Cluster network model of ion

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. 

The Cluster-Network Model of Ion Clustering in Perfluorosulfonated Membranes... 

T.D. Gierke and W.Y. Hsu, The Cluster Network Model of Ion Qustering in Perfluorosulfonated Membranes. In A. Eisenberg and H.L. Yeager (eds), Perfluorinated lonomer Membranes, ACS Symposium Series 180, American Chemical Society (1982), p. 283. 

Membrane Morphology Structural Models Cluster-Network Models of Ion Aggregation... 

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... 

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. 

In the next section we will present the data and arguments on which the cluster-network model is based. We will also discuss the effects of equivalent weight, ion form, and water content on the dimensions and composition of the clusters. In the third section we will present a formalism, which follows from the cluster-network model, based on absolute reaction rate theory (2) and hydroxyl rejection in "Nation perfluorinated membranes. Finally we will outline the concepts of percolation theory and demonstrate that ion transport trough "Nation" is well described by percolation. 

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.

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. 

Based on the cluster-network model, the dependence of current efficiency on the polymer structure was first developed by Gierke [34]. This postulates that clusters with diameters of 4 nm are distributed throughout the matrix and connected to each other by short narrow channels 1 nm in diameter—the cluster separation distance being 5 nm. It should be noted that this structure was developed based on experimental evidence [23]. High caustic current efficiency, according to this model, is a result of the repulsive electrostatic interaction between the OH ions and the fixed ionic charges on the surface... 

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... 

The transport properties of perfluorinated ionomers are of particular interest due to their use as membrane separators in chloralkali cells. Gierke and Hsu have developed a cluster network model for these systems which suggests that the ionic clusters are inverted micellar structures. In this model, the absorbed water phase is predicted to separate into approximately spherical domains and the ion-exchange groups are near the interface, probably imbedded in the aqueous phase. Based on water... 

Based on the cluster network model [72], the perfluorinated membranes undergo phase separation on a molecular scale when swollen by contact of water. Clusters are formed when sodium ions (Na ) separated from the fixed ironic sites joints the aqueous water separated from the fluorocarbon matrix. The ions and the sorbed solutions are all in clusters. A cluster s diameter varies from 3 to 5 nm and contains approximately 70 ion-exchange sites. The clusters are connected by short narrow channels with diameter of 1 nm estimated from hydraulic permeability data. The channels are formed by fixed ionic sites hydrated and embedded with water phase. 

Ludwig s (2001) review discusses water clusters and water cluster models. One of the water clusters discussed by Ludwig is the icosahedral cluster developed by Chaplin (1999). A fluctuating network of water molecules, with local icosahedral symmetry, was proposed by Chaplin (1999) it contains, when complete, 280 fully hydrogen-bonded water molecules. This structure allows explanation of a number of the anomalous properties of water, including its temperature-density and pressure-viscosity behaviors, the radial distribution pattern, the change in water properties on supercooling, and the solvation properties of ions, hydrophobic molecules, carbohydrates, and macromolecules (Chaplin, 1999, 2001, 2004). 

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