AC and DC conductivity of ionic liquid containing polyvinylidene fluoride thin films

Abstract

Polarisation processes and charge transport in polyvinylidene fluoride (PVDF) with a small amount (0.01–10 wt%) of the ionic liquid (IL) 1-ethyl-3-methylimidazolium nitrate ($\hbox {[EMIM]}^+[\hbox {NO}_3]^-$) are investigated by means of dielectric spectroscopy. The response of PVDF that contains more than 0.01 wt% IL is dominated by a low-frequency relaxation which shows typical signatures of electrode polarisation. Furthermore, the $\alpha _{{\rm a}}$ relaxation, related to the glass transition, disappears for IL contents of more than 1 wt%, which indicates that the amorphous phase loses its glass-forming properties and undergoes structural changes. The DC conductivity is determined from the low-frequency limit of the AC conductivity and from the dielectric loss peak related to the electrode polarisation. DC conductivities of $10^{-10}$ to $10^{-2}\,\hbox {S}/\hbox {m}$ are obtained—increasing with IL content and temperature. The dependence of the DC conductivity on the IL content follows a power law with an exponent greater than one, indicating an increase in the ion mobility. The temperature dependence of the DC conductivity shows Vogel–Fulcher–Tammann behaviour, which implies that charge transport is coupled to polymer chain motion. Mobile ion densities and ion mobilities are calculated from the DC conductivity and the dielectric loss related to electrode polarisation, with the results that less than one per cent of the total ion concentration contributes to the conductivity and that the strong increase in conductivity with temperature is mainly caused by a strong increase in ion mobility. This leads to the conclusion that in particular the ion mobility must be reduced in order to decrease the DC conductivity.

Appendix: Calculation of the total ion density and of the CH2–CF2 dipole concentration

Under the assumption that ions do not penetrate into crystallites, the total ion concentration within the film is given by

$$\begin{aligned} n_\mathrm{tot} &=\frac{\rho _\mathrm{IL}N_A}{m_\mathrm{mol,IL}} \cdot \frac{V_\mathrm{IL}}{V_\mathrm{film}}\cdot \frac{1}{(1-c)}= \frac{\rho _\mathrm{film}N_A}{m_\mathrm{mol,IL}}\cdot \frac{m_\mathrm{IL}}{m_\mathrm{film}}\cdot \frac{1}{(1-c)}\\ &\approx \frac{\rho _\mathrm{PVDF}N_A}{m_\mathrm{mol,IL}}\cdot \frac{m_\mathrm{IL}}{m_\mathrm{PVDF}+m_\mathrm{IL}}\cdot \frac{1}{(1-c)}, \end{aligned}$$

where $c\equiv m_\mathrm{c}/m_\mathrm{film}$ is the crystallinity ($m_\mathrm{c}$ mass of crystalline portion, $m_\mathrm{film}$ mass of the film).

For a film containing 1 wt% IL, $m_\mathrm{IL}=1.0$ g, $m_\mathrm{PVDF}=99.0$ g.

The density of the IL is not exactly known and is difficult to determine because [EMIM][$\hbox {NO}_3$] is hygroscopic. However, for an estimate, it can be assumed that the density is not far from the densities of other related ILs, which lie between 1100 and 1500 kg/m$^3$ (IoLiTec GmbH, Germany). The density of the solid PVDF homopolymer is $\rho _\mathrm{PVDF}=1780\,\hbox {kg}/\hbox {m}^{-3}$. Thus, for low IL contents, $\rho _\mathrm{film}\approx \rho _\mathrm{PVDF}$ is a reasonable approximation.

The crystallinity of the film increases by addition of the IL to the solution: for the 5 wt% film, $c=47$ and for the pure PVDF film, $c=36$ % were obtained, respectively [10].

By use of $c=0.36,\,c=0.40$ and $c=0.47$ for the 0.1, 1 and 5 wt% IL films, respectively, total ion concentrations in the amorphous fraction of $n_\mathrm{tot}=9.65\times 10^{24},\,1.03\times 10^{26}$ and $5.83\times 10^{26}\,\hbox {m}^{-3}$, respectively, are calculated.

The total $\hbox {CH}_2$–CF₂ dipole concentration is

$$\begin{aligned} n_{\rm d}=\frac{\rho _\mathrm{PVDF} N_A}{m_\mathrm{mol, unit VDF}}. \end{aligned}$$

With the density $\rho _\mathrm{PVDF}=1780\,\hbox {kg}/\hbox {m}^{-3}$ and the molar mass $m_\mathrm{mol, unit VDF}=0.064$ kg/mol, $n_{\rm d}=1.67\times 10^{28}\,\hbox {m}^{-3}$ is obtained.

$n_{\rm d}\gg n_\mathrm{ion}$, even for 5 wt% IL.