Eigen and Zundel ions

Bernal Uruchurtu MI, Ruiz-L6pez MF (2007) Eigen and Zundel ions in aqueous environments. A theoretical study using semi-empirical force fields. In Hemandez-Lamoneda R (ed) Beyond standard quantum chemistry applications from gas to condensded phases. Transworld Research Network, Kerala, pp 65-85 Serrano-Andres L, Fulscher MP, Karlstrom G (1997) Solvent effects on electronic spectra studied by multiconfigurational perturbation theory. Int J Quantum Chem 65(2) 167-181... 

Structural diffusion is provided by various complexes bare hydronium ion, Eigen complexes, and - Zundel complexes. Structural diffusion of bare hydronium ion and Eigen complexes occurs by proton hops between two water molecules. Two or more protons and several water molecules are involved in the structural diffusion of Zundel complexes. The contribution of mechanisms to the overall mobility depends on the temperature. Eigen and Zundel complexes prevail at room temperature, whereas bare hydronium ions dominate at high temperatures. Excess proton mobility of water has Arrhenius-like (-> Arrhenius equation) temperature dependence with the - activation energy about 0.11 eV. 

First of all, what was considered were bare hydronium H3+0 ions with three equivalent protons, a hydrated hydronium ion with three strongly bound water molecules (i.e., Eigen cluster H904+), and the symmetric H502+ complex in which a proton is shared between two water molecules (i.e., the Zundel ion). Many intermediates or more-complex states of the hydrated proton, H+(H20) , may also exist. All clusters have a finite lifetime and transform between each other during charge transport. Due to the variation of the relative abundance of these three basic states, proton transfer may occur via different pathways. 

If the hydroxonium ions migrated only hydrodynam-ically A° 85 cm2 would be expected, which value can easily be derived by using the -> Stokes law and the known values of the -+ self-diffusion coefficient of water, the radius of the ion and the - viscosity. (See also proton, - Eigen complexes, - Zundel complexes, charge transfer, - Dahms-Ruff theory.)... 

Along the walls of the aqueous domain, where the sulfonate groups are tethered, hydration of the reactants (either the hydro-nium ion or the water molecule) is possible by the oxygen atoms in SOs" because hydrated protons form Zundel-ion-like and Eigen-ion-like configurations with the end groups. This reaction can be represented by the following equation... 

Further, the coarse grained nature of the algorithm will allow the extension of modeling of proton transport in bulk water to PFSA membranes because hydrated protons form similar Zundel-ion-like stractme and Eigen-ion-like structure with the oxygen of the sulfonate groups, which can be easily integrated into the RMD formalism. 

The system, for which proton-transfer reactions are investigated best, is very simple and complex at the same time liquid water. Numerous theoretical studies - mainly based on different types of molecular-dynamics simulations - have been published in the last decades that try to reveal the secrets behind the proton-transport properties of water. Generally, these studies make use of an excess proton which might be solvated in two different ways either as a so-called Eigen ion (or Eigen complex) H9O/ or as a so-called Zundel ion (Zundel complex) H502i In the first, the excess proton is complexed by... 

Fig. 2 Eigen-Zundel-Eigen (EZE) proton-mobility mechanism. The positive charge is either located at the hydronium ion (left and right structure), which is the center of the Eigen complex HsO/ (equal to HsO (1120)3), or delocalised over the Zundel ion HsOi " (central structure). Hydrogen bonds are depicted as dashed lines.

One of the best investigated, yet not fully understood, transport processes is that in water. So far, the dispute about the Zundel and Eigen ion being the transporting species has been settled partly. Many studies favour the Eigen ion the Zundel ion is considered to be a transition state during the proton transfer. Similar species have been observed in phosphonic and phosphoric acid. However, the presented studies did not put emphasis in the distinction between those two cationic species. 

Figure 13.13 From left to right, a proton in an Eigen ion migrates to form a Zundel ion, and then proceed to form another Eigen ion. Only the hydration shell of the lower water molecules is shown.

Paddison and Elliott concluded that the conformation of fhe backbone, fhe side chain flexibilify, and fhe degree of associafion and aggregation of fhe side chains under low hydration defermine fhe formafion of protonic species (Zundel and/or Eigen ions)/ These calculations for single ionomer chains do not account for ionomer aggregafion. Therefore, fhey insufficienfly represent the membrane morphology and correlation effects between backbones, side chains, protons, and water. 

While it is beyond the scope of this review to elucidate details of the current views of proton transport across hydrogen bonds in aqueous systems, the reader is referred to the paper by Eikerling et al 148 j hese authors describe the three main options as follows (1) An excess proton can be a part of an H3O+ ion in which all of the three protons are equivalent. (2) The proton is placed between the two water molecules in the hydrogen bond in an HsOz" " grouping, in the view of Zundel. (3) The proton is a part of an Eigen H9O4+ cluster comprised of an H3O+ ion and three H2O molecules strongly attached to each of the three protons of the HaO" " species. ... 

In this first task, each excess proton is permanently attached to a hydronium ion. This assumption prohibits stractural diffusion of the proton. However, for the purposes of the first task, namely the generation of molecular-level stmcture of the hydrated membrane and its interfaces, this approximation is adequate. For the second task, namely the generation of transport properties, this limitation is removed. Although, the classical MD simulations in task I cannot quantitatively characterize the stmctural diffusion mechanism, from the analysis of the hydration structure of the hydronium ions in these simulations the characteristics of Zundel and Eigen ion (which are necessary for structural diffusion) can be studied. 

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