The effective conversion of carbon dioxide (CO2) into cyclic carbonates requires porous materials with high ionic content and large specific surface area. Herein, we developed a new systematic ...post-synthetic modification strategy for synthesizing imidazolium-based hypercrosslinked ionic polymers (HIPs) with high ionic content (up to 2.1 mmol g−1) and large specific surface area (385 m2 g−1) from porous hypercrosslinked polymers (HCPs) through addition reaction and quaternization. The obtained HIPs were efficient in CO2 capture and conversion. Under the synergistic effect of high ionic content, large specific surface area, and plentiful micro/mesoporosity, the metal-free catalyst HCP-CH2-ImCl-1 exhibited quantitative selectivities, high catalytic yields, and good substrate compatibility for the conversion of CO2 into cyclic carbonates at atmospheric pressure (0.1 MPa) in a shorter reaction time in the absence of cocatalysts, solvents, and additives. High catalytic yields (styrene oxide, 120 °C, 8 h, 94% yield; 100 °C, 20 h, 93% yield) can be achieved by appropriately extending the reaction times at low temperature, and the reaction times are shorter than other porous materials under the same conditions. This work provides a new strategy for synthesizing an efficient metal-free heterogeneous catalyst with high ionic content and a large specific surface area from HCPs for the conversion of CO2 into cyclic carbonates. It also demonstrates that the ionic content and specific surface area must be coordinated to obtain high catalytic activity for CO2 cycloaddition reaction.
In this paper, we study the normalized solutions for the nonlinear critical Kirchhoff equations with combined nonlinearities in
R
4
. In particular, in the case of
N
=
4
, there is a new mass-energy ...doubly critical phenomenon for Kirchhoff equation with combined nonlinearities that the mass critical exponent
2
+
8
N
is equal to the energy critical exponent
2
N
N
−
2
, which remains unsolved in the existing literature. To deal with the special difficulties created by the nonlocal term and doubly critical term, we develop a perturbed Pohožaev constraint method based on the splitting properties of the Brézis-Lieb lemma, and make some subtle energy estimates. By decomposing Pohožaev manifold and constructing fiber map, we prove the existence of a positive normalized ground state. Moreover, we also explore the asymptotic behavior of the obtained normalized solutions. These conclusions extend some known ones in previous papers.
In this paper, we study the following fractional Kirchhoff equation with critical growth a+b∫R3|(−Δ)s2u|2dx(−Δ)su+λu=μ|u|q−2u+|u|2s∗−2uinR3,under the constraint ∫R3|u|2dx=c2, where s∈(0,1), a,b,c>0, ...2<q<2s∗, μ>0, and λ∈R appears as a Lagrange multiplier. The equation has been extensively studied in the case s∈(34,1). In contrast, no existence result of normalized solutions is available for the case s∈(0,34. Because the complicated competition between the Kirchhoff nonlocal term and the Sobolev critical term, such problem cannot be studied by applying standard variational methods, even by restricting its underlying energy functional on the Pohožaev manifold. In this paper, by using appropriate transform, we first get the equivalent system of the above problem. With the equivalence result, we obtain the nonexistence, existence and multiplicity of normalized solutions in the case s∈(0,34.
Multi-layer structures possess highly geometrically tunable optical resonances to change the surface plasmon frequencies in the wide range. A simple analytic model is presented to describe the ...plasmon hybridization of multi-layer metamaterial structures with multipole resonances. We theoretically demonstrate that the number of plasmon modes increases with the number of layers, which results in the enlargement of the localized resonant optical band gap. To explore the interaction between incident fields and multi-layer structures, we derive the closed-form perturbed field in terms of a generalized polarization matrix, whose dimension matches the number of layers. This enables us to obtain the eigenmode frequencies and their corresponding eigenfunctions for three-dimensional multi-layer concentric spheres and two-dimensional multi-layer concentric cylinders in a vacuum setting. These findings offer nanoscientists a general design principle that can be applied to facilitate the proper selection of the metamaterial parameters, thereby inducing the desired resonance and enabling customized applications to be realized.
•Theoretical breakthrough: An algebraic framework for analyzing the plasmon modes is derived for multi-layered structures.•Numerically, it is quite easy to compute all the eigen modes by finding the roots to the exact polynomial derived.•Numerical findings: increase of layers could help to enlarge localized resonant band gap.
The maritime communication network is assembled by emergent network technologies. However, the adverse maritime environment impedes the efficiency of resources allocation in maritime communication ...network. Here we show a joint sleeping scheduling and opportunistic transmission scheme in delay-tolerant maritime wireless communication networks based on software defined networking (SDN) to find a better tradeoff between the energy consumption and the delay. Specifically, an energy-limited delay tolerant networking (DTN) node deployed in the ocean receives/transmits data from/to vessels within its communication range. To further save the energy, a long-term energy minimization problem is formulated with sleeping scheduling and opportunistic transmission. After that, a multi-objective minimization problem of energy and delay is first modeled by Lyapunov optimization (LO), which then is solved by convex optimization. Both mathematical analyses and simulation results demonstrate how the maritime communication network allocates satisfactorily with the proposed allocation scheme.
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•The HIPs with high ionic density (up to 3.01 mmol g−1) were synthesized through Friedel-Crafts alkylation of ionic monomers with multiple ionic pairs.•The ionic content and specific ...surface area of HIPs can be finely tuned by changing the type of ionic monomers and crosslinkers and their molar ratio.•The catalyst HBIM-6Br-DCX(3) exhibited excellent catalytic activity (90% yield) for cycloaddition of CO2 with styrene oxide at 120 ℃, 1 bar simulated flue gas (15% CO2 and 85 % N2) in 15 h.•The catalyst can be easily separable and maintained high reusability and stability after running five times.
Designing and preparing hypercrosslinked ionic polymers (HIPs) with high ionic density for CO2 conversion is a significant challenge in materials science. Herein, the simple Friedel-Crafts alkylation synthesized a series of imidazolium-based HIPs with different ionic densities and porosities. Among these HIPs, HBIM-6Br-DCX(3) with high ionic content (2.31 mmol g−1) was prepared through Friedel-Crafts alkylation of alpha'-Dichloro-p-xylene with a monomer BIM-6Br, in which BIM-6Br produced from the reaction of 1,2,3,4,5,6-hexakis(bromomethyl)benzene with 1-benzylimidazole. What's more, in the absence of co-catalysts, solvents and additives, the metal-free catalyst HBIM-6Br-DCX(3) exhibited excellent catalytic activity for the conversion of CO2 with various epoxides into corresponding cyclic carbonates at atmospheric pressure in the ultrashort reaction time because its high ionic density provides abundant imidazolium cations and bromide anions as active sites, and 99% yield and 99% selectivity were achieved for cycloaddition of CO2 with epichlorohydrin and epibromohydrin within 1 h. The reaction time is shorter than most reported porous ionic polymer catalysts under the same conditions (styrene oxide, 120 ℃, 4 h, 99% yield; 100 ℃, 10 h, 97% yield). Notably, styrene oxide (SO) was converted into styrene carbonate (SC) with 90% yield under simulated flue gas (1 bar, 15% CO2 and 85 % N2) in 15 h. Furthermore, the catalyst was easily separable and maintained high reusability and stability after running five times. This work provides a new strategy to synthesize HIPs with high ionic density and the obtained HIPs can be used as efficient catalysts for rapidly converting CO2 with epoxides into cyclic carbonates at low pressure.
Multi-layer structures are ubiquitous in constructing metamaterial devices to realise various frontier applications including super-resolution imaging and invisibility cloaking. In this paper, we ...develop a general mathematical framework for studying elastostatics within multi-layer material structures in R d , d = 2, 3. The multi-layer structure is formed by concentric balls and each layer is filled by either a regular elastic material or an elastic metamaterial. The number of layers can be arbitrary and the material parameters in each layer may be different from one another. In practice, the multi-layer structure can serve as the building block for various material devices. Considering the impingement of an incident field on the multi-layer structure, we first derive the exact perturbed field in terms of an elastic momentum matrix, whose dimension is the same as the number of layers. By highly intricate and delicate analysis, we derive a comprehensive study of the spectral properties of the elastic momentum matrix. This enables us to establish a handy algebraic framework for studying polariton resonances associated with multi-layer metamaterial structures, which forms the fundamental basis for many metamaterial applications.
•The metal-free HIPs catalysts with multi-ionic sites, high ionic density and hydrogen bond donors were synthesized.•The introduction of HIPs with multi-ionic sites has a synergistic effect on the ...improvement of catalytic performance for CO2 cycloaddition reaction.•The catalyst HBIM(0.5)@QA-Br exhibited excellent catalytic activity for cycloaddition of CO2 with epoxides at atmospheric pressure in the short reaction time.
High catalytic activity for the conversion of CO2 into cyclic carbonates requires the preparation of porous ionic catalysts with multi-active sites and high ionic density. Herein, a series of hypercrosslinked ionic polymers (HIPs) with multi-ionic sites, high ionic density and hydrogen bond donors (imino group) were synthesized through the one-pot Friedel–Crafts alkylation and post-synthetic strategies. Adsorption measurements showed that HIPs exhibited outstanding CO2 uptakes (1.80−2.97 mmol g − 1, 273 K and 1 bar). Importantly, under the synergistic effects of multi-ionic sites, high ionic density and hydrogen bond donors, the metal-free catalyst HBIM(0.5)@QA-Br showed excellent catalytic yield (99%) and selectivity (99%) for cycloaddition of CO2 with epichlorohydrin at 140 °C, 0.1 MPa CO2 in 2 h. By extending the time appropriately, high catalytic yields (styrene oxide, 140 °C, 4 h, 99% yield; 120 °C, 6.5 h, 93% yield; 100 °C, 16 h, 94% yield) were achieved at low temperature. In addition, the catalyst can be easily reused with stable recyclability. This work not only provides a new strategy to prepare metal-free porous ionic catalysts with multi-ionic sites and hydrogen bond donors but also demonstrated that the synergistic catalysis of multi-ionic sites is helpful to promote CO2 conversion.
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