Perfluorinated cluster-network model

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. 

Since the conductivity of electrolytes and the cross section and thickness of the membrane are known, a can be determined from the voltage drops across the three pairs of probe electrodes 1-2, 3-4 and 5-6. The sodium current efficiency (CE) can also be determined by titrating the amount of caustic soda generated over a given period of time. The confinement chambers around the working electrodes are used to eliminate free bubbles near the membrane. Our normalized transport data for sulfonate, carboxylate and sulfonamide ionomers are plotted In Figure 5 the universal percolative nature of perfluorinated ionomers can be clearly eeij. The prefactor sulfonate ionomers. The exponent t is 1.5 0.1 in reasonable agreement with theory and the thresholds are between 8 to 10 vol. %, which are consistent with the bimodal distribution in cluster size postulated by the cluster-network model (5.18). This theory has also been applied recently to delineate sodium selectivity of perfluorinated ionomers (20). 

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 this work we propose a model for ionic clustering, which we have called the cluster-network model (2), to account for hydroxyl rejection in nNafionM perfluorinated membranes. In developing this model we have been guided by two requirements 1. the model should be consistent with the available data on the microscopic structure of the polymer (1-5) 2. the model should... 

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.

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... 

FIGURE 8. Cluster-network model proposed by Gierke. Reprinted with permission from T. D. Gierke and W. Y. Hsu, in Perfluorinated Ionomer Membranes (Eds. A. Eisenberg and H. L. Yeager), Chap. 13, ACS Symp. Ser. No. 180, 1980, p. 286. Copyright (1980) American Chemical Society. 

Gierke and Hsu [23] proposed, based on the cluster-network model, that the conductivity of the perfluorinated polymeric membranes can be described by the equation ... 

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. 

Based on the cluster network model, further studies propose an interpretation of the percolation properties of proton conductivity as a function of water content by using a random network model [102], which is a modification of the cluster network model. This model includes an intermediate region wherein the side chains ending with pendant sulfonic acid groups, which are bonded to the perfluorinated backbones, tend to form cluster within the overall structure of the material resulting in the formation of hydrated regions. Unlike the cluster network model, the... 

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. 

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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