Proton structural diffusion

These studies showed that sulfonate groups surrounding the hydronium ion at low X sterically hinder the hydration of fhe hydronium ion. The interfacial structure of sulfonafe pendanfs in fhe membrane was studied by analyzing structural and dynamical parameters such as density of the hydrated polymer radial distribution functions of wafer, ionomers, and protons water coordination numbers of side chains and diffusion coefficients of water and protons. The diffusion coefficienf of wafer agreed well with experimental data for hydronium ions, fhe diffusion coefficienf was found to be 6-10 times smaller than the value for bulk wafer. 

The total electro-osmotic coefficient = Whydr + mo includes a contribution of hydrodynamic coupling (Whydr) and a molecular contribution related to the diffusion of mobile protonated complexes—namely, H3O. The relative importance, n ydr and depends on the prevailing mode of proton transport in pores. If structural diffusion of protons prevails (see Section 6.7.1), is expected to be small and Whydr- If/ ori the other hand, proton mobility is mainly due to the diffusion of protonated water clusters via the so-called "vehicle mechanism," a significant molecular contribution to n can be expected. The value of is thus closely tied to the relative contributions to proton mobility of structural diffusion and vehicle mechanism. ... 

Structural diffusion is favored by conditions that enhance the stiffness of the hydrogen-bonded network between water molecules low temperatures and low acid concentration. The decrease in water content leads to an effective increase in the concentration of acid protons, which in turn suppresses the contribution of structural diffusion, as found in aqueous acidic solutions. This agrees with the finding of an enhanced contribution of vehicular transport in PEMs at low hydration. Such an observation is also supported by recent studies of molecular mechanisms of proton transport in PEMs at minimal hydration. ... 

Structure diffusion (i.e., the Grotthuss mechanism) of protons in bulk water requires formation and cleavage of hydrogen bonds of water molecules in the second hydration shell of the hydrated proton (see Section 3.1) therefore, any constraint to the dynamics of the water molecules will decrease the mobility of the protons. Thus, knowledge of the state or nature of the water in the membrane is critical to understanding the mechanisms of proton transfer and transport in PEMs. 

Molecular details of the structure diffusion mechanism with the hydrogen-bond breaking and forming and the proton transfer between the different phos-... 

The detection of other molecules, such as ammonia, requires the use of a porous catalytic metal. To obtain a gas response from the NH3 molecule, it is believed that active sites of triple points are required where the molecules are in contact with the metal, insulator, and ambient [30, 31]. It has been shown that gas species such as hydrogen atoms or protons also diffuse out onto the exposed oxide surface in between the metal grains [Figure 2.1(b)] [32, 33]. Furthermore, Lofdahl et al. have performed experiments that provide clear evidence that hydrogen atoms or protons also diffuse under the metal from the triple point [34]. The hollow structure of the metal surface facing the insulator has been revealed by Abom et al. [35]. 

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. 

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... 

Some attempts to inclnde structural diffusion exist. The mechanism of proton transport in bulk water has been studied by various molecular modeling techniques like the Car-Parinello ab initio molecnlar dynamics simnlations (CPAIMD), mixed quan-tnm and classical mechanics technique (QM/MM), E " ... 

The structural diffusion of proton can be represented by the following equation ... 

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.

Figure 25. The estimated (bold line) structural diffusivity of the proton from Eq. (11) as a function of temperature is used as the reference for the structural diffusivi-ties obtained from RSI (triangle) and RSII (square).

The simulated and experimental hydronium diffusivities both increase with increasing water contents. The simulated values are lower than the experimental values, presumably, due to the fact that the simulations report only the vehicular contribution to the proton diffusivity, whereas the experiment measures the total proton diffusivity. Experimentally, Nafion has higher proton diffusivity than SSC at low water contents and lower proton diffusivity than SSC at high water contents. The vehicular diffusion coefficients of the hydronium ion measured from simulation are higher for Nafion than in SSC PFSA at all water contents. Clearly a detailed understanding of the total proton diffusivity as a function of polymer architecture requires a model capable of structural diffusion. 

The structural diffusion of proton in a PFSA membrane can be described by three reactions depending upon the reactants and the surrounding environment. If the channels that compose the aqueous domain are sufficiently large, there may be a bulk-like region near the center of the channel, where the water stracture is similar to bulk water and where, therefore, we can expect the reaction to take place as in Eq. (2),... 

The thermal activation energy of proton conductivity at intermediate and high water content is similar to that in dilute aqueous acidic solutions (see Fig. 6). From this similarity it has been concluded that proton transfer in PEMs proceeds, like in the bulk, according to the Grotthus structural diffusion mechanism (see below). For decreasing water content a very slight trend towards... 

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