Microscopic muon dynamics in the polymer electrolyte poly(ethylene oxide)

The microscopic dynamics of protons (${\mathrm{H}}^{+}$) in poly(ethylene oxide) (PEO) have been investigated through a study of implanted positive muons (${\mathrm{Mu}}^{+}$), which can be considered a light proton analog. The exponential decay of the muon spin polarization in zero magnetic field indicated that ${\mathrm{Mu}}^{+}$ hopping is in the fast fluctuation limit between 140 and 310 K and the relaxation rate was found to be sensitive to the glass transition. ${\mathrm{Mu}}^{+}$ dynamics in PEO was monitored via the relaxation of the muon spin polarization in a transverse field of 10 mT. Activated hopping of ${\mathrm{Mu}}^{+}$ was observed above the glass transition temperature with an activation barrier of $122\pm 1$ meV. The temperature dependence of the diamagnetic muon polarization in PEO can be explained by diffusion of radiolytic electrons.

Figure 1

ZF-$\mu \mathrm{SR}$ spectra of PEO at 160, 225, and 310 K. The solid lines are fits to Eq. (3).

Figure 2

Temperature dependence of the polarizations of the relaxing and nonrelaxing signals obtained from the the ZF-$\mu \mathrm{SR}$ [Eq. (3)] and TF-$\mu \mathrm{SR}$ spectra [Eq. (5)].

Figure 3

Temperature dependence of the zero-field spin relaxation rate in PEO obtained from Eq. (3).

Figure 4

TF-$\mu \mathrm{SR}$ spectra of PEO in an applied field of 10 mT at 160 and 310 K. The solid lines are fits to Eq. (5).

Figure 5

Plot of $1/T_2^{\mu }$ versus temperature for PEO. The line for $T> T_{\mathrm{g}}$ are fits to Eq. (11) and the line for $T< T_{\mathrm{g}}$ are fits to Eq. (6). The dotted line is the extrapolation of Eq. (6) above $T_{\mathrm{g}}$.

Figure 6

Arrhenius plot of $ln[\mu \mathrm{s}/T_2^{\mu }]$ versus inverse temperature for PEO. The lines for $T> T_{\mathrm{g}}$ are fits to Eq. (11) and the lines for $T< T_{\mathrm{g}}$ are fits to Eq. (6).

Figure 7

Diamagnetic polarization, $P_{\mathrm{D}}$, versus $T^{-1/2}$ in PEO. The solid lines are fits to Eq. (13).

Figure 8

${\mathrm{Mu}}^{+}$ and ${\mathrm{H}}^{+}$ hopping in alcohols and ethers.