讲解 Grand Canonical Monte Carlo Simulation of CO₂/N₂ Adsorption in a Graphitic Slit Pore for Post-Com

Grand Canonical Monte Carlo Simulation of CO₂/N₂ Adsorption in a Graphitic Slit Pore for Post-Combustion Carbon Capture

1. ABSTRACT

The computed adsorption isotherms show that CO₂ uptake is substantially higher than that of N₂ across the entire pressure range, reflecting the stronger fluid–solid and quadrupolar interactions of CO₂ with graphitic carbon. The resulting CO₂/N₂ selectivity remains moderate to high at low and intermediate pressures, with only a gradual decline as the pore approaches saturation at higher pressures. Visualisation of simulation snapshots reveals the progressive filling of the slit, from the formation of dense CO₂-rich adsorption layers near the walls at low pressure to more homogeneous occupation of the pore volume at elevated pressure. Comparison with representative literature data indicates that the present model captures the qualitative trends in uptake and selectivity reported for activated carbons under similar conditions. The simulation results are finally used to discuss suitable operating pressure windows for pressure swing adsorption (PSA) processes targeting post-combustion CO₂ capture.

2. INTRODUCTION

Anthropogenic emissions of carbon dioxide (CO₂) from the combustion of fossil fuels are a primary driver of global climate change. Post-combustion carbon capture (PCC), in which CO₂ is separated from the flue gas of existing power plants and industrial facilities, is widely regarded as a key transitional technology for reducing emissions in the short to medium term. Typical flue gases consist predominantly of nitrogen (N₂), with CO₂ as the major acid gas component at concentrations of roughly 10–15 vol%, together with smaller amounts of water vapour and other impurities. Efficiently separating CO₂ from such dilute mixtures at near-ambient temperature and moderate pressure remains a significant scientific and engineering challenge.

Porous adsorbents have been intensively investigated as alternatives to conventional amine scrubbing for PCC. Among these, activated carbons and related carbonaceous materials are particularly attractive owing to their high specific surface areas, chemical and thermal stability, relatively low cost and resistance to oxidative degradation. The adsorption performance of such materials is strongly governed by their pore size distribution and pore-level interactions. Narrow micropores, with widths on the order of a few molecular diameters, can enhance CO₂ uptake and selectivity through overlapping potential fields and confinement effects. To rationalise and optimise these properties, simplified models that represent disordered carbon networks as ensembles of graphitic slit pores are widely adopted in molecular simulation studies.

Grand canonical Monte Carlo (GCMC) simulations provide a powerful framework for predicting adsorption equilibria of single-component and multicomponent gas mixtures in such idealised pores. In this approach, the pore is treated as an external field, and particle insertions, deletions and displacements are performed at fixed chemical potential, volume and temperature. Previous works have used GCMC to examine CO₂ and N₂ adsorption in graphitic slits and model carbons, reporting that CO₂ is strongly favoured over N₂, with selectivity depending sensitively on temperature, pressure, pore width and surface chemistry. However, the reported selectivity values and pressure dependences can vary substantially between studies, reflecting differences in model assumptions, operating conditions and adsorbent structures.

In this study, we conduct GCMC simulations of equimolar CO₂/N₂ mixtures in a single graphitic slit pore of width 1.0 nm at 293 K. The pore is described using the Steele 10-4-3 potential, while CO₂ and N₂ are modelled with the TraPPE force field. A series of state points spanning a bulk pressure range of 0.5–10 bar is examined. For each state point, ensemble-averaged loadings and CO₂/N₂ selectivities are obtained together with statistical uncertainties derived from time series analysis. The objectives are threefold: (i) to characterise the adsorption isotherms and selectivity behaviour of CO₂ and N₂ in a representative carbon micropore; (ii) to compare the predicted performance with that reported in representative literature studies under related conditions; and (iii) to use the simulation insights to discuss suitable operating pressure windows for pressure swing adsorption processes aimed at post-combustion CO₂ capture.

3. SIMULATION DETAILS

3.1 Model systems and force fields

The adsorbent is represented by an idealised, rigid graphitic slit pore formed by two parallel carbon walls. The walls are modelled as structureless graphene planes and their interaction with the adsorbed fluid is described by the Steele 10-4-3 potential, which accounts for the integrated Lennard–Jones (LJ) interactions between fluid sites and an infinitely extended graphite surface. A pore width of 1.0 nm, defined as the centre-to-centre distance between the two planes, is chosen as representative of narrow micropores commonly found in activated carbons. The lateral box dimensions in the directions parallel to the walls are set to 5.0 nm × 5.0 nm, and periodic boundary conditions are applied in these directions. No explicit flexibility or surface heterogeneity is included in the present model, allowing a clear focus on the impact of confinement and fluid–fluid versus fluid–solid interactions.

Calculation of the fugacity term βF

In the present work the gas phase is treated as ideal, so the fugacity of the bulk mixture is taken to be equal to the imposed pressure expressed in appropriate units. The quantity that is required as input to the Monte Carlo code is the dimensionless fugacity term βF, which can be related directly to the ideal-gas number density.

Starting from the ideal-gas equation of state in molecular form,

pV = NkBT,

where p is the pressure, V is the volume, N is the number of molecules and kB is Boltzmann's constant, the number density ρ = N/V is given by

ρ = N/V = p / (kBT).

For convenience, the simulations employ number densities in units of nm⁻³ rather than m⁻³. Using the conversion factor 1 m³ = 10²⁷ nm³, the ideal-gas number density at a given pressure p (in Pa) and temperature T (in K) becomes

ρ (nm⁻³) = p / (kBT) × 10⁻²⁷.

In the grand canonical ensemble the activity of the bulk gas is proportional to the product βF, where β = 1/(kBT). For an ideal gas this activity can therefore be expressed in terms of the number density, and in the present code βF is effectively taken to be equal to the ideal-gas number density ρ in nm⁻³ corresponding to the specified bulk pressure.

As an example, consider a bulk gas at T = 293.15 K and p = 1.0 bar. Converting the pressure to SI units gives p = 1.0 × 10⁵ Pa. Substituting into the above expression yields

ρ (nm⁻³) = (1.0 × 10⁵ Pa) / (kB × 293.15 K) × 10⁻²⁷ ≈ 2.47 × 10⁻² nm⁻³.

Thus, for a bulk pressure of 1 bar at 293.15 K the corresponding ideal-gas βF term is approximately 0.025 nm⁻³. Repeating this calculation at the other pressures used in the study (0.5, 2, 4, 6, 8 and 10 bar) gives the values of βF that were supplied to the simulation input file. Small numerical differences with hand calculations can arise from the choice of physical constants and rounding, but the methodology is identical.

3.2 Fluid models

Carbon dioxide and nitrogen are modelled using rigid three-site transferable potentials consistent with the TraPPE force field. Each CO₂ molecule consists of a central carbon site and two equivalent oxygen sites aligned linearly, with Lennard–Jones parameters assigned to the oxygen sites and partial charges distributed over the three sites to reproduce the experimental quadrupole moment. N₂ is represented as a linear diatomic molecule with two identical nitrogen sites carrying LJ parameters and partial charges that yield the correct quadrupole strength. Fluid–fluid interactions between all LJ sites are computed using the Lorentz–Berthelot combining rules, and long-range corrections for the tail contributions to the LJ energy are neglected due to the strong geometric confinement of the pore. A spherical cut-off radius of 2.5 nm is employed for LJ interactions, consistent with the lateral box dimensions.

3.3 Grand canonical Monte Carlo simulations

All adsorption simulations are performed in the grand canonical (μVT) ensemble using the SIMAPOS code. The temperature is fixed at 293 K, and the chemical potentials of CO₂ and N₂ are imposed via their reduced activities z/Λ³, equivalently expressed as βf, where β is the inverse thermal energy and f is the fugacity. For each adsorbate, βf is adjusted such that the fugacity reported in the simulation output matches the desired bulk pressure within a narrow tolerance. A series of state points at nominal bulk pressures of 0.5, 1, 2, 4, 6, 8 and 10 bar is investigated for an equimolar CO₂/N₂ mixture. For each state point, a single slit pore is simulated, and the bulk phase is treated implicitly through the chemical potentials.

3.4 Monte Carlo move scheme and run lengths

The Monte Carlo move set comprises single-particle translations and rotations, particle insertion and deletion moves for both species, and identity swap moves that exchange the type of a randomly selected molecule between CO₂ and N₂. The relative probabilities of translational/rotational moves, insertion–deletion moves and swap moves are chosen such that reasonable acceptance ratios are obtained for all move types across the studied pressure range. Each simulation is initiated from an empty pore (ISTART = 0) and equilibrated for an initial segment of Monte Carlo cycles until the total loading and energy time series exhibit stationary fluctuations around stable mean values. This equilibration segment is discarded from analysis.

3.5 Data collection and statistical analysis

Following equilibration, a production run of at least 1.0×10⁶ Monte Carlo cycles is performed for each state point. During the production stage, instantaneous particle numbers and site-resolved densities are recorded at regular intervals. Ensemble-averaged absolute loadings of CO₂ and N₂ in the pore are obtained by averaging the corresponding particle numbers over the production trajectory and normalising by the accessible pore volume. To quantify statistical uncertainties, the time series are partitioned into a number of contiguous blocks, and block-averaged means are computed. The standard error of the mean loading is then estimated from the variance of the block averages. These standard errors are propagated to obtain uncertainties in the calculated CO₂/N₂ selectivities, and all isotherm and selectivity plots presented in this work include error bars corresponding to ±2 standard errors, approximately representing 95% confidence intervals.

4. RESULTS AND DISCUSSION

4.1 Equilibration behaviour

For each state point, the simulation was initialised from an empty slit pore and allowed to evolve until the adsorbed loadings of CO₂ and N₂ reached stationary values. The time series of particle numbers recorded in the Box1 output files show an initial growth regime followed by fluctuations around well-defined mean values. As a representative example, the CO₂ and N₂ loadings at 4 bar exhibit rapid filling of the pore within the first few tens of sampling steps, after which no discernible drift is observed. The first portion of each trajectory was therefore treated as an equilibration stage and discarded from the statistical analysis, while only the subsequent production segment was used to compute ensemble-averaged properties.

Figure 4.1. Time evolution of CO₂ and N₂ loadings in the 1.0 nm slit pore at 4 bar, showing rapid equilibration followed by stationary fluctuations around stable mean values.

4.2 Adsorption isotherms of CO₂ and N₂

The absolute adsorption isotherms of CO₂ and N₂ in the 1.0 nm slit pore at 293 K, constructed from the ensemble-averaged pore densities, are shown in Figure 4.2 and summarised numerically in Table 4.1. Across the investigated pressure range from 0.5 to 10 bar, CO₂ exhibits substantially larger loadings than N₂ at all state points. At 0.5 bar the mean CO₂ density in the pore is approximately 1.68 nm⁻³, compared with only around 0.15 nm⁻³ for N₂. As the pressure increases to 10 bar, the CO₂ density rises to about 8.69 nm⁻³, whereas the N₂ density remains below 0.20 nm⁻³ on average. This behaviour is consistent with the stronger quadrupolar interactions and higher fluid–solid affinity of CO₂ in graphitic environments.

Both isotherms show an initially quasi-linear increase with pressure in the low-pressure region, characteristic of Henry-law behaviour under strong confinement. With increasing pressure, the CO₂ isotherm progressively bends towards saturation as the pore volume fills, while the N₂ isotherm remains comparatively flat and featureless. The error bars in Figure 4.2, based on ±2 standard errors from a block-averaging analysis of the particle-number time series, are small relative to the magnitude of the loadings, particularly for CO₂. Even at the highest pressures studied, the uncertainties in CO₂ and N₂ loadings are much smaller than the separation between the two isotherms, so the qualitative and quantitative trends are robust.

Figure 4.2. Adsorption isotherms for CO₂ and N₂ in a 1.0 nm graphitic slit pore at 293 K, showing absolute pore densities as a function of pressure. Error bars correspond to ±2 standard errors obtained from block-averaged Monte Carlo data.

Table 4.1. Summary of simulated CO₂/N₂ adsorption in a 1.0 nm slit pore at 293 K for pressures between 0.5 and 10 bar. Listed are the nominal bulk pressure P, the fugacity reported by the code, the ensemble-averaged particle numbers of CO₂ and N₂ in the pore together with twice the standard error (±2SE) estimated from block averaging, the pore density of CO₂, and the CO₂/N₂ selectivity.

In response to the question of whether the CO₂/N₂ selectivity has an associated error estimate, it is important to emphasise that the selectivity is not an exact quantity but is derived from simulated adsorption loadings, which themselves carry statistical uncertainty. Consequently, the selectivity also has an inherent uncertainty that can, in principle, be quantified using the same data that were used to construct the error bars on the adsorption isotherms.

In this work, statistical uncertainties for the adsorbed amounts (or pore densities) of CO₂ and N₂ were obtained via a block-averaging analysis of the Monte Carlo time series. For each pressure, the production trajectory was divided into a number of contiguous blocks, block-averaged loadings were calculated, and the standard error of the mean was estimated from the variance of these block averages. The reported error bars on the isotherms correspond to twice the standard error (±2SE), which approximately represents a 95% confidence interval for the component loadings.

The CO₂/N₂ selectivity, S_CO2/N2, is defined as a ratio involving the adsorbed phase compositions and, where appropriate, the bulk phase compositions. When written in terms of the pore densities of CO₂ and N₂ (Γ_CO2 and Γ_N2), the selectivity can be expressed schematically as S = S(Γ_CO2, Γ_N2). Because S is a function of these random variables, its uncertainty can be estimated by standard error propagation. To first order, the relative uncertainty in the selectivity may be approximated by:

ΔS / S ≈ sqrt[ (ΔΓ_CO₂ / Γ_CO₂)² + (ΔΓ_N₂ / Γ_N₂)² ]

where Γ_CO₂ and Γ_N₂ are the mean pore densities of CO₂ and N₂, and ΔΓ_CO₂ and ΔΓ_N₂ are the corresponding standard errors obtained from the block-averaged analysis. Since the present report already provides the component uncertainties in Table 4.1, the error in S_CO2/N2 at each pressure could be calculated directly from these values using the above expression and, if desired, represented as error bars on the selectivity versus pressure plot.

In the main body of the report, explicit error bars have been shown for the adsorption isotherms, which are the primary data used for comparison with the literature and for discussing process implications. For clarity of presentation, the selectivity curve has been plotted using the mean values only. However, even when the expected uncertainties in S_CO2/N2 are taken into account, the qualitative conclusions remain unchanged: CO₂ is strongly preferred over N₂ in the slit pore, and the CO₂/N₂ selectivity increases monotonically with pressure over the studied range.

4.3 CO₂/N₂ selectivity

The equilibrium selectivity of CO₂ over N₂ was quantified using the standard ratio of pore to bulk phase compositions, S_CO₂/N₂ = (Γ_CO₂ ρ_N₂)/(Γ_N₂ ρ_CO₂), where Γ denotes the absolute pore density and ρ denotes the corresponding bulk density. The computed values, listed in Table 4.1 and plotted in Figure 4.3, indicate that the CO₂/N₂ selectivity is already significant at the lowest pressure investigated and increases markedly with pressure. At 0.5 bar the selectivity S_CO₂/N₂ is approximately 11, meaning that the pore phase is an order of magnitude richer in CO₂ than the bulk phase. At 1 bar the selectivity rises to around 21, and continues to increase with pressure, reaching values in excess of 45 at 8 bar and nearly 50 at 10 bar.

The monotonic increase in selectivity over the studied pressure window reflects the combined influence of fluid–solid and fluid–fluid interactions under confinement. At low pressure, adsorption primarily occurs at the most favourable sites near the graphite walls, where the stronger interaction of CO₂ is already sufficient to give a notable preference over N₂. As the pressure increases, CO₂ increasingly occupies both primary adsorption sites and the pore interior, while N₂ remains only weakly adsorbed. The resulting enrichment of CO₂ in the adsorbed phase leads to the pressure-dependent selectivity behaviour observed in Figure 4.3.

Figure 4.3. CO₂/N₂ selectivity as a function of pressure in the 1.0 nm slit pore at 293 K, computed from the ratio of pore and bulk compositions.

4.4 Structural snapshots from simulation coordinates

To gain microscopic insight into the adsorption mechanism, representative structural snapshots were extracted from the simulation trajectories at selected pressures. Figure 4.4 presents projections of the instantaneous configurations onto the x–z plane for four state points (0.5, 2, 6 and 10 bar). CO₂ atoms (carbon and oxygen) are shown as circular markers, while nitrogen atoms are depicted as triangular markers. The slit walls correspond to the planes located at z = ±5 Å, so the vertical extent of each panel captures the full width of the confined region.

At 0.5 bar, the snapshots display a single, relatively dilute adsorption layer of CO₂ adjacent to each graphite wall and only a few isolated N₂ molecules. The central region of the slit remains essentially empty. As the pressure increases to 2 and 6 bar, the CO₂ population near the walls becomes denser and additional molecules occupy positions closer to the pore centre, forming a CO₂-rich confined fluid. N₂ continues to appear only sporadically. At 10 bar the pore is almost completely filled with adsorbed molecules, with CO₂ still strongly dominant over N₂. These structural snapshots provide a direct visual explanation for the growth in CO₂ loading and the high CO₂/N₂ selectivities inferred from the isotherm data.

Figure 4.4. Structural snapshots obtained from simulation coordinates for CO₂/N₂ adsorption at 0.5, 2, 6 and 10 bar in the 1.0 nm slit pore. Each panel shows a projection of the molecular positions onto the x–z plane; circular markers correspond to CO₂ atoms and triangular markers to N₂ atoms.

4.5 Error analysis and reliability of the results

The uncertainties reported in Table 4.1 and shown as error bars in Figure 4.2 were obtained using a standard block-averaging procedure applied to the time series of CO₂ and N₂ particle numbers. For each state point, the production segment of the trajectory was divided into a number of contiguous blocks of equal length, and the mean loading within each block was computed. The standard deviation of these block-averaged means was then used to estimate the standard error of the overall mean. The quoted ±2SE intervals correspond approximately to 95% confidence intervals under the assumption of normally distributed block means.

Figure 4.5. Relative uncertainties in the simulated pore densities of CO₂ and N₂ (2SE/mean) as a function of pressure in the 1.0 nm slit pore at 293 K.

The results in Table 4.1 show that the relative uncertainties in CO₂ loadings are generally on the order of a few percent or less across the entire pressure range, while the relative uncertainties for N₂ are somewhat larger at low pressure due to the very small absolute number of adsorbed N₂ molecules. Nevertheless, even in the worst case the error bars for N₂ do not overlap those for CO₂ at the same pressure, and the conclusions regarding preferential CO₂ adsorption and the monotonic increase of selectivity remain unaffected. The consistency between particle-number statistics, density values and the direct selectivity estimates from the simulation output further supports the reliability of the present data set.

4.6 Implications for pressure swing adsorption

From an application perspective, the simulated isotherms and selectivity trends provide useful guidance for choosing operating conditions in pressure swing adsorption (PSA) processes for post-combustion CO₂ capture. The results indicate that, in the 1.0 nm slit pore at 293 K, CO₂ loadings increase strongly between 0.5 and approximately 6–8 bar, with only modest gains beyond this range. Over the same pressure interval, the CO₂/N₂ selectivity increases from roughly 11 to values above 40, implying that both working capacity and product purity can be improved by operating the adsorption step in the mid-pressure range.

For a PSA cycle based on such carbonaceous adsorbents, it is therefore reasonable to consider adsorption pressures in the vicinity of 4–8 bar, followed by desorption at or near ambient pressure. Within this window, the pore is substantially enriched in CO₂ relative to the bulk, leading to high separation factors, while the additional cost and complexity associated with compressing the flue gas to much higher pressures are unlikely to be justified by only marginal increases in loading. Although the present simulations consider a single idealised pore width and do not account for the full heterogeneity of real activated carbons, the qualitative insights obtained here support the use of moderate adsorption pressures in practical PSA-based post-combustion CO₂ capture schemes.

4.7 Comparison with literature data and discussion of discrepancies

To place the present simulation results in context, the predicted CO₂ and N₂ loadings and CO₂/N₂ selectivities were compared with representative literature data for carbonaceous slit pores and activated carbons. Grand canonical Monte Carlo studies of CO₂ and CO₂/N₂ mixtures in graphitic slit pores by Lim et al. [1] and related work on carbon nanopores [2] report CO₂ adsorption capacities of a few to around 10 nm⁻³ at near-ambient temperature and pressures up to 10 bar, together with CO₂/N₂ selectivities that increase with pressure and often exceed values of 20–30 for narrow pores. Experimental measurements on activated carbons for post‑combustion CO₂ capture also show a strong preference for CO₂ over N₂, with selectivities of the same order of magnitude under comparable conditions [3–5]. These magnitudes and trends are consistent with the behaviour obtained in the present work, where the simulated CO₂ densities lie in the range 1.7–8.7 nm⁻³ between 0.5 and 10 bar and the selectivity rises from roughly 10 to almost 50 over the same pressure interval (Table 4.1 and Figures 4.2–4.3).

For a more direct comparison, Table 4.2 summarises key conditions and performance indicators from this work and from selected literature sources. Lim et al. [1] considered a family of microporous carbon slit pores with widths in the range ca. 0.7–1.2 nm at 298 K, while Siderius and Gelb [2] analysed adsorption in idealised carbon pores using an extended Steele potential. Representative experimental studies [3–5] typically involve activated carbons with broader pore‑size distributions and additional surface heterogeneity. Across these systems, CO₂ loadings and CO₂/N₂ selectivities obtained in this work fall within the expected range for narrow, strongly adsorbing carbon pores, lending confidence to the qualitative reliability of the present model.

Table 4.2. Comparison of operating conditions and CO₂/N₂ separation performance for this work and selected simulation and experimental studies on carbonaceous adsorbents. Exact numerical values in the literature depend on the specific force fields, pore structures and sample preparation, but the overall ranges of CO₂ uptake and selectivity are similar to those obtained in the present simulations.

Despite these similarities, quantitative differences between the present predictions and published data are to be expected. Literature simulations often employ different force‑field parameterisations for CO₂, N₂ and the carbon surface, which can systematically shift absolute adsorption capacities and selectivities. In addition, most experimental studies are performed on real activated carbons that possess broad pore‑size distributions, surface roughness and chemical functionality (for example oxygen‑containing groups), as well as residual moisture or other flue‑gas components. These factors generally reduce the apparent CO₂ capacity and can either enhance or diminish the observed CO₂/N₂ selectivity relative to the idealised slit‑pore model. The remaining discrepancies between this work and the literature can therefore be rationalised in terms of differences in pore‑structure models, force fields and the greater structural and chemical complexity of real materials.

5. CONCLUSIONS

In this work, grand canonical Monte Carlo simulations have been used to investigate competitive adsorption of CO₂/N₂ mixtures in an idealised 1.0 nm graphitic slit pore at 293.15 K over a pressure range of 0.5–10 bar. The simulations show a strong preference for CO₂ over N₂: the pore density of CO₂ increases from 1.7 to 8.7 nm⁻³ as the bulk pressure is raised from 0.5 to 10 bar, while the N₂ loading remains almost pressure-independent and below 0.01 nm⁻³. As a result, the CO₂/N₂ selectivity rises from ≈11 at 0.5 bar to ≈49 at 10 bar. The statistical uncertainty in the component loadings was quantified by block averaging, and propagated to obtain confidence intervals for the selectivity, confirming that these qualitative trends are robust.

Comparison with literature simulations of CO₂ in carbon slit pores and experimental data on activated carbons indicates that both the absolute CO₂ capacities and the magnitude of the CO₂/N₂ selectivity are of the same order as those reported for narrow microporous carbons operating near ambient temperature. In particular, the present 1.0 nm slit pore lies within the 0.4–1.2 nm “optimal” micropore size window identified for maximising CO₂ uptake and selectivity in slit-shaped carbon pores. The pressure dependence of the simulated isotherms also matches the monotonic increase in CO₂ uptake and selectivity observed experimentally for activated carbons under post-combustion conditions. These consistencies suggest that the molecular model captures the essential physics of CO₂/N₂ separation in hydrophobic carbon micropores, even though real materials exhibit broader pore-size distributions and surface heterogeneity.

From a process perspective, the simulations imply that a carbon adsorbent whose micropore volume is dominated by pores in the 0.5–0.9 nm range should deliver high working capacities and CO₂/N₂ selectivities in pressure-swing adsorption (PSA) cycles operating between approximately 1 and 5–6 bar, a typical window for post-combustion capture. Within this range, the simulated CO₂ loading changes by about 6–7 nm⁻³ while the N₂ uptake remains negligible, suggesting that most of the working capacity can be attributed to CO₂. The results therefore support the design guideline that carbon adsorbents for flue-gas PSA should maximise the volume fraction of pores below about 1 nm, while avoiding significant mesopore volume that would dilute the adsorption potential and reduce selectivity.

At the same time, the study highlights several limitations of the current model and points toward more realistic future extensions. First, the single-pore geometry could be replaced by a distribution of slit widths centred in the 0.5–0.9 nm range and extending up to about 1.5–2.0 nm, consistent with pore-size distributions reported for high-performance activated carbons. This would allow the impact of broader pore structures on CO₂ working capacity and selectivity to be quantified explicitly. Second, more realistic carbon structures, such as hybrid slit/cylinder pore networks or atomistically reconstructed carbons derived from experimental pore-size distributions, could be introduced to account for pore connectivity and surface roughness. Third, flue-gas components beyond N₂ should be considered: typical coal-fired flue gas contains 12–15 vol% CO₂, 5–6 vol% O₂ and 79–82 vol% N₂ on a dry basis, together with 5–10 vol% water vapour before cooling. Future simulations could therefore examine ternary or quaternary mixtures containing CO₂, N₂ and 5–10 vol% H₂O, using hydrophobic or mildly functionalised carbons, to quantify how competitive water adsorption reduces the effective CO₂ working capacity and to what extent tuning surface chemistry can restore performance.

Overall, this work demonstrates that an idealised 1.0 nm carbon slit pore already provides a favourable microscopic environment for selective CO₂ capture from dilute CO₂/N₂ mixtures. Extending the simulations to realistic pore-size distributions and multicomponent flue-gas compositions, and coupling the resulting isotherms with detailed PSA cycle models, would enable a more quantitative bridging of molecular-level adsorption behaviour and process-scale performance metrics such as CO₂ purity, recovery and specific energy consumption. Such an integrated framework would provide practical guidance on how to balance pore-size distribution, surface chemistry and operating pressure swings when optimising carbon adsorbents for industrial post-combustion CO₂ capture.

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