*3.1. Crystallization*

Exemplary DSC heating thermograms of star-shaped and linear PLLAs sheared at 170 ◦C and then cooled to RT at 30 ◦C/min, collected in Figure 1, exhibit glass transition with Tg at approx. 60–61 ◦C, cold crystallization exotherms and melting endotherms, with peaks at Tcc close to 100 ◦C and T m above 170 ◦C, respectively. In addition, on the thermograms, small pre-melting exotherms are visible, with maxima close to 160 ◦C, which originated from the recrystallization of the disordered alpha' to the ordered alpha orthorhombic form [8]. During heating at 5 ◦C/min, the cold-crystallization occurred in a relatively low temperature range and the crystallization exotherms and the melting endotherms did not overlap, which facilitated integration of the peaks and calculation of enthalpies of the processes. The melting enthalpy, Δ Hmc, of crystals formed during cooling, before the heating in DSC, was calculated by subtracting the enthalpies of exothermic effects of crystallization and recrystallization, Δ Hcc and Δ Hrc, respectively, from the melting enthalpy, Δ H m.

For the control specimens, Δ Hmc was small, or even close to zero, indicating that they were amorphous or with low crystallinity. However, Δ Hmc of the sheared specimens was markedly larger, proving that crystallinity developed in PLLAs during the post-shearing cooling. The differences between the thermograms in Figure 1 evidence that the effect of shear depended on the molar mass, but also on the macromolecular architecture of PLLAs studied.

**Figure 1.** DSC heating thermograms of PLLAs sheared at 20/s for 5 s at 150 ◦C and next cooled at 30 ◦C/min, and thermograms of control specimens cooled at 30 ◦C/min. The curves shifted vertically for clarity.

It must be noted that such approach does not take into account the temperature dependence of heat of fusion, due to which ΔHcc of the cold-crystallized crystals can be lower than their melting enthalpy. However, although Tm – Tcc was up to about 70 ◦C, in most cases ΔHcc was significantly smaller than ΔHmc, therefore reducing the overestimation of the latter. Another effect that should be considered is the difference in the heat of fusion of the ordered alpha form and the disordered alpha' form of PLLA. It is known that between 100 and 120 ◦C PLLA crystallizes not only in the ordered alpha modification but also in the disordered alpha' form. Below 100 ◦C, PLLA crystallizes from the quiescent melt only in the alpha' form [8], although the alpha form was found after shear-induced crystallization at 96 ◦C [44]. Although the heat of fusion of the alpha'crystals is significantly lower than that of the alpha modification [45], the influence of that on ΔHmc can be neglected, because of the alpha' to alpha recrystallization prior to melting. In addition, the alpha' to alpha recrystallization occurring near 160 ◦C and also reorganization occurring in the alpha phase prior to melting, further reduce the possible overestimation of ΔHmc.

Figure 2 illustrates the effect of shearing conditions and post-shearing cooling on ΔHmc and mass crystallinity, χc of linear and star PLLAs. The ΔHmc values are averages, based on at least two or three measurements. The mass crystallinity, χc, was calculated from ΔHmc, assuming that the heat of fusion of 100% crystalline PLLA is 106 J/g [46].

**Figure 2.** Melting enthalpy, ΔHmc, of crystalline phase formed in PLLAs during cooling at 10 and 30 ◦C/min after shearing at 170◦C (**a**) and 150 ◦C (**b**,**<sup>c</sup>**) versus shear rate, .*γ*.

The control specimens cooled at 30 ◦C/min were practically amorphous, whereas in those cooled at 10 ◦C/min crystallization occurred, although ΔHmc and the corresponding χc were small, being the largest for L121, close to 20 J/g and 19%, respectively, as previously found for the same polymer [24]. Shearing at 150 and 170 ◦C enhanced crystallization in all PLLAs. In general, ΔHmc increased with .*γ*, although weakly in most cases, or was even independent of .*γ*, most possibly due to the same final shear strain achieved during all experiments. Moreover, ΔHmc of L339 sheared at 170 ◦C and L240 sheared at 150 ◦C, and next cooled at 10 ◦C/min, reached very high values even for .*γ* of only 5/s.

Shearing at 170 ◦C followed by cooling at 30 ◦C/min resulted in rather low ΔHmc of all PLLAs, up to about 15 J/g, except L240 and L339, for which ΔHmc. values were higher. A decrease of v to 10 ◦C/min enhanced the post-shearing crystallization in all PLLAs. As seen in Figure 2a, ΔHmc values of PLLAs with Mw close to 120 kg/mol ranging from 24 to 30 J/g were similar. Slightly higher ΔHmc of 31–32 J/g was found for 6S245, and even higher up to 44 J/g for L240. The effect of shear on the crystallization of L339 was the strongest, which was reflected in ΔHmc close to 50 J/g. A decrease of Ts to 150 ◦C intensified the post-shearing crystallization at both cooling rates. L339 crystallized during shearing at 150 ◦C; hence, studies of its post-shearing nonisothermal crystallization were impossible. As seen in Figure 2b, ΔHmc. values of PLLAs with Mw close to 120 kg/mol, cooled at 30 ◦C/min, increased up to 21–29 J/g, and those of 6S245 and L240 to 44 and 48 J/g, respectively. Slower cooling, at 10 ◦C/min, resulted in higher ΔHmc, in the range of 34–47 J/g for PLLAs with Mw close to 120 J/g, whereas in the range of 43–49 J/g and 55 J/g for 6S245 and L240, respectively, as s shown in Figure 2c.

DSC measurements allow us to determine only the final χc developed during postshearing cooling, whereas the light depolarization method enables us to follow the increase of αvr during crystallization. To compare the crystallinity increase in specimens with different final crystallinity, volume crystallinity αv(T) equal to αvr(T) χv, was plotted in Figure 3, where χv is the final volume crystallinity calculated based on χc and the densities of the amorphous and crystalline phases of PLA [47]. As it is explained above, χc was calculated based on the melting enthalpy of crystals formed during post-shearing cooling, ΔHmc. It should be mentioned that the lower melting enthalpy of the alpha' phase was not accounted for because ΔHmc was determined from the melting endotherm preceded by the pre-melting recrystallization of alpha' to alpha form. Differentiation of αv(T) with respect to temperature permitted to obtain the temperature dependencies of crystallization rate. It appears that the lower Ts, slower cooling and higher Mw of PLLA resulted in the higher temperature range of crystallization. The effect of .*γ*, Ts and v, as well as of Mw of PLLA and its macromolecular architecture, on Tc was similar to that on ΔHmc, as it is shown in Figure 4. Tc correlated with ΔHmc and crystallinity, the higher the former the larger the latter. Tc increased with decreasing Ts and v, and with increasing .*γ*. The highest Tc values were found for L339, lower for L240 and 6S245, and even lower for 4S123, 6S120 and L121, showing the influence of Mw, but also of the macromolecular architecture.

The results show a crucial role of Ts and v. The lower Ts increased the relaxation times of macromolecules and lowered the energy barrier for nucleation, thus enhancing the shear-induced crystallization. In turn, the slower cooling enabled a longer time for crystallization before too low temperature was reached, increasing therefore Tc, ΔHmc and χc, the latter determined based on ΔHmc. However, not only the shearing conditions and v determined the post-shearing crystallization. Tc and ΔHmc were strongly influenced by molar masses of PLLAs, as can be expected, but they were also affected by macromolecular architecture. Figure 2b shows that in the case of cooling at 30 ◦C/min, the shearing at 150 ◦C had the weakest effect on L121, stronger on 6S120, and the strongest on 4S123 crystallization. Figure 2a,c show that during cooling at 10 ◦C/min Tc and ΔHmc values of all PLLAs with Mw near 120 kg/mol were similar. However, it must be reminded that in the temperature range of 120–145 ◦C the crystal growth rate of L121 was higher than that of the other PLLAs studied [24]. The crystallization kinetics is governed by both the crystal growth rate and the nucleation rate [48], hence, similar Tc and ΔHmc values

of L121, 6S120 and 4S123 are suggestive of much stronger nucleation in the two latter. The control specimens cooled at 30 ◦C/min were practically amorphous but crystallized during cooling at 10 ◦C/min. The shear-induced increase of ΔHmc and Tc of specimens cooled at 10 ◦C/min is plotted in Figure 5 and Figure S1 in Supplementary Information (SI), respectively. The plots clearly show that the shear enhanced more the crystallization of 4S123 and 6S120 than that of L121, despite the higher Mz of the latter.

**Figure 3.** Development of crystallinity determined by light depolarization method (**a**) and derivative of crystallinity with respect to temperature (**b**) in PLLAs during cooling at 10 ◦C/min after shearing at 20/s, 150 ◦C. The curves in Figure 3b shifted vertically for clarity.

**Figure 4.** Crystallization peak temperature, Tc, during cooling of PLLAs at 10 and 30 ◦C/min after shearing at 170 ◦C (**a**) and 150 ◦C (**b**,**<sup>c</sup>**) versus shear rate, .*γ*.

**Figure 5.** Increase of melting enthalpy, ΔHmc-ΔHmcq, of crystalline phase formed in PLLAs during cooling at 10 ◦C/min caused by shearing at 170 ◦C (**a**) and 150 ◦C (**b**) versus shear rate, .*γ*. ΔHmcq denotes the melting enthalpy of crystals formed during cooling at 10 ◦C/min in control specimens.

The enhancement of the effect of shear in 6S120 and 4S123 as compared to L121 was undoubtedly caused by the star architecture of macromolecules, which hindered the relaxation of the stretched macromolecular chain network. In contrast to that, the shearinduced crystallization in 6S245 and L240, was similar, and even stronger in the latter, as shown in Figures 2 and 5. Although 6S245 and L240 had similar Mn and Mw, Mz of L240, 414 kg/mol, exceeded that of 6S245, 294 kg/mol, evidencing the higher content of larger macromolecules, which presence compensated the effect of 6S245 star architecture on the shear-induced crystallization. In the flow-induced crystallization of a polymer a high molar mass tail of its molar mass distribution plays a crucial role, due to long relaxation times, and at Mw of 240–245 kg/mol its effect compensated that of star architecture. It is also of importance that due to its higher molar mass, the number of branching points in 6S245 was smaller than in 6S120, hence their effect on the macromolecular mobility was reduced.

The crystallization, which was not completed during cooling continued during subsequent heating in DSC, resulting in cold-crystallization exotherms with peaks at Tcc of 97–109 ◦C, as shown in Figure 1. In many cases, pre-melting exotherms, with maxima at 159–164 ◦C, evidenced the alpha' to alpha form recrystallization. Usually, single melting

peaks were observed, with Tm of 174–179 ◦C, although some of them with shoulders. As shown in Figure 6, ΔHm values of the control specimens of 6S245 were equal to 37–38 J/g, whereas those of the other control PLLAs studied were higher, ranging from 43 to 51 J/g. The sheared PLLAs exhibited increased ΔHm of 39–55 J/g. The lowest values of ΔHm were those of 6S245 cooled at 10 ◦C/min after shearing at 170 ◦C, and cooled at 30 ◦C/min after shearing at 150 ◦C, as seen in Figure 6. In turn, among PLLAs sheared at 150 ◦C and cooled at 10 ◦C/min, L240 exhibited the highest ΔHm, as evidenced in Figure 6c. These differences reflect the different ability of PLLAs studied to crystallize, as described in [24], and the different effect of shear influenced by the molar masses and macromolecular architecture of the studied PLLAs.

**Figure 6.** Melting enthalpy, ΔHm, measured during DSC heating at 5 ◦C/min of PLLAs previously cooled at 10 and 30 ◦C/min, after shearing at 170 ◦C (**a**) and 150 ◦C (**b**,**<sup>c</sup>**) versus shear rate, .*γ*.
