4,671 research outputs found
Integral Equations with Hypersingular Kernels -- Theory and Applications to Fracture Mechanics
Hypersingular integrals of the type I_{\alpha}(T_n,m,r) = \int_{-1}^{1}
\hpsngAbs \frac{T_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 and
I_{\alpha}(U_n,m,r) = \int_{-1}^{1} \hpsngAbs
\frac{U_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 are investigated for
general integers (positive) and (non-negative), where and
are the Tchebyshev polynomials of the 1st and 2nd kinds, respectively.
Exact formulas are derived for the cases and ; most of them corresponding to new solutions derived in this paper.
Moreover, a systematic approach for evaluating these integrals when and is provided. The integrals are also evaluated as in order
to calculate stress intensity factors (SIFs). Examples involving crack problems
are given and discussed with emphasis on the linkage between mathematics and
mechanics of fracture. The examples include classical linear elastic fracture
mechanics (LEFM), functionally graded materials (FGM), and gradient elasticity
theory. An appendix, with closed form solutions for a broad class of integrals,
supplements the paper
Exploring the Way to Approach the Efficiency Limit of Perovskite Solar Cells by Drift-Diffusion Model
Drift-diffusion model is an indispensable modeling tool to understand the
carrier dynamics (transport, recombination, and collection) and simulate
practical-efficiency of solar cells (SCs) through taking into account various
carrier recombination losses existing in multilayered device structures.
Exploring the way to predict and approach the SC efficiency limit by using the
drift-diffusion model will enable us to gain more physical insights and design
guidelines for emerging photovoltaics, particularly perovskite solar cells. Our
work finds out that two procedures are the prerequisites for predicting and
approaching the SC efficiency limit. Firstly, the intrinsic radiative
recombination needs to be corrected after adopting optical designs which will
significantly affect the open-circuit voltage at its Shockley-Queisser limit.
Through considering a detailed balance between emission and absorption of
semiconductor materials at the thermal equilibrium, and the Boltzmann
statistics at the non-equilibrium, we offer a different approach to derive the
accurate expression of intrinsic radiative recombination with the optical
corrections for semiconductor materials. The new expression captures light
trapping of the absorbed photons and angular restriction of the emitted photons
simultaneously, which are ignored in the traditional Roosbroeck-Shockley
expression. Secondly, the contact characteristics of the electrodes need to be
carefully engineered to eliminate the charge accumulation and surface
recombination at the electrodes. The selective contact or blocking layer
incorporated nonselective contact that inhibits the surface recombination at
the electrode is another important prerequisite. With the two procedures, the
accurate prediction of efficiency limit and precise evaluation of efficiency
degradation for perovskite solar cells are attainable by the drift-diffusion
model.Comment: 32 pages, 11 figure
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
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