Proton transport pore-scale models

S0l., So2 and SHlo refer to the respective source terms owing to the ORR, e is the electrolyte phase potential, cGl is the oxygen concentration and cHlo is the water vapor concentration, Ke is the proton conductivity duly modified w.r.t. to the actual electrolyte volume fraction, Dsa is the oxygen diffusivity and is the vapor diffusivity. The details about the DNS model for pore-scale description of species and charge transport in the CL microstructure along with its capability of discerning the compositional influence on the CL performance as well as local overpotential and reaction current distributions are furnished in our work.25 27,67... 

Because of the complexity of hydrated PEMs, a full atomistic modeling of proton transport is impractical. The generic problem is a disparity of time and space scales. While elementary molecular dynamics events occur on a femtosecond time scale, the time interval between consecutive transfer events is usually 3 orders of magnitude greater. The smallest pore may be a few tenth of nanometer while the largest may be a few tens of nanometers. The molecular dynamics events that protons transfer between the water filled pores may have a timescale of 100-1000 ns. This combination of time and spatial scales are far out of the domain for AIMD but in the domain of MD and KMC as shown in Fig. 2. Because of this difficulty, in the models the complexity of the systems is restricted. In fact in many models the dynamics of excess protons in liquid water is considered as an approximation for proton conduction in a hydrated Nation membrane. The conformations and energetics of proton dissociation in acid/water clusters were also evaluated as approximations for those in a Nation membrane.16,19 20 22 24 25... 

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. 

In general, pores swell nonuniformly, as seen in the section Water Sorption and Swelling of PEMs. As a simplification, the random network was assumed to consist of two types of pores. Nonswollen or dry pores (referred to as red pores) permit only a small residual conductance resulting from tightly bound surface water. Swollen or wet pores (referred to as blue pores) contain extra water with high bulklike conductance. Water uptake corresponds to the swelling of wet pores and to the increase of their relative fraction. In this model, proton transport in the PEM is mapped as a percolation problem, wherein randomly distributed sites represent pores of variable size and conductance. The distinction of red and blue pores accounts for variations of proton transport properties due to different water environments at the microscopic scale, as discussed in the section Water in PEMs Classification Schemes. ... 

This coarse-grained molecular dynamics model helped consolidate the main features of microstructure formation in CLs of PEFCs. These showed that the final microstructure depends on carbon particle choices and ionomer-carbon interactions. While ionomer sidechains are buried inside hydrophilic domains with a weak contact to carbon domains, the ionomer backbones are attached to the surface of carbon agglomerates. The evolving structural characteristics of the catalyst layers (CL) are particularly important for further analysis of transport of protons, electrons, reactant molecules (O2) and water as well as the distribution of electrocatalytic activity at Pt/water interfaces. In principle, such meso-scale simulation studies allow relating of these properties to the selection of solvent, carbon (particle sizes and wettability), catalyst loading, and level of membrane hydration in the catalyst layer. There is still a lack of explicit experimental data with which these results could be compared. Versatile experimental techniques have to be employed to study particle-particle interactions, structural characteristics of phases and interfaces, and phase correlations of carbon, ionomer, and water in pores. 

As concerns the second assumption, direct access to the gas pore network is not a stringent requirement for keeping the Pt surface active. The condensed phases of water and ionomer possess finite oxygen permeabilities, which will render oxygen concentrations finite at electrolyte-covered Pt particles. Again, this is an issue of nonuniform reaction rate distributions that will be dealt with in the section Hierarchical Model of CCL Operation. In that section, a two-scale performance model will be presented, which couples transport and distribution of protons and oxygen at the agglomerate level and at the macroscopic scale. 

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