1 Introduction

Polyhydroxyalkanoates (PHAs) represent some unique biopolymeric metabolites of microorganism in terms of their biosynthesis, biological functions and functionality in their applications. They are naturally synthesized by bacteria serving as energy storage and are often semi-crystalline. These biopolymers are increasingly becoming a focus of research due to their biodegradability and biocompatibility^[1]. As renewable materials, they have shown some potential to replace, at least in partial, the non-degradable petroleum-based ones^[2]. Moreover, these biopolymers are the environmentally friendly materials, even when degraded; the products are hydroxycaboxylic acids, some of which are normal biological metabolite such as 3-hydroxybutyric acid also known as “ketone body”. Ultimately, the degradation products are carbon dioxide and water which were from environment in the first place during biosynthesis, thus leading to no new or extra CO₂ load to the environment^[3].

Amongst them, poly(3-hydroxybutyrate) (PHB) may also have some potential as biomedical materials since its biodegraded product, 3-hydroxybutyrate, is the ketone body present in human blood plasma. However, its industrial application remains limited, owing to several inherent deficiencies^[3] including poor mechanical properties such as brittleness due to its high crystallinity and narrow thermal processing window^{[4, 5]}. To overcome these drawbacks, a number of strategies have been developed including preparing miscible blends with other flexible biodegradable polymers or plasticizer of low molecular weight ^[5-8], and using chemical and biological routes to synthesize block copolymers^[9-11]. A number of copolymers with other similar hydroxyalkanoate monomer units have been developed, such as poly(3-hydroxybutyrate-co-3- hydroxyvalerate) ([P(HB-HV)])^[12-14], poly(3-hydroxybutyrate-co-4-hydroxybutyrate) ([P(3-HB-4-HB)])^[15-17], poly(3-hy-droxybutyrate-co-3-hydroxypropionate) ([P(HB-HP)])^{[18, 19]} and poly(3-hydrorate-co-3- hydroxyhexanoate) ([P(HB-HHX)])^{[20, 21]}, via biosynthetic routes of a variety of bacteria. Compared with PHB, these copolymers exhibit decreased segmental rotation temperature (T_s), melting point (T_m) and crystallinity, leading to reduced brittleness and enhanced flexibility. These studies have shown that the above limitations can be overcome by the preparation of multi-block copolymers from PHB with segments of other biodegradable macromolecules.

It is conceivable that the structural, dynamic and interactional properties of PHB and its copolymers are key factors governing their properties in biological function and functionality in applications. Therefore, the elucidation of such properties is fundamentally important to understand the mode of actions of these polyesters in the living organisms and the functionality in their applications. Extensive researches have been carried out on structure and molecular dynamics of PHB and some of its copolymers using a variety of techniques including dielectric relaxation^[22], dynamic mechanical analysis (DMA)^[23] and nuclear magnetic resonance (NMR) spectroscopy^[24-26].

For PHB, of the various cold-crystallized samples, dielectric relaxation results have shown that the presence of semi-crystalline morphology such as crystallinity had a significant effect on the glass-rubber relaxation characteristics as compared to the wholly amorphous material^[27]. DMA results showed that T_m, T_s, temperature to flow (T_flow), and moduli decrease as the content of 3-hydroxyvalerate (HV) increases in poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) random copolymers. These techniques, however, can provide limited information about the structural features related to dynamics. In addition, Klinowski et al.^[28] had reported another two crystalline phases, α-orthorhombic phase and β-orthorhombic phase, existed apart from the amorphous phase by ¹³C NMR lineshape analysis and the normalized infrared spectroscopy. Using spectral deconvolution, the results indicated large differences in molecular mobility between the crystalline and amorphous regions of PHB. Our previous work^[29] about the structural characteristics of the semi-crystalline biopolymer PHB and its copolymers PHBV showed that the domain sizes of the crystalline regions decreased whilst the mobile domain sizes increased with the HV co-monomer contents increasing. In addition, it had been observed that introduction of HV enhanced molecular mobility of the biopolymers and raised the ratio of the amorphous to the crystalline region^[29].

However, less work has been conducted on the molecular dynamics of these materials. Little information is available on the relationship between the macroscopic properties and the molecular structure and dynamics at the molecular level, which are undoubtedly useful for understanding the materials and indeed important for the future design of new materials. Consequently, a number of questions remain unanswered, such as ‘what is the nature of the molecular dynamics for the different domains of these biopolymers’, ‘how does the content of 3-hydroxyvalerate affect the molecular dynamics’, and ‘is there any relationship between the molecular dynamics and their macroscopic properties’. To answer some of the questions, the molecular dynamics need to be studied, and a promising way for the study is NMR relaxation time measurement since it provides not only dynamic information but also related structural information. Normally such studies are carried out by measuring ¹H spin-lattice relaxation times in the laboratory frame (T₁) and rotating frame (T_1ρ), and spin-spin relaxation time (T₂) as a function of either magnetic field strength or temperature. However, the former requires a broad range of magnets, which is often unrealistically expensive though field cycling techniques are now available.

In the present study, T₁, T_1ρ and T₂ measurements as a function of temperature combined with differential scanning calorimetry (DSC) analysis are employed to investigate the molecular dynamics of semi-crystalline PHB and copolymers PHBV containing 5 wt. % (PHBV5) and 12 wt. % (PHBV12) 3-hydroxyvalerate monomer in different regions and dynamic states.

2 Experimental section 2.1 Materials

PHB (M_W = 470 000 g/mol), PHBV5 and PHBV12 were purchased from Aldrich Chemical Co., Inc. (Milwaukee, WI.USA No. 80181-31-3) and used with further processing. Fig. 1 shows the schematic form of their chemical structures. All samples were dried for at least 24 h under vacuum at the temperature of 353 K and sealed into 10 mm NMR tubes for NMR measurements.

2.2 DSC experiment

DSC analyses were conducted on a Perkin-Elmer DSC-4 with a heating rate of 10 K/min under liquid nitrogen. 5~10 mg of powdered sample was sealed in an aluminium pan and placed in the DSC instrument. Sample temperature was scanned between 223 K and 473 K as follows: samples were first heated from223 K to 473 K and maintained at 473 K for 1 min; then cooled to 223 K rapidly, and reheated to 473 K, after that cooled to 223 K again at a cooling rate of 100 K/min.

2.3 ¹H relaxation time measurements

T₁, T_1ρ, and proton second moment (M_2r), were measured on a Bruker AC 80 NMR spectrometer operating at proton frequency of 80.13 MHz with 10 mm probe head over the temperature range of 150~370 K. The proton 90° pulse length was 10.8 μs. The sample temperature was controlled with a Bruker variable temperature unit, VT-2000, and stable within ± 1 K. An increment of 10 K was used and experiments were always started from the lowest temperature. A total of 15 min waiting time for each temperature was allowed to ensure temperature stabilization and equilibration. The actual sample temperatures on Bruker AC 80 spectrometer were calibrated by directly inserting a pre-calibrated thermal couple into a sample-filled tube in the probe head. The errors in the measurements of T₁ and T_1ρ were estimated to be about 5%. A total of 1 024 data points were collected with 32 scans and 100 kHz sweep width in these measurements.

T₁ was measured using the standard inversion recovery method [recycle delay-180°_x-τ-90°_x-acquisition]. The recycle delay was at least 5 times of proton T₁. Relaxation delay time, τ, was chosen from 0.1 ms to 10 s depending on the length of T_1. The relaxation processes for all the polymers were found to be monoexponential over the whole temperature range studied.

¹H T_1ρ was measured using a standard spin-lock pulse sequence [recycle delay-90°_x-τ_SL-acquisition] where spin lock time, τ_SL, was chosen from 0.1 ms to 15 ms depending on the length of T_1ρ. The decays of nuclear magnetization for all these polymers were found to be bi-exponential over the whole temperature range studied.

M_2r was measured using solid echo pulse sequence [recycle delay-90°_x-τ₁-90°_y-τ-acquisition]. The recycle delay was 6 s. τ was chosen to be 5 μs, just slightly longer than the dead time (about 4.3 μs) of the spectrometer, and τ₁ was used from 1 μs to 18 μs depending on the length of T₂. The solid echoes were fitted to a modified Gaussian function^[30] to obtain the values of M_2r.

All relaxation time values were extracted by curve fitting using a Ladenburg-Marquardt nonlinear curve-fitting routine installed in a personal computer.

3 Results and discussion 3.1 DSC

Fig. 2 shows the DSC thermograms of PHB and its copolymers (PHBV5, PHBV12) in the temperature range of 223~473 K. There is no significant difference among the glass transition temperatures (T_g, about 270 K) of the three samples. The endothermic peaks at 439.7, 429.4 and 426.3 K indicate T_m values of the lamellar (α-orthorhombic) crystal of PHB, PHBV5 and PHBV12, respectively. The peaks at 417.8 K and 414.8 K in PHBV5 and PHBV12, respectively, are attributed to a transition of α-orthorhombic to β-orthorhombic form (from the amorphous domain between the orthorhombic α-form lamellar)^[31]. Due to the coexistence of crystalline and amorphous phases in the PHB matrix and its relative higher degree of crystallinity, the melting peak of PHB was so broad that the β-orthorhombic form was not observed. Furthermore, with the increased content of HV, the β-orthorhombic form increases, this indicates that the conformational change of PHBV12 is more prominent than that of PHBV5 and PHB. Crystallization of the α-form of PHBV12 took place at 340.2 K on cooling, whereas those of PHB and PHBV5 were not observed. Taking 146 J/g for 100% crystalline of PHB^[32], the DSC analysis indicated that the PHB sample had a degree of crystallinity α of 68.4%, which was calculated based on the formula α (%) = 100 ^*∆H_m/∆H ^{[33, 34]}, where ∆H_m is the enthalpy of the peak and ∆H denotes the enthalpy of melting process of a pure crystalline sample^[32]. According to the DSC experimental results, the crystallinity was estimated as 60.3% and 56.7% for PHBV5 and PHBV12, respectively. These DSC results were well consistent with our previous NMR measurements^[29] further confirming that T_g, T_m and crystallinity of PHB decreased with the increased content of HV co-monomers.

3.2 ¹H spin-lattice relaxation in the laboratory frame

¹H spin-lattice relaxation rate in the laboratory frame, R₁, as a function of temperature is shown in Fig. 3. We can find that in all three biopolymers studied, a R₁ maximum was observable at about 184 K, indicating the presence of a motion as an efficient proton relaxation process. This is probably associated with the three-fold reorientation of methyl groups in PHB or rotational motions of either methyl or ethyl moieties in PHBV5 and PHBV12. Although the R₁ maxima were at about the same temperature (182~185 K), their maximum R₁ values were obviously different (tabulated in Table 1). Another maximum appeared at about 323 K for PHBV12, which probably corresponded to the segmental backbone rotation process. While in PHB and PHBV5, the maxima moved to higher temperatures (> 350 K). This difference is probably attributable to the differences in their molecular packing and will be further discussed in later section. To evaluate the data quantitatively, the experimental data were fitted to the well-known Kubo-Tomita expression^[35] [Eq. (1)]. We assumed that two relaxation processes corresponding to the side chain motion and segmental rotation respectively dominated the spin-lattice relaxation time. The observed spin-lattice relaxation rate ${R_{lobs}}$ is:

$ {R_{lobs}} = \frac{1}{{{T_1}}} = \sum\limits_{i \ge 1} {{C_i}} \left( {\frac{{{\tau _{ci}}}}{{1 + \omega _0^2\tau _{ci}^2}} + \frac{{4{\tau _{ci}}}}{{1 + 4\omega _0^2\tau _{ci}^2}}} \right) $

(1)

Where ${\omega _{\rm{0}}}$ is the ¹H Larmor frequency and ${\tau _{ci}}$ is the rotational correlation time of the motion responsible for spin-lattice relaxation, which follows the Arrhenius law:

$ {\tau _{ci}} = {\tau _{0i}}\exp \left( {\frac{{{E_{{\rm{a}}i}}}}{{RT}}} \right) $

(2)

Where ${\tau _{0i}}$ is the pre-exponential factor corresponding to the rotational correlation time at infinite temperature (T), E_a is the activation energy and R is the gas constant; ${C_i}$ is the relaxation constant and is related to the second moment (∆M₂) modulated by the motions as described in Eq. (3), assuming that the motion occurring is fast on the NMR relaxation time scale. The ${C_i}$ value for the side chain methyl group in the presence of rapid rotation is given by:

$ {C_i} = \frac{2}{3}\Delta {M_2}{\gamma ^2} = \frac{1}{2}\frac{{{n_i}}}{N}\frac{{{\gamma ^4}{\hbar ^2}}}{{^{{r^6}}}} $

(3)

Where N is the total number of protons in the molecule, ${n_i}$ is the number of protons in the methyl groups contributing to the relaxation process, and r is the average inter-proton distance in the methyl groups. γ is the proton magnetogyric ratio.

Fig. 3 shows the theoretical fitting of the experimental data for the three biopolymers by the two components form of the relaxation theory described in Eq. (1) and (2). For PHB, the 3-fold reorientation of methyl group has a τ₀ value of (1.22±0.31)×10^﹣12 s and E_a value of (10.74±0.40) kJ/mol, these values broadly agree with those of the polycrystalline methyl groups^[36], and similar results also have been found for other methyl and ethyl moieties in the solid state^[37]. At higher temperature (above 350 K), the process attributed to the segmental rotation has a τ₀ value of (2.61±0.55)×10^﹣12 s and E_a value of (21.08±4.61) kJ/mol. For PHBV5 and PHBV12, the τ₀ values of side chain motion are (2.70±0.60)×10^﹣12 and (1.55±0.36)×10^﹣12 s, and E_a values are (9.40±0.36) and (10.03±0.36) kJ/mol, respectively; segmental rotation processes at higher temperature (359 K and 323 K for PHBV5 and PHBV12, respectively) have τ₀ values of (1.71±4.68)×10^﹣14 and (1.05±0.38)×10^﹣13 s, and E_a values of (33.44±7.40) and (25.03±2.46) kJ/mol, respectively. The relaxation constant (C) and the maximum relaxation rate (R_1max) of different motional processes are also obtained and tabulated in Table 1. Using the obtained values of C_i through the fitting procedure, the calculated average inter-proton distance of methyl group in PHB is 0.182 nm according to the Eq. (2), which agrees satisfactorily with that of other methyl group. These results showed that the weighted average relaxation rate R₁ of two processes speeded up with the increasing of HV co-monomer content.

3.3 ¹H spin-lattice relaxation in the rotating frame

For all the three biopolymers, bi-exponential T_1ρrelaxation times were observed over the temperature range of 150~370 K. These fast and slow components of T_1ρ may correspond to amorphous and crystalline regions, respectively, since our previous study showed that the long ¹H T_1ρ components are associated with the crystalline structure while the short ones are associated with the amorphous regions. For both the crystalline (Fig. 4) and amorphous (Fig. 5) regions, the temperature dependence of R_1ρ shows two maxima, implying the presence of two main relaxation processes: one occurs at the low temperature range of 150~250 K and the other one at the high temperature region of 250~370 K. The experimental data associated with the two regions were fitted to the two thermally-activated motions according to the relaxation theory described in Eq. (4) which is similar to that in R₁ analysis:

$ {R_{{\rm{1}}\rho }} = \frac{1}{{{T_{1\rho }}}} = \frac{3}{2}\sum\limits_{i \ge 1} {{C_i}\left( {\frac{{{\tau _{ci}}}}{{1 + 4\omega _{ei}^2\tau _{ci}^2}} + \frac{5}{3} \times \frac{{{\tau _{ci}}}}{{1 + \omega _0^2\tau _{ci}^2}} + \frac{2}{3} \times \frac{{{\tau _{ci}}}}{{1 + 4\omega _0^2\tau _{ci}^2}}} \right)} $

(4)

Where ${\omega _0}$, C_i and ${\tau _{ci}}$ have the same meanings as in Eq. (1) and (2). ${\omega _{ei}}$ is the effective field for relaxation in frequency unit, which is often dependent on the spin-lock frequency, ${\omega _{{\rm{SL}}}}$, and the local dipolar field, ${\omega _{\rm{L}}}$.

In the present situation, the applied ${\omega _{{\rm{SL}}}}$ is about 60 kHz, ${\omega _{\rm{L}}}$ is about 40 kHz. The relaxation maxima appeared at about 224 K and 304 K, and at these temperatures ${\tau _{ci}}$ has about the same order of magnitude as T₂. Therefore, the effects of local dipolar field must be taken into consideration by the McCall-Douglass equation^[38]:

$ {\omega _{\rm{e}}} = \sqrt {\omega _{{\rm{SL}}}^2 + \omega _{\rm{L}}^2} $

(5)

In practice, ${\omega _{\rm{L}}}$ is temperature dependent and was modeled by a double sigmoid function^{[36, 38, 39]} for the three materials to give the closest possible values to the experimental ones within the temperature range studied.

For PHB, PHBV5 and PHBV12, the experimental data agreed well with the theoretical ones for crystalline regions (shown in Fig. 4) and amorphous regions (shown in Fig. 5). Motional parameters obtained are tabulated in Table 2 and 3. The peak in the low temperature range should be attributed to side chain motion process owing to its activation energy (E_a≈4.17, 3.96, 3.14 kJ/mol in the crystalline regions; E_a≈6.62, 3.39, 6.23 kJ/mol in the amorphous regions) and correlation times of molecular motions (τ₀≈9.70×10^﹣8, 7.73×10^﹣8, 1.31×10^﹣7 s in the crystalline regions; τ₀≈2.08×10^﹣8, 1.53×10^﹣7, 2.21×10^﹣8 s in the amorphous regions). The high temperature processes (304 K) may be associated with segmental motions of backbone of the polymer chain. Their motional parameters (E_a≈22.24, 16.80, 19.46 kJ/mol; τ₀≈2.40×10^﹣10, 2.01×10^﹣9, 4.70×10^﹣10 s corresponding to the crystalline regions and E_a≈29.86, 43.63, 31.00 kJ/mol; τ₀≈1.47×10^﹣11, 2.38×10^﹣14, 3.93×10^﹣12 s corresponding to the amorphous regions of PHB, PHBV5 and PHBV12 respectively) were also obtained by curve fitting. For amorphous regions, the relaxation rates, R_1ρ, of PHB, PHBV5 and PHBV12 increased with the increasing of the HV co-monomers contents (Fig. 4). For crystalline regions, R_1ρ of the three materials present the similar tendency as amorphous regions (Fig. 5). However, over the whole temperature range, the relaxation rate of molecular motions in amorphous region is much faster than that in crystalline region (shown in Fig. 4 and 5). These results obviously indicate that the addition of HV co-monomers exerts more influences on the amorphous regions than crystalline regions. The molecular dynamic parameters obtained by R_1ρ analysis can also be explained on the molecular level that the molecular structures are modified and molecular motions are enhanced by adding HV co-monomers in both the amorphous and crystalline regions.

3.4 Second moment M_2r of wide-line ¹H NMR spectrum

The free induction decays of PHB, PHBV5 and PHBV12 cannot be described simply by either a Gaussian or an exponential decay function. Nevertheless, a much better approximation can be made by a modified Gaussian function^[30], shown in Eq. (6):

$ I(t) = {I_0}\exp (\frac{{ - {a^2}{t^2}}}{2})\frac{{\sin bt}}{{bt}} $

(6)

The rationale of using Eq. (6) is that the wide-line ¹H NMR spectrum is assumed to be a rectangular line shape with a total width 2b, convoluted with a Gaussian line shape with a standard deviation a^[40]. One of the most useful way to evaluate this kind of free induction decay (FID) is to use the residual second moment, M_2r, which is a measurement of the strength of the dipolar interactions and can be calculated as M_2r = a²+b²/3. In general, M_2r is expected to decrease when the motional correlation time ${\tau _c}$ is comparable to the inverse of line-width, i.e.,

$ {\tau _c} = {(\gamma \sqrt {{M_{2{\rm{r}}}}} )^{ - 1}} $

(7)

Temperature dependence of M_2r for the PHB, PHBV5 and PHBV12 is shown in Fig. 6. For PHB, at low temperature (e.g. 150 K), the measured M_2r value is about 0.132 mT². It decreases to 0.101 mT² as the temperature approaches 184 K and then remains almost constant (a first plateau) in the temperature range of 184~278 K. The reduction of M_2r is due to the three-fold (C₃) reorientation of methyl groups at about 180 K, which is consistent with the above R₁ and R_1ρanalyses. The M_2r value further decreases gradually with increasing temperature and eventually reaches a second plateau of 0.071 mT² at about 360 K. This reduction is attributed to the breakdown of the segments of the biopolymer chains above its segmental rotation temperature 278 K. M_2r of PHBV5 and PHBV12 show similar tendency to that of PHB. But their values decrease from 0.11 mT² and 0.092 mT² at low temperature (about 150 K) to 0.083 mT² and 0.067 mT² at 184 K, respectively. Then they remain almost constant in the temperature range of 184~280 K. And M_2r decrease gradually with a further increase of temperature and eventually reach the second plateaus of 0.05 mT² and 0.044 mT² at 350 K, respectively. From the experimental data, we can reasonably conclude that the three-fold reorientation of methyl groups plays a major role at temperatures below 280 K, while at temperatures above 350 K the segmental rotation process dominates the main relaxation pathway. Furthermore, as can be seen from the experimental results of these materials, the higher content of HV, the narrower of the ¹H line-width of NMR spectrum and the faster molecular motions of them. This can assist the understanding of relationship between the macroscopic properties and molecular structures and dynamics on molecular level.

4 Conclusion

The molecular dynamics of the semi-crystalline biopolymer PHB and its copolymers PHBV have been well characterized by means of ¹H relaxation time measurements. Our results indicate that the major relaxation pathways in PHB and its copolymers PHBV are the side chain motion and segmental rotation of polymer backbone chain. The correlation times and activation energies of molecular motions for PHB and PHBV copolymers are determined by fitting the T₁ and T_1ρexperimental data with a theory formula. These results can be explained on molecular level that the structures of PHB are modified and molecular motions are enhanced by adding HV co-monomers, which is consistent with the DSC results.

Acknowledgement We acknowledge that DSC measurements were performed at the Analytical Centre, Wuhan University of Technology.