**5. Estimation of the Glass Transition Temperature**

*T<sup>g</sup>* can reflect whether a polymer blend is completely miscible. A fully miscible PBAT/PLA blend exhibits a single *Tg*. Generally, the *T<sup>g</sup>* value of binary miscible PBAT/PLA blends is predictable based on the Fox equation:

$$\frac{1}{T\_{\mathcal{X}}(\text{Blend})} = \frac{m\_{\text{PBAT}}}{T\_{\mathcal{X}}(\text{PBAT})} + \frac{1 - m\_{\text{PBAT}}}{T\_{\mathcal{X}}(\text{PLA})} \tag{13}$$

where *Tg*(Blend) is the predicted glass transition temperature of the miscible PBAT/PLA blend; *m*PBAT is the mass (weight) fraction of PBAT; *Tg*(PBAT) and *Tg*(PLA) are the glass transition temperature of neat PBAT and neat PLA, respectively.

The value of *Tg*(PBAT) and *Tg*(PLA) was −28.3 ◦C and 61.6 ◦C, respectively [4]. For details of the *Tg*(Blend) calculation, see the Supplementary Material on the sheet "Fox". The composition-dependent *T<sup>g</sup>* of miscible PBAT/PLA blends is shown graphically (Figure 8).

*Tg*(Blend) tends to decrease with an increasing mass fraction of PBAT. The glass transition temperature is slightly below 40 ◦C for PBAT/PLA (20/80). This value is about 10 ◦C for PBAT/PLA (50/50). Moreover, this value decreases to approximately −15 ◦C when the ratio of PBAT/PLA is 80/20. To the author's best knowledge, the glass transition temperatures have not been studied for fully miscible PBAT/PLA blends without compatibilizers. Unmodified PBAT/PLA blends with a wide range of ratios (0/100, 10/90, . . . 90/10, 100/0) have been reported to have two almost unchanged glass transition temperatures at about −30 ◦C and 61 ◦C, which correspond to the *T<sup>g</sup>* of neat PBAT and PLA in the DSC [4].

**5. Estimation of the Glass Transition Temperature** 

blends is predictable based on the Fox equation:

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transition temperature of neat PBAT and neat PLA, respectively.

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*Tg* can reflect whether a polymer blend is completely miscible. A fully miscible PBAT/PLA blend exhibits a single *Tg*. Generally, the *Tg* value of binary miscible PBAT/PLA

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The value of *Tg*(PBAT) and *Tg*(PLA) was –28.3 °C and 61.6 °C, respectively [4]. For details of the *Tg*(Blend) calculation, see the Supplementary Material on the sheet "Fox". The composition-dependent *Tg* of miscible PBAT/PLA blends is shown graphically (Fig-

where *Tg*(Blend) is the predicted glass transition temperature of the miscible PBAT/PLA blend; *m*PBAT is the mass (weight) fraction of PBAT; *Tg*(PBAT) and *Tg*(PLA) are the glass

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**Figure 8.** Glass transition temperature of miscible PBAT/PLA blends. **Figure 8.** Glass transition temperature of miscible PBAT/PLA blends.

#### *Tg*(Blend) tends to decrease with an increasing mass fraction of PBAT. The glass tran-**6. Conclusions**

ure 8).

sition temperature is slightly below 40 °C for PBAT/PLA (20/80). This value is about 10 °C for PBAT/PLA (50/50). Moreover, this value decreases to approximately –15 °C when the ratio of PBAT/PLA is 80/20. To the author's best knowledge, the glass transition temperatures have not been studied for fully miscible PBAT/PLA blends without compatibilizers. Unmodified PBAT/PLA blends with a wide range of ratios (0/100, 10/90, … 90/10, 100/0) have been reported to have two almost unchanged glass transition temperatures at about –30 °C and 61 °C, which correspond to the *Tg* of neat PBAT and PLA in the DSC [4]. **6. Conclusions**  In this study, the blend miscibility of PBAT/PLA blends was predicted. The solubility parameters calculated using the group contribution methods of van Krevelen and Hoy had a mean difference of 0.49 MPa1/2 between alternating PBAT and PLA. To a certain extent, a higher affinity would be possible between the two polymers when the monomers BA and BT reach a molar ratio exceeding 1 to 1. In this way, the structural optimization of PBAT will fundamentally improve the solubility of PBAT and PLA. Furthermore, a simulation of the miscibility of PBAT/PLA blends was established by using the calculated HiSP and different parameters. According to the simulation, the state of a PBAT/PLA blend can vary from immiscible to miscible, depending strongly on the molecular weights and weight ratio of both polymers at a constant temperature. Generally, the higher the molecular weights, the lower the predicted probability of the blend miscibility. Another tendency is that the higher the temperature, the higher the probability of the blend miscibility. The blends *Mn*52/30 displayed negative values in the whole range of compositions at 463 K. If *Mn*52/30 were melt-blended and then stored at a temperature above the *Tg* of In this study, the blend miscibility of PBAT/PLA blends was predicted. The solubility parameters calculated using the group contribution methods of van Krevelen and Hoy had a mean difference of 0.49 MPa1/2 between alternating PBAT and PLA. To a certain extent, a higher affinity would be possible between the two polymers when the monomers BA and BT reach a molar ratio exceeding 1 to 1. In this way, the structural optimization of PBAT will fundamentally improve the solubility of PBAT and PLA. Furthermore, a simulation of the miscibility of PBAT/PLA blends was established by using the calculated HiSP and different parameters. According to the simulation, the state of a PBAT/PLA blend can vary from immiscible to miscible, depending strongly on the molecular weights and weight ratio of both polymers at a constant temperature. Generally, the higher the molecular weights, the lower the predicted probability of the blend miscibility. Another tendency is that the higher the temperature, the higher the probability of the blend miscibility. The blends *Mn*52/30 displayed negative values in the whole range of compositions at 463 K. If *Mn*52/30 were melt-blended and then stored at a temperature above the *T<sup>g</sup>* of PBAT (−28 ◦C, approx. 245 K) for enough long time, the miscibility could change from miscible to partially miscible or immiscible, due to the mobility of PBAT chains. The blends *Mn*30/30 showed negative values of ∆*G<sup>M</sup>* both at 296 K and 463 K, according to the simulation. However, spinodal decomposition of *Mn*30/30 can appear at 296 K (at 30% volume fraction of PBAT) due to the negative value of ∆*G<sup>M</sup>* and the curvature of the spinodal. Moreover, the glass transition temperature of miscible PBAT/PLA blends was calculated using the Fox equation. A single *T<sup>g</sup>* would show at about 40 ◦C, 10 ◦C, and −15 ◦C for PBAT/PLA blends with the composition of (20/80), (50/50), and (80/20), respectively. This study gives the theoretical prediction of the miscibility for PBAT/PLA blends. The next scientific challenge will be the experimental discovery of to what extent the theoretical prediction is consistent with the practical results, especially the molecular weight-dependent miscibility of PBAT and PLA.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/polym13142339/s1, Excel table with the sheets of "vanKrevelen", "Hoy", "Flory–Huggins" and "Fox".

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** For details of the data used in this paper, see the supplementary material.

**Acknowledgments:** The author gives sincere thanks to Rodion Kopitzky (Fraunhofer UMSICHT) for discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.
