Degradation Kinetics of Solid Sorbents for Direct Air Capture Under Simulated Realistic Atmospheric Conditions: Accelerated Aging Protocols, Mechanistic Pathways, and Predictive Modeling

Abstract

Solid sorbents based on amine-functionalized porous substrates represent one of the most promising material classes for direct air capture (DAC) of CO ₂ , yet quantitative understanding of their long-term stability under field-relevant conditions remains severely limited. This study presents a systematic investigation of sorbent degradation kinetics for three representative material archetypes—polyethylenimine-impregnated mesoporous silica (PEI/SiO ₂ ), tethered aminopropylsilane-modified silica (APS/SiO ₂ ), and diamine-functionalized metal–organic frameworks (diamine-MOF)—subjected to accelerated aging under conditions designed to faithfully replicate the range of humidity, temperature, and trace pollutant concentrations encountered in realistic atmospheric deployment. A purpose-built aging apparatus was used to expose sorbents to controlled cycles of thermal oxidative stress (25–120 °C), relative humidity fluctuations (5–95% RH), and trace co-contaminants including SO ₂ , NO _x , and O ₃ at sub-ppm concentrations. Capacity loss was quantified gravimetrically and by breakthrough analysis over 500 equivalent-cycle aging sequences. Kinetic data were fitted to a two-pathway degradation model incorporating a pseudo-first-order urea-forming oxidative route and a Prout–Tompkins autocatalytic pathway activated preferentially by trace oxidants. The model yielded activation energies of 68.4 ± 3.1 kJ mol ⁻¹ and 44.7 ± 2.8 kJ mol ⁻¹ for the two respective routes, with strong agreement between predicted and observed capacity trajectories (R ² > 0.97 across all systems). PEI/SiO ₂ exhibited the highest susceptibility to oxidative degradation, losing 41% of initial CO ₂ capture capacity after 500 cycles under the most aggressive aging scenario. Tethered APS/SiO ₂ demonstrated intermediate stability, while diamine-MOF materials showed substantially superior retention of capacity but were sensitive to SO ₂ poisoning at concentrations as low as 50 ppb. These results provide a mechanistic and quantitative foundation for designing next-generation DAC materials and for projecting real-world sorbent lifetimes under geographically diverse deployment conditions.

Keywords: direct air capture, CO ₂ sorbents, degradation kinetics, accelerated aging, carbon capture, amine sorbents, solid sorbents, atmospheric stability, urea formation, metal-organic frameworks

1. Introduction

The imperative to reduce atmospheric CO ₂ concentrations below levels consistent with limiting global mean temperature rise to 1.5–2.0 °C above pre-industrial baselines has elevated direct air capture technologies from academic curiosity to serious engineering proposition within a remarkably compressed timeframe (IPCC, 2022; Lackner et al., 2012). Unlike post-combustion carbon capture, which benefits from high partial pressures of CO ₂ in concentrated flue gas streams, DAC must contend with CO ₂ at approximately 420 ppm in ambient air—a concentration some 300-fold lower than typical power plant flue gas (Jones, 2011; Sanz-Pérez et al., 2016). This thermodynamic reality imposes severe constraints on sorbent design: materials must exhibit both extraordinarily high selectivity for CO ₂ over the dominant N ₂ and O ₂ components of air and sufficient adsorption capacity at ultra-dilute conditions to achieve energetically and economically viable capture.

Solid sorbents, particularly those derived from amine-functionalized mesoporous silicas, polymeric supports, and metal–organic frameworks, have emerged as leading candidates for temperature–vacuum swing adsorption (TVSA) and temperature–moisture swing adsorption (TMSA) DAC cycles (Choi et al., 2011; McDonald et al., 2015; Wurzbacher et al., 2012). The amine functional groups—whether covalently tethered to support surfaces or physically impregnated as polymeric species—react with CO ₂ and co-adsorbed water to form carbamate and bicarbonate species, conferring thermodynamic selectivity at low partial pressures (Bollini et al., 2012; Didas et al., 2015). Laboratory-scale performance metrics for these materials are, by now, relatively well-documented. Published working capacities range from roughly 1.0 to 4.5 mmol CO ₂ g ⁻¹ sorbent depending on material architecture, amine loading, and operating conditions (Goeppert et al., 2011; McDonald et al., 2015; Serna-Guerrero & Sayari, 2010).

What remains far less well understood, and what represents arguably the most critical bottleneck to commercial deployment, is the question of durability. Ambient air is not the clean, controlled mixture assumed in many laboratory experiments. Real deployment sites expose sorbents to diurnal temperature swings of 20–40 °C, seasonal humidity variations spanning from near-zero in arid climates to near-saturation in tropical ones, ultraviolet radiation, particulate matter, and a complex mixture of trace reactive species including SO ₂ , NO _x , O ₃ , volatile organic compounds, and hydrogen sulfide (Aziz et al., 2012; Veneman et al., 2015). Even at sub-ppm concentrations, these species can interact with reactive amine sites in ways that irreversibly consume functional groups or alter the structural integrity of the sorbent support. Oxidative degradation of amines to form amides, imides, and cyclic urea species—documented extensively in post-combustion capture contexts—is thermodynamically favored and proceeds at measurable rates even at ambient temperatures given sufficient oxygen exposure time (Drage et al., 2008; Heydari-Gorji & Sayari, 2012).

The absence of reliable, mechanistically grounded kinetic models for sorbent capacity loss creates a significant problem for techno-economic analysis and for material development. Without the ability to project how a sorbent will perform after, say, 50,000 capture–regeneration cycles over ten years in a humid subtropical climate versus a cold, arid highland environment, it is impossible to compare total cost of ownership across competing material and process architectures (Fasihi et al., 2019; Realmonte et al., 2019). Similarly, accelerated aging protocols used in the literature vary enormously in conditions and metrics, making inter-study comparisons nearly impossible (Veneman et al., 2015; Wurzbacher et al., 2016).

This paper addresses these gaps through three interlocking contributions. First, we describe the design and validation of an accelerated aging apparatus and associated protocol suite that compresses representative multi-year field exposures into laboratory-feasible experimental timescales while maintaining mechanistic fidelity to actual atmospheric stressor distributions. Second, we present detailed capacity loss data for three sorbent archetypes under individually controlled and combinatorially varied stressor conditions, analyzed to separate contributions from thermal, oxidative, moisture-induced, and chemical-poisoning degradation pathways. Third, we develop and validate a coupled kinetic model that captures the essential physics and chemistry of multi-pathway degradation and enables extrapolation to arbitrary field conditions. Together, these contributions provide a quantitative framework for evaluating and improving solid DAC sorbents that we believe will be of direct utility to both materials researchers and process engineers.

2. Background and Theoretical Framework

2.1 Chemistry of Amine-Based CO ₂ Sorbents

The central active species in amine-functionalized DAC sorbents are primary, secondary, and tertiary amine groups that react with CO ₂ through well-established pathways. In the presence of water, primary and secondary amines react with CO ₂ predominantly via carbamate formation (Eq. 1) or, at higher water activities, through bicarbonate formation mediated by water as a co-reactant (Eq. 2):

Carbamate formation (Eq. 1) yields one mole of CO ₂ captured per two moles of amine nitrogen, whereas bicarbonate formation (Eq. 2) achieves one-to-one stoichiometry, making it more nitrogen-efficient but also more sensitive to water activity (Bollini et al., 2012; Didas et al., 2015). The balance between these pathways is critically important for understanding both performance and degradation behavior, because the bicarbonate pathway requires hydration of CO ₂ -amine surface species and thus creates conditions—specifically, the presence of liquid or quasi-liquid water layers—that also facilitate oxidative and hydrolytic degradation reactions.

The regeneration step, typically accomplished by temperature swing (to 80–120 °C for solid sorbents) or a combination of temperature and partial pressure reduction, reverses these equilibria and releases concentrated CO ₂ . However, each regeneration cycle also exposes the sorbent to elevated temperatures and, unless inert gas purging is employed, to oxygen, which initiates oxidative degradation cascades (Drage et al., 2008; Heydari-Gorji & Sayari, 2012).

2.2 Known Degradation Pathways

At least five distinct degradation pathways have been identified in prior literature for amine-functionalized solid sorbents, though quantitative kinetic data for most remain sparse at realistic DAC conditions:

1. Oxidative degradation: Oxygen reacts with amine groups, particularly primary amines, to form amides, imines, aldimines, and ultimately cyclic urea species. This pathway is accelerated by elevated temperature and is catalyzed by trace metal impurities in silica supports (Heydari-Gorji & Sayari, 2012; Veneman et al., 2015).
2. Thermal urea formation: At regeneration temperatures above approximately 70–80 °C, adjacent amine groups can react with CO ₂ still bound to the surface during the early desorption phase, forming thermally stable cyclic urea species that irreversibly consume two amine nitrogens per CO ₂ molecule (Drage et al., 2008; Serna-Guerrero & Sayari, 2010).
3. Acid gas poisoning: SO ₂ , NO ₂ , and HCl react rapidly and often irreversibly with amine groups to form stable sulfamate, nitrate/nitrite, and chloride salts (Aziz et al., 2012; Sjostrom & Krutka, 2010).
4. Hydrolytic degradation: Extended exposure to liquid water or steam can hydrolyze Si–C bonds in covalently tethered aminosilane systems, leading to physical loss of functional groups from the support surface (Choi et al., 2011; Didas et al., 2015).
5. Physical restructuring: Cyclic swelling and shrinkage of polymer-impregnated sorbents (relevant to PEI/SiO ₂ ) driven by moisture absorption and thermal cycles can lead to pore blockage, phase separation, and physical loss of impregnated polymer (Goeppert et al., 2011; Sanz-Pérez et al., 2016).

2.3 Kinetic Modeling Approaches for Sorbent Degradation

Kinetic modeling of sorbent capacity loss is complicated by the simultaneous operation of multiple degradation pathways, nonlinear interactions among stressors, and the heterogeneous nature of the sorbent surface. Several modeling frameworks have been applied in analogous contexts—notably, liquid amine solvent degradation in post-combustion capture—but direct application to solid sorbents requires modification to account for the constrained geometry of surface-bound or pore-confined amine species (Rao & Rubin, 2002; Sexton & Rochelle, 2009).

The simplest approach, pseudo-first-order capacity decay, models the remaining fractional capacity as:

where is the initial CO ₂ capture capacity, is capacity at time , and is an observed pseudo-first-order rate constant. While useful for single-stressor scenarios and short timescales, Eq. (3) consistently fails to capture the sigmoidal or multi-phase capacity loss trajectories observed experimentally under combined stressor conditions, where early rapid decay gives way to a slower regime attributable to a more stable residual amine population (Veneman et al., 2015).

A more physically meaningful framework, adapted from the Prout–Tompkins autocatalytic model originally developed for solid-state reactions, has been proposed for systems where degradation products catalyze further degradation (Prout & Tompkins, 1944). The fractional conversion is described by:

where is the Prout–Tompkins rate constant and and are empirical exponents characterizing the autocatalytic and termination behavior, respectively. This model has the attractive feature of naturally capturing sigmoidal degradation trajectories but adds two additional fitting parameters relative to Eq. (3).

In this work, we propose and validate a two-pathway parallel model that distinguishes the oxidative urea-forming route (subscript ox) from a combined thermal/hydrolytic route (subscript th), each described by its own kinetics and exhibiting distinct temperature and humidity dependences:

Each rate constant follows an Arrhenius temperature dependence:

where is the pre-exponential factor, is the activation energy for pathway , is the universal gas constant, and is absolute temperature. The functional forms and are determined by the mechanistic pathway and are detailed in Section 4.3.

3. Methodology

3.1 Sorbent Materials and Preparation

Three sorbent systems were studied, selected to represent the primary architectural classes currently pursued in the DAC literature. All materials were synthesized in-house to ensure precise control over loading and purity.

PEI/SiO ₂ (Class I, impregnated polymer): Branched polyethylenimine (Sigma-Aldrich, M _w ≈ 800 g mol ⁻¹ , 50 wt% solution in water) was impregnated onto mesoporous silica (MCM-41 type, surface area 850 m ² g ⁻¹ , mean pore diameter 3.8 nm) at a nominal loading of 50 wt% PEI by wetness impregnation, followed by drying at 60 °C under vacuum for 24 h. This loading level was chosen based on literature evidence that it maximizes CO ₂ capture capacity while maintaining acceptable pore accessibility (Didas et al., 2015; Goeppert et al., 2011).

APS/SiO ₂ (Class II, covalently tethered monoamine): (3-Aminopropyl)trimethoxysilane (APTMS, 97%, Acros Organics) was grafted onto the same MCM-41 silica via post-synthesis grafting from anhydrous toluene at 80 °C for 24 h under nitrogen atmosphere. The resulting material was Soxhlet-extracted with ethanol to remove unreacted silane and dried at 100 °C. Nitrogen content measured by elemental analysis was 2.31 ± 0.04 mmol N g ⁻¹ , corresponding to surface coverage of approximately 1.8 amine groups nm ⁻² (Didas et al., 2015).

Diamine-MOF (Class III, appended diamine on metal–organic framework): Mg ₂ (dobpdc) (dobpdc ⁴⁻ = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate) was synthesized following the procedure of McDonald et al. (2015), and N,N′-dimethylethylenediamine (mmen) was grafted by immersion of activated Mg ₂ (dobpdc) in a solution of mmen in hexane (10 vol%) for 18 h, followed by solvent removal under vacuum. This material was chosen because of its exceptional CO ₂ capacity at low partial pressures and its mechanistically distinct cooperative insertion mechanism (McDonald et al., 2015).

Key physical and chemical properties of all three sorbent types prior to aging are summarized in Table 1.

3.2 Accelerated Aging Apparatus and Protocol Design

A purpose-built multi-stressor aging apparatus was designed and constructed to expose sorbent samples simultaneously or sequentially to controlled combinations of thermal, oxidative, humidity, and trace pollutant stressors. The apparatus (schematically shown in Figure 1) consists of five primary modules: (1) a gas mixing manifold with mass flow controllers (Brooks Instrument, ±0.5% FS) capable of blending air, CO ₂ , N ₂ , O ₂ , and calibrated trace gas standards (SO ₂ , NO ₂ , O ₃ ); (2) a humidity control module incorporating a Nafion membrane humidifier and dew-point hygrometer (Vaisala HMT338, ±0.2°C dew point); (3) a thermostatted sample cell bank housing twelve identical fixed-bed sorbent columns (2.5 cm ID × 15 cm length) in parallel; (4) an inline CO ₂ analyzer (LI-COR LI-840A, ±1 ppm resolution) with multiplexed sampling capability; and (5) a PLC-based control system for automated cycle execution.

Accelerated aging protocols were developed following a structured approach grounded in time–temperature superposition principles and informed by meteorological data from five geographically diverse reference sites (coastal tropical, semiarid, temperate maritime, cold continental, and high-altitude arid) obtained from publicly available ERA5 reanalysis datasets (Hersbach et al., 2020). The acceleration factor—the ratio of degradation rate under accelerated conditions to degradation rate under nominal field conditions—was estimated from pilot Arrhenius experiments and targeted to be in the range 20–50×, yielding a mapping of approximately 1 accelerated day to 20–50 actual field days. Table 2 summarizes the protocol matrix.

Each accelerated aging experiment consisted of 500 consecutive adsorption–regeneration cycles. A single cycle comprised a 45-minute adsorption phase (dry or humid 400 ppm CO ₂ in air at 25 °C) followed by a 45-minute temperature-swing regeneration phase (ramp to target regeneration temperature at 5 °C min ⁻¹ , hold 15 min, cool at passive rate). CO ₂ capture capacity was measured quantitatively at cycle 1, 5, 10, 25, 50, 100, 200, 350, and 500 by integrating the breakthrough curve against a blank column. To prevent accumulation of trace pollutant species during non-poisoning runs, a zero-grade air bypass was implemented during measurement cycles.

3.3 Characterization Methods

Post-aging structural and chemical characterization was performed at cycles 0, 50, 200, and 500 using destructive sampling from dedicated parallel columns reserved for each time point. Characterization techniques employed were as follows:

• Nitrogen physisorption (BET/BJH): Measured at 77 K on a Micromeritics ASAP 2020 after outgassing at 80 °C for 12 h. Surface area, pore volume, and pore size distribution were determined.
• Elemental analysis (CHN): Performed on a Thermo Scientific Flash 2000 analyzer to track total nitrogen content as a proxy for retained amine loading.
• Thermogravimetric analysis coupled with mass spectrometry (TGA-MS): Conducted on a Netzsch STA 449 F3 coupled to a QMS 403 D Aëolos in flowing air and N ₂ at 10 K min ⁻¹ to 900 °C. Mass-to-charge ratios monitored included m/z = 18 (H ₂ O), 44 (CO ₂ ), 30 (NO or CH ₂ O), and 64 (SO ₂ ).
• Attenuated total reflectance Fourier-transform infrared spectroscopy (ATR-FTIR): Measured on a Bruker Tensor 27 with a germanium ATR crystal, 64 scans at 4 cm ⁻¹ resolution. Peak assignments followed established references for amine, amide, urea, and sulfonate functional groups (Drage et al., 2008; Heydari-Gorji & Sayari, 2012).
• Scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM-EDX): Performed on a Zeiss Sigma 300 at 5 kV acceleration voltage on gold-sputter-coated samples to assess morphological changes and elemental mapping of sulfur and nitrogen distribution.
• Solid-state ¹³ C and ¹⁵ N cross-polarization magic angle spinning NMR (CP-MAS NMR): Conducted at 9.4 T (100 MHz for ¹³ C) on a Bruker Avance III spectrometer to identify specific carbon and nitrogen bonding environments, including carbamate, urea, amide, and imine species.

3.4 Kinetic Model Parameter Estimation

Kinetic model parameters were estimated by nonlinear least-squares minimization of the sum of squared residuals between modeled and observed fractional capacity loss trajectories, implemented in Python 3.10 using the scipy.optimize.curve_fit function with trust-region reflective algorithm. Parameter confidence intervals (95%) were estimated from the covariance matrix of the fit. Model discrimination between competing kinetic forms (Eq. 3, Eq. 4, and the proposed two-pathway model, Eq. 5) was performed using the corrected Akaike Information Criterion (AIC _c ) to account for model complexity (Burnham & Anderson, 2002).

The temperature dependence of rate constants (Eq. 6) was determined from isothermal aging experiments conducted at five temperatures (40, 60, 80, 100, 120 °C) under identical gas compositions. Activation energies and pre-exponential factors were extracted from Arrhenius plots of versus by linear regression (weighted by inverse variance).

4. Results

4.1 Baseline Performance and Initial Characterization

Prior to aging, the three sorbents displayed the anticipated differences in CO ₂ capture capacity, amine efficiency, and textural properties (Table 1). The diamine-MOF system exhibited a markedly higher amine efficiency (0.79 mol CO ₂ / mol N) compared to the silica-supported materials, consistent with the cooperative insertion mechanism described by McDonald et al. (2015), wherein each diamine pair captures one CO ₂ molecule with 1:1 amine-pair-to-CO ₂ stoichiometry in a structurally ordered insertion reaction rather than the less-ordered carbamate/bicarbonate partitioning of surface-grafted or impregnated species. The PEI/SiO ₂ system exhibited the lowest amine efficiency (0.41), as expected for a high-loading impregnated polymer where a significant fraction of interior PEI amine groups are sterically inaccessible or participate in inter-chain hydrogen bonding that reduces CO ₂ reactivity (Goeppert et al., 2011).

Under P-Baseline conditions (N ₂ regeneration, 80 °C), all three sorbents showed minimal capacity loss over 500 cycles, with total reductions of 4.2 ± 0.8% (PEI/SiO ₂ ), 3.1 ± 0.6% (APS/SiO ₂ ), and 5.8 ± 1.1% (diamine-MOF). The slightly higher baseline decay of diamine-MOF likely reflects gradual desorption of non-covalently anchored mmen ligand during repeated thermal cycling, consistent with observations in the original McDonald et al. (2015) study. These baseline values establish the irreducible minimum degradation rate attributable to the cyclic thermal treatment alone and serve as the subtracted background in subsequent multi-stressor analyses.

4.2 Capacity Loss Under Individual Stressors

Figure 2 presents the normalized CO ₂ capture capacity () as a function of cycle number for all three sorbents under protocols P-ThermalHigh, P-HumidHigh, P-OxidHigh, P-SO2Low, P-SO2High, and P-NOxO3, compared to the P-Baseline reference.

Several important trends emerge from Figure 2 and the underlying data. Under the P-ThermalHigh protocol (120 °C regeneration in air), PEI/SiO ₂ exhibited severe capacity loss, reaching after 500 cycles—a 38% total reduction. The loss trajectory followed a concave-up (accelerating) profile characteristic of autocatalytic or cascade degradation, consistent with the onset of urea formation and oxidative chain reactions in the PEI polymer matrix. APS/SiO ₂ was considerably more thermally robust under high-temperature oxidative conditions, retaining 81% of initial capacity at cycle 500. The superior stability of covalently tethered monoamine species relative to impregnated PEI under oxidative thermal stress has been noted previously (Didas et al., 2015; Heydari-Gorji & Sayari, 2012) and is attributed to the greater isolation of individual amine sites in the grafted material, which limits the propagation of oxidative chain reactions. The diamine-MOF system showed the least thermal degradation in the absence of pollutants, retaining 89% capacity after 500 cycles under P-ThermalHigh, suggesting that the crystalline MOF framework effectively protects the diamine species from bulk-phase oxidation at these conditions.

The P-SO2High protocol (500 ppb SO ₂ ) revealed a strikingly different ranking. Diamine-MOF showed the most rapid capacity decline under SO ₂ exposure, losing 35% of capacity in just 100 cycles before leveling off to a residual capacity plateau around . This behavior is entirely consistent with the known high reactivity of SO ₂ with secondary amine groups to form stable sulfamide and sulfonate species (Aziz et al., 2012; Sjostrom & Krutka, 2010). The structured amine-metal coordination in the MOF may actually enhance SO ₂ accessibility by concentrating amine sites in ordered, open channels, thereby increasing effective contact with the trace pollutant. PEI/SiO ₂ , counterintuitively, showed the lowest fractional SO ₂ sensitivity: the dense PEI polymer matrix appears to provide kinetic shielding of interior amine sites, with SO ₂ penetration depth limited by rapid reaction with surface-exposed amines that creates a protective sulfonate crust. This same shielding mechanism, of course, limits overall CO ₂ capture capacity in the first place.

At 50 ppb SO ₂ (P-SO2Low, broadly representative of urban-proximal or industrial-adjacent deployment sites), all three sorbents showed more modest but still economically significant degradation. Diamine-MOF lost 18% capacity over 500 cycles even at this low concentration, indicating that even trace-level SO ₂ represents a meaningful long-term operational concern for MOF-based DAC systems.

Under P-HumidHigh (humidity cycling from 5 to 95% RH), APS/SiO ₂ showed the greatest susceptibility among the three materials, losing 22% capacity over 500 cycles. CHN analysis of aged samples confirmed that a significant fraction (approximately 30% of total N loss) resulted from hydrolytic cleavage of Si–C bonds, consistent with the known sensitivity of aminopropylsilane grafts to liquid-like water condensation in pores (Choi et al., 2011). PEI/SiO ₂ was relatively insensitive to humidity cycling per se, with TGA-MS confirming that the primary effect of humidity was a modest redistribution of PEI within the pore network rather than chemical degradation—a form of physical aging rather than chemical degradation.

4.3 Combined Stressor Effects and Synergistic Interactions

Results from the P-Combined protocol—representing the most aggressive multi-stressor scenario—are summarized in Figure 3 alongside model predictions from the two-pathway kinetic model (Eq. 5).

Under P-Combined conditions, PEI/SiO ₂ suffered the most severe degradation, with at cycle 500, representing a 41% overall capacity loss. Critically, the observed combined-stressor degradation rate was greater than the sum of individual stressor effects modeled independently—that is, clear synergistic interactions were detected. Analysis via the two-pathway model indicated that trace SO ₂ and NO ₂ significantly increased the effective rate constant for the oxidative pathway ( increased by a factor of 2.3 ± 0.4 relative to the no-pollutant high-temperature protocol), likely because sulfonate and nitrosamine species formed from pollutant reactions serve as radical initiation sites that catalyze further oxidative degradation of the surrounding PEI matrix.

The diamine-MOF showed a total capacity loss of 47% under P-Combined, making it—despite its excellent performance under clean, well-controlled conditions—the most vulnerable material overall when pollutant exposure is included. This finding has direct and sobering implications for MOF-based DAC deployment in urban or industrially influenced settings and suggests that effective air filtration upstream of DAC units using MOF sorbents may be essential for economic viability.

4.4 Kinetic Model Fitting and Parameter Estimates

Table 3 summarizes the best-fit kinetic model parameters for the two-pathway model (Eq. 5) for all three sorbents, along with the AIC _c -based model comparison metrics for the three candidate models evaluated.

The two-pathway model provided substantially better fits to the experimental data than either simple pseudo-first-order decay or a single Prout–Tompkins model (negative ΔAIC _c values of 24–32 units relative to Eq. 3, and 10–16 units relative to Eq. 4), indicating that the mechanistic separation of oxidative and thermal/hydrolytic contributions is empirically justified and not merely a curve-fitting exercise. The activation energy for the oxidative pathway (approximately 65–71 kJ mol ⁻¹ across materials) is broadly consistent with literature values for amine oxidation by molecular oxygen in comparable systems—Heydari-Gorji and Sayari (2012) reported an activation energy of approximately 62 kJ mol ⁻¹ for PEI oxidation on SBA-15 silica, and Drage et al. (2008) estimated 71 kJ mol ⁻¹ for PEI on activated carbon. The thermal/hydrolytic pathway activation energies (41–48 kJ mol ⁻¹ ) are lower, consistent with a combination of physical reorganization (lower barrier) and urea-forming chemistry (which has been estimated at 45–55 kJ mol ⁻¹ based on density functional theory calculations; Manz & Sholl, 2010).

The Arrhenius analysis is illustrated in Figure 4, showing linear Arrhenius plots for both pathways across all three sorbents, confirming the validity of the assumed exponential temperature dependence over the 40–120 °C range studied.

4.5 Structural and Chemical Characterization of Aged Sorbents

Structural and chemical analysis of sorbents at progressive aging stages provided mechanistic context for the kinetic observations and confirmed the proposed degradation pathways.

BET surface area analysis revealed progressive pore blocking in PEI/SiO ₂ under oxidative conditions, with surface area declining from 142 m ² g ⁻¹ (fresh) to 89 m ² g ⁻¹ at cycle 500 under P-OxidHigh. This is consistent with cross-linking and structural rearrangement of the PEI polymer, which increases its effective hydrodynamic volume within the silica pore network. In contrast, APS/SiO ₂ showed minimal BET surface area change (612 → 594 m ² g ⁻¹ ) under the same conditions, confirming that covalently tethered monoamines do not undergo the same type of polymer-scale restructuring. The diamine-MOF showed partial framework amorphization under P-Combined, with BET surface area declining from 1,840 to 1,320 m ² g ⁻¹ at cycle 500—a 28% reduction—suggesting that the cumulative acid exposure from SO ₂ and NO ₂ reacted with the metal–carboxylate framework coordination bonds, partially compromising the MOF crystallinity.

ATR-FTIR spectra (Figure 5) of aged PEI/SiO ₂ samples showed progressive growth of absorption bands at 1,680 cm ⁻¹ (C=O stretch of urea), 1,650 cm ⁻¹ (amide C=O stretch), and 1,550 cm ⁻¹ (amide N–H bend), with corresponding diminution of the primary amine N–H stretching bands at 3,350 and 3,290 cm ⁻¹ . These assignments are consistent with those reported by Heydari-Gorji and Sayari (2012) and Drage et al. (2008) for oxidatively degraded PEI sorbents. Sulfonate features (strong S=O asymmetric stretch at 1,220 cm ⁻¹ ) were clearly evident in samples exposed to SO ₂ -containing protocols, quantitatively proportional to the SO ₂ exposure dose.

Solid-state ¹³ C CP-MAS NMR provided additional resolution of specific carbon environments in degraded PEI/SiO ₂ samples. Fresh materials showed peaks at approximately δ = 38–42 ppm (CH ₂ –NH ₂ , CH ₂ –NH, and CH ₂ –N< carbons in PEI). After 500 cycles under P-OxidHigh, a new peak at δ = 162 ppm grew in, attributable to urea carbonyl carbon, and peaks at δ = 170–172 ppm appeared, consistent with amide carbonyls. Integration of these peaks, referenced to the invariant silica framework, gave a quantitative estimate that approximately 28% of the total PEI nitrogen had been converted to urea or amide species at cycle 500 under P-OxidHigh, and approximately 41% under P-Combined—in excellent agreement with the capacity loss data.

5. Discussion

5.1 Mechanistic Interpretation of Multi-Pathway Degradation

The convergence of kinetic modeling, spectroscopic analysis, and structural characterization paints a mechanistically coherent picture of sorbent degradation that differs in important ways depending on the architectural class of the sorbent. For impregnated polymer sorbents (PEI/SiO ₂ ), the dominant long-term degradation mechanism under realistic multi-stressor conditions is oxidative, mediated by molecular oxygen and catalytically enhanced by trace acidic pollutants. The mechanism appears to involve initial oxidation of primary amine groups to form aldimines or hydroxylamines, which subsequently react intramolecularly or with adjacent amine groups to form cyclic urea structures. This pathway has been characterized in elegant detail for PEI in post-combustion contexts (Sexton & Rochelle, 2009), and the present results confirm its dominance in the DAC context as well, albeit at lower absolute rates due to lower temperatures. The autocatalytic character captured by the Prout–Tompkins model exponents () is consistent with a propagation mechanism where early degradation products (likely radical species or Lewis-acidic metal ion impurities mobilized by oxidation) catalyze further amine degradation in their immediate vicinity, creating local degradation "hot spots" that spread through the PEI matrix.

For tethered monoamine systems (APS/SiO ₂ ), the physical isolation of individual aminopropyl chains prevents propagation of oxidative chain reactions—each amine site degrades independently rather than as part of a coupled polymer system. This accounts for the substantially lower Prout–Tompkins m and n exponents for APS/SiO ₂ and explains its better resistance to autocatalytic degradation. The primary vulnerability of APS/SiO ₂ is instead the hydrolytic Si–C bond cleavage pathway, which operates continuously in the presence of condensed water and has a lower activation energy (~40 kJ mol ⁻¹ ) than the oxidative pathway. In practical terms, this means that APS/SiO ₂ degrades relatively uniformly regardless of temperature and that deployment in high-humidity environments is particularly challenging.

The diamine-MOF system presents the most nuanced degradation behavior. Its exceptional performance under clean conditions—and particularly its high amine efficiency, which reflects a thermodynamically distinct cooperative insertion mechanism—makes it highly attractive in principle. However, the combination of high amine accessibility (the very feature responsible for its high efficiency) and the chemical reactivity of secondary amine groups with SO ₂ creates a critical vulnerability. The ordered, channel-like structure of Mg ₂ (dobpdc) that promotes CO ₂ uptake also allows trace SO ₂ to diffuse rapidly to interior amine sites, whereas the disordered PEI polymer creates diffusion barriers that partially protect interior sites. The partial framework amorphization observed under P-Combined conditions adds a structural degradation component absent in the silica-supported systems, indicating that MOF stability under combined acid gas and humidity stress requires dedicated engineering attention—perhaps through post-synthetic hydrophobic functionalization of the MOF external surface or via hybridization with protective silica coatings (Didas et al., 2015; McDonald et al., 2015).

5.2 Validity and Limitations of the Kinetic Model

The two-pathway kinetic model (Eq. 5, Eq. 6) provides an excellent empirical description of the observed capacity loss trajectories (R ² > 0.97 across all systems and protocols) and is preferred over simpler alternatives by a large AIC _c margin. Several important limitations deserve explicit acknowledgment, however.

First, the model is parameterized using accelerated aging data obtained over a compressed temperature range (40–120 °C), and extrapolation to longer timescales at lower ambient temperatures involves significant extrapolation uncertainty. The Arrhenius assumption that the same elementary mechanisms operate at ambient temperatures as at the elevated aging temperatures is plausible based on spectroscopic evidence but has not been directly validated at 10–25 °C over decadal timescales. Non-Arrhenius behavior arising from glass transition effects in PEI (which has a glass transition temperature near 25–35 °C) could introduce systematic errors in very low temperature extrapolations.

Second, the model treats humidity effects implicitly through the thermal pathway rate constant rather than explicitly through a separate water-activity-dependent term. This simplification is adequate for the protocols tested here but may underestimate capacity loss in scenarios where high relative humidity is maintained throughout the entire adsorption–regeneration cycle rather than varying cyclically. A more complete model would incorporate an explicit term in , requiring additional experimental campaigns across a wider humidity matrix.

Third, and perhaps most importantly, the model does not explicitly account for heterogeneous intraparticle diffusion effects. Real sorbent pellets used in engineering-scale contactors are typically 1–5 mm in diameter, and the rate of oxygen and pollutant diffusion into the pellet interior during regeneration may be significantly lower than in the fine powder samples (<200 μm) used in this study. This would be expected to attenuate the effective degradation rate at the pellet scale, particularly for PEI/SiO ₂ where the polymer matrix provides significant additional diffusion resistance. Engineering-scale aging studies on pelletized sorbents are strongly recommended as a follow-up to this work.

5.3 Implications for Material Development

The mechanistic insights developed here point to several specific material design strategies that could meaningfully extend sorbent operational lifetimes. For PEI-based systems, the most impactful intervention would be to reduce oxygen penetration during regeneration—either by using inert gas purging (N ₂ or steam) rather than air during the thermal desorption step or by crosslinking the PEI matrix to inhibit the structural rearrangements that amplify oxidative cascade reactions. Steam regeneration has the additional benefit of lowering the effective regeneration temperature needed to achieve desorption due to the co-adsorption thermodynamics, potentially reducing thermal stress as well (Wurzbacher et al., 2016).

For tethered amine systems, improving Si–C bond hydrolytic stability is the priority. Replacement of aminopropylsilane with more hydrolytically robust linkers—for instance, amino-ethyl-thio-propyl or amino-bearing carbon chain grafts via more stable C–C coupling chemistry—could substantially reduce the moisture-driven capacity loss rate (Didas et al., 2015). Alternatively, post-synthesis silylation of residual silanol groups with hydrophobic capping agents could reduce the degree of water condensation in pores, reducing the thermodynamic driving force for hydrolysis.

For diamine-MOF systems, the challenge is fundamentally different: it is not the amine–framework bond but rather the amine–SO ₂ reaction that governs lifetime under polluted conditions. Two complementary approaches seem promising: (1) upstream acid gas scrubbing using low-cost base-impregnated activated carbon guard beds to reduce SO ₂ and NO ₂ below the threshold of detectable sorbent impact (our results suggest this threshold is somewhere below 50 ppb SO ₂ on a per-cycle basis for MOF systems); and (2) development of diamine variants where the secondary amine nitrogen is sterically shielded to reduce SO ₂ accessibility while retaining CO ₂ reactivity—a nontrivial but potentially achievable design challenge given the rich synthetic flexibility of diamine chemistry.

5.4 Field Deployment Projections and Economic Implications

Using the calibrated two-pathway kinetic model, we projected sorbent capacity retention over a 10-year deployment horizon for the five reference atmospheric environments considered in the protocol development phase, assuming standard DAC process conditions (12 cycles per day, regeneration at 100 °C in air). Figure 6 summarizes these projections for all three sorbent archetypes.

The projections reveal striking geographic variability in projected sorbent lifetime. PEI/SiO ₂ is projected to fall below the 75% capacity threshold in approximately 3.2 years in a hot, humid tropical coastal environment (high temperature, high humidity, moderate SO ₂ ) but could potentially last 7–9 years in a cold, dry continental climate where both thermal and oxidative degradation rates are dramatically suppressed. This geographic sensitivity has profound implications for DAC siting strategy and lifecycle cost analysis. A DAC facility in an equatorial region may require sorbent replacement more than twice as often as a facility at high latitude or altitude, all else being equal—a cost differential that current techno-economic assessments may substantially underestimate (Fasihi et al., 2019; Realmonte et al., 2019).

Diamine-MOF systems show the most extreme geographic sensitivity, with SO ₂ -driven capacity loss dominating outcomes in urban and industrial-adjacent sites to such a degree that their projected useful life at unfiltered conditions falls below two years in the worst-case scenario (500 ppb average SO ₂ ). Importantly, this vulnerability is essentially independent of temperature and humidity—the SO ₂ poisoning pathway exhibits very low activation energy and thus is only weakly suppressed by cooler temperatures. This suggests that location selection and/or upstream purification are not optional add-ons but rather fundamental design requirements for MOF-based DAC.

6. Conclusion

This study has addressed a critical gap in the knowledge base for solid-sorbent direct air capture by delivering, for the first time, a systematic, multi-stressor accelerated aging dataset spanning three representative sorbent archetypes under conditions specifically designed to replicate the range of atmospheric environments relevant to real-world DAC deployment. The central findings can be summarized as follows.

First, the two-pathway kinetic model developed here—separating oxidative (Prout–Tompkins autocatalytic) and thermal/hydrolytic (pseudo-first-order) degradation routes—provides a mechanistically grounded and statistically superior description of multi-stressor capacity loss compared to simpler alternatives, with R ² > 0.97 across all system/protocol combinations. The extracted activation energies (68.4 kJ mol ⁻¹ for the oxidative pathway, 44.7 kJ mol ⁻¹ for the thermal pathway) are physically reasonable and consistent with independent literature benchmarks.

Second, the three sorbent archetypes studied exhibit fundamentally different vulnerability profiles. PEI/SiO ₂ is most susceptible to oxidative degradation and loses up to 41% of capacity over 500 cycles under combined atmospheric stressors. Its kinetic shielding of interior amine sites provides paradoxical but real protection against trace pollutant poisoning. APS/SiO ₂ is intermediate in thermal/oxidative stability but is the most vulnerable to hydrolytic degradation in high-humidity environments. Diamine-MOF systems show the best performance under clean, controlled conditions but are acutely sensitive to SO ₂ even at sub-100-ppb concentrations, making them high-risk candidates for unfiltered urban or industrial deployment without upstream acid gas treatment.

Third, strong synergistic interactions among stressors—particularly between thermal stress and trace pollutants—mean that single-stressor aging tests significantly underestimate degradation rates under realistic combined conditions. The combined stressor protocol developed here accelerates degradation by up to 48-fold relative to nominal baseline conditions while maintaining mechanistic fidelity, providing a practical and validated tool for future sorbent screening and materials development.

Fourth, field deployment projections derived from the calibrated kinetic model highlight dramatic geographic variability in projected sorbent lifetimes—ranging from under three years in hot, polluted tropical environments to nearly a decade in cold, clean continental settings. This variability must be incorporated into techno-economic analyses and siting decisions for DAC facilities.

Together, these results establish a quantitative foundation for the rational design of more durable DAC sorbents and provide actionable guidance for process engineering choices—including regeneration gas selection, operating temperature limits, upstream filtration requirements, and maintenance scheduling—that can substantially extend sorbent operational lifetimes and reduce the total cost of direct air capture at scale. Future work should extend this framework to pelletized sorbent geometries, explicitly incorporate ultraviolet photodegradation effects relevant to open-atmosphere contactors, and develop validated protective coating strategies for the most promising material candidates.

References