Eigen ions

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. 

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. 

The degree of hydration of hydronium has relevance to structural diffusion as it requires the presence of Eigen ion (HsO + 3 H2O), which is discussed in detail in Section III. Figure 14 supports the experimental observation of low proton conductivity at low water contents due in part to the reduction of stractural diffusion because the probability of finding HsO surrounded by sufficient H2O molecules is lower. Figure 14 shows that at intermediate water contents, the probabilities for hydronium ions hydrated with three or more H2O molecules are higher in Nafion than in... 

Figure 23. Description of six geometric triggers required for structural diffusion (a) O -O separation must form a Zundel ion (b) O -H separation must exceed the equilibrium bond distance (c) Z0 H 0 is nearly linear in the Zundel ion (d) Lone pair of electrons in the water should point towards the proton (e) Initial H3O forms an Eigen ion (f) Eigen cation is formed around final H3O. These six geometric triggers must he satisfied along with the energetic trigger for the reaction to take place. O of H3O, gray O of H2O, black H, white.

H to be transferred, the O of the H2O, and each of the two H of the H2O be near the equilibrium H-O-H bond angles for HsO. In, other words, one of the two lone electron pairs in the water must be directed at the incoming H. The fifth trigger requires the HsO to be properly hydrated. Examination of Eigen ion in Fig. 22 (b) reveals minimum level of hydration required. Each of the non-reactive H on HsO is required to be within certain distance of an O of adjacent non-reactive H2O by the trigger. The sixth and the... 

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 above-described features are reproduced in a high level quantum-molecular-dynamics simulation of an excess proton in water [30, 31]. In accordance with results from several other groups, this finds the excess proton either as part of a dimer (H5O2+, Zundel -ion) or as part of a hydrated hydronium ion (H9O4+, Eigen -ion) (Fig. 23.3). 

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. 1 In the Eigen ion H9O/ (shown on the left) the positive charge is formally located at the central hydronium ion, which is the center of the Eigen complex. In the Zundel ion H5O2 the proton is complexed by only two water molecules (shown on the right). 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 5.2 Schematic of the structure of Zundel and Eigen ions, and the hydro en b d formation and breaking processes that occur in the two short-life complexes dur transport [14]. (For color version of this figure, the reader is referred to the onlina... 

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.

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