Cluster network

Contrary to the 6-12 mixed halide phase, the three-dimensional cluster network of this structure is based on chlorine bridges only. As detailed in [17] an interesting relationship exists between this 6-13- and the [(Zr6B)Cli4] ([Nb6Cli4]) structure [19], which is shown in Fig. 5.6. The transformation of Nb6Cli4... 

Farrell, H. M., Jr., Qi, P. X., and Uversky, V. N. (2006a). New views of protein structure Applications to the caseins. In "Advances in Biopolymers Molecules, Clusters, Networks and Interactions", pp. 52-70. American Chemical Society, Washington, DC. 

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... 

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...

This oversimplified random network model proved to be rather useful for understanding water fluxes and proton transport properties of PEMs in fuel cells. - - - It helped rationalize the percolation transition in proton conductivity upon water uptake as a continuous reorganization of the cluster network due to swelling and merging of individual clusters and the emergence of new necks linking them. ... 

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... 

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. ... 

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

Based on the fiber diffraction data and the morphological constraints imposed by Geirke s cluster-network model,Starkweather developed a model for the crystalline structure of perfluorosulfonate iono-mers. " Given a 1 nm wall space between clusters. 

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...

Variations in pH, concentration, and temperature have a profound effect on the condensation pathway. Acidic media, high concentrations of reagents, and lower temperatures favor the formation of chains or loosely cross-linked chains. Basic media, dilute solutions, and higher temperatures favor the formation of rings, cages, and cluster networks (Figure 9.4). 

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

Finally, we would like to stress again that it was the addition of small amounts of C and N in the synthesis of higher borides which caused these new structures to form. As a result, hitherto unknown configurations of the rare earth atoms confined in the boron cluster network were observed to appear, leading to these interesting properties. 

First of all, a rare earth existence diagram is given in Figure 45 for all the higher boride compounds discussed in this review. As noted before, size constraints on the voids which are created among the boron cluster networks result in different ranges of possible rare earth elements for the different compounds. 

The water cluster examples in Table 6 are meant to illustrate a somewhat more difficult minimization problem. Optimal cluster-network geometries are more difficult to locate not only because of the difficulty in constructing good starting points the optimal configurations are dominated by long-range nonbonded forces that are computationally not feasible to consider in preconditioners. 

The established concepts predict some features of the Payne effect, that are independent of the specific types of filler. These features are in good agreement with experimental studies. For example, the Kraus-exponent m of the G drop with increasing deformation is entirely determined by the structure of the cluster network [58, 59]. Another example is the scaling relation at Eq. (70) predicting a specific power law behavior of the elastic modulus as a function of the filler volume fraction. The exponent reflects the characteristic structure of the fractal heterogeneity of the CCA-cluster network. 

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