Vinylene/olefin-linked two-dimensional covalent organic frameworks (v-2D-COFs) have emerged as advanced semiconducting materials with excellent in-plane conjugation, high chemical stabilities, and precisely tunable electronic structures. Exploring new linkage chemistry for the reticular construction of v-2D-COFs remains in infancy and challenging. Herein, we present a solid-state benzobisoxazole-mediated aldol polycondensation reaction for the construction of two novel isomeric benzobisoxazole-bridged v-2D-COFs (v-2D-COF-NO1 and v-2D-COF-NO2) with trans and cis configurations of benzobisoxazole. Interestingly, the isomeric benzobisoxazole linkers endow the two v-2D-COFs with distinct optoelectronic and electrochemical properties, ranging from light absorption and emission to charge-transfer properties. When employed as the photocathode, v-2D-COF-NO1 exhibits a photocurrent of up to ∼18 μA/cm2 under AM 1.5G irradiation at −0.3 V vs reversible hydrogen electrode (RHE), which is twice the value of v-2D-COF-NO2 (∼9.1 μA/cm2). With Pt as a cocatalyst, v-2D-COF-NO1 demonstrates a photocatalytic hydrogen evolution rate of ∼1.97 mmol h–1 g–1, also in clear contrast to that of v-2D-COF-NO2 (∼0.86 mmol h–1 g–1) under identical conditions. This work demonstrates the synthesis of v-2D-COFs via benzobisoxazole-mediated aldol polycondensation with isomeric structures and distinct photocatalytic properties.

In this paper, an improved superconvergence analysis is presented for both the Crouzeix-Raviart element and the Morley element. The main idea of the analysis is to employ a discrete Helmholtz decomposition of the difference between the canonical interpolation and the finite element solution for the first order mixed Raviart-Thomas element and the mixed Hellan-Herrmann-Johnson element, respectively. This in particular allows for proving a full one order superconvergence result for these two mixed finite elements. Finally, a full one order superconvergence result of both the Crouzeix-Raviart element and the Morley element follows from their special relations with the first order mixed Raviart-Thomas element and the mixed Hellan-Herrmann-Johnson element respectively.

Vinylene/olefin-linked two-dimensional covalent organic frameworks (v-2D-COFs), featured with vinylene-linked in-plane conjugations, high chemical stabilities, and designable chemical structures, are promising for optoelectronic/photocatalytic applications. Developing v-2D-COFs with superior πconjugation and optoelectronic properties is meaningful but remains challenging. In this work, we present the crystalline benzobisthiazole-bridged unsubstituted v-2D-COF (v-2D-COF-NS1 and v-2D-COF-NS2) synthesized via a benzothiazolemediated aldol-type polycondensation. Interestingly, the resultant v-2D-COF exhibits a high chemical stability under both strong acidic (12 M HCl) and basic conditions (saturated KOH) due to the robust vinylene-linked skeletons. Moreover, the electrondeficient thiazole units and 2D π-conjugations endow v-2D-COFs (i.e., v-2D-COF-NS1) a narrow band gap of ∼1.85 eV with a conduction band of −3.65 eV vs vacuum, which are desirable for photocatalytic hydrogen evolution. As such, the v-2D-COF-NS1based photoelectrode gives a photocurrent up to ∼47 μA cm −2 at 0.3 V vs reversible hydrogen electrode (RHE), which is much higher than the value of the corresponding linear polymer (LP-NS1) and outstanding among the reported COF photoelectrodes. Under a continuous visible light irradiation, v-2D-COF-NS1 generates hydrogen gas with an excellent rate of ∼4.4 mmol h −1 g −1 over 12 h. This work demonstrates the synthesis of unsubstituted v-2D-COFs that intrinsically contain benzobisthiazole-based building blocks and shows great potential in photocatalytic reactions.