Cluster swelling behavior

The perfluorinated, carboxylated and sulfonated ionomer membranes form the ionic clusters of a few nm in size, as in the case of the hydrocarbon-based ionomers such as polyethylene,polystyrene and polybutadiene(9). The ionic clusters strongly affect physical properties of the membranes, e.g., the swelling behavior of the membranes (amount of water uptaken by the membranes, W and... 

Other MD simulations predicted markedly larger values of the percolation threshold (Devanathan et al., 2007b Elliott and Paddison, 2007). Discrepancies in calculated percolation thresholds could be artifacts of overly simplistic representations of ionomer chains in molecular-level simulations. Atomistic models fail in reproducing sizes and shapes of water clusters and polymer aggregates as well as in predicting percolation thresholds, swelling behavior, and related transport properties, if the monomeric sequences that they employ are too short. Notably, for the same reason, many simulations would be inept to reproduce the persistence length of the base ionomer. 

The built-in and operation stresses are the consequences of the large swelling and shrinkage of the ionomer membrane when it uptakes and loses water. This is frequently referred to as dimensional instability in the literature. Water in the PFSA membrane is an essential ingredient of its proton conduction behavior. Water affects the morphology13,14 of the ionic clusters (at nanoscale) which... 

In general, tte diffusivities of penetrants that swell glassy and rubbery polymers increase with concentratioiu The sorption i tterms are normally well-described by the Flory-Hug ns equaticm. Clustering of penetrant can also occur and cause deviations from this behavior In the case of as prdymers and strong swelling solvents, so-called Case II transport can occur . As drown in Fig. 6 an initial linear increase in samjde weight with time characterizes II uptake in film samples. 

Type III behavior occurs when there is a preference for penetrant penetrant pairs to form. In this case, solubility increases with increasing pressure, and diffusion decreases with increasing concentration, because penetrant pairs or clusters are less mobile than isolated molecules. This type of behavior is also associated with swelling of the sample. 

Freed et al. developed the lattice cluster theory (LCT) specifically to account for diversity of segmental structures, affecting blend miscibility, viz., the critical point [ c, cj)c, chain swelling [T ], as well as the scale and intensity of composition fluctuations (Freed and Bawendi 1989 Foreman and Freed 1997 Freed and Dudowicz 1998, 2005 Dudowicz et al. 2002). As an example, several monomeric and polymeric stmctures are shown in Fig. 18.15, and LCT predictions of the phase behavior the authors are discussed in details. 

With respect to the drug percolation threshold, this critical point shows much less influence on the behavior of hydrophilic matrices when compare to inert matrix tablets. This is attributed to the fact that in swellable matrices the existence of an infinite cluster of drug is not necessary to obtain its complete release. In these systems the polymer swells and enables the water penetration through the whole systems without the need of a percolating cluster of soluble substances. Therefore, little differences have been found between matrices formulated below and above the drug percolation threshold [13,93,96]. 

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