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We report the use of polymer N -heterocyclic carbenes (NHCs) to control the microenvironment surrounding metal nanocatalysts, thereby enhancing their catalytic performance in CO 2 electroreduction. Three polymer NHC ligands were designed with different hydrophobicity: hydrophilic poly(ethylene oxide) (PEO–NHC), hydrophobic polystyrene (PS–NHC), and amphiphilic block copolymer (BCP) (PEO- b -PS–NHC). All three polymer NHCs exhibited enhanced reactivity of gold nanoparticles (AuNPs) during CO 2 electroreduction by suppressing proton reduction. Notably, the incorporation of hydrophobic PS segments in both PS–NHC and PEO- b -PS–NHC led to a twofold increase in the partial current density for CO formation, as compared to the hydrophilic PEO–NHC. While polymer ligands did not hinder ion diffusion, their hydrophobicity altered the localized hydrogen bonding structures of water. This was confirmed experimentally and theoretically through attenuated total reflectance surface-enhanced infrared absorption spectroscopy and molecular dynamics simulation, demonstrating improved CO 2 diffusion and subsequent reduction in the presence of hydrophobic polymers. Furthermore, NHCs exhibited reasonable stability under reductive conditions, preserving the structural integrity of AuNPs, unlike thiol-ended polymers. The combination of NHC binding motifs with hydrophobic polymers provides valuable insights into controlling the microenvironment of metal nanocatalysts, offering a bioinspired strategy for the design of artificial metalloenzymes. 

Abstract This report presents adaptive artificial compression methods in which the time-step and artificial compression parameter ε are independently adapted. The resulting algorithms are supported by analysis and numerical tests. The first and second-order methods are embedded. As a result, the computational, cognitive, and space complexities of the adaptive ε , k algorithms are negligibly greater than that of the simplest, first-order, constant ε , constant k artificial compression method. 

Abstract Artificial compression methods are used in computational fluid dynamics as a cost‐effective way of solving for the velocity and pressure in a flow. However, relaxation of compressibility in these algorithms yields nonphysical oscillations in the pressure. This report presents analysis and computational tests of time filters to reduce nonphysical acoustic waves in artificial compression methods. 

Artificial compression methods create nonphysical acoustic waves. Time filters, often used in geophysical fluid dynamics, are shown in this paper to selectively damp these acoustics. We analyze the stability of a two‐step artificial compression method with the Robert–Asselin (RA) time filter, and provide tests delineating the filter's positive effects on both stability and accuracy.