LIST OF TABLES AND FIGURES

LIST OF TABLES AND FIGURES

Tables Chap. III

tab. III.1: Change of coordinates (n.i. = not interesting). Chap. V

tab. V.1: Morphological parameters at several porosities. tab. V.2: Parameters of water and nitrogen for (eq. V.4.2).

tab. V.3: Conductivities of ACP (i.e. YDC15) and PCP (i.e. BCY15) as reported by Van herle et al. (1996) and Katahira et al. (2000).

tab. V.4: Conditions and kinetic parameters used in base-case. Chap. VI

tab. VI.1: Conditions and parameters concerning sample 1. tab. VI.2: Conditions and parameters concerning sample 2.

tab. VI.3: Several performance indexes concerning gas transport for porosity equal to 0.4 and 0.5.

tab. VI.4: Several performance indexes concerning gas transport for different mean dimensions of particles.

tab. VI.5: Several indexes concerning gas transport in base-case for tCM = 130µm.

Figures Chap. I

fig. I.1: Comparison between thermodynamic and electrochemical conversion of chemical energy.

fig. I.2: Schematic representation of different types of fuel cells. fig. I.3: Simplified scheme of an anionic conducting SOFC. fig. I.4: Simplified scheme of a protonic conducting SOFC.

fig. I.5: The IDEAL-Cell concept: a) PCFC and SOFC; b) the combination; c) IDEAL-Cell.

fig. I.6: Schematic representation of the IDEAL-Cell in steady-state (ACP: anion-conducting phase; el: electric conductor; PCP: proton-anion-conducting phase).

Chap. II

fig. II.1: Overall mechanism of water recombination. fig. II.2: Scheme of an ideal electric condenser.

fig. II.3: 2D representation of the porous composite structure of the CM with the 3 different paths.

fig. II.4: Example of water transport in PCP (pw,1 > pw,2).

fig. II.5: Schematic representation of the experimental set up.

fig. II.6: Schematic representation of the output i(t) of a real system when a sinusoidal input

η

(t) is imposed.

fig. II.7: Nyquist plots (i.e. impedance curves) of elementary circuits. Chap. III

fig. III.1: Types of clusters in a binary random packing. fig. III.2: Explanation of the meaning of Zk,l and Zk.

fig. III.3: Angles of contact between overlapping particles.

fig. III.4: Representation of the hypothetical sphere and the areas As and Ac.

fig. III.5: Estimation of Nk,l by using Suzuki and Oshima or Chen et al. theory and

comparison with simulated results in the range P = [0.25,4].

fig. III.6: Comparison of coordination numbers predicted by several theories and results from computer simulations: a) P = 3; b) P = 0.33.

fig. III.7: Comparison between Nk,lN calculated by using our theory with simulated

results in the range P = [0.25,4].

fig. III.8: Comparison of coordination numbers predicted by our theory and results from computer simulations: a) P = 3; b) P = 0.33.

fig. III.9: Comparison among Zk,l estimated by different theories.

fig. III.10: Comparison among Zk,k estimated by different theories.

fig. III.11: Estimation of Z and comparison with simulated results.

fig. III.12: Comparison between ζl-th predicted by different theories and simulated or

experimental results.

fig. III.13: Comparison between

ψ

l-th predicted by different theories and simulated or

experimental results.

fig. III.14: Comparison between pl predicted by correlations and simulated results.

fig. III.15: Graphic meaning of the assumptions: a) before sintering; b) sintering; c) after sintering.

fig. III.16: Definition of apparent conductivity.

fig. III.17: Comparison among Choi et al. results with Costamagna et al. and Nam and Jeon correlations for apparent conductivity.

fig. III.18: Current across overlapping particles: simulation with COMSOL.

fig. III.19: Simulated results of current across particles at several angles of contact. fig. III.20: a) Geometry of the 2D model; b) Limit cases; c) Example of solution.

fig. III.21: Results from 2D simulations compared with ∆Vn/∆Vtot as calculated in limit

cases with N = 51.

fig. III.22: a) BCC configuration; b) Changing of the position of the center within the cell.

fig. III.23: a) Cross section and b) 3D view of a simulated structure with a single component (radius: 2.56*10-2m; mean angle of contact: 15°; porosity:

34.4%).

fig. III.24: Overlapping of spheres: circumference created by the intersection. fig. III.25: Local system of reference.

fig. III.26: 3D grid with BCC positions filled: a) how to fill the grid on BCC positions; b) position to be controlled (white) and its neighbours (grey).

fig. III.27: Mesh of the domain (2D example).

fig. III.28: Simulation to estimate apparent conductivity in BCC structure.

fig. III.29: Comparison between our simulated results (P = 1) and Choi et al. results (P = 1.431); Costamagna et al. and Nam and Jeon correlations are reported too.

fig. III.30: Apparent conductivity for θ = 15° as results of our simulations with tidy structures.

fig. III.31: Length of TPB per unit volume vs composition of k-particles at different radii of particles for a binary not polydisperse mixture without pore formers. fig. III.32: Effect of porosity on the length of TPB per unit volume for a not

polydisperse mixture.

fig. III.33: Length of TPB per unit volume vs composition at different porosities for monosized particles: comparison between our model (solid) and others (dot). fig. III.34: Mean hydraulic radius vs composition at different porosities and particles

sizes.

fig. III.35: Effect of radius of pore formers on the length of TPB per unit volume for a not polydisperse mixture.

fig. III.36: Length of TPB per unit volume for polydisperse and monosized mixtures (symmetrical numerical distribution).

fig. III.37: Length of TPB per unit volume for polydisperse and monosized mixtures (symmetrical volumetric distribution).

Chap. IV

fig. IV.1: Representation of water adsorption in PCP.

fig. IV.2: a) Representation of a case study of water adsorption in PCP; b) situation if DOH > DO after a few seconds.

fig. IV.3: Net transport of water through PCP.

fig. IV.4: Schematic representation of: a) transport of water (diffusion) b) transport of protons (migration) in PCP.

Chap. V

fig. V.1: Reduction of the model of the CM from 3D to axial symmetric 2D.

fig. V.2: Schematization of boundary conditions in (3) and (5) for water adsorbed in PCP for a generic case.

fig. V.3: Particle size distributions of a) PCP and b) ACP as given by the supplier (Marion Technologies).

fig. V.4: Energy luggage: schematic representation of the losses of energy in CM. fig. V.5: Schematic representation of the calculus of currents.

fig. V.6: Schematization of fluxes of water and nitrogen in gas phase for

η

CM > 0 for:

a) xw ≈ 0; b) xw ≈ 1.

fig. V.7: Mesh of geometry for a) steady-state simulations; b) dynamic simulations. Chap. VI

fig. VI.1: Pictures reporting a) overpotential; b) pressure; c) molar fraction of water; d) concentration of protonic defects; e) difference of potential at local equilibrium; f) ratio between diffusive and total flux of water in gas phase for base-case.

fig. VI.2: Comparison between experimental (dots) and simulated polarization curve for sample 1.

fig. VI.3: Comparison between experimental (dots) and simulated polarization curve for sample 2.

fig. VI.5: Overpotential vs axial coordinate on the axis of symmetry in base-case. fig. VI.6: Sensitivity on i0: effects on density of current in the base-case.

fig. VI.7: Profiles of overpotential

η

along the axial coordinate at several kinetic parameters i0 for the base-case.

fig. VI.8: Sensitivity on kd: effects on density of current in the base-case.

fig. VI.9: Sensitivity on σapp_{/σ: effects on density of current in the base-case.}

fig. VI.10: Sensitivity on Dw,PCP: effects on density of current in the base-case.

fig. VI.11: Effect of an increase of diffusivity of water in PCP on the flow of water that leaves the CM in adsorbed form through the protonic electrolyte.

fig. VI.12: Effect of a variation of external molar fraction of water in base-case at fixed difference of potential at terminals of the cell.

fig. VI.13: Overpotential

η

CM as a function of external molar fraction of water in order

to obtain a constant value of difference of potential at terminals.

fig. VI.14: Effect of change of porosity on the performance of the CM in base-case. fig. VI.15: Effect of variation of mean dimension of particles in base-case.

fig. VI.16: Effect of variation of radius of CM on maximum pressure in base-case. fig. VI.17: Effect of variation of radius of CM on density of current in base-case. fig. VI.18: Effect of variation of thickness of CM on polarization resistance in

base-case.

fig. VI.19: Schematic representation of the reduction of thickness in ohmic regime. fig. VI.20: Field of overpotential

η

in the base-case for tCM = 130µm.

fig. VI.21: Field of overpotential

η

g,evac in the base-case for tCM = 130µm.

fig. VI.22: Effect of variation thickness of protonic electrolyte on density of current in base-case.

fig. VI.23: Effect of an increase of thickness of protonic electrolyte on the flow of water that leaves the CM in adsorbed form through the protonic electrolyte.

fig. VI.24: Simulated impedance curve of the CM in base-case with xwex = 0.03.

fig. VI.25: Analogy with an equivalent circuit: a) circuit R1+(R2//C); b) its impedance

curve.

fig. VI.26: Fields of a) partial pressure of water b) difference of potential at local equilibrium for f = 1Hz at t = 19.5s in the same conditions of fig. VI.24. fig. VI.27: Experimental impedance curve of the whole cell for sample 2.