Membranes microscopic model

Before discussing the models and their approaches in more detail, some mention should be made on the microscopic models and the overall physical picture of Nafion. Since membrane-only models, especially the microscopic ones, are covered in another review, the discussion below is shortened. 

Eikerling et al. ° used a similar approach except that they focus mainly on convective transport. As mentioned above, they use a pore-size distribution for Nafion and percolation phenomena to describe water flow through two different pore types in the membrane. Their model is also more microscopic and statistically rigorous than that of Weber and Newman. Overall, only through combination models can a physically based description of transport in membranes be accomplished that takes into account all of the experimental findings. 

Various modeling approaches have been used for the catalyst layers, with different degrees of success. The approach taken usually depends on how the other parts of the fuel cell are being modeled and what the overall goal of the model is. Just as with membrane modeling, there are two main classes of models. There are the microscopic models, which include pore-level models as well as more detailed quantum models. The quantum models deal with detailed reaction mechanisms and elementary transfer reactions and transition states. They are beyond the scope of this review and are discussed elsewhere, along with the issues of the nature of the electro catalysts. 

The balances approaches have to necessarily incorporate approximations and fundamental hypotheses, which reduce the prediction capability of the latter. Every hypothesis comes from a postulated droplet-formation mechanism. The formation mechanism, however, depends significantly on the mentioned operating, membrane and phase parameters, thus, it is very difficult to find one mechanism valid for all possible parameters values. Consequently, more accurate computation procedures, such as the microscopic modeling or methods using the minimization of the droplet surface, are necessary for the detailed description of droplet formation and accurate predictions. 

For small curvatures, Eq. (6.15) shows that the curvature energy of a thin film is characterized by the three parameters k, k, and cq. The qualitative behavior of any system, including such properties such as the equilibrium shape, magnitude of thermal fluctuations, and any phase transitions, can of course be calculated as a function of these constants. However, the physics of the system can be radically different depending on the physical parameters e.g., a change in cq can induce shape changes in the system. It is thus of interest to relate the bending elastic moduli and the spontaneous curvature to the physics of the particular system of interest. This section first shows how these parameters are related to the pressure distribution in the membrane and then presents a simple but instructive microscopic model that relates k, and Co to more molecular properties. 

Membrane modelling has been considered from both the nano/microscopic and the macroscopic viewpoints, but little has been done to bridge these two limits. The breadth of microscopic modelling work for PEMs encompasses molecular dynamics simulations [17] and statistical mechanics modelling [18-21]. Most applications have focused on Nafion, and interestingly, some models even apply macroscopic transport relations to the microscopic transport within a pore of a membrane [41]. While the focus of this Chapter is on macroscopic models required for computational simulations of complete fuel cells [12,13,15], the proposed modelling framework is based on fundamental relations describing molecular transport phenomena. 

In terms of both quantitative and qualitative modeling, PEMs have been modeled within two extremes, the macroscopic and the microscopic, as discussed in various chapters in this book and in recent review articles [1, 9, 10]. The microscopic models provide the fundamental understanding of processes like diffusion and conduction in the membrane on a single-pore level. They allow for the evaluation of how small perturbations like heterogeneity of pores and electric fields affect transport, as well as the incorporation of small-scale effects. 

Morphology of Nafion Membranes Microscopic and Mesoscopic Modeling... 

For the description of the chain-melting phase transition of pure lipid bilayer membranes the microscopic model of Pink and collaborators has been adopted. This model takes into account the acyl-chain conformational statistics and the van der Waals interaction between various conformers in a detailed way, while the excluded volume effect is accounted for by assigning each lipid chain to a site in a triangular lattice. The acyl chain conformations are represented by ten single chain states a , each described by a cross-sectional area A , an internal energy Ea and an internal degeneracy Da- The second membrane component is assumed to be a stiff, hydrophobically smooth molecule with no internal degrees of freedom and a cross-sectional area Ac- The model parameters will be chosen so that the mixture display the properties of the DPPC-cholesterol bilayer system for small concentrations of cholesterol [3]. The impurity will hereafter be called cholesterol . 

On the basis of electron microscopic studies, Robertson (1967) has modified the Danielli-Davson model, presenting a new model—the unit membrane hypothesis—for all cell membranes. This model was similar to that of Danielli-Davson but with a few significant changes. The number of bimolecular phospholipid layers in Robertson s model was restricted to one, and the membrane was considered to be asymmetrical, with mucopolysaccharide or mucoprotein on the outside and unconjugated protein on the inner part of the membrane (Fig. 2). The... 

Perfluorosulfonated membranes have a microscopic phase-separated structure with hydrophobic regions and hydrophilic domain. Hydrophobic regions provide the mechanical support and hydrophilic ionic domains provide proton transport channel. Many morphological models for PFSA have been developed based on SAXS and wide-angle x-ray scattering (WAXS) experiments of the membranes. However, because of the random chemical structure of the PFSA copolymer, morphological variation with water content and complexity of coorganized crystalline and ionic domains, limited characteristic detail proved by the SAXS and WAXS experiments, the structure of the PFSl has been still subject of debate. Here, a brief description of seven membrane structure models is provided. 

Numerous models are based on statistical mechanics, molecular dynamics, and other types of macroscopic phenomena. These models are valuable because they provide a fundamental understanding of behaviors of related species and of conduction through different proton-water complexes. Almost all microscopic models treat the membrane as a two-phase system. Although these models provide valuable information, they are usually too complex to be integrated into an overall fuel cell model. How the membrane structure changes as a function of water content is still under investigation and unclear. 

There is quite a large body of literature on films of biological substances and related model compounds, much of it made possible by the sophisticated microscopic techniques discussed in Section IV-3E. There is considerable interest in biomembranes and how they can be modeled by lipid monolayers [35]. In this section we briefly discuss lipid monolayers, lipolytic enzyme reactions, and model systems for studies of biological recognition. The related subjects of membranes and vesicles are covered in the following section. 

Biological membranes provide the essential barrier between cells and the organelles of which cells are composed. Cellular membranes are complicated extensive biomolecular sheetlike structures, mostly fonned by lipid molecules held together by cooperative nonco-valent interactions. A membrane is not a static structure, but rather a complex dynamical two-dimensional liquid crystalline fluid mosaic of oriented proteins and lipids. A number of experimental approaches can be used to investigate and characterize biological membranes. However, the complexity of membranes is such that experimental data remain very difficult to interpret at the microscopic level. In recent years, computational studies of membranes based on detailed atomic models, as summarized in Chapter 21, have greatly increased the ability to interpret experimental data, yielding a much-improved picture of the structure and dynamics of lipid bilayers and the relationship of those properties to membrane function [21]. 

In order to design a zeoHte membrane-based process a good model description of the multicomponent mass transport properties is required. Moreover, this will reduce the amount of practical work required in the development of zeolite membranes and MRs. Concerning intracrystaUine mass transport, a decent continuum approach is available within a Maxwell-Stefan framework for mass transport [98-100]. The well-defined geometry of zeoHtes, however, gives rise to microscopic effects, like specific adsorption sites and nonisotropic diffusion, which become manifested at the macroscale. It remains challenging to incorporate these microscopic effects into a generalized model and to obtain an accurate multicomponent prediction of a real membrane. 

Further progress in understanding membrane instability and nonlocality requires development of microscopic theory and modeling. Analysis of membrane thickness fluctuations derived from molecular dynamics simulations can serve such a purpose. A possible difficulty with such analysis must be mentioned. In a natural environment isolated membranes assume a stressless state. However, MD modeling requires imposition of special boundary conditions corresponding to a stressed state of the membrane (see Refs. 84,87,112). This stress can interfere with the fluctuations of membrane shape and thickness, an effect that must be accounted for in analyzing data extracted from computer experiments. 

The first membrane model to be widely accepted was that proposed by Danielli and Davson in 1935 [528]. On the basis of the observation that proteins could be adsorbed to oil droplets obtained from mackerel eggs and other research, the two scientists at University College in London proposed the sandwich of lipids model (Fig. 7.2), where a bilayer is covered on both sides by a layer of protein. The model underwent revisions over the years, as more was learned from electron microscopic and X-ray diffraction studies. It was eventually replaced in the 1970s by the current model of the membrane, known as the fluid mosaic model, proposed by Singer and Nicolson [529,530]. In the new model (Fig. 7.3), the lipid bilayer was retained, but the proteins were proposed to be globular and to freely float within the lipid bilayer, some spanning the entire bilayer. 

The thickness of the membrane phase can be either macroscopic ( thick )—membranes with a thickness greater than micrometres—or microscopic ( thin ), i.e. with thicknesses comparable to molecular dimensions (biological membranes and their models, bilayer lipid films). Thick membranes are crystalline, glassy or liquid, while thin membranes possess the properties of liquid crystals (fluid) or gels (crystalline). 

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