Nafion cluster-network model

Figure 1. Cluster-network model for the morphology of hydrated Nafion. (Adapted with permission from ref 16. Copyright 1983 Elsevier.)...

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... 

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. 

Fig. 15. Cluster network model for highly cation-permselective Nafion membranes126). Counterions are largely concentrated in the high-charge shaded regions which provide somewhat tortuous, but continuous (low activation energy), diffusion pathways. Coions are largely confined to the central cluster regions and must, therefore, overcome a high electrical barrier, in order to diffuse from one cluster to the next...

Figure 3 Schematic representation of the two-phase cluster-network model for Nafion membrane.

A model for ionic clustering in "Nafion" (registered trademark of E. I. du Pont de Nemours and Co.) perfluorinated membranes is proposed. This "cluster-network" model suggests that the solvent and ion exchange sites phase separate from the fluorocarbon matrix into inverted micellar structures which are connected by short narrow channels. This model is used to describe ion transport and hydroxyl rejection in "Nafion" membrane products. We also demonstrate that transport processes occurring in "Nafion" are well described by percolation theory. 

Figure 5. Cluster-network model for Nafion perfluorinated membranes. The polymeric ions and absorbed electrolyte phase separate from the fluorocarbon backbone into approximately spherical clusters connected by short, narrow channels. The polymeric charges are most likely embedded in the solution near the interface between the electrolyte and fluorocarbon backbone. This configuration minimizes both the hydrophobic interaction of water with the backbone and the electrostatic repulsion of proximate sulfonate groups. The dimensions shown were deduced from experiments. The shaded areas around the interface and inside a channel are the double layer regions from which the hydroxyl ions are excluded electrostatically.

To test this theory, the room temperature conductivity of "Nafion" perfluorinated resins was measured as a function of electrolyte uptake by a standard a.c. technique for liquid electrolytes (15). The data obey the percolation prediction very well. Figure 9 is a log-log plot of the measured conductivity against the excell volume fraction of electrolyte (c-c ). The principal experimental uncertainty was in the determination of c as shown by the horizontal error bars. The dashed line is a non-linear least square law to the data points. The best fit value for the threshold c is 10% which is less than the ideal value of 15% for a completely random system. This observation is consistent with a bimodal cluster distribution required by the cluster-network model. In accord with the theoretical prediction, the critical exponent n as determined from the slope of... 

Summary. We have shown that ion transport in "Nafion" per-fluorinated membrane is controlled by percolation, which means that the connectivity of ion clusters is critical. This basically reflects the heterogeneous nature of a wet membrane. Although transport across a membrane is usually perceived as a one-dimensional process, our analysis suggests that it is distinctly three-dimensional in "Nafion". (Compare the experimental values of c and n with those listed in Table 7.) This is not totally unexpected since ion clusters are typically 5.0 nm, whereas a membrane is normally several mils thick. We have also uncovered an ionic insulator-to-conductor transition at 10 volume % of electrolyte uptake. Similar transitions are expected in other ion-containing polymers, and the Cluster-Network model may find useful application to ion transport in other ion containing polymers. Finally, our transport and current efficiency data are consistent with the Cluster-Network model, but not the conventional Donnan equilibrium. 

Figure 4.21 Cluster network model of perfluorocarbon cation exchange membrane (Nafion ).

Nafion membrane is a nonreinforced film based on Nafion ionomers in acid (H" ") form. Under PEM fuel cell operating conditions, the Nafion membrane is the most practical solid electrolyte due to its unique structure, excellent thermal and mechanical stability, and high proton conductivity (but it is also an isolator for electronic conduction). According to the cluster network model [63-66] of Nafion membrane, Nafion contains some sulfonic ion clusters with a diameter of approximately 4nm. The clusters are equally distributed within a continuous fluorocarbon lattice, and are interconnected by narrow channels with a diameter of about 1 nm this provides passages for the transport of protons. Figure 1.8 shows this cluster network model. Proton... 

FIGURE 1.8 Cluster network model for the Nafion memlwane [63 6]. (For coIot version of this figure, the reader is referred to the online version of this book.)... 

FIGURE 1.11 Ionic cluster-network model for Nafion membranes. (Reproduced with permission from Hsu, W.Y. and Gierke, T.D., J. Membr. ScL, 13, 307, 1983.)... 

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 physical model can be used to describe trends seen in experimental data. For example, the interconnectivity of the cluster network is predicted to have a profound effect on a membrane s transport properties. The percolation threshold for conductivity should increase when the clusters become smaller, which could be due to a stiflfer and/or more crystalline polymer matrix. These smaller clusters would also mean that the membrane would exhibit lower electro-osmotic coefficients, larger liquid water uptakes, and a greater dependence of the various properties on water content than in Nafion . In fact, these predictions are what is seen in such systems as sulfonated polyetherketones [19, 72] and Dow membranes [73, 74] or when the equivalent weight [22] or drying temperature [4, 6] of Nafion is increased. 

The reasons for the success of this model are elaborated in the next section, which also addresses the physicochemical and transport properties of Nafion . It may be noted that the existence of cluster networks in the perfluorinated membranes was demonstrated by Gierke et al. [40] by transmission electron microscopy. 

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