Proton Transport in Water and Aqueous Networks

Water was born to conduct protons (see Special Issue Is life possible without water [67]). The conductance of distilled water is miserable due to a negligible concentration of free protons (10 mol/liter), but the proton mobility in water is approximately five times higher than the mobility of an alkali cation (e.g. Na ), an object of similar size as the hydronium (HaO ) ion [68]. So, donated protons can run fast through the aqueous phase. Excess protons result from dissociation of acidic molecules or molecular groups, e.g. in solutions of strong acids, hydrated polymer-electrolytes, or proteins. In acidic solutions both the protons and counter-anions are mobile. In polymer-electrolyte membranes and in proteins only protons are mobile in the connected aqueous phase while the counter anions are mostly a part of an immobile skeleton. 

Experimental studies of temperature-dependent proton mobility have a long and dramatic history. In a modern sense they date back to the works of Johnston [69] and Noyes [70,71 ], followed much later by the studies of the pressure dependence by Eucken [72,73], Gierer and Wirtz [74], Gierer [75], and Franck, Hartmaim and Hensel [76]. Reference [77] gives a comprehensive overview of aqueous proton conductivity and the early experimental data, based on the concept of the excess mobility, responsible for the difference of the observed proton mobihty from the one provided by the classical hydrodynamic motion of the hydronium ion. 

The excess mobihty-vs.-temperature curve was found to exhibit a max-immn at elevated temperatures near 150 °C, achievable at elevated pressure. The magnitude of the proton mobihty in pure water was not addressed in those studies, although attempts to determine it were made by Kohhausch at the end of the 19th centmy [78]. Focus was instead on the conductance of strong acids such as HCl in the Umit of infinite dilution. The difference of the measured conductance and the limiting conductance of a salt of a cation with size similar to that of was attributed to excess proton mobility, based on the assmnption that the hydrodynamic radius of both ions is similar. The excess mobility was taken to represent non-classical proton hops on top of the classical hydrodynamic motion of the HsO .  

Proton conductivity in bulk aqueous solution can be contrasted with proton conductance in water-saturated polymer electrolyte membranes, such as per-fluorinated sulfonic acids [49,50,79], where protons are the only charge carrier 

There are other caveats with the simplest notion of excess proton mobihty, and the comparison with membrane proton conductance at water saturation. Subtracting the hmiting conductance of Na ions, which move only by the classical mechanism, essentially cancels the classical conductance of HsO . However, the cancelation cannot be complete, because HsO exhibits classical motion only for part of the time. Nevertheless, the difference can be used as a measure of non-classical contributions to proton conductance. It is more precise the smaller the classical, hydrodynamic contribution to the proton mobihty. 

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