Grotthuss structural diffusion

Recently, we studied the water dependence in mixtures of water and the protonated form of Nafion [53] using both standard force field models and an empirical valence bond model to account for the Grotthuss structural diffusion mechanism of aqueous proton transport. Results showed a transition of an irregularly shaped filamentous (cylindrical) structure in the case of low water (A = 5, where A is defined as the ratio of water molecules to sulfonate groups) to a structure more in accord with the above-discussed models of nano-separation, where larger clusters form which are connected by narrow bridges. A comparison of aqueous cluster sizes indicated, for a simulation time of 30 ns, no percolating clusters for A = 5, whereas at A = 10 most water molecules were located in a connected cluster (see [53]). Other structural... 

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. 

The most important property of PVPA is conductivity based on hydrogen bonding, which allovt proton transport via a Grotthuss type mechanism (structural diffusion). The conductivity is the key property of PVPA, which is successfully used to obtain polymer electrolyte membranes by copolymerization or blending with appropriate materials. The applications of these materials have greatly expanded and now have many roles in the modern industrial economy. 

Kreuer etal. [21] provided an in-depth review of the basic mechanisms of transport in proton conductors. Transport of the proton can occur by two mechanisms structural diffusion and vehicular diSusion. Vehicular diffusion is the classical Einstein diffusive motion. The structural diffusion is associated with hopping of the proton along water molecules (the so-called Grotthuss mechanism). In the nanosized confined hydrophihc spaces within the membrane, both mechanisms are operative. What is important here is that the underlying mechanism of transport in PEMs changes as a function the level of hydration. Understanding the nature of these mechanisms and their dependence on the level of hydration and molecular structure is important in the development of advanced PEM materials that are more tolerant of higher temperatures and lower levels of saturation. 

It was accepted in the above-presented equations that diffusion coefficients of all the particles were equal. If the size of complexes or ligands is similar, such an assumption is justified. However, it is known that H" " and OH" ions distinguish themselves from other by their greater mobility, which is determined by the so-called structural diffusion (Grotthuss mechanism) involving a shift of structural units as a result of rearrangement of the protons without a considerable shift of water molecules themselves. 

Ab initio methods provide elegant solutions to the problem of simulating proton diffusion and conduction with the vehicular and Grotthuss mechanism. Modeling of water and representative Nation clusters has been readily performed. Notable findings include the formation of a defect structure in the ordered liquid water cluster. The activation energy for the defect formation is similar to that for conduction of proton in Nafion membrane. Classical MD methods can only account for physical diffusion of proton but can create very realistic model... 

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