Non-Fickian water vapor sorption dynamics by Nafion membranes

A chemo-mechanical model for describing sorption hysteresis in a glassy polyurethane

Hysteretic sorption and desorption of water is observed from 0 to 95% relative humidity and 298-333 K on a glassy polyurethane foam. It is postulated that sorption-induced swelling of the glassy polyurethane increases the concentration of accessible hydrogen-bonding adsorption sites for water. The accessibility of sites is kinetically controlled due to the restricted thermal motions of chains in the glassy polymer, causing a difference in accessible site concentrations during sorption and desorption. This discrepancy leads to hysteresis in the sorbed concentrations of water. A coupled chemo-mechanical model relating volumetric strain, adsorption site concentration, and sorbed water concentration is employed to describe water sorption hysteresis in the glassy polyurethane. This model not only describes the final mass uptake for each relative humidity step, but also captures the dynamics of water uptake, which exhibit diffusion and relaxation rate-controlled regimes.

Modeling dynamic swelling of polymer-based artificial muscles

Polymer-based artificial muscles are lightweight, are flexible, can have variable stiffness, and provide actuation in applications in which heavy actuators are not feasible. Achieving device requirements, such as strain, strain rate, lifetime, achievable work, and efficiency, requires material and muscle geometry design. This study is motivated by the possibility of significant actuation from twisted and coiled polymer (TCP) fibers that rely on radial swelling to produce reversible work. Modeling the actuation of advanced polymers is essential for defining design metrics. An analytical thermodynamic expression based on Flory-Rehner Theory was combined with a numerical transport model in order to simulate transient swelling of a polymeric network driven by diffusion and migration. Radial swelling of polymer fibers was modeled, including parametric studies and comparison to experimental data. By increasing the transport distance, swelling is shown to increase the time to equilibrium, but this can be more than compensated by applying voltage to take advantage of ion migration/electroosmotic drag. This work indicates that, in addition to migration, dimensions smaller than 100 micrometers here are needed to achieve the sub-second response times of natural muscles. The impact of polymer swelling on transport in polymers is directly evaluated by locally accounting for the length increase of discrete elements due to solvent presence, which cannot be done analytically. Furthermore, strain and work done by swelling a TCP is modelled, and the benefit of anisotropic swelling and constant modulus is quantified.

Resistive Response of Carbon Nanotube-Based Composites Subjected to Water Aging

This work aimed to monitor, through the changes in electrical resistance, the evolution of the mechanical properties due to aging caused by water sorption in carbon nanotube-based epoxy composites. The epoxy/CNT nanocomposites were prepared by dispersing the filler in the precursor through the ultra-sonication process and mixing the hardener by mechanical stirring. After an evaluation of the electrical properties, detected through a two-probe electrical measurement method, of nanocomposites at different percentages by weight of the filler (0.025, 0.05, 0.1, 0.3, 0.5, and 1.0), a concentration (0.1% by weight), close to that of the electrical percolation threshold, was chosen to evaluate the resistive response. This specific concentration was selected in order to obtain maximized values of the variation detected for the changes in the electrical resistance resulting from phenomena of structural relaxations/rearrangements due to water absorption. In particular, the electrical conductivity value switched from 8.2 × 10^-14 S/m for the unfilled epoxy resin to 6.3 × 10^-2 S/m for carbon nanotube-based epoxy composite at 0.1% by weight of the nanofiller. The water sorption caused a reduction in the mechanical properties (storage modulus and tan δ) due to swelling and plasticization phenomena, which caused the structural reorganization of the conductive interparticle contacts in the matrix with a consequent variation in the electrical resistance of the material. The found 'non-Fickian' water diffusion behavior was very similar to the variation in the electrical resistance with time. This last correlation allows the association of the measurement of the electrical resistance with the quantity of absorbed water and, therefore, with the aging of the material to water absorption, through the sensitivity factor (β). The resistive nature of the composite can be used to monitor the amount of water absorption and the changes in the structure of the material subject to water aging.

Modelling Methods and Validation Techniques for CFD Simulations of PEM Fuel Cells

The large-scale adoption of fuel cells system for sustainable power generation will require the combined use of both multidimensional models and of dedicated testing techniques, in order to evolve the current technology beyond its present status. This requires an unprecedented understanding of concurrent and interacting fluid dynamics, material and electrochemical processes. In this review article, Polymer Electrolyte Membrane Fuel Cells (PEMFC) are analysed. In the first part, the most common approaches for multi-phase/multi-physics modelling are presented in their governing equations, inherent limitations and accurate materials characterisation for diffusion layers, membrane and catalyst layers. This provides a thorough overview of key aspects to be included in multidimensional CFD models. In the second part, advanced diagnostic techniques are surveyed, indicating testing practices to accurately characterise the cell operation. These can be used to validate models, complementing the conventional observation of the current–voltage curve with key operating parameters, thus defining a joint modelling/testing environment. The two sections complement each other in portraying a unified framework of interrelated physical/chemical processes, laying the foundation of a robust and complete understanding of PEMFC. This is needed to advance the current technology and to consciously use the ever-growing availability of computational resources in the next future.

Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review

Theoretical models used to describe the proton-conductive membrane in polymer electrolyte membrane fuel cells (PEMFCs) are reviewed, within the specific context of practical, physicochemical simulations of PEMFC device-scale performance and macroscopically observable behaviour. Reported models and their parameterisation (especially for Nafion 1100 materials) are compiled into a single source with consistent notation. Detailed attention is given to the Springer-Zawodzinski-Gottesfeld, Weber-Newman, and "binary friction model" methods of coupling proton transport with water uptake and diffusive water transport; alongside, data are compiled for the corresponding parameterisation of proton conductivity, water sorption isotherm, water diffusion coefficient, and electroosmotic drag coefficient. Subsequent sections address the formulation and parameterisation of models incorporating interfacial transport resistances, hydraulic transport of water, swelling and mechanical properties, transient and non-isothermal phenomena, and transport of dilute gases and other contaminants. Lastly, a section is dedicated to the formulation of models predicting the rate of membrane degradation and its influence on PEMFC behaviour.

Influence of Thickness on Water Absorption and Tensile Strength of BFRP Laminates in Water or Alkaline Solution and a Thickness-Dependent Accelerated Ageing Method for BFRP Laminates

This paper first presented an experimental study on water absorption and tensile properties of basalt fiber-reinforced polymer (BFRP) laminates with different specimen thicknesses (i.e., 1, 2, and 4 mm) subjected to 60 °C deionized water or alkaline solution for an ageing time up to 180 days. The degradation mechanism of BFRP laminates in solution immersion was also explored combined with micro-morphology analysis by scanning electronic microscopy (SEM). The test results indicated that the water absorption and tensile properties of BFRP laminates were dramatically influenced by specimen thickness. When the BFRP laminates with different thicknesses were immersed in the solution for the same ageing time, the water absorption of the specimens decreased firstly before reaching their peak water absorption and then increased in the later stage with the increase of specimen thickness, while the tensile strength retention sustaining increased as specimen thickness increased. The reason is that the thinner the specimen, the more severe the degradation. In this study, a new accelerated ageing method was proposed to predict the long-term water absorption and tensile strength of BFRP laminates. The accelerated factor of the proposed method was determined based on the specimen thickness. The proposed method was verified by test results with a good accuracy, indicating that the method could be used to predict long-term water absorption and tensile strength retention of BFRP laminates by considering specimen thickness in accelerating tests.

Thickness Dependence of the Diffusivity and Solubility of Cyclohexane in Nanoscale Bitumen Films

Diffusivity and solubility of cyclohexane in nanoscale bitumen films coated on hydrophilic substrates at ambient conditions were studied using a gravimetric analyzer. Three substrates were used, and they are as follows: sample A, monodisperse spherical glass beads; sample B, polydisperse spherical glass beads mixed with polydisperse irregular-shape kaolin clay particles; and sample C, irregular-shape residual solids generated from a solvent extraction process of an oil sand ore. All of the above samples had a mean diameter of 150 μm. Diffusion coefficients were determined based upon the initial rates of cyclohexane absorption when bitumen-coated samples at various amounts (thicknesses) were exposed to a carrier gas with cyclohexane vapors at two levels of relative saturations (RSs), and they were found to be in the range of 10^-18 to 10^-16 m²/s. A double-first-order kinetics model fits well to the absorption data, suggesting that there exists a concentration gradient of polar (or nonpolar) bitumen molecules in the nanoscale films. This is because the hydrophilic substrates attract the relatively polar fraction of bitumen molecules to the region close to the substrates and the nonpolar fraction resides in the region near the free surface. As a result, the measured diffusion coefficients exhibited positive thickness dependence when the thickness of the bitumen films was at the nanoscale. The molecules near the substrates tended to diffuse slower than those in the free surface region. However, diffusivity was insensitive to the cyclohexane RS. On the other hand, the measured solubility of cyclohexane in the nanoscale bitumen films exhibited no thickness dependence but strong cyclohexane RS dependence. These results suggest that solubility is not affected by the inhomogeneous distribution of bitumen molecules in the nanoscale films and that it follows more or less Henry's law.

Water Vapor Sorption Properties of Polyethylene Terephthalate over a Wide Range of Humidity and Temperature

The dynamic and equilibrium water vapor sorption properties of amorphous polyethylene terephthalate were determined via gravimetric analysis over a wide range of temperatures (23-70 °C) and humidities (0-90% RH). At low temperature and relative humidity, the dynamics of the sorption process was Fickian. Increasing the temperature or relative humidity induced a distinct up-swing effect, which was associated with a plasticization/clustering phenomenon. For high temperatures and relative humidity, a densification of the polymer was evidenced. In addition to the classical Fickian diffusion, a new parameter was introduced to express the structural modifications of PET. Finally, two partial pressures were defined as thresholds that control the transition between these three phases. A simplified state diagram was finally proposed. In addition, the thermal dependence of these sorption modes was also determined and reported. The enthalpy of Henry's water sorption and the activation energy of diffusion were independent of vapor pressure and followed an Arrhenius law.

New Insights into Perfluorinated Sulfonic-Acid Ionomers

In this comprehensive review, recent progress and developments on perfluorinated sulfonic-acid (PFSA) membranes have been summarized on many key topics. Although quite well investigated for decades, PFSA ionomers' complex behavior, along with their key role in many emerging technologies, have presented significant scientific challenges but also helped create a unique cross-disciplinary research field to overcome such challenges. Research and progress on PFSAs, especially when considered with their applications, are at the forefront of bridging electrochemistry and polymer (physics), which have also opened up development of state-of-the-art in situ characterization techniques as well as multiphysics computation models. Topics reviewed stem from correlating the various physical (e.g., mechanical) and transport properties with morphology and structure across time and length scales. In addition, topics of recent interest such as structure/transport correlations and modeling, composite PFSA membranes, degradation phenomena, and PFSA thin films are presented. Throughout, the impact of PFSA chemistry and side-chain is also discussed to present a broader perspective.

Using Indentation to Quantify Transport Properties of Nanophase-Segregated Polymer Thin Films

Indentation of hydrated Nafion thin films reveals that both the in-plane diffusivity of water and the intrinsic permeability of the phase-segregated network decrease dramatically with decreasing film thickness. Using pore-network theory, this decrease in diffusivity is attributed to both an increase in ionic-domain heterogeneity and a reduction in ionic-domain connectivity upon confinement.

Fast Water Diffusion and Long-Term Polymer Reorganization during Nafion Membrane Hydration Evidenced by Time-Resolved Small-Angle Neutron Scattering

We report a small-angle neutron scattering study of liquid water sorption in Nafion membranes. The swelling of hydrophilic domains was measured on the nanoscale by combining in situ time-resolved and long-term static experiments, yielding kinetic curves recorded over an unprecedented time scale, from hundreds of milliseconds to several years. At low water content, typically below 5 water molecules per ionic group, a limited subdiffusive regime was observed and ascribed to nanoconfinement and local interactions between charged species and water molecules. Further ultrafast and thermally activated swelling due to massive liquid water sorption was observed and analyzed by using Fick's equation. The extracted mutual water diffusion coefficients are in good agreement with pulsed field gradient NMR self-diffusion coefficient values, evidencing a water diffusion-driven process due to concentration gradients within the Nafion membrane. Finally, after completion of the ultrafast regime, the kinetic swelling curves exhibit a remarkable long-term behavior scaling as the logarithm of time, showing that the polymer membrane can continuously accommodate additional water molecules upon hydration stress. The present nanoscale kinetics results provide insights into the vapor-versus-liquid sorption mechanisms, the nanostructure of Nafion, and the role of polymer reorganization modes, highlighting that the membrane can never reach a steady state.

Model-Based Control of a Continuous Coating Line for Proton Exchange Membrane Fuel Cell Electrode Assembly

The most expensive component of a fuel cell is the membrane electrode assembly (MEA), which consists of an ionomer membrane coated with catalyst material. Best-performing MEAs are currently fabricated by depositing and drying liquid catalyst ink on the membrane; however, this process is limited to individual preparation by hand due to the membrane’s rapid water absorption that leads to shape deformation and coating defects. A continuous coating line can reduce the cost and time needed to fabricate the MEA, incentivizing the commercialization and widespread adoption of fuel cells. A pilot-scale membrane coating line was designed for such a task and is described in this paper. Accurate process control is necessary to prevent manufacturing defects from occurring in the coating line. A linear-quadratic-Gaussian (LQG) controller was developed based on a physics-based model of the coating process to optimally control the temperature and humidity of the drying zones. The process controller was implemented in the pilot-scale coating line proving effective in preventing defects.

Effect of water sorption on the electronic conductivity of porous polymer electrolyte membrane fuel cell catalyst layers

A method is described for measuring the effective electronic conductivity of porous fuel cell catalyst layers (CLs) as a function of relative humidity (RH). Four formulations of CLs with different carbon black (CB) contents and ionomer equivalent weights (EWs) were tested. The van der Pauw method was used to measure the sheet resistance (RS), which increased with RH for all samples. The increase was attributed to ionomer swelling upon water uptake, which affects the connectivity of CB aggregates. Greater increases in RS were observed for samples with lower EW, which uptake more water on a mass basis per mass ionomer. Transient RS measurements were taken during absorption and desorption, and the resistance kinetics were fit using a double exponential decay model. No hysteresis was observed, and the absorption and desorption kinetics were virtually symmetric. Thickness measurements were attempted at different RHs, but no discernible changes were observed. This finding led to the conclusion that the conducting Pt/C volume fraction does not change with RH, which suggests that effective medium theory models that depend on volume fraction alone cannot explain the reduction in conductivity with RH. The merits of percolation-based models were discussed. Optical micrographs revealed an extensive network of "mud cracks" in some samples. The influence of water sorption on CL conductivity is primarily explained by ionomer swelling, and its effects on the quantity and quality of interaggregate contacts were discussed.

Elucidating Water Transport Mechanisms in Nafion Thin Films

Ion-exchange membranes are critical components of hydrogen fuel cells, where these ionomers can be confined to nanoscale thicknesses, altering the physical properties of these films from that of bulk membranes. Therefore, it is important to develop methods capable of measuring and elucidating the transport mechanisms under thin film confinement compared to bulk Nafion. In this study, water sorption and diffusion in a Nafion thin film were measured using time-resolved in situ polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS). Interfacial mass transport limitations were confirmed to be minimal, while restricted water diffusion was observed, where the effective diffusion coefficient of water in the thin Nafion film was many orders of magnitude lower (between 4 and 5 orders of magnitude) than those reported for bulk membranes and was dependent on the initial hydration state of the Nafion. Furthermore, the response of the hydrophobic domains (Teflon backbone) to the swelling of the hydrophilic domains (ionic clusters) was shown to be orders of magnitude slower than that of bulk Nafion.

Energy harvesting from humidity changes with a flexible coaxial electrode solid-state cell

A measurable Gibbs free energy is obtained in a coaxial electrode cell from concentration gradients induced by changes in the relative humidity.

Asymmetric bi-layer PFSA membranes as model systems for the study of water management in the PEMFC

New bi-layer PFSA membranes made of Nafion® NRE212 and Aquivion™ E79-05s with different equivalent weights are prepared with the aim of managing water repartition in the PEMFC.

Understanding Water Uptake and Transport in Nafion Using X-ray Microtomography

To develop new ionomers and optimize existing ones, there is a need to understand their structure/function relationships experimentally. In this letter, synchrotron X-ray microtomography is used to examine water distributions within Nafion, the most commonly used ionomer. Simultaneous high spatial (∼1 μm) and temporal (∼10 min) resolutions, previously unattained by other techniques, clearly show the nonlinear water profile across the membrane thickness, with a continuous transition from dynamic to steady-state transport coefficients with the requisite water-content dependence. The data also demonstrate the importance of the interfacial condition in controlling the water profile and help to answer some long-standing debates in the literature.

Microscopic analysis of current and mechanical properties of nafion® studied by atomic force microscopy

The conductivity of fuel cell membranes as well as their mechanical properties at the nanometer scale were characterized using advanced tapping mode atomic force microscopy (AFM) techniques. AFM produces high-resolution images under continuous current flow of the conductive structure at the membrane surface and provides some insight into the bulk conducting network in Nafion membranes. The correlation of conductivity with other mechanical properties, such as adhesion force, deformation and stiffness, were simultaneously measured with the current and provided an indication of subsurface phase separations and phase distribution at the surface of the membrane. The distribution of conductive pores at the surface was identified by the formation of water droplets. A comparison of nanostructure models with high-resolution current images is discussed in detail.

Subsecond Morphological Changes in Nafion during Water Uptake Detected by Small-Angle X-ray Scattering

The ability of the Nafion membrane to absorb water rapidly and create a network of hydrated interconnected water domains provides this material with an unmatched ability to conduct ions through a chemically and mechanically robust membrane. The morphology and composition of these hydrated membranes significantly affects their transport properties and performance. This work demonstrates that differences in interfacial interactions between the membranes exposed to vapor or liquid water can cause significant changes in kinetics of water uptake. In situ small-angle X-ray scattering (SAXS) experiments captured the rapid swelling of the membrane in liquid water with a nanostructure rearrangement on the order of seconds. For membranes in contact with water vapor, morphological changes are four orders-of-magnitude slower than in liquid water, suggesting that interfacial resistance limits the penetration of water into the membrane. Also, upon water absorption from liquid water, a structural rearrangement from a distribution of spherical and cylindrical domains to exclusively cylindrical-like domains is suggested. These differences in water-uptake kinetics and morphology provide a new perspective into Schroeder's paradox, which dictates a different water content for vapor- and liquid-equilibrated ionomers at unit activity. The findings of this work provide critical insights into the fast kinetics of water absorption of the Nafion membrane, which can aid in the design of energy conversion devices that operate under frequent changes in environmental conditions.

Effect of interfacial water transport resistance on coupled proton and water transport across Nafion

Dynamic and steady-state water flux, current density, and resistance across a Nafion 115 membrane-electrode-assembly (MEA) were measured as functions of temperature, water activity, and applied potential. After step changes in applied potential, the current, MEA resistance, and water flux evolved to new values over 3000-5000 s, indicating a slow redistribution of water in the membrane. Steady-state current density initially increased linearly with increasing potential and then saturated at higher applied potentials. Water flux increases in the direction of current flow resulting from electro-osmotic drag. The coupled transport of water and protons was modeled with an explicit accounting for electro-osmotic drag, water diffusion, and interfacial water transport resistance across the vapor/membrane interface. The model shows that water is dragged inside the membrane by the proton current, but the net water flux into and out of the membrane is controlled by interfacial water transport at the membrane/vapor interface. The coupling of electro-osmotic drag and interfacial water transport redistributes the water in the membrane. Because water entering the membrane is limited by interfacial transport, an increase in current depletes water from the anode side of the membrane, increasing the membrane resistance there, which in turn limits the current. This feedback loop between current density and membrane resistance determines the stable steady-state operation at a fixed applied potential that results in current saturation. We show that interfacial water transport resistance substantially reduces the impact of electro-osmotic drag on polymer electrolyte membrane fuel cell operation.

Using 2H labeling with neutron radiography for the study of solid polymer electrolyte water transport properties

A method combining (2)H labeling of different sources of H atoms (hydrogen, water vapor) with neutron imaging for the analysis of transport parameters in the bulk and at the interfaces of Nafion polymer electrolyte membranes is proposed. The use of different isotope compositions in the steady state allows evaluation of the relation between bulk and interface transport parameters, but relies on literature data for evaluating absolute values. By using transients of isotope composition, absolute values of these parameters including the self-diffusion coefficient of H can be extracted, making this method an attractive alternative to self-diffusion measurements using nuclear magnetic resonance (NMR), allowing measurements in precisely controlled conditions in real fuel cell structures. First measurements were realized on samples with and without electrodes and we report values of the self-diffusion coefficient of the same order of magnitude as values measured using NMR, although with slightly higher numbers. In our particular case, lower interfacial exchange rates for water transport were observed for samples with an electrode.

The kinetics of water sorption in Nafion membranes: a small-angle neutron scattering study

The optimization of the water management in proton exchange membrane fuel cells is a major issue for the large-scale development of this technology. In addition to the operating conditions, the membrane water sorption and transport processes obviously control the water management. The main objective of this work is to provide new experimental evidence based on the use of the small-angle neutron scattering (SANS) technique in order to allow a better understanding of water sorption processes. SANS spectra were recorded for membranes equilibrated with either water vapor or liquid. Sorption kinetics data were determined and the SANS spectra were analyzed using the method developed for extracting water concentration profiles across the membrane in operating fuel cells. The water concentration profiles across the membrane are completely flat, which indicates that the water diffusion within the membrane is not the limiting process. This result provides new insight into the numerous data published on these properties. For the first time, the swelling kinetics of a Nafion membrane immersed in liquid water is studied and a complete swelling is obtained in less than 1 min.