Definitions

# Grotthuss mechanism

The Grotthuss Mechanism is the mechanism by which an 'excess' proton or protonic defect diffuses through the hydrogen bond network of water molecules or other hydrogen-bonded liquids through the formation/cleavage of covalent bonds.

In his seminal 1806 publication “Theory of decomposition of liquids by electrical currents”, Theodor Grotthuss proposed a unique theory of water conductivity. Grotthuss envisioned the electrolytic reaction as a sort of ‘bucket line’ where each oxygen atom simultaneously passes and receives a single hydrogen atom. It was an astonishing theory to propose at the time, since the water molecule was thought to be OH not H2O and the existence of ions was not fully understood. On its 200th anniversary his article was reviewed by Cukierman.

OH$cdot$OH$cdot$OH ? O-$cdot$HO$cdot$HO $cdot$H+

Although Grotthuss was using an incorrect empirical formula of water his description of the passing of protons through the cooperation of neighboring water molecules proved to be remarkably fortuitous.

## Proton Transport Mechanism / Proton Hopping mechanism

The Grotthuss Mechanism is now a general name for the proton-hopping-mechanism. In liquid water the solvation of the excess proton is idealized by two forms; the H9O4+ (Eigen cation) or H5O2+ (Zundel cation). While the transport mechanism is believed to involve the inter-conversion between these two solvation structures, the details of the hopping/transport mechanism is still debated. Currently there are two plausible mechanisms:
I) Eigen to Zundel to Eigen (E-Z-E), on the basis of experimental NMR data,
II) Zundel to Zundel (Z-Z), on the basis of molecular dynamics simulation.

In 2007, Omer Markovitch and Noam Agmon reported for the first time the energetics of the hydronium solvation shells and suggested that the activation energies of the two proposed mechanisms do not agree with their calculated hydrogen bond strengths, but mechanism (I) might be the better candidate of the two.
Addition: By use of conditional & time-dependent radial distribution functions (RDF), it was shown that the hydronium RDF can be decomposed into contributions from two distinct structures, Eigen & Zundel. The first peak in g(r) of the Eigen structure is similar to the equilibrium, standart, RDF, only slightly more ordered, while the first peak of the Zundel structure is actualy split into two peaks. The actual proton transfer event was then traced (after synchronizing all PT events so that t=0 is the actual event time), revealing that the hydronium indeed starts from an Eigen state, and quickly transforms into the Zundel state as the proton is being transferred, with the first peak of g(r) splitting into two.

## The anomalous diffusion of protons

The Grotthuss mechanism explains the unusually high diffusion of the proton relative to other the typical ionic diffusion of other cations (Table 1) which is due simply to random thermal motion i.e. Brownian motion.

Table 1

 Cation Mobility / cm2 V−1 s−1 NH4+ 0.763×10−3 Na+ 0.519×10−3 K+ 0.762×10−3 H+ 3.62×10−3

## References

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