Proton transport in bulk water

Besides these generalities, little is known about proton transfer towards an electrode surface. Based on classical molecular dynamics, it has been suggested that the ratedetermining step is the orientation of the HsO with one proton towards the surface [Pecina and Schmickler, 1998] this would be in line with proton transport in bulk water, where the proton transfer itself occurs without a barrier, once the participating molecules have a suitable orientation. This is also supported by a recent quantum chemical study of hydrogen evolution on a Pt(lll) surface [Skulason et al., 2007], in which the barrier for proton transfer to the surface was found to be lower than 0.15 eV. This extensive study used a highly idealized model for the solution—a bilayer of water with a few protons added—and it is not clear how this simplification affects the result. However, a fully quantum chemical model must necessarily limit the number of particles, and this study is probably among the best that one can do at present. 

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 functional form of the triggers ate based on transition state, as determined by the quantum mechanical calculation and their numerical values are parameterized to satisfy the macroscopically determined rate constant and activation energy. Local equilibration at the end of the reaction helps in maintaining the correct heat of reaction and structure. For the vahdation of the algorithm, it has been implemented to study proton transport in bulk water. In bulk water the two components of the total diffusivity were found to be uncorrelated. 

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 mobility in the pore includes molecular mechanisms of proton transport in bulk water and along the array of charged surface groups. An idealized two-state approach based on this distinction was considered in [82]. This simple model can reproduce a continuous transition from surface-like to... 

MD simulations based on empirical interaction functions are able to overcome some of the statistical Hmitations of the ab initio MD scheme. It is possible, at least for single pore environments to calculate proton mobihties in a statistically accurate way. The chemical natiue of proton transfer, i.e., the structural diffusion from one hydrated cluster to the next, is efficiently taken into account by the use of empirical valence bond (EVB) models, which have been introduced by Warshel [ 134] and later extensively used for aqueous proton transport in bulk water by Vuilleuimier and Borgis [92,135,136] and the group of Voth [93,137-141]. hi the simplest version of such a model, a two-state EVB model [102], the proton can be regarded as being in a superposition state between two different valence bond states, the first one corresponding... 

However, intriguing phenomena arise if the SGs density at polymer-water interfaces is increased. In the regime of high SG density, proton transport in PEMs become similar to proton transport at acid-functionalized surfaces. Surface proton conduction phenomena are of importance to processes in biology. Yet, experimental findings of ultrafast proton transport at densely packed arrays of anionic SG have remained controversial. Theoretically, understanding of the underlying mechanisms is less advanced than for proton transport in bulk water. 

Near the surface, AG is dominated by the Coulomb energy profile and, therefore, it is approximately equal to the difference of the electrostatic potentials at the proton positions before and after the transfer. This difference depends strongly on the distance of the proton from the surface. Values of AG were found in the range of 0.5 eV. This value decreases, however, to the activation energy of proton transport in bulk water when the proton-surface separation exceeds 3 A (the thickness of one monolayer of water). Moreover, the electrostatic activation energy is a function of the separation between surface charges, which lies in the range of 7 to 15 A. 

The value of AFa for the collective transition is 2-3 times larger than the activation energy of proton transport in bulk water (0.1 eV), as expected, based on the increased hydrogen bond strength. It is to be seen in refinements of metadynamics simulations whether different choice of CVs and evaluation of longer SGs will reduce AFa significantly. 

In this model, proton transport in the membrane is mapped on a percolation problem, wherein randomly distributed sites represent pores of variable sizes and fhus variable conductance. The distinction of pores of differenf color (red or blue) corresponds to interfacial or by bulk-like proton transport. Water uptake by wet pores controls the transition between these mechanisms. The chemical structure of the membrane is factored in at the subordinate structural levels, as discussed in the previous subsections. 

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. 

Finally, the H30+ ion can drift classically as a whole. However, this, also called physical diffusion, is only one of the contributions to the proton transport and is not the dominating contribution in bulk water. 

To date, our reactive molecular dynamics simulations of proton transport have been limited to bulk water. However, the extension of Ae RMD algorithm to proton transport in PFSA membranes is analogous to what has been done in bulk water and simi-... 

This notion is supported by a large number of independent experimental data, related to structure and mobility in these membranes. It implies furthermore a distinction of proton mobility in various water environments, strongly bound surface water and liquidlike bulk water, and the existence of water-filled pores as network forming elements. Appropriate theoretical treatment of such systems involves random network models of proton conductivity and concepts from percolation theory, and includes hydraulic permeation as a prevailing mechanism of water transport under operation conditions. On the basis of these concepts a consistent approach to membrane performance can be presented. 

Proton diffusion can occur via two mechanisms, structural diffusion and vehicle diffusion [37]. It is the combination of these two diffusion mechanisms that confers protonic defects exceptional conductivity in liquid water. The conductivity of protons in aqueous systems of bulk water can be viewed as the limiting case for conductivity in PFSA membranes. When aqueous systems interact with the environment, such as in an acidic polymer membrane, the interaction reduces the conductivity of protons compared to that in bulk water [37]. In addition to the mechanisms described above, transport properties and conductivity of the aqueous phase of an acidic polymer membrane will also be effected by interactions with the sulfonate heads, and by restriction of the size of the aqueous phase that forms within acidic polymer membranes [32]. The effects of the introduction of the membrane can be considered on the molecular scale and on a longer-range scale, see Refs. [16, 32]. Of particular relevance to macroscopic models are the diffusion coefficients. As the amount of water sorbed by the membrane increases and the molecular scale effects are reduced, the properties approach those of bulk water on the molecular scale [32]. 

There are different ways to depict membrane operation based on proton transport in it. The oversimplified scenario is to consider the polymer as an inert porous container for the water domains, which form the active phase for proton transport. In this scenario, proton transport is primarily treated as a phenomenon in bulk water [1,8,90], perturbed to some degree by the presence of the charged pore walls, whose influence becomes increasingly important the narrower are the aqueous channels. At the moleciflar scale, transport of excess protons in liquid water is extensively studied. Expanding on this view of molecular mechanisms, straightforward geometric approaches, familiar from the theory of rigid porous media or composites [ 104,105], coifld be applied to relate the water distribution in membranes to its macroscopic transport properties. Relevant correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake and proton conductivities in PEMs were studied in [22,107]. Random network models and simpler models of the porous structure were employed. 

As corroborated above the effect of arrangement and fluctuations of charged surface groups on proton transport in membranes is the more pronoimced the smaller the water content in the membrane is. Squeezing the pore leaves no room for bulk-Uke transfer. Upon deswelling of pores, sidechain separations are likely to decrease [33]. The proton concentration, smface charge density and corresponding electrostatic interactions will thus increase, and explicit sidechain-sidechain correlations will become more pronoimced. The process will lead to with an array of micelles loosely connected by ultrathin aqueous necks, as described in [31]. 

The mechanism of protonic transport in ZrP is not yet known. Nevertheless, the fact that the conductivity is dominated by surface transport may be explained considering that, due to steric effects, the diffusion and/or reorientation of protonic species on the surface should be easier than in the bulk in addition the ionogenic groups of the surface can be more hydrated than the inner ones, thus facilitating their dissociation and water protonation. 

---