Introduction

An important question in designing industrial rubber products is whether vulcanized natural rubber (NR) is oriented under strain even at low extensions. Industrial rubbers, such as tires, are always used at a low extension ratio, α⩽2, and therefore designs of tires are influenced by the molecular orientation of stretched rubbers with a low extension. Until now, there have been two contrasting views about the orientation of stretched NR.1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 One is that stretched NR is not oriented at a low extension ratio of α⩽2.1, 2, 3, 4, 5, 6, 7, 8 This opinion has been supported by X-ray diffraction (XRD) and birefringence experiments. Only an amorphous halo was observed at stretched NR α⩽2, and strain-induced crystallization of NR occurred from an extension ratio of α=2.5 by XRD experiments.1, 2, 3, 4, 5, 6, 7 The birefringence result shows that growth of the crystal in definitional constraint programming (DCP)-cured NR occurred at an extension ratio of α=2.5–3.5.8 On the other hand, Fourier transform infrared dichroism, pulse-nuclear magnetic resonance (NMR) and solid-state NMR support another opinion that stretched rubber is oriented even at a low extension of α⩽2, although the degree of orientation is not so large.9, 10, 11 From Fourier transform infrared dichroism, the average orientation function derived from Fourier transform infrared spectra as a function of α tends to show a linear relationship in the range of α from 1 to ∼4.9 The short T2 component in the pulse-NMR experiments of stretched NR also shows a linear relationship between T2 and α from 1 to ∼4.10 In our previous study using carbon-13 direct polarization (13C DP) NMR, we showed that isoprene units of rubber polymers oriented by uniaxial stretching even at α=2.11 The study also suggests that a high molecular motion remains in molecular orientation.11 We assume that the different opinions about the molecular orientation of stretched NR at low extensions comes from the high motion of the stretched NR chain. It is likely that orientation occurs partially even if the value of α is less than 2. However, such an orientation cannot be detected by XRD and birefringence because of high molecular motion and the small degree of orientation. At a value of α more than 2, the degree of orientation is speculated to be larger and then crystallization can be detected at α=2.5 by these methods. Solid-state NMR and Fourier transform infrared are forceful methods for detecting molecular orientations, even for mobile amorphous samples, and therefore may be more suitable for disclosing the molecular orientation and dynamics of stretched rubber samples.12, 13, 14, 15, 16, 17, 18

In this study, the molecular dynamics and orientation of vulcanized NR stretched at a low extension ratio α were studied by 13C DP-magic angle spinning (MAS) NMR, 13C CP-MAS NMR, 13C DP NMR without MAS, 13C cross-polarization (CP) NMR without MAS and density functional theory (DFT) calculations.

Experimental procedure

Materials

Table 1 summarizes the recipe of the vulcanized NR samples used in this study. These rubber samples, which consist of rubber bands with an inner diameter of 2.5 mm and rubber discs with a diameter of 7 mm, were cured at 170 °C for 10 min.

Table 1 Recipe of the samples used in this study (in phr)
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Solid-state NMR measurements

13C solid-state NMR spectra were observed by using a Bruker Avance 400 spectrometer (Bruker Biospin GmbH, Rheinstette, German), equipped with a 7 mmφ MAS or a 10 mmφ static probehead operating at 100.6 MHz. To observe the high-resolution NMR spectra of stretched NR, we designed a rubber-stretching kit19 (Sumitomo Rubber Industries Ltd., Chuo-ku, Kobe, Japan) that enables MAS measurements. Rubber bands were stretched by the rubber-stretching kit (Figure 1), after which the 13C DP-MAS NMR spectra of stretched rubbers at α=2 and 4 were measured under a 1H dipolar decoupling condition at 25 °C. 13C DP-MAS spectra with dipolar decoupling of 29.4 kHz at 25 °C, and 13C CP-MAS spectra with dipolar decoupling of 57.5 kHz at −55 °C were observed for rubber samples without stretching (α=1). MAS speed was 5.0 kHz for the former measurements, and 3.0 or 4.0 kHz for the latter measurements. The π/2 pulse width was 4.35 μs and the repetition time was 6 s. Rubber bands with α=2 were uniaxially stretched, as reported in the previous study.13 The π/2 pulse width was 8.5 μs and the delay time was 5 s. The dmfit program20 was used for spectral fittings.

Figure 1
figure 1

Schematic diagram of a kit used to obtain 13C NMR MAS spectra of stretched rubbers.

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DFT calculations of 13C-shielding components

The Gaussian 03 Rev.D.02 program package (Gaussian, Inc., Wallingford, CT USA) was used for DFT calculations of 13C-shielding tensor components. The B3LYP exchange-correlation functional and the 6-311++G(d,p) basis set were used. A simplified model of polyisoprene, CH3-CH2-C(CH3)=CH-CH2-CH3 with cis form was used for the calculation. As DFT calculations provided absolute shielding values, we converted the calculated chemical shielding to chemical shift values using the following equation:

In this equation, the value of 184.05 p.p.m. was the absolute shielding of the 13C nucleus of tetramethylsilane calculated using the same basis set.

Results and discussion

Restriction of molecular mobility of NR by stretching

Figure 2 shows the 13C DP-MAS NMR spectra of vulcanized NR without stretching (α=1 (a)) and with stretching (α=2 (b) and α=4 (c)).

Figure 2
figure 2

13C DP-MAS NMR spectra of vulcanized natural rubber (NR) without stretching (α=1) (a), with stretching of α=2 (b) and α=4 (c). The structure of polyisoprene, which is the major constituent of NR, and signal assignment are also shown.

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The five peaks observed at 24.1, 27.3, 33.0, 125.9 and 135.4 p.p.m. are assigned to individual carbons of cis-1,4-polyisoprene as indicated.21 By stretching the vulcanized NR, the 13C chemical shifts of the five peaks are unchanged and any strain-induced new peaks cannot be observed. However, the linewidths of the five peaks become slightly large with increasing α, although the degree of broadening is small. As linewidth is inversely proportional to the T2 relaxation time that relates to molecular mobility,22 the molecular motion of vulcanized NR seems to be slightly restricted by stretching.

Molecular orientation of the stretched NR at α=2

The main factor causing the restriction of molecular mobility is likely to be the molecular orientation of stretched NR. To verify the molecular orientation of the stretched NR, we carried out static NMR experiments of stretched and unstretched NR by changing the angle of the stretched direction relative to the applied magnetic field. Here, we concentrate on the behavior of two carbon signals, C2 and C3 in NR, with large chemical shift anisotropies.

Figures 3a–c show the 13C DP-static NMR spectra of two carbons, C2 and C3, of the stretched NR with α=2 at θ=0°, 45° and 90°, where the angle, θ, is defined as the angle between the stretching direction and the applied magnetic field.

Figure 3
figure 3

13C DP-static NMR spectra (C2 and C3 in the olefinic region) of uniaxially stretched natural rubber (NR) with α=2 observed at various angles, θ, between the stretching direction and the applied NMR magnetic field: θ=0° (a), 45° (b) and 90° (c). The 13C DP-static NMR spectrum of the circularly stretched NR (Figure 1) is shown as (d).

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By tilting θ from 0° to 90°, gradual downfield shifts of Δδ=3.0–3.1 p.p.m. were observed for both the C2 and C3 carbons. This result indicates that isoprene units of rubber polymers are slightly oriented by stretching even at α=2.11 However, the amount of downfield shifts is quite small compared with the common range of 13C chemical shift anisotropies (generally Δδ=δ11–δ33=approximately several tens to several hundred p.p.m.).23, 24 In the circularly stretched NR at α=2, mixed patterns of oriented peaks are observed for each carbon (Figure 3d). Thus, the circularly stretched NR includes various directions of orientation in the spectrum. These results also confirm that rubber polymers are oriented by stretching at α=2.

In addition, to prove that θ-dependent shifts of stretched NR are not artificial, θ-dependent observation was also performed for the mixture of stretched and unstretched NR samples. In the spectrum of Figure 4a of the stretched NR containing unstretched NR, an additional small peak is clearly observed for each C2 and C3 carbon. These peaks are almost independent of the angle θ as shown in Figures 4a–c, and peak positions are the same as those observed for the unstretched NR sample (Figure 4d).

Figure 4
figure 4

13C DP-static NMR spectra (C2 and C3 in the olefinic region) of a mixture of uniaxially stretched natural rubber (NR) and small amounts of unstretched NR observed at θ=0° (a), 45° (b) and 90° (c). The spectrum (d) of only unstretched NR is also shown.

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Therefore, we have found that the θ-dependent downfield shifts observed in the stretched NR are not artificial and come from the orientation of the rubber chain by stretching as a time average.

Apparently, these findings conflict with the XRD results that only amorphous halo was observed in the stretched NR at α⩽2. This conflict must be caused by the dissimilarity of easily observable components using XRD and NMR methods. The XRD method predominantly observes crystalline components in polymer chains. With regard to the characterization of molecular orientation, it seems difficult to observe the oriented components undergoing vigorous molecular motion using the XRD method. On the contrary, NMR measurements in this study can analyze all components in polymer chains, including amorphous components. Observation of orientations is also possible for polymer chains with high molecular mobility. Considering both views of NMR and XRD, it is suggested that NR is oriented by stretching at α=2, whereas the degree of orientation is small and oriented crystals are not formed.

In spite of the molecular orientation of stretched NR, the range of 13C chemical shift change caused by varying the angle θ is surprisingly small (about 3 p.p.m.). The small range of 13C chemical shift anisotropy (CSA) of the stretched NR is expected to be the result of anisotropical motional narrowing, such as a rotation around one axis.25, 26, 27

Range of chemical shift anisotropy of frozen NR

To determine the original range of 13C CSA of NR when the rubber molecular motion is frozen, 13C spectra of NR were measured at −55 °C. Figure 5 shows 13C CP static (a) and low-speed MAS NMR spectra ((b) and (c)) at −55 °C of the C2 and C3 carbons of unstretched NR. Here, the MAS speeds of Figures 5b and c were 3 and 4 kHz, respectively. As the ranges of 13C CSAs (Δδ=δ11–δ33) are almost unchanged at less than −50 °C, a temperature of −55 °C is adopted.

Figure 5
figure 5

13C CP static and low-speed MAS NMR spectra of the olefinic region of natural rubber (NR) at −55 °C: static (a), 3 kHz magic angle spinning (MAS) (b), 4 kHz MAS (c). The fitting spectra of 3 and 4 kHz MAS are shown in (e) and (f), respectively, and the simulated static spectrum is shown in (d). Linewidths were set to be 900 Hz for simulated MAS spectra and the line-broadening factor was set to be 1 kHz for the simulated static spectrum. Lorentzian was used as the line-broadening function for spectral simulation.

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The ranges of 13C CSAs are considered to be more than 100 p.p.m., as determined from Figure 5a. The exact principal values of CSAs can be determined by spectral fittings to low-speed MAS spectra as shown in Figures 5b and c. As a result, the CSA principal values of the C2 and C3 carbons of NR were determined as (δ11, δ22, δ33)=(225.0, 133.2, 48.0) and (209.3, 107.0, 61.1), respectively (Table 2).

Table 2 Experimental and calculated chemical shifts of the C1–C4 carbons of natural rubber (NR)
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The simulated static spectrum shown in Figure 5d with these CSA values is very close to its corresponding experimental spectrum in Figure 5a, although the upperfield skirt of the experimental spectrum in Figure 5a overlaps with the downfield skirt of aliphatic carbon peaks. Thus, the ranges of 13C CSAs (Δδ=δ11–δ33) of olefinic carbons are more than 140 p.p.m. when molecular motion is frozen.

Motional narrowing of CSA by anisotropic motion of stretched NR

Although the CSA ranges (Δδ=δ11–δ33) of C2 and C3 carbons of NR at frozen molecular motion are over 140 p.p.m., the observed ranges of the chemical shift change of stretched NR by varying the angle θ are only 3 p.p.m. This seems to be caused by the rapid molecular rotation around one axis.25, 26, 27

Figure 6 shows simulated CSA patterns of the C2 carbon: (a) frozen molecular motion of unstretched NR and (b) stretched NR at room temperature.

Figure 6
figure 6

Simulated chemical shift anisotropy (CSA) patterns of C2 carbon: frozen molecular motion of unstretched natural rubber (NR) (a) and stretched NR at room temperature (b). The CSA pattern of frozen molecular motion is simulated from the experimental CSA principal values of C2 carbon. The CSA pattern of stretched NR is simulated from the chemical shift values of stretched NR at θ=0° and 90°. δ11 and δ33 in spectrum (b) correspond to θ=90° and 0°, respectively. δ22 was calculated on the basis of the equation δiso=(δ11+δ22+δ33)/3. The line-broadening factor was set to be 10 Hz for simulated static spectra.

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The CSA pattern of frozen molecular motion is simulated from the experimental CSA principal values of the C2 carbon. Conversely, the pattern of stretched NR is simulated from the chemical shift values of stretched NR at θ=0° and 90°, as seen in Figures 3a and c. The chemical shift of the C2 carbon of stretched NR at θ=0° (δ=133.6 p.p.m.) is very close to the δ22 value at frozen molecular motion (δ=133.2 p.p.m.). The chemical shift of stretched NR at θ=90° (δ=136.7 p.p.m.) coincides with the averaged value of δ11 and δ33 at frozen molecular motion (δ=136.5 p.p.m.). This finding indicates that isoprene units of the rubber chain in the stretched NR rapidly rotate around the δ22 direction of the C2 carbon and therefore the chemical shifts, δ11 and δ33, perpendicular to the rotation axis should be averaged. By disclosing the relationship between the rotation axis (δ22 direction of the C2) and the isoprene molecular axis, the molecular dynamics in stretched NR are clarified. As the CSA directions of NR carbons are impossible to determine experimentally, we performed DFT calculations using a model compound of NR to determine the directions of the CSA principal axes of 13C shielding.

Dynamics of the oriented polymer chain of stretched NR

Figure 7 shows the directions of the CSA principal axes of 13C shieldings of C1–C4 carbons of a polyisoprene model molecule with cis conformation as determined by DFT calculations.

Figure 7
figure 7

Directions of chemical shift anisotropy principal axes of 13C shielding of a model molecule of polyisoprene with cis-conformation determined by density functional theory calculations.

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We found that the δ22 component of the C2 carbon lies approximately along the C=C bond of the isoprene unit of NR, although the δ22 direction actually forms an angle of 7° relative to the C=C bond. δ11 and δ33 components are almost aligned perpendicular to the C=C bond. Therefore, isoprene units of oriented polymer chains in stretched NR rotate rapidly around one axis, which makes an angle of several degrees with respect to the C=C bond direction. This result suggests that isoprene polymer chains are slightly oriented as a time average. We compared the calculated values of motionally narrowed anisotropies with the experimental CSA range observed at the θ changing experiment of stretched NR as seen in Figures 3a–c. The motionally narrowed anisotropy can be expressed by the following equation:25

where angles α, β are the Euler angles defining the transformation from the principal axis system of (δ11, δ22, δ33) to the molecular rotation frame. In the case of the C2 carbon, the motionally narrowed anisotropy is calculated at Δδ (=δ⊥−δ∥)= −3.7 p.p.m. The δ22 direction of C2 carbon is assumed to be the rotation axis, and the experimental CSA principal values of (δ11, δ22, δ33) obtained in Figure 5 are used for calculation. The motionally narrowed anisotropy value of −3.7 p.p.m. is very similar to the experimental CSA range of C2 carbon of Δδ= −3.1 p.p.m., which is obtained from the θ changing experiment of the stretched NR sample as seen in Figures 3a–c. In the case of C3 carbon, the motionally narrowed anisotropy is calculated at Δδ (=δ⊥−δ∥)= −3.5 p.p.m., which is also very similar to the experimental CSA range of the C3 carbon of Δδ= −3.1 p.p.m.

Although the CSA principal values of C3 carbon are different from those of C2 carbon, the motionally narrowed anisotropy of C3 carbon becomes almost similar to that of C2 carbon. This is because of the small difference in CSA principal axes between C2 and C3 carbons. The δ22 direction of C3 carbon results in a small difference to the rotation axis. According to DFT calculations, the δ22 direction of C3 carbon forms an angle of about 20°, relative to the δ22 direction of C2 carbon, which is assumed to be the rotation axis. Therefore, the small ranges of θ-dependent chemical shifts of olefinic C2 and C3 carbons in stretched NR can be explained as the result of the motionally narrowed anisotropies of C2 and C3 carbons. The motionally narrowed anisotropy values of C2 and C3 carbons calculated from the experimental CSA principal values are also summarized in Table 2.

Motionally narrowed anisotropies are also calculated from simulated CSA principal values by DFT calculations. Using the simulated values for calculation, the motionally narrowed anisotropies can be calculated not only for olefinic C2 and C3 carbons but also for aliphatic C1 and C4 carbons. The experimental CSA principal values of aliphatic C1 and C4 carbons cannot be determined because of their very small spinning side bands and signal overlapping. The simulated CSA principal values of all C1–C4 carbons and the motionally narrowed anisotropies calculated from simulated CSA values are also summarized in Table 2.

Conclusion

The molecular dynamics of orientated polymer chains of stretched NR have been successfully studied by solid-state 13C NMR and DFT calculations. From 13C DP-MAS NMR data, we found that 13C linewidths of NR become broader when the extension ratio is raised. This means that the mobility of the polymer chains of NR is restricted by stretching. From the 13C DP-static NMR experiments of uniaxially stretched NR at an extension ratio of α=2 with several stretching directions relative to the magnetic field, we observed that the 13C chemical shifts of two NR olefinic C2 and C3 carbons change by varying the stretching directions to the magnetic field. This suggests that isoprene units of rubber polymers become oriented by stretching even at a low extension ratio of α=2. In spite of the molecular orientation of stretched NR, ranges of 13C chemical shift changes caused by varying the stretching direction are small. The small chemical shift changes are due to rapid molecular rotation around one axis. The motionally narrowed anisotropy of the C2 carbon of NR suggests that the isoprene units of the rubber polymer chain in stretched NR rapidly rotate around the δ22 direction of the C2 carbon. The DFT calculation shows that the δ22 direction of the C2 carbon lies approximately along the C=C bond of polyisoprene. The motionally narrowed anisotropy of C3 carbon supports the motional narrowing. Therefore, it is concluded that isoprene units of rubber chains in stretched NR become oriented and undergo rapid molecular rotation around an axis almost aligned with the C=C bond direction of polyisoprene.