Water molecules in confined geometries like nanopores and biological ion channels exhibit structural and dynamical properties very different from those found in free solution. Protein channels that open aqueous pores through biological membranes provide a complex spatial and electrostatic environment that decreases the translational and rotational mobility of water molecules, thus altering the effective dielectric constant of the pore water. By using the Booth equation, we study the effect of the large electric field created by ionizable residues of an hour-glass shaped channel, the bacterial porin OmpF, on the pore water dielectric constant, ε_w. We find a space-dependent significant reduction (down to 20) of ε_w that may explain some ad hoc assumptions about the dielectric constant of the protein and the water pore made to reconcile model calculations with measurements of permeation properties and pK_a’s of protein residues. The electric potential calculations based on the OmpF protein atomic structure and the Booth field-dependent dielectric constant show that protein dielectric constants ca. 10 yield good agreement with molecular dynamics simulations as well as permeation experiments.

The zeolitic imidazolate frameworks (ZIFs) ZIF-8, ZIF-67, and a Zn/Co bimetallic mixture (ZMix) were synthesized and used as fillers in the preparation of composite sulfonated poly(ether ether ketone) (SPEEK) membranes. The presence of the ZIFs in the polymeric matrix enhanced proton transport relative to that observed for SPEEK or ZIFs alone. The real and imaginary parts of the complex conductivity were obtained by electrochemical impedance spectroscopy (EIS), and the temperature and frequency dependence of the real part of the conductivity were analyzed. The results at different temperatures show that the direct current (dc) conductivity was three orders of magnitude higher for composite membranes than for SPEEK, and that of the SPEEK/ZMix membrane was higher than those for SPEEK/Z8 and SPEEK/Z67, respectively. This behavior turns out to be more evident as the temperature increases: the conductivity of the SPEEK/ZMix was 8.5 × 10⁻³ S·cm⁻¹, while for the SPEEK/Z8 and SPEEK/Z67 membranes, the values were 2.5 × 10⁻³ S·cm⁻¹ and 1.6 × 10⁻³ S·cm⁻¹, respectively, at 120 °C. Similarly, the real and imaginary parts of the complex dielectric constant were obtained, and an analysis of tan δ was carried out for all of the membranes under study. Using this value, the diffusion coefficient and the charge carrier density were obtained using the analysis of electrode polarization (EP).