Heat transport in a PEFC: Exact solutions and a novel method for measuring thermal conductivities of the catalyst layers and membrane

We develop a model of heat transport in the membrane–electrode assembly of a polymer electrolyte fuel cell. The exact analytical solutions to model equations are derived. Rather cumbersome solutions lead to remarkably simple formulas for the temperature of the anode and the cathode sides of the membrane. Based on these formulas a novel method for measuring thermal conductivities of the catalyst layers and membrane in a working fuel cell environment is proposed.     

Water transport coefficient distribution through the membrane in a polymer electrolyte fuel cell

The net water transport coefficient through the membrane, defined as the ratio of the net water flux from the anode to cathode to the protonic flux, is used as a quantitative measure of water management in a polymer electrolyte fuel cell (PEFC). In this paper we report on experimental measurements of the net water transport coefficient distribution for the first time. This is accomplished by making simultaneous current and species distribution measurements along the flow channel of an instrumented PEFC via a multi-channel potentiostat and two micro gas chromatographs. The net water transport coefficient profile along the flow channels is then determined by a control-volume analysis under various anode and cathode inlet relative humidity (RH) at 80 °C and 2 atm. It is found that the local current density is dominated by the membrane hydration and that the gas RH has a large effect on water transport through the membrane. Very small or negative water transport coefficients are obtained, indicating strong water back diffusion through the 30 μm Gore-Select^® membrane used in this study.     

Operating characteristics and energy distribution in transferred plasma arc systems

A specially designed plasma chamber was constructed to study the operating characteristics of a dc plasma-transferred arc of argon, struck between a fluid convective cathode and a water-cooled anode. The arc voltage increased markedly with arc length and with an increase in the inlet velocity of the argon flow past the cathode tip, and much less with an increase in current. Radiation from the plasma column to the chamber walls and transfer of energy to the anode were the two principal modes of transfer of the arc energy. The former was dominant in the case of long arcs and at high inlet argon velocities. At the anode, the major contribution was from electron transfer, which occurred on a very small area of the anode (～5 mm in diameter). Convective heat transfer from the plasma was somewhat less. In all cases, the arc energy contributions to cathode cooling and to the exit gas enthalpy were small. From total heat flux and radiative heat transfer measurements, it was estimated that the plasma temperature just above the anode was in the range 10,000–12,000 K. Preliminary experiments with an anode consisting of molten copper showed that the arc root was no longer fixed but moved around continuously. The arc was othwewise quite stable, and its operating characteristics differed little from those reported for solid anodes, in spite of the greater extent of metal vaporization.     

Transport properties of 2F <==> F2 in a temperature gradient as studied by molecular dynamics simulations

We calculate transport properties of a reacting mixture of F and F(2) from results of non-equilibrium molecular dynamics simulations. The reaction investigated is controlled by thermal diffusion and is close to local chemical equilibrium. The simulations show that a formulation of the transport problem in terms of classical non-equilibrium thermodynamics theory is sound. The chemical reaction has a large effect on the magnitude and temperature dependence of the thermal conductivity and the interdiffusion coefficient. The increase in the thermal conductivity in the presence of the chemical reaction, can be understood as a response to an imposed temperature gradient, which reduces the entropy production. The heat of transfer for the Soret stationary state was more than 100 kJ mol(-1), meaning that the Dufour and Soret effects are non-negligible in reacting mixtures. This sheds new light on the transport properties of reacting mixtures.     

A Sheath Collision Model with Thermionic Electron Emission and the Schottky Correction Factor for Work Function of Wall Material

This paper is a further development of the collisional sheath model at the thermionic cathode for two temperature modeling of thermal arcs that was recently suggested by Pekker and Hussary. In the present work, the Schottky correction factor to the work function of the electrode material is calculated taking into account the friction of ions in the sheath, while in the model of Pekker and Hussary it was calculated neglecting this friction. The model is applied to the cathode spot at the tungsten cathode in argon. It is demonstrated that a virtual cathode can be formed in the atmospheric pressure argon plasma at the cathode surface if the cathode current density is sufficiently small. The heat flux to the thermionic cathode due to charged particles and the heat flux to the plasma due to thermionic electrons are calculated. The obtained results are compared with the model of Pekker and Hussary. The sheath potential drop and the heat fluxes calculated by this model can be used as boundary conditions at the wall for the electric potential and for the energy equations for the electrons and heavy particles (ions and neutrals) in two temperature modeling of thermal plasma.     

Molecular theory of irreversibility

A generalization of the Gibbs entropy postulate is proposed based on the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy of equations as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that it reaches its maximum at equilibrium and is coherent with the second law. By using a generalization of the Liouville equation describing the evolution of the distribution vector, it is demonstrated that the entropy production is a non-negative quantity. Moreover, following the procedure of nonequilibrium thermodynamics a transport matrix is introduced and a microscopic expression for this is derived. This framework allows one to perform the thermodynamic analysis of nonequilibrium steady states with smooth phase-space distribution functions which, as proven here, constitute the states of minimum entropy production when one considers small departures from stationarity.     

Gas dynamics in channels of a gas-feed direct methanol fuel cell: exact solutions

The gas dynamics in channels on both sides of a gas-feed direct methanol fuel cell (DFMC) are considered. The basic equations for the flow velocity and density are derived, taking into account the mass and momentum transfer through the channel/backing layer interface. For the practical case of small inlet velocities the analog of the Bernoulli equation is formulated and the exact solution of nonlinear gas dynamics equations is obtained. It is shown that the flow in both the cathode and anode channels is incompressible (its density is constant) and electrochemical reactions affect only the flow velocity v. Simple formulae for v as a function of local current density and effective water drag coefficient are derived.     

Modeling and experimental study of a transferred arc stabilized with argon and flowing in a controlled-atmosphere chamber filled with argon at atmospheric pressure

For a transferred arc with a flat anode working at atmospheric pressure in an argon atmosphere, the influence of the gas injector design close to the cathode tip has been systematically studied for arc currents below 300 A, gas flowrates between 5 and 60 slm, and anode-cathode distances between 10 and 46 mm. Two types of injector configurations hare been studied: a cylindrical one with its wall parallel to the cathode axis and a conical one with the same cone angle as that of the cathode tip. The arc temperature was measured using flit, absolute intensity of ArI and ArII lines. Beside the roltagc and arc current, the losses at the cathode and at the anode were continuously recorded. An elliptic model was used to calculate the flow velocity, the temperature, and the current density close to the cathode and in the arc column. This model was either laminar or turbulent (K - ), with the empirical constants being functions of the Reynolds nunther of turbulence. A cathode sheath with nonequilibrium conditions was used to obtain accurate cathode boundary conditions. Experiments and modeling hart shown the benefits of using conical injectors which constrict drasfically the plasma_ flow and enhance the gas velocity and the current density, thus increasing the heat flux to the anode. With the cylindrical injector, recirculations close to the cathode lip modify deeply its heating and reduce the plasma jet constriction: velocities and temperatures are lower when the recirculation velocity is higher. This results in lower heat fluxes to the anode compared to the conical injector.     

Electrokinetic transport of red blood cells in microcapillaries

Electrokinetic flow of a suspension of erythrocytes (red blood cells, RBCs) in 20 num cylindrical fused-silica capillaries is examined in the present work. Flow direction anomalies are observed experimentally and tentatively explained by the development of a pH gradient between the cathode well and the anode well due to electrolysis reactions at the electrodes. This pH gradient alters the local zeta potentials of both the capillary and the RBC and thus the local electroendosmotic liquid flow (EOF) velocities and RBC electrophoretic (EP) velocities. The two velocities are opposite in direction but with EOF dominating such that the RBC moves toward the cathode, opposite to the anode migration observed in bulk conditions. The opposing zeta potentials also lead to RBC aggregation at the anode end for low fields less than 25 V/cm. As the electroendosmotic velocity decreases at the anode end due to decreasing pH, pressure-driven back flow develops to oppose the original EOF at the remaining portions of the capillary ensuring constant fluid flux. When the anode EOF velocity is smaller in magnitude than the EP velocity, reversal of blood cell transport is observed after a short transient time in which a pH gradient forms. RBC velocities and pH dependencies on electric field and MgCl(2) concentration are presented along with data showing the accumulation of charge separation across the capillary. Also, a short-term solution to the pH gradient formation is presented that could help thwart development of pH gradients in micro-devices at lower voltages.     

Theoretical considerations on fuel cell electrodes design for in operando transmission X-ray absorption spectroscopy of the cell cathode

Conventional design of fuel cell electrodes for transmission X-ray absorption spectroscopy of the cell cathode includes Pt removal from a small anode spot. This spot serves as a transparent window for an X-ray beam probing the state of the cathode Pt atoms. A model shows that the current distribution over the surface of the cathode sample in front of the spot is strongly nonuniform, and hence, the sample does not necessarily represent the state of Pt atoms in a working fuel cell. The model suggests making the cathode sample in the form of a narrow ring, with Pt atoms being removed from the internal disk. Current density distribution over the ring surface is nearly homogeneous and close to the mean cell current density. The width of the ring should be in the order of the thickness of the membrane separating the anode and cathode.     

YSZ传导膜H_2S固体氧化物燃料电池

研究了Y2O3稳定的ZrO2(YSZ)氧离子传导膜H2S固体氧化物燃料电池性能。掺杂NiS、电解质、Ag粉和淀粉制备了双金属复合MoS2阳极催化剂,掺杂电解质、Ag粉和淀粉制备了复合NiO阴极催化剂,用扫描电镜对YSZ和膜电极组装(MEA)进行了表征,比较了不同电极催化剂的性能和极化过程,考察了不同温度对电池性能的影响。结果表明,双金属复合MoS2/NiS阳极催化剂在H2S环境下比Pt和单金属MoS2催化剂稳定,复合NiO阴极催化剂比Pt性能好,在电极催化剂中加入Ag可显著提高电极的导电性;与Pt电极相比,复合MoS2阳极和复合NiO阴极催化剂的过电位较小,阳极的极化比阴极侧小;温度升高,电池的电流密度与功率密度增加,电化学性能变好。在750℃、800℃、850℃和900℃及101.13 kPa时,结构为H2S、(复合MoS2阳极催化剂)/YSZ氧离子传导膜/(复合NiO阴极催化剂)、空气的燃料电池最大功率密度分别为30 mW/cm2、70 mW/cm2、155 mW/cm2及295 mW/cm2、最大电流密度分别为120 mA/cm2、240 mA/cm2、560 mA/cm2和890 mA/cm2。     

Estimating the temperature dependence of peptide folding entropies and free enthalpies from total energies in molecular dynamics simulations

The temperature dependence of thermodynamic quantities, such as heat capacity, entropy and free enthalpy, may be obtained by using well-known equations that relate these quantities to the enthalpy of the molecular system of interest at a range of temperatures. In turn, the enthalpy of a molecular system can be estimated from molecular dynamics simulations of an appropriate model. To demonstrate this, we have investigated the temperature dependence of the enthalpy, heat capacity, entropy and free enthalpy of a system that consists of a beta-heptapeptide in methanol and have used the statistical mechanics relationships to describe the thermodynamics of the folding/unfolding equilibrium of the peptide. The results illustrate the power of current molecular simulation force fields and techniques in establishing the link between thermodynamic quantities and conformational distributions.     

Single solid-oxide fuel cells with supporting ni-cermet anode

Single solid-oxide fuel cells (SOFCs) with a porous (36-41%) supporting Ni-cermet anode are manufactured and tested. The effect of the thickness of the supporting Ni-cermet anode on the electrochemical characteristics of single SOFCs is studied. It is shown that polarization losses on electrodes at the current density of 1.2 A/cm² increase by about 2 times from 0.13 to 0.25 V at an increase in the thickness of the supporting Ni-cermet anode from 0.40 to 1.27 mm. The impedance spectroscopy method is used to identify relaxation processes responsible for the behavior of the fuel cell anode and cathode. It is found that a significant percentage of polarization losses on the anode is due to transport limitations in fuel supply to the three-phase nickel/electrolyte/gas phase interface and removal of the reaction products away from it.     

Oxygen reduction kinetics on graphite cathodes in sediment microbial fuel cells

Sediment microbial fuel cells (SMFCs) have been used as renewable power sources for sensors in fresh and ocean waters. Organic compounds at the anode drive anodic reactions, while oxygen drives cathodic reactions. An understanding of oxygen reduction kinetics and the factors that determine graphite cathode performance is needed to predict cathodic current and potential losses, and eventually to estimate the power production of SMFCs. Our goals were to (1) experimentally quantify the dependence of oxygen reduction kinetics on temperature, electrode potential, and dissolved oxygen concentration for the graphite cathodes of SMFCs and (2) develop a mechanistic model. To accomplish this, we monitored current on polarized cathodes in river and ocean SMFCs. We found that (1) after oxygen reduction is initiated, the current density is linearly dependent on polarization potential for both SMFC types; (2) current density magnitude increases linearly with temperature in river SMFCs but remains constant with temperature in ocean SMFCs; (3) the standard heterogeneous rate constant controls the current density temperature dependence; (4) river and ocean SMFC graphite cathodes have large potential losses, estimated by the model to be 470 mV and 614 mV, respectively; and (5) the electrochemical potential available at the cathode is the primary factor controlling reduction kinetic rates. The mechanistic model based on thermodynamic and electrochemical principles successfully fit and predicted the data. The data, experimental system, and model can be used in future studies to guide SMFC design and deployment, assess SMFC current production, test cathode material performance, and predict cathode contamination.     

A Membrane‐Free Neutral pH Formate Fuel Cell Enabled by a Selective Nickel Sulfide Oxygen Reduction Catalyst

Polymer electrolyte membranes employed in contemporary fuel cells severely limit device design and restrict catalyst choice, but are essential for preventing short‐circuiting reactions at unselective anode and cathode catalysts. Herein, we report that nickel sulfide Ni₃S₂ is a highly selective catalyst for the oxygen reduction reaction in the presence of 1.0 m formate. We combine this selective cathode with a carbon‐supported palladium (Pd/C) anode to establish a membrane‐free, room‐temperature formate fuel cell that operates under benign neutral pH conditions. Proof‐of‐concept cells display open circuit voltages of approximately 0.7 V and peak power values greater than 1 mW cm⁻², significantly outperforming the identical device employing an unselective platinum (Pt) cathode. The work establishes the power of selective catalysis to enable versatile membrane‐free fuel cells.     

A non-equilibrium thermodynamics approach to model mass and heat transport for water pervaporation through a zeolite membrane

Pervaporation through zeolite membranes involves local heat effects and combined heat and mass transport. The current state-of-the-art Maxwell–Stefan (M–S) models do not take these effects into account. In this study, transport equations for the coupled heat and mass transport through a zeolite membrane are derived from the framework of non-equilibrium thermodynamics (NET). Moreover, the assumption of equilibrium between the adjacent bulk phases at the feed and permeate sides of the zeolite layer is abandoned in favor of local equilibrium. The equations have been used to model pervaporation of water through a 2 m thick NaA type zeolite membrane, deposited on an asymmetric -alumina support, at a feed temperature of 348 K. Assuming a flux of 10 kg m⁻² h⁻¹(0.15 mol m⁻² s⁻¹), the transport through the zeolite layer, as well as the liquid feed side boundary layer and the support layers is modeled. The activity, fugacity, and temperature profiles are calculated with and without taking coupling effects and surfaces into account. The profiles show distinct differences between the two cases. Including the surface effects leads to discontinuities in the activity and temperature at the membrane interfaces. A significantly higher temperature drop of 1.3 K is calculated across the zeolite, compared to 0.4 K when surface and coupling effects are not accounted for. The calculated decrease in temperature over the zeolite layer is dominated by the surfaces. This could indicate that temperature polarization is, to a large extent, a surface effect. The heat flux induces an extra driving force for mass transport, reducing the activity difference over the membrane. A positive jump in activity is observed at the interfaces, revealing the mass transport across the interfaces is governed by the coupling with the heat flux. The support layers contribute significantly to the total mass transport resistance.     

Fuel cell oxygen cathode with Nafion and platinum: the effect of active layer heating on overall cathode characteristics

A fuel cell with Nafion and platinum is considered. The effect of heating of the oxygen cathode active layer on the cathode overall characteristics (current and power density) is taken into account for the first time. Attention is focused on calculations of Tafel plots of oxygen cathodes and also on how the active layer temperature changes with the potential. Calculation parameters are as follows: fuel cell initial temperature, cathode active layer thickness, gas-diffusion layer effective heat conductivity and thickness. The following conditions of cathode operation are studied: (1) heat formed in the cathode active layer is almost completely removed, no active layer heating is observed, the active-layer temperature remains equal to that of fuel cell operation; (2) heat removal is impeded, the heat conductivity of the gas-diffusion layer is insufficiently high to remove heat. In the latter case, the active layer temperature may increase by several tens of degrees. A fundamental difference of Tafel plots for the catalytic layers studied in model experiments and the cathodic active layers is demonstrated. In the latter case, the first Tafel plot segment may extend further up to potentials of ∼0.6 V.     

Potential and flux decomposition for dynamical systems and non-equilibrium thermodynamics: curvature, gauge field, and generalized fluctuation-dissipation theorem

The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance. The response due to a small perturbation can be expressed by a spontaneous fluctuation. For non-equilibrium systems, we derived a generalized FDT that the response function is composed of two parts: (1) a spontaneous correlation representing the relaxation which is present in the near equilibrium systems with detailed balance and (2) a correlation related to the persistence of the curl flux in steady state, which is also in part linked to a internal curvature of a gauge field. The generalized FDT is also related to the fluctuation theorem. In the equal time limit, the generalized FDT naturally leads to non-equilibrium thermodynamics where the entropy production rate can be decomposed into spontaneous relaxation driven by gradient force and house keeping contribution driven by the non-zero flux that sustains the non-equilibrium environment and breaks the detailed balance. On any particular path, the medium heat dissipation due to the non-zero curl flux is analogous to the Wilson lines of an Abelian gauge theory.     

Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems

A common assumption in the glass science community is that the entropy of a glass can be calculated by integration of measured heat capacity curves through the glass transition. Such integration assumes that glass is an equilibrium material and that the glass transition is a reversible process. However, as a nonequilibrium and nonergodic material, the equations from equilibrium thermodynamics are not directly applicable to the glassy state. Here we investigate the connection between heat capacity and configurational entropy in broken ergodic systems such as glass. We show that it is not possible, in general, to calculate the entropy of a glass from heat capacity curves alone, since additional information must be known related to the details of microscopic fluctuations. Our analysis demonstrates that a time-average formalism is essential to account correctly for the experimentally observed dependence of thermodynamic properties on observation time, e.g., in specific heat spectroscopy. This result serves as experimental and theoretical proof for the nonexistence of residual glass entropy at absolute zero temperature. Example measurements are shown for Corning code 7059 glass.