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Gas Separations using Nanoporous Atomically Thin Membranes: Recent Theoretical, Simulation, and Experimental Advances
Abstract Porous graphene and other atomically thin 2D materials are regarded as highly promising membrane materials for high‐performance gas separations due to their atomic thickness, large‐scale synthesizability, excellent mechanical strength, and chemical stability. When these atomically thin materials contain a high areal density of gas‐sieving nanoscale pores, they can exhibit both high gas permeances and high selectivities, which is beneficial for reducing the cost of gas‐separation processes. Here, recent modeling and experimental advances in nanoporous atomically thin membranes for gas separations is discussed. The major challenges involved, including controlling pore size distributions, scaling up the membrane area, and matching theory with experimental results, are also highlighted. Finally, important future directions are proposed for real gas‐separation applications of nanoporous atomically thin membranes.
Investigating microstructure evolution in block copolymer membranes
Block copolymer self-assembly in conjunction with nonsolvent-induced phase separation (SNIPS) has been increasingly leveraged to fabricate integral-asymmetric membranes. The large number of formulation and processing parameters associated with SNIPS, however, has prevented the reliable construction of high performance membranes. In this study, we apply dynamical self-consistent field theory to model the SNIPS process and investigate the effect of various parameters on the membrane morphology: solvent selectivity, nonsolvent selectivity, initial film composition, and glass transition composition. We examine how solvent selectivity and concentration of polymers in the film impact the structure of micelles that connect to form the membrane matrix. In particular, we find that preserving the order in the surface layer and forming a connection between the supporting and surface layer are nontrivial and sensitive to each parameter studied. Furthermore, the effect of each parameter is discussed, and suggestions are made for successfully fabricating viable block copolymer membranes.
Highly Efficient Urea Oxidation via Nesting Nano-Nickel Oxide in Eggshell Membrane-Derived Carbon
Here, we reported a strategy of using an eggshell membrane to produce hierarchically porous carbon as a low-cost substrate for synthesizing a nano-nickel oxide catalyst (C@NiO), which can effectively turn biowaste—urea—into energy through an electrochemical approach. Here, the interwoven carbon networks within NiO led to highly efficient urea oxidation due to the strong synergistic effect. The as-prepared electrode only needed 1.36 V versus reversible hydrogen electrode to realize a high efficiency of 10 mA cm –2 in 1.0 M KOH with 0.33 M urea and delivered an even higher current density of 25 mA cm –2 at 1.46 V, which is smaller than that of the porous carbon and commercial Pt/C catalyst. Benefiting from theoretical calculations, Ni(III) active species and the porous carbon further enabled the electrocatalyst to effectively inhibit the “CO 2 poisoning” of electrocatalysts, as well as ensuring its superior performance for urea oxidation.
Fluorine-Free Ion-Selective Membrane with Enhanced Mg 2+ Transport for Mg-Organic Batteries
Magnesium batteries offer a safer alternative for next-generation battery technology due to their insusceptibility to dendrite deposition. Selective membranes tailored for magnesium-ion conduction will unlock further technological advancement. Herein, we demonstrate fluorine-free magnesiated sulfonated poly(ether ether ketone) (Mg-SPEEK) selective membranes capable of facilitating magnesium-ion conduction while effectively rejecting soluble organic species. These membranes demonstrate a reversible Mg plating and stripping Coulombic efficiency (CE) of 85.4% and an ionic conductivity of 3.3 × 10 –4 S cm –1 at room temperature, surpassing those for a Mg-Nafion selective membrane. Theoretical density functional theory (DFT) calculations reveal that SPEEK possesses more localized charge centers along its backbone compared with Nafion, potentially facilitating enhanced ion conduction. Finally, full cells assembled with Mg-SPEEK coupled with the organic cathode pyrene-4,5,9,10-tetraone (PTO) and Mg metal demonstrated significantly improved capacity retention as compared to those assembled with conventional nonselective separators.
An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS
Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.
Extended Donnan-Manning theory for selective ion partition and transport in ion exchange membrane
The use of ion exchange membranes (IEMs) for electrochemical ion-ion separation leverages the selectivity of the IEMs toward like-charged species via valence difference and/or other ion membrane interactions. A mechanistic model that relates selectivity with membrane structural and chemical properties is lacking in the literature. Here, in this study, we extend the Manning’s counter-ion condensation model for describing ion partition and ion mobility inside IEMs to mixed salts scenarios. We evaluate the extended Donnan-Manning model against experimental data from literature and compare the performance the Donnan-Manning model to that of the ideal Donnan model and the Donnan-Affinity model. Our analysis shows that, despite its structural complexity, the Donnan-Manning model has less fitting parameters than the Donnan-Affinity model and generally outperforms the two other models in predicting counter-ion and co-ion partition. With the assumption of a higher mobility of condensed ions than that of uncondensed ions, the generalized Manning’s model can also predict counter-ion mobility selectivity for cation exchange membranes, but its performance for predicting mobility selectivity for anion exchange membranes is still unsatisfactory.
Strain-Modified Raman Responses in Monolayer MoS 2 Nanobubbles Resolved at 5 nm
The formation of nanoscale bubbles is an unavoidable consequence during the transfer of two-dimensional materials onto target substrates, driven by van der Waals interactions at the interface. While often viewed as imperfections, these nanoscale bubbles have garnered considerable scientific interest due to the substantial in-plane strain gradients they induce, which in turn give rise to a variety of intriguing optoelectronic effects, particularly in semiconducting transition metal dichalcogenides. Determining and analyzing the strain distribution within nanobubbles at the nanoscale is crucial for advancing our understanding of these underlying strain-induced effects. Here, we present a high-resolution scanning tunneling microscopy-based tip-enhanced Raman spectroscopic investigation of localized nanoscale strain distribution within the nanobubbles formed between monolayer MoS 2 and Au interface. By employing cryogenic temperature (78 K), we successfully differentiate the nanoscale Raman signatures between nanobubble edge and pristine MoS 2 . We verify a maximum tensile strain of ∽1.15–1.34% at the nanobubble edge, which gradually diminishes toward the center, yielding a cross-sectional strain profile consistent with a doughnut-shaped distribution. Furthermore, we report to achieve ∽5 nm spatial resolution in probing such edge-localized strain within the nanobubble. In addition, comparative average strain analysis of such MoS 2 nanobubbles is conducted via geometric mechanistic analysis such as membrane and nonlinear plate theories, providing key insight into the geometric nature near the bubble edge. Our work provide fundamental information about strain-induced nanoscale chemical understanding of 2D materials on the nanometer scale, paving the way for practical applications of nanobubbles in strain-engineered optoelectronic devices.
Irreversible thermodynamics of curved lipid membranes. II. Permeability and osmosis
We present a theory that combines the framework of irreversible thermodynamics with modified integral theorems to model arbitrarily curved and deforming membranes immersed in bulk fluid solutions. We study the coupling between the mechanics and permeability of a viscous and elastically bendable membrane, and a multicomponent bulk fluid solution. An equation for the internal entropy production for irreversibilities at the membrane is derived, determining the generalized thermodynamic forces and fluxes, from which we identify the deviatoric stress as a novel driving force for permeability. A complete set of equations of motion, constitutive laws, and boundary conditions to model the lipid membrane and bulk fluid system are provided.
The current status of high temperature electrochemistry-based CO 2 transport membranes and reactors for direct CO 2 capture and conversion
The concept of direct CO 2 capture and conversion has attracted significant interest from industries and academia in recent decades due to its potential to address the current grand challenge of global warming/climate change, rapid depletion of fossil fuels and realization of a future carbon neutral ecosystem. The incumbent benchmark technology for CO 2 capture is the post-combustion flue-gas “amine washing”, which is energy intensive and costly for large-scale commercial implementation. The CO 2 conversion technologies, on the other hand, are still at their infancy with many technical challenges to overcome, but primarily being explored in laboratory-scale, low-temperature, solution-based and high-temperature, solid-oxide-based electrochemical cells with renewable electricity perceived as the energy input. In this article, we provide a comprehensive overview on an emergent class of high-temperature electrochemical CO 2 transport membranes that can capture and convert CO 2 into valuable chemicals in single catalytic reactor fashion. The review starts with the chemistry and transport theory of three basic types of membranes purposely designed for different CO 2 feedstocks and downstream conversions. A range of key functional materials used in these membranes and their microstructural/electrochemical properties important to the CO 2 transport are then thoroughly discussed in conjunction with the effects of surface modifications and operating conditions. Several types of combined CO 2 capture and conversion catalytic reactors based on these membranes are also assessed with a focus on their working principles, system configurations and performance demonstrations. Finally, challenges and prospective of these electrochemical CO 2 transport membranes and their associated conversion reactors are candidly discussed for future development.
Experimental observation of nonlinear relation between pressure and water flux is consistent with the solution-diffusion model
In several recent studies, it has been proposed that the fundamental understanding of penetrant transport in dense polymer membranes occurring via the solution-diffusion model, which has been the generally accepted theoretical framework for describing penetrant transport in such materials for the past several decades, is flawed. An alternate mechanistic framework based on the idea of two-phase flow in a porous medium (i.e., pore-flow) has been broadly advanced instead, with proponents of this approach claiming that the pore-flow theoretical framework provides the necessary mechanistic insight to design novel polymeric membrane materials for emerging applications. In this study, we show experimental results for hydraulic permeation of water that are entirely consistent with the solution-diffusion theory, without modification, for three dense polymeric membranes: crosslinked poly(ethylene glycol diacrylate) (XLPEGDA), Nafion 117 ionomer in the sodium counterion form (Nafion 117-Na), and cellulose acetate (CA). By measuring water flux at transmembrane pressures up to 240 bar, we observe a nonlinear relationship between the transmembrane pressure (TMP) and water flux, J w , for XLPEGDA and Nafion 117-Na, while this relationship is linear for CA. We demonstrate that the behavior of these three materials is described via the solution-diffusion model. According to the solution-diffusion model, flux is, to a good approximation, proportional to the transmembrane concentration difference induced by the pressure difference across the membrane, rather than to TMP itself. Water sorption isotherms are reported for all three materials. They further justify the nonlinear relationship between TMP and J w observed in XLPEGDA and Nafion 117-Na, emphasizing that the nonlinearity in the flux/TMP relationship stems from nonlinearities in the sorption isotherm with pressure. Additionally, the relationship between water flux and TMP can be predicted, a priori, with no adjustable parameters when a predictive model for the diffusion coefficient of water is employed in conjunction with the experimental water sorption isotherms in the solution-diffusion model. Furthermore, our results demonstrate the validity of the solution-diffusion model to describe transport of penetrants in dense polymer membranes, while highlighting the sensitivity of the solution-diffusion model to the many physical and mathematical simplifications commonly applied to the theory in literature.
Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements
Here we propose new quadrature schemes that asymptotically require only four in-plane points for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree p of the elements. The quadrature points are Greville abscissae associated with pth-order B-spline basis functions whose continuities depend on the specific Galerkin formulations, and the quadrature weights are calculated by solving a linear moment fitting problem in each parametric direction. The proposed shell element formulations are shown through numerical studies to be rank sufficient and to be free of spurious modes. The studies reveal comparable accuracy, in terms of both displacement and stress, compared with fully integrated spline-based shell elements, while at the same time reducing storage and computational cost associated with forming element stiffness and mass matrices and force vectors. The high accuracy with low computational cost makes the proposed quadratures along with higher-order spline bases, in particular polynomial orders, p = 5 and 6, good choices for alleviating membrane and shear locking in shells.
Multiscale modeling of solute diffusion in triblock copolymer membranes
We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model’s predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Furthermore, our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.
Anyonic Membranes and Pontryagin Statistics
Anyons, unique to two spatial dimensions, underlie extraordinary phenomena such as the fractional quantum Hall effect, but their generalization to higher dimensions has remained elusive. The topology of Eilenberg-MacLane spaces constrains the loop statistics to be only bosonic or fermionic in any dimension. In this work, we introduce the novel anyonic statistics for membrane excitations in four dimensions. Analogous to the $\mathbb{Z}_N$-particle exhibiting $\mathbb{Z}_{N\times \gcd(2,N)}$ anyonic statistics in two dimensions, we show that the $\mathbb{Z}_N$-membrane possesses $\mathbb{Z}_{N\times \gcd(3,N)}$ anyonic statistics in four dimensions. Given unitary volume operators that create membrane excitations on the boundary, we propose an explicit 56-step unitary sequence that detects the membrane statistics. We further analyze the boundary theory of $(5{+}1)$D 1-form $\mathbb{Z}_N$ symmetry-protected topological phases and demonstrate that their domain walls realize all possible anyonic membrane statistics. We then show that the $\mathbb{Z}_3$ subgroup persists in all higher dimensions. In addition to the standard fermionic $\mathbb{Z}_2$ membrane statistics arising from Stiefel-Whitney classes, membranes also exhibit $\mathbb{Z}_3$ statistics associated with Pontryagin classes. We explicitly verify that the 56-step process detects the nontrivial $\mathbb{Z}_3$ statistics in 5, 6, and 7 spatial dimensions. Furthermore, in 7 and higher dimensions, the statistics of membrane excitations stabilize to $\mathbb{Z}_{2} \times \mathbb{Z}_{3}$, with the $\mathbb{Z}_3$ sector consistently captured by this process.
Computational Evaluation of Carriers in Facilitated Transport Membranes for Postcombustion Carbon Capture
Incorporating molecular amines as mobile carriers in facilitated transport membranes (FTMs) has been demonstrated to significantly enhance the CO 2 permeance and CO 2 /N 2 selectivity of the membrane for CO 2 capture from flue gas. In this study, by employing computational techniques including density functional theory calculations and molecular simulations, the role of mobile carriers has been systematically studied at a molecular level from the perspectives of the amine–CO 2 reaction chemistry, diffusivities of carriers and gases, and N 2 solubility. The latter two properties were also investigated as a function of water uptake. The water uptake values of FTMs were experimentally quantified too. The introduction of mobile carriers was shown to substantially enhance the diffusivities of CO 2 reaction products compared to FTMs without mobile carriers. The choice of mobile carriers was also demonstrated to influence the separation performance. Computationally, 2-(1-piperazinyl)ethylamine sarcosinate (PZEA-Sar) exhibited a faster reaction kinetics and slightly higher CO 2 absorption capacity as compared to piperazine glycinate (PZ-Gly). Experimentally, the FTM incorporating PZEA-Sar mobile carriers also showed a higher CO 2 permeance. The good agreement validated the computational models employed and insights generated in this study. In conclusion, the outcomes of this work shed light on the future design and selection of carrier structures, and the adopted computational approaches can be employed to discover promising mobile carrier candidates.
13 C NMR study of amino acid salts in facilitated transport membranes for post-combustion carbon capture
Some of amino acid salts (AASs) have been demonstrated to be effective mobile carriers in facilitated transport membranes (FTMs) to achieve superior CO 2 permeance and CO 2 /N 2 selectivity for CO 2 capture from flue gas. Understandings of how the structures of different AASs affect the chemistry of the amine–CO 2 reaction are essential for the future development of more efficient AAS mobile carriers. In this study, the reaction chemistry of selected AASs with CO 2 was investigated by 13 C nuclear magnetic resonance (NMR) spectroscopy. The CO 2 loading and the distribution of major reaction products, including carbamate and bicarbonate products of each studied AAS were quantitatively analyzed. The positive correlation between the CO 2 loading of AAS (mol CO 2 /g AAS) and the CO 2 permeance of FTMs suggested that AAS with a higher CO 2 loading may improve the performance of FTMs. Our results also showed that increasing the steric hindrance of AAS could be a practical way to promote the bicarbonate reaction pathway and thus potentially increase the CO 2 loading (mol CO 2 /mol AAS). Moreover, 2-(1-piperazinyl)ethylamine (PZEA) was found to be a more effective multi-amine than piperazine (PZ) for synthesizing AASs due to the presence of more effective nitrogen sites per molecule. The superior CO 2 permeance of the PZEA-Sar membrane is also attributed to its more uniform membrane formation. As a result, the knowledge gained from this study will inform the rational design of more effective AAS carriers for CO 2 capture.
Theoretical Pathway toward Improved Reverse Osmosis Membrane Selectivity for Neutral Solutes: Inspiration from Gas Separations
We report highly rigid membrane materials with tailored structures have exhibited permeabilities and selectivities that exceed the polymer upper bound in gaseous and organic solvent separations for challenging mixtures containing species that are similar in size and shape. One potential question is whether such membrane materials can maintain meaningful guest diffusivities in situations where the microporous spaces are essentially full of guest molecules. Here, we use a simplified transition state theory approach to estimate the diffusivity of water and small organics within a microporous membrane. The transition state theory model is parameterized using experimental values from zeolites and carbon molecular sieve materials found in the literature. We demonstrate the differences in transport and Maxwell–Stefan diffusivities based on guest species loading with different isotherm behaviors. These calculations theorize a path forward for highly selective reverse osmosis membranes for aqueous phase separations.
Iridium Oxide Coordinatively Unsaturated Active Sites Govern the Electrocatalytic Oxidation of Water
A special membrane electrode assembly to measure operando X-ray absorption spectra and resonant photoemission spectra of mesoporous templated iridium oxide films is used. These films are calcined to different temperatures to mediate the catalyst activity. By combining operando resonant photoemission measurements of different films with ab initio simulations these are able to unambiguously distinguish µ 2 -O (bridging oxygen) and µ 1 -O (terminal oxygen) in the near-surface regions of the catalysts. The intrinsic activity of iridium oxide scales with the formation of µ1-O (terminal oxygen) is found. Importantly, it is shown that the peroxo species do not accumulate under reaction conditions. Rather, the formation of µ 1 -O species, which are active in O-O bond formation during the OER, is the most oxidized oxygen species observed, which is consistent with an O-O rate-limiting step. Thus, the oxygen species taking part in the electrochemical oxidation of water on iridium electrodes are more involved and complex than previously stated. This result highlights the importance of employing theory together with true and complementary operando measurements capable of probing different aspects of catalysts surfaces during operation.