the volume fraction of crystals at time, t; K is the rate constant that includes the temperature dependent terms, and also contains information regarding diffusion and nucleation rates; n is the Avrami exponent which depends on the types of processes that occur during nucleation and growth. However, Lorenzo et al. [35] suggested that direct use of Equation (2) would have encountered many practical problems due to that there exists an initial crystallization time or the induction time, t 0 , for the beginning of the crystallization, which is different from the absolute time, t. Therefore, they believed that time count must start from time equal to t 0 , and a minor modification has to be introduced into the Avrami classical equation, by taking into consideration the experimental induction time t 0 . Hence, Equation (2) can be then rewritten as: By taking the logarithm of Equation (3), twice, one can then obtain the isothermal crystallization parameters: Subsequently, the double logarithm of amorphous fraction can be plotted against the logarithm of time. Furthermore, the term X (t − t 0 ) can be calculated according to Equation (2) by determining the area under the crystallization isotherm, at each instant, and taking the ratio of the areas at each time interval to the total area. The rate constant, K, can be obtained from the intercepts, and n from the slope of the line. Figure 4a-c represents the typical WAXD patterns with crystallization time for PLLA isothermally crystallized at 100, 110 and 120 • C, respectively. It can be observed from Figure 4a-c that only the amorphous peak occurs at the beginning of crystallization time for all samples, and with increasing time, the crystallization peaks can be observed, and the intensity of crystal peaks increases for all the PLLA samples.
Based on Equation (1), the calculated crystallinity of PLLA with crystallization time is shown in Figure 6d-f. As can be seen, the crystallinity of PLLA increases with crystallization time and keeps constant at the end of the crystallization. For example, the crystallinity (Figure 6d) of PLLA crystallized at 100 • C for 12 min (Figure 6a) is about 0.42 (± 5%) and invariant as the time increases, indicating that the crystallization process is almost finished. By normalizing the crystallinity with crystallization time, the relative crystallinity, X(t − t 0 ), can be obtained as a function of time, as shown in Figure 7a. It can be also observed that the time required for complete crystallization of PLLA has the identical trend in variation with the crystallization temperature. Figure 7b shows a plot of ln [−ln (1 − X(t − t 0 ))] versus ln(t − t 0 ) for PLLA isothermally crystallized at different temperatures. The graph was obtained by using the Equation (4). As can be seen from Figure 5, the experimental data of PLLA appear to fit the Avrami equation perfectly, since the Avrami plot is expected to be throughout the entire time period for isothermal crystallization. From Figure 7b, the crystallization parameters from the Avrami equation, such as Avrami exponent n, crystallization half time t 1/2 , and crystallization rate constant K for PLLA are obtained (see in Table 2). It is to be noted here that the value of Avrami exponent n decreases from 2.8 to 2.5, as the isothermal crystallization temperature increased from 100 • C to 120 • C. On the basis of this result, it can be clearly inferred that PLLA exhibited homogeneous nucleation, and the crystal growth in a three-dimensional mode when crystallization was carried out at 100 • C. As the crystallization temperature increases, the motion of chains is bound to increase, thereby resulting in a faster growth for the spherulites. After the spherulites grow to a point where they start to impinge on each other, the newly formed crystal nuclei can only grow in a one-and/or two-dimensional way because of space limitation; this results in a decreased value of the Avrami exponent. Based on Equation (1), the calculated crystallinity of PLLA with crystallization time is shown in Figure 6d-f. As can be seen, the crystallinity of PLLA increases with crystallization time and keeps constant at the end of the crystallization. For example, the crystallinity (Figure 6d) of PLLA crystallized at 100 °C for 12 min (Figure 6a) is about 0.42 (± 5%) and invariant as the time increases, indicating that the crystallization process is almost finished. By normalizing the crystallinity with crystallization time, the relative crystallinity, X(t-t0), can be obtained as a function of time, as shown in Figure 7a. It can be also observed that the time required for complete crystallization of PLLA has the identical trend in variation with the crystallization temperature. Figure 7b shows a plot of ln [-ln (1 -X(t -t0))] versus ln(t -t0) for PLLA isothermally crystallized at different temperatures. The graph was obtained by using the Equation (4). As can be seen from Figure 5b, the experimental data of PLLA appear to fit the Avrami equation perfectly, since the Avrami plot is expected to be throughout the entire time period for isothermal crystallization. From Figure 7b, the crystallization parameters from the Avrami equation, such as Avrami exponent n, crystallization half time t1/2, and crystallization rate constant K for PLLA are obtained (see in Table 1). It is to be noted here that the value of Avrami exponent n decreases from 2.8 to 2.5, as the isothermal crystallization temperature increased from 100 °C to 120 °C. On the basis of this result, it can be clearly inferred that PLLA exhibited homogeneous nucleation, and the crystal growth in a three-dimensional mode when crystallization was carried out at 100 °C. As the crystallization temperature increases, the motion of chains is bound to increase, thereby resulting in a faster growth for the spherulites. After the spherulites grow to a point where they start to impinge on each other, the newly formed crystal nuclei can only grow in a one-and/or two-dimensional way because of space limitation; this results in a decreased value of the Avrami exponent.   It can also be found that the bulk crystallization rate of PLLA, characterized by crys tallization half time, t1/2, decreased from 1133 s to 407 s as the crystallization temperatur was decreased from 120 °C to 100 °C, thus indicating a faster crystallization rate for PLLA when crystallized at a lower temperature. The slow crystallization rate at higher temper ature shows that the crystallization rate is essentially dependent on the nucleation an growth process. At higher temperatures, the growth rate is faster while the nucleatio rate, as determined by the nucleation-free energy, is very slow, resulting in a slower rat of crystallization.

Growth Rate Parameters of Isothermally Crystallized PLLA
The spherulite growth rates (G) for PLLA obtained at the temperatures between 10 °C and 150 °C are shown in Figure 6, which have been used to examined in terms of sec ondary nucleation theory [36]. The general expression for the growth rate of a linear po ymer crystal with folded chains is given by  It can also be found that the bulk crystallization rate of PLLA, characterized by crystallization half time, t 1/2 , decreased from 1133 s to 407 s as the crystallization temperature was decreased from 120 • C to 100 • C, thus indicating a faster crystallization rate for PLLA when crystallized at a lower temperature. The slow crystallization rate at higher temperature shows that the crystallization rate is essentially dependent on the nucleation and growth process. At higher temperatures, the growth rate is faster while the nucleation rate, as determined by the nucleation-free energy, is very slow, resulting in a slower rate of crystallization.

Growth Rate Parameters of Isothermally Crystallized PLLA
The spherulite growth rates (G) for PLLA obtained at the temperatures between 100 • C and 150 • C are shown in Figure 6, which have been used to examined in terms of secondary Polymers 2021, 13, 3377 9 of 11 nucleation theory [36]. The general expression for the growth rate of a linear polymer crystal with folded chains is given by where K g is the nucleation constant; ∆T is the supercooling difined by T 0 m − T c , T 0 m is the equilibrium melting point, here the value of T 0 m = 469.6 K is used according to our previous paper [7]; f is a factor given as 2T c /(T 0 m + T c ). U* = 1500 cal·mol −1 represents the activation energy for segment diffusion to the site of crystallization; R is the gas constant; T ∞ = T g − 50 K is the Vogel-Fulcher-Tamman-Hesse (VFTH) parameters describing the transport of polymer segments across the liquid or crystal interface; and G 0 is the front factor.
As shown in Figure 8b, by taking the logarithm of Equation (4), the lnG + U*/R(T c − T ∞ ) changes linearly with 1/T c ∆Tf, which we can obtain the values of K g and lnG 0 from the slope and intercept, respectively. To obtain the sufficient direct information on the growth front of PLLA spherulites, we calculated the surface free energies σσ e by further analyzing the nucleation constant K g .  (6) where the variable reflects the regime behavior and = 4 for regimes I and III, and 2 for regime II. b is the layer thickness; σ is the lateral surface free energy; σe is the fold surface free energy; Δhf is the heat of fusion per unit volume; and kB Boltzmann's constant.
Here, the value of = 2 was used due to the explored Tc ranging in the regime II, Δhf = 174 ×10 6 J·m −3 was used and the value of the layer thickness should be taken as 0.53 nm for PLLA crystals based on the previous report [37,38].
The value of σσe estimated is about 745 × 10 6 J 2 ·m −4 , similar to the results reported by Vasanthakumari and Pennings [39]. We then estimated the fold surface free energy, σe could to be 61.9 × 10 3 J·m −3 , by using the value of the lateral surface free energy, σ =12.03 × 10 3 J·m −3 , obtained by Vasanthakumari and Pennings [39]. Although Vasanthakumari and Pennings calculated the σe with low molecular weight, the similar value of σe shows that fold surface at growth front for PLLA is independent on the molecular weight, which is verified by Pan et al. [40] who suggested that chains folding processing was dependent on the Tc, regardless of the molecular weight.

Conclusions
Through the present work, the morphology, structure and isothermal crystallization The nucleation parameter K g is given as where the variable y reflects the regime behavior and y = 4 for regimes I and III, and 2 for regime II. b is the layer thickness; σ is the lateral surface free energy; σ e is the fold surface free energy; ∆h f is the heat of fusion per unit volume; and k B Boltzmann's constant. Here, the value of y = 2 was used due to the explored T c ranging in the regime II, ∆h f = 174 × 10 6 J·m −3 was used and the value of the layer thickness should be taken as 0.53 nm for PLLA crystals based on the previous report [37,38]. The value of σσ e estimated is about 745 × 10 6 J 2 ·m −4 , similar to the results reported by Vasanthakumari and Pennings [39]. We then estimated the fold surface free energy, σ e could to be 61.9 × 10 3 J·m −3 , by using the value of the lateral surface free energy, σ = 12.03 × 10 3 J·m −3 , obtained by Vasanthakumari and Pennings [39]. Although Vasanthakumari and Pennings calculated the σ e with low molecular weight, the similar value of σ e shows that fold surface at growth front for PLLA is independent on the molecular weight, which is verified by Pan et al. [40] who suggested that chains folding processing was dependent on the T c , regardless of the molecular weight.

Conclusions
Through the present work, the morphology, structure and isothermal crystallization kinetics of PLLA were explored at different crystallization temperatures through a combination of analytical techniques (POM and WAXD). It was found that, during the isothermal crystallization, the mechanism of crystallization of PLLA changes with temperature and mixed growth mechanism (two dimensional and three-dimensional growth of crystals) was present, resulting in the decrease of Avrami exponent n. At low or high temperatures, the crystallization rate is observed to be slower, apparently stemming from to the slow growth rate, or nucleation rate. Therefore, this work opens up potential avenues for the design of degradable PLLA products, with tunable physical attributes, for future medical and other environmentally friendly applications.