Linear Viscoelastic and dielectric behavior of Phosphonium Ionomers

Linear viscoelastic (LVE) and dielectric (DRS) responses were examined for polysiloxane-based phosphonium-ionomers with fractions of ionic monomers $f$ $=$ 0 to 0.3; the other monomers have short poly(ethylene oxide) side chains. LVE of these samples shows a glassy relaxation followed by a terminal polymer relaxation that is increasingly delayed with increase of $f$. The glassy relaxation broadens when $f$ \textgreater\ 0.1. DRS of these samples shows a segmental $\alpha $ process associated with motion of monomers, followed by an additional $\sim$ 100X slower $\alpha _{\mathrm{2}}$ process before electrode polarization. A detailed comparison between LVE and DRS reveals that the $\alpha_{\mathrm{2}}$ relaxation in DRS corresponds to a characteristic modulus of $k_{\mathrm{B}}T$ per ionic group in LVE. This result strongly suggests that the molecular origin of the $\alpha_{\mathrm{2}}$ relaxation is the dissociation/association of the ionic groups from/into the ionic clusters, consistent with the observed magnitude of the $\alpha_{\mathrm{2}}$ relaxation increasing with ion content. Based on this molecular view, we can predict the terminal polymer relaxation from the $\alpha_{\mathrm{2}}$ relaxation time obtained in DRS, assuming this is the lifetime of ionic associations in a sticky Rouse model. Meanwhile, the broadening of glassy mode distribution with increasing $f$ \textgreater\ 0.1 is attributed to an enhanced cooperation for motion of glassy segments. This enhancement is possibly due to decrease of distance between the ionic groups with increasing $f$, leading to stronger overlap of polarizability volumes.