Molecularly engineering polymeric membranes for H2/CO2 separation at 100–300 °C

Over the last two decades, polymers with superior H₂/CO₂ separation properties at 100–300 °C have gathered significant interest for H₂ purification and CO₂ capture. This timely review presents various strategies adopted to molecularly engineer polymers for this application. We first elucidate the Robeson's upper bound at elevated temperatures for H₂/CO₂ separation and the advantages of high-temperature operation (such as improved solubility selectivity and absence of CO₂ plasticization), compared with conventional membrane gas separations at ~35 °C. Second, we describe commercially relevant membranes for the separation and highlight materials with free volumes tuned to discriminate H₂ and CO₂, including functional polymers (such as polybenzimidazole) and engineered polymers by cross-linking, blending, thermal treatment, thermal rearrangement, and carbonization. Third, we succinctly discuss mixed matrix materials containing size-sieving or H₂-sorptive nanofillers with attractive H₂/CO₂ separation properties.     

Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators

Numerical Algorithms - In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert...     

Existence of multi-solitary waves with logarithmic relative distances for the NLS equation

We construct 2-solitary wave solutions with logarithmic distance to the nonlinear Schrödinger equation,

$\mathrm{i}{?}_{t}u+\mathrm{\Delta }u+|u{|}^{p?1}u=0,t\in \mathbb{R},x\in {\mathbb{R}}^d,$

in mass-subcritical cases $1<p<1+\frac{4}{d}$ and mass-supercritical cases $1+\frac{4}{d}<p<\frac{d+2}{d?2}$, i.e. solutions $u(t)$ satisfying

${6u(t)?{\mathrm{e}}^{\mathrm{i}\gamma (t)}\sum _{k=1}^{2}Q(??x_k(t))6}_{H^1}\to 0$

and

$|x_1(t)?x_2(t)|～2\log ?t,\text{as}t\to +\infty ,$

where Q is the ground state. The logarithmic distance is related to strong interactions between solitary waves.In the integrable case ($d=1$ and $p=3$), the existence of such solutions is known by inverse scattering (E. Olmedilla, Multiple pole solutions of the nonlinear Schrödinger equation, Physica D 25 (1987) 330–346; T. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972) 62–69). The mass-critical case $p=1+\frac{4}{d}$ exhibits a specific behavior related to blow-up, previously studied in Y. Martel, P. Raphaël (Strongly interacting blow up bubbles for the mass critical NLS, Ann. Sci. Éc. Norm. Supér. 51 (2018) 701–737).     

On periodic subsolutions to steady second-order systems and applications

Bostan and Namah (Remarks on bounded solutions of steady Hamilton–Jacobi equations, C. R. Acad. Sci. Paris, Ser. I 347(15–16) (2009) 873–878) proved that constant functions are the only bounded solutions to $H(Du)=H(0)$ when H is superlinear and strictly convex. In this short note, we present a proof other than that of Bostan and Namah for equations that can be easily applied to some types of possibly degenerate parabolic systems. Our proof applies for periodic subsolutions instead of bounded solutions like that of Bostan and Namah; however, we need periodic subsolutions, which is quite restrictive. We do not consider Hopf–Lax's formula in our proof, so we can relax some restrictions on H. We also present an application to the large-time behavior of solutions to degenerate parabolic systems.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

Acetyl Methyl Torsion in N‐Ethylacetamide: A Challenge for Microwave Spectroscopy and Quantum Chemistry

The gas‐phase structures and parameters describing acetyl methyl torsion of N‐ethylacetamide are determined with high accuracy, using a combination of molecular beam Fourier‐transform microwave spectroscopy and quantum chemical calculations. Conformational studies at the MP2 level of theory yield four minima on the energy surface. The most energetically favorable conformer, which possesses C₁ symmetry, is assigned. Due to the torsional barrier of 73.4782(1) cm^?1 of the acetyl methyl group, fine splitting up to 4.9 GHz is found in the spectrum. The conformational structure is not only confirmed by the rotational constants, but also by the orientation of the internal rotor. The ¹⁴N quadrupole hyperfine splittings are analyzed and the deduced coupling constants are compared with the calculated values.     

Visible-Light-Induced Control over Reversible Single-Chain Nanoparticle Folding

We introduce a class of single-chain nanoparticles (SCNPs) that respond to visible light (λ_max=415 nm) with complete unfolding from their compact structure into linear chain analogues. The initial folding is achieved by a simple esterification reaction of the polymer backbone constituted of acrylic acid and polyethylene glycol carrying monomer units, introducing bimane moieties, which allow for the photochemical unfolding, reversing the ester-bond formation. The compaction and the light driven unfolding proceed cleanly and are readily followed by size exclusion chromatography (SEC) and diffusion ordered NMR spectroscopy (DOSY), monitoring the change in the hydrodynamic radius (R_H). Importantly, the folding reaction and the light-induced unfolding are reversible, supported by the high conversion of the photo cleavage. As the unfolding reaction occurs in aqueous systems, the system holds promise for controlling the unfolding of SCNPs in biological environments.     

Nitrile Oxide‐Norbornene Cycloaddition as a Bioorthogonal Crosslinking Reaction for the Preparation of Hydrogels

This communication describes the first application of cycloaddition between an in situ generated nitrile oxide with norbornene leading to a polymer crosslinking reaction for the preparation of poly(ethylene glycol) hydrogels under physiological conditions. Hydrogels with high water content and robust physical strength are readily formed within 2–5 min by a simple two‐solution mixing method which allows 3D encapsulation of neuronal cells. This bioorthogonal crosslinking reaction provides a simple yet highly effective method for preparation of hydrogels to be used in bioengineering.