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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In this paper, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half...
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Higher education system is not only a complex nonlinear system, but also a complex adaptive system;Order and disorder is one of the most important concepts, the system works from disorderly to orderly is also an adapt...
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We synthesized four n-type conjugated polymers comprising a bithiophene imide (BTI) unit and 3,3 ',4,4 '-tetrafluoro-2,2 '-bithiophene (4FBT) or (E)-1,2-bis(3,4-difluorothien-2-yl)ethene (4FTVT) via direct...
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We synthesized four n-type conjugated polymers comprising a bithiophene imide (BTI) unit and 3,3 ',4,4 '-tetrafluoro-2,2 '-bithiophene (4FBT) or (E)-1,2-bis(3,4-difluorothien-2-yl)ethene (4FTVT) via direct arylation polycondensation, and comprehensively studied the optical, electrochemical and charge transport properties of the polymers. Increasing the BTI acceptor unit from one to two in the repeating unit slightly decreased the frontier molecular orbital levels of the polymers and blue-shifted their absorption spectra. Moreover, this change altered the molecular packing from an edge-on backbone orientation to bimodal packing with mixed edge-on and face-on orientations. When used as semiconductor layers in organic thin-film transistors, all four polymers exhibited unipolar n-type transport behavior with the highest saturation and a linear electron mobility of 0.72 and 0.67 cm(2) V-1 s(-1), respectively. Our findings suggest that direct arylation polycondensation can serve as an ecofriendly protocol for the synthesis of high-performance n-type conjugated polymers based on BTI through careful molecular design.
Six polythiophenes (PThs) were synthesized via direct arylation polycondensation (DArP) with beta-fluorinated bithiophenes, that is, 4,4' -difluoro-2,2'-bithiophene (2FBT) and 3,3',4,4'-tetrafluoro-2,2...
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Six polythiophenes (PThs) were synthesized via direct arylation polycondensation (DArP) with beta-fluorinated bithiophenes, that is, 4,4' -difluoro-2,2'-bithiophene (2FBT) and 3,3',4,4'-tetrafluoro-2,2'-bithiophene (4FBT), as the C-H monomers and 5,5'-dibromo-2,2'-bithiophenes DCBT-2Br, DABT-2Br, and DTBT-2Br that carry alkoxycarbonyl, alkyl, and alkylthienyl side chains at 4,4'-positions, respectively, as the C-Br monomers. Both 2FBT and 4FBT are highly reactive for DArP, and high molecular weight PThs with unobservable chain defects were successfully synthesized from 2FBT/DCBT-2Br, 2FBT/DABT-2Br, 2FBT/DTBT-2Br, and 4FBT/DTBT-2Br. However, the DArP of 4FBT with DCBT-2Br and DABT-2Br produced PThs containing C-H/C-H homo-coupling defects along with relatively lower molecular weights. Detailed theoretical analysis suggests that the occurrence of C-Br reduction-provoked C-H/C-H homo-coupling for 4FBT/DCBT-2Br and 4FBT/DABT-2Br monomer pairs originated from the poor selectivity between the cis- and trans-forms of transition states in the concerted metalation-deprotonation (CMD) process is responsible for the formation of structural defects and depressed molecular weights. This research reveals that a C-H monomer with high reactivity and selectivity is not sufficient for the synthesis of well-defined conjugated polymers via DArP, and the structure of the C-Br monomer also has a significant impact on the results of DArP via influencing the catalytic cycles.
In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality is achieved for anisotropic free boundary Wulff shapes in a convex...
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Sustainable synthesis of polythiophenes (e.g.,P3HT) is highly desired for the development of low-cost organicsolar cells. Regulating the regioregularity of P3HT is a promisingway to boost its performance. Yet, few eco...
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Sustainable synthesis of polythiophenes (e.g.,P3HT) is highly desired for the development of low-cost organicsolar cells. Regulating the regioregularity of P3HT is a promisingway to boost its performance. Yet, few eco-friendly methods canprepare P3HT with tunable regioregularity. Herein, we put forwarda facile strategy tofinely modulate the regioregularity of P3HTfrom 90% to 98% by tuning the molar ratio of two ligands in directarylation polycondensation. Moreover, the ligand effect onregioregularity is well elucidated with DFT calculations, and theregioregularity effect of P3HT in non-fullerene solar cells isclarified for thefirst time. Our calorimetric, microscopic, and scattering results show that regioregularity strongly impacts thepolymer crystallinity and phase separation, and device performance of the blendfilms. The P3HT batch with a regioregularity of 95%yields an unprecedented power conversion efficiency of 10.82%. Importantly, this realizationfirmly provides optimism for cheapmaterials such as polythiophenes, which are made via eco-friendly polycondensation for the application of solar cells and beyond.
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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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, by isometrically embedding (Sn+1gSn+1) into Rn+2, and using nonlinear analysis on the codimension-2 graphs, we will show that the level-sets of the distance function from the boundary of any open set in...
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