Ion dynamics in pendant and backbone polymerized ionic liquids: A view from high-pressure dielectric experiments and free-volume model

Polymerized ionic liquids (PILs) are typically single-ion conductors, where one kind of ionic species is either placed as the pendant group to the chain (pendant PILs) or directly incorporated into the polymeric backbone (backbone PILs). This paper compares the thermodynamics, ionic dynamics, and mechanical properties of pendant and backbone PILs. The results indicate that near the glass transition, the energy barrier for ion hopping is much lower for pendant PIL while the backbone PIL shows a much stronger sensitivity to pressure. At the same time, a free-volume based model was proposed here to understand the ion dynamics of both studied PILs at high-pressure conditions. The determined critical volume, quantifying the minimal volume required for ion hopping, of the pendant PIL is significantly reduced compared to the backbone PIL, which is most likely the reason for the enhanced ionic conductivity of the pendant PIL near the glass transition. We found that the proposed model is equivalent to the commonly used pressure counterpart of the Vogel-Fulcher-Tammann equation.

Figure 1

The specific heat capacity of (a) TPIL and (b) PHVI at ambient pressure conditions determined from DSC.

Figure 2

The real part of the complex conductivity (a) and the imaginary part of the complex electric modulus (b) as functions of frequency at selected temperatures as indicated for PHVI at 0.1 MPa.

Figure 3

The temperature dependences of ${\tau }_{\sigma }, {\tau }_{\mathrm{s}}$, and ${\sigma }_{\mathrm{DC}}$ for studied PILs. The data are parametrized by using VFT $(T>T_g)$ and Arrhenius $(T<T_g)$ equations. The determined VFT fitting parameters for PHVI are ${\log }_{10}{\tau }_{\sigma \infty }=-12.68\pm 0.20\mathrm{s}, D_{\mathrm{VF}}=12.12\pm 0.91, T_{\mathrm{VF}}=196.11\pm 3.81\mathrm{K} \left({\tau }_{\mathrm{sigma}}\right)$; ${\log }_{10}{\sigma }_{\mathrm{DC}\infty }=0.29\pm 0.13\mathrm{S}\mathrm{c}{\mathrm{m}}^{–1}, D_{\mathrm{VF}}=9.59\pm 0.54, T_{\mathrm{VF}}=208.20\pm 2.82\mathrm{K}$ (${\sigma }_{\mathrm{DC}}$); ${\log }_{10}{\tau }_{\sigma \infty }=-19.59\pm 1.31\mathrm{s}, D_{\mathrm{VF}}=18.18\pm 2.95, T_{\mathrm{VF}}=229.17\pm 6.21\mathrm{K}$ (${\tau }_{\mathrm{s}}$); and for TPIL are ${\log }_{10}{\tau }_{\sigma \infty }=-12.19\pm 0.17\mathrm{s}, D_{\mathrm{VF}}=4.28\pm 0.18, T_{\mathrm{VF}}=211.04\pm 0.76\mathrm{K}$ (${\tau }_{\sigma }$); ${\log }_{10}{\sigma }_{\mathrm{DCc}\infty }=0.02\pm 0.12\mathrm{S}\mathrm{c}{\mathrm{m}}^{–1}, D_{\mathrm{VF}}=4.80\pm 0.20, T_{\mathrm{VF}}=208.41\pm 0.99\mathrm{K}$ (${\sigma }_{\mathrm{DC}}$); ${\log }_{10}{\tau }_{s\infty }=-10.54\pm 0.14\mathrm{s}, D_{\mathrm{VF}}=2.37\pm 0.10, T_{\mathrm{VF}}=225.05\pm 0.59\mathrm{K}$ (${\tau }_{\mathrm{s}}$).

Figure 4

(a) The representative $M^{\prime }$($f$) spectra of PHVI from 20 to 420 MPa at $T=349\mathrm{K}$; (b) ${\tau }_{\sigma }$ as a function of $P$ at isothermal conditions; (c) The isobaric plots of ${\log }_{10}{\tau }_{\sigma }$ vs $1000T^{–1}$ at 0.1, 100, 200, and 300 MPa; (d) the plot of $T_{\mathrm{g}}$ as a function of $P$; the line denotes the fitting results by using the Anderson-Anderson equation.

Figure 5

The isothermal ${\log }_{10}{\tau }_{\sigma }\left(P\right)$ data of studied PILs are parametrized by using Duclot equation [(a), (b)] and modified Duclot equation [(c), (d)], respectively.