Solid-State Nuclear Magnetic Resonance (NMR) and Nuclear Magnetic Relaxation Time Analyses of Molecular Mobility and Compatibility of Plasticized Polyhydroxyalkanoates (PHA) Copolymers

The molecular mobility and compatibility of plasticized polyhydroxyalkanoates (PHA) were investigated, focusing on changes due to copolymerization using either flexible poly (butylene succinate) (PBS) or rigid poly(lactic acid) (PLA) units. For the case of a poly(3-hydroxybutyrate) (PHB) unit in plasticized PHA, copolymerization of either PBS or PLA decreased 1H and 13C spin-lattice relaxation times in the laboratory frame (T1H and T1C) in the same manner, while PBS produced a lower 1H spin-lattice relaxation time in the rotating frame (T1ρH) than PLA. Both the signals of 1H MAS (magic-angle spinning) and 13C PST (pulse saturation transfer) MAS nuclear magnetic resonance (NMR) spectra were sharpened and increased by copolymerization with PBS. A variable temperature relaxation time analysis showed that the decrease of T1H values was dominated by the 1H spin diffusion via the interface between PHB and the added polyester because of the good compatibility. Meanwhile, the decrease of T1C values was dominated by increasingly rapid molecular motions of PHB because of the lowered crystallinity due to the plasticization. Slow molecular motions (kHz order) were enhanced more by the addition of PBS than PLA, although rapid molecular motions (MHz order) were enhanced by either polyester. Several NMR parameters were beneficial for analyzing the manufacturing process as the indexes of polymer compatibility and molecular motions.


Introduction
For the development of a post-petroleum society, recycling resources from biomass is a high priority. Poly(lactic acid) (PLA) is the most popular biomass-based polymer and is used for daily necessities; however, there is a problem of food security because of the use of edible starch as a main raw material. As one solution to this problem, polyhydroxyalkanoates (PHA) have attracted attention as a biomass-based polymer made from non-edible materials. PHA is the generic name for a biopolyester family, consisting of the following polymers, poly(3-hydroxybutylate) (PHB) and poly(3-hydroxyvalerate) (PHV), including their isomeric polymers and co-polymers; the characteristic properties of PHA resulting from the chain length and composition could be tuned to various industrial applications [1]. Microbial production is the most commonly used method for supplying PHA; not only carbohydrates but also fatty acids were used as the carbon source depending on the bacterial strain employed [2][3][4]. For mechanical applications, crystal structures and crystallization kinetics have The crushed sample was placed on a sample holder and then the X-ray diffraction (XRD) under Cu Kα irradiation was measured on a RINT-Ultima II diffratometer (Rigaku Co. Ltd., Tokyo, Japan). The diffratometer was operating at 40 kV and 40 mA and the diffractogram was recorded at 2θ angles between 5 • and 40 • .

Nuclear Magnetic Resonance (NMR) Measurements at Ambient Temperature
Solution nuclear magnetic resonance (NMR) spectra were measured on a Varian INOVA-300 (Palo Alto, CA, USA) with a Varian 5 mm four-nucleus auto-NMR triple-resonance liquid probe in CDCl 3 as a solvent. 1 H NMR spectra were collected at 299.95 MHz with a 7.0 µs π/2 pulse for the 1 H nuclei and 3.74 s acquisition period over a 4.5 kHz spectra width with 1.2 s recycle delay in 16-128 transients. 13 C NMR spectra were collected at 75.43 MHz with a 6.5 µs π/2 pulse for the 13 C nuclei and 1.82 s acquisition period over a 16.5 kHz spectra width with 1.19 s recycle delay in 2048-15,000 transients.
Solid-state NMR spectra were measured on a Varian 400 NMR system spectrometer (Palo Alto, CA, USA) with a Varian 4 mm double-resonance T3 solid probe. The samples were placed in a 4 mm ZrO 2 rotor spun at 15 kHz over a temperature range of 20-22 • C. Solid-state 13 C MAS NMR spectra were measured at 100.56 MHz for the 13 C nuclei and were collected with a 40 ms acquisition period over a 30.7 kHz spectral width in 1024-2048 transients. Proton decoupling was performed with an 86 kHz 1 H decoupling radio frequency with a small phase incremental alteration (SPINAL) decoupling pulse sequence. The cross polarization and magic angle spinning (CP-MAS) NMR spectra were measured with a 5.0 s recycle delay using a ramped-amplitude pulse sequence with a 2 ms contact time and a 2.5 µs π/2 pulse for the 1  angle spinning (PST-MAS) NMR spectra were measured with a 2.6 µs π/2 pulse for the 13 C nuclei with a 5 s recycle delay after saturation of 1 H nuclei with 13 consecutive 2.5 µs pulses and a 27.5 µs delay.

Nuclear Magnetic Relaxation Time Analyses
The 1 H spin-lattice relaxation time in the laboratory frame (T 1 H) was indirectly measured via detection of 13 C resonance enhanced by cross-polarization, applied after a π pulse to 1 H nuclei with the inversion recovery method. The 13 C spin-lattice relaxation time in the laboratory frame (T 1 C) was measured with the conventional Torchia's pulse sequence [28]. The 1 H spin-lattice relaxation time in the rotating frame (T 1ρ H) was indirectly measured via detection of 13 C resonance enhanced by cross-polarization applied after a π/2-τ-spin lock pulse (86 kHz of radio frequency) with variable spin lock times over a range of 100-8000 µs. The relaxation time analyses were performed with the same solid-state probe with the same contact time and acquisition period used for the 13 C CP-MAS NMR spectrum.

Variable Temperature Solid-State NMR and Relaxation Time Measurements
Variable temperature solid-state NMR spectra and relaxation times were also measured on the same spectrometer and probe as the ambient temperature measurements. Low-temperature measurement was started at a low temperature side of −40 • C and the temperature increased to 10 • C. High-temperature measurement was started at a low temperature side of 30 • C and heating to 50 • C. One step of heating consisted of 10 • C ( 1 H MAS NMR, T 1 H, T 1 C high temperature) or 20 • C (T 1 C low temperature). The samples were placed in a 4 mm ZrO 2 rotor spun at 12 kHz (low temperature) and 15 kHz (high temperature) under nitrogen flow. Low temperature 1 H MAS NMR spectra were measured at 399.88 MHz for the 1 H nuclei and were collected with a 2.9 µs π/2 pulse for the 1 H nuclei and 20 ms acquisition period over a 30.5 kHz spectral width in 4 transients, and a 3 s recycle delay. Low and high temperature T 1 H and T 1 C were measured using the same acquisition parameters as described above. Each low and high temperature measurement was performed independently because it was difficult to control low temperature for a long time due to the use for liquid nitrogen.

Polymer Properties of Plasticized Polyhydroxyalkanoates (PHA) Pellets
The pre-plasticized PHB pellet showed poor processability because of stiffness and low solubility. Copolymerization with the biodegradable polyesters, PBS and PLA, improved the mechanical properties of PHA. According to the catalog specification values, copolymerization with PBS increased elongation and Izod impact strength, while copolymerization with PLA increased melt flow rate and flexural modulus. Actually, when installing a sample into the solid-state NMR rotor, the pre-plasticized PHB was difficult to cut and/or crush, even though the plasticized PHA copolymers were easily deformable to prepare a solid-state NMR sample.
In order to determine in detail the constituents of the plasticized PHA pellets connected with the mechanical properties, solution NMR spectra were measured in CDCl 3 . Figure 1a shows 1 H NMR spectra of the pre-plasticized PHB and the plasticized PHA pellets. The PHA4422P pellet (3) showed three PHB signals, doublet (CH 3 , 1.28 ppm), quartet-doublet (CH 2 , 5.24 ppm), and quartet (CH, 5.26 ppm), which can be also observed for the original PHB (1). PHA4422P also had small amount of poly(4-hydrobutyrate) (P4HB) [29], and the added PBS for the copolymerization. One can see a trace peak at 0.98 ppm, in which region a CH 3 group of PHA having long alkyl groups might appear; however, the actual structure could not be assigned at this time. Meanwhile, 1 H NMR spectra also indicated that the PHA5533L pellet (4) consisted of PHB, the added PLA, and a small amount of PBS and P4HB. Minor constituents in each pellet could be confirmed by 13 C NMR spectra (Figure 1b). The signals of P4HB in both PHA4422P (3) and PHA5533L (4) also appeared not only in the aliphatic region but also in the carbonyl region. The improvement of mechanical properties due to the copolymerization with the biodegradable polyesters could be explained by a change of thermal characteristics. Figure 2 shows the DSC curves for the modified PHA pellets and the reference polymers. The melting peak (Tm) of the original PHB (1) appeared at a relatively high temperature (174 °C) with no other endothermic and exothermic peaks. Of the constituent polyesters used for the copolymerization, PBS (2) had a lower Tm (112 °C) while PLA (5) also had a high Tm (171 °C). Interestingly, the copolymerization resulted in a decrease of Tm to a value lower than the initial Tm of the constituent polyesters, although the heat capacities of both plasticized PHA pellets were smaller than the original PHB. The PHA4422P pellet (3) had a lower Tm (89 °C) with higher temperature small endothermic peaks. In contrast, the PHA5533L pellet (4) had a glass transition peak with relaxation (Tg: 64 °C) and cold crystallization (Tcc: 95 °C), and a quite high Tm (150 °C). Considering the DSC results together with the solution NMR, small amounts of P4HB and PBS were extremely effective for changing the thermal properties of the PHA5533L pellet. Moreover, the DSC results showed that the plasticization of PHA improved processability because of the decrease of Tm (PBS) or Tg (PLA).   The improvement of mechanical properties due to the copolymerization with the biodegradable polyesters could be explained by a change of thermal characteristics. Figure 2 shows the DSC curves for the modified PHA pellets and the reference polymers. The melting peak (T m ) of the original PHB (1) appeared at a relatively high temperature (174 • C) with no other endothermic and exothermic peaks. Of the constituent polyesters used for the copolymerization, PBS (2) had a lower T m (112 • C) while PLA (5) also had a high T m (171 • C). Interestingly, the copolymerization resulted in a decrease of T m to a value lower than the initial T m of the constituent polyesters, although the heat capacities of both plasticized PHA pellets were smaller than the original PHB. The PHA4422P pellet (3) had a lower T m (89 • C) with higher temperature small endothermic peaks. In contrast, the PHA5533L pellet (4) had a glass transition peak with relaxation (T g : 64 • C) and cold crystallization (T cc : 95 • C), and a quite high T m (150 • C). Considering the DSC results together with the solution NMR, small amounts of P4HB and PBS were extremely effective for changing the thermal properties of the PHA5533L pellet. Moreover, the DSC results showed that the plasticization of PHA improved processability because of the decrease of T m (PBS) or T g (PLA). The improvement of mechanical properties due to the copolymerization with the biodegradable polyesters could be explained by a change of thermal characteristics. Figure 2 shows the DSC curves for the modified PHA pellets and the reference polymers. The melting peak (Tm) of the original PHB (1) appeared at a relatively high temperature (174 °C) with no other endothermic and exothermic peaks. Of the constituent polyesters used for the copolymerization, PBS (2) had a lower Tm (112 °C) while PLA (5) also had a high Tm (171 °C). Interestingly, the copolymerization resulted in a decrease of Tm to a value lower than the initial Tm of the constituent polyesters, although the heat capacities of both plasticized PHA pellets were smaller than the original PHB. The PHA4422P pellet (3) had a lower Tm (89 °C) with higher temperature small endothermic peaks. In contrast, the PHA5533L pellet (4) had a glass transition peak with relaxation (Tg: 64 °C) and cold crystallization (Tcc: 95 °C), and a quite high Tm (150 °C). Considering the DSC results together with the solution NMR, small amounts of P4HB and PBS were extremely effective for changing the thermal properties of the PHA5533L pellet. Moreover, the DSC results showed that the plasticization of PHA improved processability because of the decrease of Tm (PBS) or Tg (PLA).    The copolymerization with the biodegradable polyesters also changed the crystallinity of the PHA. Figure 3 shows changes in the XRD patterns of PHA by the addition of other polyesters. The original PHB (1) had moderate crystallinity, showing orthorhombic crystal planes with major sharp peaks at 2θ = 13.5 • (020) and 16.9 • (110). After the copolymerization of PHA with PBS [PHA4422P (3)], new peaks that originated from PBS appeared at 2θ = 19.6 • (020) and 22.6 • (110) overlapped with the (021) and (111) peaks of PBS [30]. At the same time, the amorphous peak of PHA clearly increased. The copolymerization of PHA with PLA [PHA5533L (4)] increased further the amorphous peak of PHA; only a small peak of PLA was observed at 2θ = 16.4 • (100) [24]. In both cases of PHA4422P and PHA5533L, characteristic XRD peaks from P4HB could not be assigned. The XRD results showed that the copolymerization of both biodegradable polymers decreased the crystallinity of PHA and that the decrease was more pronounced for the copolymerization with PLA than with PBS. The copolymerization with the biodegradable polyesters also changed the crystallinity of the PHA. Figure 3 shows changes in the XRD patterns of PHA by the addition of other polyesters. The original PHB (1) had moderate crystallinity, showing orthorhombic crystal planes with major sharp peaks at 2θ = 13.5° (020) and 16.9° (110). After the copolymerization of PHA with PBS [PHA4422P (3)], new peaks that originated from PBS appeared at 2θ = 19.6° (020) and 22.6° (110) overlapped with the (021) and (111) peaks of PBS [30]. At the same time, the amorphous peak of PHA clearly increased. The copolymerization of PHA with PLA [PHA5533L (4)] increased further the amorphous peak of PHA; only a small peak of PLA was observed at 2θ = 16.4° (100) [24]. In both cases of PHA4422P and PHA5533L, characteristic XRD peaks from P4HB could not be assigned. The XRD results showed that the copolymerization of both biodegradable polymers decreased the crystallinity of PHA and that the decrease was more pronounced for the copolymerization with PLA than with PBS.

13 C Magic-Angle Spinning (MAS) NMR of Plasticized PHA Copolymers and Constituent Polymers
Solid-state 13 C NMR is a powerful tool for analyzing the crystallinity and mobility of polymer chains. The 13 C CP-MAS NMR variant is commonly used in polymer science; it utilizes the magnetization transfer from 1 H nuclei to 13 C nuclei, enhancing the signal of a rigid substituent. Figure 4a shows 13 C CP-MAS NMR spectra of plasticized PHA copolymers and constituent polymers. Each signal for the polymer constituents, PHB (1), PBS (2) and PLA (5) could be effectively detected in the 13 C CP-MAS NMR spectra regardless of the flexibility and the rigidity of each polymer. The 13 C CP-MAS signals of the plasticized PHA4422P (3) could be assigned as PHB and PBS, while those of the plasticized PHA5533L (4) as PHB, PLA, and PBS. The isomeric polymer P4HB could be also detected in both PHA4422P (3) and PHA5533L (4).
Meanwhile, 13 C PST-MAS NMR is a method utilizing the nuclear Overhauser effect, resulting in the enhancement of a signal of a substituent having high mobility near a hydrogen atom [27]. Figure  4b shows 13 C PST-MAS NMR spectra of plasticized PHA copolymers and constituent polymers. Actually, the CH3 group of PLA (5) and the OCH2CH2 group of PBS (2) showed larger intensities than other substituents because the amplitudes of their molecular motions were higher. For the pre-plasticized PHB (1), the CH3 group had a high signal intensity compared to the other signals. Interestingly, the copolymerization of PHA with PBS [PHA4422P (3)] increased the signal from CH2 and CH3 groups accompanied by the appearance of signals from the minor isomeric polymer P4HB. In both PHA (1) and PHA4422P (3), trace signals appeared at the higher field near the CH3 groups' signal. These small signals originated from trace amounts of PHA having long alkyl groups. In contrast, the copolymerization of PHA with PLA [PHA5533L (4)] did not increase the CH2 and CH3 groups' signals but only gave the sum of the signals of PHA, P4HB, PLA, and PBS. The results of the

13 C Magic-Angle Spinning (MAS) NMR of Plasticized PHA Copolymers and Constituent Polymers
Solid-state 13 C NMR is a powerful tool for analyzing the crystallinity and mobility of polymer chains. The 13 C CP-MAS NMR variant is commonly used in polymer science; it utilizes the magnetization transfer from 1 H nuclei to 13 C nuclei, enhancing the signal of a rigid substituent. Figure 4a shows 13 C CP-MAS NMR spectra of plasticized PHA copolymers and constituent polymers. Each signal for the polymer constituents, PHB (1), PBS (2) and PLA (5) could be effectively detected in the 13 C CP-MAS NMR spectra regardless of the flexibility and the rigidity of each polymer. The 13 C CP-MAS signals of the plasticized PHA4422P (3) could be assigned as PHB and PBS, while those of the plasticized PHA5533L (4) as PHB, PLA, and PBS. The isomeric polymer P4HB could be also detected in both PHA4422P (3) and PHA5533L (4).
Meanwhile, 13 C PST-MAS NMR is a method utilizing the nuclear Overhauser effect, resulting in the enhancement of a signal of a substituent having high mobility near a hydrogen atom [27]. Figure 4b shows 13 C PST-MAS NMR spectra of plasticized PHA copolymers and constituent polymers. Actually, the CH 3 group of PLA (5) and the OCH 2 CH 2 group of PBS (2) showed larger intensities than other substituents because the amplitudes of their molecular motions were higher. For the pre-plasticized PHB (1), the CH 3 group had a high signal intensity compared to the other signals. Interestingly, the copolymerization of PHA with PBS [PHA4422P (3)] increased the signal from CH 2 and CH 3 groups accompanied by the appearance of signals from the minor isomeric polymer P4HB. In both PHA (1) and PHA4422P (3), trace signals appeared at the higher field near the CH 3 groups' signal. These small signals originated from trace amounts of PHA having long alkyl groups. In contrast, the copolymerization of PHA with PLA [PHA5533L (4)] did not increase the CH 2 and CH 3

Spin-Lattice Relaxation Times in the Laboratory Frame of Plasticized PHA Copolymers and Constituent Polymers
The 1 H spin-lattice relaxation time in the laboratory frame (T1H) is reduced by rapid molecular motions matched to the Larmor frequency. For example, the 1 H spin-lattice relaxation in the laboratory frame (T1H relaxation) of PLA is promoted by the rotation of a CH3 group around its C3 axis. Moreover, the T1H value of each substituent in the same polymer chain adopts an averaged value because of 1 H spin diffusion. Figure 5a shows T1H values of plasticized PHA copolymers and constituent polymers. As described in the above paragraph, the T1H values of PLA (5) were averaged by the spin diffusion to have almost the same values (1.1 s) due to the T1H relaxation via the rotation of the CH3 group. Although the T1H values of PBS (2) also showed averaged values (1.2 s) similar to PLA, the T1H relaxation of PBS cannot be explained directly by molecular motions of a specific substituent, such as a CH3 group. Moreover, the T1H values of PHB (1) had longer averaged values (2.0 s) even though the T1H relaxation occurred via the motion of CH3 group. The different T1H values of PLA (5) and PHB (1) having the same T1H relaxation route were due to whether the frequency of CH3 motion matched the Larmor frequency, or not.
Copolymerization with the biodegradable polyesters significantly decreased the T1H values of PHB. For the plasticized PHA4422P (3)

Spin-Lattice Relaxation Times in the Laboratory Frame of Plasticized PHA Copolymers and Constituent Polymers
The 1 H spin-lattice relaxation time in the laboratory frame (T 1 H) is reduced by rapid molecular motions matched to the Larmor frequency. For example, the 1 H spin-lattice relaxation in the laboratory frame (T 1 H relaxation) of PLA is promoted by the rotation of a CH 3 group around its C 3 axis. Moreover, the T 1 H value of each substituent in the same polymer chain adopts an averaged value because of 1 H spin diffusion. Figure 5a shows T 1 H values of plasticized PHA copolymers and constituent polymers. As described in the above paragraph, the T 1 H values of PLA (5)  These T 1 H reductions were caused by the enhancement of the T 1 H relaxation due to the heterogeneity that arose from the amorphous moiety, as we have previously described for PLA copolymer fibers [24]. These T1H reductions were caused by the enhancement of the T1H relaxation due to the heterogeneity that arose from the amorphous moiety, as we have previously described for PLA copolymer fibers [24]. The 13 C spin-lattice relaxation time in the laboratory frame (T1C) can provide information on molecular motions for each substituent more directly because it excludes the effect of 1 H spin diffusion. Figure 5b shows T1C values of plasticized PHA copolymers and constituent polymers. One can see a different T1C value for each substituent in the pre-plasticized PHB (1): C=O, 37 s; CH, 89 s; CH2, 92 s; CH3, 2.4 s. The T1C value of CH3 nearly equaled the T1H (2.0 s) value because the 13 C spin-lattice relaxation (T1C relaxation) was also promoted by the CH3 rotation, the same as for the T1H relaxation. This closeness between the T1C relaxation of CH3 and the T1H due to the CH3 rotation also arose in PLA (5) (T1C, 1.4 s; T1H, 1.1); however, the C=O group (56 s) showed a longer value than the CH group (38 s) in PLA, unlike the pre-plasticized PHB. One can also see the longer T1C value of the C=O group (64 s) and moderate T1C values of CH2 groups (15-30 s) in PBS (2). Although PBS had high flexibility, the molecular motion of each substituent did not match with the Larmor frequency of the 13 C nuclei.
The reduction of T1C values due to the copolymerization was also observed not only in PHA4422P (3)  the T1C values of the PLA unit CH3 in PHA5533L (4) were slightly reduced by the copolymerization, compared with the original T1C values. Since the copolymerization with either PBS or PLA decreased the crystallinity of the PHB unit (Figure 3), the reduction of the T1C values of the PHB unit could be also explained by a change of T1C relaxation due to the heterogeneity arising from the amorphous moiety. We will discuss the relationship of the heterogeneity with the compatibility of the copolymer components and molecular mobility later. The 13 C spin-lattice relaxation time in the laboratory frame (T 1 C) can provide information on molecular motions for each substituent more directly because it excludes the effect of 1 H spin diffusion. Figure 5b shows T 1 C values of plasticized PHA copolymers and constituent polymers. One can see a different T 1 C value for each substituent in the pre-plasticized PHB (1): C=O, 37 s; CH, 89 s; CH 2 , 92 s; CH 3 , 2.4 s. The T 1 C value of CH 3 nearly equaled the T 1 H (2.0 s) value because the 13 C spin-lattice relaxation (T 1 C relaxation) was also promoted by the CH 3 rotation, the same as for the T 1 H relaxation. This closeness between the T 1 C relaxation of CH 3 and the T 1 H due to the CH 3 rotation also arose in PLA (5) (T 1 C, 1.4 s; T 1 H, 1.1); however, the C=O group (56 s) showed a longer value than the CH group (38 s) in PLA, unlike the pre-plasticized PHB. One can also see the longer T 1 C value of the C=O group (64 s) and moderate T 1 C values of CH 2 groups (15-30 s) in PBS (2). Although PBS had high flexibility, the molecular motion of each substituent did not match with the Larmor frequency of the 13 C nuclei.
The reduction of T 1 C values due to the copolymerization was also observed not only in PHA4422P (3) but also in PHA5533L (4) (3) and the T 1 C values of the PLA unit CH 3 in PHA5533L (4) were slightly reduced by the copolymerization, compared with the original T 1 C values. Since the copolymerization with either PBS or PLA decreased the crystallinity of the PHB unit (Figure 3), the reduction of the T 1 C values of the PHB unit could be also explained by a change of T 1 C relaxation due to the heterogeneity arising from the amorphous moiety. We will discuss the relationship of the heterogeneity with the compatibility of the copolymer components and molecular mobility later.

Spin-Lattice Relaxation Time in the Rotating Frame of Plasticized PHA Copolymers and Constituent Polymers
The 1 H spin-lattice relaxation in the rotating frame (T 1ρ H relaxation) is promoted by molecular motions near the spin-locking frequency, which is much less than the Larmor frequency. That is, the 1 H spin-lattice relaxation time in the rotating frame (T 1ρ H) is affected more than the T 1 H value by slower molecular motions, such as the main chain motion of polymers. Figure 6 shows T 1ρ H values of plasticized PHA copolymers and constituent polymers. The significant decreases of the T 1 H values for PHB due to the copolymerization with PBS and PLA were also observed for the T 1ρ H values. The original PHB (1)

Spin-lattice Relaxation Time in the Rotating Frame of Plasticized PHA Copolymers and Constituent Polymers
The 1 H spin-lattice relaxation in the rotating frame (T1ρH relaxation) is promoted by molecular motions near the spin-locking frequency, which is much less than the Larmor frequency. That is, the 1 H spin-lattice relaxation time in the rotating frame (T1ρH) is affected more than the T1H value by slower molecular motions, such as the main chain motion of polymers. Figure 6 shows T1ρH values of plasticized PHA copolymers and constituent polymers. The significant decreases of the T1H values for PHB due to the copolymerization with PBS and PLA were also observed for the T1ρH values. The original PHB (1)   As shown above, since the spin-lattice relaxation times in the laboratory frame (T1H and T1C) showed a similar trend between PHA4422P (PBS) and PHA5533L (PLA), rapid molecular motions (MHz) matched with the Larmor frequency in both plasticized PHA copolymers was enhanced by the plasticization. On the other hand, the spin-lattice relaxation time in the rotating frame (T1ρH) decreased more in PHA4422P. Therefore, the plasticization with the flexible PBS enhanced slow molecular motions (kHz) corresponding to the spin-locking frequency more than did PLA. We previously discussed the correlation of increase of the PST-MAS signals and T1ρH values for phenol formaldehyde resin-impregnated soft wood [25]. Similar to this previous result, the increases of the 13 C PST-MAS NMR signals here could be explained by the enhancement of slow molecular motions (kHz) due to the plasticization with PBS. We will discuss the increase of 1 H MAS NMR signals related to the slow molecular motion in the next subsection.  As shown above, since the spin-lattice relaxation times in the laboratory frame (T 1 H and T 1 C) showed a similar trend between PHA4422P (PBS) and PHA5533L (PLA), rapid molecular motions (MHz) matched with the Larmor frequency in both plasticized PHA copolymers was enhanced by the plasticization. On the other hand, the spin-lattice relaxation time in the rotating frame (T 1ρ H) decreased more in PHA4422P. Therefore, the plasticization with the flexible PBS enhanced slow molecular motions (kHz) corresponding to the spin-locking frequency more than did PLA. We previously discussed the correlation of increase of the PST-MAS signals and T 1ρ H values for phenol formaldehyde resin-impregnated soft wood [25]. Similar to this previous result, the increases of the 13 C PST-MAS NMR signals here could be explained by the enhancement of slow molecular motions (kHz) due to the plasticization with PBS. We will discuss the increase of 1 H MAS NMR signals related to the slow molecular motion in the next subsection. Figure 7 shows variable temperature 1 H MAS NMR spectra of plasticized PHA copolymers and constituent polymers. Because of strong dipolar-dipolar interactions of 1 H nuclei with each other, the 1 H signals in the solid-state NMR appear as broad overlapped signals. The original PHB (1) showed only such signals, which changed little with increasing temperature; the CH 3 signal sharpened and increased and the broader peaks in the CH and CH 2 regions decreased at the same time. This showed that the molecular mobility of PHB (1) alone remained almost unchanged by the temperature rise. For the flexible PBS (2), however, every signal significantly sharpened and increased with increasing temperature, even though only very broad and weak peaks appeared at low temperatures (−40 • C). That is, the mobility of flexible PBS (2) was greatly affected by the temperature rise, resulting in a sharpened and larger 1 H MAS signals. Interestingly, the copolymerization of PHA with PBS [PHA4422P (3)] enlarged and sharpened the signals of not only the PBS unit but also the PHB unit. The rate of increase of the 1 H signals for both PHA and PBS units in PHA4422P (3) was greater than for PBS (2) alone; thus, the copolymerization of PHA with PBS increased the mobility of not only the PHA unit but also the PBS unit compared with the original polymers. Meanwhile, the 1 H signal intensity of rigid PLA (5) decreased with increasing temperature as seen for woody materials [26,27]. These 1 H signal decreases may occur due to sensitivity change of the detecting coil in the probe; now, we are still searching other reasons related to the magnetic relaxation. The plasticized PHA5533L (4) showed only the overlapped 1 H signal of PHB and PLA units, which simply changed in the same manner as each polymer alone, with no increase in signal or sharpness. According to the variable 1 H MAS NMR results, the flexibility of the polymer significantly enhanced slow molecular motions (kHz) corresponding to the T 1ρ H relaxation, resulting in sharp and large 1 H signals after plasticization with PBS. The slow molecular motion (kHz order) corresponded to the motion of polymer chains, which was enhanced at temperatures over −10 • C. sharpened and increased and the broader peaks in the CH and CH2 regions decreased at the same time. This showed that the molecular mobility of PHB (1) alone remained almost unchanged by the temperature rise. For the flexible PBS (2), however, every signal significantly sharpened and increased with increasing temperature, even though only very broad and weak peaks appeared at low temperatures (−40 °C). That is, the mobility of flexible PBS (2) was greatly affected by the temperature rise, resulting in a sharpened and larger 1 H MAS signals. Interestingly, the copolymerization of PHA with PBS [PHA4422P (3)] enlarged and sharpened the signals of not only the PBS unit but also the PHB unit. The rate of increase of the 1 H signals for both PHA and PBS units in PHA4422P (3) was greater than for PBS (2) alone; thus, the copolymerization of PHA with PBS increased the mobility of not only the PHA unit but also the PBS unit compared with the original polymers. Meanwhile, the 1 H signal intensity of rigid PLA (5) decreased with increasing temperature as seen for woody materials [26,27]. These 1 H signal decreases may occur due to sensitivity change of the detecting coil in the probe; now, we are still searching other reasons related to the magnetic relaxation. The plasticized PHA5533L (4) showed only the overlapped 1 H signal of PHB and PLA units, which simply changed in the same manner as each polymer alone, with no increase in signal or sharpness. According to the variable 1 H MAS NMR results, the flexibility of the polymer significantly enhanced slow molecular motions (kHz) corresponding to the T1ρH relaxation, resulting in sharp and large 1 H signals after plasticization with PBS. The slow molecular motion (kHz order) corresponded to the motion of polymer chains, which was enhanced at temperatures over −10 °C.

Changes of Spin-Lattice Relaxation Times in the Laboratory Frame with Rising Temperature
In order to investigate the rapid molecular motions (MHz) that participated in the spin-lattice relaxation in the laboratory frame, rising temperature T1H and T1C measurements were performed in two temperature regions. The T1H and T1C changes due to the temperature rises are summarized in Figures 8 and 9, respectively.
The change in trends of T1H and T1C values was closely related to the existence of CH3 groups.

Changes of Spin-Lattice Relaxation Times in the Laboratory Frame with Rising Temperature
In order to investigate the rapid molecular motions (MHz) that participated in the spin-lattice relaxation in the laboratory frame, rising temperature T 1 H and T 1 C measurements were performed in two temperature regions. The T 1 H and T 1 C changes due to the temperature rises are summarized in Figures 8 and 9, respectively.
The different change trend that correlates with the existence of CH3 groups was also observed in the T1C values. The T1C values of CH3 groups increased monotonically with increasing temperature in both PHB (1) (black line) and PLA (5) (green line) up to 50 °C (Figure 9a). Conversely, a decrease with rising temperature was observed for the T1C value of each substituent in PBS (Figure 9b, orange line). The CH2 group in PHB (43 ppm) has a very long T1C value (over 80 s), which increased in the low temperature and decreased in the high temperature regions (Figure 9b, black line). These trends of T1 values showed that the rotation of CH3 in PHB and PLA had a lower correlation time (τc) than molecular motions of CH2 in PHB and PBS.  (Figure 7). Although a T1H reduction of the PHA unit was also observed in PHA5533L (4) (Figure 8a, blue line), no inflection points of the T1H curve were observed in the low-temperature region and the 1 H MAS NMR spectra changed only slightly in PHA5533L (4). These results indicated that the polymer compatibility between PHA and PLA was less improved in PHA5533L (4) although the T1H relaxation was enhanced by the heterogeneity. . T1C changes of CH3 (a) and CH2 (b) groups in plasticized PHA copolymers with rising temperature. The temperature was increased from 40 °C to 0 °C (low-temperature side) and from 20 °C to 50 °C (high-temperature side).
The T1C value of the CH2 groups in the plasticized PHA copolymers gave information about rapid molecular motions (MHz order) of the polymer chain. In all temperature ranges, the PHB unit of the plasticized PHA copolymers has a low T1C value, compared with the pre-plasticized PHB, although the PBS units had similar T1C values regardless of the plasticization. The heterogeneity that had arisen from the amorphous moiety also increased the molecular mobility of the PHB chain, which enhanced the T1C relaxation to produce the lowered T1C value of the PHB unit. Meanwhile, the T1C value of CH3 groups in the plasticized PHA copolymers provides information on the local motion of CH3 closely related to the T1H relaxation. The reduction of the T1C value of CH3 groups . T 1 C changes of CH 3 (a) and CH 2 (b) groups in plasticized PHA copolymers with rising temperature. The temperature was increased from 40 • C to 0 • C (low-temperature side) and from 20 • C to 50 • C (high-temperature side).
The change in trends of T 1 H and T 1 C values was closely related to the existence of CH 3 groups. The T 1 H values of PHB (1) (Figure 8a, black line) and PLA (5) (Figure 8b, green line), both of which had CH 3 groups, increased with increasing temperature except for the high temperature region of PHB (1). In contrast, PBS (2) (Figure 8b, orange line), which had no CH 3 group, decreased with increasing temperature; the rate of decrease was significantly faster in the low-temperature region. The different change trend that correlates with the existence of CH 3 groups was also observed in the T 1 C values. The T 1 C values of CH 3 groups increased monotonically with increasing temperature in both PHB (1) (black line) and PLA (5) (green line) up to 50 • C (Figure 9a). Conversely, a decrease with rising temperature was observed for the T 1 C value of each substituent in PBS (Figure 9b, orange line). The CH 2 group in PHB (43 ppm) has a very long T 1 C value (over 80 s), which increased in the low temperature and decreased in the high temperature regions (Figure 9b, black line). These trends of T 1 values showed that the rotation of CH 3 in PHB and PLA had a lower correlation time (τ c ) than molecular motions of CH 2 in PHB and PBS.
Although the T 1 H value of the PHA unit in PHA4422P (3) (Figure 7). Although a T 1 H reduction of the PHA unit was also observed in PHA5533L (4) (Figure 8a, blue line), no inflection points of the T 1 H curve were observed in the low-temperature region and the 1 H MAS NMR spectra changed only slightly in PHA5533L (4). These results indicated that the polymer compatibility between PHA and PLA was less improved in PHA5533L (4) although the T 1 H relaxation was enhanced by the heterogeneity.
The T 1 C value of the CH 2 groups in the plasticized PHA copolymers gave information about rapid molecular motions (MHz order) of the polymer chain. In all temperature ranges, the PHB unit of the plasticized PHA copolymers has a low T 1 C value, compared with the pre-plasticized PHB, although the PBS units had similar T 1 C values regardless of the plasticization. The heterogeneity that had arisen from the amorphous moiety also increased the molecular mobility of the PHB chain, which enhanced the T 1 C relaxation to produce the lowered T 1 C value of the PHB unit. Meanwhile, the T 1 C value of CH 3 groups in the plasticized PHA copolymers provides information on the local motion of CH 3 closely related to the T 1 H relaxation. The reduction of the T 1 C value of CH 3 groups due to copolymerization was limited, unlike the T 1 H value. Thus, the change of T 1 H was not caused by the molecular motion of CH 3 groups, but by the interaction between constituent polymers.
In conclusion, T 1 H values can act as an index of polymer compatibility due to plasticization, while T 1 C values of CH 2 groups can provide an index of rapid molecular motions of constituent polymers. Moreover, the T 1ρ H values can index slow molecular motions of the polymer main chain, along with the 1 H and 13 C PST-MAS NMR spectra. Since copolymerization of PHA with PBS improved elongation and impact properties, the increase in slow molecular motions and compatibility of the PHA/PBS copolymer is possibly related to such polymer properties. Next, we are planning to study other biomass-based polymers to relate polymer properties to the indexes in solid-state NMR analytical methods proposed in the present study.

Conclusions
With the aim of extending the application of solid-state NMR to biomass-based polymers, two kinds of biodegradable polyesters, poly (butylene succinate) (PBS) and poly(lactic acid) (PLA), were examined for the plasticization of the biopolymers of no nutritional use, polyhydroxyalkanoates (PHA). Both biodegradable polyesters improved the thermal properties of PHA; the flexible PBS decreased the melting point of PHB while the rigid PLA added a glass transition point to PHB. Moreover, the biodegradable polyesters lowered the crystallinity of poly(3-hydroxybutyrate) (PHB). 1 H MAS NMR spectra at −40 • C showed broad and overlapped signals for all polymers measured. With increasing temperature, the PHA/PBS copolymer showed larger and sharper 1 H MAS signals of the PHB unit while those of the PHA/PLA copolymer remained similarly broad to those of the original PHB. The 13 C PST-MAS signals of the PHB unit were increased by copolymerization with PBS, in addition to the 1 H MAS signals. Since 1 H spin-lattice relaxation in the rotating frame (T 1ρ H) was decreased more by the copolymerization with PBS than PLA, the addition of PBS increased the amplitudes of slow molecular motions (kHz order) of the polymer chain related to the spin-locking frequency. Meanwhile, 1 H and 13 C spin-lattice relaxation times in the laboratory frame (T 1 H and T 1 C), which were reflected matching with rapid molecular motions (MHz order), were reduced by copolymerization not only with PBS but also with PLA. In other words, the disordered PHB chain in the amorphous moiety due to the copolymerization improved polymer compatibility between PHB and the added polyester and amplified rapid molecular motions. The compatibility enhanced the T 1 H relaxation such that the time reduced and approached the T 1 H values of the plasticized PHA. The increased rapid molecular motions of the PHB substituent promoted the T 1 C relaxation to shorten the T 1 C value of CH 2 in the plasticized PHA. Our present study makes it possible to use solid-state NMR parameters as the index of molecular mobility and polymer compatibility. Studies of production process and mechanical properties using other biomass-based polymers using the solid-state NMR parameters are currently in progress.