Ionomers bundles

The reference set of parameters was provided in Eikerling and Berg (2011). In the case of material-specific parameters, Nafion is the benchmark system. The pore walls should be considered as hydrophilic. Hence, 0 = 0 is a reasonable choice. For the mean value of the wall charge density, a value ao = —0.08 C m was taken at the fixed reference radius of 7 o = 1 nm. This value depends on the lEC and the structure of ionomer bundles. 

The theory of bundle formation in the section Aggregation Prenomena in Solutions of Charged Polymers provides sizes, as well as electrostatic and elastic properties of ionomer bundles. The theory of water sorption and swelling, described in this section, gives a statistical distribution of pore size and local stress in pores. The merging point of both theories is a theory of fracture formation in charged polymer... 

Molecular modeling of PT at dense arrays of protogenic surface groups (SGs) demands ab initio quantum mechanical calculations. The starting point for the development of a viable model of surface proton conduction in PEM is the self-organized PEM morphology at the mesoscopic scale. Eigure 2.30a illustrates the random array of hydrated and ionized sidechains that are anchored to the surface of ionomer bundles. 

Theoretical studies of ionomer aggregation in solution can rationalize and predict stable configurations of ionomer bundles as a function of basic ionomer properties. Theoretical results can be highly insightful to narrow down the configuration space for molecular simulations. 

Radius of cylindrical unit cell that contains single ionomer bundle (cm) Rod length in membrane (cm)... 

Chapter 2 dwells on all aspects of the structure and functioning of polymer electrolyte membranes. The detailed treatment is limited to water-based proton conductors, as, arguably, water is nature s favorite medium for the purpose. A central concept in this chapter is the spontaneous formation of ionomer bundles. It is a linchpin between polymer physics, macromolecular self-assembly, phase separation, elasticity of ionomer walls, water sorption behavior, proton density distribution, coupled transport of protons and water, and membrane performance. 

At low water content the quasi-crystalline motif in the distribution of inverted micelles is strong the size of the micelle is smaller than the persistence length of the bundles of backbone-chains forming the membrane skeleton. A legitimate question arises then how can one build a quasicrystalline structure of inverted micelles (aqueous droplets supported by hydrated sidechains), if the sidechains are attached to the backbones In an attempt to answer this question, a more detailed morphological model of Nafion-type ionomers was suggested [31] a quasi-crystalline arrangement of units cells as depicted in Fig. 1. 

FIGURE 2.3 Self-organization in ionomer solution into cylindrical fibrils or bundles (Rubatat et al., 2002) and further assembly of bundles into possible superstructures with cage-like (lose-levich et al., 2004) cylindrical (Rubatat et al., 2004, 2002 Schmidt-Rohr and Chen, 2008) or lamellar-like morphology (Tsang et al., 2009). 

Rod-like ionomer lonomer bundles Unit cell with bundle... 

Molecular simulations of ionomer systems that employ classical force fields to describe interactions between atomic and molecular species are more flexible in terms of system size and simulation time but they must fulfill a number of other requirements they should account for sufficient details of the chemical ionomer architecture and accurately represent molecular interactions. Moreover, they should be consistent with basic polymer properties like persistence length, aggregation or phase separation behavior, ion distributions around fibrils or bundles of hydrophobic backbones, polymer elastic properties, and microscopic swelling. They should provide insights on transport properties at relevant time and length scales. Classical all-atom molecular dynamics methods are routinely applied to model equilibrium fluctuations in biological systems and condensed matter on length scales of tens of nanometers and timescales of 100 ns. 

For the case of elongation of bundles or walls of ionomer domains with uniform contraction of the crosssection, the relation becomes... 

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