Electrochemical oxidation/reduction of radicals is a green and environmentally friendly approach to generating fuels. These reactions, however, suffer from sluggish kinetics due to a low local concentration of radicals around the electrocatalyst. A large applied electrode potential can enhance the fuel generation efficiency via enhancing the radical concentration around the electrocatalyst sites, but this comes at the cost of electricity. Here, we report about a ~45% saving in energy to achieve an electrochemical hydrogen generation rate of 3×10 16 molecules cm -2 s -1 (current density: 10 mA/cm 2 ) through localized electric field-induced enhancement in the reagent concentration (LEFIRC) at laser-induced periodic surface structured (LIPSS) electrodes. The finite element model is used to simulate the spatial distribution of the electric field to understand the effects of LIPSS geometric parameters in field localization. When the LIPSS patterned electrodes are used as substrates to support Pt/C and RuO 2 electrocatalysts, the η 10 overpotentials for HER and OER are decreased by 40.4 and 25%, respectively. Moreover, the capability of the LIPSS-patterned electrodes to operate at significantly reduced energy is also demonstrated in a range of electrolytes, including alkaline, acidic, neutral, and seawater. Importantly, when two LIPSS patterned electrodes were assembled as the anode and cathode into a cell, it requires 330 mVs of lower electric potential with enhanced stability over a similar cell made of pristine electrodes to drive a current density of 10 mA/cm 2 . This work demonstrates a physical and versatile approach of electrode surface patterning to boost electrocatalytic fuel generation performance and can be applied to any metal and semiconductor catalysts for a range of electrochemical reactions.
We prove Korovkin-type theorems in the setting of infinite dimensional Hilbert space operators. The classical Korovkin theorem unified several approximation processes. Also, the non-commutative versions of the theorem were obtained in various settings such as Banach algebras, $$C^{*}$$
C
∗
-algebras and lattices etc. The Korovkin-type theorem in the context of preconditioning large linear systems with Toeplitz structure can be found in the recent literature. In this article, we obtain a Korovkin-type theorem on $$B({\mathcal {H}})$$
B
(
H
)
which generalizes all such results in the recent literature. As an application of this result, we obtain Korovkin-type approximation for Toeplitz operators acting on various function spaces including Bergman space $$A^{2}({\mathbb {D}})$$
A
2
(
D
)
, Fock space $$F^{2}({\mathbb {C}})$$
F
2
(
C
)
etc. These results are closely related to the preconditioning problem for operator equations with Toeplitz structure on the unit disk $${\mathbb {D}}$$
D
and on the whole complex plane $${\mathbb {C}}$$
C
. It is worthwhile to notice that so far such results are available for Toeplitz operators on circle only. This also establishes the role of Korovkin-type approximation techniques on function spaces with certain oscillation property. To address the function theoretic questions using these operator theory tools will be an interesting area of further research.
Organometallic lead bromide and iodide perovskite single crystals (PSCs) are potential candidates for terahertz applications. Herein, we performed terahertz time-domain spectroscopy (THz-TDS) in the frequency range of 0.1–3.0 THz on different thicknesses of MAPbBr3 (0.3, 0.6, and 0.8 mm) and MAPbI3 (0.6, 0.8, 0.9, 1.3, and 2.3 mm). The measurements were carried out with respect to the position (along the focal area), azimuthal rotation of the PSCs, and incidence angles of the reference THz pulse on the PSCs’ surface. Based on the transmitted THz pulses from PSCs from the above measurements, we calculated the real and imaginary parts of the refractive index, dielectric constants, absorption coefficients, and dark conductivity. These optical parameters tend to increase with decreases in the PSCs’ thicknesses. The transmission spectra of the terahertz electric field indicate that the measured optical properties do not vary significantly with the position and orientation of PSCs. The real parts of the refractive index and dielectric constants are higher than the imaginary values for both PSCs. On the other hand, a slight blueshift in the optical phonon vibrations corresponding to Pb-Br/I-Pb and Pb-Br/I bonds is observed with an increase in thickness. Interestingly, the phonon vibrations do not vary with the incidence angle of the THz pulses on the same crystal’s surface. The optical parameters based on THz-TDS reveal that the PSCs satisfy the requirement for tunable THz devices which need suitable, sensitive, and stable absorption properties between 0.1 and 3 THz.
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