Gierke model

Fig. 2.20 The Gierke model of a cluster network in Nafion. Dimensions are expressed in nm. The shaded area is the double layer region, containing the immobilized —SO3 groups with corresponding number of counterions M+. Anions are expelled from this region electrostatically...

The basic conclusions of the Gierke model were supported by the results of the DuPont [34], Kyoto [35] and Grenoble [36] groups and by many further studies (see e.g. [37]. Claims of cylindrical micelles [38] or flat lamellar structures [39-41] have also been made, but the occurrence of such structures is more typical for E-membranes. For N-membranes the concept of spherical or quasi-spherical micelles continues to be the most common conjecture about the phase segregation in the membrane, particularly in view of reports on the absence of elongated objects in the patterns of reconstruction of SAXS data [42]. 

Gierke model of nanoclusters in perfluoro-sulfonic acid materials. 

In the Gierke model, the formation of a critical number of necks signals the percolation transition in proton conductivity, that is, the emergence of an uninterrupted... 

Random network models, based upon assumptions of the Gierke model, proved useful for understanding water fluxes and proton transport properties of the PEM in fuel cells. They helped in rationalizing the percolation transition in proton conductivity upon water uptake. 

Inhibition of anion transport in Nation was attributed to the inhomogeneous structure of the ion exchange sites in the polymer network (Gierke cluster network model). It was found that Nation contains (even in... 

The earliest fully atomistic molecular dynamic (MD) studies of a simplified Nation model using polyelectrolyte analogs showed the formation of a percolating structure of water-filled channels, which is consistent with the basic ideas of the cluster-network model of Hsu and Gierke. The first MD... 

The original cluster-network model proposed by Gierke et al. (also referred to as the cluster-channel model) has been the most widely referenced model in the history of perfluorosulfonate ionomers. Despite the very large number of papers and reports that have strictly relied on this model to explain a wide variety of physical properties and other characteristics of Nafion, this model was never meant to be a definitive description of the actual morphology of Nafion, and the authors recognized that further experimental work would be required to completely define the nature of ionic clustering in these iono-mers. For example, the paracrystalline, cubic lattice... 

This view stands in contrast to the condition of having well-defined spherical clusters and sharp phase boundaries as depicted in the model of Gierke et al. 

The cluster-network model of Gierke et al. has already been discussed in the Introduction as being the first realistic model for rationalizing a number of properties of Nafion membranes. 

Many of today s models are based on the early physical models of Hsu and Gierke and Yeager and Steck. These models, along with the relevant experimental data, were reviewed recently by Weber and Newman. Out of their analysis came a... 

Gierke, T., Hsu, W. (1982). The cluster-network model of ion clustering in perfluoro-sulfonated membranes. In "Perfluorinated lonomer Membranes", American Chemical Society Symp. Series 180, Washington, DC. 

Figure 3. Two models describing the microphases of swollen Nation membranes. Top Gierke s [48] suggestion of aqueous inverse spherical micelles connected by water-filled cylindrical channels. Bottom Yeager and Steck s [49] three-region model of a water/ionomer mixture without regular structure. Regions A, B and C are the hydrophobic polymer, the solvent bridges and the hydrophilic regions, respectively.

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