Introduction

Currently, biodegradable polymer has an important role for better life. Many studies have been studied how to improve their applications by improving the properties of the polymer to achieve the specific property requirement. Poly(lactic acid), PLA, is a polymer which received much commercial attention because of its biodegradability, good biocompatibility, and high strength [1,2,3]. In particular, it produces from renewable raw materials. Nevertheless, with some disadvantages which are brittleness and low crystallization rate, so it cannot be used in some applications. To solve this problem, the blending PLA with other polymers is one of the most used methods because it can control the properties of the blends by adjusting their compositions to get the desired properties. Examples of these polymers are polycaprolactone, PCL [4, 5], poly(butylene adipate-co-terephthalate), PBAT [6] and poly(butylene succinate-co-adipate), PBSA [7].

Among these, polymer that has been one of the most attention and interest to be studied in this research for improving the properties of PLA is poly(butylene succinate), PBS. PBS has high flexibility and a high crystallization rate which allows high-speed industrial process. Hassan et al. [8] studied the blends of PLA and PBS with various compositions. The result showed that thermal stability of the blends was higher than that of pure PLA. The tensile strength and modulus of the blends decreased with the increasing of PBS content. Addition of PBS in PLA decreased the brittleness and elongation properties of the blends. It is clear that the addition of PBS up to 20% by mass in the blend was appropriate to be used as fibers and the 60% by mass of PBS in the blends would be suitable for packaging applications. Bhatia et al. [9] studied the PLA/PBS blends, and it was a miscible blend at up to 80/20 by mass composition.

Generally, improving the crystallization rate and morphology of polymer can be achieved by adding nucleating agents. In this study, Talc has chosen for use as nucleating agent. There have been reported that it has ability to be an efficacious nucleating agent. Li and Huneault [10] studied the effect of heterogeneous nucleation on PLA by adding 1% by mass of talc, 1% by mass of calcium lactate and 0.5% by mass of sodium stearate as nucleating agents and 5 and 10% by mass of PEG as plasticizers. The isothermal data showed that talc is highly effective in nucleating the PLA in the temperature range of 80–120 °C. The non-isothermal data showed that the combination of nucleating agent and plasticizer is necessary to develop significant crystallinity at high cooling rate. Moreover, Battegazzore et al. [11] studied thermal properties of PLA with talc and the result showed that PLA did not crystallize unless adding talc as nucleating agent. They were found that talc can decrease the crystallization temperature about 23 °C and the amount of crystallinity increased higher than that of pure PLA after cooling. The amount of crystalline phase increased from 2.7 to 9.1% as increasing of talc content from 1 to 15% by mass. Kinetics of crystallization process was described by using Avrami equation. The result showed that micro-composite of PLA/talc had two-dimensional of growth kinetics as epitaxial growth. Mechanical property results showed that addition 5% by mass of talc increased modulus which was a result of the reinforcement of talc. However, the amount of talc which less than 5% by mass did not affect the modulus.

Theoretical modeling of isothermal crystallization kinetics

Isothermal crystallization kinetics based on the Avrami model [12,13,14,15]

A theoretical model of Avrami was used to describe the kinetics of crystallization for the substance under the conditions of constant temperature from the assumption that the number of nucleation nuclei is formed randomly on the area and the expansion or the growth of the nucleus, with a radius equal nucleus. The Avrami equation that used to describe the isothermal crystallization process in polymers is shown as following Eq. (1):

$$\alpha \left( t \right) = \left[ {1 - \exp \left( { - K_{\text{A}} t^{{{\text n}_{\text{A}} }} } \right)} \right]$$
(1)

where α(t) is the fraction of the crystallized material at time t, KA is the Avrami crystallization rate and nA is the Avrami constant. In general, the Avrami equation is often converted into the traditional linear form as following Eq. (2):

$$\ln \left[ { - \ln \left( {1 - \alpha \left( t \right)} \right)} \right] = \ln (K_{\text{A}} ) + n_{\text{A}} \ln \left( t \right)$$
(2)

The higher value of KA means faster crystallization and the lower one takes longer time to crystallize. The nA value depends on the growth dimension and type of nucleation. The nA and KA values are obtained from the slope and interception on the y-axis of the graph from the relationship between ln[− ln(1 − α(t))] versus ln(t).

The half-time of crystallization, t1/2, is obtained from following Eq. (3)

$$t_{{\frac{1}{2}}} = \left( {\ln \left( 2 \right)/K_{\text{A}} } \right)^ \frac {1} {\text{n}}$$
(3)

Typically, t1/2 is often used to characterize the rate of crystallization directly. Moreover, the growth rate of the crystal (G) can be explained by the inverse of t1/2 as following Eq. (4):

$$G = 1/t_{{\frac{1}{2}}}$$
(4)

Isothermal crystallization kinetics based on the Tobin model [15, 16]

Tobin’s theory is a model that shows the development model of the Avrami equation. Tobin’s equation is shown as follows (5):

$$\alpha \left( t \right) = \left( {K_{\text{T}} t} \right)^{{{\text n}_{\text{T }} }} /1 + \left( {K_{\text{T}} t} \right)^{{{\text n}_{\text{T}} }}$$
(5)

where α(t) is the fraction of crystallized material at time t, KT is Tobin crystallization rate which independent on size of crystalline and Tobin constant (nT). In addition, nT is controlled directly by the different types of nuclei and growth mechanisms. The Tobin equation is generally often converted into the traditional linear form as following Eq. (6):

$$\log \left( {\alpha_{\text{t}} /\left( {1 - \alpha_{\text{t}} } \right)} \right) = \log (K_{\text{T}} ) + n_{\text{T}} \log (t)$$
(6)

The nT and KT values are obtained from the slope and interception on the y-axis of the graph from the relationship between log(αt/(1 − αt)) versus log(t).

Theoretical modeling of non-isothermal crystallization kinetics

The Avrami equation is the most widely used to describe isothermal crystallization kinetics. However, it is not appropriate for non-isothermal crystallization in which the temperature constant changes and the complexity of non-isothermal crystallization such as nucleation and temperature-crystal growth dependent [12]. Then, the Avrami equation is improved to be explaining with non-isothermal crystallization.

For non-isothermal crystallization, time of crystallization can be calculated as following Eq. (7):

$$t = \left( {T_{\text{o}} - T} \right)/\varphi$$
(7)

where t is time of crystallization, To is the initiate temperature of crystallization and T is the temperature at time t and φ is cooling rate (°C min−1).

Non-isothermal crystallization kinetics based on the Jeziorny model [12, 13, 17,18,19]

Jeziorny explains non-isothermal crystallization by modification the theoretical models of Avrami. Jeziorny suggested that the Jeziorny constant, Zt (as same value as KA from the Avrami equation, which indicates the rate of crystallization of Avrami), is influenced by the cooling rate (φ). So, the crystallization rate constant (Zc) in non-isothermal crystallization can be validated by having the cooling rate term as shown in following Eq. (8):

$$\ln (Z_{\text{c}} ) = \ln (Z_{\text{t}} )/\varphi$$
(8)

Non-isothermal crystallization kinetics based on the Ozawa model [12, 13, 19, 20]

A theoretical model of Ozawa was used to describe the non-isothermal crystallization kinetics by developing the theoretical models of Avrami from the assumption that the non-isothermal crystallization process is a small step of isothermal crystallization. The fractional crystallinity (α) at time t is shown in following Eq. (9):

$$\alpha \left( t \right) = [1 - \exp \left( { - K_{\text{o}}^{\text{m}} /\varphi } \right)]$$
(9)

where Ko is Ozawa crystallization rate which depends on temperature, φ is cooling rate, and m is Ozawa constant. In general, this equation is often converted to the traditional linear form as following Eq. (10):

$$\ln \left[ { - \ln \left( {1 - \alpha \left( t \right)} \right)} \right] = \ln (K_{\text{o}} ) - m\ln \left( \varphi \right)$$
(10)

where m and Ko values are obtained from the slope and interception on the y-axis of the graph from the relationship between ln[−ln(1 − α(t))] versus ln(φ), respectively.

Experimental

Materials

Poly(lactic acid) (PLA), trade name is IngeoIM Biopolymer 2003D (NatureWorks, Purac, Netherlands) with a number-average molecular mass of 61,000 as determined by dilute-solution viscosity measurements in chloroform at 25 °C. The PLA pellets were translucent and semi-crystalline with glass transition temperature (Tg) of 61 °C and melting temperature (Tm) of 156 °C. Poly(butylene succinate) (PBS), trade name is GS Pla® FZ91PD (Mitsubishi Chemical Corporation, China). The PBS pellets were milky white color with a number-average molecular mass of 30,000 and Tg of − 30 °C and Tm of 110 °C. As a nucleating agent, talc (Talcum powder) was obtained from Sigma-Aldrich with a molecular mass of 379.27 g mol−1.

Preparation of PLA/PBS blends with talc by melt blending

PLA and PBS powders were prepared by using grinder and dried in a vacuum oven for 24 h at 70 °C, prior to use. Then, PLA and PBS were weighed in glass container in ratio of 90/10 by mass and mixed with talc 0.1% of polymer mass. The mixtures were heated at a temperature of 180 ± 5 °C and stirred using high-torque mechanical stirrer with a speed of 40 rpm, under nitrogen gas atmosphere, for 20 min in nitrogen atmosphere until the blend was melted homogeneously. The blend was then taken from the glass container, cut it into small pieces and keep in desiccator before further use.

Characterization

Isothermal crystallization kinetics

Differential scanning calorimetry (DSC, Perkin-Elmer Pyris 7) was used as a tool to observe the isothermal crystallization characteristics. A sample (10 ± 1 mg) was put into an aluminum pan and hermetically sealed. The samples were then heated from 20 to 200 °C at a heating rate of 20 °C min−1 and maintained at this temperature for 2 min to remove the thermal history. Subsequently, the sample was quenched to 20 °C at a cooling rate of 10 °C min−1, reheated to 200 °C at a heating rate of 10 °C min−1, and hold for 2 min. For the kinetic study, the sample was quenched to desired crystallization temperatures; 70, 80, 90, 100, 110 and 120 °C. They were held at each isothermal temperature to allow the complete crystallization. Moreover, the melting behavior of the isothermally crystallized samples was observed by reheating to 200 °C at a rate of 10 °C min−1 in a nitrogen atmosphere.

Non-isothermal crystallization kinetics

To observe the non-isothermal crystallization characteristics, a sample (10 ± 1 mg) was put into an aluminum pan and hermetically sealed. The samples were then heated from 20 to 200 °C at a heating rate of 20 °C min−1 and maintained at this temperature for 2 min to remove the thermal history. Subsequently, the samples were quenched to 20 °C at a cooling rate of 5, 10, 20, 40, 60, 80 and 100 °C min−1 and reheated to 200 °C at a rate of 10 °C min−1 in a nitrogen atmosphere.

Results and discussion

Isothermal crystallization behaviors

Figure 1 shows DSC curves of the PLA/PBS blends with 0.1% by mass of talc at isothermal temperatures of 70, 80, 90, 100, 110 and 120 °C. And, Fig. 2 shows DSC melting curves of the PLA/PBS blends with 0.1% by mass of talc after isothermal crystallization at various temperatures. The results show that the different isothermal temperatures gave the different crystallization times and the amounts of crystallinity. There was no exothermic peak at isothermal temperature at 70 and 80 °C. This suggests that no crystalline occurred at these temperatures. It corresponds to their DSC melting curves which the endothermic peaks of the crystallization were observed, implying the crystalline occurred during heating. On the other hand, at the isothermal temperatures of 90, 100, 110 and 120 °C, it can be seen the clear exothermic peak, resulting from the crystallization. From Fig. 1, it indicates that the completion of the crystallization blending process at 100 °C took the shortest time which compared to those of the other isothermal temperatures.

Fig. 1
figure 1

The DSC curves of the PLA/PBS blends with 0.1% by mass of talc at isothermal temperatures of 70 °C, 80 °C, 90 °C, 100 °C, 110 °C, and 120 °C

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Fig. 2
figure 2

The DSC melting curves of the PLA/PBS blends with 0.1% by mass of talc after isothermal crystallization at the various temperatures

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Isothermal crystallization kinetics based on the Avrami model

The integral crystallization curves of the PLA/PBS blends with 0.1% by mass of talc at the various isothermal crystallization temperatures are shown in Fig. 3. The percentage relative of crystallinity increased when the crystallization time was increased. At 100 °C isothermal temperature, the crystallization process occurred earlier and gave the highest crystallization rate. This gave similar result for 110 °C isothermal temperature. Nevertheless, the crystallization process and the crystallization rate decreased at 120 °C isothermal temperature significantly. The Avrami parameters, Avrami exponents (nA), Avrami crystallization rate (KA) and half-time of crystallization (t1/2) were estimated from ln[− ln(1 − α(t))] versus ln(t) plot and are shown in Fig. 4 and Table 1.

Fig. 3
figure 3

The integral crystallization curves (based on the Avrami model) of the PLA/PBS blends with 0.1% by mass of talc at the various isothermal crystallization temperatures

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Fig. 4
figure 4

The plot of ln[− ln(1 − α(t))] versus ln(t) of the PLA/PBS blends with 0.1% by mass of talc at the various isothermal crystallization temperatures (based on the Avrami model)

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Table 1 Avrami’s isothermal crystallization kinetic parameters of PLA/PBS blends with 0.1% by mass of talc
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The nA value is dependent upon the growth dimension and type of nucleation. From Table 1, the average nA value was 2.6 which close to 3 which indicated that spherulitic growth from instantaneous nuclei of heterogeneous nucleation and it occurred from additive. The nA value increased from 2.3 to 2.9 with increasing temperatures is possibly also due to the type of crystal growth from 2 to 3 growth dimension [21]. The higher KA value means faster crystallization process and the highest KA is found to be at 100 °C. The half-time of crystallization (t1/2) showed the minimum value at the same temperature, 100 °C and gave the highest growth rate as in Fig. 5.

Fig. 5
figure 5

The effect of talc on the half-time of crystallization as a function of the isothermal temperature (based on the Avrami model)

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Isothermal crystallization kinetics based on the Tobin model

The Tobin parameters were calculated from the plots of log(αt/(1 − αt)) versus log (t), as shown in Fig. 6. Tobin’s isothermal crystallization kinetic parameters of PLA/PBS blends with 0.1% by mass of talc are shown in Table 2. The nT and KT values were obtained from the slope and interception. The nT value increased from 2.9 to 3.2 with increasing isothermal temperatures. The highest KT is found to be at 100 °C, which is similar as Avrami model. The half-time of crystallization (t1/2) showed the minimum value at 100 and 110 °C and gave the highest growth rate as in Fig. 7. Tobin parameters had the trends as similar as Avrami parameters.

Fig. 6
figure 6

The plot of log(αt/(1 − αt)) versus log(t) of the PLA/PBS blends with 0.1% by mass of talc at the various isothermal crystallization temperatures (based on the Tobin model)

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Table 2 Tobin’s isothermal crystallization kinetic parameters of PLA/PBS blends with 0.1% by mass of talc
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Fig. 7
figure 7

The effect of talc on the half-time of crystallization as a function of the isothermal temperature (based on the Tobin model)

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Non-isothermal crystallization behaviors

From Fig. 8, the results showed that the crystallization peaks of PLA/PBS blends with 0.1% by mass of talc shifted to lower temperature as the cooling rate increased. It was possibly due to the crystallization at the lower cooling rate had enough time to crystallize, and the nucleation and crystal growth crystallized at a higher temperature with narrower range. On the other hand, at higher cooling rate, there was insufficient time for nucleation and crystal growth to crystallize. The crystallization peaks were in the wider range and the amount of crystal decreased. Cooling rate of 40 °C min−1 gave the highest amount of crystallinity and found to be the appropriate cooling rate for this system.

Fig. 8
figure 8

The DSC curves of heat flow as a function of temperature at different cooling rates for the PLA/PBS blends with 0.1% by mass of talc

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Non-isothermal crystallization kinetics based on the Jeziorny model

The result from the relationship between %relative crystallinity and crystallization time is shown in Fig. 9. It can be clearly seen that the higher cooling rate and the shorter time of crystallization had affected the completion of crystallization process. The Avrami plots of ln[− ln(1− Xt)] versus ln(t) are shown in Fig. 10. Avrami and Jeziorny parameters are determined and shown in Table 3.

Fig. 9
figure 9

The integral crystallization curves of the PLA/PBS blends with 0.1% by mass of talc at the various cooling rates

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Fig. 10
figure 10

The plot of ln[− ln(1 − α(t))] versus ln(t) of the PLA/PBS blends with 0.1% by mass of talc at the various cooling rates

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Table 3 Avrami and Jeziorny parameters of PLA/PBS blends with 0.1% by mass of talc at various cooling rates
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As shown in Fig. 10, there are approximately two stages of crystallization. Each curve showed the straight line in the primary stage followed by the nonlinear line in the secondary stage, which was clearly at high cooling rate. Primary nucleation is the characteristic of disorganized nucleation which is expected to be caused by a number of molecules line up next to each other and from new phase. It could imply that there are two types of nucleation. The first one is the homogeneous nucleation; the creation of a nucleus implies the formation of an interface at the boundaries of a new phase at the lower temperature. The second one is heterogeneous nucleation; the nucleation normally occurs at nucleation sites on surfaces contacting the adulterated thing or nucleating agent which was filled in polymer. The secondary nucleation occurs from contacting of the existing crystal and existing crystal or the existing crystal and wall.

In Table 3, there are various values of nA. Zou et al. reported that there are two factors which affect the value of n. The first one is due to the fast crystallization rate of polymer at high cooling rate prevents the development of spherulites, resulting a decrease in the n value. The other one is the growth site impingement of spherulites and secondary crystallization may change the crystallization mechanism [22]. Jeziorny crystallization rate and the half-time of crystallization (t1/2) showed a similar trend as Avrami model. Jeziorny crystallization rate increased when the cooling rate was increased. Nevertheless, at higher temperature was affected by secondary crystallization as n value.

Non-isothermal crystallization kinetics based on the Ozawa model

Figure 11 shows the plot ln[− ln(1 − α(t))] versus ln(φ). Normally, n and K value should have calculated from the straight line. In this study, all curves are nonlinear. This suggests that Ozawa parameters could not be calculated. Moreover, there is no explaining about changing of the crystallization mechanism which includes primary and secondary nucleation [12]. It indicated that Ozawa model was inappropriate for describing the non-isothermal crystallization of these systems.

Fig. 11
figure 11

The plot of ln[− ln(1 − α(t))] versus ln(φ) of the PLA/PBS blends with 0.1% by mass of talc at the various crystallization temperatures

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Conclusions

In this work, the blends of PLA/PBS with 0.1% by mass of talc were prepared by melt blending to optimize on the isothermal and non-isothermal crystallization kinetics. From the isothermal crystallization kinetic results indicated that the completion of the crystallization blending process at 100 °C took the shortest time. The Avrami parameters were estimated from the various isothermal crystallization temperatures and the results show that the lowest half-time of crystallization was performed at 100 °C isothermal temperature. It could be suggested that at 100 °C isothermal temperature was a suitable temperature for a cycle time for PLA/PBS for crystallization. The smaller the t1/2 value exhibited the higher the crystallization rate. The Tobin parameters were also estimated and it shows that the nT value has higher value than that of nA approximately about 0.3. Moreover, Tobin parameters had the trends as similar as Avrami parameters.

From the non-isothermal crystallization kinetic results indicated that the crystallization peaks shifted to lower temperature when the cooling rate increased. Nevertheless, at higher cooling rate, there was insufficient time for nucleation and crystal growth to crystallize. So, the crystallization peak was wider, and the amount of crystal was lower. Cooling rate of 40 °C min−1 gave the highest amount of crystallinity and was found to be the appropriate rate for this condition. Non-isothermal crystallization kinetics based on the Jeziorny model indicated that there are two stages of crystallization which are straight line in the primary stage followed by the nonlinear line in the secondary stage, which was clearly at high cooling rate. Jeziorny crystallization rate and the half-time of crystallization showed a similar trend as Avrami model. Jeziorny crystallization rate increased when the cooling rate was increased. Nevertheless, at higher temperature was affected by secondary crystallization as indicated by n value. It was also found that Ozawa model was inappropriate for describing the non-isothermal crystallization of these systems. Based on current finding, talc is suitable to be the nucleating agent for PLA/PBS blends. This study provides useful information on the polymer processing which could estimate the reduction of the crystallization time and may enable its wider applications.