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At least 847 records · Page 47

Molecular Tuning of Ether Cosolvent Chemistry for High-Voltage Sodium-Ion Batteries

Ethers as electrolyte cosolvents in sodium-ion batteries (SIBs) provide favorable Na + solvation and interfacial properties, but their low oxidative stability limits their use in high-voltage SIBs. Herein, we address this limitation via molecular tuning of ether cosolvents for high-voltage (4.2 V) hard carbon || NaNi 0.33 Fe 0.33 Mn 0.33 O 2 full cells. Tetrahydropyran (THP) is functionalized with a nitrile group to form tetrahydropyran-4-carbonitrile (THPCN). To delineate the effect of nitrile functionalization and benchmark ether against a conventional carbonate, THP, THPCN, and diethyl carbonate (DEC) are evaluated as cosolvents with ethylene carbonate. Nitrile functionalization lowers the HOMO energy of the ether, extends the electrolyte stability window, and alters Na⁺ solvation. Spectroscopic techniques and molecular dynamics simulations reveal that THPCN exhibits predominantly aggregate-dominated solvation (95.1 %) with weakened Na + -solvent interactions, producing the most anion-rich environment relative to DEC and THP cosolvents. THPCN-modified solvation promotes the formation of highly conductive, fluorine-enriched interphases that suppress parasitic reactions. Pouch full cells with THPCN sustained ~ 600 cycles at 4.2 V, outperforming THP and DEC. Operando gas analysis reveals that THPCN reduces CO 2 generation by 45% and H 2 generation by 30% relative to THP. Furthermore, the findings demonstrate nitrile functionalization as a molecular design strategy to stabilize ethers and enable high-voltage SIBs.

25 ENERGY STORAGE↗

Tensor renormalization group approach to the $O(2)$ models via symmetry-twisted partition functions

We investigate critical phenomena in the $O(2)$ models using symmetry-twisted partition functions that can be efficiently computed within the tensor renormalization group framework. We first demonstrate, taking the three-dimensional model as an example, that symmetry-twisted partition functions detect the spontaneous breaking of global continuous symmetry. We then consider the same model in two dimensions, where the Berezinskii--Kosterlitz--Thouless (BKT) transition occurs. Since symmetry-twisted partition functions directly provide the helicity modulus at a finite twist angle, we determine the BKT transition point. These results are presented based on Ref.~\cite{Akiyama:2026dzg}. Finally, in addition to the original paper~\cite{Akiyama:2026dzg}, we apply this approach to the two-dimensional generalized $O(2)$ model and confirm that it successfully identifies the phase transitions between the ferromagnetic and nematic phases, as well as between the nematic and paramagnetic phases.

Akiyama, Shinichiro [Tsukuba U., CCS; Tokyo U., IC↗

Mechanically and Thermally Enhanced 3D-Printed Photocurable Polymer Nanocomposites Containing Functionalized Chitin Nanowhiskers by Stereolithography

Additive manufacturing, or simply 3D printing (3DP), where objects are built through layer-wise material deposition, has gained significant academic and industrial attention as a result of the development of advanced and functional materials requiring rapid, customized, and flexible solutions. In the context of green manufacturing, diversifying environmentally and economically sustainable material portfolios is an essential endeavor for the success of 3DP technology that uses widely available, highly valuable, and renewable materials. Here, we used stereolithography (SLA) for processing methacrylate-based photocurable resins containing crab shell-derived chitin nanowhiskers (CNWs), which are surface-functionalized by reactive acrylate groups. Results from full spectral, thermal, structural, and topological analyses corroborate not only the surface functionalization of CNWs but also indicate the presence of these photocurable CNW (pCNW) fillers in the 3D-printed nanocomposites. Owing to the strong interfacial bond induced by the physical and chemical crosslinking between the pCNW and methacrylate (MA) polymer matrix, the internally formulated nanocomposites displayed enhanced thermomechanical properties (e.g., storage modulus and glass transition temperature) compared to those of commercially available pure SLA resins. For instance, the inclusion of 0.5 wt % pCNW improved the tensile strength and stiffness to up to 78 and 71%, respectively, without compromising the toughness and ductility of the printed material. Accordingly, this result also evidences the compatibility between the filler and resin materials. Consequently, the formation of a crosslinked network in the nanocomposite structure results in a higher thermal stability and activation energy (i.e., up to ~79%) for all the hybrid materials than the pristine MA. Finally, the high-resolution SLA print features, dimensional accuracy, and enhanced mechanical performance of our microstructure-forming functionalized chitin-based nanocomposites make them promising materials for a wide range of robust and high-performance industrial applications.

36 MATERIALS SCIENCE↗

Metal-hydrogen-pi-bonded organic frameworks

We report the synthesis and characterization of a new series of permanently porous, three-dimensional metal–organic frameworks (MOFs), M-HAF-2 (M = Fe, Ga, or In), constructed from tetratopic, hydroxamate-based, chelating linkers. Here, the structure of M-HAF-2 was determined by three-dimensional electron diffraction (3D ED), revealing a unique interpenetrated hcb-a net topology. This unusual topology is enabled by the presence of free hydroxamic acid groups, which lead to the formation of a diverse network of cooperative interactions comprising metal–hydroxamate coordination interactions at single metal nodes, staggered π–π interactions between linkers, and H-bonding interactions between metal-coordinated and free hydroxamate groups. Such extensive, multimodal interconnectivity is reminiscent of the complex, noncovalent interaction networks of proteins and endows M-HAF-2 frameworks with high thermal and chemical stability and allows them to readily undergo postsynthetic metal ion exchange (PSE) between trivalent metal ions. We demonstrate that M-HAF-2 can serve as versatile porous materials for ionic separations, aided by one-dimensional channels lined by continuously π-stacked aromatic groups and H-bonding hydroxamate functionalities. As an addition to the small group of hydroxamic acid-based MOFs, M-HAF-2 represents a structural merger between MOFs and hydrogen-bonded organic frameworks (HOFs) and illustrates the utility of non-canonical metal-coordinating functionalities in the discovery of new bonding and topological patterns in reticular materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chitosan as a Canvas for Studies of Macromolecular Controls on CaCO 3 Biological Crystallization

A mechanistic understanding of how macromolecules, typically as an organic matrix, nucleate and grow crystals to produce functional biomineral structures remains elusive. Advances in structural biology indicate that polysaccharides (e.g., chitin) and negatively charged proteoglycans (due to carboxyl, sulfate, and phosphate groups) are ubiquitous in biocrystallization settings and play greater roles than currently recognized. This review highlights studies of CaCO 3 crystallization onto chitinous materials and demonstrates that a broader understanding of macromolecular controls on mineralization has not emerged. With recent advances in biopolymer chemistry, it is now possible to prepare chitosan-based hydrogels with tailored functional group compositions. By deploying these characterized compounds in hypothesis-based studies of nucleation rate, quantitative relationships between energy barrier to crystallization, macromolecule composition, and solvent structuring can be determined. Finally, this foundational knowledge will help researchers understand composition-structure-function controls on mineralization in living systems and tune the designs of new materials for advanced applications.

15 GEOTHERMAL ENERGY↗

100th Anniversary of Macromolecular Science Viewpoint: Fundamentals for the Future of Macromolecular Nitroxide Radicals

Macromolecular radicals, radical polymers, and polyradicals bear unique functionalities derived from their pendant radical groups. Here, the increasing need for organic functional materials is driving the growth in research interest in macromolecular radicals for batteries, electronics, memory, and imaging. This Viewpoint summarizes the current state-of-knowledge regarding the macromolecular nitroxide radicals’ redox mechanism, conductivity, chain conformation, controlled polymerization, network structure, conjugated forms, and applications. The nitroxide radical group is the focus because it is the most widely studied. Although most literature focuses upon applications, an emerging body of work is highlighting the fundamental physicochemical properties of macromolecular radicals. To this end, this Viewpoint recommends areas of opportunity in fundamental studies and best practices in reporting.

36 MATERIALS SCIENCE↗

Effects of spin-orbit coupling and very large supercells on the description of acceptors in CdTe

Predicting accurate shallow donor and acceptor levels in semiconductors has been quite challenging using periodic boundary conditions as implemented in current density functional theory codes. The reason is that the wave functions associated with the shallow centers are quite extended and are not fully contained in the supercell (typically with a few hundred atoms) so impurities in the periodically repeated image cells interact with each other. Errors of ~0.1 eV are expected, and these are of the same order of magnitude as the ionization energies themselves. In the case of acceptors in CdTe, this problem is exacerbated by the strong spin-orbit coupling that split the Te-related states at the top of the valence band, making the calculations at least 8 times more expensive. CdTe is an important solar-cell material with record high efficiency of 22%. One of the main limiting factors to increasing the efficiency towards the theoretical limit of ~30% is the often reported very low hole concentration. Pushing to the limit of computational capability by using very large supercells with spin-orbit coupling we report the results of hybrid functional calculations of group-V acceptors in CdTe. We show that extrapolation to the dilute limit leads to an interpretation of the experimental data that is qualitatively different from previous DFT and hybrid functional calculation reports. We find that the group-V impurities indeed behave as shallow acceptors and that the corresponding compensating AX-centers are unstable and do not limit p-type doping. We address the differences between our results and previous theoretical predictions and show that our calculated ionization energies predict hole concentrations that are in excellent agreement with recent temperature-dependent Hall measurements on high-quality single-crystal samples.

14 SOLAR ENERGY↗

Theoretical and Experimental Insights into CO 2 Capture and Methanation over Amine-Grafted Ru-Based Catalysts

Carbon capture and storage (CCS) technologies, along with CO 2 capture and conversion methods, have emerged as crucial research areas to address rising CO 2 emissions. In this study, we seek to understand the mechanistic role of amines in enabling lower-energy pathways for CO 2 conversion. Our research focuses on the development and analysis of dual-functional materials (DFMs) engineered for the reactive capture and conversion (RCC) of CO 2 into methane, utilizing Ru catalysts grafted with amine groups. We employ Density Functional Theory (DFT) calculations using methylamine as a model amine to investigate the impact of amine groups on CO 2 methanation on a Ru(0001) surface, both in the presence and absence of amine groups. The amine ligand alters the carbon coordination environment, promoting direct C–O dissociation and potentially destabilizing the CO* adsorbate, thereby reducing the risk of CO poisoning. Additionally, we observe a preference for hydrogenation, although it becomes more energetically uphill in the amine-bound scenario. Our experiments, however, report similar CO 2 conversion and CH 4 production rates over the synthesized catalysts “Ru/TiO 2 ” and the amine (N-(2-aminoethyl)-3-aminoproplytrimethoxysilane (“diaminosilane”)) deposited catalyst “Diamine−Ru/TiO 2 ”. By constructing comparative reaction-free energy diagrams and performing microkinetic modeling (MKM) simulations, we link our theoretical findings with experimentally observed CO 2 uptake, conversion, and methane production rates. A microkinetic model was employed to investigate the anomaly, showing reduced amine–carbon complex coverage and increased CO 2 coverage at all temperatures. The MKM simulations consistently confirmed these trends. In conclusion, this comprehensive approach offers key insights into the role of the amine-CO 2 bond in methanation, highlighting a pathway toward lower-energy, more efficient CO 2 capture and conversion processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermodynamics of calcium binding to heparin: Implications of solvation and water structuring for polysaccharide biofunctions

Heparan sulfates are found in all animal tissues and have essential roles in living systems. This family of biomacromolecules modulates binding to calcium ions (Ca 2+ ) in low free energy reactions that influence biochemical processes from cell signaling and anticoagulant efficacy to biomineralization. Despite their ubiquity, the thermodynamic basis for how heparans and similarly functionalized biomolecules regulate Ca 2+ interactions is not yet established. Using heparosan (Control) and heparins with different positions of sulfate groups, we quantify how SO 3 − and COO − content and SO 3 − position modulate Ca 2+ binding by isothermal titration calorimetry. The free energy of all heparin-Ca2+ interactions (ΔG rxn ) is dominated by entropic contributions due to favorable water release from polar, hydrophilic groups. Heparin with both sulfate esters (O-SO 3 − ) and sulfamides (N-SO 3 − ) has the strongest binding to Ca 2+ compared to heparosan and to heparin with only O-SO 3 − groups (~3X). By linking Ca 2+ binding thermodynamics to measurements of the interfacial energy for calcite (CaCO 3 ) crystallization onto polysaccharides, we show molecule-specific differences in nucleation rate can be explained by differences in water structuring during Ca 2+ interactions. A large entropic term (-TΔS rxn ) upon Ca 2+ –polysaccharide binding correlates with high interfacial energy to CaCO 3 nucleation. Combining our measurements with literature values indicates many Ca 2+ –polysaccharide interactions have a shared thermodynamic signature. The resulting enthalpy–entropy compensation relationship suggests these interactions are generally dominated by water restructuring involving few conformational changes, distinct from Ca 2+ –protein binding. Our findings quantify the thermodynamic origins of heparin-specific interactions with Ca 2+ and demonstrate the contributions of solvation and functional group position during biomacromolecule-mediated ion regulation.

15 GEOTHERMAL ENERGY↗

A Classification of G -invariant Shallow Neural Networks

When trying to fit a deep neural network (DNN) to a G-invariant target function with G a group, it only makes sense to constrain the DNN to be G-invariant as well. However, there can be many different ways to do this, thus raising the problem of “G-invariant neural architecture design”: What is the optimal Ginvariant architecture for a given problem? Before we can consider the optimization problem itself, we must understand the search space, the architectures in it, and how they relate to one another. In this paper, we take a first step towards this goal; we prove a theorem that gives a classification of all G-invariant single-hidden-layer or “shallow” neural network (G-SNN) architectures with ReLU activation for any finite orthogonal group G, and we prove a second theorem that characterizes the inclusion maps or “network morphisms” between the architectures that can be leveraged during neural architecture search (NAS). The proof is based on a correspondence of every G-SNN to a signed permutation representation of G acting on the hidden neurons; the classification is equivalently given in terms of the first cohomology classes of G, thus admitting a topological interpretation. The G-SNN architectures corresponding to nontrivial cohomology classes have, to our knowledge, never been explicitly identified in the literature previously. Using a code implementation, we enumerate the G-SNN architectures for some example groups G and visualize their structure. Lastly, we prove that architectures corresponding to inequivalent cohomology classes coincide in function space only when their weight matrices are zero, and we discuss the implications of this for NAS.

Agrawal, Devanshu↗

Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical 𝑂⁡(2) nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature 𝑇 𝑐 = 2.2017⁢(2) with the critical exponent 𝜈 = 0.663⁢(33) for the 3D 𝑂⁡(2) model. In addition, we also study the Berezinskii–Kosterlitz–Thouless (BKT) criticality of the 2D classical 𝑂⁡(2) model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, 𝑇 BKT = 0.8928⁢(2).

lattice field theory↗

Combining glomerular basement membrane and tubular basement membrane assessment improves the prediction of diabetic end‐stage renal disease

Abstract Background To address the prognostic value of combining tubular basement membrane (TBM) and glomerular basement membrane (GBM) thickness in diabetic nephropathy (DN). Methods This retrospective study enrolled 110 patients with type 2 diabetes and biopsy‐proven DN from 2011 to 2018. The pathological findings were confirmed according to the Renal Pathology Society classifications. GBM and TBM thicknesses were determined using the Haas' direct measurement/arithmetic mean method and orthogonal intercept method, respectively. Cox proportional hazard models were used to investigate the hazard ratios (HRs) for the influence of combined GBM and TBM thickness for predicting end‐stage renal disease (ESRD). Results Patients were assigned to three groups according to the median GBM and TBM thickness: GBM lo TBM lo (GBM < 681 nm and TBM < 1200 nm), GBM hi TBM lo /GBM lo TBM hi (GBM ≥ 681 nm and TBM < 1200 nm, or GBM < 681 nm and TBM ≥ 1200 nm), and GBM hi TBM hi (GBM ≥ 681 nm and TBM ≥ 1200 nm). The GBM hi TBM lo /GBM lo TBM hi and GBM hi TBM hi groups displayed poorer renal function, a more severe glomerular classification and interstitial inflammation, and poorer renal survival rates than the GBM lo TBM lo group The GBM hi TBM lo /GBM lo TBM hi and GBM hi TBM hi groups had adjusted HRs of 1.49 (95% confidence interval [CI], 1.21‐9.75) and 3.07 (95% CI, 2.87‐12.78), respectively, compared with the GBM lo TBM lo group. Conclusions TBM thickness enhanced GBM thickness for renal prognosis in patients with type 2 diabetes.

Zhao, Lijun↗

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Acid-Base Equilibrium and Dielectric Environment Regulate Charge in Supramolecular Nanofibers

Peptide amphiphiles are a class of molecules that can self-assemble into a variety of supramolecular structures, including high-aspect-ratio nanofibers. It is challenging to model and predict the charges in these supramolecular nanofibers because the ionization state of the peptides are not fixed but liable to change due to the acid-base equilibrium that is coupled to the structural organization of the peptide amphiphile molecules. Here, we have developed a theoretical model to describe and predict the amount of charge found on self-assembled peptide amphiphiles as a function of pH and ion concentration. In particular, we computed the amount of charge of peptide amphiphiles nanofibers with the sequence C 16 − V 2 A 2 E 2 . In our theoretical formulation, we consider charge regulation of the carboxylic acid groups, which involves the acid-base chemical equilibrium of the glutamic acid residues and the possibility of ion condensation. The charge regulation is coupled with the local dielectric environment by allowing for a varying dielectric constant that also includes a position-dependent electrostatic solvation energy for the charged species. We find that the charges on the glutamic acid residues of the peptide amphiphile nanofiber are much lower than the same functional group in aqueous solution. There is a strong coupling between the charging via the acid-base equilibrium and the local dielectric environment. Our model predicts a much lower degree of deprotonation for a position-dependent relative dielectric constant compared to a constant dielectric background. Furthermore, the shape and size of the electrostatic potential as well as the counterion distribution are quantitatively and qualitatively different. These results indicate that an accurate model of peptide amphiphile self-assembly must take into account charge regulation of acidic groups through acid–base equilibria and ion condensation, as well as coupling to the local dielectric environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dual Modification of MOFs Improves Dispersion and Ionic Conductivity of Mixed Matrix Membranes

Nonaqueous redox flow batteries (NARFBs) are a promising class of energy storage devices, but the lack of a chemically stable, conductive membrane that exhibits size-selectivity over redox-active species prevents their broader implementation. Recently, metal–organic frameworks (MOFs) have been implemented into mixed-matrix membranes (MMMs) for NARFBs, but the effects of the MOF linker functionality on membrane properties are not well-understood. In this work, we develop a series of MOF-based MMMs by blending postsynthetically modified variants of UiO-66-NH2 with poly(ethylene-co-vinyl acetate). The modification of UiO-66-NH2 with sulfate groups initially resulted in poor dispersion throughout the MMMs, but when dual-modified with poly(N-isopropylacrylamide), MOF dispersion throughout the MMM was improved, and ionic conductivity was significantly higher than the UiO-66-NH2 MMMs. Furthermore, the dual-modified MMMs demonstrated excellent size-selectivity by blocking redox active species transport. This work demonstrates a synergy between the MOF functional groups to improve MMM properties critical for the development of practical NARFBs.

Carey, Cassidy A.↗

Equilibrium carbon isotope fractionation factors of hydrocarbons: Semi-empirical force-field method

Here, we have calculated the reduced partition function ratios for carbon isotopes (β-factor) of 67 hydrocarbons (alkanes, alkenes, alkynes, cycloalkanes, and aromatics), including their 267 single-substituted isotopomers. The calculations were performed using the harmonic oscillator – rigid rotator model and the Urey / Bigeleisen-Mayer approach. Normal frequencies of molecular vibrations of the isotopologues were calculated from the molecular structures data and valence field force constants stored in the Light-handled Elucidation of Vibrations (LEV) database elaborated by Dr. Gribov and his colleagues in Russia. The LEV database is constructed from experimental spectroscopic and structural data by solving inverse problems of molecular vibrations. The LEV is internally consistent and the most comprehensive database available to date. The β-factor were calculated in the temperature range of 200–800 K with a 10 K step. Our calculations predict that the β-factors increase with an increasing number of C atoms within the same groups of hydrocarbons (e.g., alkanes). Our calculations also show a general descending order of 13 C enrichments among the different groups of hydrocarbons: cycloalkanes, aromatics, alkenes (double bonds) and isoalkanes, alkanes, alkynes (triple bonds). Position-specific, intramolecular isotope effects within hydrocarbons are determined by the β-factors of C in the different functional groups in the order: quaternary (C), tertiary (methine, CH), secondary (methylene, CH 2 ), primary (methyl, CH 3 ) and double bond (C=C), saturated bond (C - C), triple bond (HC≡). Our calculations on bulk and position-specific carbon isotope β-factors of the hydrocarbons, which are generally consistent with very limited ab initio calculations in the literature, are internally consistent and the most comprehensive to date for future applications to position-specific isotope geochemistry of hydrocarbons.

58 GEOSCIENCES↗

Role of Polycyclic Aromatic Alkylammonium Cations in Tuning the Electronic Properties and Band Alignment of Two-Dimensional Hybrid Perovskite Semiconductors

Two-dimensional hybrid organic–inorganic perovskites (HOIPs) have recently drawn intense attention as potential photovoltaic materials. However, n = 1 two-dimensional (2D) HOIPs face the challenge of low conductivity between the inorganic layers, leading to unsatisfactory device performance. Interestingly, 2D HOIPs employing π-conjugated molecules as organic moieties show energy and charge transfers between organic and inorganic layers, indicating potentially efficient carrier transport for photovoltaic applications. Nevertheless, the development of 2D HOIP-based solar cells especially utilizing polycyclic aromatic alkylammonium as cations is in its infancy. Herein, we investigated the electronic structure and band alignment of a series of n = 1 2D Ruddlesden–Popper (RP) phase HOIPs containing different polycyclic aromatic groups and alkyl chains, based on density functional theory calculations. We find that the polycyclic aromatic group plays an important role in controlling the functionality of 2D HOIPs by directly modifying band-edge states, and the band alignment at the organic–inorganic interface can be designed to promote either exciton trapping or dissociation for light-emitting or photovoltaic applications, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effects of threshold resummation for large-x PDF in large momentum effective theory

Parton distribution functions (PDFs) at large x are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum P z expansion of lattice quasi-PDFs, we investigate large x PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum xP z , and the threshold soft function, associated with the spectator momentum (1 − x)P z . The renormalization group equation of the soft function enables the resummation of the threshold double logarithms α k ln 2k (1 − x), which is crucial for a reliable and controllable calculation of large x PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − x)P z approaches Λ QCD , but remains valid when both xP z and (1 − x)P z are much larger than Λ QCD . Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.

factorization↗