The electrical double-layer at a solid electrode does not m general behave as a pure capacitance but rather as an impedance displaying a frequency-independent phase angle different from 90 o Ways are indicated how to analyse the interracial impedance ,f such a complication arises in the presence of a faradalc process, both on the supposition that the double-layer behavlour is due to surface mhomogenelty and on the supposition that it is a double-layer property per se As examples, the equations derived are successfully apphed to a totally Irreversible and an ac quasi-reversible electrode process at a gold electrodeAccording to conventional double-layer theories, the impedance Z of an ideally polarized electrode consists of a capacitance (Cd) in series with the solution resistance (R e), and consequently the corresponding complex plane diagram (Z" vs. Z') should exhibit a straight vertical line intersecting the horizontal axis at Z' = R e, while the ordinates along this line equal Z" = (~0Cd) -a.This ideal behaviour is experimentally best observed at mercury/(aqueous) solution interfaces, for example at a dropping mercury electrode (DME), a hanging mercury drop electrode (HMDE), or a mercury pool electrode. Deviations from ldeality may occur in these cases, owing to rather trivial effects such as capdlary response or creeping [1], shielding by the glass capillary [2,3], and contamination of the mercury surface. The result of such effects is usually a curved complex plane plot, approaching the straight vertical line at higher frequencies. A less trivial deviation may be caused by diffusion-controlled adsorption of species present at a low concentration.Also at solid electrodes interfering effects, especially contamination and surface roughness, are hkely to be present, but apart from these a more marked behavlour 0022-0728/84/$03 00

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ABSTRACT'The reduction of H+ from 1 M FICiO, and 1 IV NaCIO., solurions at polycrystalline and single crystal faces of very pure gold electrode; is studied by determining the forward rate constant kr as a funcrion of porential and of H' concentration.The tecchniques applied are dc current and impedance measurements both with a step-wise variation of dc poIentia1 (duration 4 s). and dc current measurements with a continuous potential variation. The consistency of the results is extensively lested and found to be qui!e satisfactory. Plots of In k, vs. potential are curved and exhibit limiting slopes corresponding to values for the operational transfer coefficient o = 1 at positive and a = 0.5 at negative potentials. This behaviour is discussed in terms of mechanistic models described in the literature and also an alternative mechanism is tentatively proposed An increase in the rate constants is observed when the purity of the gold is iess. The slight differences in the rate constants observed, al single crystal faces of the same purity but wirh different crystallographic orientation are discussed. (I) INTRODUCTIONThe study of electrochemical kinetics at solid electrodes has often suffered from the poor quality of experimental results. As compared to the use of the dropping mercury electrode as a working electrode, the problems arising with solid electrodes became painfully clear and practically all of the meaningful data and theories on electrode kinetics were obtained and tested at the dropping mercury electrode. This is even more true in

The literature values of the limiting ionic conductivities of H(+), OH(-), K(+), Cl(-), Ag(+), and Na(+) in water between 0 and 156 degrees C are analyzed as for the two possible mechanisms of conduction, i.e., controlled by an activation process or by the rotation of the water molecules. Plots of the data versus T(1/2) give straight lines for H(+) and OH(-), which supports the rotation control mechanism for these ions. The other ions give curved plots and therefore are investigated in terms of the activation control mechanism. A remarkable phenomenon is discovered, namely, that except for H(+), the graphs for the other ions on extrapolation to lower temperatures have a common intersection point, T(0)(1/2), with the abscissa corresponding to T(0) = 243.4 K, i.e., -30 degrees C. This seems to indicate the presence of a virtual phase transition at about -30 degrees C, foreboding itself at higher temperatures. Below this temperature the supercooled water does not allow ions to migrate. Also, diffusion of solutes is found to cease, and dissociation constants drop to zero. The values of many physical properties of water appear also to approach zero at -30 degrees C, viz. the self-diffusion coefficient, reciprocal dielectric relaxation time, and solubilities of sparingly soluble salts. From data on the fluidity (reciprocal viscosity) and self-ionization constant it follows that the transition temperature of supercooled D(2)O is 9 degrees higher than of H(2)O. From the nearly quadratic shape of the several temperature dependencies it is inferred that the phase transition in question possibly is of some higher order. Implications for the transport number of protons to be expected in supercooled water are finally discussed.

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