実験報告書様式（一般利用課題・成果公開利用）
提出日 Date of Report

MLF Experimental Report
課題番号 Project No.

装置責任者 Name of responsible person

2015A0107

Kenji Nakajima

実験課題名 Title of experiment

装置名 Name of Instrument/（BL No.）

Systematic studies on hierarchic structure and dynamics in model

BL-14

rubber materials: heterogeneous local dynamics in rubbers

実施日 Date of Experiment

実験責任者名 Name of principal investigator

2016/3/28 ～ 2016/4/1

Toshiji Kanaya
所属 Affiliation
High Energy Accelerator Research Organization (KEK)
試料、実験方法、利用の結果得られた主なデータ、考察、結論等を、記述して下さい。（適宜、図表添付のこと）
Please report your samples, experimental method and results, discussion and conclusions. Please add figures andtables for better explanation.
1. 試料 Name of sample(s) and chemical formula, or compositions including physical form.
Polybutadiene rubbers (-(C4H6)n-) including silica filler (SiO2) (volume fraction of 0, 0.2) were used for sample
and the thicknesses of prepared samples were at around 0.2mm.

2. 実験方法及び結果 （実験がうまくいかなかった場合、その理由を記述してください。）
Experimental method and results.

If you failed to conduct experiment as planned, please describe reasons.

Neutron scattering studies are now looking towards realistic materials (or industrial materials) in addition to
traditional scientific researches on simple model materials. In soft matter, intensive studies are now performed on
industrial rubber materials such as mobile tire and rubber base-isolated structure. However, generally speaking,the realistic rubber materials have complicated structure and dynamics in wide spatial and time scales, which are
dominated by many factors such as fillers, aggregations of fillers, crosslinks between polymers, coupling agents
between filler and polymer. Hence, it is not easy to interpret the complicated results or extract useful information
for industries from the results.
To understand the data on the realistic (industrial) complicated rubber materials and to fill up the gap ofstudies between the realistic (industrial) and ideal materials we propose systematic studies on some model rubbermaterials by means of various kinds of quantum beams. In this experiment, we focus on polybutadiene (PB)
including silica powder fillers with no crosslinks using BL14 at J-PARC to see the local heterogeneousdynamics.
Dynamic scattering laws S(Q, ω) in the range Q = 1.8 Å−1 at 300 K are shown in Fig.1. The narrowing of S(Q,ω) by an addition of silica can be observed with an energy resolution of 0.35 meV, suggesting that the motion ofPB is slowed down by an addition of silica. To understand this result in detail, we adopted theKohlrausch-Williams-Watts (KWW) function to describe the observed S(Q, ω), and the following model1

2. 実験方法及び結果（つづき） Experimental method and results (continued)
function was proposed.

({ [S (Q, ω ) = A (1 − EISF )F exp − (t τ )β]}+ EISFδ (ω ))⊗ R(Q, ω ) (1)where A, EISF, τ, and β are the amplitude of therelaxation function, the elastic incoherent structure factor,
the relaxation time, and the distribution of the relaxation
function, respectively. It should be noted that the KWW
function is utilized in the time domain, necessitating that
we adopt the Fourier-transformed KWW function(F(KWW)) in the frequency region. R(Q, ω) indicates theinstrumental resolution function. Fig. 1 shows the resultsof the fits to S(Q, ω) with Eq. (1) at Q = 1.8 Å−1 and 300
K. The S(Q, ω) from both samples are fitted fairly well by
Eq. (1), confirming the appropriate model function
selection.

Fig. 1 Dynamic scattering laws S(Q, ω)
normalized at the peak top at 300 K in the range
Q = 1.8 Å−1. The solid line is the instrumental

The dependence values of the average relaxation time
<τ> and the relaxation time distribution β at 300 K in theresolution function.

range Q = 1.8 Å−1 on the volume fraction of silica areshown in Fig. 2. <τ> was calculated using Eq. (2)[1]:
where Γ is a gamma function.
τ   1 τ =  Γ β  β (2)The increase of <τ> and EISF in the silica volume
fraction were evaluated, suggesting that themotion of mobile component is slowed down andthe fraction of immobile component is increased
with increases in the silica volume fraction. The
detailed analysis is still on progress.

Fig. 2 Volume fraction of silica dependence of<τ> and EISF at 300 K in the range Q = 1. 8 Å−1.

Reference[1] F. Alvarez et al., J. Phys. Rev. B 44, 7306 (1991).

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