Transport of Protons and Water

Solvated proton condncting polymers and composite membranes should govern the transport of protons and water by micro structural control. The objective of this attempt is to take advantage of the high proton conductance in watery systems and to control the proton condnctivity by a sophisticated water management. Nevertheless, the condnctivity is strongly dependent on the water content, which also inflnences the mechanical properties by e.g. swelling. 

Transport of protons and water are the two phenomena of prime interest. Prior to examining the mechanisms that govern their transport, it is useful to review some of the background briefly that informs model formulation, including relevant aspects of membrane morphology, hydration behaviour and sorption isotherms. 

Schmidt, V.M., D. Tegtmeyer, and J. Heitbaum. 1995. Transport of protons and water through polyaniline membranes studied with online mass-spectrometry. / Electroanal Chem 385 149. 

At least three major scales must be distinguished in simulations of heterogeneous media (i) the atomistic scale, required to account for electronic structure effects in catalytic systems or for molecular and hydrogen bond fluctuations that govern the transport of protons and water (ii) the scale of the electrochemical double layer, ranging from several A to a few nm at this level, simulations should account for potential and ion distributions in the metal-electrolyte interfacial region and (iii) the scale of about 10 nm to 1 pm, to describe transport and reaction in heterogeneous media as a function of composition and porous structure. 

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. 

Nafion has been the subject of extensive characterization studies [1]. Its microstructure has been exhaustively studied by scattering methods, especially small angle X-ray scattering (SAXS) and small angle neutron scattering (SANS) [19-23]. Mechanical properties of Nafion as functions of temperature have been used to identify temperature-induced transitions [2,24—27]. Transport of protons and water has also been the subject of numerous studies over the past 25 years [28-34]. However, there has been limited progress in coimecting the chemical structure of Nafion to mechanical and transport properties, especially how these properties are altered due to environmental conditions. In this chapter, we will review recent studies of mechanical and transport properties of Nafion done under controlled conditions of water activity and temperature. 

The proton conductivity plays an important role in determining fuel cell performance. Therefore, it is very necessary to investigate the membrane conduction mechanism. For the pristine SPEK membrane, the proton conduction is dependent on water. The hydrophobic domain (polymer backbone) provides the morphological stability and prevents the membrane from dissolving in water. The sulfonic acid functional groups aggregate to form hydrophilic domains that are hydrated in the presence of water. And the connected hydrophilic domain is responsible for the transport of protons and water. 

Molecular-level studies of mechanisms of proton and water transport in PEMs require quantum mechanical calculations these mechanisms determine the conductance of water-filled nanosized pathways in PEMs. Also at molecular to nanoscopic scale, elementary steps of molecular adsorption, surface diffusion, charge transfer, recombination, and desorption proceed on the surfaces of nanoscale catalyst particles these fundamental processes control the electrocatalytic activity of the accessible catalyst surface. Studies of stable conformations of supported nanoparticles as well as of the processes on their surface require density functional theory (DFT) calculations, molecular... 

The excellent prospects of PEFCs as well as the undesirable dependence of current PEMs on bulk-like water for proton conduction motivate the vast research in materials synthesis and experimental characterization of novel PEMs. A major incentive in this realm is the development of membranes that are suitable for operation at intermediate temperatures (120-200°C). Inevitably, aqueous-based PEMs for operation at higher temperatures (T > 90°C) and low relative humidity have to attain high rates of proton transport with a minimal amount of water that is tightly bound to a stable host polymer.33 37,40,42,43 yj-jg development of new PEMs thus warrants efforts in understanding of proton and water transport phenomena under such conditions. We will address this in Section 6.7.3. 

The study of the dynamical behavior of water molecules and protons as a function of the state of hydration is of great importance for understanding the mechanisms of proton and water transport and their coupling. Such studies can rationalize the influence of the random self-organized polymer morphology and water uptake on effective physicochemical properties (i.e., proton conductivity, water permeation rates, and electro-osmotic drag coefficients). 

Molecular modeling of PT at dense interfacial arrays of protogenic surface groups in PEMs needs ab initio quantum mechanical calculations. In spite of fhe dramafic increase in computational capabilihes, it is still "but a dream" to perform full ab initio calculations of proton and water transport within realistic pores or even porous networks of PEMs. This venture faces two major obstacles structural complexity and the rarity of proton transfer events. The former defines a need for simplified model systems. The latter enforces the use of advanced compufahonal techniques that permit an efficient sampling of rare evenfs. ... 

Paddison, S.J. Paul, R. Zawodzinski, T.A. A statistical mechanical model of proton and water transport in a proton exchange membrane. J. Electrochem. Soc. 2000, 147 (2), 617-626. 

The development of membranes for fuel cells is a highly complex task. The primary functionalities, (i) transport of protons and (ii) separation of reactants and electrons, have to be provided and sustained for the required operating time. Optimization of the composition and structure of the material to maximize conductivity and mechanical robustness involves careful balancing of synthesis and process parameters. The ultimate membrane qualification test is the fuel cell experiment. It is evident that the membrane is not a stand-alone component, but is combined with the electrodes in the membrane electrode assembly (MEA). Interfacial properties, influence on anode and cathode electrocatalysis, and water management are the key aspects to be considered and optimized in this ensemble. 

A major incentive of this article will be to stress the complicating traits of the membrane environment on effective proton transport and fuel cell performance. The polymer affects distribution and structme of water and dynamics of protons and water molecules at multiple scales. In order to describe the conductivity of the membrane, one needs to take into account explicit polymer-water interactions at molecular level, interfacial phenomena at polymer-water interfaces at mesoscopic scale and the statistical geometry and topology of randomly distributed aqueous and polymeric domains at macroscopic scale. 

In real membranes, transport properties of protons and water molecules can be obtained by an effective interpolation between the bulk and the interfacial mechanisms, as explored in [82]. Subsequently, we will consider theoretical approaches along this general scheme, increasing in complexity and covering scales from molecular to macroscopic. 

Membrane operation in the fuel cell is affected by structinal characteristics and detailed microscopic mechanisms or proton transport, discussed above. However, at the level of macroscopic membrane performance in an operating fuel cell with fluxes of protons and water, only phenomenological approaches are feasible. Essentially, in this context, the membrane is considered as an effective, macrohomogeneous medium. All structures and processes are averaged over micro-to-mesoscopic domains, referred to as representative elementary volume elements (REVs). At the same time, these REVs are small compared to membrane thickness so that non-uniform distributions of water content and proton conductivities across the membrane could be studied. 

An extensive hterature is devoted to the physics of water channels formation and to the mechanism of proton and water transport in membranes. In this section, we give a brief overview relevant to the analytical modelling of fuel cells. A detailed review of phenomenological membrane transport models is given in (Weber and Newman, 2007). Atomistic modelling and experiments on proton transport in membranes are reviewed in (Kreuer et al., 2004). Recent advances in mesoscopic membrane modelling are discussed in (Promislow and Wetton, 2009). The reader is referred to these works for a detailed discussion of the transport processes in polymer membranes. 

This section presents a review of atomistic simulations and of a recently introduced meso-scale computational method to evaluate key factors affecting the morphology of CLs. Most of the effort in molecular dynamics simulations for PEFCs has concentrated on dynamic motion of proton and water through the hydrated membrane [96-104], Little attempt has been made to employ MD techniques for elucidating the structure and transport of CLs, particularly in three-phase systems of carbon/Pt, ionomer, and gas phase. In the following subsections, we discuss various MD simulations to study the transport and dynamic behavior of CLs in terms of water and proton diffusivity, Pt-supported electrocatalyst, and microstructure formation. 

For all of these matters, it is of utmost importance to understand (i) ionomer selforganization in PEMs, (ii) the thermodynamic state of water as a function of external conditions, (iii) pore swelling and network reorganization upon water uptake, and (iv) associated transport properties of protons and water. These relations will be developed in Chapter 2. 

The main assumptions of the simple bulk conductivity model are valid at high water contents. This wording implies that a lower characteristic value of water content exists, below which the model is invalid. This value emerges as an important membrane characteristic. It will be discussed below, based on an assessment of water sorption properties and dynamics of proton and water transport. 

At X > Xs, capillary effects control the equilibration of water with the polymer. In this regime, the values of molecular mobilities of protons and water approach the corresponding values in free bulk water, and hydrodynamic effects control transport phenomena. The PEM conductivity is described well by Equation 2.1. Highly functionalized polymer-water interfaces have a minor impact on transport mechanisms in this regime. An important consequence of this picture is that molecular-level studies of proton transport that account for details of ionomer structure are required strictly only for X <. At X >, it is sufficient to employ the well-established mechanism... 

Recent models of proton and water transport in PEMs tend to support the notion of cylindrical pore networks. A qualitative distinction between superstructures will be made below, based on the analysis of water sorption data and evaluation of the implications of pore network reorganization upon water uptake. 

Electro-osmotic drag phenomena are closely related to the distribution and mobility of protons in pores. The molecular contribution can be obtained by direct molecular dynamics simulations of protons and water in single ionomer pores, as reviewed in the sections Proton Transport in Water and Stimulating Proton Transport in a Pore. The hydrodynamic contribution to nd can be studied, at least qualitatively, using continuum dielectric approaches. The solution of the Poisson-Boltzmann equation... 

The electro-osmotic coupling of proton and water transport depends on the molecular mechanism of proton transport. It is useful to distinguish a molecular and a hydro-dynamic contribution to the electro-osmotic drag coefficient. The latter contribution increases strongly with water uptake and temperature. 

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