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The diffusion of "simple ions" in solution, such as sodium Na+ and chlorine Cl- ions in a salty soup, takes place via migration of these ions in space. Expressed in a simple picture, this is similar to a courier walking through a pedestrian zone in order to deliver a letter. Acids, which are liquids with a high concentration of unbound hydrogen ions (H+ or protons), share dramatically fast proton mobilities in comparison with simple solutions.
All the evidence points to the speculation that protons in acids move by another mechanism than simple ions. One can get a rough idea of what can happen by coming back to the courier metaphor. What would he do if the pedestrian zone is so overcrowded that he can barely move? If he were smart, he would pass his express letter to a neighbor to pass on to his neighbor etc. If everything works out, the message will at the end be handed over to its final destination. Even better: it will arrive faster than before because passing the letter along a chain of people from one hand to the next takes practically no time! Protons in acids play the same game, roughly speaking. In this case it is called "structural diffusion" or "Grotthuss diffusion" in honor of C. J. T. de Grotthuss who ingeniously introduced this concept as early as 1806. However, the microscopic knowledge of nature was very limited at that time: for instance liquid water was assumed to be composed of "HO molecules" instead of H2O as we know today.
A more detailed explanation had to await the twentieth century with the birth of statistical and quantum mechanics. Many eminent theoreticians, among them Hückel, Fowler, Wannier and Eyring, proposed theories to explain the Grotthuss mechanism. The emerging picture is that the proton H+ is chemically bonded and forms a structural defect. Furthermore it is this very defect and not an individual proton which effectively migrates in acids by interconverting weak (hydrogen) bonds into strong (covalent) bonds and vice versa. This is similar to the immobilized courier who passes his letter from one hand to the next instead of moving himself. However, important aspects of the Grotthuss mechanisms remained highly controversial.
At the heart of the present investigation are fully quantum-mechanical simulations performed on a parallel supercomputer Cray-T3E/816 of the Max Planck Society. A pictorial realization of the structural diffusion process can be gleaned from the particle density snaphots in Fig. 1. Initially, the protonic defect is found to be localized as an H9O4+ structure possessing an H3O+ core that donates three hydrogen bonds to neighboring water molecules, see Fig. 1(a). In the second frame (b), one of the three protons of the H3O+ core migrates along its hydrogen bond and forms an H5O2+ complex, in which this proton becomes equally shared between two water molecules. As the transfer is completed, an H9O4+ complex is formed once again, but now centered on a neighboring core molecule, as depicted in Fig. 1(c). The onset of further migration takes place in (d), where the defect converts into another H5O2+ configuration. Overall, the structural defect is displaced from (a) to (d) over a distance corresponding to approximately twice the average water-water distance, viz. about 5 Angstrom. Each individual particle, however, moves by only a fraction of an Angstrom.
Figure 1:
Perspective view of three-dimensional representative quantum configurations
belonging to the proton migration path of one proton in liquid water composed of
32 H2O molecules. Only the non-periodically replicated atoms (oxygens: red,
hydrogens: grey) and covalent bonds (O-H) are included; hydrogen bonds (O...H,
green) are sketched only in panel (a). The defect is indicated by yellow
(oxygens) and black (hydrogens).The "blurring" of the atom positions and
delocalization of the defect is due exclusively to quantum effects.
This scenario, found solely by solving first-principles quantum-mechanical equations, is the basic sequence of proton transfers according to Grotthuss's old perception. Detailed quantitative analysis shows that two defects, H9O4+ and H5O2+, which have been discussed controversially in the literature, are both important for proton diffusion, but only in the sense of "limiting" or "ideal" structures. Therefore, the protonic defect is best visualized as a "fluxional complex", and proton diffusion cannot be understood in terms of one or the other defect as argued previously. Furthermore, it is found that quantum tunneling does not play a role, whereas the very fluxionality is induced by quantum-mechanical zero-point motion of the excess proton which is shared between water molecules. These quantum fluctuations also sometimes lead to situations where the defect is actually delocalized over several hydrogen bonds. But despite this effect, the net displacement of the defect, which is finally responsible for the macroscopic proton conductivity of acids, is caused mainly by classical thermal fluctuations in the hydrogen-bonded network around the defect.
Published: 15-1-99
Contact: Dominik Marx
Max Planck Institute for Solid State Research
Stuttgart/Germany
Phone: +49-711-689-1653
Fax: +49-711-689-1702
Journal
Nature