**3.4 Results on polybutadiene with nano-silica**

Tyre rubber has been continuously developed to improve various aspects of its performance, such as its grip, fuel consumption and wear resistance, by adding fillers such as silica nanoparticles and cross-linking agents [46, 47]. However, the microscopic mechanisms behind these improvements are still not fully elucidated and a better understanding is needed to further improve tyre products. Many studies have shown that confined polymer layers around nanoparticles affect the rubber's macroscopic properties [48–57]. Molecular-scale dynamics studies have also revealed that the presence of nanoparticles slows down the microscopic segmental α-relaxation motion and increases its heterogeneity [52, 53]. However, we still do not have a complete picture of the microscopic dynamics for these systems. Additionally, the effect of the particle size on the microscopic dynamics has not been elucidated.

To elucidate the effect of nanoparticles on the microscopic α-relaxation dynamics of polymers, we studied the microscopic dynamics of a polybutadiene (PB) and silica nanoparticle mixture by SR-based QEGS using multi-line TDI. Two types of samples were used for this experiment: pure 1,4-PB and 1,4-PB nanocomposites with silica nanoparticles. Two PB nanocomposites, PB-silica20 and PB-silica100, were prepared with 20 vol% of silica nanoparticles with average diameters of 20 and 100 nm, respectively. The glass transition temperature *T*<sup>g</sup> of pure PB was determined to be �180 K and no *T*<sup>g</sup> difference could be detected among the three samples.

**Figure 8** shows the obtained wide-angle X-ray scattering (WAXS) profile of the two nanoparticle samples. From these WAXS results, we confirmed that the position of the main peak, mainly reflecting the intermolecular correlation of the PB, had changed very little and was covered by the *q* region in the quasi-elastic scattering measurements (see the bar in the figure). Least-squares fits were performed for the obtained PB time spectrum using Eq. (4) modelling the normalised intermediate scattering function with a KWW profile. The value of *β*KWW for pure PB was determined to be 0.48 � 0.10 at *<sup>q</sup>* � 14 nm�<sup>1</sup> , which is consistent with the previously reported *β*KWW value of 0.45 [42]. We obtained *τ* by setting *β*KWW to be 0.45 for the pure PB spectra and then calculated the mean relaxation time h i*τ* from h i*τ* ¼ *τ* Γð Þ 1*=β*KWW *=β*KWW, where Γ is the gamma function [42].

Next, for the PB nanocomposites with silica nanoparticles, the polymer dynamics was studied through the analysis of the relaxation time extracted from the intermediate scattering function, while also considering its non-relaxing component originating from the stable nanoparticles. For the polymer nanocomposite systems, it is known that the contribution of the α-relaxation of polymers to the intermediate scattering function can be treated as a KWW function [48, 49]. Therefore, we used the function *F q*ð Þ¼ *; <sup>t</sup> f q*ð Þ exp �½ � *<sup>t</sup>=τ*ð Þ*<sup>q</sup> <sup>β</sup>*KWWð Þ*<sup>q</sup>* n o <sup>þ</sup> *c q*ð Þ to fit the normalised intermediate scattering function for the time spectra of PB-silica100 and PB-silica20, where *c q*ð Þ is the contribution of the non-relaxing component. By fitting the time spectra obtained for PB-silica100 at 250 K, we determined that the contribution of the non-relaxing component was *<sup>c</sup>* = 0.22 � 0.07 at *<sup>q</sup>* � 14 nm�<sup>1</sup> , assuming *β*KWW = 0.45. We used these values to analyse the time spectra of both PB-silica20 and PB-silica100 because (i) the volume fraction of silica nanoparticles was the

below *T*αβ. Here *T*αβ denotes the transition temperature. Therefore, the VFT law was used to fit data above *T*αβ at each *q,* whereas the Arrhenius equation was used for data below *T*αβ. We thus conclude that the α process occurs above *T*αβ, as suggested by the corresponding VFT behaviour, and it changes to the JG-β process below *T*αβ, similar to what was observed in OTP. The observation here that the α process changes to the JG-β process at *T*αβ above the first peak in *S*(*q*) contradicts the NSE results on PB [44] where no transition was observed in the high *q* range. It should be emphasised that this new transition finding at the higher *q* range can be attributed to the appropriate time and spatial resolutions of the SR-based QEGS technique for

*Temperature dependence of the mean relaxation time* h i *<sup>τ</sup>*KWW *obtained for PB at q = 9.6 (*○*, chain line), 15 (*● *, thin solid line), 21 (⎕, dotted line), 27 (*■ *, dashed line), 32 (Δ, two-dot chain line) and 39 (*▲*, thick solid line) nm and fitting curves given by symbols and lines, respectively. Thick dashed line represents*

*Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications*

An extended mode coupling theory (eMCT) has been proposed to account for hopping processes [45]. This theory predicts a dynamical transition from the α process to a local, hopping-dominated, relaxation process at *Tc*. In other words, this transition corresponds to the switch of the temperature dependence from the VFT law to the Arrhenius law. In the eMCT framework, the transition from the α process to the JG-β process corresponds to the transition from the hydrodynamic continuous motion to the hopping motion. The fact that the transition above the first peak occurs near *Tc* supports this interpretation. In the present experiment, however, we observed that the α process persisted even below *T*αβ (�*T*c) near the first S(q) peak. In other words, no transition occurred near the first peak. In this sense, the eMCT

The question still remains as to why the α process lasts even below *T*αβ at the first peak. Richter et al. have intensively studied relaxation processes in PB using NSE [42, 43] and found that the α process was observed at the first peak in *S*(*q*), whereas the JG-β process was observed at the valley in *S*(*q*) as mentioned above. These results agree with our observations below *T*αβ. The key point of their results is that the intermolecular interaction is very important for understanding the transition. It has been demonstrated that the first peak in *S*(*q*), the intermolecular correlation, is

the strongest, leading to cooperative motion. However, at the valley, the

intermolecular correlations are weaker than the first peak, and molecules move less cooperatively or freely. Hence, the cooperative α process is dominant at the first peak, and the isolated motion or the slow JG-β process is dominant at the valley. According to the eMCT, the α-relaxation changes to the JG-β one (hopping process)

observing the branching phenomenon.

*temperature dependence of viscosity timescale τη*ð Þ *T .*

**Figure 7.**

**72**

cannot be directly applied to our results.

PB-silica100. Here, the volume fractions of silica nanoparticles in the PB-silica20 and PB-silica100 nanocomposites were the same, but the PB-silica20 surface area was on average 25 times larger than the PB-silica100 surface area. Therefore, the obtained results suggest that the polymer α-relaxation dynamics was restricted by contact with the surfaces of the nanoparticles and became even more restricted as the surface area increased. This result is consistent with the conventional idea that the α-relaxation times of polymers slow down due to interactions (chemical attachment and physical absorption) between the polymer and the silica nanoparticles on the surface [46, 47]. Additionally, these results demonstrate that QEGS can be used to reveal the polymer dynamics in nanocomposites and for characterising their microscopic dynamics; these insights will be important for advancing industrial materials such as tyre rubber. In the future, investigating the confinement effects of surface polymers/silica nanoparticles that are more similar to industrial tyre rubber will yield more specific information about improving tyre performance. The details

*Synchrotron Radiation-Based Quasi-Elastic Scattering Using Mössbauer Gamma Ray…*

Quasi-elastic scattering techniques using Mössbauer gamma rays are promising approaches for revealing nanosecond and microsecond dynamics directly from the microscopic viewpoint. Currently, quasi-elastic scattering systems using the gamma rays TDI have been developed and utilised for application studies. Additionally, by using a band-width variable 57Fe-NBMs, we expect that the timescale of measurable dynamics will be expanded (e.g., up to sub 100 pico-second). Developing techniques that expand the timescales of measurements (i.e., between sub 100 picoseconds and sub-microseconds), such as energy-domain quasi-elastic scattering systems combined with time-domain quasi-elastic scattering systems, is highly

Moreover, various new X-ray-based techniques are proposed for studying microscopic dynamics, based on focusing monochromators [59], or X-ray echo spectroscopy [60] or free electron lasers (e.g., four-wave mixing experiments) [61]. The combination of these new X-rays (and gamma rays)-based techniques expands the timescales of the measurements significantly (e.g., from femtoseconds to microseconds). Future studies will open new methodologies for depicting the

microscopic structural dynamics of condensed matter by X-rays.

of this work can be found in Ref. [21].

*DOI: http://dx.doi.org/10.5772/intechopen.88898*

**4. Conclusions and perspectives**

desirable.

**75**

*WAXS profile obtained for pure PB and PB-Si100 at room temperature, and for PB-silica20 at 270 K. The bar represents the q region of the quasi-elastic scattering measurements.*

#### **Figure 9.**

*Temperature dependence of the averaged relaxation times obtained for pure PB, PB-silica20 and PB-silica100 at q = 14 nm*�*<sup>1</sup> . The error bars indicate the standard deviations, and the line indicates the α-relaxation times obtained by dielectric relaxation spectroscopy [58].*

same for both samples and the *c* value could also be assumed to be the same and (ii) the non-relaxing component of the polymer was found to be negligible in a mixture of PB and carbon black nanoparticles in the *q* range of the first peak [48, 49].

**Figure 9** shows the temperature dependence obtained for h i*τ* . The α-relaxation times of pure PB obtained by dielectric relaxation spectroscopy (depicted as a line in **Figure 9**) demonstrate that our results are consistent with the dielectric relaxation spectroscopy results [58]. The temperature dependencies of h i*τ* obtained for PBsilica20 and PB-silica100 also show divergent behaviour, although the VFT parameters appear to be different compared to pure PB. At 250 K, the α-relaxation times obtained at *q* = 14 nm�<sup>1</sup> for PB-silica20 and PB-silica100 were longer than those for pure PB, and this relation holds true throughout the studied temperature region. These data suggest that the nanoparticles cause the polymer α-relaxation motion to slow down. Moreover, the dynamics of PB-silica20 were much slower than

*Synchrotron Radiation-Based Quasi-Elastic Scattering Using Mössbauer Gamma Ray… DOI: http://dx.doi.org/10.5772/intechopen.88898*

PB-silica100. Here, the volume fractions of silica nanoparticles in the PB-silica20 and PB-silica100 nanocomposites were the same, but the PB-silica20 surface area was on average 25 times larger than the PB-silica100 surface area. Therefore, the obtained results suggest that the polymer α-relaxation dynamics was restricted by contact with the surfaces of the nanoparticles and became even more restricted as the surface area increased. This result is consistent with the conventional idea that the α-relaxation times of polymers slow down due to interactions (chemical attachment and physical absorption) between the polymer and the silica nanoparticles on the surface [46, 47]. Additionally, these results demonstrate that QEGS can be used to reveal the polymer dynamics in nanocomposites and for characterising their microscopic dynamics; these insights will be important for advancing industrial materials such as tyre rubber. In the future, investigating the confinement effects of surface polymers/silica nanoparticles that are more similar to industrial tyre rubber will yield more specific information about improving tyre performance. The details of this work can be found in Ref. [21].

#### **4. Conclusions and perspectives**

Quasi-elastic scattering techniques using Mössbauer gamma rays are promising approaches for revealing nanosecond and microsecond dynamics directly from the microscopic viewpoint. Currently, quasi-elastic scattering systems using the gamma rays TDI have been developed and utilised for application studies. Additionally, by using a band-width variable 57Fe-NBMs, we expect that the timescale of measurable dynamics will be expanded (e.g., up to sub 100 pico-second). Developing techniques that expand the timescales of measurements (i.e., between sub 100 picoseconds and sub-microseconds), such as energy-domain quasi-elastic scattering systems combined with time-domain quasi-elastic scattering systems, is highly desirable.

Moreover, various new X-ray-based techniques are proposed for studying microscopic dynamics, based on focusing monochromators [59], or X-ray echo spectroscopy [60] or free electron lasers (e.g., four-wave mixing experiments) [61]. The combination of these new X-rays (and gamma rays)-based techniques expands the timescales of the measurements significantly (e.g., from femtoseconds to microseconds). Future studies will open new methodologies for depicting the microscopic structural dynamics of condensed matter by X-rays.

same for both samples and the *c* value could also be assumed to be the same and (ii) the non-relaxing component of the polymer was found to be negligible in a mixture of PB and carbon black nanoparticles in the *q* range of the first peak [48, 49].

*Temperature dependence of the averaged relaxation times obtained for pure PB, PB-silica20 and PB-silica100*

*. The error bars indicate the standard deviations, and the line indicates the α-relaxation times*

*WAXS profile obtained for pure PB and PB-Si100 at room temperature, and for PB-silica20 at 270 K. The bar*

*represents the q region of the quasi-elastic scattering measurements.*

*Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications*

**Figure 8.**

**Figure 9.**

**74**

*at q = 14 nm*�*<sup>1</sup>*

*obtained by dielectric relaxation spectroscopy [58].*

**Figure 9** shows the temperature dependence obtained for h i*τ* . The α-relaxation times of pure PB obtained by dielectric relaxation spectroscopy (depicted as a line in **Figure 9**) demonstrate that our results are consistent with the dielectric relaxation spectroscopy results [58]. The temperature dependencies of h i*τ* obtained for PBsilica20 and PB-silica100 also show divergent behaviour, although the VFT parameters appear to be different compared to pure PB. At 250 K, the α-relaxation times obtained at *q* = 14 nm�<sup>1</sup> for PB-silica20 and PB-silica100 were longer than those for pure PB, and this relation holds true throughout the studied temperature region. These data suggest that the nanoparticles cause the polymer α-relaxation motion to slow down. Moreover, the dynamics of PB-silica20 were much slower than

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