Equivalent weight (EW) is the number of grams of dry Nafion per mole of sulfonic acid groups when the material is in the acid form. This is an average EW in the sense that the comonomer sequence distribution (that is usually unknown to the investigator and largely unreported) gives a distribution in m in this formula. EW can be ascertained by acid-base titration, by analysis of atomic sulfur, and by FT-IR spectroscopy. The relationship between EW and m is EW ) 100m + 446 so that, for example, the side chains are separated by around 14 CF2 units in a membrane of 1100 EW. Common at the time of this writing are Nafion 117 films. The designation “117” refers to a film having 1100 EW and a nominal thickness of 0.007 in., although 115 and 112 films have also been available. Early-reported studies involved 1200 EW samples as well as special experimental varieties, some being rather thin. The equivalent weight is related to the property more often seen in the field of conventional ion exchange resins, namely the ion exchange capacity (IEC), by the equation IEC ) 1000/EW. The mention of the molecular weight of high equivalent weight (EW > 1000 g‚mol-1) Nafion is almost absent in the literature, although the range 105-106 Da has been mentioned. As this polymer does not form true solutions, the common methods of light scattering and gel permeation chromatography cannot be used to determine molecular weight as well as the size and shape of isolated, truly dissolved molecules. Studies of the structure of this polymer in solvent (albeit not a true solution) will be mentioned in the scattering section of this review. It should be noted that Curtin et al. performed size exclusion chromatography determinations of the molecular weight distribution in Nafion aqueous dispersions after they were heated to high temperatures (230, 250, and 270 °C).1 Before heating, there was a high molecular weight shoulder on a bimodal distribution, due to molecular aggregates, but this shoulder disappeared upon heating, which indicated that the aggregates were disrupted. The peaks for the monomodal distribution for the heated samples were all located at molecular weights slightly higher than 105 g‚mol-1. Also, light scattering experiments revealed that the radius of gyration had a linear dependence on the molar mass of the aggregates, which suggests that the particles are in the form of rods or ribbons, or at least some elongated structure. Nafion ionomers are usually derived from the thermoplastic -SO2F precursor form that can be extruded into sheets of required thickness. Strong interactions between the ionic groups are an obstacle to melt processing. This precursor does not possess the clustered morphology that will be of great concern in this article but does possess Teflon-like crystallinity which persists when the sulfonyl fluoride form is converted to, for example, the K+ form by reacting it with KOH in water and DMSO. Thereafter, the -SO3H form is achieved by soaking the film in a sufficiently concentrated aqueous acid solution. Extrusion of the sulfonyl fluoride precursor can cause microstructural orientation in the machine direction, * Address correspondence to either author. Phone: 601-266-5595/ 4480. Fax: 601-266-5635. E-mail: Kenneth.Mauritz@usm.edu; RBMoore@usm.edu. 4535 Chem. Rev. 2004, 104, 4535−4585

State of Understanding of Nafion

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1131&context=usdoepub

A review of polymer electrolyte membrane fuel cells: Technology, applications,and needs on fundamental research

1. Introduction 46372. Theoretical Methodologies and Simulation Tools 46402.1. Ab Initio Quantum Chemistry 46412.2. Molecular Dynamics 46422.2.1. Classical Molecular Dynamics and MonteCarlo Simulations46432.2.2. Empirical Valence Bond Models 46442.2.3. Ab Initio Molecular Dynamics (AIMD) 46452.3. Poisson−Boltzmann Theory 46452.4. Nonequilibrium Statistical Mechanical IonTransport Modeling46462.5. Dielectric Saturation 46473. Transport Mechanisms 46483.1. Proton Conduction Mechanisms 46483.1.1. Homogeneous Media 46483.1.2. Heterogeneous Systems (ConfinementEffects)46553.2. Mechanisms of Parasitic Transport 46613.2.1. Solvated Acidic Polymers 46613.2.2. Oxides 46654. Phenomenology of Transport inProton-Conducting Materials for Fuel-CellApplications46664.1. Hydrated Acidic Polymers 46664.2. PBI−H

/pdf/transport-in-proton-conductors-for-fuel-cell-applications-3gvrtpo4jv.pdf

Transport in proton conductors for fuel-cell applications: simulations, elementary reactions, and phenomenology.

When Szent-Gyorgyi called water the “matrix of life”,1 he was echoing an old sentiment. Paracelsus in the 16th century said that “water was the matrix of the world and of all its creatures.”2 But Paracelsus’s notion of a matrixsan active substance imbued with fecund, life-giving propertiess was quite different from the picture that, until very recently, molecular biologists have tended to hold of water’s role in the chemistry of life. Although acknowledging that liquid water has some unusual and important physical and chemical propertiessits potency as a solvent, its ability to form hydrogen bonds, its amphoteric naturesbiologists have regarded it essentially as the backdrop on which life’s molecular components are arrayed. It used to be common practice, for example, to perform computer simulations of biomolecules in a vacuum. Partly this was because the computational intensity of simulating a polypeptide chain was challenging even without accounting for solvent molecules too, but it also reflected the prevailing notion that water does little more than temper or moderate the basic physicochemical interactions responsible for molecular biology. What Gerstein and Levitt said 9 years ago remains true today: “When scientists publish models of biological molecules in journals, they usually draw their models in bright colors and place them against a plain, black background”.3 Curiously, this neglect of water as an active component of the cell went hand in hand with the assumption that life could not exist without it. That was basically an empirical conclusion derived from our experience of life on Earth: environments without liquid water cannot sustain life, and special strategies are needed to cope with situations in which, because of extremes of either heat or cold, the liquid is scarce.4-6 The recent confirmation that there is at least one world rich in organic molecules on which rivers and perhaps shallow seas or bogs are filled with nonaqueous fluidsthe liquid hydrocarbons of Titan7smight now bring some focus, even urgency, to the question of whether water is indeed a * E-mail: p.ball@nature.com. Philip Ball is a science writer and a consultant editor for Nature, where he worked as an editor for physical sciences for more than 10 years. He holds a Ph.D. in physics from the University of Bristol, where he worked on the statistical mechanics of phase transitions in the liquid state. His book H2O: A Biography of Water (Weidenfeld & Nicolson, 1999) was a survey of the current state of knowledge about the behavior of water in situations ranging from planetary geomorphology to cell biology. He frequently writes about aspects of water science for both the popular and the technical media.

https://www.philipball.co.uk/images/stories/docs/pdf/ChemRev_final.pdf

Water as an Active Constituent in Cell Biology

We provide a phenomenological description of proton conductance in polymer electrolyte membranes, based on contemporary views of proton transfer processes in condensed media and a model for heterogeneous polymer electrolyte membrane structure. The description combines the proton transfer events in a single pore with the total pore-network performance and, thereby, relates structural and kinetic characteristics of the membrane. The theory addresses specific experimentally studied issues such as the effect of the density of proton localization sites (equivalent weight) of the membrane material and the water content of the pores. The effect of the average distance between the sulfonate groups, which changes during membrane swelling, is analyzed in particular, and the factors which determine the temperature dependence of the macroscopic membrane conductance are disclosed. Numerical estimates of the specific membrane conductivity obtained from the theory agree very well with typical experimental data, thereby confirming the appropriateness of the theoretical concepts. Moreover, the versatility of the models offers a useful and transparent frame for combining the analysis of both experimental data and the results of molecular dynamics simulations.

/pdf/mechanisms-of-proton-conductance-in-polymer-electrolyte-19smwke062.pdf

Mechanisms of Proton Conductance in Polymer Electrolyte Membranes

Single-molecule electron transfer in electrochemical environments.

The excess proton mobility in water has attracted scientific attention for more than a century. Detailed theoretical concepts and models are also presently in strong focus in efforts toward understanding this ubiquitous phenomenon. In the present report, we discuss a theoretical framework for rationalizing the excess proton mobility, based on computer simulations, theory of proton transfer (PT) in condensed media, and analysis of classical proton conductivity experiments over broad temperature ranges. The mechanistic options involved are (i) classical hydrodynamic motion of the hydronium ion (H3O+), (ii) proton transfer from hydronium to a neighboring water molecule, and (iii) structural diffusion of the Zundel complex (H5O2+), the processes all controlled by orientational fluctuations or hydrogen bond breaking in neighboring hydration shells. Spontaneous conversion of excess proton states between Zundel and hydrated hydronium states and between hydrated and bare hydronium states are the crucial parts of ...

/pdf/kinetics-of-proton-transport-in-water-4cng7kkq5w.pdf

Kinetics of proton transport in water

A theoretical frame for in situ electrochemical scanning tunneling microscopy (STM) of large adsorbed redox molecules is provided. The in situ STM process is viewed as two consecutive interfacial single-step electron transfer (ET) processes with full vibrational relaxation between the steps. The process is therefore a cycle of consecutive molecular reduction and reoxidation. This extends previous approaches where resonance tunneling, or coherent single-channel ET, were in focus. The dependence of the tunneling current on the bias voltage and overvoltage is calculated when both transitions are either fully adiabatic or fully diabatic, and when one transition is fully adiabatic and the other one fully diabatic. A particular feature of the fully adiabatic limit is that each oxidation−reduction cycle is composed of manifolds of individual interfacial ET events at both electrodes, enhancing electron tunneling significantly compared to single-ET. The voltage dependences show spectrocopy-like features. Particula...

Alexander M. Kuznetsov

Papers

Mechanisms of Proton Conductance in Polymer Electrolyte Membranes

Single-molecule electron transfer in electrochemical environments.

Kinetics of proton transport in water

Mechanisms of in Situ Scanning Tunnelling Microscopy of Organized Redox Molecular Assemblies

Theory of charge transfer kinetics at solid-polar liquid interfaces