Anodes for protonic ceramic fuel cells (PCFCs)

One of the more promising possibilities for future “green” electrical energy generation is the protonic ceramic fuel cell (PCFC). PCFCs offer a low-pollution technology to generate electricity electrochemically with high efficiency. Reducing the operating temperature of solid oxide fuel cells (SOFCs) to the 500-700°C range is desirable to reduce fabrication costs and improve overall longevity. This aim can be achieved by using protonic ceramic fuel cells (PCFCs) due to their higher electrolyte conductivity at these temperatures than traditional ceramic oxide-ion conducting membranes. This thesis deals with the state of the art Ni-BaZr0.85Y0.15O3-δ cermet anodes for PCFCs. The study of PCFCs is in its initial stage and currently only a few methods have been developed to prepare suitable anodes via solid state mechanical mixing of the relevant oxides or by combustion routes using nitrate precursors. This thesis aims to highlight the disadvantages of these traditional methods of anode preparation and to, instead, offer a novel, efficient and low cost nitrate free combustion route to prepare Ni-BaZr0.85Y0.15O3-δ cermet anodes for PCFCs. A wide range of techniques mainly X-ray diffraction (XRD), scanning electron microscopy (SEM), environmental scanning electron microscopy, (ESEM) and electrochemical impedance spectroscopy (EIS) were employed in the cermet anode study. The work also offers a fundamental examination of the effect of porosity, redox cycling behaviour, involvement of proton conducting oxide phase in PCFC cermet anodes and finally progresses to study the electrochemical performance of a state of the art anode supported PCFC. The polarisation behaviour of anodes has been assessed as a function of temperature (T), water vapour (pH2O), hydrogen partial pressures (pH2) and phase purity for electrodes of comparable microstructure. The impedance spectra generally show two arcs at high frequency R2 and low frequency R3 at 600 °C, which correspond to the electrode polarisation resistance. Work shows that the R2 and R3 terms correspond to proton transport and dissociative H2 adsorption on electrode surface, respectively. The polarization resistance of the cermet anode (Rp) was shown to be significantly affected by porosity, with the PCFC cermet anode with the lowest porosity exhibiting the lowest Rp under standard operating conditions. This result highlights that porogens are not required for peak performance in PCFC anodes, a result contrary to that of their oxide-ion conducting anode counterparts. In-situ redox cycling studies demonstrate that polarisation behaviour was drastically impaired by redox cycling. In-situ measurements using an environmental scanning electron microscopy (ESEM) reveal that degradation proceeds due to volume expansion of the Ni-phase during the re-oxidation stage of redox cycling.The anode supported thin BCZY44 based protonic ceramic fuel cell, formed using a peak performing Ni-BaZr0.85Y0.15O3-δ cermet anode with no porogen, shows promising results in fuel cell testing conditions at intermediate temperatures with good durability and an overall performance that exceeds current literature data.

Spectra of graphs obtained by a generalization of the join graph operation

Taking a Fiedler’s result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity.

On the Faria's inequality for the Laplacian and signless Laplacian spectra: a unified approach

Let p(G)p(G) and q(G)q(G) be the number of pendant vertices and quasi-pendant vertices of a simple undirected graph G, respectively. Let m_L±(G)(1) be the multiplicity of 1 as eigenvalue of a matrix which can be either the Laplacian or the signless Laplacian of a graph G. A result due to I. Faria states that mL±(G)(1) is bounded below by p(G)−q(G). Let r(G) be the number of internal vertices of G. If r(G)=q(G), following a unified approach we prove that mL±(G)(1)=p(G)−q(G). If r(G)>q(G) then we determine the equality mL±(G)(1)=p(G)−q(G)+mN±(1), where mN±(1) denotes the multiplicity of 1 as eigenvalue of a matrix N±. This matrix is obtained from either the Laplacian or signless Laplacian matrix of the subgraph induced by the internal vertices which are non-quasi-pendant vertices. Furthermore, conditions for 1 to be an eigenvalue of a principal submatrix are deduced and applied to some families of graphs.