Proton transport Random network model

This oversimplified random network model proved to be rather useful for understanding water fluxes and proton transport properties of PEMs in fuel cells. - - - It helped rationalize the percolation transition in proton conductivity upon water uptake as a continuous reorganization of the cluster network due to swelling and merging of individual clusters and the emergence of new necks linking them. ... 

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. 

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. 

Efforts of polymer scientists and fuel cell developers alike are driven by one question What specific properties of the polymeric host material determine the transport properties of a PEM, especially proton conductivity The answer depends on the evaluated regime of the water content. At water content above kc, relevant structural properties are related to the porous PEM morphology, described by volumetric composition, pore size distribution and pore network connectivity. As seen in previous sections, effective parameters of interest are lEC, pKa, and the tensile modulus of polymer walls. In this regime, approaches familiar from the theory of porous media or composites (Kirkpatrick, 1973 Stauffer and Aharony, 1994), can be applied to relate the water distribution in membranes to its transport properties. Random network models and simpler models of the porous structure were employed in Eikerling et al. (1997, 2001) to study correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake, and proton conductivity, as will be discussed in the section Random Network Model of Membrane Conductivity. ... 

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. ... 

The percolation model suggests that it may not be necessary to have a rigid geometry and definite pathway for conduction, as implied by the proton-wire model of membrane transport (Nagle and Mille, 1981). For proton pumps the fluctuating random percolation networks would serve for diffusion of the ion across the water-poor protein surface, to where the active site would apply a vectorial kick. In this view the special nonrandom structure of the active site would be limited in size to a dimension commensurate with that found for active sites of proteins such as enzymes. Control is possible conduction could be switched on or off by the addition or subtraction of a few elements, shifting the fractional occupancy up or down across the percolation threshold. Statistical assemblies of conducting elements need only partially fill a surface or volume to obtain conduction. For a surface the percolation threshold is at half-saturation of the sites. For a three-dimensional pore only one-sixth of the sites need be filled. 

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