Synchrotron-radiation-based perturbed angular correlations used in the investigation of rotational dynamics in soft matter

A new method, synchrotron-radiation-based perturbed angular correlations, was applied to study rotational dynamics of Mössbauer atoms in soft condensed matter, using incoherent nuclear resonant scattering of synchrotron radiation. A theory was developed that describes the correlations for the scattering by an ensemble of randomly oriented spins under the influence of rotational relaxation. In a feasibility study a molecular glass former doped by probe molecules was investigated above the glass transition up to the normal liquid state. A comparison of the obtained rotational relaxation rates with data from dielectric spectroscopy shows that the probe molecules reproduce the dynamics of the glass former.

Figure 1

Schemes of the principle and of the experimental setup for TDPAC (left side) and SRPAC (right side).

Figure 2

Geometry of SRPAC. The $x$ and $y$ axes lie in the plane of the storage ring.

Figure 3

Time dependence of the SRPAC signal $I(\vartheta ;t)$ (in log scale) for the angle $\vartheta$ equal to (from top) 0°, 45°, and 90°. The bottom curve shows the time dependence of the NFS intensity. The parameters of the simulation are ${\tau }_0=141.1\mathrm{ns}$ and $\Omega =24∕{\tau }_0$.

Figure 4

Simulation of the perturbation factor $G_{22}\left(t\right)$ for various ratios of $\lambda ∕\Omega$ in the frame of the SCM according to Eq. (10). The parameters of the simulation are ${\tau }_0=141.1\mathrm{ns}$ and $\Omega =24∕{\tau }_0$.

Figure 5

Side view of the experimental setup of SRPAC with PM—premonochromator, HRM—high-resolution monochromator, and APD—avalanche photodiode. The axis sample-APD corresponds to the $z$ axis of Fig. 2.

Figure 6

Time evolution of the SRPAC signal (in log scale) for several temperatures. The solid lines are fits by the theory given by Eqs. (3, 10).

Figure 7

Time evolution of the SRPAC signal (in log scale) measured along the $z$ axis $(\vartheta =0°)$ and along the $x$ axis $(\vartheta =90°)$ in Fig. 2. The solid lines are fits by the theory given by Eqs. (3, 10).

Figure 8

Time evolution of the anisotropy $2A_{22}{G}_{22}\left(t\right)$ for several temperatures. The solid lines are fits by the theory given by Eqs. (3, 10).

Figure 9

Temperature dependence of the quadrupole frequency $\Omega$ obtained by SRPAC (엯) and of the effective quadrupole frequency ${\Omega }_e$ obtained by SRPAC (●) and by NFS (⋆).

Figure 10

The relaxation rate $\lambda$ (in log scale) obtained from SRPAC as a function of inverse temperature $1000∕T$. The solid lines are the Arrhenius and the Vogel-Fulcher-Tammann fits in the low- and high-temperature regions, respectively. The lower limit of sensitivity is about $1.5\times {10}^6{\mathrm{s}}^{-1}$ as seen from the data point at $160\mathrm{K}$.

Figure 11

Inverse temperature dependence of the different relaxation processes (in log scale) in DBP. The left side scale denotes the relaxation rate of the FC molecules obtained from SRPAC (●). The right side scale denotes the relaxation frequency obtained from dielectric spectroscopy for pure DBP from Ref. 55 (⋆) and Ref. 56 (엯). The solid line is the same Arrhenius dependence as in Fig. 10.