Revisiting Non-Conventional Crystallinity-Induced Effects on Molecular Mobility in Sustainable Diblock Copolymers of Poly(propylene adipate) and Polylactide

This work deals with molecular mobility in renewable block copolymers based on polylactide (PLA) and poly(propylene adipate) (PPAd). In particular, we assess non-trivial effects on the mobility arising from the implementation of crystallization. Differential scanning calorimetry, polarized light microscopy and broadband dielectric spectroscopy were employed in combination for this study. The materials were subjected to various thermal treatments aiming at the manipulation of crystallization, namely, fast and slow cooling, isothermal melt- and cold-crystallization. Subsequently, we evaluated the changes recorded in the overall thermal behavior, semicrystalline morphology and molecular mobility (segmental and local). The molecular dynamics map for neat PPAd is presented here for the first time. Unexpectedly, the glass transition temperature, Tg, in the amorphous state drops upon crystallization by 8–50 K. The drop becomes stronger with the increase in the PPAd fraction. Compared to the amorphous state, crystallization leads to significantly faster segmental dynamics with severely suppressed cooperativity. For the PLA/PPAd copolymers, the effects are systematically stronger in the cold- as compared to the melt-crystallization, whereas the opposite happens for neat PLA. The local βPLA relaxation of PLA was, interestingly, recorded to almost vanish upon crystallization. This suggests that the corresponding molecular groups (carbonyl) are strongly involved and immobilized within the semicrystalline regions. The overall results suggest the involvement of either spatial nanoconfinement imposed on the mobile chains within the inter-crystal amorphous areas and/or a crystallization-driven effect of nanophase separation. The latter phase separation seems to be at the origins of the significant discrepancy recorded between the calorimetric and dielectric recordings on Tg in the copolymers. Once again, compared to more conventional techniques such as calorimetry, dielectric spectroscopy was proved a powerful and quite sensitive tool in recording such effects as well as in providing indirect indications for the polymer chains’ topology.


Introduction
Polymers are all over the world, from everyday life uses to industrial and space applications [1,2]. This is mainly due to the combination of unique properties of polymers (high performance), the relatively easy processing and low economic cost of production. During the last decades, there has been a significant growth in environmental concerns, which, in the case of polymers, is reflected in the oil-based molecular origin of the most on segmental mobility in PLA/PPAd blends as compared to neat PLA and initial PPAd. The investigation mainly involves the implementation of three states regarding crystallinity, namely, amorphous, isothermally melt-crystallized and isothermally cold-crystallized. Finally, we construct the corresponding molecular mobility (dynamics) map for these cases. This is the first recording of the molecular dynamics for initial PPAd, to the best of our knowledge.

Materials
The materials investigated here are diblock copolymers based on PLA and PPAd, synthesized in a previous work by Terzopoulou et al. [30]. Briefly, the copolymers were prepared by using an initial PPAd polymer of low M n~6 kg/mol, forming the first block, onto which the second block of PLA was build, in situ, via ring opening polymerization of L-lactide at 180 • C ( Figure 1). The samples differ in the mass ratio PLA (%)/PPAd (%) as 95/5, 85/15 and 75/25 and are listed in Table 1 along with values on the estimated average molar masses (M n ). As reference samples, we comparatively study the initial PPAd (the same as that used in the copolymer preparation) and a neat PLA prepared by a similar ROP route (Table 1). Regarding the initial scope of these copolymers, this was a success as the enzymatic degradation of PLA is significantly accelerated in the copolymers as compared to PLA in bulk.
Molecules 2022, 27, x FOR PEER REVIEW 3 of 22 crystallization protocols. We employ the combination of differential scanning calorimetry (DSC), polarized light microscopy (PLM) and broadband dielectric spectroscopy (BDS) to study the effects on segmental mobility in PLA/PPAd blends as compared to neat PLA and initial PPAd. The investigation mainly involves the implementation of three states regarding crystallinity, namely, amorphous, isothermally melt-crystallized and isothermally cold-crystallized. Finally, we construct the corresponding molecular mobility (dynamics) map for these cases. This is the first recording of the molecular dynamics for initial PPAd, to the best of our knowledge.

Materials
The materials investigated here are diblock copolymers based on PLA and PPAd, synthesized in a previous work by Terzopoulou et al. [30]. Briefly, the copolymers were prepared by using an initial PPAd polymer of low Mn ~ 6 kg/mol, forming the first block, onto which the second block of PLA was build, in situ, via ring opening polymerization of L-lactide at 180 °C ( Figure 1). The samples differ in the mass ratio PLA (%)/PPAd (%) as 95/5, 85/15 and 75/25 and are listed in Table 1 along with values on the estimated average molar masses (Mn). As reference samples, we comparatively study the initial PPAd (the same as that used in the copolymer preparation) and a neat PLA prepared by a similar ROP route (Table 1). Regarding the initial scope of these copolymers, this was a success as the enzymatic degradation of PLA is significantly accelerated in the copolymers as compared to PLA in bulk.   [30]. Included are the values for the selected temperatures of isothermal annealing of crystallization, Tanneal,mc and Tanneal,cc, for melt-and cold-crystallization, respectively.

Sample
Code Name

Differential Scanning Calorimetry
The glass transition and crystallization of the block copolymers as well as initial PLA and PPAd were assessed by DSC. To that aim, we employed a TA Q200 calorimeter (TA, New Castle, DE, USA), combined with a liquid nitrogen control system. The instrument had been calibrated with indium for temperature and enthalpy and sapphires for heat   [30]. Included are the values for the selected temperatures of isothermal annealing of crystallization, T anneal,mc and T anneal,cc , for melt-and cold-crystallization, respectively.

Sample
Code Name M n (g/mol) The glass transition and crystallization of the block copolymers as well as initial PLA and PPAd were assessed by DSC. To that aim, we employed a TA Q200 calorimeter (TA, New Castle, DE, USA), combined with a liquid nitrogen control system. The instrument had been calibrated with indium for temperature and enthalpy and sapphires for heat capacity. The thermograms were recorded in N 2 atmosphere of high purity (99.995%) and within the range from −110 to 200 • C. In total, five (5) scans were performed, schematically described in Figure 2, first involving a heating scan for erasing thermal history (Scan 1), and four main scans aiming at manipulating crystallization. In particular, in Scan 2, the melted samples were cooled at 10 K/min, in Scan 3, the melted samples were cooled at the highest achievable rate in order to eliminate crystallization, while in Scans 4 and 5, the samples were subjected to isothermal melt-and cold-crystallization annealings at selected temperatures (T anneal,mc and T anneal,cc , respectively), different for each sample and chosen based on the results of the previous Scans 2 and 3. Details on the selection of T anneal are given along with the experimental results. The values for T anneal are listed in Table 1. Upon each crystallization treatment, the sample was cooled to −110 • C and subsequently a final heating scan was recorded. The heating rate was fixed for all scans at 10 K/min. capacity. The thermograms were recorded in N2 atmosphere of high purity (99.995%) and within the range from −110 to 200 °C. In total, five (5) scans were performed, schematically described in Figure 2, first involving a heating scan for erasing thermal history (Scan 1), and four main scans aiming at manipulating crystallization. In particular, in Scan 2, the melted samples were cooled at 10 K/min, in Scan 3, the melted samples were cooled at the highest achievable rate in order to eliminate crystallization, while in Scans 4 and 5, the samples were subjected to isothermal melt-and cold-crystallization annealings at selected temperatures (Tanneal,mc and Tanneal,cc, respectively), different for each sample and chosen based on the results of the previous Scans 2 and 3. Details on the selection of Tanneal are given along with the experimental results. The values for Tanneal are listed in Table 1. Upon each crystallization treatment, the sample was cooled to −110 °C and subsequently a final heating scan was recorded. The heating rate was fixed for all scans at 10 K/min. The characteristic temperature of the glass transition step, Tg, was estimated from the heating curve as the point of half increase in the heat capacity. Crystallization and melting events were evaluated in terms of peak temperature maxima, onsets and enthalpy changes (ΔH in J/g). The crystalline fraction, CF, was estimated by both the melt-and cold-crystallization peaks, both isothermals and non-isothermals, and by comparing the crystallization enthalpy (ΔΗ, respectively) with the theoretical heat of fusion for a 100% crystalline PLA, ΔΗ100%,PLA, usually taken as 93 J/g [42] according to Equation (1).
Please note that, more recently, compared to the work by Fischer et al. [42], there more alternative values for ΔΗ100%,PLA have been reported, considering the individual crystal polymorphs of PLA (α and α′) [43,44].

Polarized Light Microscopy
The PLM technique was employed to follow the effect of the copolymer composition on the semicrystalline morphology. PLM micrographs were recorded isothermally during melt-and cold-crystallization at the same Tanneal,mc and Tanneal,cc as those employed in DSC ( Table 1). The micrographs were recorded by means of a Nikon Optiphot-1 polarizing The characteristic temperature of the glass transition step, T g , was estimated from the heating curve as the point of half increase in the heat capacity. Crystallization and melting events were evaluated in terms of peak temperature maxima, onsets and enthalpy changes (∆H in J/g). The crystalline fraction, CF, was estimated by both the melt-and cold-crystallization peaks, both isothermals and non-isothermals, and by comparing the crystallization enthalpy (∆H, respectively) with the theoretical heat of fusion for a 100% crystalline PLA, ∆H 100%,PLA , usually taken as 93 J/g [42] according to Equation (1).
Please note that, more recently, compared to the work by Fischer et al. [42], there more alternative values for ∆H 100%,PLA have been reported, considering the individual crystal polymorphs of PLA (α and α ) [43,44].

Polarized Light Microscopy
The PLM technique was employed to follow the effect of the copolymer composition on the semicrystalline morphology. PLM micrographs were recorded isothermally during melt-and cold-crystallization at the same T anneal,mc and T anneal,cc as those employed in DSC ( Table 1). The micrographs were recorded by means of a Nikon Optiphot-1 polarizing microscope equipped with a Linkam THMS 600 heated stage, a Linkam TP91 control unit and a Jenoptik Gryphax Arktur camera.
From the data of PLM, the spherulitic growth rate was followed during isothermal melt-crystallization, at the same T anneal,mc as those in DSC. In the isothermal crystallization step, a minimum of three spherulites were followed during their free growth before they impinged on one another. Then, the radius of each spherulite was measured and plotted as a function of time. From this plot, the slope represents the spherulitic growth rate (G) at the selected T anneal,mc . The latter estimation was technically impossible for the case of cold-crystallization.

Broadband Dielectric Spectroscopy
The molecular mobility, with emphasis on segmental mobility, was investigated by BDS [45], employing a Novocontrol BDS setup (Novocontrol GmbH, Montabaur, Germany). Pieces of the produced sample were initially placed and melted between finely polished brash electrodes of 14 mm in diameter. Silica spacers of~100 µm in thickness were used in order to prevent the electrical contact of the electrodes and keep them parallel with each other. Consistent with the above techniques, three thermal protocols were adopted for BDS, namely, preparing (1) amorphous samples by melting and fast cooling, (2) isothermally meltcrystallized samples at T anneal,mc and (3) isothermally cold-crystallized samples at T anneal,cc . For each sample and protocol, the complex dielectric permittivity, ε (Equation (2)), was recorded in N 2 (g) nitrogen flow, isothermally as a function of frequency, f, in the range from 10 -1 to 10 6 Hz and in the temperature range between −150 and 120 • C, upon heating in steps of 5 and 10 K. ε The permittivity spectra are mainly complex as they consist of multiple contributions (relaxation mechanisms). Therefore, the spectra were analysed by the fitting of special models, mainly, the Havriliak-Negami, HN [45,46], function (Equation (3)).
Therein, ε ∞ describes the value of the real part of dielectric permittivity, ε , for f >> f 0 , ∆ε is the dielectric strength, f 0 is a characteristic frequency related to the frequency of maximum dielectric loss and α HN and β HN are shape parameters, for width and symmetry, respectively. Upon this analysis, we constructed the timescale map of local and segmental relaxations. The local processes usually obey the Arrhenius equation [45,47] (Equation (4)), as they exhibit a temperature-independent activation energy, E act . On the other hand, the segmental relaxations, related to the glass transition, demonstrate a different timescale due to their cooperative character, usually described by the Vogel-Fulcher-Tammann-Hesse (VFTH) expression [45,48] (Equation (5)), within which, D is the so-called fragility strength parameter [48] and is related to the measure of cooperativity, namely, the fragility index, m (Equation (6)).

Crystallization and Glass Transition
In Figure 3, we present the calorimetric results for Scans 2 and 3, upon erasing any thermal history. During cooling at 10 K/min (Figure 3a), all copolymers crystallize at 100 • C, similarly to neat PLA. Initial PPAd crystallizes at −10 • C, exhibiting an enthalpy change of~21 J/g. During the subsequent heating at 10 K/min, PPAd exhibits a T g of −61 • C. The corresponding heat capacity change ∆c p = 0.42 J/g·K. On the other hand, the T g of neat PLA equals 43 • C. The addition of PPAd in the copolymers results in a decrease in the T g from 39 • C down to the quite low value of −42 • C. This suppression, along with the absence of a second glass transition step in the copolymers, suggests the homogeneity (no significant micro-phase separation) of the copolymers, which was actually the goal of said synthesis.

Crystallization and Glass Transition
In Figure 3, we present the calorimetric results for Scans 2 and 3, upon erasing any thermal history. During cooling at 10 K/min (Figure 3a), all copolymers crystallize at ~100 °C, similarly to neat PLA. Initial PPAd crystallizes at −10 °C, exhibiting an enthalpy change of ~21 J/g. During the subsequent heating at 10 K/min, PPAd exhibits a Tg of −61 °C. The corresponding heat capacity change Δcp = 0.42 J/g•K. On the other hand, the Tg of neat PLA equals 43 °C. The addition of PPAd in the copolymers results in a decrease in the Tg from 39 °C down to the quite low value of −42 °C. This suppression, along with the absence of a second glass transition step in the copolymers, suggests the homogeneity (no significant micro-phase separation) of the copolymers, which was actually the goal of said synthesis. The results shown in Figure 3b involve the effects of the copolymer composition as well as the effects of crystallinity on Tg. Therefore, to assess the direct effects of composition on Tg, we performed measurements on amorphous samples. These are shown in Figure 3c, i.e., via the heating scan recorded upon a prior fast cooling. With the increase in PPAd content from 0 to 25%, the glass transition temperature decreases from 51 down to 11 °C. The drop in Tg of PLA by the addition of PPAd on the same polymer chain was rationalized in terms of the plasticization effect of the small PPAd blocks. The effect is also The results shown in Figure 3b involve the effects of the copolymer composition as well as the effects of crystallinity on T g . Therefore, to assess the direct effects of composition on T g , we performed measurements on amorphous samples. These are shown in Figure 3c, i.e., via the heating scan recorded upon a prior fast cooling. With the increase in PPAd content from 0 to 25%, the glass transition temperature decreases from 51 down to 11 • C. The drop in T g of PLA by the addition of PPAd on the same polymer chain was rationalized in terms of the plasticization effect of the small PPAd blocks. The effect is also facilitated by the overall shortening of the copolymer chains [26]. The surprising effect is the further lowering of T g with the implementation of crystallinity, as, conversely, the presence of crystals would be expected to hinder the polymer chains diffusion and, subsequently, to elevate the T g [16,[49][50][51] (and references therein). So far, these results confirm previous recordings on the same systems [26], which actually generated the interest for the present 'follow-up' study.
Based on the results of Scan 2 (Figure 3a), in particular, from the temperature range wherein the sample is neither melted nor has crystallization begun, we have selected suitable temperatures (Table 1) to perform the isothermal melt-crystallization annealing, T anneal,mc . Then, based on the results of Scan 3 (Figure 3c), we have chosen suitable T to perform the cold-isothermal crystallization annealings, T anneal,cc (Table 1), namely, to be above T g and below the event of cold-crystallization. In particular, the T anneal values were chosen as the T just before (3-5 K) the initiation of each non-isothermal crystallization event. The corresponding DSC results are shown in Figure 4.
presence of crystals would be expected to hinder the polymer chains diffusion and, subsequently, to elevate the Tg [16,[49][50][51] (and references therein). So far, these results confirm previous recordings on the same systems [26], which actually generated the interest for the present 'follow-up' study.
Based on the results of Scan 2 (Figure 3a), in particular, from the temperature range wherein the sample is neither melted nor has crystallization begun, we have selected suitable temperatures (Table 1) to perform the isothermal melt-crystallization annealing, Tanneal,mc. Then, based on the results of Scan 3 (Figure 3c), we have chosen suitable T to perform the cold-isothermal crystallization annealings, Tanneal,cc (Table 1), namely, to be above Tg and below the event of cold-crystallization. In particular, the Tanneal values were chosen as the T just before (3-5 K) the initiation of each non-isothermal crystallization event. The corresponding DSC results are shown in Figure 4. In Figure 4a,c, we present the time evolutions of crystallization, while in Figure 4b,d, we show the subsequent heating scans. Almost all systems, including neat PLA, exhibit similar crystallization rates. The exception to this behaviour is the cold-crystallization of 75/25, which is somewhat retarded. The effects are actually due to the different Tanneal selected for the different samples, thus, the result on the crystallization rate should not be compared between the different samples for drawing conclusions on the direct effect of In Figure 4a,c, we present the time evolutions of crystallization, while in Figure 4b,d, we show the subsequent heating scans. Almost all systems, including neat PLA, exhibit similar crystallization rates. The exception to this behaviour is the cold-crystallization of 75/25, which is somewhat retarded. The effects are actually due to the different T anneal selected for the different samples, thus, the result on the crystallization rate should not be compared between the different samples for drawing conclusions on the direct effect of the copolymeric structure on the nucleation and crystal growth (e.g., the performance of Avrami analysis [52]). For the most clear conclusions, the results of Figure 4 (Scans 4 and 5) have been evaluated and are discussed in terms of crystalline fraction (CF, Equation (1)) and the overall results (Scans 2-5) in terms of characteristic temperatures, namely, crystallization, T c , onset of crystallization, T c,onset , cold-crystallization, T cc , onset of cold-crystallization, T c,onset , and glass transition temperature. Please note that the T g is always estimated from the corresponding heating scan.
It is important to note that, based on the results of Figure 3a, the temperature range of the crystallization of the copolymers coincides to that of neat PLA, not PPAd. Therefore, we have concluded that the recorded crystallization should involve the PLA-rich phases. Thus, in Equation (1), the crystallization enthalpy (∆H) used for calculations has been normalized to the PLA mass content, w PLA (∆H/w PLA ). Otherwise, it would not be correct to compare the recorded ∆H to the heat of fusion of PLA.
In Figure 5, we follow the effects of the PPAd loading and of each thermal treatment on CF. CF = 0 upon the fast cooling, which denotes that the cooling rate of~100 K/min (in the temperature range of the expected crystallization) is sufficient to eliminate crystallization [21,23]. However, this rate is not sufficient to prevent nucleation, which is also expected for conventional cooling in PLA [23]. For Scans 3-5, in Figure 5a, CF drops monotonically by~10% with the addition of PPAd. The same happens with the characteristic Ts of crystallization (melt and cold) in Figure 5b, which drops by about 10-40 K (depending on the thermal treatment). The results suggest that both the amounts as well as the rates of crystallization (nucleation/lamellae packings) are slower/hindered in the copolymers. The retarded lamellae packing should have an impact on the quality (density and/or size) of the spherulites. This is partly confirmed by the lowering of the melting temperature, T m , with PPAd loading (see Figures 3b,c and 4b,d). The situation seems to be more complex for the case of Scan 2 (non-isothermal crystallization), within which both the CF and T c do not seem to vary significantly. In our previous work [26] on the same systems, we presented PLM results for the crystallization during the cooling of Scan 2 which showed non-systematic effects on the rate of crystallization (faster for PLA and 85/15 and slower for 95/05 and 75/25) while the final size of the spherulites was found to increase in the copolymers. Additionally, compared to most scans, the isothermal cold-crystallization has resulted in both lower CF and T c . This is most probably due to poor mobility of the chains during crystallization, which is reflected in the doubled (on average) crystallization times needed (Figure 4c), compared to the case of melt-crystallization. 5) have been evaluated and are discussed in terms of crystalline fraction (CF, Equation (1)) and the overall results (Scans 2-5) in terms of characteristic temperatures, namely, crystallization, Tc, onset of crystallization, Tc,onset, cold-crystallization, Tcc, onset of coldcrystallization, Tc,onset, and glass transition temperature. Please note that the Tg is always estimated from the corresponding heating scan.
It is important to note that, based on the results of Figure 3a, the temperature range of the crystallization of the copolymers coincides to that of neat PLA, not PPAd. Therefore, we have concluded that the recorded crystallization should involve the PLA-rich phases. Thus, in Equation (1), the crystallization enthalpy (ΔH) used for calculations has been normalized to the PLA mass content, wPLA (ΔH/wPLA). Otherwise, it would not be correct to compare the recorded ΔΗ to the heat of fusion of PLA.
In Figure 5, we follow the effects of the PPAd loading and of each thermal treatment on CF. CF = 0 upon the fast cooling, which denotes that the cooling rate of ~100 K/min (in the temperature range of the expected crystallization) is sufficient to eliminate crystallization [21,23]. However, this rate is not sufficient to prevent nucleation, which is also expected for conventional cooling in PLA [23]. For Scans 3-5, in Figure 5a, CF drops monotonically by ~10% with the addition of PPAd. The same happens with the characteristic Ts of crystallization (melt and cold) in Figure 5b, which drops by about 10-40 K (depending on the thermal treatment). The results suggest that both the amounts as well as the rates of crystallization (nucleation/lamellae packings) are slower/hindered in the copolymers. The retarded lamellae packing should have an impact on the quality (density and/or size) of the spherulites. This is partly confirmed by the lowering of the melting temperature, Tm, with PPAd loading (see Figures 3b,c and 4b,d). The situation seems to be more complex for the case of Scan 2 (non-isothermal crystallization), within which both the CF and Tc do not seem to vary significantly. In our previous work [26] on the same systems, we presented PLM results for the crystallization during the cooling of Scan 2 which showed non-systematic effects on the rate of crystallization (faster for PLA and 85/15 and slower for 95/05 and 75/25) while the final size of the spherulites was found to increase in the copolymers. Additionally, compared to most scans, the isothermal cold-crystallization has resulted in both lower CF and Tc. This is most probably due to poor mobility of the chains during crystallization, which is reflected in the doubled (on average) crystallization times needed (Figure 4c), compared to the case of melt-crystallization.  From the results of PLM ( Figure 6) during melt-crystallization, we were able to estimate the spherulitic growth rate, G, which is presented in Figure 7. G increases in the copolymers from~270 (neat PLA) up to~520 µm/min (75/25) with the increase in PPAd. The effect could be correlated with the easier diffusion of the chains as manifested by the lowering of T g .
From the results of PLM ( Figure 6) during melt-crystallization, we were able to estimate the spherulitic growth rate, G, which is presented in Figure 7. G increases in the copolymers from ~270 (neat PLA) up to ~520 μm/min (75/25) with the increase in PPAd. The effect could be correlated with the easier diffusion of the chains as manifested by the lowering of Tg.  Regarding the semicrystalline morphology upon the isothermal cold-crystallization (right side of Figure 6), we could not conclude its to effects on the size of the formed spherulites. However, from a more careful look at the data and upon repeating the measurements on various spots and different samples, we observed that, contrary to PLA, 95/05 and 85/15, in the case of 75/25 the formed spherulites are smaller, and the sample volume Regarding the semicrystalline morphology upon the isothermal cold-crystallization (right side of Figure 6), we could not conclude its to effects on the size of the formed spherulites. However, from a more careful look at the data and upon repeating the measurements on various spots and different samples, we observed that, contrary to PLA, 95/05 and 85/15, in the case of 75/25 the formed spherulites are smaller, and the sample volume is not completely filled with crystals. The latter also seems true in the case of meltcrystallization. We will come back at this point later. Finally, we observe for the copolymers that the spherulites exhibit the so called 'ring-banded' structure [53]. This is quite clear in 85/15 and 75/25. The phenomenon is expected when the polymer chains consist of both crystallizable and non-crystallizable segments and low M n , in general, such as in our case. Ring-banded spherulites have been observed for both PLA [54] and poly(butylene adipate) [55].
We may come now to the most interesting effect recorded herein. The basis for the discussion of this is Figure 8. Therein, we have plotted together the heating curves of Scans 3, 4 and 5 (Figure 8a). The results clearly show that the glass transition step is sharp and strong (high ∆c p ) in the case of the amorphous samples. Upon crystallization (both types), the glass transition becomes more broad and weaker, which is expected, nevertheless, it migrates toward lower temperatures. In terms of T g , in Figure 8b, it is shown that whereas in the amorphous state the addition of PPAd leads to a maximum drop of T g by~40 K (75/25), the implementation of crystallinity additionally lowers the T g by 8 K in PLA, 15 K in 95/05 and~50 K in 85/15 and 75/25. The effect seems controversial considering the expected effects of crystallinity, usually imposed on conventional polymers, hindering the mobility of the chains and elevating the T g [16,[49][50][51]. Before attempting to provide physically rational explanations for this, we will discuss the results in terms of molecular dynamics obtained via BDS and the corresponding critical analysis.

Molecular Mobility (BDS)
In Figures 9-11, we present raw BDS data in various forms. The molecular mobility is usually assessed in BDS by following the imaginary part of the dielectric permittivity, ε″, which is considered to be related with the dielectric loss [45,56]. An example of raw ε″(f) is shown in Figure 9a for initial PPAd. At T < Tg the dipolar relaxation mechanisms recorded as peaks in ε″(f) are considered to arise from local molecular motions of corresponding polar groups. These secondary relaxation mechanisms are generally named as β, γ, δ, etc. [45]. Then, as T increases and approaches Tg, the dielectric signal increases by one or more orders of magnitude and the strong main relaxation enters the frequency Before attempting to provide physically rational explanations for this, we will discuss the results in terms of molecular dynamics obtained via BDS and the corresponding critical analysis.

Molecular Mobility (BDS)
In Figures 9-11, we present raw BDS data in various forms. The molecular mobility is usually assessed in BDS by following the imaginary part of the dielectric permittivity, ε , which is considered to be related with the dielectric loss [45,56]. An example of raw ε (f ) is shown in Figure 9a for initial PPAd. At T < T g the dipolar relaxation mechanisms recorded as peaks in ε (f ) are considered to arise from local molecular motions of corresponding polar groups. These secondary relaxation mechanisms are generally named as β, γ, δ, etc. [45]. Then, as T increases and approaches T g , the dielectric signal increases by one or more orders of magnitude and the strong main relaxation enters the frequency window. This is the case of the dielectric analogue of glass transition usually called 'α relaxation', as it monitors the segmental mobility of the polymer chains via the relaxation of the dipoles perpendicularly distributed on the main polymer chain [45]. cal analysis.

Molecular Mobility (BDS)
In Figures 9-11, we present raw BDS data in various forms. The molecular mobility is usually assessed in BDS by following the imaginary part of the dielectric permittivity, ε″, which is considered to be related with the dielectric loss [45,56]. An example of raw ε″(f) is shown in Figure 9a for initial PPAd. At T < Tg the dipolar relaxation mechanisms recorded as peaks in ε″(f) are considered to arise from local molecular motions of corresponding polar groups. These secondary relaxation mechanisms are generally named as β, γ, δ, etc. [45]. Then, as T increases and approaches Tg, the dielectric signal increases by one or more orders of magnitude and the strong main relaxation enters the frequency window. This is the case of the dielectric analogue of glass transition usually called 'α relaxation', as it monitors the segmental mobility of the polymer chains via the relaxation of the dipoles perpendicularly distributed on the main polymer chain [45].  In Figure 9a, we can follow the local γ PPAd located between 10 2 and 10 3 Hz at −110 • C and the segmental α PPAd located between~10 2 and 10 3 Hz at −50 • C by the naked eye for PPAd. The relaxation peaks migrate toward higher frequencies upon increasing temperature (increasing the provided thermal energy) due to acceleration of the corresponding molecular groups. To facilitate a more direct comparison with calorimetry, the raw BDS data (isothermal curves, Figures 9a and 10) can be presented upon replotting to the form of 'isochronal' ε (T) curves. These are shown in Figure 9b for all samples in the initially amorphous state and at f~125 Hz. Therein, PLA exhibits a local and a segmental relaxation, β PLA and α PLA , respectively.
Regarding the situation is the copolymers, the recorded relaxations can be followed in the isothermal ( Figure 10) and isochronal ( Figure 11) plots, that are used for comparisons both between the different copolymer compositions and amorphous-semicrystalline states.
The copolymers' spectra are more complex than those of the individual homopolymers, we have performed critical analysis of the spectra and constructed the molecular mobility maps. These maps show the timescale for all relaxations (i.e., dynamics), in terms of the peak frequency maxima, logf max , against the inverse temperature, 1000/T (otherwise called Arrhenius plots).
In Figure 12, we present the overall maps for the initial PPAd and neat amorphous PLA. Therein, for PLA, β PLA is shown, a local process originating from fluctuations or twisting motions of the -C=O group at the backbone of PLA (inset to Figure 12) [57][58][59]. β PLA exhibits linear behavior (obeying the Arrhenius law) and an activation energy of 50 kJ/mol. At higher temperature, the α PLA is recorded, with its timescale points wellfitted with the VFTH equation (curved line in Figure 12), denoting the cooperative character of the main relaxation. The fragility index for α PLA was estimated m α = 178. Please also note that the good agreement between the BDS points on α PLA relaxation and the calorimetric T g (=51 • C, DSC line in Figure 12). From the BDS points, we may estimate the 'dielectric glass transition temperature' as the point where the extrapolation of the VFTH fitting meets the equivalent frequency of DSC, f eq , with logf eq~− 2.8, as the relaxation time in DSC is 100 s. This way, T g,diel was estimated as~50 • C for PLA.   In Figure 9a, we can follow the local γPPAd located between 10 2 and 10 3 Hz at −110 °C and the segmental αPPAd located between ~10 2 and 10 3 Hz at −50 °C by the naked eye for PPAd. The relaxation peaks migrate toward higher frequencies upon increasing temperature (increasing the provided thermal energy) due to acceleration of the corresponding molecular groups. To facilitate a more direct comparison with calorimetry, the raw BDS data (isothermal curves, Figures 9a and 10) can be presented upon replotting to the form of 'isochronal' ε″(T) curves. These are shown in Figure 9b for all samples in the initially amorphous state and at f ~ 125 Hz. Therein, PLA exhibits a local and a segmental relaxation, βPLA and αPLA, respectively.
Regarding the situation is the copolymers, the recorded relaxations can be followed in the isothermal ( Figure 10) and isochronal ( Figure 11) plots, that are used for comparisons both between the different copolymer compositions and amorphous-semicrystalline states.
Τhe copolymers' spectra are more complex than those of the individual homopolymers, we have performed critical analysis of the spectra and constructed the molecular mobility maps. These maps show the timescale for all relaxations (i.e., dynamics), in terms of the peak frequency maxima, logfmax, against the inverse temperature, 1000/T (otherwise called Arrhenius plots).
In Figure 12, we present the overall maps for the initial PPAd and neat amorphous PLA. Therein, for PLA, βPLA is shown, a local process originating from fluctuations or twisting motions of the -C=O group at the backbone of PLA (inset to Figure 12) [57][58][59]. To the best of our knowledge, the full range timescale map for PPAd is presented here for the first time. In Figure 12, the fastest relaxation is γ PPAd , which is expected to screen the most localized mobility of the polymer. Unfortunately, there are still limited data in the literature on the dynamics of these relatively new class of polymers. By simply comparing the structure-dynamics of PPAd with other polymers exhibiting partial similarities in their structure, such as poly(ethylene glycol)s, poly(n-alkylene acrylate)s [60][61][62][63], we have suggested [26] that γ PPAd could arise from the crankshaft motions of methylene sequences at the chain backbone (inset scheme to Figure 12). γ PPAd follows the Arrhenius trend and the corresponding E act is~43 kJ/mol. At higher temperatures, another local-like was revealed, only via the fitting, as the process is quite weak. Due to the latter, this relaxation could not be resolved (safely) within the copolymers [26]. This process is named β PPAd . The timescale points of β PPAd are almost identical to those for β PLA . Therefore, we suspect that it has similar molecular origins, as PLA and PPAd both carry backbone -C=O groups ( Figure 12, inset scheme). Results from previous works on the similar polymer, poly(butylene adipate) [32,39], provide support for the proposed origins for β PPAd . At T ≥ T g , the segmental α PPAd is recorded. We should report, from the methodological point of view, that α PPAd was fitted by an asymmetric HN term (Equation (3)) with α HN~0 .6-0.7 and β HN~0 .6. As in the case of neat PLA, the dielectric and calorimetric T g values, respectively, −62 and −61 • C, are also quite alike in terms of initial PPAd. Finally, another more retarded and weaker relaxation located close to α PPAd was resolved. The relaxation can also be identified by the naked eye, e.g., in Figures 9b and 11c,d, as a shoulder of α PPAd . The process could be fitted by a symmetric HN term (β HN = 1) with α HN~0 .4-0.6. In Figure 12, its timescale denotes cooperative character, whereas its extrapolation to the f eq of DSC meets the region of the calorimetry T g . These facts denote that this process depends on segmental mobility and is either coupled with α PPAd or a modified version of α PPAd . Thus, the process is named here as α . Recalling the low M n~6 kg/mol of neat PPAd, this 'coupling' of α PPAd and α , resembles the situation between the main relaxations and the so-called Normal Mode relaxation [64][65][66]. Normal Mode arises from the fluctuation of the polymer chain end-to-end vector [57]. The relaxation is mainly recordable for short polymer chains (low M n ) such as those in our case. However, Normal Mode relaxations are generally stronger and narrower (higher α HN ) than α . More work is needed to shed light on the molecular origins of α . βPLA exhibits linear behavior (obeying the Arrhenius law) and an activation energy of ~50 kJ/mol. At higher temperature, the αPLA is recorded, with its timescale points well-fitted with the VFTH equation (curved line in Figure 12), denoting the cooperative character of the main relaxation. The fragility index for αPLA was estimated mα = 178. Please also note that the good agreement between the BDS points on αPLA relaxation and the calorimetric Tg (=51 °C, DSC line in Figure 12). From the BDS points, we may estimate the 'dielectric glass transition temperature' as the point where the extrapolation of the VFTH fitting meets the equivalent frequency of DSC, feq, with logfeq ~ −2.8, as the relaxation time in DSC is ~100 s. This way, Tg,diel was estimated as ~50 °C for PLA. To the best of our knowledge, the full range timescale map for PPAd is presented here for the first time. In Figure 12, the fastest relaxation is γPPAd, which is expected to screen the most localized mobility of the polymer. Unfortunately, there are still limited data in the literature on the dynamics of these relatively new class of polymers. By simply comparing the structure-dynamics of PPAd with other polymers exhibiting partial similarities in their structure, such as poly(ethylene glycol)s, poly(n-alkylene acrylate)s [60][61][62][63], we have suggested [26] that γPPAd could arise from the crankshaft motions of methylene sequences at the chain backbone (inset scheme to Figure 12). γPPAd follows the Arrhenius trend and the corresponding Eact is ~43 kJ/mol. At higher temperatures, another local-like was revealed, only via the fitting, as the process is quite weak. Due to the latter, this relaxation could not be resolved (safely) within the copolymers [26]. This process is named βPPAd. The timescale points of βPPAd are almost identical to those for βPLA. Therefore, we suspect that it has similar molecular origins, as PLA and PPAd both carry backbone -C=O groups (Figure 12, inset scheme). Results from previous works on the similar polymer, poly(butylene adipate) [32,39], provide support for the proposed origins for βPPAd. At T ≥ Tg, the segmental αPPAd is recorded. We should report, from the methodological point At this point, we turn the focus onto the copolymers. The changes imposed on local dynamics in the PLA/PPAd copolymers have been discussed in our previous work [26]. The main focus here is on the main dynamics. Before that, however, we should focus on β PLA . In Figures 10b,d and 11a, β PLA is quite strong in the amorphous state. Upon melt-crystallization, strikingly, the relaxation is almost eliminated. This suggests that the corresponding molecular group (backbone carbonyl) is strongly involved and immobilized within the semicrystalline regions. Interestingly, upon cold-crystallization, β PLA is suppressed as compared to the amorphous state, however, to a lesser extent than the meltcrystallized state. This difference can be rationalized by the lower CF cc as compared to CF mc ( Figure 5a) and/or by the expected looser lamellae packing in the case of cold-crystallization. In previous excellent works by Ezquerra and co-workers [39,67] who studied polyesters, including poly(butylene adipate), similar effects on the local relaxations were revealed, assigned to changes in the chain-chain associations also related to crystallinity.
Focusing on segmental mobility, we follow in the comparative dynamics maps of Figure 13, which at all cases shows that the involvement of crystallization leads to accelerated segmental mobility. In neat PLA (Figure 13a), cold-crystallization accelerates α PLA , while melt-crystallization accelerates it even more. Simultaneously, the cooperativity of α PLA seems to vanish, as manifested by the transition from the VFTH behavior (amorphous) to linear Arrhenius-like behavior (semicrystalline). Qualitatively similar effects are recorded on the α relaxation in the copolymers, α copol , whereas an opposite impact as compared to neat PLA is recorded in the copolymers, within which, cold-crystallization leads to more extensive acceleration than the melt-crystallization. Obviously, the strength of the main relaxation is suppressed upon crystallization in all cases. Due to this strength suppression, we were able to distinguish double segmental dynamics in the semicrystalline copolymers 85/15 and 75/25. We recall that in the amorphous state, only 75/25 exhibited two relaxations, α copol and α PPAd [26]. This was evaluated as an indication of nanophase separation for 75/25 [26].
In Figure 14, we concentrate the overall dynamics data in terms of T g,diel ( Figure 14a) and fragility (cooperativity, Figure 14b). The impact of PPAd addition is systematically the acceleration in dynamics and suppression in fragility (mainly the vanishing of cooperativity). These effects are strongly enhanced, i.e., in the same direction, when crystallization is implemented.
These are non-trivial effects imposed by crystallization, at least for conventional polymers/homopolymers, as the presence of crystallites is considered a factor that tends to decelerate the segmental mobility [68].
We should keep in mind that, upon crystallization, the fraction of mobile amorphous PLA is decreasing. Thus, at first approximation, the plasticization effect of PPAd within the amorphous areas could be more pronounced, as compared to the fully amorphous state (Scan 3). One scenario that could further explain the overall data on mobility and crystallization is in terms of spatial confinements and constraints imposed by crystallization on the amorphous PLA and PLA-PPAd chains. The spatial confinement would have a strong impact when the amorphous zones formed between the crystallites are of dimensions comparable to the cooperativity length, ξ, [16,69] namely, some nanometers [70][71][72][73][74]. Values in such a situation cannot be easily checked, especially, the dimensions of the inter-chain distances in particular. The advanced structural characterization technique of small-angle X-ray scattering could provide further insight on this point [75,76].
The results shown in Figures 13 and 14 can also be discussed from an alternative point of view for the copolymers. It is interesting that upon crystallization, the segmental dynamics tend to approach the fast dynamics of the initial PPAd. Considered together with the mobility maps, the shape parameters and the temperature dependences on α copol (not shown), we suspect that upon crystallization, the mobility of PLA (i.e., the contribution of α PLA to α copol ) vanishes. The effect is stronger for cold-crystallization in the copolymers. Due to that, a weaker relaxation was revealed, the timescale of which resembles that of α PPAd . This could be the modified, decelerated, version of bulky α PPAd in the copolymers [26,33]. According to this scenario, partly compatible with the previous one, the majority of PLA is 'dielectrically immobilized' within the formed crystals and both the local backbone groups and the overall chains are dielectrically inactive (vanishing of β PLA and α PLA ). In this context, the PLA-like segmental dynamics disappears and the 'semicrystalline' α relaxation is dominated by the PPAd-phases. This implies that crystallization of the PLA-rich phases leads to some kind of further phase separation of the PPAd segments, which are more active, at least dielectrically.   In Figure 14, we concentrate the overall dynamics data in terms of Tg,diel ( Figure 14a) and fragility (cooperativity, Figure 14b). The impact of PPAd addition is systematically the acceleration in dynamics and suppression in fragility (mainly the vanishing of cooperativity). These effects are strongly enhanced, i.e., in the same direction, when crystallization is implemented. These are non-trivial effects imposed by crystallization, at least for conventional polymers/homopolymers, as the presence of crystallites is considered a factor that tends to decelerate the segmental mobility [68].
We should keep in mind that, upon crystallization, the fraction of mobile amorphous PLA is decreasing. Thus, at first approximation, the plasticization effect of PPAd within the amorphous areas could be more pronounced, as compared to the fully amorphous state (Scan 3). One scenario that could further explain the overall data on mobility and crystallization is in terms of spatial confinements and constraints imposed by crystallization on the amorphous PLA and PLA-PPAd chains. The spatial confinement would have a strong impact when the amorphous zones formed between the crystallites are of dimensions comparable to the cooperativity length, ξ, [16,69] namely, some nanometers [70][71][72][73][74]. Values in such a situation cannot be easily checked, especially, the dimensions of the interchain distances in particular. The advanced structural characterization technique of smallangle X-ray scattering could provide further insight on this point [75,76]. In this context, it is worthy to note that from the methodological point of view, the significant mismatch between the calorimetric and the dielectric T g in the case of copolymers upon crystallization is shown in Figure 14a. Despite the general comment involving the 'in principle' different techniques that follow different modes (thermal events vs. dielectric relaxations) [56,59,77], we gain indications that, most probably, DSC is able to record the amorphous part of PLA (high calorimetric T g ), whereas BDS is not. Thus, the T g,diel in the semicrystalline state mainly follow the dynamics of PPAd (lower T g in Figure 14a).
A final point worthy of discussion refers to the ionic conductivity effects in Figures 10 and 11. Therein, it follows that a sharp increase in the dielectric signal is recorded at temperatures well above T g . As mentioned previously, this originates in the transportation of small charges (ions) throughout the sample. Obviously, the transportation of ions can take place only via the rubbery domains. In the copolymer, the ionic conductivity always dominates the signal at T > T g of the copolymer. In none of the samples, amorphous or semicrystalline states, do we record a contribution of the ionic conductivity at lower temperatures, in particular at T > T g of initial PPAd. This more macroscopic observation suggests, on the one hand, that the PLA-PPAd distribution is excellent, and, on the other hand, in any state, there is no continuity of the pure PPAd phase throughout the copolymer's volume. A similar situation had been recorded in a previous work on PLA/poly(butylene adipate) diblock copolymers [32]. On the contrary, in polymeric blends of PLA and poly(ethylene adipate) (PEAd), exhibiting partial miscibility, we recorded significant continuous paths of PEAd throughout the copolymer volume, as manifested by strong ionic conductivity arising from PEAd [33].

Conclusions
Diblock copolymers of PPAd and PLA, prepared by ROP of lactic acid onto PPAd segments of low M n , are studied here regarding crystallization-induced effects on molecular mobility. In the amorphous state, the materials were found to be homogeneous with the PPAd playing a plasticization role on T g , systematically lowering with PPAd. Upon carefully chosen crystallization treatments, isothermal melt-and cold-crystallization, as well as non-isothermal crystallization, an interesting effect was revealed. T g is significantly suppressed in the presence of crystals, by 8 to 50 K. This effect is, at first glance, controversial as the crystals usual hinder the chains' mobility, leading to the elevation of the T g . The T g drop was, interestingly, found to be facilitated by the increasing PPAd amount in the copolymers. For the highest amount of PPAd (25%), partial phase nano-separation was revealed, only by BDS [26], via the individual recording of the weak α PPAd relaxation next to the bulk-like α copol . This is here proposed to be responsible for the formation of smaller crystals, not being able to completely fill the whole sample's volume. The phase separation was also recorded upon crystallization, for 25% and 15% PPAd, as the PLA-originating dielectric response was suppressed overall, and that of PPAd rose 'artificially'. Upon crystallization, the fragility index of segmental dynamics was found to severely decrease, and in some cases, to even vanish. The overall effects suggest the involvement of spatial nanoconfinement of the amorphous polymer between the spherulites or, in a more complex situation, involving additional PLA/PPAd separation driven by the crystal's formation. Overall, crystallization seems to make PPAd the dominant polymer over PLA in terms of the mobility of the copolymers. This is found true for both the segmental and the local mobility, as, for example, the local β PLA is quite strong in the amorphous state and almost vanishes upon crystallization. This scenario enabled the rationalizing of the significant discrepancy regarding T g as recorded between DSC and BDS, with the dielectric T g being lower in all copolymers than the calorimetric one.