Gierke cluster network model

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... 

In terms of the structure within the membrane, the idealized Hsu and Gierke cluster-network model is used as a picture where the pathways between the clusters are interfacial regions. These pathways are termed collapsed channels since they can be expanded by liquid water to form a liquid-filled channel. In essence, the collapsed channels are sulfonic acid sites surrounded by the polymer matrix having a low enough concentration such that the overall pathway between two clusters remains hydrophobic. In other words, they are composed of bridging ionic sites [31] and the electrostatic energy density is too low compared to the polymer elasticity to allow for a bulk-like water phase to form and expand the channels. In all, for a vapor-equilibrated membrane the structure is that of ionic domains that are hydrophilic and contain some bulk-like water. These clusters are connected by... 

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... 

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. 

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. 

Gierke also considered that these clusters are interconnected by short, narrow channels in the fluorocarbon backbone network. The diameter of these channels is about 1 mm estimated from hydraulic permeability data. He further considered that the Bragg spacing ( 5nm from SAXS data) can represent the distance between clusters. The cluster-network model is a phenomenological description. Recently, Hsu and Gierke " have derived a semi-phenomenological expression to correlate the variation of cluster diameter with water content, equivalent weight, and cation form of the membrane. They have shown that the short channels are thermodynamically stable. 

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. 

Effective conductivity of the membrane is related to its macroscopic morphology, viz. the random heterogeneous domain structure of polymer and solvent phases. On the basis of Gierke s cluster network model, a random network model of microporous PEMs was developed in [22]. This approach highlighted the importance of connectivity and swelling properties of pores. Random distributions of pores and channels as their interconnections were assumed. The connectivity between pores was considered as a phenomenological parameter. 

The structures of PFSA membranes have been analyzed and discussed by many researchers, and the cluster-network model for hydrated membranes proposed by Gierke [22] has been a basic model symbolic of the PFSA characteristics up to now. As for the structure of the diluted aqueous solution of PFSA, it is important to understand the structure of ionomer dispersion and catalyst ink, comprising catalyst particles, ionomer, and solvent, for the preparation of cast membrane and catalyst layer, respectively. Aldebert et al. 

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 ... 

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... 

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. 

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... 

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...

---