Augmenting Graphs to Minimize the Radius

We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time (5/3-?)-approximation algorithm, for any ? > 0, unless P = NP. We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth

Oxygen Hydration Mechanism for the Oxygen Reduction Reaction at Pt and Pd Fuel Cell Catalysts

We report the reaction pathways and barriers for the oxygen reduction reaction (ORR) on platinum, both for gas phase and in solution, based on quantum mechanics calculations (PBE-DFT) on semi-infinite slabs. We find a new mechanism in solution: O_2 → 2O_(ad) (E_(act) = 0.00 eV), O_(ad) + H_2O_(ad) → 2OH_(ad) (E_(act) = 0.50 eV), OH_(ad) + H_(ad) → H_2O_(ad) (E_(act) = 0.24 eV), in which OH_(ad) is formed by the hydration of surface O_(ad). For the gas phase (hydrophilic phase of Nafion), we find that the favored step for activation of the O_2 is H_(ad) + O_(2ad) → HOO_(ad) (E_(act) = 0.30 eV) → HO_(ad) + O_(ad) (E_(act) = 0.12 eV) followed by O_(ad) + H_2O_(ad) → 2OH_(ad) (E_(act) = 0.23 eV), OH_(ad) + H_(ad) → H_2O_(ad) (E_(act) = 0.14 eV). This suggests that to improve the efficiency of ORR catalysts, we should focus on decreasing the barrier for Oad hydration while providing hydrophobic conditions for the OH and H_2O formation steps

Theoretical Study of Solvent Effects on the Platinum-Catalyzed Oxygen Reduction Reaction

We report here density functional theory (DFT) studies (PBE) of the reaction intermediates and barriers involved in the oxygen reduction reaction (ORR) on a platinum fuel cell catalyst. Solvent effects were taken into account by applying continuum Poisson−Boltzmann theory to the bound adsorbates and to the transition states of the various reactions on the platinum (111) surface. Our calculations show that the solvent effects change significantly the reaction barriers compared with those in the gas-phase environment (without solvation). The O_2 dissociation barrier decreases from 0.58 to 0.27 eV, whereas the H + O → OH formation barrier increases from 0.73 to 1.09 eV. In the water-solvated phase, OH formation becomes the rate-determining step for both ORR mechanisms, O_2 dissociation and OOH association, proposed earlier for the gas-phase environment. Both mechanisms become significantly less favorable for the platinum catalytic surface in water solvent, suggesting that alternative mechanisms must be considered to describe properly the ORR on the platinum surface

Mechanism for Degradation of Nafion in PEM Fuel Cells from Quantum Mechanics Calculations

We report results of quantum mechanics (QM) mechanistic studies of Nafion membrane degradation in a polymer electrolyte membrane (PEM) fuel cell. Experiments suggest that Nafion degradation is caused by generation of trace radical species (such as OH^●, H^●) only when in the presence of H_2, O_2, and Pt. We use density functional theory (DFT) to construct the potential energy surfaces for various plausible reactions involving intermediates that might be formed when Nafion is exposed to H_2 (or H^+) and O_2 in the presence of the Pt catalyst. We find a barrier of 0.53 eV for OH radical formation from HOOH chemisorbed on Pt(111) and of 0.76 eV from chemisorbed OOH_(ad), suggesting that OH might be present during the ORR, particularly when the fuel cell is turned on and off. Based on the QM, we propose two chemical mechanisms for OH radical attack on the Nafion polymer: (1) OH attack on the S–C bond to form H_2SO_4 plus a carbon radical (barrier: 0.96 eV) followed by decomposition of the carbon radical to form an epoxide (barrier: 1.40 eV). (2) OH attack on H_2 crossover gas to form hydrogen radical (barrier: 0.04 eV), which subsequently attacks a C–F bond to form HF plus carbon radicals (barrier as low as 1.00 eV). This carbon radical can then decompose to form a ketone plus a carbon radical with a barrier of 0.86 eV. The products (HF, OCF_2, SCF_2) of these proposed mechanisms have all been observed by F NMR in the fuel cell exit gases along with the decrease in pH expected from our mechanism