International Workshop on

“Non-Equilibrium Thermodynamics”

on the occasion of

Prof. Signe Kjelstrup’s 60th Birthday

September 3-4, 2009 NTNU, Trondheim, Norway

Onsager room, D3-114

Program

Abstracts

Lists of Signe Kjelstrup’s PhD students, master students and visiting postdoc’s

Participants

Sponsers

Organization committee:

Dick Bedeaux (NTNU, NO) Terje Bruvoll (NTNU, NO) Torleif Holt (SINTEF, NO)

Steffen Møller-Holst (SINTEF, NO) Preben Vie (IFE, NO)

Program

Thursday, September 3, 2009, morning session

Discussion leader: Dick Bedeaux

9:00 Registration/Coffee 10:00 Opening by Bjørn Hafskjold 10:20 Yasuhiko Ito, Doshisha University, Japan,

The Application of Non-Equilibrium Thermodynamics to the Energy Analysis of Some Electrochemical Reactors

11:00 Discussion 11:30 Group picture 12.00 Lunch

afternoon session

Discussion leader: Fernando Bresme

13:00 Isabella Inzoli, Saudi Arabia,

Diffusion of butane, heat conduction, thermal diffusion for zeolite membranes; a study using non-equilibrium molecular dynamics

13:40 Discussion 13:50 Jon Pharoah, Queens Univ., Kingston, Canada.

Modelling heat and water transport in a reindeer nose 14:30 Discussion 14:40 Tea 15:00 Eivind Johannessen, StatoilHydro, Trondheim, Norway

The state of minimum entropy production in optimally controlled systems 15:40 Discussion 15:50 Tatsuhiro Okada, Nat. Inst. of Materials and Chem. Research, Tsukuba, Japan.

Ion and water characteristics of Nafion membranes 16:30 Discussion 17:00 Reception

Friday, September 4, 2009, morning session

Discussion leader: Miguel Rubi

8:30 Fernando Bresme, Imperial College, London, UK Water polarization under thermal gradients

9:10 Discussion 9:20 Jose Ortiz de Zarate, Universidad Complutense, Madrid, Spain.

Concentration fluctuations in non-isothermal reaction-diffusion systems 10:00 Discussion 10:10 Coffee 10:30 Joachim Gross, Technical Univ. Delft, Netherlands

Non-equilibrium thermodynamics of interfaces using classical density functional theory

11:10 Discussion 12:00

Lunch

afternoon session

Discussion leader: Dick Bedeaux

13.00 Miguel Rubi, University of Barcelona, Spain. Mesoscopic non-equilibrium thermodynamics

13:40 Discussion 13:50 Audun Røsjorde, StatoilHydro, Oslo, Norway.

Verification of Onsager’s reciprocal relations for evaporation/condensation using molecular dynamics

14:30 Discussion 14:40 Tea 15:00 Marc-Olivier Coppens, Rensselaer Polytechn Inst, USA

Nature Inspired Engineering of Fuel Cells 15:40

Discussion 15:50

End

.

Abstracts

The Application of Non-equilibrium Thermodynamics to the Energy Analysis of Some Electrochemical Reactors

Yasuhiko Ito

Department of Environmental Systems Science, Faculty of Science and Engineering,

Doshisha University, Kyotanabe, Kyoto 610-0321, Japan E-mail:yasito@mail.doshisha.ac.jp

When it is desired to improve the energy conversion efficiency or the temperature control of an electrochemical reactor, it is important to consider the overall energy balance in the reactor. For example, if heat is not supplied to electrodes where an endothermic process takes place, a drop in temperature may result, which may lead to an increase in cell voltage, or, in molten salt electrochemical reactors, even freezing of the electrolyte. Conversely, if heat is not properly removed from electrode where exothermic process takes place, a rise in temperature may result. This may lead to a breakdown of the cell material or electrolyte vaporization. In order to maintain optimum temperature at the electrodes, it is helpful to know the magnitude of the reversible heat changes during the operations of the electrochemical reactors. This includes the Peltier heat for each electrode. This presentation describes some experimental case studies conducted by the author and his collaborators from the above-mentioned aspects. In contrast to other work in this field, we deal with the applications of a theory of non-equilibrium thermodynamics developed by the group in which Prof.Signe Kjelstrup has played the most important role. Examples selected in the presentation include the energy analyses of electrochemical reactors for high temperature water electrolysis, molten salt electrolytic processes, thermally regenerative fuel cells, and others. References (1) “Non-Equilibrium Thermodynamics of Heterogeneous Systems”, Signe Kjelstrup and Dick Bedeaux, World Scientific (2008) (2) “Irreversible Thermodynamics: Theory and Applications”, K.S,Fφrland, T. Fφrland and S.K.Ratkje, John Wiley & Sons (1988) (3) “Energy Analysis of a Steady-State Electrochemical Reactor”, Y.Ito, F.R.Foulkes and S.Yoshizawa, J.Electrochem.Soc., 129(9), pp.1936-1943 (1982)

(4) “Electrode Heat Balance of Electrochemical Cells: Application to Water Electrolysis”, Y.Ito, H.Kaiya, S.Yoshizawa, S.K.Ratkje and T. Fφrland, J.Electrochem.Soc., 131 (11), pp.2504-2509 (1984) (5) “The single electrode Peltier heats of Li+/Li, H2/H- and Li+/Pd-Li couples in molten LiCl-KCl systems”, H.Nakajima, T.Nohira and Y.Ito, Electrochim.Acta, Vol.49, pp.4987-4991 (2004)

Diffusion of butane, heat conduction and thermal diffusion into and through a zeolite membrane; a study using non-equilibrium

molecular dynamics

Isabella Inzoli1, Signe Kjelstrup1, Dick Bedeaux1, Jean-Marc Simon2

1 Department of Chemistry, Norwegian University of Science and Technology, Trondheim 7491-Norway

2 Institut Carnot de Bourgogne, UMR- 5209 CNRS- Université de Bourgogne, 9, Av. Savary, 21000 Dijon, France, jmsimon@u-bourgogne.fr

1. Introduction Understanding the adsorption and the diffusion of molecules through a porous material is of crucial importance in catalytic and separation processes. Experimental investigations of such transports are very difficult, because of the small surface thickness, typically a few nanometers. In this work non-equilibrium molecular dynamics simulations have been used to study the simultaneous transport of gas and heat into a silicalite membrane. Both transport through the silicalite pores and across the external surface are investigated. These transport processes are described by non-equilibrium thermodynamics (NET) [1]. NET is a new theory in the context of zeolite transport and a purpose of this work has therefore also been to test the usefulness and viability of this theory.

2. Model and simulation details As a model system, we have taken a silicalite-1 crystal, with n-butane as representative of an organic molecule to be transported. The silicalite was composed of 36 unit cells ([2 6 3]) and was modelled with a flexible atomic model, allowing for stretching and bending of bonds. Butane was described using the united atom model. Both crystal and the gas molecules interacted with a truncated and shifted Lennard-Jones potential. In order to obtain the transport properties in the crystal, i.e. the inter-diffusion coefficient, the thermal conductivity and the heat of transfer, constant temperature gradients and mass fluxes were created in the zeolite pores. Specific non-equilibrium molecular dynamics algorithms were developed for the purpose [2]. The different surface resistivities, i.e. the resistance to heat transfer, the coupling coefficient and the resistance to mass transfer, were instead obtained applying stationary mass and heat fluxes across the external surface of the membrane. Details about the simulations can be found elsewhere [3].

3. Results and discussion Transport properties in the zeolite pores The inter-diffusion coefficient, the thermal conductivity and the Soret effect, representing mass transfer induced by thermal forces, were obtained at different butane concentrations and temperature gradients. The coefficients did not depend on the driving forces, demonstrating that the description in terms of non-equilibrium thermodynamics was sound. The inter-diffusion coefficient (D) increased with the butane concentration, see Fig. 1. We found, for 360K and for an average concentration of 4 molecules per unit cell, a value of D = 7±1 x 10−8 m2/s, which is well within the range of earlier observations of butane in zeolite. The thermal conductivity was found to be nearly independent of the amount of adsorbed butane, equal to 1.46 ± 0.07 W/m K, meaning that heat is conducted almost solely through the crystal lattice in the system. The measurable heat of transfer, which gives the impact on the heat flux by the mass flux, was around 10 kJ/mol. This value is larger than that of the partial molar enthalpy of the adsorbed butane and, for a typical butane flux of some mol/m2s, can lead to sizable heat effects. Moreover, with different set of simulations we gave numerical evidence that the total heat of transfer, given by the sum of the measurable heat of transfer and the partial molar enthalpy of the adsorbed molecules, is independent of the butane concentration but depends on the temperature only, see Fig. 2. This adds a new rout for the estimation of the heats of transfer: a variation between the heats of transfer between two concentrations is equal to minus the variation of the partial molar enthalpy of the component between the same concentrations. Transport resistivities of the external surface Three independent coefficients were derived for the whole surface for the first time, namely the resistance to heat transfer, the resistance to mass transfer and the coupling coefficient.

Fig 2 Heat of transfer q* (triangles) and total heat of transfer Q* (circles) as a function of the average concentration for two sets of simulations at different average temperatures.

Fig. 1 Inter-diffusion coefficient D as a function of the butane concentration at constant temperature (T=360K).

Fig 3 Surface resistivity to heat transfer as a function

of the gas pressure at constant surface temperature. Fig 4 Coupling resistivity of the surface as a function of the gas pressure at constant surface temperature.

The surface resistivity to heat transfer decreased as the gas pressure or the temperature increased (see Fig. 3), while the surface resistivity to mass transfer was rather independent of the temperature and the gas pressure. We found a negative coupling resistivity which increased in absolute value with a decrease in the gas pressure, see Fig. 4. This coefficient gives the effect of a thermal driving force on the mass flux. The negative value means that a positive thermal force hampers a mass flux. In this sense, the coupling coefficient adds to the thermal resistance to mass flow. The resistivity to heat transfer as well as the coupling coefficient for the surface ware found to be three orders of magnitude higher than those obtained for the silicalite pores. The surface was further decomposed into a zeolite side and a gas side; the influence of the two sides on the determination of the overall surface properties was analyzed. The resistivity to heat transfer was mostly determined by the gas side of the surface while the resistivity to mass transfer as well as the value of the coupling coefficient was dominated by the zeolite side. 4. Conclusion We used molecular dynamics simulation to obtain the transport properties of butane through the pores of a silicalite membrane and to get access, for the first time, to the resistivities of heat and mass transport of the external surface. We showed that the external surface, even on small scales like here, can be regarded as a separate thermodynamic system with properties independent of those of the adjacent phases. We pointed out the role of the coupling phenomena between heat and mass transport, and the fact that they cannot be neglected in the description of adsorption kinetics. References [1] S. Kjelstrup, D. Bedeaux, Non-Equilibrium Thermodynamics of Heterogeneous Systems, World Scientific, London, 2007. [2] I. Inzoli, J. M. Simon, S. Kjelstrup and D. Bedeaux, Thermal diffusion and partial molar enthalpy variations of n-butane in silicalite-1, Journal of Physical Chemistry B, 112 (2008), pp 14937-14951. [3] I. Inzoli, S. Kjelstrup, D. Bedeaux and J. M. Simon, Transport coefficients of n-butane into and through the surface of a silicalite-1 from non-equilibrium molecular dynamics study, Microporous and Mesoporous materials, 125 (2009) 112-125.

Reindeer Noses, Fluid Mechanics and Non-Equilibrium Thermodynamics

J.G. Pharoah

Queen’s-RMC Fuel Cell Research Centre

Queen’s University Kingston, ON, K7L 3N6, CANADA

The reindeer nose is a fascinating system which is critical for the survival of the animal. As such, it is interesting to gain a detailed understanding of how this system provides an evolutionary advantage to the reindeer as well as how inspiration can be drawn in order to guide the design and operation of engineered systems. The nose represents an integrated heat and moisture exchanger, permitting the animal retain metabolic heat and to prevent undue expenditures of energy in rehydrating with snow or ice. Further, as arterial blood flows heat the incoming air and get cooled, the animal has the capacity to redirect the locally cooled blood directly to the brain when needed. In this talk, a simplified engineering model will be presented and analyzed for the heat exchange rates as a function of respiration rates. The operation of this model will be discussed in the context of equi-partition of entropy. Finally, the differences between the simplified model and real system will be critically discussed with a particular emphasis on how the geometry of the airflow passages can contribute to maximizing transport while minimizing losses. The state of minimum entropy production in optimally controlled

systems

Eivind Johannessen

StatoilHydro, Trondheim, Norway Minimization of the entropy production of a process gives valuable insight about the nature of energy efficient design and operation. Properties of the state of minimum entropy production are discussed1. It is shown when equipartition theorems; equipartition of entropy production (EoEP) and equipartition of forces (EoF), are valid. One important assumption is that all driving forces in the system can be controlled independently. This is seldom possible in reality, but numerical solutions of entropy production minimization problems for industrial applications show that EoEP and EoF are good approximations of the minimum, at least for some parts of the process. These numerical findings are summarized as a hypothesis. Related to this is the “highway in state space”. The highway represents the most energy efficient way to travel a long distance in state space. Remarkably, the local entropy production and the driving forces are often almost constant along the highway. Chemical reactors, distillation columns, heat exchangers and LNG production are used as examples. Reference: Johannessen, E., The state of minimum entropy production in an optimally controlled system, Dr. Ing. Thesis, NTNU, Trondheim, Norway, 2004.

ION AND WATER TRANSPORT IN NAFION MEMBRANES

Tatsuhiro Okada

Tsukuba Fuel Cell Laboratory, Inc., National Institute of Advanced Industrial Science and Technology, Higashi 1-1-1, Central 5-2, Tsukuba, Ibaraki 305-8565, Japan

BACKGROUND

Over the years the ion conducting polymer electrolytes are becoming of central issue in the application of energy and environment fields. Especially in fuel cell applications, the ion conductivity and water sorption behaviors in the membranes are important topics that are directly related to the high power density of fuel cells.

Design of new conceptual polymer electrolytes depends on the knowledge of mechanisms of equilibrium and transport behaviors of ions and water in the membrane. This paper gives such methodology dealing multi-component membrane systems that applies also for a solution of various problems, e.g. water management in fuel cell technology. MULTI-COMPONENT SYSTEMS

Although H+ is the only transporting ion in fuel cell membranes, researches on mixed cation systems offer much more information on molecular interactions in the polymer. This is done by electrochemical methods based on irreversible thermodynamic equations. These include: streaming potential, ionic transference numbers, impedance measurements, pulsed-field-gradient spin-echo NMR, ionic mobility in mixed cation systems, etc. Several types of cations, alkali and alkaline earth cations, transition metal cations and alkyl ammonium ions in Nafion and related membranes are discussed. GENERAL LAW OF ION AND WATER TRANSPORT

Ionic size, hydration degree, affinity to sulfonic acid groups are major factors determining the mobility of cations in the membrane. Relative size of ions with hydration shell against the size of ionic channels should be a model to discuss the ion mobility and polymer structure. DESIGN OF NEW MEMBRANES

A strategy of designing low cost membranes as the alternative to the present perfluorinated ionomer membranes is presented based on the above results: high ionic site density, high water content and modification of channel structures of ion conducting paths. These factors contradict each other, and a partially cross-linked polymer chain with hydrophilic ion transport paths in phase-separated structures is recommended. References 1. K.-D. Kreuer, S. J. Paddison, E. Spohr, M. Schuster, Chem. Rev. 104, 4637 (2004). 2. K. S. Førland, T. Førland, S. Kjelstrup-Ratkje, Irreversible Thermodynamics: Theory and

Applications, John Wiley and Sons, New York (1988). 3. T. Okada, M. Saito, and K. Hayamizu, in P. N. Jiang ed., Electroanalytical Chemistry

Research Developments, Nova Science Pub. Inc., New York (2007).

Non-equilibrium studies of “hot” water: from bulk to interfaces

Fernando Bresme

Department of Chemistry, Imperial College, SW7 2AZ, London, United Kingdom Water plays an essential role as solvent where many chemical and biochemical reactions take place. The equilibrium behaviour of water and water solutions is well understood from a microscopic basis. In comparison there have been few studies dealing with the non-equilibrium behaviour of water in bulk and at interfaces. The investigation of the water response to external fields, particularly thermal gradients, is important to understand processes of relevance in chemistry, physics and biology: chemical reactions at surfaces, condensation and evaporation in the atmosphere, heating of nanomaterials by external fields, energy transfer in biomolecules, … In this talk I will discuss our recent efforts to understand the microscopic behaviour of bulk and interfacial water under thermal gradients. Non-equilibrium molecular dynamics computer simulations provide a powerful approach to investigate water under non-equilibrium conditions. Using this technique we have recently discovered that bulk water polarizes under temperature gradients, generating strong electrostatic fields. This behaviour might be relevant to design nanomaterials and to understand biological processes. Moreover, I will discuss thermal transport across nanoparticle and bio-nanoparticle (protein) water interfaces, as well as its relevance in nanofluids and molecular motors. F. Bresme, A. Lervik, D. Bedeaux and S. Kjelstrup, Water polarization under thermal gradients, Phys. Rev. Lett. 101 (2008) 020602-4.

Thermal fluctuations in Nonequilibrium Thermodynamics

Jose M. Ortiz de Zarate

Complutense University. Madrid, Spain. In this presentation I show how Nonequilibrium Thermodynamics is not only a theory of fluxes, but that it also yields a theory of fluctuations. The fluctuations theory is obtained by supplementing the dissipative fluxes with a random thermal noise component and by adopting a simple hypothesis for the thermal-noise correlations (fluctuation dissipation theorem). Using an incompressible fluid subjected to a temperature gradient as an example, one can show how fluctuating hydrodynamics can be used to calculate the fluctuations of macroscopically relevant quantities: temperature, pressure, etc. This method has the advantage of being readily extrapolable to study fluctuations around nonequilibrium steady states, leading to predictions that have been verified experimentally. J.M. Ortiz de Zarate and J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid mixtures, Elsevier, Amsterdam, 2006.

Non-equilibrium Thermodynamics of Interfaces with the Classical Density Functional Theory

Joachim Gross, Eivind Johannessen, Dick Bedeaux

Delft University of Technology, Engineering Thermodynamics, The Netherlands & Norwegian University of Science and Technology, Dept. of Chemistry, Norway

An interface between a vapor and a liquid phase constitutes a resistance to heat and mass transport. The coupled transport resistances can be measured [1], they can be determined from molecular simulations [2], or they can be calculated from the van der Waals square gradient model [3]. We here express transport resistances of the interface with integral relations [4,5] and evaluate these relations with the classical density functional theory (DFT). The DFT formalism allows for a description of thermodynamic properties across an interface with good quantitative agreement to molecular simulations; and for appropriate expressions of the Helmholtz energy also with good agreement to experimental data. For pure compounds, the integral relations express the interfacial resistances to heat transport, to mass transport and the coupling coefficients of heat and mass transport. Required is thereby only the local heat transport resistance rqq(z) and the local enthalpy (of an equilibrium interface). The integral relations are derived assuming the local validity of the Gibbs-Helmholtz relation across the interface. The validity of the integral relations has been verified from molecular simulation results [6]. The enthalpy is in our approach taken from a DFT formalism. The local heat transport resistance rqq(z) is correlated with two parameters. These two parameters turn out to be temperature-independent and all interfacial resistivities can be consistently described with good accuracy. [1] V. K. Badam, V. Kumar, F. Durst, and K. Kumar, Exp. Therm. Fluid Sci. 32, 249, 2007.

G. Fang and C. A. Ward, Phys. Rev. E 59, 417 1999; D. Bedeaux and S. Kjelstrup, Physica A 270, 413 1999.

[2] J. Ge, S. Kjelstrup, D. Bedeaux, J. M. Simon, and B. Rousseau, Phys. Rev. E 75, 061604 2007 (and references therein)

[3] E. Johannessen and D. Bedeaux, Physica A 330, 354, 2003; D. Bedeaux, E. Johannessen, and A. Røsjorde, Physica A 330, 329, 2003; E. Johannessen and D. Bedeaux, Physica A 330, 354, 2003; E. Johannessen and D. Bedeaux, Physica A 336, 252, 2004

[4] E. Johannessen and D. Bedeaux, Physica A 370, 258, 2006 [5] K.S. Glavatskiy and D. Bedeaux, Phys. Rev. E 77, 061101, 2008 [6] J. M. Simon, D. Bedeaux, S. Kjelstrup, J. Xu, and E. Johannessen, J. Phys. Chem. B 110,

18528, 2006; J. Ge, D. Bedeaux, J. M. Simon, and S. Kjelstrup, Physica A 385, 421,2007_.

Heat exchange at the nanoscale: non-equilibrium Stefan-Boltzmann law and non-monotonous conductance

J.M. Rubi

Departament de Fisica Fonamental, Facultat de Física, Universitat de Barcelona,

Av. Diagonal 647, 08028 Barcelona, Spain.

The study of energy transfer mechanisms at the nanoscale has aroused increasing interest due to the emergence of the interdisciplinary field of nanoscience where such wide-ranging fields as for example solid state physics, nanothermodynamics or electrical engineering coexist. One of the basic problems in this field is to determine the energy exchange between two nanoparticles at different temperatures. The way in which this energy is transfered depends crucially on the distance between the particles. For sufficiently large distances, heat exchange proceeds via thermal radiation, through emission or absorption of photons whereas at smaller distances Coulomb interaction (near-field radiation) is the dominant mechanism. We present a theory, which uses mesoscopic non-equilibrium thermodynamics [1] and the multipolar expansion of the electrostatic field, to derive a non-equilibrium Stefan-Boltzmann law and to describe the exchange of energy between two nanoparticles at different temperature for arbitrary small distances. Our analysis performed when the two nanoparticles are separated by a few submicrons explains the rapid growth of the conductance observed in the simulation. We show that the non-monotonic behavior of the thermal conductance between two nanoparticles when they are brought into contact is originated by an intricate phase space dynamics resulting from the thermally activated jumping through a rough energy landscape. A hierarchy of relaxation times plays the key role in the description of this complex phase space behaviour. Our theory enables us to analyze the heat transfer just before and at the moment of contact and to explain why heat transport when the particles are dispersed may be more efficient than in the case in which the particles are in contact. [1]. D. Reguera, J. M. Rubi and J. M. G. Vilar, J. Phys. Chem. B 109, 21502 (2005). [2]. A. Perez-Madrid, J.M. Rubi and L.C. Lapas, Phys. Rev. B 77, 155417 (2008). [3]. A. Perez-Madrid, J.M. Rubi and L.C. Lapas, Phys. Rev. Lett., 103, 048301 (2009)

Verification of Onsager’s reciprocal relations for evaporation and condensation using non-equilibrium molecular dynamics

Audun Røsjorde

StatoilHydro, Oslo, Norway

Non-equilibrium molecular dynamics (NEMD) simulations are used to study heat and mass transfer across a vapour-liquid interface for a one-component system using a Lennard-Jones spline potential. Based on the expression for the entropy production of the system, a set of suitable conjugated fluxes and forces is derived for the vapour-liquid interface. These equations contain four phenomenological coefficients, so-called Onsager coefficients, which are unknown. A widely accepted assumption is the matrix containing the coefficients is symmetrical. By carrying out approximately 50 NEMD simulations, this symmetry is verified within the accuracy of the calculations. This is the first verification of the Onsager relations for transport through a surface using molecular dynamics. The interfacial film transfer coefficients are found to be functions of the surface temperature alone. New expressions are given for the kinetic theory values of these coefficients which only depend on the surface temperature. J. Xu, S. Kjelstrup, D. Bedeaux, A. Røsjorde and L. Rekvig, Verification of Onsager’s Reciprocal Relations for Evaporation and Condensation using Non-equilibrium Molecular Dynamics. J. Colloid and Interface Sc. 299 (2006) 452-463

Nature-Inspired Engineering of a Polymer Electrolyte Membrane Fuel Cell

Marc-Olivier Coppens1, Jon Pharoah2, Peter Pfeifer3 and Signe Kjelstrup4

Center for Advanced Study, The Norwegian Academy of Science and Letters

Drammensveien 78, Oslo, Norway

1 Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA, E-mail: coppens@rpi.edu, Tel +1-518-276-2671 2 Fuel Cell Research Center, Kingston, Ontario, Canada K7L5L9 3 Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA. 4 Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway Polymer electrolyte membrane (PEM) fuel cells generate electricity from the electrochemical oxidation of hydrogen gas to protons on the anode, and reduction of oxygen gas by protons to water on the cathode, with protons moving from anode to cathode through the wetted polymer electrolyte (nafion) membrane separating the two. Two major limitations to the widespread use of PEM fuel cells are catalyst cost (Pt) and thermodynamic efficiency. We present a new fuel cell design that considerably reduces the necessary amount of catalyst and increases energy efficiency. We focus especially on the cathode, where reactions are diffusion limited at high current densities, and a significant overpotential limits efficiency. The proposed innovative design draws its inspiration from the self-similar structure of the lung: (1) a fractal, branching gas distributor uniformly spreads oxygen to the cathode catalyst, conveniently and efficiently bridging a wide range of scales; (2) the catalyst is given a hierarchical porous structure, with a uniform distribution of large (micron-sized) pore channels to facilitate gas access to and from the nanoporous Pt/C/nafion composite, where the reactions occur. This nature-inspired design guarantees an as uniform as possible operation of the fuel cell, hereby maximizing energetic and catalytic efficiency per unit volume. We demonstrate this analytically on the basis of the second law of thermodynamics and constrained optimization of the catalytic yield per unit volume, for a desired power output. Considerable impact on cell performance is demonstrated by means of a practical example.

Dr. Ing. /PhD / Dr.techn. Students supervised by Signe Kjelstrup 1. Torleif Holt, Transport and equilibrium properties of a cation exchange membrane (1983) 2. Einar Eng Johnsen, On liquid junction potentials and a solid state pH electrode (1989) 3. Andreas Grimstvedt, Thermocell studies of sulphate mixture and melts relevant for aluminium

electrolysis (1992) 4. Kristin Syverud, Ion and water transfer in a potassium selective PVC membrane, (1992) 5. Steffen Møller-Holst, Electrode and membrane performance studies, (1996) 6. Magnar Ottøy, Mass and heat transfer in ion-exchange membranes (1996) 7. Belinda Flem, Peltier heats in cryolite melts with alumina (1996) 8. Ellen Marie Hansen, Modelling of aluminium electrolysis cells using nonequilibrium

thermodynamics (1997); Leiden University, The Netherlands 9. Erik Sauar, Energy efficient process design by equipartition of forces (1998) 10. Lars Nummedal, Entropy production minimization of chemical reactors and heat exchangers

(2001) 11. Preben Vie, Characterisation and optimisation of the polymer electrolyte fuel cell (2002) 12. Gelein de Koeijer, Energy efficient operation of distillation columns and a reactor applying

irreversible thermodynamics (2002) 13. Audun Røsjorde, Minimization of entropy production in separate and connected processes (2004) 14. Eivind Johannessen, The state of minimum entropy production in an optimally controlled

system (2004) 15. Anita Zvolinschi, On exergy analysis and entropy production minimsation in industrial

ecology (2006) 16. Anne Kristine Meland, Impedance diagrams in the Polymer Electrolyte Membrane Fuel Cell

(2007) 17. Isabella Inzoli, Coupled transports of heat and mass at the surface of an inside silicalite (2008) 18. Ole-Erich Haas, Transport on a nanoscale; quasi-elastic neutron scattering and molecular

dynamic studies (2009) In progress: 19. Jing Xu Transport phenomena in a temperature gradient studied by NEMD. A chemical

reaction and a phase transition (2009) 20. Odne Burheim (2009) 21. Thor Anders Aarhaug (2010) 22. Leen van der Ham (2011) 23. Anders Lervik (2011) 24. Mari Voldsund (2012) 25. Sondre Schnell Kvalvaag (2013)

Master (M.Sc. /siv.ing.) students supervised by Signe Kjelstrup 1. Liv Taraldsen: Studie over membraners ionerefleksjonskoeffisienter, 1977 2. Unni Merete Steinsmo: En undersøkelse av likevektsfordelingen av alkali-og jordalkali klorider mellom en vannoppløsning og en kationselektiv ionebytter, 1978 3. Thorry Kiær: Temperatureffekt på beskyttelsespotensial for stål i sjøvann, 1980 4. Torgrim Låg: Ledningsevne av oljeførende bergarter, 1983 5. Martha Skjerven: Viskositet av emulsjoner, 1984 6. Anne Kristiansen: Vanntransport i betong, 1984 7. Kirsten Knudsen: Strømtetthet for katodisk beskyttelse, 1984 8. Inghild Helgesen: Diffusjon og ladningstransport av karbonat over rørledningsbelegg, 1984 9. Hilde Frigstad: Ionetransport i mitokondriemembran, 1984 10. Elling Stangeland: Effekt av temperaturgradienter på fordeling av organiske komponenter

i væskefase, 1984 11. Einar Eng Johnsen: Ionetransport i mitokondrier, 1985 12. Anne Hillestad: Vannpermeabilitet i ionebyttermembraner, 1985 13. Kari Stette: Volumendringer ved utfelling av kalsiumsulfat i saltoppløsninger, 1986 14. Hege Lunde: Volumendringer ved utfelling av bariumsulfat i saltoppløsninger, 1986 15. Kristin Syverud: Termoelektrisk potensial i galvanisk celle med KCl-elektrolytt, 1986 16. Trude Gullaksen: Termodynamikk for utbyttingslikevekter, 1986 17. Tone Aarrestad: Elektriske mobiliteter i saltblandinger, 1986 18. Pål Romundstad: Termodynamikk for brenselceller, 1988 19. Pål Falnes, Ion transport in mitochondria, 1989, Medical College of Ohio, USA 20. Magnar Ottøy: Transporttall for en ionebyttermembran, 1990 21. Belinda Flem: Aluminiumselektrolyse beskrevet med klassisk og irreversibel termodynamikk, H 1991 22. Rune Heggø: Varmetransport i Hall-Heroult cellen, H 1992 23. Kristin Eine: Dynamic response of ion-selective electrodes, V93,

hos: Prof. Klara Toth, Univ. of Budapest, Ungarn 24. Lennar Jerfald: Water transport in cation exchange membranes, V93,

hos: Dr. Okada, Tsukuba City, Japan 25. Kenneth Friestad: Ion transport in cation exchange membranes, V93,

hos: Dr. Okada, Tsukuba City, Japan 26. Rune Holmen, Vanntransporttall i ionebyttermembraner, H93 27. Thomas Løver: Quantitative Quadropole Mass Spectrocopy for the Measurement of Current Efficiency of the Hall-Heroult Aluminium Reduction Cells,

hos: prof. B. Welch, University of Auckland, V94 28. Erik Sauar: Process Design Based on Optimum Entropy Production, H94 29. Oddvar Gorseth: Water Transport in Membranes for Fuel Cells, V95

hos: Dr.Okada, Tsukuba Science City, Japan 30. Ellen Marie Kristiansen: Molten Salt Hydrates for Heat Storage Applications,

hos: prof. W. Voigt, Bergakademi Freiberg, V95 31. Rolf Jarle Aaberg: Bubblelayer Resistance in Cells with Horizontal Electrodes,

hos: Prof. B. Welch, University of Auckland, V95 32. Monica Strømgård: The Effect of Charge Carriers on the Analytically Important Parameters of Liquid Membrane Electrodes, hos: K. Toth, University of Budapest,

V95 33. Preben Vie: Transporttall for multikomponent system, V95 34. Vibeke Andersson: Wellbore stability in shales. Production of an artificial shale, H96,

hos: Shell Research Laboratories, Rijswiik, Nederland 35. Einar Gjelsvik, Freezing from cryolite melts. Theory and experiments.

hos: prof. B. Welch, University of Auckland, V94 36. Heidi Feldborg: Elektrodeoverflateeffekter i en faststoff oksid bresenlcelle, H96 37. Anne Kristine Meland: Termiske effekter i polymerbrenselceller, H96 38. Ingrid Tjerandsen: Katode for peroksid-produksjon, H95 39. Lars Nummedal, Thermal osmosis, H96, Leiden University, Nederland 40. Trond Vegard Island, Modeling chemical reactors using equipartition of forces, H97 41. Ivar Syversen, An environmental study of fuel cells in vehicles using LCA-methodology, | H97 42. Karl Isak Skau, Application of Irreversible Thermodynamics to Heterogeneous Catalysis,

Leiden University, hos: D. Bedeaux, Leiden University, H98 43. Thomas Lunde Jensen, Pressure reduction of hydrocarbon mixtures, H98 44. Trond Heldal, Vanntransport i polymermembran brenselceller, V99 45. Eivind Johannesen, Reaktoroptimalisering med irreversible termodynamikk:

Metanolreaktoren, H99 46. Audun Røsjorde; Transfer coefficients for evaporation, H99 47. Espen Foss Johansen, Supertargeting for the optimal structure of a mass exchange network, hos: prof. Z. Fonyo, Technical University of Budapest, Ungarn, V00 48. Magne Kawai Knag, Transported Entropies in Indium Doped Calcium Zirconate, hos: Prof. Yamamoto, and Dr. Amezawa, University of Kyoto, Japan, V2000 49. Kristin Bingen, Numerisk simulering av en PEM celle,

hos: Ole Melhus, Institutt for termo-, mekanikk og fluid-dynamikk, H2001 50. Helge Weydahl, Potential, Temperature and Heat Flux Profiles in a Fuel Cell and its

Equivalent Electrolysis Cell, Hovedoppgave for cand.scient. graden V02 51. Inger Austrem, The exergy efficiency for hydrogen fired power plants,

The Industrial Ecology Program, H02 52. Silja Jaatun, Biomembran med albedo effect, V04 53. Anders Lervik, Energy dissipation in biomolecular motors, July 2008 54. Espen Hvidsten Dahl, Hydraulic permeability of fluoridic solutions in Nafion, October 08 55. Mari Voldsund, Modelling distillation with nonequilibrium thermodynamics, June 09 56. Sondre Schnell Kvalvåg, A fluctuation method to calculate partial molar quantities from

molecular dynamics simulations, Aug. 09 In progress at NTNU 58. Ingrid Aaen, H09 59.Øyvind Wilhelmsen, H09 Master students at TU Delft

1. Frank Strijk, Exergy analysis and irreversible thermodynamics applied to the distillation of ideal binary mixtures, July 1993

2. Gelein de Koeijer, Thermodynamic analysis of the sequencing, feed tray and interstage heat exchanger location in multi-component destillation, V97, TU Delft, Nederland

3. Robert Stemmer, Coupled mass and heat transport in zeolite membranes, 2007 4. Leen van der Ham, Minimising entropy production in a H2SO4 decomposer for the

thermochemical production of H2 from H2O, April 2008

Postdoctoral fellows/ Visiting scientists Prof. Keith Garlid, Medical College of Ohio, US, 1987/88 Dr. Pirkko Forsell, Helsinki University of Techncology, 1988/89 Dr. Tatsuhiro Okada, National Institute of Materials Research, Tsukuba, Japan, 1990/1991 Dr. Jõrg Breer, University of Aachen, Germany, 1990/92 Ass. Prof. Dr. Yoichi Tomii, University of Kyoto, 1991/92 Dr. Erica Brendler, University of Freiberg, Germany, 1992/93 Dr. Victor Sharivkher, University of Southampton, GB, 1995 Ass. Prof. Xu Qian, University of North-East China, 1996 Dr. Perumal Pugazhendi, 1998 Prof. Torben Smith Sørensen, DUT, 1999 Prof. Miguel Rubi, U of Barcelona, 2001 Ass. Prof. Ger Koper, TU Delft, 2002 Ass.prof. Jose Ortiz de Zarate, Universidad Complutense Madrid, 2007 Prof. Jan Sengers, University of Maryland, USA, 2007 Ass.prof. Fernando Bresme, Imperial College, London, 2007, 2008 Ass. Prof. Jean-Marc Simon, University of Bourgogne, 2006, 2007/08 Ass.prof. Daniel Barragan, National University of Colombia, 2008 Prof. Peter Pfeifer, University of Missouri, 2008 Dr. Stefan Gheorghiu, Institute of Complex Studies, Bucharest, 2008 Ass. Prof. Jon Pharoah, Queens University, 2008/09 Prof. Marc-Olivier Coppens, Rensselear Polytechnic, USA, 2008 Ass. Prof. Levent Akyalcin, University of Anadolou, 1999/2000, 2008/09 Planned visits Dr. Stud. Diego Fernando Mendoza, National University of Colombia, 2009- Dr. Fulong Ning, China University of Geosciences, Wuhan, 2009- Prof. Gian Paolo Beretta, University of Brescia, Italy

Participants Prof. Dr. Levent Akyalcin, NTNU, Trondheim, Norway, levent.akyalcin@chem.ntnu.no Sema Akyalcin, NTNU, Trondheim, Norway, sema.akyalcin@chem.ntnu.noProf. Dr. Bjørn Alsberg, NTNU, Trondheim, Norway, alsberg @chem.ntnu.noProf. Dr. Dick Bedeaux, NTNU, Trondheim, Norway, dick.bedeaux@chem.ntnu.noOdne Burheim, NTNU, Trondheim, Norway, burheim@chem.ntnu.no Prof. Dr. Fernando Bresme, Imperial College, London, UK, f.bresme@imperial.ac.ukTerje Bruvoll, NTNU, Trondheim, Norway, bruvoll@chem.ntnu.no Dr. Claire Chassagne, Technical University Delft, The Netherlands, chassagnec@yahoo.fr Jan Chylik, Czech Techn. Univ. of Prague, Tsjekkia, janchylik@centrum.cz Prof. Dr. Marc-Olivier Coppens, Rensselaer Polytechnic Institute, Troy, NY, USA, coppens@rpi.eduProf. Dr. Yasuhiro Fukunaka, Kyoto University, Japan, hirofukunaka@yahoo.co.jpS.M. Ganesan, NTNU, Trondheim, Norway, ganesan.s.m@ntnu.no Kirill S. Glavatskiy, NTNU, Trondheim, Norway, k.s.glavatskiy@gmail.com Prof. Dr. Joachim Gross, Technical University Delft, The Netherlands, J.Gross@tudelft.nlDr. Morten Grøva, NTNU, Trondheim, Norway, morten.grova@ntnu.no Prof. Dr. Bjørn Hafskjold, NTNU, Trondheim, Norway, bjorn.hafskjold@ntnu.no Dr. Ellen Nordgard Hansen, ellen@nordgard-hansen.net Dr. Torleif Holt, SINTEF, Trondheim, Norway, Torleif.Holt@sintef.noDr. Joop ter Horst, Technical University Delft, The Netherlands, J.H.terHorst@tudelft.nl Prof. Dr. Ola Hunderi, NTNU, Trondheim, Norway, ola.hunderi@ntnu.no Dr. Isabella Inzoli, Saudi Arábia, isabella.inzoli@nt.ntnu.no Prof. Dr. Yasuhiko Ito, Doshisha University, Japan, yasito@mail.doshisha.ac.jp Dr. Eivind Johannessen, StatoilHydro, Trondheim, Norway, EIJOH@StatoilHydro.com Prof. Dr. Signe Kjelstrup, NTNU, Trondheim, Norway, signe.kjelstrup@chem.ntnu.noProf. Dr. Henrik Koch, NTNU, Trondheim, Norway, henrik.koch@chem.ntnu.noSondre Schnell Kvalvåg, NTNU, Trondheim, Norway Hannah Lampert, Aachen University, Germany, hannah.lampert@rwth-aachen.de Anders Lervik, NTNU, Trondheim, Norway, anders.lervik@chem.ntnu.noDr. Tunyan Liu, NTNU, Trondheim, Norway, Clark_liu@yahoo.com:cn Prof. Dr. Torbjørn Ljones, NTNU, Trondheim, Norway, torbjorn.ljones@chem.ntnu.no Maria Lohse, TU Bergakademie Freiberg, Germany, Maria.Lohse@student.tu-freiberg.de Miriam Mekki, NTNU, Trondheim, Norway, mekki@stud,ntnu.noDiego Fernando Mendoza, NTNU, Trondheim, Norway, Dr. Per Thomas Moe, NTNU, Trondheim, Norway, per.t.moe@ntnu.no Dr. Steffen Møller-Holst, SINTEF, Trondheim, Norway, Steffen.Moller-Holst@sintef.no Prof. Dr. David Nicholson, NTNU, Trondheim, Norway, david.nicholson@chem.ntnu.no Dr. Tom-Nils Nilsen, NTNU, Trondheim, Norway, Tom-Nils.Nilsen@NT.NTNU.no Prof. Dr. Tatsuhiro Okada, Nat. Inst. of Materials and Chem. Research, Tsukuba, Japan, okada.t@angel.ocn.ne.jp Prof. Dr. José Ortiz de Zarate, Universidad Complutense, Madrid, Spain, jmortizz@fis.ucm.es Prof. Dr. Jon Pharoah, Queens University, Kingston, Canada, pharoah@me.queensu.ca Prof. Dr. Miguel Rubi, University of Barcelona, Spain, mrubi@ub.edu Dr. Audun Røsjorde, StatoilHydro, Oslo, Norway, AUDR@StatoilHydro.comDr. Leonard Sagis, Landbouw Univ. Wageningen, The Netherlands, Leonard.Sagis@wur.nl Ragnhild Skorpa, NTNU, Trondheim, Norway, skorpa@stud.ntnu.no Prof. Dr. Jean-Marc Simon, Universite de Bourgogne, Dijon, France,

jmsimon@u-bourgogne.fr

Tom-Gøran Skog, NTNU, Trondheim, Norway, tom-goran.skog@chemeng.ntnu.no Marit Takla, NTNU, Trondheim, Norway, maritta@stud.ntnu.no Jing Xu, StatoilHydro, Trondheim, Norway, jing.xu@chem.ntnu.no Dr. Preben J.S.Vie, IFE, Oslo, Norway, preben.vie@ife.no Dr. Thijs Vlugt, Technical University Delft, The Netherlands, t.j.h.vlugt@tudelft.nlMari Volsund, NTNU, Trondheim, Norway Oivind Wilhelmsen, NTNU, Trondheim, Norway, oivindwi@stud.ntnu.noProf. Dr. Tor Ytrehus, NTNU, Trondheim, Norway, tor.ytrehus@ntnu.no Prof. Dr. Andrei V. Zvelindovski, University of Central Lancashire, Preston, UK, avzvelindovsky@uclan.ac.uk

Sponsors

Delft Physical Chemistry Fund

Gas Technology Centre, NTNU-SINTEF

NTNU, Institute of Chemistry

NTNU, Physical Chemistry

Institute for Energy Technology