In this paper, we utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. One of new crucial ingredient...
In this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente’s result [32] to the anisotropic case and He-L...
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In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://***/10.1007/s00526-019-1603-3), and prove a rigidity resu...
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3,4-Difluorothiophene-substituted aryls, i.e., 1,4-bis(3,4-difluorothiophen-2-yl)-benzene (Ph-2FTh), 1,4-bis(3,4-difluorothiophen-2-yl)-2,5-difluorobenzene (2FPh-2FTh), and 4,7-bis(3,4-difluorothiophen-2-yl)-2,1,3-ben...
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3,4-Difluorothiophene-substituted aryls, i.e., 1,4-bis(3,4-difluorothiophen-2-yl)-benzene (Ph-2FTh), 1,4-bis(3,4-difluorothiophen-2-yl)-2,5-difluorobenzene (2FPh-2FTh), and 4,7-bis(3,4-difluorothiophen-2-yl)-2,1,3-benzothiadiazole (BTz-2FTh), are synthesized as CH monomers for the synthesis of conjugated polymers (CPs) via direct arylation polycondensation (DArP) with diketopyrrolopyrrole (DPP) and isoindigo (IID) derivatives as CBr monomers. The Gibbs free energies of activation for direct arylation (& UDelta;G298 K, kcal mol-1) for & alpha;CH bonds of thiophene moieties as calculated by density functional theory (DFT) are 14.3, 16.5, and 16.4 kcal mol-1 for Ph-2FTh, 2FPh-2FTh and BTz-2FTh, respectively, meaning that inserting an electron-deficient unit in 3,3 & PRIME;,4,4 & PRIME;-tetrafluoro-2,2 & PRIME;-bithiophene (4FBT, & UDelta;G298K: 14.6 kcal mol-1) may cause a reactivity decrease of the CH monomers. Photophysical and semiconducting properties of the resulting six CPs (i.e., DPP-Ph, DPP-2FPh, DPP-BTz, 2FIID-Ph, 2FIID-2FPh, and 2FIID-BTz) are characterized in detail. DPP-based CPs show ambipolar transport properties while IID-based ones exhibited n-type behavior owing to the deeper frontier molecular orbital energy levels of IID-based CPs. With source/drain electrodes modified with polyethylenimine ethoxylated, n-channel organic thin-film transistors with maximum electron mobility of 0.40, 0.54, 0.29, 0.05, 0.16, and 0.01 cm2 V-1 s-1 for DPP-Ph, DPP-2FPh, DPP-BTz, 2FIID-Ph, 2FIID-2FPh, and 2FIID-BTz, respectively, are fabricated. DPP-2FPh exhibits the best device performance due to the good film morphology and the highest intermolecular packing order. Three CH monomers Ph-2FTh, 2FPh-2FTh, and BTz-2FTh with 3,4-difluorothiophene as terminal units and phenyl, 2,5-difluorophenyl and benzothiadiazole as central units are synthesized for direct arylation polycondensation to diketopyrrolopyrrole- and isoindigo-based high-mobility conjugated polymers. n-Channel org
Herein, NiZn bimetallic oxides derived from calcination treatment of metal-organic frameworks (MOFs) were successfully loaded onto the carbon black waste as support obtained from the oil refinery. The resulting hybrid...
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Herein, NiZn bimetallic oxides derived from calcination treatment of metal-organic frameworks (MOFs) were successfully loaded onto the carbon black waste as support obtained from the oil refinery. The resulting hybrids could serve as environmentally friendly and cost-effective catalysts for the deoxygenation of biomass-derived fatty acids under an inert atmosphere. An online pyrolysis-gas chromatography/mass spectrometry (Py-GC/ MS) system was employed to evaluate their deoxygenation performance. The optimized catalysts demonstrated remarkably high stearic acid conversion of 99.6% and selectivity towards C8-C17 olefins of 57.2%. Furthermore, these catalysts with varying metal loadings also exhibited excellent efficiency in deoxygenation reactions of other types of fatty acids, such as myristic acid and palmitic acid, achieving conversion exceeding 85% and selectivities towards olefins of ca. 50%. When converting coconut oil, the supported NiZn bimetallic oxides showed excellent selectivity towards olefins (>60%). Furthermore, in-situ DRIFTS results suggest that fatty alcohols might be the key intermediates in the deoxidation reactions of fatty acid. This study not only demonstrates the great potential for obtaining valuable chemicals from biomass but also provides some insights into the fabrication of catalyst materials by using industrial solid waste.
In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the se...
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In this paper we prove the following Willmore-type inequality: On an unbounded closed convex set K ⊂ Rn+1 (n ≥ 2), for any embedded hypersurface Σ ⊂ K with boundary ∂Σ ⊂ ∂K satisfying a certain contact angle condit...
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