Functional constraints on phenomenological coefficients.

Thermodynamic fluxes (diffusion fluxes, heat flux, etc.) are often proportional to thermodynamic forces (gradients of chemical potentials, temperature, etc.) via the matrix of phenomenological coefficients. Onsager's relations imply that the matrix is symmetric, which reduces the number of unknown coefficients is reduced. In this article we demonstrate that for a class of nonequilibrium thermodynamic models in addition to Onsager's relations the phenomenological coefficients must share the same functional dependence on the local thermodynamic state variables. Thermodynamic models and experimental data should be validated through consistency with the functional constraint. We present examples of coupled heat and mass transport (thermodiffusion) and coupled charge and mass transport (electro-osmotic drag). Additionally, these newly identified constraints further reduce the number of experiments needed to describe the phenomenological coefficient.

Effects of hydrophobicity of diffusion layer on the electroreduction of biomass derivatives in polymer electrolyte membrane reactors.

For the first time, the hydrophobicity design of a diffusion layer based on the volatility of hydrogenation reactants in aqueous solutions is reported. The hydrophobicity of the diffusion layer greatly influences the hydrogenation performance of two model biomass derivatives, namely, butanone and maleic acid, in polymer electrolyte membrane reactors operated at atmospheric pressure. Hydrophobic carbon paper repels aqueous solutions, but highly volatile butanone can permeate in vapor form and achieve a high hydrogenation rate, whereas, for nonvolatile maleic acid, great mass transfer resistance prevents hydrogenation. With a hydrophilic stainless-steel welded mesh diffusion layer, aqueous solutions of both butanone and maleic acid permeate in liquid form. Hydrogenation of maleic acid reaches a similar level as that of butanone. The maximum reaction rate is 340 nmol cm(-2) s(-1) for both hydrogenation systems and the current efficiency reaches 70 %. These results are better than those reported in the literature.

Viscosity of Nafion oligomers as a function of hydration and counterion type: a molecular dynamics study.

The design of fuel cells and lithium ion batteries is constrained, in part, by mechanical creep and perforation of the polymer electrolyte, a process that is poorly understood at the molecular level. The mechanical stiffness (quantified as shear viscosity) and structure of a widely used polymer electrolyte, Nafion, are studied in the limit of a low solvent volume fraction (≤26% v/v H2O) using molecular dynamics simulations. The viscosity is shown to increase by up to 4 orders of magnitude in response to changes in composition representing as little as 2 wt % of system. Two types of compositional changes are considered, changes in solvent volume fraction and counterion type. A system with a counterion X(v+) for every v Nafion monomers and y water molecules is denoted as (RSO3)vX·(H2O)y. The following trend is observed in viscosity: (RSO3)2Ca > RSO3Na > RSO3H·(H2O)3 > RSO3H ≈ RSO3H·(H2O)10. This trend correlates with changes in the strength of the SO3(-)/X(v+)/SO3(-) cross-links and the size of the cross-link networks. Counterion type is shown to strongly influence the morphology. The simulations are able to reproduce some important experimental trends without crystalline domains or high-MW effects like entanglements, providing a simplified understanding of the mechanical properties of Nafion.

Molecular dynamics simulations of water permeation across Nafion membrane interfaces.

Permeation of water across the membrane/vapor and membrane/liquid-water interfaces of Nafion is studied using nonequilibrium molecular dynamics (NEMD) simulations, providing direct calculations of mass-transfer resistance. Water mass transfer within one nanometer of the vapor interface is shown to be 2 orders of magnitude slower than at any other point within the membrane, in qualitative agreement with permeation experiments. This interfacial resistance is much stronger than the resistance suggested by prior simulation work calculating self-diffusivity near the interface. The key difference between the prior approach and the NEMD approach is that the NEMD approach implicitly incorporates changes in solubility in the direction normal to the interface. Water is shown to be very insoluble near the vapor interface, which is rich in hydrophobic perfluorocarbon chains, in agreement with advancing contact angle experiments. Hydrophilic side chains are buried beneath this hydrophobic layer and aligned toward the interior of the membrane. Hydrophilic pores are not exposed to the vapor interface as proposed in prior theoretical work. At the membrane/liquid-water interface, highly swollen polymer chains extend into the liquid-water phase, forming a nanoscopically rough interface that is consistent with atomic force microscopy experiments. In these swollen conformations, hydrophilic side chains are exposed to the liquid-water phase, suggesting that the interface is hydrophilic, in agreement with receding contact angle experiments. The mass-transfer resistance of this interface is negligible compared to that of the bulk, in qualitative agreement with permeation experiments. The water activity at the vapor and liquid-water interfaces are nearly the same, yet large conformational and transport differences are observed, consistent with a mass-transfer-based understanding of Schroeder's paradox for Nafion.

Water slug to drop and film transitions in gas-flow channels.

Water emerging from micrometer-sized pores into millimeter-sized gas-flow channels forms drops. The drops grow until the force from the flowing gas is sufficient to detach the drops as either (1) slugs that completely occlude the cross section of the channel and move at the superficial gas velocity, (2) drops that partially occlude the channel and move at a velocity that is less than the gas velocity, or (3) films that flow continuously, occluding part of the channel. At steady state, small residual water droplets, ∼100 µm in diameter, left in corners and on surface defects from previous drops, are key in determining the shape of water drops at detachment. Slugs are formed at low-gas-phase Reynolds numbers (ReG) in both hydrophilic and hydrophobic channels. Drops are shed in Teflon-coated hydrophobic channels for ReG > 30. Films are formed in acrylic hydrophilic channels for ReG > 30. Slugs form when growing drops encounter residual water droplets that nucleate the drop to slug transition. Drops are shed when the force exerted by the flowing gas on growing drops exceeds the force needed to advance the gas/liquid/solid contact line before they grow to the critical size for the drop to slug transition. Drops grow by "stick-slip" of the solid-liquid-gas contact lines and with pinned contact lines until the force on the drops results in either the downstream contact angle becoming greater than the dynamic advancing contact angle or the upstream contact angle becoming less than the dynamic receding contact angle. The upstream contact line never detaches for hydrophilic channels, which is why films form. The shape of water drops and the detachment energies are shown to be well approximated by the force balance between the force needed to advance the drop's contact lines and the force that the flowing gas exerts on a stationary drop.

Molecular dynamics simulations of water sorption in a perfluorosulfonic acid membrane.

Atomistic molecular dynamics simulations are reported over a wide range of water contents and temperatures to obtain a better understanding of the structural and transport aspects of water sorption in Nafion, a perfluorosulfonic acid membrane, under equilibrium conditions. For the short Nafion chains studied, good agreement is found between the water sorption isotherms from simulations and experiments at intermediate hydration (2 ≲ λ ≲ 7, where λ is the number of water molecules per sulfonate group), suggesting that, in that range, the isotherm is insensitive to effects of polymer chain relaxation. If polymer chain relaxation were important for water sorption at these conditions, then the water uptake of experimental membranes, which contain very long chains, might be far from equilibrium, making it difficult to obtain agreement with equilibrated, short-chain simulations. At λ ≲ 7, strong water-sulfonate interactions, rather than chain relaxation, may control water sorption, despite the fact that chain relaxation time increases dramatically with decreasing hydration. Evidence for strong water-sulfonate interactions is found in the observation that sulfonate groups share water molecules in their first coordination shells at λ ≲ 7. Strong water-sulfonate interactions are also observed to influence transport properties like water diffusivity, and are as important for understanding these transport properties as larger-scale phenomena like morphology and percolation transitions. Finally, at low humidity (λ ≈ 1-2), rod-like hydrophilic clusters are observed, as well as a mechanism of water diffusion that differs qualitatively from that of water at high hydration (λ ≳ 7) and in the bulk, pure-component phase.

Water slug formation and motion in gas flow channels: the effects of geometry, surface wettability, and gravity.

Water emerging from ∼100 µm pores into millimeter-size gas flow channels forms drops that grow and become slugs which span the flow channel. Flowing gas causes the slugs to detach and move down the channel. The effect of channel geometry, surface wettability, and gravity on the formation and motion of water slugs has been analyzed using high-speed video images of the drops and differential pressure-time traces. Drops grow and appear, assuming a sequence of shapes that minimize the total interfacial energy of the gas-liquid and liquid-solid interfaces. The drops are initially spherical caps centered on the pore (the liquid contacts one wall). Above a certain size, the drops move to the corner, forming "corner drops" (the liquid contacts two walls). Corner drops grow across the channel, evolving into partial liquid bridges (drops confined by three walls), and finally the drops span the channel cross-section forming slugs (contacting all four walls). Smaller slugs are formed in channels with hydrophobic walls than in channels with hydrophilic walls. Smaller slugs are formed in channels with curved walls than in square or rectangular channels. Slugs move when the differential gas pressure overcomes the force to move the advancing and receding gas-liquid-solid contact lines of the slugs. Residual water left behind in corners by moving slugs reduces the barriers for drops to form slugs, causing the steady-state slug volumes to be smaller than those seen at start-up in dry channels.

Drop detachment and motion on fuel cell electrode materials.

Liquid water is pushed through flow channels of fuel cells, where one surface is a porous carbon electrode made up of carbon fibers. Water drops grow on the fibrous carbon surface in the gas flow channel. The drops adhere to the superficial fiber surfaces but exhibit little penetration into the voids between the fibers. The fibrous surfaces are hydrophobic, but there is a substantial threshold force necessary to initiate water drop motion. Once the water drops begin to move, however, the adhesive force decreases and drops move with minimal friction, similar to motion on superhydrophobic materials. We report here studies of water wetting and water drop motion on typical porous carbon materials (carbon paper and carbon cloth) employed in fuel cells. The static coefficient of friction on these textured surfaces is comparable to that for smooth Teflon. But the dynamic coefficient of friction is several orders of magnitude smaller on the textured surfaces than on smooth Teflon. Carbon cloth displays a much smaller static contact angle hysteresis than carbon paper due to its two-scale roughness. The dynamic contact angle hysteresis for carbon paper is greatly reduced compared to the static contact angle hysteresis. Enhanced dynamic hydrophobicity is suggested to result from the extent to which a dynamic contact line can track topological heterogeneities of the liquid/solid interface.

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.

Diffusion and interfacial transport of water in Nafion.

Water absorption, membrane swelling, and self-diffusivity of water in 1100 equivalent weight Nafion were measured as functions of temperature and water activity. Free volume per water at 80 °C, determined from water uptake and volume expansion data, decreases with water content in the membrane from 12 cm(3)/mol at λ = 0.5 H(2)O/SO(3) to 1.5 cm(3)/mol at λ = 4. The change in free volume with water content displays a transition at λ = 4. Limiting water self-diffusivity in Nafion was determined by pulsed gradient spin echo NMR at long delay times. The limiting self-diffusivity increases exponentially with water activity; the rate of increase of diffusivity with water content shows a transition at λ = 4. The tortuosity of the hydrophilic domains in Nafion decreased from 20 at low membrane water activity to 3 at λ = 4. It suggested a change in the connectivity of the hydrophilic domains absorbed water occurs at λ ∼ 4. The diffusivity results were employed to separate the contributions of diffusional and interfacial resistance for water transport across Nafion membranes, which enabled the determination of the interfacial mass transport coefficients. A diffusion model was developed which incorporated activity-dependent diffusivity, volume expansion, and the interfacial resistance, and was used to resolve the water activity profiles in the membrane.

Measurement of the mean inner potentials of anthracene and naphthalene.

The mean inner potential in metals, insulators, and semiconductors provides fundamental information regarding the electronic structure of the material. Here, we measure the mean inner potentials of the two archetype linear polyacenes: anthracence and naphthalene. We determine the mean inner potentials of single crystalline anthracene of 5.9 V (+/-0.3 V), and naphthalene of 5.4 V (+/-0.3 V) based on analysis of Kikuchi patterns observed using high-pressure reflection high energy electron diffraction. We show that the inner potential of a range of organic molecular semiconductors can be estimated from their diamagnetic susceptibilities.

Water permeation through Nafion membranes: the role of water activity.

The permeation of water through 1100 equivalent weight Nation membranes has been measured for film thicknesses of 51-254 microm, temperatures of 30-80 degrees C, and water activities (a(w)) from 0.3 to 1 (liquid water). Water permeation coefficients increased with water content in Nafion. For feed side water activity in the range 0 < a(w) < 0.8, permeation coefficients increased linearly with water activity and scaled inversely with membrane thickness. The permeation coefficients were independent of membrane thickness when the feed side of the membrane was in contact with liquid water (a(w) = 1). The permeation coefficient for a 127 microm thick membrane increased by a factor of 10 between contacting the feed side of the membrane to water vapor (a(w) = 0.9) compared to liquid water (a(w) = 1). Water permeation couples interfacial transport across the fluid membrane interface with water transport through the hydrophilic phase of Nafion. At low water activity the hydrophilic volume fraction is small and permeation is limited by water diffusion. The volume fraction of the hydrophilic phase increases with water activity, increasing water transport. As a(w) --> 1, the effective transport rate increased by almost an order of magnitude, resulting in a change of the limiting transport resistance from water permeation across the membrane to interfacial mass transport at the gas/membrane interface.

Wetting and absorption of water drops on Nafion films.

Water drops on Nafion films caused the surface to switch from being hydrophobic to being hydrophilic. Contact angle hysteresis of >70 degrees between advancing and receding values were obtained by the Wilhelmy plate technique. Sessile drop measurements were consistent with the advancing contact angle; the sessile drop contact angle was 108 degrees . Water drop adhesion, as measured by the detachment angle on an inclined plane, showed much stronger water adhesion on Nafion than Teflon. Sessile water and methanol drops caused dry Nafion films to deflect. The flexure went through a maximum with time. Flexure increased with contact area of the drop, but was insensitive to the film thickness. Methanol drops spread more on Nafion and caused larger film flexure than water. The results suggest that the Nafion surface was initially hydrophobic but water and methanol drops caused hydrophilic sulfonic acid domains to be drawn to the Nafion surface. Local swelling of the film beneath the water drop caused the film to buckle. The maximum flexure is suggested to result from motion of a water swelling front through the Nafion film.