Molecular Modeling of bIm-Substituted Mixed- Linker ZIFs for H2 Separation: A GCMC and MD Study

Molecular Modeling of bIm-Substituted Mixed- Linker ZIFs for H2 Separation: A GCMC and MD Study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Molecular Modeling of bIm-Substituted Mixed- Linker ZIFs for H2 Separation: A GCMC and MD Study Krsna Anand, Mohamad Rezi Abdul Hamid, Mohd F. Ismail, Wan Azlina W.A.K.G, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9281024/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract In this study, grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations were employed to investigate ZIF-8, ZIF-7, and a series of ZIF-7-8 frameworks with increasing benzimidazolate (bIm) content. Benchmarking against literature adsorption isotherms identified the Universal Force Field (UFF) as the most reliable model for describing gas-framework interactions. Increasing the bIm content enhanced the framework polarity and CO 2 uptake but reduced the pore accessibility, thereby decreasing diffusivity. In contrast, H 2 maintained high diffusivity owing to its small size and weak interaction with the framework. Among the studied structures, ZIF-7-8 (33% bIm) achieved optimal diffusion selectivity (H 2 /CO 2 = 400, H 2 /CH 4 = 20.5), reflecting a balance between polarity and pore accessibility. Radial distribution function (RDF) analysis showed CO 2 clustering near the bIm nitrogen sites, whereas CH 4 and H 2 remained more uniformly distributed. These results provide molecular-level insights into how the linker composition modulates the transport behavior, offering predictive guidance for the design of mixed-linker ZIF membranes for efficient H 2 purification. Gas separation Grand canonical Monte Carlo (GCMC) Mixed-linker design Molecular dynamics (MD) Zeolitic imidazolate frameworks (ZIFs) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Hydrogen (H 2 ) has emerged as a cornerstone of the global energy transition, serving as a clean energy carrier and a strategic feedstock for chemical production. Its zero-carbon combustion profile and high gravimetric energy density make it a compelling alternative for decarbonizing sectors where direct electrification is technically or economically constrained, such as ammonia synthesis, petroleum refining, long-haul transport, and steel production [ 1 ]. As global efforts to mitigate climate change intensify, the role of H 2 in enabling low-emission energy systems has become increasingly pronounced. Technologies such as metal hydride tanks exemplify emerging storage solutions designed to integrate H 2 into renewable-centric infrastructures [ 2 ]. The global demand for H 2 , particularly high-purity grades, is steadily increasing. Current global production is estimated at approximately 55 million tons per year, with a compound annual growth rate of nearly 6%, reflecting the expanding industrial footprint of H 2 [ 3 ]. Despite this growth, approximately 95% of global H 2 production still depends on fossil fuels, including coal, oil, and natural gas, highlighting the sector's entrenched reliance on carbon-intensive feedstocks and the urgency of transitioning to low-carbon alternatives [ 4 ]. According to the International Energy Agency (2021), meeting net-zero emission targets by 2050 will require scaling up low-carbon H 2 production to more than 500 million tons annually, supported by transformative advancements in purification and delivery technologies [ 5 ]. Industrial H 2 is commonly produced through steam methane reforming (SMR), partial oxidation, and biomass gasification, all of which generate gas mixtures containing H 2 , carbon dioxide (CO 2 ), methane (CH 4 ), carbon monoxide (CO), and water (H 2 O) [ 6 ]. To meet the ISO 14687 standard for fuel-cell-grade H 2 (≥ 99.97% purity), the effective separation of H 2 from these contaminants is essential. However, this task remains technically challenging owing to the physicochemical similarities and closely matched kinetic diameters of H 2 (2.89 Å), CO 2 (3.30 Å), and CH 4 (3.80 Å), which complicate selective purification [ 7 ]. Although traditional separation technologies, such as pressure swing adsorption (PSA) and cryogenic distillation, are industrially mature, they suffer from significant drawbacks: they are energy-intensive, capital-heavy, and offer limited tunability for precise molecular discrimination [ 8 , 9 ]. These limitations hinder their deployment in flexible, distributed H 2 systems envisioned for next-generation energy infrastructure. In contrast, membrane-based separations utilizing nanoporous materials offer several advantages: lower energy footprints, more straightforward modular integration, and molecular-level selectivity [ 10 ]. Among the nanoporous materials investigated for gas separation, zeolites and metal-organic frameworks (MOFs), particularly zeolitic imidazolate frameworks (ZIFs), have garnered significant attention. ZIFs combine the thermal and mechanical stabilities of zeolites with the modular chemistry and tunability of MOFs, creating highly customizable crystalline platforms that are ideal for gas separation. Their molecular-sieving behavior enables them to differentiate gases with closely spaced kinetic diameters, leveraging subtle differences in size, shape, and polarizability, making them well-suited for selective H 2 transport [ 11 ]. Despite their excellent structural stability and high gas-sieving capacity, traditional zeolites are constrained by rigid pore networks, which limit their effectiveness in separating gases larger or smaller than their intrinsic aperture size [ 12 – 15 ]. Moreover, pore tuning of zeolites to target other gas mixtures is not as straightforward as that of MOFs. In contrast, ZIFs offer low defect densities, energy-efficient and scalable synthesis, and enhanced tunability via coordination bond flexibility [ 16 ]. The labile nature of coordination bonding in ZIFs makes them more amenable to pore-size tuning. These qualities have sparked interest in their use for gas separation applications, with ZIF-8 being a prominent choice due to its exceptional propylene and propane separation capabilities [ 17 , 18 ]. ZIF-8 is constructed by tetrahedrally coordinating zinc (Zn) metal nodes with 2-methylimidazolate (mIm) linkers to form a microporous crystalline material with a sodalite (SOD) framework. ZIF-8 is versatile for structural modifications, which can be achieved through molecular design or by altering the metals/linkers within the framework [ 19 ]. Despite these advantages, the intrinsic crystalline structure of ZIF-8 imposes a characteristic pore aperture of approximately 0.34 nm, which restricts the accessible size range of guest molecules [ 20 ]. This limitation hampers ZIF-8 gas separation efficiency and utility in separating gas pairs with closely matched molecular sizes, particularly those involving H 2 , CH 4 , and CO 2 . To overcome this constraint, researchers have explored multivariate ZIF strategies, in which ZIF-8 is modified via metal substitution or mixed-linker incorporation, enabling more nuanced control over pore size, flexibility, and host-guest interactions [ 21 ]. One promising approach is the ZIF-7-8 hybrid, a mixed-linker framework that combines mIm and benzimidazolate (bIm) linkers within an SOD-type lattice. ZIF-7 and ZIF-8 share an identical topology but differ in linker chemistry; the inclusion of bIm, which is bulkier and more polar than mIm, alters the electrostatic potential, pore window size, and framework rigidity, all of which are critical for enhancing molecular selectivity [ 22 ]. Krokidas et al. [ 23 ] conducted one of the earliest and most comprehensive molecular simulation studies on ZIF-7-8, employing a fully flexible force field to capture the effect of partial bIm substitution (23–33%) on structural and transport properties. Their simulations showed that increasing the bIm content reduced the average aperture size from 3.46 Å to 2.3 Å, significantly enhancing the CO 2 /CH 4 diffusivity selectivity from 12.7 to 1900, while preserving the cubic symmetry of the unit cell. This study established a critical structure-performance threshold: beyond 35% bIm, framework distortion increases, compromising the selectivity and structural integrity. Subsequent experimental studies have highlighted additional complexities that were not fully captured by the simulations. Using pulsed-field gradient NMR, Berens et al. [ 24 ] demonstrated that although diffusion in ZIF-7-8 was slower than that in ZIF-8, which is consistent with pore narrowing, larger sorbates such as ethane and ethylene induced transient aperture expansion, suggesting gate-opening behavior. Åhlén et al. [ 25 ] further confirmed this behavior by demonstrating CO 2 sorption hysteresis and enhanced CO 2 /N 2 selectivity at high bIm ratios. Despite the narrow aperture, large molecules such as SF 6 were excluded, affirming the dual role of steric exclusion and electrostatic modulation imparted by bIm. These findings highlight the dual performance of ZIF-7-8. Although linker substitution enhances molecular discrimination through aperture narrowing and polarity modulation, it also introduces framework flexibility, which complicates predictive modeling. Previous studies, most notably by Krokidas et al. [ 23 ], evaluated adsorption and transport under infinite dilution conditions. In this approach, adsorption thermodynamics were estimated via Widom test-particle insertion, which determines the excess chemical potential of a single inserted molecule, while diffusion kinetics were derived using transition-state theory (TST), in which hopping rates were calculated from the motion of an isolated guest across pore windows. Because both methods effectively consider only a single molecule within the framework, the finite-loading effects and guest-guest interactions were neglected. Although this methodology is well-suited for isolating intrinsic steric barriers, it does not capture adsorption-diffusion coupling under realistic operating conditions. Furthermore, prior studies have predominantly focused on CO 2 -rich systems, leaving H 2 -related separations largely unexplored. Despite the strategic importance of H 2 /CO 2 and H 2 /CH 4 separations in pre-combustion capture and H 2 -enriched fuel applications, no existing work has systematically evaluated the behavior of H 2 in ZIF-7-8. Furthermore, the influence of the bIm:mIm substitution ratio on the H 2 /CO 2 and H 2 /CH 4 separation performances has not been systematically investigated. In particular, no previous study has integrated grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simultaneously resolve the equilibrium adsorption and transport dynamics of H 2 in ZIF-7-8. This gap is notable given the strong research bias toward ZIF-8, which accounted for nearly 70% of all ZIF-based simulation studies on gas separations between 2009 and 2019 [ 26 ]. The computational neglect of hybrid frameworks such as ZIF-7-8 is mainly attributable to the absence of validated design strategies that account for the structural complexity of mixed-linker systems [ 21 ]. To address this gap, this study systematically investigates H 2 separation in ZIF-8, ZIF-7, and mixed-linker ZIF-7-8 frameworks. Adsorption thermodynamics are evaluated using GCMC simulations, while MD simulations quantify the self-diffusion coefficients ( D s ), radial distribution functions (RDFs), and separation selectivities. An Arrhenius analysis is performed to determine the activation energy for H 2 diffusion, providing mechanistic insight into temperature-dependent transport behavior. This study further examines the influence of gas loading on D s . By systematically varying the bIm content in the ZIF-7-8 models, this study elucidates how linker polarity, pore structure, and framework dynamics collectively govern the gas separation performance, thereby contributing to the rational design of ZIF-based membranes and adsorbents for efficient H 2 purification. 2. Methodology 2.1 Structural model development The reference structures for ZIF-8 and ZIF-7 were obtained from the Cambridge Crystallographic Data Centre (CCDC) under the deposition codes VELVOY and VELVIS, respectively [ 27 ]. ZIF-8, which is composed of zinc ions tetrahedrally coordinated to mIm linkers, was used as the primary template for constructing mixed-linker ZIF-7-8 models. ZIF-7, composed entirely of bIm linkers, was included to evaluate the adsorption and diffusion behavior at complete substitution (100% bIm), thereby providing a compositional extreme for comparison with ZIF-8 and the intermediate mixed-linker structures. Initial model building was performed using Avogadro [ 28 ]. Three mixed-linker variants containing 11%, 22%, and 33% bIm substitutions were constructed, with compositions listed in Table S1 (Supplementary Information). These models retained the crystallographic symmetry and framework connectivity of the parent structure while introducing controlled chemical heterogeneity within the pore environment. Increasing bIm incorporation modifies the linker polarity and pore surface characteristics, thereby altering the host-guest interactions. The upper substitution limit of 33% was selected based on literature reports showing that the incorporation of more than two bIm linkers per six-membered ring, corresponding to substitution levels above 33%, induces structural distortion and loss of the SOD topology [ 23 ]. To maintain this stability criterion, mixed-linker configurations were generated by randomly substituting mIm with bIm linkers while limiting each six-membered ring to a maximum of two bIm linkers. The behavior beyond the reported stability threshold was examined. Additional models with 44%, 55%, and 61% bIm substitutions were constructed. These models were generated to identify the compositional limit at which the SOD framework began to lose structural stability. Based on this screening, detailed adsorption and transport analyses were restricted to compositions of 33% bIm or lower, whereas higher-substitution models were used solely to determine the structural stability threshold. The corresponding results are presented in Tables S14 and S15 (Supplementary Information). 2.2 Gas models and interaction parameters The gas molecules H 2 , CH 4 , and CO 2 were modeled as rigid guest species to maintain consistency across all GCMC and MD simulations. CO 2 was represented by the three-site rigid TraPPE model [ 29 ], CH 4 was treated as a single-site united-atom model using the TraPPE-UA model [ 30 ], and H 2 was described using the Buch single-site model [ 31 ]. The corresponding Lennard-Jones (LJ) parameters and partial charges for all gas models are summarized in Table 1 . Table 1 LJ parameters and partial charges for gas molecules Site Model Epsilon, \(\:\varvec{\epsilon\:}\:\) (K) Sigma, σ (Å) Partial charge, q (e) H 2 Buch 34.2 2.96 0.00 CH 4 TraPPE-UA 148.0 3.73 0.00 C (in CO 2 ) TraPPE 27.0 2.80 + 0.70 O (in CO 2 ) 79.0 3.05 -0.35 2.3 Grand canonical Monte Carlo (GCMC) GCMC simulations were performed at 298 K over a pressure range of 0–30 bar to evaluate the single-component adsorption isotherms of H 2 , CH 4 , and CO 2 in the ZIF-8, ZIF-7, and mixed-linker ZIF-7-8 frameworks. All simulations were performed using the RASPA simulation package [ 32 ]. Framework-sorbate interactions were modeled using the 12 − 6 LJ potential, and cross-interaction parameters were determined using the Lorentz-Berthelot mixing rules, as given by Eq. ( 1 ) and Eq. ( 2 ): $$\:{\epsilon\:}_{ij}=\sqrt{{\epsilon\:}_{i}{\epsilon\:}_{j}}$$ 1 $$\:{\sigma\:}_{ij}=\frac{{\sigma\:}_{i}+{\sigma\:}_{j}}{2}$$ 2 where ε i and σ i are LJ parameters of species i . Periodic boundary conditions (PBC) were applied in the x, y, and z directions. The cutoff radius was set to half the length of the box. Electrostatic interactions were modeled using Ewald summation with PBC to ensure accurate treatment of long-range Coulombic forces. The unit cell for ZIF-8 was modeled as a cubic box with dimensions of 16.991 × 16.991 × 16.991 Å 3 , which served as a template for model construction. All GCMC simulations were performed using a 1 × 1 × 1 unit cell for each framework. The force field selection was validated by simulating the adsorption isotherms of CO 2 , CH 4 , and H 2 in ZIF-8 and comparing the results with the reported experimental and computational data. Among these gases, CO 2 provides the most stringent test of the interaction potential due to its strong quadrupole moment and pronounced electrostatic interactions with the framework. In contrast, CH 4 and H 2 interact primarily via weaker dispersion forces. Therefore, a force field capable of accurately reproducing the CO 2 adsorption behavior is expected to reliably describe the adsorption of CH 4 and H 2 as well. Among the tested force fields (UFF, DREIDING, GenericMOFs, and AMBER) [ 33 – 36 ], the force field that showed the best agreement with the CO 2 adsorption isotherms in the literature was selected for all subsequent adsorption simulations. The framework was treated as rigid throughout, which is consistent with the common GCMC practice for equilibrium uptake studies. The parameters for the potential model are listed in Tables S2 and S3 (Supplementary Information). Each simulation consisted of 10,000 initialization and 25,000 production cycles. Standard Monte Carlo moves (translation, rotation, reinsertion, and swap) were employed with equal probability to ensure adequate sampling of the configurational space. The isosteric heat of adsorption (∆ Q st ) was computed for each gas to quantify the strength of the guest-host interaction. It was calculated using Eq. (3). $$\:\varDelta\:{Q}_{st}=\:\frac{⟨NU⟩-\:⟨U⟩⟨N⟩}{⟨{N}^{2}⟩-\:{⟨N⟩}^{2}}+\:{k}_{B}T\:\:\:\:\:\:\left(3\right)$$ where N is the number of adsorbed molecules, U is the total configuration energy, T is the absolute temperature, and k B is the Boltzmann constant. The angle brackets ⟨·⟩ represent the ensemble averages obtained over GCMC production cycles. In addition, the helium void fraction was evaluated to characterize the accessible porosity of each framework. To support the adsorption results, pore structure descriptors were evaluated using Zeo + + based on geometry-optimized framework models [ 37 ]. A probe radius of 1.86 Å was used to calculate the largest cavity diameter (LCD) and pore-limiting diameter (PLD). These structural parameters provide critical insights into how steric constraints and pore architecture govern the thermodynamic and kinetic aspects of gas uptake in ZIF. The adsorbed amount was defined in excess quantity ( N exc ) to be consistent with the experimental data, as shown in Eq. (4). $$\:{N}_{exc}=\:{N}_{abs}-{\rho\:}_{bulk}{V}_{free}\:\:\:\:\:\:\:\:\:\:\:\left(4\right)$$ where N abs is the absolute amount, V free is the free pore volume of the adsorbent, and ρ bulk is the sorbate density. 2.4 Molecular dynamics (MD) 2.4.1 Simulation setup All MD simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [ 38 ]. Model preparation and simulation setup were facilitated using the Atomic Simulation Environment (ASE) and LAMMPS interface, while trajectory analysis and visualization were conducted using Visual Molecular Dynamics (VMD) [ 38 , 39 ]. The simulation box was defined as a 2 × 2 × 2 supercell, and PBC was applied in all three spatial directions. A larger supercell was used to reduce the noise in the mean square displacement (MSD) calculations and improve the reliability of the D s estimates. A flexible force field was employed to accurately capture the dynamic behavior of MOFs, particularly when framework breathing and aperture modulation affected transport. The force field parameters for the parent ZIF-8 framework were obtained from the AMBER-based force field parameterized by Hertäg et al.[ 34 ] For the mixed-linker framework, parameters were adopted from Krokidas et al. [ 23 ], who extended the Hertäg et al.[ 34 ] ZIF-8 force field to mixed-linker ZIF-7-8 systems. In this parameterization, the force constants for bond stretching and angle bending were derived from the Cartesian Hessian matrix, whereas the torsional potentials and LJ parameters were obtained from the default AMBER parameter set. The complete set of parameters used in the potential model is provided in Tables S4-S12 (Supplementary Information). Table 2 lists the potential styles used in the simulation. Table 2 Force field potential style Potential Style Pair potential Lennard-Jones and Coulombic Bond potential Harmonic Angle potential Harmonic Dihedral potential CHARMM Guest molecules (H 2 , CH 4 , and CO 2 ) were randomly inserted into the accessible pore regions of the framework to ensure uniform distribution and avoid overlap with the framework atoms. Energy minimization and equilibration were performed prior to the production simulations to ensure structural stability and thermal equilibrium. The system was equilibrated for 100,000 timesteps under the canonical (NVT) ensemble at 308 K using a Nosé-Hoover thermostat and a timestep of 1.0 fs. Following equilibration, a production run of 1,000,000 timesteps (1.0 ns) was conducted under the same conditions. During this phase, the D s values of H 2 , CH 4 , and CO 2 were calculated from the slope of the MSD for each gas species. The diffusion data were validated against available literature values to confirm the reliability of the simulation setup. To investigate the impact of temperature on H 2 diffusion, MD simulations were conducted over an extended range of 200 to 700 K. This window was chosen to capture the full spectrum of thermally activated transport behavior while remaining within the experimentally validated thermal stability limits of the studied frameworks. These limits substantiate the selection of the 200–700 K simulation range as a conservative yet comprehensive domain for probing temperature-dependent diffusion. The mixed-linker ZIF-7-8 variants are anticipated to exhibit intermediate thermal behavior and are thus expected to remain stable across this range. Each system was monitored through visual trajectory inspection using VMD to confirm the structural integrity during the simulations. 2.4.2 Molecular analysis. The diffusion behaviors of ZIF-8, ZIF-7, and three mixed-linker variants of ZIF-7-8 were analyzed using H 2 , CH 4 , and CO 2 as diffusants. All simulations were performed under the NVT ensemble at a standard temperature of 308 K and a particle loading of 10 molecules per unit cell (mol/uc), unless specified otherwise. The key transport properties, including the MSD, D s , and diffusion-based selectivity for H 2 /CH 4 and H 2 /CO 2 , were evaluated to assess the separation performance. In addition, the RDF was computed to characterize the spatial distribution and local ordering of the gas molecules within the pores. The simulations also investigated the effects of guest loading and temperature variations on diffusion behavior, enabling a comprehensive comparison of the transport properties across all models. Mean square displacement (MSD). MSD was employed to determine the diffusivity coefficient. MSD is the mean square of the distance travelled by a particle at time, t . The Einstein relation, depicted in Eq. (5), describes the calculation of the MSD with respect to time, t , in MD [ 40 ]. $$\:MSD=\varDelta\:{r}^{2}\left(t\right)=\underset{t\to\:\infty\:}{\text{lim}}⟨{\left|\overrightarrow{r}\left(t\right)-\overrightarrow{r}\left(0\right)\right|}^{2}⟩=\dots\:\:\:\:\:\left(5\right)$$ Self-diffusion coefficient (D s ). D s is a key transport property that quantifies the intrinsic mobility of guest molecules within porous materials and is commonly reported in molecular simulations. In this study, the D s values for CO 2 , CH 4 , and H 2 were obtained from the MD trajectories using the Einstein relation [ 40 ]. D s was derived from the ensemble-averaged MSD at a given concentration ( c ) in the adsorbent, as shown in Eq. (6). $$\:\:\:\:\:{D}_{S}\left(c\right)=\frac{1}{6N}\underset{t\to\:\infty\:}{\text{lim}}\frac{1}{t}⟨\sum\:_{i=1}^{N}{\left|\overrightarrow{r}\left(t\right)-\overrightarrow{r}\left(0\right)\right|}^{2}⟩\:\:\:\:\:\:\:\left(6\right)$$ where N represents the number of guest molecules, r i (t) is the position of molecule i at time t , and \(\:⟨\cdot\:⟩\) denotes the ensemble average over time. The prefactor 1/6 corresponds to the isotropic diffusion in three dimensions. In practice, D s is extracted from the slope of the MSD versus time plot in the long-time diffusive regime. Gas selectivity. Gas selectivity was evaluated in the MD simulations by computing the D s values of each species within the ZIF framework. The resulting diffusion selectivity between species A and B is defined as the ratio of their D s , as shown in Eq. (7) below. $$\:{\:\:\:S}_{A/B}=\left(\frac{{D}_{s,A}}{{D}_{s,B}}\right)\:\:\:\left(7\right)$$ This methodology provides mechanistic insights into the kinetic-based discrimination of gases such as H 2 , CH 4 , and CO 2 within models. Although adsorption selectivity is commonly used in equilibrium studies, this study focused exclusively on MD-derived selectivity, capturing the impact of molecular mobility and framework interactions that govern kinetic discrimination in mixed-linker ZIFs. Radial distribution function (RDF). The radial distribution function g(r) is the ratio of ⟨ ρ(r) ⟩, the average local number density of particles at a distance r , to the bulk density of particles ρ , as shown in Eq. (8). $$\:\:\:\:g\left(r\right)=\:\frac{⟨\rho\:\left(r\right)⟩}{\rho\:}\:\:\:\:\:\:\:\left(8\right)$$ RDF analysis was conducted to characterize the short-range ordering and spatial correlations between gas molecules and framework atoms within the ZIFs. The RDFs were calculated using the center of mass (CoM) positions of the gas molecules as reference points, which improved the resolution in describing molecular-scale interactions in confined porous media. RDFs were computed to analyze the following key interactions: H 2 -H 2 , H 2 -Zn, H 2 -N1, and H 2 -N2 for H 2 ; CH 4 -CH 4 , CH 4 -Zn, CH 4 -N1, and CH 4 -N2 for CH 4 ; and CO 2 -CO 2 , CO 2 -Zn, CO 2 -N1, and CO 2 -N2 for CO 2 . These pairings capture both guest-guest clustering and guest-framework affinities. All RDFs were computed using a cutoff radius of 13 Å and a histogram of 100 bins. The trajectory data were averaged over a 1-ns production run at 308 K with a 10 mol/uc loading. Arrhenius Analysis. To evaluate the temperature dependence of H 2 diffusion in ZIF-7-8 (33% bIm), an Arrhenius analysis was performed by plotting the natural logarithm of the self-diffusion coefficient (ln D s ) as a function of the inverse temperature (1 /T in K⁻¹). The diffusivity data were obtained from MD simulations at discrete temperatures (200, 298, 350, 400, 450, 500, 550, 650, and 700 K), each conducted at a loading of 10 mol/uc in the NVT ensemble. The Arrhenius equation used for fitting is shown in Eq. (9). $$\:In\:Dₛ=\:\:In\:{D}_{0}-\:\frac{{E}_{a}}{RT}\:\:\:\:\:\:\:\:\:\left(9\right)$$ where D s is the self-diffusion coefficient, D 0 is the pre-exponential factor, E a is the activation energy, R is the gas constant, and T is the absolute temperature. The fitting was performed using linear least squares regression, with diffusivity values expressed in units of m 2 /s and transformed into their natural logarithmic form. 2.5 Partial atomic charge To ensure consistent treatment of electrostatic interactions, partial atomic charges were assigned to all framework atoms using the charge assignment scheme reported by Krokidas et al. [ 23 ]. This charge model was consistently applied in both GCMC and MD simulations, and the corresponding charge values are summarized in Table S13 (Supplementary Information). 3. Results and discussion 3.1 Structural basis for the 33% bIm upper substitution limit To justify the selection of 33% bIm as the upper substitution level for the GCMC and MD analyses, the pore descriptors (LCD and PLD) were examined for higher-substitution models containing 44%, 55%, and 61% bIm. Structural analysis based on these descriptors revealed clear discontinuity at 33% bIm, indicating the onset of framework distortion (Table S14). These distortions were accompanied by a deterioration in the calculated diffusion selectivity (Table S15). The decrease in selectivity beyond 33% was attributed to structural degradation and reduced steric discrimination, reinforcing 33% bIm as the practical limit for topological stability. Consequently, detailed adsorption and transport analyses were restricted to compositions ≤ 33% bIm, whereas higher-substitution models were used solely to establish the structural stability threshold. Therefore, the corresponding results are provided only in the Supplementary Information. 3.2 Grand canonical Monte Carlo (GCMC) simulation 3.2.1 Force field validation To establish a validated and transferable modeling protocol for gas adsorption in ZIFs, the CO 2 adsorption isotherms of ZIF-8 at 298 K were simulated using four force fields: UFF, DREIDING, GenericMOFs, and AMBER [ 33 – 36 ]. The simulated isotherms were compared with the experimental and computational data reported in the literature. As shown in Fig. 1 , the UFF provided the closest agreement with the reference isotherms, accurately reproducing the curvature and magnitude of the isotherm over the entire pressure range. In contrast, the isotherms predicted by DREIDING, GenericMOFs, and AMBER systematically underestimated the adsorption uptake, particularly at higher pressure. The UFF results showed good consistency with the experimental data reported by Hwang et al. [ 41 ] and Klomkliang et al. [ 42 ] as well as with the simulation results of Pérez-Pellitero et al. [ 43 ], which followed similar adsorption trends across the studied pressure range. A larger deviation was observed relative to the predictions of Thornton et al. [ 44 ], who reported lower adsorption capacities using the TIMTAM approach, in which the ZIF-8 framework is represented by simplified analytical pore geometries rather than an atomistic model. Consequently, guest-framework interactions and electrostatic effects are not explicitly captured, leading to differences in the predicted adsorption capacities. The strong agreement between the UFF simulations and the literature supports the selection of the UFF as the most suitable force field for subsequent adsorption simulations. 3.2.2 Force field transferability for CH 4 and H 2 Following UFF validation for CO 2 adsorption, the transferability of the model was tested by simulating the CH 4 and H 2 adsorption isotherms in ZIF-8 using identical rigid framework conditions. The results were compared with the literature data from Zhou et al. [ 45 ] and Pérez-Pellitero et al. [ 43 ] to determine whether the same force field and simulation setup could reliably predict the gas uptake behavior of gases with different molecular sizes, polarizabilities, and interaction strengths. As shown in Fig. 2 , the simulated CH 4 isotherm reproduced the experimental data of Zhou et al. [ 45 ] with deviations remaining within the experimental uncertainty across a pressure range of up to 30 bar. The simulations also showed excellent agreement with the GCMC results of Pérez-Pellitero et al. [ 43 ], who modeled ZIF-8 using a rigid framework with modified UFF, and the framework charges were derived from DFT calculations. Despite variations in the model parameterization, the simulated uptake remained consistent with the reported values. This agreement highlights the robustness of the UFF framework in capturing solid-fluid interactions without requiring system-specific reparameterization. Similarly, the simulated H 2 adsorption isotherm shown in Fig. 3 aligns well with the experimental results of Zhou et al. [ 45 ], with deviations remaining within the acceptable limits throughout the pressure range. Given the low polarizability and small kinetic diameter of H 2 , an accurate modeling of its uptake relies heavily on dispersion interactions. The observed agreement implies that the UFF model, even without flexibility, offers a reasonable approximation of gas-framework interactions for H 2 under moderate pressures in rigid ZIF-8. These results confirm the transferability of the UFF, which was initially validated for CO 2 , to CH 4 and H 2 without requiring any parameter adjustments. Its consistent performance across gases with varying sizes and interaction profiles demonstrates its robustness in simulating adsorption in ZIF-8. Therefore, the UFF was adopted for all subsequent simulations involving mixed-linker ZIF-7-8 frameworks to maintain methodological consistency and enable reliable comparisons across systems. 3.2.3 Influence of bIm incorporation on gas adsorption behavior The adsorption behaviors of H 2 , CH 4 , and CO 2 were examined across the ZIF-8 to ZIF-7 series, focusing on the mixed-linker analogues ZIF-7-8 (11% bIm), ZIF-7-8 (22% bIm), and ZIF-7-8 (33% bIm), which feature the progressive incorporation of bIm. ZIF-8 served as the parent framework, while ZIF-7, comprising 100% bIm linkers, was treated as a structural boundary, representing the upper limit of framework polarity and the lower bound of pore accessibility. This compositional gradient enabled a detailed analysis of how incremental linker substitution influences adsorption thermodynamics and capacity. GCMC simulations were used to generate pressure-dependent isotherms and corresponding ∆ Q st profiles. Figure 4 presents the simulated adsorption isotherms for (a) H 2 , (b) CH 4 , and (c) CO 2 across the five ZIF variants, illustrating the gas-specific uptake behavior as a function of adsorbate properties and framework composition. Across all frameworks, the adsorption capacities followed the order CO 2 > CH 4 > H 2 , reflecting the distinct physicochemical properties of these gases. CO 2 exhibited the highest uptake due to its large quadrupole moment and high polarizability, which promote strong electrostatic interactions with the polar and π-electron-rich regions of the framework. These interactions significantly enhance the CO 2 adsorption affinity of MOFs containing open metal sites and polar functional groups [ 46 ]. This trend is consistent with the findings of Chowdhury et al. [ 47 ], who reported higher CO 2 uptake relative to CH 4 in Cu-BTC and MIL-101, attributing this trend to strong interactions between CO 2 and charged adsorption sites within the frameworks. In the mixed-linker ZIF-7-8 (33% bIm), the CO 2 uptake reached approximately 6.1 mmol/g at 10 bar, exceeding that of the parent ZIF-8 (5.5 mmol/g), indicating the enhanced adsorption affinity resulting from the incorporation of bIm linkers. The comparison was made at 10 bar because the CO 2 isotherms increase sharply at low pressures and approach a plateau at relatively low pressures, reflecting strong framework-guest interactions and early pore filling. In contrast, CH 4 adsorption increased gradually across the studied pressure range without reaching a clear plateau at 30 bar. Therefore, the CH 4 performance was evaluated at 30 bar, where ZIF-7-8 (33% bIm) reached 4.1 mmol/g, consistent with its lower polarizability and the absence of a quadrupole moment. H 2 showed the lowest uptake, reaching 0.51 mmol/g at 30 bar, which was attributed to its weak van der Waals interactions and minimal polarizability. The incorporation of π-conjugated bIm linkers increases the polarity and electronic richness of the pore environment, thereby strengthening the framework-guest interactions and enhancing the adsorption, particularly for CO 2 . The calculated LCD and PLD values are summarized in Table 3 and were used to evaluate the largest internal cavity and pore aperture sizes within the framework. ZIF-8 exhibited a PLD of 3.41 Å and an LCD of 11.39 Å, consistent with experimental and computational benchmarks [ 27 , 48 – 50 ], affirming the validity of the pore analysis approach. As the bIm fraction increased, the LCD and PLD values decreased systematically. In ZIF-7-8 (33% bIm), the PLD was reduced to 2.54 Å and the LCD to 9.12 Å, whereas in ZIF-7, complete bIm substitution resulted in an ultra-constrained framework with a PLD of 2.40 Å and an LCD of 5.59 Å. These structural contractions are directly correlated with the observed reduction in gas uptake, particularly for CO 2 and CH 4 in the most bIm-rich frameworks. Given the kinetic diameters of CO 2 (3.3 Å), CH 4 (3.8 Å), and H 2 (2.9 Å), the proximity of the ZIF-7-8 (33% bIm) PLD to the kinetic diameter of CO 2 explains its ability to maintain a relatively high uptake, despite the reduced pore size. Table 3 LCD and PLD values for ZIF-8, mixed-linker ZIF-7-8, and ZIF-7 ZIF Variant LCD (Å) PLD (Å) ZIF-7 5.5880 2.5417 ZIF-8 11.3929 3.4089 ZIF-7-8 (11% bIm) 11.3874 3.4075 ZIF-7-8 (22% bIm) 11.3874 3.4075 ZIF-7-8 (33% bIm) 9.1167 2.5441 The adsorption isotherms support this interpretation. CO 2 exhibited the steepest initial uptake and early saturation due to the strong electrostatic interactions arising from its quadrupole moment and high polarizability. In contrast, CH 4 , a nonpolar molecule, displayed gradual uptake over the pressure range and no sharp inflections, indicating uniform dispersive interactions. A slight increase in curvature with increasing bIm content suggests mild energetic heterogeneity arising from enhanced surface polarizability. H 2 , with its minimal polarizability and small kinetic diameter, exhibited linear isotherms across all frameworks, indicating uniformly weak and non-site-specific physisorption governed by Henry’s law. The introduction of bIm linkers enhanced the uptake of all three gases across the series, particularly at low pressure, where increased π-conjugation and polarity at the pore surface boosted the interaction strengths without compromising pore accessibility. Although incorporating bIm linkers enhances the framework polarity and strengthens the host-guest interactions, excessive bIm substitution introduces severe steric constraints. Figure 5 presents the pressure-dependent ∆ Q st profiles for (a) H 2 , (b) CH 4 , and (c) CO 2 , illustrating the variation in adsorption strength across the ZIF-7-8 series. For CO 2 , ∆ Q st increased from 25.99 kJ/mol in ZIF-8 to 29.28 kJ/mol in ZIF-7-8 (33% bIm), reaching a maximum value of 33.8 kJ/mol in ZIF-7. This trend reflects the stronger electrostatic and quadrupole-π interactions generated by the increased polarity and aromaticity introduced by bIm linkers. However, despite exhibiting the highest ∆ Q st value, ZIF-7 showed a significantly lower adsorption capacity due to its small PLD (2.40 Å), which restricts the accessible pore volume. In contrast, ZIF-7-8 (33% bIm) maintained stronger host-guest interactions while preserving sufficient pore accessibility, leading to a higher overall adsorption performance. For CH 4, adsorption is dominated by dispersion interactions. The ∆ Q st increased from 15.99 in ZIF-8 to 24.34 kJ/mol in ZIF-7, reflecting enhanced confinement and increased contact between the adsorbate and the framework as the pore environment became more constricted. Nevertheless, the severe steric hindrance in ZIF-7 reduces the adsorption capacity, whereas mixed-linker frameworks maintain a higher uptake due to more accessible pore space. In contrast, H 2 displayed relatively flat ∆ Q st values (5.9–9.4 kJ/mol) across all frameworks, indicating weak and non-specific physisorption governed primarily by van der Waals interactions. These results demonstrate a clear structure-property trade-off within the ZIF-7-8 series: increasing the bIm content strengthens the adsorption energetics through enhanced polarity and π-interactions, but excessive substitution reduces pore accessibility. The mixed-linker framework ZIF-7-8 (33% bIm) achieves an optimal balance between the interaction strength and geometric accessibility. The isotherm profiles and ∆ Q st behavior present a coherent picture of the gas-framework interaction landscape. CO 2 benefited the most from the increased bIm content, exhibiting high uptake and strong binding in ZIF-7-8 (33% bIm). Notably, ZIF-7 demonstrates that a high ∆ Q st does not necessarily translate to a high adsorption capacity, as excessive pore constriction limits accessibility. Among the investigated structures, ZIF-7-8 (33% bIm) achieved an optimal balance between enhanced polarity and π-interactions while maintaining sufficient pore accessibility, resulting in optimal performance within the series. 3.3 Molecular dynamics (MD) simulation 3.3.1 Diffusivity in ZIF-8: literature benchmarking and model validation To assess the reliability of the simulation methodology and force field parameters, the computed values for ZIF-8 (Table 4 ) were compared with literature data reported under comparable conditions (Table 5 ). Since all the ZIF-7-8 structures examined herein were derived by linker substitution from the ZIF-8 framework, it is essential that the force field accurately reproduces the known transport properties of ZIF-8 to ensure the reliability and transferability of the subsequent results. Table 4 D s for H 2 , CH 4 , and CO 2 in mixed-linker ZIF-7-8 variants ZIF Framework D H2 (m 2 /s) D CH4 (m 2 /s) D CO2 (m 2 /s) S H2 / CH4 S H2 / CO2 ZIF-8 2.27 × 10 − 8 2.72 × 10 − 9 7.93 × 10 –11 8.33 285.92 ZIF-7-8 (11% bIm) 2.38 × 10 − 8 1.81 × 10 − 9 7.75 × 10 –11 13.15 307.32 ZIF-7-8 (22% bIm) 2.18 × 10 − 8 1.47 × 10 − 9 6.96 × 10 –11 14.84 313.15 ZIF-7-8 (33% bIm) 2.13 × 10 − 8 1.04 × 10 − 9 5.34 × 10 –11 20.48 399.60 ZIF-7 1.42 × 10 − 9 7.85 × 10 –11 2.23 × 10 –11 18.04 63.49 Table 5 Literature-reported D s of H 2 , CH 4 , and CO 2 in ZIF-8 Gas D s (m 2 /s) Loading Temperature (K) Force Fields Ref H 2 2.62 × 10 − 8 10 mol/uc 298 K UFF [ 51 ] 4.03 × 10 − 8 5 mol/uc 295 K DREIDING [ 34 ] 5.47 × 10 − 8 10 bar 298 K UFF & DREIDING [ 52 ] 2.28 × 10 − 8 10 mol/uc 300 K UFF & AMBER [ 35 ] 1.1 × 10 − 8 − 1.8 × 10 − 8 0–30 mol/uc 300 K UFF & DREIDING [ 53 ] CH 4 3.24 × 10 − 11 5 mol/uc 285 K Zhang et al.[ 54 ] [ 55 ] 1.75 × 10 − 9 5 mol/uc 295 K DREIDING [ 34 ] 1.80 × 10 − 9 10 bar 298 K UFF & DREIDING [ 52 ] 1.70 × 10 − 9 15 mol/uc 298 K Wu et al.[ 35 ] [ 56 ] 1.40 × 10⁻ 10 12 mol/uc 298 K Experimental study [ 57 ] CO 2 1.71 × 10⁻ 10 10 mol/uc 298 K UFF [ 51 ] 3.90 × 10 − 11 10 bar 298 K UFF & DREIDING [ 52 ] 4.30 × 10 − 11 15 mol/uc 298 K Wu et al.[ 35 ] [ 56 ] 2.20× 10 − 10 10 mol/uc 298 K Experimental study [ 57 ] 5.463 × 10 − 10 6 mol/uc 300 K UFF & AMBER [ 35 ] For H 2 , the computed D s in ZIF-8 was 2.27 × 10 − 8 m 2 /s, which is in agreement with the values reported in the literature for flexible framework models. Slightly higher values have also been reported, which can be attributed to variations in the force field parameterization [ 34 , 52 ]. For CH 4 , the computed D s of 2.72 × 10 − 9 m 2 /s also lies within the range reported in the literature. Most studies report values on the order of 10 − 9 m 2 /s when flexible frameworks are employed. However, significantly lower values have been reported in some cases, such as in the study by Verploegh et al. [ 55 ], who used a different force field parameterization and lower simulation temperature. These differences highlight the sensitivity of CH 4 diffusion to the force field selection and simulation conditions. For CO 2 , the calculated diffusivity of 7.93 × 10 –11 m 2 /s is well within the range reported in the literature. Previous computational studies have reported diffusivities spanning approximately 10 -11 -10 -10 m 2 /s, depending on the force field and loading conditions. The observed diffusivity trend of H 2 > CH 4 > CO 2 reflects a balance among the molecular size, adsorption strength, and gas-framework interaction characteristics. H 2 , the smallest molecule (2.89 Å), exhibited the highest diffusivity (2.13 × 10 − 8 to 2.38 × 10 − 8 m 2 /s), which was enabled by the weak van der Waals forces, low polarizability, and minimal adsorption. CH 4 , which has a larger diameter (3.8 Å), experiences greater steric hindrance and stronger dispersion interactions, leading to reduced diffusivity (1.04 × 10 − 9 to 2.72 × 10 − 9 m 2 /s). Although CO 2 (3.3 Å) is slightly smaller than CH 4 , it displayed the lowest diffusivity (2.23 × 10 –11 to 7.93 × 10 –11 m 2 /s), driven by its strong quadrupole moment and substantial electrostatic interactions with polar sites in the framework, which enhanced adsorption and limited mobility. The agreement between the computed diffusion coefficients and literature values, together with the correct reproduction of the expected diffusivity hierarchy, further confirmed the reliability of the adopted simulation methodology and force field parameters. 2.1.1 Influence of bIm incorporation on diffusivity Incorporating bIm linkers into the ZIF-7-8 series alters the framework geometry and chemistry, which directly affects the gas diffusivity. Compared to ZIF-8, which contains only mIm linkers, the bIm-modified structures, particularly ZIF-7-8 (33% bIm), exhibit increased steric bulk and higher framework polarity. This structural modification led to a measurable reduction in the PLD, which defines the narrowest passage available for molecular transport. For example, the PLD decreased from 3.41 Å in ZIF-8 to 2.54 Å in ZIF-7-8 (33% bIm), reflecting the tighter apertures caused by bulkier bIm linkers. This reduction intensifies the geometric confinement and restricts the diffusion of larger gases such as CH 4 and CO 2 . Consequently, the diffusivities of CH 4 and CO 2 decreased from ZIF-8 to ZIF-7-8 (33% bIm) (Table 4 ). In addition to the geometric effects, the increased polarity introduced by the bIm linkers enhanced the electrostatic interactions with polar molecules such as CO 2 . These enhanced interactions resulted in longer residence time and reduced mobility, contributing to the lower CO 2 diffusivity observed in ZIF-7-8 (33% bIm) compared to ZIF-8. In contrast, H 2 diffusion was only marginally affected, with the diffusivity decreasing slightly from 2.27 × 10 − 8 to 2.13 × 10 − 8 m 2 /s across the structures. This limited sensitivity was attributed to the small kinetic diameter and weak dispersion-dominated interactions of H 2 with the framework, resulting in negligible adsorption and low diffusion barriers. The data confirmed that linker substitution modulates pore geometry and host-guest interaction strength, with pronounced effects on larger or more strongly adsorbing gases, while exerting minimal influence on the diffusion of small, weakly interacting species, such as H 2 . The diffusion selectivity ratios of H 2 /CH 4 and H 2 /CO 2 , calculated using MD, underscore the potential of ZIF-7-8 for kinetic-based gas separations. Among the frameworks investigated, ZIF-7-8 (33% bIm) demonstrated the highest selectivity. This pronounced enhancement in kinetic discrimination arises from the progressive incorporation of bIm linkers, which increase the framework polarity and induce geometric confinement within the pores. These modifications selectively hinder the mobility of larger or more strongly interacting gases, such as CH 4 and CO 2 , while having minimal effect on H 2 transport due to its small kinetic diameter and weak van der Waals interactions with the framework. The results exemplify a fundamental trade-off between adsorption strength and diffusivity: CO 2 , which forms strong electrostatic interactions with polar framework sites, exhibits reduced diffusivity, whereas H 2 retains rapid and unobstructed mobility. This contrasting behavior, captured through detailed molecular simulations, confirms that linker substitution and polarity modulation can be systematically leveraged to tune diffusion selectivity. The overall diffusivity trend (H 2 > CH 4 > CO 2 ) reflects the interplay between molecular size, adsorption energetics, and interaction type. The high H 2 /CH 4 and H 2 /CO 2 selectivity values obtained for ZIF-7-8 (33% bIm) suggest that it is a promising candidate for membrane-based H 2 separation applications. 3.4 RDF analysis: ZIF-7-8 (33% bIm) Figure 6 presents the RDF profiles for (a) H 2 , (b) CH 4 , and (c) CO 2 in ZIF-7-8 (33% bIm), illustrating the spatial correlations between the adsorbed gas molecules and key framework atoms. For each gas, the RDFs were plotted for guest-guest, guest-nitrogen (from the imidazolate linker), and guest-metal pairs. ZIF-7-8 (33% bIm) was selected for detailed analysis because it exhibited the most significant enhancement in adsorption capacity and selectivity within the series, which was attributed to its distinctive framework polarity and electrostatic field. The RDFs resolved the spatial distribution of adsorbates around specific framework sites, providing direct molecular-level insights into the structural origins of the exceptional uptake and selectivity observed in ZIF-7-8 (33% bIm). The RDF analysis of H 2 in ZIF-7-8 (33% bIm) indicated a highly delocalized adsorption environment with no evidence of site-specific binding (Fig. 6 (a)). The H 2 -H 2 correlation exhibited a broad peak at r = 3.9 Å, with a maximum g(r) = 2.5, indicating moderate guest-guest proximity due to spatial crowding rather than directional attraction. The host-guest RDFs, H 2 -Zn, H 2 -N2 (blm), and H 2 -N1 (mlm), displayed broad, low-intensity peaks ( g(r) < 1.4, r = 4.7–5.2 Å), confirming the absence of preferential coordination in the structure. Consistently, the ∆ Q st remained nearly constant between 6.78 and 6.82 kJ/mol, indicating weak and non-specific interactions. These values align with the range reported by Murray et al. [ 58 ], (4–7 kJ/mol for H 2 in MOFs), which is insufficient to drive site-specific adsorption. The absence of sharp RDF features also corresponds to the observed linearity of the H 2 adsorption isotherms and high diffusivity, where only minor reductions relative to ZIF-8 arise from steric effects rather than energetic barriers. Although bIm incorporation increases the framework polarity and introduces additional nitrogen sites, these modifications do not enhance H 2 adsorption. The RDF and ∆ Q st trends confirmed that adsorption was dominated by dispersion forces and accessible pore volume, with negligible electrostatic contributions. A similar trend was reported by Wu et al [ 59 ]. for ZIF-8/GO composites, where modest increases in H 2 uptake and isosteric heat were attributed to steric or surface effects rather than directional binding interactions. Thus, although bIm linkers alter the pore geometry and transport pathways, their influence remains limited by the inherently weak polarizability and lack of a quadrupole moment in H 2 molecules. The RDF analysis for CH 4 (Fig. 6 (b)) revealed a spatially diffuse interaction profile, consistent with the nonpolar character of the adsorbate and its weak affinity for specific framework sites. The CH 4 -CH 4 correlation exhibited a broad peak centered at r = 4.1 Å with g(r) = 2.6, indicating moderate intermolecular proximity arising from volumetric crowding rather than attractive interactions. The host-guest RDFs, CH 4 -Zn, CH 4 -N2 (blm), and CH 4 -N1 (mlm), exhibited comparable and low-intensity peaks between r = 4.7 and 5.1 Å, with g(r) = 1.1–1.3, confirming the absence of site-specific interactions across the framework. Despite the increased polarity and π-electron density of the bIm linkers, no evidence of enhanced CH 4 -framework interactions in ZIF-7-8 (33% bIm) relative to ZIF-8 was observed, as the RDFs remained broadly distributed and weak. However, the steric bulk introduced by bIm substitution reduces the accessible pore volume and introduces greater hindrance, resulting in a significant drop in CH 4 mobility (1.04 × 10 − 9 m 2 /s for ZIF-7-8 (33% bIm) vs. 2.72 × 10 − 9 m 2 /s for ZIF-8). This finding aligns with the high-pressure gravimetric data reported by Arami-Niya et al. [ 60 ], who observed that the CH 4 uptake in ZIF-7 remained negligible at low pressures and increased sharply only above 1245 kPa, owing to the gate-opening transition. Given the structural similarity of ZIF-7-8 (33% bIm) to ZIF-7, particularly the incorporation of bIm linkers, these findings support the conclusion that CH 4 uptake is driven by steric accessibility in a flexible pore environment rather than by strong host-guest interactions. As shown in Fig. 6 (c), the RDF between the carbon atom of CO 2 and the nitrogen atom of the bIm linker (N2) exhibits a sharp peak at r = 2.8 Å with a peak height of g(r) = 2.3, indicating that N2 is the preferred site for interactions. The sharpness and proximity of this peak indicate directional electrostatic attraction driven by quadrupolar stabilization and enhanced electron density associated with the aromatic bIm unit. In contrast, weaker and more diffuse interactions were observed for CO 2 -N1 at r = 3.5 Å ( g(r) = 1.6) and CO 2 -Zn at r = 4.2 Å ( g(r) = 1.5), indicating weaker and less frequent interactions with the mIm linker and metal centers. The CO 2 -CO 2 RDF presents a well-defined peak at r = 3.9 Å and g(r) = 3.2, indicating significant guest-guest proximity near high-affinity N2 regions and suggesting cooperative pore filling rather than isolated adsorption. These simulation results are consistent with the high-resolution neutron diffraction study by Zhao et al. [ 61 ], which demonstrated preferential CO 2 adsorption in ZIF-7 within cavities formed by Zn-bIm rings, where linker rotation generated access channels for CO 2 . The close correspondence between these experimental observations and the simulated RDF profile underscores the pivotal role of bIm in creating electronically favorable and sterically accessible adsorption sites, thereby controlling the CO 2 selectivity within the mixed-linker framework. 3.5 Impact of guest loading on D s of H 2 in ZIF-7-8 (33% bIm) The D s of H 2 in ZIF-7-8 (33% bIm), as shown in Fig. 7 , exhibited a significant monotonic decline with increasing loading from 3 to 40 mol/uc at 308 K under the NVT conditions. At 3 mol/uc, the D s of H 2 in ZIF-7-8 (33% bIm) reached 2.03 × 10 − 8 m 2 /s, indicative of a dilute regime in which H 2 experiences minimal resistance, negligible guest-guest interactions, and nearly unrestricted access to the pore network. Despite the presence of sterically bulkier bIm linkers, the framework retained sufficient openness and conformational flexibility to support efficient diffusion under low loading. As the loading increased beyond 5 mol/uc, a progressive decline in D s was observed, reaching 8.85 × 10 − 9 m 2 /s at 40 mol/uc. This reduction is attributed to the accumulation of guest molecules, which reduces the available free volume and increases the frequency of intermolecular collisions, thereby imposing kinetic limitations on diffusion. Under these conditions, transport is predominantly constrained by steric effects arising from crowding within the pore channels rather than by strong host-guest interactions, consistent with the weak and delocalized interactions of H 2 , as indicated by the RDF and ∆ Q st analyses. Similar behaviors have been reported in previous studies. Chmelik et al.[ 62 ] observed a significant decrease in H 2 diffusivity with increasing occupancy due to steric congestion within the pores, while Pantatosaki et al.[ 63 ] reported a comparable decline in ZIF-8 using QENS, attributing it to intermolecular collisions dominating gate-opening effects at high loadings. In ZIF-7-8 (33% bIm), the incorporation of bulky bIm linkers further reduced the accessible window area, amplifying the steric obstruction relative to ZIF-8 and reinforcing the crowding effect at high loadings. 3.6 Impact of temperature on D s of H 2 in ZIF-7-8 (33% bIm) The temperature dependence of H 2 diffusion in ZIF-7-8 (33% bIm) was investigated via MD simulations over the temperature range of 200–700 K under moderate loading. ZIF-8 has been shown to retain structural integrity up to 500°C (773 K) under an inert atmosphere and 350°C (623 K) in an oxidative environment, as evidenced by thermogravimetric and XRD analyses [ 64 ]. Further studies confirm stability up to 600°C (873 K), beyond which decomposition becomes significant [ 65 , 66 ]. In contrast, ZIF-7 maintains its crystalline framework up to 400°C (673 K) under inert conditions before structural collapse occurs [ 66 ]. These reported stability limits indicate that the temperature range employed in the present simulations remains within the thermally stable regime of the framework. As shown in Fig. 8 , the D s of H 2 increases significantly with temperature, rising from 4.2 × 10 − 9 m 2 /s at 200 K to a peak value of 4.5 × 10 − 8 m 2 /s at 600 K. This trend is characteristic of thermally activated diffusion, in which elevated thermal energy enhances the ability of gas molecules to overcome the steric barriers imposed by pore apertures and framework topography. The observed increase in D s with temperature arises from the improved kinetic energy of H 2 molecules, which reduces their average residence time within the adsorption sites and increases the likelihood of overcoming the local energy barriers imposed by framework topology. As thermal energy increases, the molecules experience more frequent and longer-range displacements, resulting in a steeper MSD slope over time and, consequently, higher D s . This effect reflects a thermodynamically driven enhancement of molecular displacement rather than a change in the diffusion mechanism, indicating that at elevated temperatures, the dynamic interaction between the guest molecules and the framework becomes less restrictive. The Arrhenius plot in Fig. 9 , constructed from ln D s versus 1/ T , displays a clear linear relationship with a correlation coefficient (R²) of 0.9963. This high degree of linearity supports the conclusion that a consistent thermally activated regime governs H 2 diffusion in ZIF-7-8 (33% bIm) over the studied temperature range (200–700 K). The derived activation energy of 5.2 kJ/mol reflects the average energetic barrier for H 2 motion through the framework, indicating weak physisorptive interactions with the pore environment. The intercept value of -16.151 corresponds to the logarithm of the pre-exponential factor, which measures the theoretical diffusion limit in the absence of activation barriers. These values indicate a regime dominated by weak steric resistance and physisorptive interactions. Although Verploegh et al. [ 55 ] reported poor linearity (R² = 0.29) for H 2 diffusion in ZIF-8 over a limited temperature range (0-150°C) using only four data points, their observations were attributed to the nearly barrierless diffusion environment in ZIF-8. In contrast, this study employed a broader temperature range, enabling a more accurate identification of diffusion trends and improved statistical reliability in the Arrhenius analysis. Moreover, the bIm linkers in ZIF-7-8 (33% bIm) introduced moderate structural rigidity, generating sufficient energetic heterogeneity to produce measurable activation behavior, even for light gases such as H 2 . These distinctions affirm that, in ZIF-7-8 (33% bIm), H 2 diffusion is governed by a stable, thermally responsive mechanism, underscoring the potential of the framework for temperature-tuned separation applications. 4. Conclusion This study elucidated gas adsorption and diffusion in mixed-linker ZIF-7-8 by integrating GCMC and MD simulations. Using rigid-framework GCMC, the UFF most reliably reproduced single-component isotherms and isosteric heats across ZIFs, capturing the CO 2 > CH 4 > H 2 uptake order. Increasing the bIm content strengthened CO 2 adsorption through greater framework polarity and π-electron density, with ZIF-7-8 (33% bIm) providing the highest capacity while preserving pore accessibility. MD simulations using a flexible lattice revealed mobility trends inverse to adsorption strength (H 2 > CH 4 > CO 2 ) and identified ZIF-7-8 (33% bIm) as the optimal composition, balancing enhanced CO 2 uptake with unimpeded H 2 transport. This study reveals a clear trade-off between adsorption strength and molecular mobility, demonstrating that stronger host-guest interactions enhance adsorption while simultaneously limiting molecular transport. A direct correlation between PLD and diffusion selectivity was established, demonstrating that controlled aperture narrowing enhances selectivity without fully restricting transport. The results identify 33% bIm as a critical compositional threshold at which pore geometry, adsorption strength, and diffusion behavior converge to produce optimal separation performance. The introduction of bIm linkers creates heterogeneous adsorption environments that selectively enhance CO 2 interactions through nitrogen-rich sites. RDF analyses linked gas-specific interactions to nitrogen-rich bIm sites, particularly for CO 2 . Loading-dependent simulations showed a monotonic decline in H 2 diffusivity, and temperature-dependent analyses followed the Arrhenius behavior, yielding a defined activation energy for H 2 transport. These findings highlight the nuanced interplay between framework chemistry and pore geometry that governs separation, positioning ZIF-7-8 (33% bIm) for membrane-based H 2 purification. Declarations Acknowledgment . The authors would like to thank Universiti Putra Malaysia for providing research grant through GPB - Geran Putra Berimpak with the vote number of 9809800 (Project No. GPB/2024/9809800 - Assessing Composite Structure in High-Flux Metal Organic Frameworks Based Mixed Matrix membrane for Carbon Capture Application). The authors would also like to thank the Department of Chemical and Environmental Engineering, the Sustainable Process Engineering Research Center (SPERC), and the Department of Chemistry, Universiti Putra Malaysia, Serdang, Selangor, Malaysia, for their valuable support and contributions to this research. Author contributions . Krsna Anand: writing – original draft, conceptualization, data curation, formal analysis; methodology. Mohamad Rezi Abdul Hamid: supervision, validation, writing – review & editing. Mohd F Ismail: supervision, writing – review & editing. Wan Azlina W.A.K.G: supervision, validation. Musab Abdul Razak: conceptualization, supervision, validation, writing – review & editing. Conflict of Interest . The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data and code availability. All data that support the findings of this study are included within the article (and any supplementary files). Supplementary information. The Supporting Information (PDF) includes detailed molecular models, force field parameters, and simulation protocols used in this study; model compositions (Table S1); framework models and atom typing for ZIF-8, ZIF-7-8, and ZIF-7 with visual atom-type schemes (Figures S1-S3); rigid force field parameters used for GCMC adsorption, including force field selection and the final UFF parameters (Tables S2-S3); flexible force field parameters for MD simulations (Tables S4-S12); partial charge assignments (Table S13); and compositional limit analyses (Tables S14-S15). Ethical approval. Not Applicable References International Energy Agency, (2019) The Future of Hydrogen X. Lin, W. Xie, Q. Zhu, H. Yang, Q. Li, Rational optimization of metal hydride tank with LaNi4.25Al0.75 as hydrogen storage medium. Chem. Eng. J. 421 , 127844 (2021). https://doi.org/10.1016/j.cej.2020.127844 C.M. Kalamaras, A.M. Efstathiou, (2013) Hydrogen Production Technologies: Current State and Future Developments. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9281024","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":615688038,"identity":"065695e9-5c34-480e-820a-2d3fb2897d5f","order_by":0,"name":"Krsna Anand","email":"","orcid":"","institution":"Universiti Putra Malaysia","correspondingAuthor":false,"prefix":"","firstName":"Krsna","middleName":"","lastName":"Anand","suffix":""},{"id":615688040,"identity":"caf0b634-5462-458b-bd69-4f4de9cca092","order_by":1,"name":"Mohamad Rezi Abdul Hamid","email":"","orcid":"","institution":"Universiti Putra Malaysia","correspondingAuthor":false,"prefix":"","firstName":"Mohamad","middleName":"Rezi Abdul","lastName":"Hamid","suffix":""},{"id":615688042,"identity":"9139c528-867b-451b-813b-afccda8580f1","order_by":2,"name":"Mohd F. 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[45] and Pérez-Pellitero et al. [43]\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/b54e0bbb62332d183ea05b84.png"},{"id":106305158,"identity":"20f354ab-e08e-40ce-a9cd-0e72a1d489d1","added_by":"auto","created_at":"2026-04-07 09:44:54","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":48192,"visible":true,"origin":"","legend":"\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e adsorption isotherms in ZIF-8 at 298 K using the UFF, benchmarked against experimental data from Zhou et al. [45]\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/44a4f280187be681a25a3fdb.png"},{"id":106305161,"identity":"2177fff0-afb0-496e-93d0-64ebfb291eed","added_by":"auto","created_at":"2026-04-07 09:44:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":97935,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eAdsorption isotherms of (a) \u003c/em\u003eH\u003csub\u003e2\u003c/sub\u003e\u003cem\u003e, (b) \u003c/em\u003eCH\u003csub\u003e4\u003c/sub\u003e\u003cem\u003e, and (c) \u003c/em\u003eCO\u003csub\u003e2\u003c/sub\u003e\u003cem\u003e in ZIF-8 (red solid), ZIF-7-8 with 11% bIm (black dotted), 22% bIm (black dashed), and 33% bIm (black solid), and ZIF-7 (blue solid) at 298 K using the UFF. The inset in (a) shows a magnified view of the adsorption isotherm of H\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/b55e8f758c5482b4586a08b1.png"},{"id":106404149,"identity":"cfdffa6d-91ad-4810-9e65-466bddbfb754","added_by":"auto","created_at":"2026-04-08 09:15:32","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":97570,"visible":true,"origin":"","legend":"\u003cp\u003e∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e of (a) H\u003csub\u003e2\u003c/sub\u003e, (b) CH\u003csub\u003e4\u003c/sub\u003e, and (c) CO\u003csub\u003e2\u003c/sub\u003e in ZIF-8 (red solid), ZIF-7-8 with 11% bIm (black dotted), 22% bIm (black dashed), and 33% bIm (black solid), and ZIF-7 (blue solid) as a function of pressure at 298 K\u003c/p\u003e","description":"","filename":"Fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/21e8f4a3d952b4a120d0db2b.png"},{"id":106404753,"identity":"6c20afc2-7d9d-449f-9d3e-cb1889b2db13","added_by":"auto","created_at":"2026-04-08 09:16:58","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":111814,"visible":true,"origin":"","legend":"\u003cp\u003eRDF profiles of (a) H\u003csub\u003e2\u003c/sub\u003e, (b) CH\u003csub\u003e4\u003c/sub\u003e, and (c) CO\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm). The solid black lines represent guest-guest correlations (H\u003csub\u003e2\u003c/sub\u003e-H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e-CH\u003csub\u003e4\u003c/sub\u003e, CO\u003csub\u003e2\u003c/sub\u003e-CO\u003csub\u003e2\u003c/sub\u003e), the dashed lines represent guest-linker nitrogen from mIm correlations (H\u003csub\u003e2\u003c/sub\u003e-N1, CH\u003csub\u003e4\u003c/sub\u003e-N1, CO\u003csub\u003e2\u003c/sub\u003e-N1), the dash-dot lines represent guest-linker nitrogen from bIm correlations (H\u003csub\u003e2\u003c/sub\u003e-N2, CH\u003csub\u003e4\u003c/sub\u003e-N2, CO\u003csub\u003e2\u003c/sub\u003e-N2),\u0026nbsp; and the dotted lines represent guest-Zn correlations (H\u003csub\u003e2\u003c/sub\u003e-Zn, CH\u003csub\u003e4\u003c/sub\u003e-Zn, CO\u003csub\u003e2\u003c/sub\u003e-Zn)\u003c/p\u003e","description":"","filename":"Fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/65ea8d9f2d76ac1b3ee3d7bc.png"},{"id":106305163,"identity":"5616aaff-d725-471b-859b-2e8d31f12585","added_by":"auto","created_at":"2026-04-07 09:44:54","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":47057,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm) as a function of loading at 308 K\u003c/p\u003e","description":"","filename":"Fig7.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/bd7d8beb430b1e5c4816cbce.png"},{"id":106305165,"identity":"436089ac-d6f1-41fb-8ee4-ed5285a7ab33","added_by":"auto","created_at":"2026-04-07 09:44:54","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":50742,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature dependence of the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm) at moderate loading\u003c/p\u003e","description":"","filename":"Fig8.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/601f1e1d711e918ef9d6c250.png"},{"id":106305164,"identity":"45bba155-aedf-47ff-8681-7e641767dec7","added_by":"auto","created_at":"2026-04-07 09:44:54","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":53036,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eArrhenius plot for \u003c/em\u003eH\u003csub\u003e2\u003c/sub\u003e\u003cem\u003e diffusion in ZIF-7-8 (33% bIm), showing ln D\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e vs 1/T at moderate loading\u003c/em\u003e\u003c/p\u003e","description":"","filename":"Fig9.png","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/27fb047c78dd534d66d0aaad.png"},{"id":106405966,"identity":"c2e1a44e-58ab-4033-9297-26218e57945b","added_by":"auto","created_at":"2026-04-08 09:29:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2124749,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/918e7b65-6798-4541-ba4d-8dab213d2ab8.pdf"},{"id":106305156,"identity":"ff638152-f7e4-4534-9d12-870ae722cb74","added_by":"auto","created_at":"2026-04-07 09:44:53","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":434541,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-9281024/v1/2db9736a40a62f8db0ba30a0.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Molecular Modeling of bIm-Substituted Mixed- Linker ZIFs for H2 Separation: A GCMC and MD Study","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHydrogen (H\u003csub\u003e2\u003c/sub\u003e) has emerged as a cornerstone of the global energy transition, serving as a clean energy carrier and a strategic feedstock for chemical production. Its zero-carbon combustion profile and high gravimetric energy density make it a compelling alternative for decarbonizing sectors where direct electrification is technically or economically constrained, such as ammonia synthesis, petroleum refining, long-haul transport, and steel production [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. As global efforts to mitigate climate change intensify, the role of H\u003csub\u003e2\u003c/sub\u003e in enabling low-emission energy systems has become increasingly pronounced. Technologies such as metal hydride tanks exemplify emerging storage solutions designed to integrate H\u003csub\u003e2\u003c/sub\u003e into renewable-centric infrastructures [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe global demand for H\u003csub\u003e2\u003c/sub\u003e, particularly high-purity grades, is steadily increasing. Current global production is estimated at approximately 55\u0026nbsp;million tons per year, with a compound annual growth rate of nearly 6%, reflecting the expanding industrial footprint of H\u003csub\u003e2\u003c/sub\u003e [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Despite this growth, approximately 95% of global H\u003csub\u003e2\u003c/sub\u003e production still depends on fossil fuels, including coal, oil, and natural gas, highlighting the sector's entrenched reliance on carbon-intensive feedstocks and the urgency of transitioning to low-carbon alternatives [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. According to the International Energy Agency (2021), meeting net-zero emission targets by 2050 will require scaling up low-carbon H\u003csub\u003e2\u003c/sub\u003e production to more than 500\u0026nbsp;million tons annually, supported by transformative advancements in purification and delivery technologies [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIndustrial H\u003csub\u003e2\u003c/sub\u003e is commonly produced through steam methane reforming (SMR), partial oxidation, and biomass gasification, all of which generate gas mixtures containing H\u003csub\u003e2\u003c/sub\u003e, carbon dioxide (CO\u003csub\u003e2\u003c/sub\u003e), methane (CH\u003csub\u003e4\u003c/sub\u003e), carbon monoxide (CO), and water (H\u003csub\u003e2\u003c/sub\u003eO) [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. To meet the ISO 14687 standard for fuel-cell-grade H\u003csub\u003e2\u003c/sub\u003e (\u0026ge;\u0026thinsp;99.97% purity), the effective separation of H\u003csub\u003e2\u003c/sub\u003e from these contaminants is essential. However, this task remains technically challenging owing to the physicochemical similarities and closely matched kinetic diameters of H\u003csub\u003e2\u003c/sub\u003e (2.89 \u0026Aring;), CO\u003csub\u003e2\u003c/sub\u003e (3.30 \u0026Aring;), and CH\u003csub\u003e4\u003c/sub\u003e (3.80 \u0026Aring;), which complicate selective purification [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Although traditional separation technologies, such as pressure swing adsorption (PSA) and cryogenic distillation, are industrially mature, they suffer from significant drawbacks: they are energy-intensive, capital-heavy, and offer limited tunability for precise molecular discrimination [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. These limitations hinder their deployment in flexible, distributed H\u003csub\u003e2\u003c/sub\u003e systems envisioned for next-generation energy infrastructure. In contrast, membrane-based separations utilizing nanoporous materials offer several advantages: lower energy footprints, more straightforward modular integration, and molecular-level selectivity [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAmong the nanoporous materials investigated for gas separation, zeolites and metal-organic frameworks (MOFs), particularly zeolitic imidazolate frameworks (ZIFs), have garnered significant attention. ZIFs combine the thermal and mechanical stabilities of zeolites with the modular chemistry and tunability of MOFs, creating highly customizable crystalline platforms that are ideal for gas separation. Their molecular-sieving behavior enables them to differentiate gases with closely spaced kinetic diameters, leveraging subtle differences in size, shape, and polarizability, making them well-suited for selective H\u003csub\u003e2\u003c/sub\u003e transport [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDespite their excellent structural stability and high gas-sieving capacity, traditional zeolites are constrained by rigid pore networks, which limit their effectiveness in separating gases larger or smaller than their intrinsic aperture size [\u003cspan additionalcitationids=\"CR13 CR14\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Moreover, pore tuning of zeolites to target other gas mixtures is not as straightforward as that of MOFs. In contrast, ZIFs offer low defect densities, energy-efficient and scalable synthesis, and enhanced tunability via coordination bond flexibility [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The labile nature of coordination bonding in ZIFs makes them more amenable to pore-size tuning. These qualities have sparked interest in their use for gas separation applications, with ZIF-8 being a prominent choice due to its exceptional propylene and propane separation capabilities [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. ZIF-8 is constructed by tetrahedrally coordinating zinc (Zn) metal nodes with 2-methylimidazolate (mIm) linkers to form a microporous crystalline material with a sodalite (SOD) framework. ZIF-8 is versatile for structural modifications, which can be achieved through molecular design or by altering the metals/linkers within the framework [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDespite these advantages, the intrinsic crystalline structure of ZIF-8 imposes a characteristic pore aperture of approximately 0.34 nm, which restricts the accessible size range of guest molecules [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. This limitation hampers ZIF-8 gas separation efficiency and utility in separating gas pairs with closely matched molecular sizes, particularly those involving H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e. To overcome this constraint, researchers have explored multivariate ZIF strategies, in which ZIF-8 is modified via metal substitution or mixed-linker incorporation, enabling more nuanced control over pore size, flexibility, and host-guest interactions [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. One promising approach is the ZIF-7-8 hybrid, a mixed-linker framework that combines mIm and benzimidazolate (bIm) linkers within an SOD-type lattice. ZIF-7 and ZIF-8 share an identical topology but differ in linker chemistry; the inclusion of bIm, which is bulkier and more polar than mIm, alters the electrostatic potential, pore window size, and framework rigidity, all of which are critical for enhancing molecular selectivity [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eKrokidas et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] conducted one of the earliest and most comprehensive molecular simulation studies on ZIF-7-8, employing a fully flexible force field to capture the effect of partial bIm substitution (23\u0026ndash;33%) on structural and transport properties. Their simulations showed that increasing the bIm content reduced the average aperture size from 3.46 \u0026Aring; to 2.3 \u0026Aring;, significantly enhancing the CO\u003csub\u003e2\u003c/sub\u003e/CH\u003csub\u003e4\u003c/sub\u003e diffusivity selectivity from 12.7 to 1900, while preserving the cubic symmetry of the unit cell. This study established a critical structure-performance threshold: beyond 35% bIm, framework distortion increases, compromising the selectivity and structural integrity. Subsequent experimental studies have highlighted additional complexities that were not fully captured by the simulations. Using pulsed-field gradient NMR, Berens et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] demonstrated that although diffusion in ZIF-7-8 was slower than that in ZIF-8, which is consistent with pore narrowing, larger sorbates such as ethane and ethylene induced transient aperture expansion, suggesting gate-opening behavior. \u0026Aring;hl\u0026eacute;n et al. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] further confirmed this behavior by demonstrating CO\u003csub\u003e2\u003c/sub\u003e sorption hysteresis and enhanced CO\u003csub\u003e2\u003c/sub\u003e/N\u003csub\u003e2\u003c/sub\u003e selectivity at high bIm ratios. Despite the narrow aperture, large molecules such as SF\u003csub\u003e6\u003c/sub\u003e were excluded, affirming the dual role of steric exclusion and electrostatic modulation imparted by bIm.\u003c/p\u003e \u003cp\u003eThese findings highlight the dual performance of ZIF-7-8. Although linker substitution enhances molecular discrimination through aperture narrowing and polarity modulation, it also introduces framework flexibility, which complicates predictive modeling. Previous studies, most notably by Krokidas et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], evaluated adsorption and transport under infinite dilution conditions. In this approach, adsorption thermodynamics were estimated via Widom test-particle insertion, which determines the excess chemical potential of a single inserted molecule, while diffusion kinetics were derived using transition-state theory (TST), in which hopping rates were calculated from the motion of an isolated guest across pore windows. Because both methods effectively consider only a single molecule within the framework, the finite-loading effects and guest-guest interactions were neglected. Although this methodology is well-suited for isolating intrinsic steric barriers, it does not capture adsorption-diffusion coupling under realistic operating conditions. Furthermore, prior studies have predominantly focused on CO\u003csub\u003e2\u003c/sub\u003e-rich systems, leaving H\u003csub\u003e2\u003c/sub\u003e-related separations largely unexplored. Despite the strategic importance of H\u003csub\u003e2\u003c/sub\u003e/CO\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e/CH\u003csub\u003e4\u003c/sub\u003e separations in pre-combustion capture and H\u003csub\u003e2\u003c/sub\u003e-enriched fuel applications, no existing work has systematically evaluated the behavior of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8. Furthermore, the influence of the bIm:mIm substitution ratio on the H\u003csub\u003e2\u003c/sub\u003e/CO\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e/CH\u003csub\u003e4\u003c/sub\u003e separation performances has not been systematically investigated. In particular, no previous study has integrated grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simultaneously resolve the equilibrium adsorption and transport dynamics of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8. This gap is notable given the strong research bias toward ZIF-8, which accounted for nearly 70% of all ZIF-based simulation studies on gas separations between 2009 and 2019 [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The computational neglect of hybrid frameworks such as ZIF-7-8 is mainly attributable to the absence of validated design strategies that account for the structural complexity of mixed-linker systems [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo address this gap, this study systematically investigates H\u003csub\u003e2\u003c/sub\u003e separation in ZIF-8, ZIF-7, and mixed-linker ZIF-7-8 frameworks. Adsorption thermodynamics are evaluated using GCMC simulations, while MD simulations quantify the self-diffusion coefficients (\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e), radial distribution functions (RDFs), and separation selectivities. An Arrhenius analysis is performed to determine the activation energy for H\u003csub\u003e2\u003c/sub\u003e diffusion, providing mechanistic insight into temperature-dependent transport behavior. This study further examines the influence of gas loading on \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e. By systematically varying the bIm content in the ZIF-7-8 models, this study elucidates how linker polarity, pore structure, and framework dynamics collectively govern the gas separation performance, thereby contributing to the rational design of ZIF-based membranes and adsorbents for efficient H\u003csub\u003e2\u003c/sub\u003e purification.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1 Structural model development\u003c/h2\u003e\n\u003cp\u003eThe reference structures for ZIF-8 and ZIF-7 were obtained from the Cambridge Crystallographic Data Centre (CCDC) under the deposition codes VELVOY and VELVIS, respectively [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e]. ZIF-8, which is composed of zinc ions tetrahedrally coordinated to mIm linkers, was used as the primary template for constructing mixed-linker ZIF-7-8 models. ZIF-7, composed entirely of bIm linkers, was included to evaluate the adsorption and diffusion behavior at complete substitution (100% bIm), thereby providing a compositional extreme for comparison with ZIF-8 and the intermediate mixed-linker structures. Initial model building was performed using Avogadro [\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eThree mixed-linker variants containing 11%, 22%, and 33% bIm substitutions were constructed, with compositions listed in Table \u003cspan class=\"InternalRef\"\u003eS1\u003c/span\u003e (Supplementary Information). These models retained the crystallographic symmetry and framework connectivity of the parent structure while introducing controlled chemical heterogeneity within the pore environment. Increasing bIm incorporation modifies the linker polarity and pore surface characteristics, thereby altering the host-guest interactions. The upper substitution limit of 33% was selected based on literature reports showing that the incorporation of more than two bIm linkers per six-membered ring, corresponding to substitution levels above 33%, induces structural distortion and loss of the SOD topology [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. To maintain this stability criterion, mixed-linker configurations were generated by randomly substituting mIm with bIm linkers while limiting each six-membered ring to a maximum of two bIm linkers. The behavior beyond the reported stability threshold was examined. Additional models with 44%, 55%, and 61% bIm substitutions were constructed. These models were generated to identify the compositional limit at which the SOD framework began to lose structural stability. Based on this screening, detailed adsorption and transport analyses were restricted to compositions of 33% bIm or lower, whereas higher-substitution models were used solely to determine the structural stability threshold. The corresponding results are presented in Tables S14 and S15 (Supplementary Information).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2 Gas models and interaction parameters\u003c/h2\u003e\n\u003cp\u003eThe gas molecules H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e were modeled as rigid guest species to maintain consistency across all GCMC and MD simulations. CO\u003csub\u003e2\u003c/sub\u003e was represented by the three-site rigid TraPPE model [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e], CH\u003csub\u003e4\u003c/sub\u003e was treated as a single-site united-atom model using the TraPPE-UA model [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e], and H\u003csub\u003e2\u003c/sub\u003e was described using the Buch single-site model [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e]. The corresponding Lennard-Jones (LJ) parameters and partial charges for all gas models are summarized in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eLJ parameters and partial charges for gas molecules\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSite\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eModel\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eEpsilon, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{\\epsilon\\:}\\:\\)\u003c/span\u003e\u003c/span\u003e(K)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eSigma, \u0026sigma; (\u0026Aring;)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePartial charge, \u003cem\u003eq\u003c/em\u003e (e)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBuch\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e34.2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.96\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.00\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCH\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTraPPE-UA\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e148.0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.73\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.00\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eC (in CO\u003csub\u003e2\u003c/sub\u003e)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"2\" align=\"left\"\u003e\n\u003cp\u003eTraPPE\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e27.0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e+\u0026thinsp;0.70\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eO (in CO\u003csub\u003e2\u003c/sub\u003e)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e79.0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.05\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e-0.35\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e2.3 Grand canonical Monte Carlo (GCMC)\u003c/h2\u003e\n\u003cp\u003eGCMC simulations were performed at 298 K over a pressure range of 0\u0026ndash;30 bar to evaluate the single-component adsorption isotherms of H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e in the ZIF-8, ZIF-7, and mixed-linker ZIF-7-8 frameworks. All simulations were performed using the RASPA simulation package [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e]. Framework-sorbate interactions were modeled using the 12\u0026thinsp;\u0026minus;\u0026thinsp;6 LJ potential, and cross-interaction parameters were determined using the Lorentz-Berthelot mixing rules, as given by Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) and Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e):\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$$\\:{\\epsilon\\:}_{ij}=\\sqrt{{\\epsilon\\:}_{i}{\\epsilon\\:}_{j}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$$\\:{\\sigma\\:}_{ij}=\\frac{{\\sigma\\:}_{i}+{\\sigma\\:}_{j}}{2}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003e\u0026epsilon;\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e and \u003cem\u003e\u0026sigma;\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e are LJ parameters of species \u003cem\u003ei\u003c/em\u003e. Periodic boundary conditions (PBC) were applied in the x, y, and z directions. The cutoff radius was set to half the length of the box. Electrostatic interactions were modeled using Ewald summation with PBC to ensure accurate treatment of long-range Coulombic forces. The unit cell for ZIF-8 was modeled as a cubic box with dimensions of 16.991 \u0026times; 16.991 \u0026times; 16.991 \u0026Aring;\u003csup\u003e3\u003c/sup\u003e, which served as a template for model construction. All GCMC simulations were performed using a 1 \u0026times; 1 \u0026times; 1 unit cell for each framework.\u003c/p\u003e\n\u003cp\u003eThe force field selection was validated by simulating the adsorption isotherms of CO\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and H\u003csub\u003e2\u003c/sub\u003e in ZIF-8 and comparing the results with the reported experimental and computational data. Among these gases, CO\u003csub\u003e2\u003c/sub\u003e provides the most stringent test of the interaction potential due to its strong quadrupole moment and pronounced electrostatic interactions with the framework. In contrast, CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e interact primarily via weaker dispersion forces. Therefore, a force field capable of accurately reproducing the CO\u003csub\u003e2\u003c/sub\u003e adsorption behavior is expected to reliably describe the adsorption of CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e as well. Among the tested force fields (UFF, DREIDING, GenericMOFs, and AMBER) [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e], the force field that showed the best agreement with the CO\u003csub\u003e2\u003c/sub\u003e adsorption isotherms in the literature was selected for all subsequent adsorption simulations. The framework was treated as rigid throughout, which is consistent with the common GCMC practice for equilibrium uptake studies. The parameters for the potential model are listed in Tables S2 and S3 (Supplementary Information).\u003c/p\u003e\n\u003cp\u003eEach simulation consisted of 10,000 initialization and 25,000 production cycles. Standard Monte Carlo moves (translation, rotation, reinsertion, and swap) were employed with equal probability to ensure adequate sampling of the configurational space. The isosteric heat of adsorption (∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e) was computed for each gas to quantify the strength of the guest-host interaction. It was calculated using Eq.\u0026nbsp;(3).\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$$\\:\\varDelta\\:{Q}_{st}=\\:\\frac{\u0026lang;NU\u0026rang;-\\:\u0026lang;U\u0026rang;\u0026lang;N\u0026rang;}{\u0026lang;{N}^{2}\u0026rang;-\\:{\u0026lang;N\u0026rang;}^{2}}+\\:{k}_{B}T\\:\\:\\:\\:\\:\\:\\left(3\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eN\u003c/em\u003e is the number of adsorbed molecules, \u003cem\u003eU\u003c/em\u003e is the total configuration energy, \u003cem\u003eT\u003c/em\u003e is the absolute temperature, and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e is the Boltzmann constant. The angle brackets ⟨\u0026middot;⟩ represent the ensemble averages obtained over GCMC production cycles. In addition, the helium void fraction was evaluated to characterize the accessible porosity of each framework. To support the adsorption results, pore structure descriptors were evaluated using Zeo\u0026thinsp;+\u0026thinsp;+\u0026thinsp;based on geometry-optimized framework models [\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e]. A probe radius of 1.86 \u0026Aring; was used to calculate the largest cavity diameter (LCD) and pore-limiting diameter (PLD). These structural parameters provide critical insights into how steric constraints and pore architecture govern the thermodynamic and kinetic aspects of gas uptake in ZIF. The adsorbed amount was defined in excess quantity (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eexc\u003c/em\u003e\u003c/sub\u003e) to be consistent with the experimental data, as shown in Eq.\u0026nbsp;(4).\u003c/p\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$$\\:{N}_{exc}=\\:{N}_{abs}-{\\rho\\:}_{bulk}{V}_{free}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(4\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eabs\u003c/em\u003e\u003c/sub\u003e is the absolute amount, \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003efree\u003c/em\u003e\u003c/sub\u003e is the free pore volume of the adsorbent, and \u003cem\u003e\u0026rho;\u003c/em\u003e\u003csub\u003e\u003cem\u003ebulk\u003c/em\u003e\u003c/sub\u003e is the sorbate density.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e2.4 Molecular dynamics (MD)\u003c/h2\u003e\n\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n\u003ch2\u003e2.4.1 Simulation setup\u003c/h2\u003e\n\u003cp\u003eAll MD simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. Model preparation and simulation setup were facilitated using the Atomic Simulation Environment (ASE) and LAMMPS interface, while trajectory analysis and visualization were conducted using Visual Molecular Dynamics (VMD) [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e]. The simulation box was defined as a 2 \u0026times; 2 \u0026times; 2 supercell, and PBC was applied in all three spatial directions. A larger supercell was used to reduce the noise in the mean square displacement (MSD) calculations and improve the reliability of the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e estimates.\u003c/p\u003e\n\u003cp\u003eA flexible force field was employed to accurately capture the dynamic behavior of MOFs, particularly when framework breathing and aperture modulation affected transport. The force field parameters for the parent ZIF-8 framework were obtained from the AMBER-based force field parameterized by Hert\u0026auml;g et al.[\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e] For the mixed-linker framework, parameters were adopted from Krokidas et al. [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e], who extended the Hert\u0026auml;g et al.[\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e] ZIF-8 force field to mixed-linker ZIF-7-8 systems. In this parameterization, the force constants for bond stretching and angle bending were derived from the Cartesian Hessian matrix, whereas the torsional potentials and LJ parameters were obtained from the default AMBER parameter set. The complete set of parameters used in the potential model is provided in Tables S4-S12 (Supplementary Information). Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e lists the potential styles used in the simulation.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eForce field potential style\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePotential\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eStyle\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePair potential\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eLennard-Jones and Coulombic\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eBond potential\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eHarmonic\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAngle potential\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eHarmonic\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eDihedral potential\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCHARMM\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eGuest molecules (H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e) were randomly inserted into the accessible pore regions of the framework to ensure uniform distribution and avoid overlap with the framework atoms. Energy minimization and equilibration were performed prior to the production simulations to ensure structural stability and thermal equilibrium. The system was equilibrated for 100,000 timesteps under the canonical (NVT) ensemble at 308 K using a Nos\u0026eacute;-Hoover thermostat and a timestep of 1.0 fs. Following equilibration, a production run of 1,000,000 timesteps (1.0 ns) was conducted under the same conditions. During this phase, the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e values of H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e were calculated from the slope of the MSD for each gas species. The diffusion data were validated against available literature values to confirm the reliability of the simulation setup.\u003c/p\u003e\n\u003cp\u003eTo investigate the impact of temperature on H\u003csub\u003e2\u003c/sub\u003e diffusion, MD simulations were conducted over an extended range of 200 to 700 K. This window was chosen to capture the full spectrum of thermally activated transport behavior while remaining within the experimentally validated thermal stability limits of the studied frameworks. These limits substantiate the selection of the 200\u0026ndash;700 K simulation range as a conservative yet comprehensive domain for probing temperature-dependent diffusion. The mixed-linker ZIF-7-8 variants are anticipated to exhibit intermediate thermal behavior and are thus expected to remain stable across this range. Each system was monitored through visual trajectory inspection using VMD to confirm the structural integrity during the simulations.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\n\u003ch2\u003e2.4.2 Molecular analysis.\u003c/h2\u003e\n\u003cp\u003eThe diffusion behaviors of ZIF-8, ZIF-7, and three mixed-linker variants of ZIF-7-8 were analyzed using H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e as diffusants. All simulations were performed under the NVT ensemble at a standard temperature of 308 K and a particle loading of 10 molecules per unit cell (mol/uc), unless specified otherwise. The key transport properties, including the MSD, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e, and diffusion-based selectivity for H\u003csub\u003e2\u003c/sub\u003e/CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e/CO\u003csub\u003e2\u003c/sub\u003e, were evaluated to assess the separation performance. In addition, the RDF was computed to characterize the spatial distribution and local ordering of the gas molecules within the pores. The simulations also investigated the effects of guest loading and temperature variations on diffusion behavior, enabling a comprehensive comparison of the transport properties across all models.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eMean square displacement (MSD).\u003c/em\u003e MSD was employed to determine the diffusivity coefficient. MSD is the mean square of the distance travelled by a particle at time, \u003cem\u003et\u003c/em\u003e. The Einstein relation, depicted in Eq.\u0026nbsp;(5), describes the calculation of the MSD with respect to time, \u003cem\u003et\u003c/em\u003e, in MD [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equc\" class=\"mathdisplay\"\u003e$$\\:MSD=\\varDelta\\:{r}^{2}\\left(t\\right)=\\underset{t\\to\\:\\infty\\:}{\\text{lim}}\u0026lang;{\\left|\\overrightarrow{r}\\left(t\\right)-\\overrightarrow{r}\\left(0\\right)\\right|}^{2}\u0026rang;=\\dots\\:\\:\\:\\:\\:\\left(5\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cem\u003eSelf-diffusion coefficient (D\u003c/em\u003e \u003csub\u003e \u003cem\u003es\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e). D\u003c/em\u003e \u003csub\u003e \u003cem\u003es\u003c/em\u003e \u003c/sub\u003e is a key transport property that quantifies the intrinsic mobility of guest molecules within porous materials and is commonly reported in molecular simulations. In this study, the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e values for CO\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and H\u003csub\u003e2\u003c/sub\u003e were obtained from the MD trajectories using the Einstein relation [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e]. \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e was derived from the ensemble-averaged MSD at a given concentration (\u003cem\u003ec\u003c/em\u003e) in the adsorbent, as shown in Eq.\u0026nbsp;(6).\u003c/p\u003e\n\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equd\" class=\"mathdisplay\"\u003e$$\\:\\:\\:\\:\\:{D}_{S}\\left(c\\right)=\\frac{1}{6N}\\underset{t\\to\\:\\infty\\:}{\\text{lim}}\\frac{1}{t}\u0026lang;\\sum\\:_{i=1}^{N}{\\left|\\overrightarrow{r}\\left(t\\right)-\\overrightarrow{r}\\left(0\\right)\\right|}^{2}\u0026rang;\\:\\:\\:\\:\\:\\:\\:\\left(6\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eN\u003c/em\u003e represents the number of guest molecules, \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(t)\u003c/em\u003e is the position of molecule \u003cem\u003ei\u003c/em\u003e at time \u003cem\u003et\u003c/em\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:⟨\\cdot\\:⟩\\)\u003c/span\u003e\u003c/span\u003e denotes the ensemble average over time. The prefactor 1/6 corresponds to the isotropic diffusion in three dimensions. In practice, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is extracted from the slope of the MSD versus time plot in the long-time diffusive regime.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eGas selectivity.\u003c/em\u003e Gas selectivity was evaluated in the MD simulations by computing the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e values of each species within the ZIF framework. The resulting diffusion selectivity between species A and B is defined as the ratio of their \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e, as shown in Eq.\u0026nbsp;(7) below.\u003c/p\u003e\n\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Eque\" class=\"mathdisplay\"\u003e$$\\:{\\:\\:\\:S}_{A/B}=\\left(\\frac{{D}_{s,A}}{{D}_{s,B}}\\right)\\:\\:\\:\\left(7\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThis methodology provides mechanistic insights into the kinetic-based discrimination of gases such as H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e within models. Although adsorption selectivity is commonly used in equilibrium studies, this study focused exclusively on MD-derived selectivity, capturing the impact of molecular mobility and framework interactions that govern kinetic discrimination in mixed-linker ZIFs.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eRadial distribution function (RDF).\u003c/em\u003e The radial distribution function \u003cem\u003eg(r)\u003c/em\u003e is the ratio of ⟨\u003cem\u003e\u0026rho;(r)\u003c/em\u003e⟩, the average local number density of particles at a distance \u003cem\u003er\u003c/em\u003e, to the bulk density of particles \u003cem\u003e\u0026rho;\u003c/em\u003e, as shown in Eq.\u0026nbsp;(8).\u003c/p\u003e\n\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equf\" class=\"mathdisplay\"\u003e$$\\:\\:\\:\\:g\\left(r\\right)=\\:\\frac{\u0026lang;\\rho\\:\\left(r\\right)\u0026rang;}{\\rho\\:}\\:\\:\\:\\:\\:\\:\\:\\left(8\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eRDF analysis was conducted to characterize the short-range ordering and spatial correlations between gas molecules and framework atoms within the ZIFs. The RDFs were calculated using the center of mass (CoM) positions of the gas molecules as reference points, which improved the resolution in describing molecular-scale interactions in confined porous media. RDFs were computed to analyze the following key interactions: H\u003csub\u003e2\u003c/sub\u003e-H\u003csub\u003e2\u003c/sub\u003e, H\u003csub\u003e2\u003c/sub\u003e-Zn, H\u003csub\u003e2\u003c/sub\u003e-N1, and H\u003csub\u003e2\u003c/sub\u003e-N2 for H\u003csub\u003e2\u003c/sub\u003e; CH\u003csub\u003e4\u003c/sub\u003e-CH\u003csub\u003e4\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e-Zn, CH\u003csub\u003e4\u003c/sub\u003e-N1, and CH\u003csub\u003e4\u003c/sub\u003e-N2 for CH\u003csub\u003e4\u003c/sub\u003e; and CO\u003csub\u003e2\u003c/sub\u003e-CO\u003csub\u003e2\u003c/sub\u003e, CO\u003csub\u003e2\u003c/sub\u003e-Zn, CO\u003csub\u003e2\u003c/sub\u003e-N1, and CO\u003csub\u003e2\u003c/sub\u003e-N2 for CO\u003csub\u003e2\u003c/sub\u003e. These pairings capture both guest-guest clustering and guest-framework affinities. All RDFs were computed using a cutoff radius of 13 \u0026Aring; and a histogram of 100 bins. The trajectory data were averaged over a 1-ns production run at 308 K with a 10 mol/uc loading.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eArrhenius Analysis.\u003c/em\u003e To evaluate the temperature dependence of H\u003csub\u003e2\u003c/sub\u003e diffusion in ZIF-7-8 (33% bIm), an Arrhenius analysis was performed by plotting the natural logarithm of the self-diffusion coefficient (ln \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e) as a function of the inverse temperature (1\u003cem\u003e/T\u003c/em\u003e in K⁻\u0026sup1;). The diffusivity data were obtained from MD simulations at discrete temperatures (200, 298, 350, 400, 450, 500, 550, 650, and 700 K), each conducted at a loading of 10 mol/uc in the NVT ensemble. The Arrhenius equation used for fitting is shown in Eq.\u0026nbsp;(9).\u003c/p\u003e\n\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equg\" class=\"mathdisplay\"\u003e$$\\:In\\:Dₛ=\\:\\:In\\:{D}_{0}-\\:\\frac{{E}_{a}}{RT}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(9\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is the self-diffusion coefficient, \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the pre-exponential factor, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e is the activation energy, \u003cem\u003eR\u003c/em\u003e is the gas constant, and \u003cem\u003eT\u003c/em\u003e is the absolute temperature. The fitting was performed using linear least squares regression, with diffusivity values expressed in units of m\u003csup\u003e2\u003c/sup\u003e/s and transformed into their natural logarithmic form.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n\u003ch2\u003e2.5 Partial atomic charge\u003c/h2\u003e\n\u003cp\u003eTo ensure consistent treatment of electrostatic interactions, partial atomic charges were assigned to all framework atoms using the charge assignment scheme reported by Krokidas et al. [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e]. This charge model was consistently applied in both GCMC and MD simulations, and the corresponding charge values are summarized in Table S13 (Supplementary Information).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003e3.1 Structural basis for the 33% bIm upper substitution limit\u003c/h2\u003e\n\u003cp\u003eTo justify the selection of 33% bIm as the upper substitution level for the GCMC and MD analyses, the pore descriptors (LCD and PLD) were examined for higher-substitution models containing 44%, 55%, and 61% bIm. Structural analysis based on these descriptors revealed clear discontinuity at 33% bIm, indicating the onset of framework distortion (Table S14). These distortions were accompanied by a deterioration in the calculated diffusion selectivity (Table S15). The decrease in selectivity beyond 33% was attributed to structural degradation and reduced steric discrimination, reinforcing 33% bIm as the practical limit for topological stability. Consequently, detailed adsorption and transport analyses were restricted to compositions\u0026thinsp;\u0026le;\u0026thinsp;33% bIm, whereas higher-substitution models were used solely to establish the structural stability threshold. Therefore, the corresponding results are provided only in the Supplementary Information.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003e3.2 Grand canonical Monte Carlo (GCMC) simulation\u003c/h2\u003e\n\u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\n\u003ch2\u003e3.2.1 Force field validation\u003c/h2\u003e\n\u003cp\u003eTo establish a validated and transferable modeling protocol for gas adsorption in ZIFs, the CO\u003csub\u003e2\u003c/sub\u003e adsorption isotherms of ZIF-8 at 298 K were simulated using four force fields: UFF, DREIDING, GenericMOFs, and AMBER [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e]. The simulated isotherms were compared with the experimental and computational data reported in the literature. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, the UFF provided the closest agreement with the reference isotherms, accurately reproducing the curvature and magnitude of the isotherm over the entire pressure range. In contrast, the isotherms predicted by DREIDING, GenericMOFs, and AMBER systematically underestimated the adsorption uptake, particularly at higher pressure. The UFF results showed good consistency with the experimental data reported by Hwang et al. [\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e] and Klomkliang et al. [\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e] as well as with the simulation results of P\u0026eacute;rez-Pellitero et al. [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e], which followed similar adsorption trends across the studied pressure range. A larger deviation was observed relative to the predictions of Thornton et al. [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e], who reported lower adsorption capacities using the TIMTAM approach, in which the ZIF-8 framework is represented by simplified analytical pore geometries rather than an atomistic model. Consequently, guest-framework interactions and electrostatic effects are not explicitly captured, leading to differences in the predicted adsorption capacities. The strong agreement between the UFF simulations and the literature supports the selection of the UFF as the most suitable force field for subsequent adsorption simulations.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\n\u003ch2\u003e3.2.2 Force field transferability for CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e\u003c/h2\u003e\n\u003cp\u003eFollowing UFF validation for CO\u003csub\u003e2\u003c/sub\u003e adsorption, the transferability of the model was tested by simulating the CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e adsorption isotherms in ZIF-8 using identical rigid framework conditions. The results were compared with the literature data from Zhou et al. [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e] and P\u0026eacute;rez-Pellitero et al. [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e] to determine whether the same force field and simulation setup could reliably predict the gas uptake behavior of gases with different molecular sizes, polarizabilities, and interaction strengths. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the simulated CH\u003csub\u003e4\u003c/sub\u003e isotherm reproduced the experimental data of Zhou et al. [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e] with deviations remaining within the experimental uncertainty across a pressure range of up to 30 bar. The simulations also showed excellent agreement with the GCMC results of P\u0026eacute;rez-Pellitero et al. [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e], who modeled ZIF-8 using a rigid framework with modified UFF, and the framework charges were derived from DFT calculations. Despite variations in the model parameterization, the simulated uptake remained consistent with the reported values. This agreement highlights the robustness of the UFF framework in capturing solid-fluid interactions without requiring system-specific reparameterization.\u003c/p\u003e\n\u003cp\u003eSimilarly, the simulated H\u003csub\u003e2\u003c/sub\u003e adsorption isotherm shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e aligns well with the experimental results of Zhou et al. [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e], with deviations remaining within the acceptable limits throughout the pressure range. Given the low polarizability and small kinetic diameter of H\u003csub\u003e2\u003c/sub\u003e, an accurate modeling of its uptake relies heavily on dispersion interactions. The observed agreement implies that the UFF model, even without flexibility, offers a reasonable approximation of gas-framework interactions for H\u003csub\u003e2\u003c/sub\u003e under moderate pressures in rigid ZIF-8.\u003c/p\u003e\n\u003cp\u003eThese results confirm the transferability of the UFF, which was initially validated for CO\u003csub\u003e2\u003c/sub\u003e, to CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e without requiring any parameter adjustments. Its consistent performance across gases with varying sizes and interaction profiles demonstrates its robustness in simulating adsorption in ZIF-8. Therefore, the UFF was adopted for all subsequent simulations involving mixed-linker ZIF-7-8 frameworks to maintain methodological consistency and enable reliable comparisons across systems.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\n\u003ch2\u003e3.2.3 Influence of bIm incorporation on gas adsorption behavior\u003c/h2\u003e\n\u003cp\u003eThe adsorption behaviors of H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e were examined across the ZIF-8 to ZIF-7 series, focusing on the mixed-linker analogues ZIF-7-8 (11% bIm), ZIF-7-8 (22% bIm), and ZIF-7-8 (33% bIm), which feature the progressive incorporation of bIm. ZIF-8 served as the parent framework, while ZIF-7, comprising 100% bIm linkers, was treated as a structural boundary, representing the upper limit of framework polarity and the lower bound of pore accessibility. This compositional gradient enabled a detailed analysis of how incremental linker substitution influences adsorption thermodynamics and capacity. GCMC simulations were used to generate pressure-dependent isotherms and corresponding ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e profiles. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e presents the simulated adsorption isotherms for (a) H\u003csub\u003e2\u003c/sub\u003e, (b) CH\u003csub\u003e4\u003c/sub\u003e, and (c) CO\u003csub\u003e2\u003c/sub\u003e across the five ZIF variants, illustrating the gas-specific uptake behavior as a function of adsorbate properties and framework composition.\u003c/p\u003e\n\u003cp\u003eAcross all frameworks, the adsorption capacities followed the order CO\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CH\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003e, reflecting the distinct physicochemical properties of these gases. CO\u003csub\u003e2\u003c/sub\u003e exhibited the highest uptake due to its large quadrupole moment and high polarizability, which promote strong electrostatic interactions with the polar and \u0026pi;-electron-rich regions of the framework. These interactions significantly enhance the CO\u003csub\u003e2\u003c/sub\u003e adsorption affinity of MOFs containing open metal sites and polar functional groups [\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e]. This trend is consistent with the findings of Chowdhury et al. [\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e], who reported higher CO\u003csub\u003e2\u003c/sub\u003e uptake relative to CH\u003csub\u003e4\u003c/sub\u003e in Cu-BTC and MIL-101, attributing this trend to strong interactions between CO\u003csub\u003e2\u003c/sub\u003e and charged adsorption sites within the frameworks. In the mixed-linker ZIF-7-8 (33% bIm), the CO\u003csub\u003e2\u003c/sub\u003e uptake reached approximately 6.1 mmol/g at 10 bar, exceeding that of the parent ZIF-8 (5.5 mmol/g), indicating the enhanced adsorption affinity resulting from the incorporation of bIm linkers. The comparison was made at 10 bar because the CO\u003csub\u003e2\u003c/sub\u003e isotherms increase sharply at low pressures and approach a plateau at relatively low pressures, reflecting strong framework-guest interactions and early pore filling. In contrast, CH\u003csub\u003e4\u003c/sub\u003e adsorption increased gradually across the studied pressure range without reaching a clear plateau at 30 bar. Therefore, the CH\u003csub\u003e4\u003c/sub\u003e performance was evaluated at 30 bar, where ZIF-7-8 (33% bIm) reached 4.1 mmol/g, consistent with its lower polarizability and the absence of a quadrupole moment. H\u003csub\u003e2\u003c/sub\u003e showed the lowest uptake, reaching 0.51 mmol/g at 30 bar, which was attributed to its weak van der Waals interactions and minimal polarizability. The incorporation of \u0026pi;-conjugated bIm linkers increases the polarity and electronic richness of the pore environment, thereby strengthening the framework-guest interactions and enhancing the adsorption, particularly for CO\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eThe calculated LCD and PLD values are summarized in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e and were used to evaluate the largest internal cavity and pore aperture sizes within the framework. ZIF-8 exhibited a PLD of 3.41 \u0026Aring; and an LCD of 11.39 \u0026Aring;, consistent with experimental and computational benchmarks [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e], affirming the validity of the pore analysis approach. As the bIm fraction increased, the LCD and PLD values decreased systematically. In ZIF-7-8 (33% bIm), the PLD was reduced to 2.54 \u0026Aring; and the LCD to 9.12 \u0026Aring;, whereas in ZIF-7, complete bIm substitution resulted in an ultra-constrained framework with a PLD of 2.40 \u0026Aring; and an LCD of 5.59 \u0026Aring;. These structural contractions are directly correlated with the observed reduction in gas uptake, particularly for CO\u003csub\u003e2\u003c/sub\u003e and CH\u003csub\u003e4\u003c/sub\u003e in the most bIm-rich frameworks. Given the kinetic diameters of CO\u003csub\u003e2\u003c/sub\u003e (3.3 \u0026Aring;), CH\u003csub\u003e4\u003c/sub\u003e (3.8 \u0026Aring;), and H\u003csub\u003e2\u003c/sub\u003e (2.9 \u0026Aring;), the proximity of the ZIF-7-8 (33% bIm) PLD to the kinetic diameter of CO\u003csub\u003e2\u003c/sub\u003e explains its ability to maintain a relatively high uptake, despite the reduced pore size.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eLCD and PLD values for ZIF-8, mixed-linker ZIF-7-8, and ZIF-7\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eZIF Variant\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eLCD (\u0026Aring;)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ePLD (\u0026Aring;)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5.5880\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.5417\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.3929\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.4089\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7-8 (11% bIm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.3874\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.4075\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7-8 (22% bIm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e11.3874\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.4075\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7-8 (33% bIm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e9.1167\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.5441\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe adsorption isotherms support this interpretation. CO\u003csub\u003e2\u003c/sub\u003e exhibited the steepest initial uptake and early saturation due to the strong electrostatic interactions arising from its quadrupole moment and high polarizability. In contrast, CH\u003csub\u003e4\u003c/sub\u003e, a nonpolar molecule, displayed gradual uptake over the pressure range and no sharp inflections, indicating uniform dispersive interactions. A slight increase in curvature with increasing bIm content suggests mild energetic heterogeneity arising from enhanced surface polarizability. H\u003csub\u003e2\u003c/sub\u003e, with its minimal polarizability and small kinetic diameter, exhibited linear isotherms across all frameworks, indicating uniformly weak and non-site-specific physisorption governed by Henry\u0026rsquo;s law. The introduction of bIm linkers enhanced the uptake of all three gases across the series, particularly at low pressure, where increased \u0026pi;-conjugation and polarity at the pore surface boosted the interaction strengths without compromising pore accessibility. Although incorporating bIm linkers enhances the framework polarity and strengthens the host-guest interactions, excessive bIm substitution introduces severe steric constraints.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e presents the pressure-dependent ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e profiles for (a) H\u003csub\u003e2\u003c/sub\u003e, (b) CH\u003csub\u003e4\u003c/sub\u003e, and (c) CO\u003csub\u003e2\u003c/sub\u003e, illustrating the variation in adsorption strength across the ZIF-7-8 series. For CO\u003csub\u003e2\u003c/sub\u003e, ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e increased from 25.99 kJ/mol in ZIF-8 to 29.28 kJ/mol in ZIF-7-8 (33% bIm), reaching a maximum value of 33.8 kJ/mol in ZIF-7. This trend reflects the stronger electrostatic and quadrupole-\u0026pi; interactions generated by the increased polarity and aromaticity introduced by bIm linkers. However, despite exhibiting the highest ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e value, ZIF-7 showed a significantly lower adsorption capacity due to its small PLD (2.40 \u0026Aring;), which restricts the accessible pore volume. In contrast, ZIF-7-8 (33% bIm) maintained stronger host-guest interactions while preserving sufficient pore accessibility, leading to a higher overall adsorption performance. For CH\u003csub\u003e4,\u003c/sub\u003e adsorption is dominated by dispersion interactions. The ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e increased from 15.99 in ZIF-8 to 24.34 kJ/mol in ZIF-7, reflecting enhanced confinement and increased contact between the adsorbate and the framework as the pore environment became more constricted. Nevertheless, the severe steric hindrance in ZIF-7 reduces the adsorption capacity, whereas mixed-linker frameworks maintain a higher uptake due to more accessible pore space. In contrast, H\u003csub\u003e2\u003c/sub\u003e displayed relatively flat ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e values (5.9\u0026ndash;9.4 kJ/mol) across all frameworks, indicating weak and non-specific physisorption governed primarily by van der Waals interactions. These results demonstrate a clear structure-property trade-off within the ZIF-7-8 series: increasing the bIm content strengthens the adsorption energetics through enhanced polarity and \u0026pi;-interactions, but excessive substitution reduces pore accessibility. The mixed-linker framework ZIF-7-8 (33% bIm) achieves an optimal balance between the interaction strength and geometric accessibility.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe isotherm profiles and ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e behavior present a coherent picture of the gas-framework interaction landscape. CO\u003csub\u003e2\u003c/sub\u003e benefited the most from the increased bIm content, exhibiting high uptake and strong binding in ZIF-7-8 (33% bIm). Notably, ZIF-7 demonstrates that a high ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e does not necessarily translate to a high adsorption capacity, as excessive pore constriction limits accessibility. Among the investigated structures, ZIF-7-8 (33% bIm) achieved an optimal balance between enhanced polarity and \u0026pi;-interactions while maintaining sufficient pore accessibility, resulting in optimal performance within the series.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n\u003ch2\u003e3.3 Molecular dynamics (MD) simulation\u003c/h2\u003e\n\u003c/div\u003e\n\u003ch3\u003e3.3.1 Diffusivity in ZIF-8: literature benchmarking and model validation\u003c/h3\u003e\n\u003cp\u003eTo assess the reliability of the simulation methodology and force field parameters, the computed values for ZIF-8 (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e) were compared with literature data reported under comparable conditions (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). Since all the ZIF-7-8 structures examined herein were derived by linker substitution from the ZIF-8 framework, it is essential that the force field accurately reproduces the known transport properties of ZIF-8 to ensure the reliability and transferability of the subsequent results.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e for H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e in mixed-linker ZIF-7-8 variants\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eZIF Framework\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003eH2\u003c/sub\u003e(m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003eCH4\u003c/sub\u003e (m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003eCO2\u003c/sub\u003e (m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003eH2\u003cem\u003e/\u003c/em\u003eCH4\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003eH2\u003cem\u003e/\u003c/em\u003eCO2\u003c/sub\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.27 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.72 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e7.93 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e8.33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e285.92\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7-8 (11% bIm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.38 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.81 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e7.75 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e13.15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e307.32\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7-8 (22% bIm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.18 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.47 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e6.96 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e14.84\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e313.15\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7-8 (33% bIm)\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.13 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.04 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e5.34 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e20.48\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e399.60\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZIF-7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.42 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e7.85 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.23 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e18.04\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e63.49\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eLiterature-reported \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e, CH\u003csub\u003e4\u003c/sub\u003e, and CO\u003csub\u003e2\u003c/sub\u003e in ZIF-8\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eGas\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e (m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eLoading\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eTemperature (K)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eForce Fields\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eRef\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"5\" align=\"left\"\u003e\n\u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.62 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e4.03 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e295 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eDREIDING\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e5.47 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10 bar\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF \u0026amp; DREIDING\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.28 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e300 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF \u0026amp; AMBER\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e \u0026minus;\u0026thinsp;1.8 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0\u0026ndash;30 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e300 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF \u0026amp; DREIDING\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"5\" align=\"left\"\u003e\n\u003cp\u003eCH\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e3.24 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e285 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eZhang et al.[\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.75 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e295 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eDREIDING\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.80 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10 bar\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF \u0026amp; DREIDING\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.70 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eWu et al.[\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.40 \u0026times; 10⁻\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e12 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExperimental study\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"5\" align=\"left\"\u003e\n\u003cp\u003eCO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e1.71 \u0026times; 10⁻\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e3.90 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10 bar\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF \u0026amp; DREIDING\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e4.30 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;11\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eWu et al.[\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e2.20\u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;10\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e298 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eExperimental study\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"char\" char=\"\u0026times;\"\u003e\n\u003cp\u003e5.463 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;10\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6 mol/uc\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e300 K\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eUFF \u0026amp; AMBER\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eFor H\u003csub\u003e2\u003c/sub\u003e, the computed \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e in ZIF-8 was 2.27 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s, which is in agreement with the values reported in the literature for flexible framework models. Slightly higher values have also been reported, which can be attributed to variations in the force field parameterization [\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e]. For CH\u003csub\u003e4\u003c/sub\u003e, the computed \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of 2.72 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s also lies within the range reported in the literature. Most studies report values on the order of 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s when flexible frameworks are employed. However, significantly lower values have been reported in some cases, such as in the study by Verploegh et al. [\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e], who used a different force field parameterization and lower simulation temperature. These differences highlight the sensitivity of CH\u003csub\u003e4\u003c/sub\u003e diffusion to the force field selection and simulation conditions. For CO\u003csub\u003e2\u003c/sub\u003e, the calculated diffusivity of 7.93 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s is well within the range reported in the literature. Previous computational studies have reported diffusivities spanning approximately 10\u003csup\u003e-11\u003c/sup\u003e-10\u003csup\u003e-10\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s, depending on the force field and loading conditions.\u003c/p\u003e\n\u003cp\u003eThe observed diffusivity trend of H\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CH\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CO\u003csub\u003e2\u003c/sub\u003e reflects a balance among the molecular size, adsorption strength, and gas-framework interaction characteristics. H\u003csub\u003e2\u003c/sub\u003e, the smallest molecule (2.89 \u0026Aring;), exhibited the highest diffusivity (2.13 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e to 2.38 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s), which was enabled by the weak van der Waals forces, low polarizability, and minimal adsorption. CH\u003csub\u003e4\u003c/sub\u003e, which has a larger diameter (3.8 \u0026Aring;), experiences greater steric hindrance and stronger dispersion interactions, leading to reduced diffusivity (1.04 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e to 2.72 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s). Although CO\u003csub\u003e2\u003c/sub\u003e (3.3 \u0026Aring;) is slightly smaller than CH\u003csub\u003e4\u003c/sub\u003e, it displayed the lowest diffusivity (2.23 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e to 7.93 \u0026times; 10\u003csup\u003e\u0026ndash;11\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s), driven by its strong quadrupole moment and substantial electrostatic interactions with polar sites in the framework, which enhanced adsorption and limited mobility. The agreement between the computed diffusion coefficients and literature values, together with the correct reproduction of the expected diffusivity hierarchy, further confirmed the reliability of the adopted simulation methodology and force field parameters.\u003c/p\u003e\n\u003cdiv id=\"Sec18\" class=\"Section3\"\u003e\n\u003cdiv class=\"Heading\"\u003e2.1.1 Influence of bIm incorporation on diffusivity\u003c/div\u003e\n\u003cp\u003eIncorporating bIm linkers into the ZIF-7-8 series alters the framework geometry and chemistry, which directly affects the gas diffusivity. Compared to ZIF-8, which contains only mIm linkers, the bIm-modified structures, particularly ZIF-7-8 (33% bIm), exhibit increased steric bulk and higher framework polarity. This structural modification led to a measurable reduction in the PLD, which defines the narrowest passage available for molecular transport. For example, the PLD decreased from 3.41 \u0026Aring; in ZIF-8 to 2.54 \u0026Aring; in ZIF-7-8 (33% bIm), reflecting the tighter apertures caused by bulkier bIm linkers. This reduction intensifies the geometric confinement and restricts the diffusion of larger gases such as CH\u003csub\u003e4\u003c/sub\u003e and CO\u003csub\u003e2\u003c/sub\u003e. Consequently, the diffusivities of CH\u003csub\u003e4\u003c/sub\u003e and CO\u003csub\u003e2\u003c/sub\u003e decreased from ZIF-8 to ZIF-7-8 (33% bIm) (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eIn addition to the geometric effects, the increased polarity introduced by the bIm linkers enhanced the electrostatic interactions with polar molecules such as CO\u003csub\u003e2\u003c/sub\u003e. These enhanced interactions resulted in longer residence time and reduced mobility, contributing to the lower CO\u003csub\u003e2\u003c/sub\u003e diffusivity observed in ZIF-7-8 (33% bIm) compared to ZIF-8. In contrast, H\u003csub\u003e2\u003c/sub\u003e diffusion was only marginally affected, with the diffusivity decreasing slightly from 2.27 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e to 2.13 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s across the structures. This limited sensitivity was attributed to the small kinetic diameter and weak dispersion-dominated interactions of H\u003csub\u003e2\u003c/sub\u003e with the framework, resulting in negligible adsorption and low diffusion barriers. The data confirmed that linker substitution modulates pore geometry and host-guest interaction strength, with pronounced effects on larger or more strongly adsorbing gases, while exerting minimal influence on the diffusion of small, weakly interacting species, such as H\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eThe diffusion selectivity ratios of H\u003csub\u003e2\u003c/sub\u003e/CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e/CO\u003csub\u003e2\u003c/sub\u003e, calculated using MD, underscore the potential of ZIF-7-8 for kinetic-based gas separations. Among the frameworks investigated, ZIF-7-8 (33% bIm) demonstrated the highest selectivity. This pronounced enhancement in kinetic discrimination arises from the progressive incorporation of bIm linkers, which increase the framework polarity and induce geometric confinement within the pores. These modifications selectively hinder the mobility of larger or more strongly interacting gases, such as CH\u003csub\u003e4\u003c/sub\u003e and CO\u003csub\u003e2\u003c/sub\u003e, while having minimal effect on H\u003csub\u003e2\u003c/sub\u003e transport due to its small kinetic diameter and weak van der Waals interactions with the framework. The results exemplify a fundamental trade-off between adsorption strength and diffusivity: CO\u003csub\u003e2\u003c/sub\u003e, which forms strong electrostatic interactions with polar framework sites, exhibits reduced diffusivity, whereas H\u003csub\u003e2\u003c/sub\u003e retains rapid and unobstructed mobility. This contrasting behavior, captured through detailed molecular simulations, confirms that linker substitution and polarity modulation can be systematically leveraged to tune diffusion selectivity. The overall diffusivity trend (H\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CH\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CO\u003csub\u003e2\u003c/sub\u003e) reflects the interplay between molecular size, adsorption energetics, and interaction type. The high H\u003csub\u003e2\u003c/sub\u003e/CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e/CO\u003csub\u003e2\u003c/sub\u003e selectivity values obtained for ZIF-7-8 (33% bIm) suggest that it is a promising candidate for membrane-based H\u003csub\u003e2\u003c/sub\u003e separation applications.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\n\u003ch2\u003e3.4 RDF analysis: ZIF-7-8 (33% bIm)\u003c/h2\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e presents the RDF profiles for (a) H\u003csub\u003e2\u003c/sub\u003e, (b) CH\u003csub\u003e4\u003c/sub\u003e, and (c) CO\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm), illustrating the spatial correlations between the adsorbed gas molecules and key framework atoms. For each gas, the RDFs were plotted for guest-guest, guest-nitrogen (from the imidazolate linker), and guest-metal pairs. ZIF-7-8 (33% bIm) was selected for detailed analysis because it exhibited the most significant enhancement in adsorption capacity and selectivity within the series, which was attributed to its distinctive framework polarity and electrostatic field. The RDFs resolved the spatial distribution of adsorbates around specific framework sites, providing direct molecular-level insights into the structural origins of the exceptional uptake and selectivity observed in ZIF-7-8 (33% bIm).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe RDF analysis of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm) indicated a highly delocalized adsorption environment with no evidence of site-specific binding (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(a)). The H\u003csub\u003e2\u003c/sub\u003e-H\u003csub\u003e2\u003c/sub\u003e correlation exhibited a broad peak at \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.9 \u0026Aring;, with a maximum \u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.5, indicating moderate guest-guest proximity due to spatial crowding rather than directional attraction. The host-guest RDFs, H\u003csub\u003e2\u003c/sub\u003e-Zn, H\u003csub\u003e2\u003c/sub\u003e-N2 (blm), and H\u003csub\u003e2\u003c/sub\u003e-N1 (mlm), displayed broad, low-intensity peaks (\u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1.4, \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.7\u0026ndash;5.2 \u0026Aring;), confirming the absence of preferential coordination in the structure. Consistently, the ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e remained nearly constant between 6.78 and 6.82 kJ/mol, indicating weak and non-specific interactions. These values align with the range reported by Murray et al. [\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e], (4\u0026ndash;7 kJ/mol for H\u003csub\u003e2\u003c/sub\u003e in MOFs), which is insufficient to drive site-specific adsorption. The absence of sharp RDF features also corresponds to the observed linearity of the H\u003csub\u003e2\u003c/sub\u003e adsorption isotherms and high diffusivity, where only minor reductions relative to ZIF-8 arise from steric effects rather than energetic barriers. Although bIm incorporation increases the framework polarity and introduces additional nitrogen sites, these modifications do not enhance H\u003csub\u003e2\u003c/sub\u003e adsorption. The RDF and ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e trends confirmed that adsorption was dominated by dispersion forces and accessible pore volume, with negligible electrostatic contributions. A similar trend was reported by Wu et al [\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e]. for ZIF-8/GO composites, where modest increases in H\u003csub\u003e2\u003c/sub\u003e uptake and isosteric heat were attributed to steric or surface effects rather than directional binding interactions. Thus, although bIm linkers alter the pore geometry and transport pathways, their influence remains limited by the inherently weak polarizability and lack of a quadrupole moment in H\u003csub\u003e2\u003c/sub\u003e molecules.\u003c/p\u003e\n\u003cp\u003eThe RDF analysis for CH\u003csub\u003e4\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(b)) revealed a spatially diffuse interaction profile, consistent with the nonpolar character of the adsorbate and its weak affinity for specific framework sites. The CH\u003csub\u003e4\u003c/sub\u003e-CH\u003csub\u003e4\u003c/sub\u003e correlation exhibited a broad peak centered at \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.1 \u0026Aring; with \u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.6, indicating moderate intermolecular proximity arising from volumetric crowding rather than attractive interactions. The host-guest RDFs, CH\u003csub\u003e4\u003c/sub\u003e-Zn, CH\u003csub\u003e4\u003c/sub\u003e-N2 (blm), and CH\u003csub\u003e4\u003c/sub\u003e-N1 (mlm), exhibited comparable and low-intensity peaks between \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.7 and 5.1 \u0026Aring;, with \u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.1\u0026ndash;1.3, confirming the absence of site-specific interactions across the framework. Despite the increased polarity and \u0026pi;-electron density of the bIm linkers, no evidence of enhanced CH\u003csub\u003e4\u003c/sub\u003e-framework interactions in ZIF-7-8 (33% bIm) relative to ZIF-8 was observed, as the RDFs remained broadly distributed and weak. However, the steric bulk introduced by bIm substitution reduces the accessible pore volume and introduces greater hindrance, resulting in a significant drop in CH\u003csub\u003e4\u003c/sub\u003e mobility (1.04 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s for ZIF-7-8 (33% bIm) vs. 2.72 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s for ZIF-8). This finding aligns with the high-pressure gravimetric data reported by Arami-Niya et al. [\u003cspan class=\"CitationRef\"\u003e60\u003c/span\u003e], who observed that the CH\u003csub\u003e4\u003c/sub\u003e uptake in ZIF-7 remained negligible at low pressures and increased sharply only above 1245 kPa, owing to the gate-opening transition. Given the structural similarity of ZIF-7-8 (33% bIm) to ZIF-7, particularly the incorporation of bIm linkers, these findings support the conclusion that CH\u003csub\u003e4\u003c/sub\u003e uptake is driven by steric accessibility in a flexible pore environment rather than by strong host-guest interactions.\u003c/p\u003e\n\u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e(c), the RDF between the carbon atom of CO\u003csub\u003e2\u003c/sub\u003e and the nitrogen atom of the bIm linker (N2) exhibits a sharp peak at \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.8 \u0026Aring; with a peak height of \u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.3, indicating that N2 is the preferred site for interactions. The sharpness and proximity of this peak indicate directional electrostatic attraction driven by quadrupolar stabilization and enhanced electron density associated with the aromatic bIm unit. In contrast, weaker and more diffuse interactions were observed for CO\u003csub\u003e2\u003c/sub\u003e-N1 at \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.5 \u0026Aring; (\u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.6) and CO\u003csub\u003e2\u003c/sub\u003e-Zn at \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.2 \u0026Aring; (\u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.5), indicating weaker and less frequent interactions with the mIm linker and metal centers. The CO\u003csub\u003e2\u003c/sub\u003e-CO\u003csub\u003e2\u003c/sub\u003e RDF presents a well-defined peak at \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.9 \u0026Aring; and \u003cem\u003eg(r)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.2, indicating significant guest-guest proximity near high-affinity N2 regions and suggesting cooperative pore filling rather than isolated adsorption. These simulation results are consistent with the high-resolution neutron diffraction study by Zhao et al. [\u003cspan class=\"CitationRef\"\u003e61\u003c/span\u003e], which demonstrated preferential CO\u003csub\u003e2\u003c/sub\u003e adsorption in ZIF-7 within cavities formed by Zn-bIm rings, where linker rotation generated access channels for CO\u003csub\u003e2\u003c/sub\u003e. The close correspondence between these experimental observations and the simulated RDF profile underscores the pivotal role of bIm in creating electronically favorable and sterically accessible adsorption sites, thereby controlling the CO\u003csub\u003e2\u003c/sub\u003e selectivity within the mixed-linker framework.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\n\u003ch2\u003e3.5 Impact of guest loading on \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm)\u003c/h2\u003e\n\u003cp\u003eThe \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm), as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, exhibited a significant monotonic decline with increasing loading from 3 to 40 mol/uc at 308 K under the NVT conditions. At 3 mol/uc, the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm) reached 2.03 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s, indicative of a dilute regime in which H\u003csub\u003e2\u003c/sub\u003e experiences minimal resistance, negligible guest-guest interactions, and nearly unrestricted access to the pore network. Despite the presence of sterically bulkier bIm linkers, the framework retained sufficient openness and conformational flexibility to support efficient diffusion under low loading.\u003c/p\u003e\n\u003cp\u003eAs the loading increased beyond 5 mol/uc, a progressive decline in \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e was observed, reaching 8.85 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s at 40 mol/uc. This reduction is attributed to the accumulation of guest molecules, which reduces the available free volume and increases the frequency of intermolecular collisions, thereby imposing kinetic limitations on diffusion. Under these conditions, transport is predominantly constrained by steric effects arising from crowding within the pore channels rather than by strong host-guest interactions, consistent with the weak and delocalized interactions of H\u003csub\u003e2\u003c/sub\u003e, as indicated by the RDF and ∆\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003est\u003c/em\u003e\u003c/sub\u003e analyses. Similar behaviors have been reported in previous studies. Chmelik et al.[\u003cspan class=\"CitationRef\"\u003e62\u003c/span\u003e] observed a significant decrease in H\u003csub\u003e2\u003c/sub\u003e diffusivity with increasing occupancy due to steric congestion within the pores, while Pantatosaki et al.[\u003cspan class=\"CitationRef\"\u003e63\u003c/span\u003e] reported a comparable decline in ZIF-8 using QENS, attributing it to intermolecular collisions dominating gate-opening effects at high loadings. In ZIF-7-8 (33% bIm), the incorporation of bulky bIm linkers further reduced the accessible window area, amplifying the steric obstruction relative to ZIF-8 and reinforcing the crowding effect at high loadings.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\n\u003ch2\u003e3.6 Impact of temperature on \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e in ZIF-7-8 (33% bIm)\u003c/h2\u003e\n\u003cp\u003eThe temperature dependence of H\u003csub\u003e2\u003c/sub\u003e diffusion in ZIF-7-8 (33% bIm) was investigated via MD simulations over the temperature range of 200\u0026ndash;700 K under moderate loading. ZIF-8 has been shown to retain structural integrity up to 500\u0026deg;C (773 K) under an inert atmosphere and 350\u0026deg;C (623 K) in an oxidative environment, as evidenced by thermogravimetric and XRD analyses [\u003cspan class=\"CitationRef\"\u003e64\u003c/span\u003e]. Further studies confirm stability up to 600\u0026deg;C (873 K), beyond which decomposition becomes significant [\u003cspan class=\"CitationRef\"\u003e65\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e66\u003c/span\u003e]. In contrast, ZIF-7 maintains its crystalline framework up to 400\u0026deg;C (673 K) under inert conditions before structural collapse occurs [\u003cspan class=\"CitationRef\"\u003e66\u003c/span\u003e]. These reported stability limits indicate that the temperature range employed in the present simulations remains within the thermally stable regime of the framework.\u003c/p\u003e\n\u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, the \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e of H\u003csub\u003e2\u003c/sub\u003e increases significantly with temperature, rising from 4.2 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s at 200 K to a peak value of 4.5 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s at 600 K. This trend is characteristic of thermally activated diffusion, in which elevated thermal energy enhances the ability of gas molecules to overcome the steric barriers imposed by pore apertures and framework topography. The observed increase in \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e with temperature arises from the improved kinetic energy of H\u003csub\u003e2\u003c/sub\u003e molecules, which reduces their average residence time within the adsorption sites and increases the likelihood of overcoming the local energy barriers imposed by framework topology. As thermal energy increases, the molecules experience more frequent and longer-range displacements, resulting in a steeper MSD slope over time and, consequently, higher \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e. This effect reflects a thermodynamically driven enhancement of molecular displacement rather than a change in the diffusion mechanism, indicating that at elevated temperatures, the dynamic interaction between the guest molecules and the framework becomes less restrictive.\u003c/p\u003e\n\u003cp\u003eThe Arrhenius plot in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e, constructed from ln \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e versus 1/\u003cem\u003eT\u003c/em\u003e, displays a clear linear relationship with a correlation coefficient (R\u0026sup2;) of 0.9963. This high degree of linearity supports the conclusion that a consistent thermally activated regime governs H\u003csub\u003e2\u003c/sub\u003e diffusion in ZIF-7-8 (33% bIm) over the studied temperature range (200\u0026ndash;700 K). The derived activation energy of 5.2 kJ/mol reflects the average energetic barrier for H\u003csub\u003e2\u003c/sub\u003e motion through the framework, indicating weak physisorptive interactions with the pore environment. The intercept value of -16.151 corresponds to the logarithm of the pre-exponential factor, which measures the theoretical diffusion limit in the absence of activation barriers. These values indicate a regime dominated by weak steric resistance and physisorptive interactions. Although Verploegh et al. [\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e] reported poor linearity (R\u0026sup2; = 0.29) for H\u003csub\u003e2\u003c/sub\u003e diffusion in ZIF-8 over a limited temperature range (0-150\u0026deg;C) using only four data points, their observations were attributed to the nearly barrierless diffusion environment in ZIF-8. In contrast, this study employed a broader temperature range, enabling a more accurate identification of diffusion trends and improved statistical reliability in the Arrhenius analysis. Moreover, the bIm linkers in ZIF-7-8 (33% bIm) introduced moderate structural rigidity, generating sufficient energetic heterogeneity to produce measurable activation behavior, even for light gases such as H\u003csub\u003e2\u003c/sub\u003e. These distinctions affirm that, in ZIF-7-8 (33% bIm), H\u003csub\u003e2\u003c/sub\u003e diffusion is governed by a stable, thermally responsive mechanism, underscoring the potential of the framework for temperature-tuned separation applications.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis study elucidated gas adsorption and diffusion in mixed-linker ZIF-7-8 by integrating GCMC and MD simulations. Using rigid-framework GCMC, the UFF most reliably reproduced single-component isotherms and isosteric heats across ZIFs, capturing the CO\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CH\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003e uptake order. Increasing the bIm content strengthened CO\u003csub\u003e2\u003c/sub\u003e adsorption through greater framework polarity and π-electron density, with ZIF-7-8 (33% bIm) providing the highest capacity while preserving pore accessibility. MD simulations using a flexible lattice revealed mobility trends inverse to adsorption strength (H\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CH\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;CO\u003csub\u003e2\u003c/sub\u003e) and identified ZIF-7-8 (33% bIm) as the optimal composition, balancing enhanced CO\u003csub\u003e2\u003c/sub\u003e uptake with unimpeded H\u003csub\u003e2\u003c/sub\u003e transport. This study reveals a clear trade-off between adsorption strength and molecular mobility, demonstrating that stronger host-guest interactions enhance adsorption while simultaneously limiting molecular transport. A direct correlation between PLD and diffusion selectivity was established, demonstrating that controlled aperture narrowing enhances selectivity without fully restricting transport. The results identify 33% bIm as a critical compositional threshold at which pore geometry, adsorption strength, and diffusion behavior converge to produce optimal separation performance. The introduction of bIm linkers creates heterogeneous adsorption environments that selectively enhance CO\u003csub\u003e2\u003c/sub\u003e interactions through nitrogen-rich sites. RDF analyses linked gas-specific interactions to nitrogen-rich bIm sites, particularly for CO\u003csub\u003e2\u003c/sub\u003e. Loading-dependent simulations showed a monotonic decline in H\u003csub\u003e2\u003c/sub\u003e diffusivity, and temperature-dependent analyses followed the Arrhenius behavior, yielding a defined activation energy for H\u003csub\u003e2\u003c/sub\u003e transport. These findings highlight the nuanced interplay between framework chemistry and pore geometry that governs separation, positioning ZIF-7-8 (33% bIm) for membrane-based H\u003csub\u003e2\u003c/sub\u003e purification.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e. The authors would like to thank Universiti Putra Malaysia for providing research grant through GPB - Geran Putra Berimpak with the vote number of 9809800 (Project No. GPB/2024/9809800 - Assessing Composite Structure in High-Flux Metal Organic Frameworks Based Mixed Matrix membrane for Carbon Capture Application). The authors would also like to thank the Department of Chemical and Environmental Engineering, the Sustainable Process Engineering Research Center (SPERC), and the Department of Chemistry, Universiti Putra Malaysia, Serdang, Selangor, Malaysia, for their valuable support and contributions to this research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e. Krsna Anand: writing – original draft, conceptualization, data curation, formal analysis; methodology. Mohamad Rezi Abdul Hamid: supervision, validation, writing – review \u0026amp; editing. Mohd F Ismail: supervision, writing – review \u0026amp; editing. Wan Azlina W.A.K.G: supervision, validation. Musab Abdul Razak: conceptualization, supervision, validation, writing – review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest\u003c/strong\u003e. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData and code availability.\u003c/strong\u003e All data that support the findings of this study are included within the article (and any supplementary files).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information.\u003c/strong\u003e The Supporting Information (PDF) includes detailed molecular models, force field parameters, and simulation protocols used in this study; model compositions (Table S1); framework models and atom typing for ZIF-8, ZIF-7-8, and ZIF-7 with visual atom-type schemes (Figures S1-S3); rigid force field parameters used for GCMC adsorption, including force field selection and the final UFF parameters (Tables S2-S3); flexible force field parameters for MD simulations (Tables S4-S12); partial charge assignments (Table S13); and compositional limit analyses (Tables S14-S15).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical approval.\u003c/strong\u003e Not Applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eInternational Energy Agency, (2019) The Future of Hydrogen\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eX. 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Soc. \u003cb\u003e136\u003c/b\u003e, 7961\u0026ndash;7971 (2014). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ja5016298\u003c/span\u003e\u003cspan address=\"10.1021/ja5016298\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-porous-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jopo","sideBox":"Learn more about [Journal of Porous Materials](http://link.springer.com/journal/10934)","snPcode":"10934","submissionUrl":"https://submission.nature.com/new-submission/10934/3","title":"Journal of Porous Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Gas separation, Grand canonical Monte Carlo (GCMC), Mixed-linker design, Molecular dynamics (MD), Zeolitic imidazolate frameworks (ZIFs)","lastPublishedDoi":"10.21203/rs.3.rs-9281024/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9281024/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations were employed to investigate ZIF-8, ZIF-7, and a series of ZIF-7-8 frameworks with increasing benzimidazolate (bIm) content. Benchmarking against literature adsorption isotherms identified the Universal Force Field (UFF) as the most reliable model for describing gas-framework interactions. Increasing the bIm content enhanced the framework polarity and CO\u003csub\u003e2\u003c/sub\u003e uptake but reduced the pore accessibility, thereby decreasing diffusivity. In contrast, H\u003csub\u003e2\u003c/sub\u003e maintained high diffusivity owing to its small size and weak interaction with the framework. Among the studied structures, ZIF-7-8 (33% bIm) achieved optimal diffusion selectivity (H\u003csub\u003e2\u003c/sub\u003e/CO\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;400, H\u003csub\u003e2\u003c/sub\u003e/CH\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;20.5), reflecting a balance between polarity and pore accessibility. Radial distribution function (RDF) analysis showed CO\u003csub\u003e2\u003c/sub\u003e clustering near the bIm nitrogen sites, whereas CH\u003csub\u003e4\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e remained more uniformly distributed. These results provide molecular-level insights into how the linker composition modulates the transport behavior, offering predictive guidance for the design of mixed-linker ZIF membranes for efficient H\u003csub\u003e2\u003c/sub\u003e purification.\u003c/p\u003e","manuscriptTitle":"Molecular Modeling of bIm-Substituted Mixed- Linker ZIFs for H2 Separation: A GCMC and MD Study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-07 09:44:49","doi":"10.21203/rs.3.rs-9281024/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-21T02:27:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"119266529945775876511219811468408601527","date":"2026-04-10T13:30:42+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-10T12:05:30+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-01T06:18:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-01T06:17:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Porous Materials","date":"2026-03-31T13:54:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-porous-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jopo","sideBox":"Learn more about [Journal of Porous Materials](http://link.springer.com/journal/10934)","snPcode":"10934","submissionUrl":"https://submission.nature.com/new-submission/10934/3","title":"Journal of Porous Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0425cfcc-47ca-43d4-94d5-416cd8cf2332","owner":[],"postedDate":"April 7th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-10T12:10:19+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-07 09:44:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9281024","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9281024","identity":"rs-9281024","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}