Membranes cluster-network

Proton conductivities of 0.1 S cm at high excess water contents in current PEMs stem from the concerted effect of a high concentration of free protons, high liquid-like proton mobility, and a well-connected cluster network of hydrated pathways. i i i i Correspondingly, the detrimental effects of membrane dehydration are multifold. It triggers morphological transitions that have been studied recently in experiment and theory.2 .i29.i ,i62 water contents below the percolation threshold, the well-hydrated pathways cease to span the complete sample, and poorly hydrated channels control the overall transports ll Moreover, the structure of water and the molecular mechanisms of proton transport change at low water contents. 

The effective conductivity of the membrane depends on its random heterogeneous morphology—namely, the size distribution and connectivity of fhe proton-bearing aqueous pafhways. On fhe basis of the cluster network model, a random network model of microporous PEMs was developed in Eikerling ef al. If included effecfs of varying connectivity of the pore network and of swelling of pores upon water uptake. The model was applied to exploring the dependence of membrane conductivity on water content and... 

An external gas pressure gradient applied between anode and cathode sides of the fuel cell may be superimposed on the internal gradient in liquid pressure. This provides a means to control the water distribution in PEMs under fuel cell operation. This picture forms the basis for the hydraulic permeation model of membrane operation that has been proposed by Eikerling et al. This basic structural approach can be rationalized on the basis of the cluster network model. It can also be adapted to include the pertinent structural pictures of Gebel et and Schmidt-Rohr 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. 

The function of spectrin superfamily proteins is particularly evident when taken in context of their cellular localization. They often form flexible links or structures that allow interactions with the cellular cyto-skeletal architecture and the membrane. In both spectrin and dystrophin, such a function is performed, but the spectrin repeats of these molecules are also able to interact with actin and contribute to binding. A portion of the dystrophin rod domain that spans residues 11-17 contains a number of basic repeats that allow a lateral interaction with filamentous actin (Rybakova et al., 2002). The homologous utrophin can also interact laterally with actin. This interaction is distinct from that of dystrophin, as the utrophin rod domain lacks the basic repeat cluster and associates with actin via the first ten spectrin repeats (Rybakova et al., 2002). /3-Spectrin also exhibits an extended contact with actin via the first spectrin repeat. In this situation, it was found that the extended contact increased the association of the adjacent ABD with actin (Li and Bennett, 1996). In conjunction with this interaction, it has been found that the second repeat is also required for maximal interaction with adducin (Li and Bennett, 1996), a protein localized at the spectrin-actin junction that is believed to contribute to the assembly of this structure in the membrane skeletal network (Gardner and Bennett, 1987). In the erythrocyte cytoskeletal lattice, /3-spectrin interacts with ankyrin, which in turn binds to the cytoplasmic domain of the membrane-associated anion exchanger. This indirect link to the cellular membrane occurs via repeat 15 of /3-spectrin (Kennedy et al., 1991) and is largely responsible for the attachment of the spectrin-actin network to the erythrocyte membrane (reviewed in Bennett and Baines, 2001). A much larger number of direct links to transmembrane proteins have been determined for the spectrin repeats of o-actinin (reviewed in Djinovic-Carugo et al, 2002). 

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

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. 

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). 

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

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.

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 ).

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. 

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... 

For a vapor-equilibrated membrane (i.e., one that is in contact with water vapor only), the physical model proposes that there is water in the ionic domains but none in the collapsed channels except for the bound water hydrating the few sulfonic acid sites present. Furthermore, the sulfonic acid sites that make up the collapsed channels are always fluctuating, but the elusters are elose enough together to form a transport pathway after the pereolation threshold has been reached. Due to the nature of the collapsed ehaimels, the membrane is treated as a homogenous single-phase system. In this sense, the water vapor does not penetrate into the cluster-network, but instead dissolves into the membrane. Thus, the vapor-equilibrated membrane transport mechanism is similar to the single-phase transport models mentioned previously. 

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. 

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. 

Fig. 19.1. Cluster network model for Nation perfluorosulphonic membrane reprinted by permission of Elsevier Science Publishers, B.V.

FIGURE 4.8.1. Cluster network model for Nafion perlluorosulfonic acid membrane [24]. (With permission from Elsevier.)... 

---