Design of polymer-based CO₂-membrane adsorbers for carbon capture

Abstract

This study focuses on the CO₂ capture performance of poly(N,N-dimethylaminopropyl acrylamide) (PDMAPAm) and poly(N-[3-(dimethylamino)propyl]-acrylamide)-b-poly(methyl methacrylate) (PDMAPAm-b-PMMA) diblock copolymers for fabrication of CO₂-responsive membrane adsorbers. By systematically varying the block composition of the diblock copolymer PDMAPAm-b-PMMA, optimal compositions for maximizing CO₂ adsorption capacity are identified. The adsorption mechanisms were characterized under both dry and humid conditions, revealing distinct physisorption and chemisorption pathways. The first major novelty of this work is the creation of a unified kinetic model that, for the first time, integrates polymerization kinetics with adsorption kinetics, allowing the CO₂ uptake capacity of membrane adsorbers to be directly predicted from the underlying polymer properties. A second key innovation is the use of this unified model to rationally design and fabricate a polymer membrane adsorber that achieves a CO₂ uptake capacity of 6 mmol g⁻¹, substantially exceeding the performance of commercially available polymer-based sorbents.

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New concepts

In this paper, we present the design and development of novel CO₂-responsive polymer membrane adsorbers, encompassing both homopolymers, poly(N,N-dimethylaminopropyl acrylamide) (PDMAPAm) and diblock copolymers, poly(N-[3-(dimethylamino)propyl]acrylamide)-b-poly(methyl methacrylate) (PDMAPAm-b-PMMA). These advanced materials exhibit a markedly higher CO₂ uptake capacity (approximately 6 mmol g⁻¹) compared to conventional polymer-based membrane adsorbers reported in the literature, such as polyethyleneimine (PEI), tetraethylenepentamine (TEPA), polyacrylonitrile (PAN), polypropylenimine (PPI), and their composites. This is a new concept in the field of polymers for storage of CO₂. A detailed investigation of adsorption mechanisms reveals distinct physisorption and chemisorption pathways, highlighting the critical steps that govern CO₂ capture performance in these newly developed polymers. Furthermore, the methodology underlying the creation of these membrane adsorbers is unique: it integrates experimental synthesis with digital modeling through a unified framework that couples polymerization reaction kinetics with CO₂ adsorption kinetics—a combined approach that, to our knowledge, has not been previously reported. This synergy between material design and process modeling establishes a new paradigm for engineering high-performance CO₂ adsorbents.

Introduction

One of the most critical aspects of our days is reducing our carbon footprint to avoid further negative impacts on the climate. Along with traditional methodologies for reducing CO₂ emissions, such as membrane separation technologies, another technology, direct air capture (DAC), has recently come into focus. DAC represents a cutting-edge approach for mitigating climate change by selectively removing carbon dioxide (CO₂) from ambient air, offering a scalable solution to reduce atmospheric greenhouse gas concentrations.^1–6 This process utilizes adsorbent materials that selectively capture and retain CO₂ molecules from atmospheric air.^2,7,8 In a typical DAC system, ambient air is directed through a contactor where it flows over the surface of the adsorbent material.^6,9 CO₂ molecules are adsorbed onto the material surface via physical interactions (physisorption) or chemical bonding (chemisorption).^6,9,10

Gas adsorption on solid surfaces generally occurs via two primary mechanisms: physisorption and chemisorption. Physisorption (or physical adsorption) arises from weak intermolecular forces, such as van der Waals interactions, leading to a more reversible and less specific attachment of gas molecules to the surface.^11,12 In contrast, chemisorption, also known as chemical adsorption, involves the formation of chemical bonds between gas molecules and the surface of the adsorbent, resulting in a stronger and often more specific interaction.^13,14 Chemical adsorption, also known as irreversible adsorption, involves a substantial electron exchange between the adsorbate molecules and the adsorbent's surface. This process results in the formation of covalent or ionic bonds¹⁵ and is characterized by strong interaction potentials, leading to high adsorption temperatures that often approach those of chemical bonds (80–240 kJ mol⁻¹).¹⁶ As with most chemical reactions, it typically requires a specific activation energy to return the system to an equilibrium state. The physisorption occurring between dry CO₂ and polymer has been investigated in our last publication.¹⁷ Therefore, the present study primarily investigates chemisorption phenomena alongside physisorption.

The advancement and optimization of adsorbent materials are pivotal for enhancing the efficiency and scalability of DAC technologies.^2,18 Diblock copolymers have demonstrated strong potential for CO₂ capture, mainly due to the high affinity between amine groups and CO₂ molecules.^19,20 In particular, diblock copolymers incorporating amine-functional segments such as poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA),^21–24 poly(N,N-dimethylallylamine) (PDMAAm),^25–28 poly(2-aminoethyl methacrylate) (PAEM),^29,30 and poly(N,N-dimethylaminopropyl acrylamide) (PDMAPAm)³¹ have emerged as promising candidates for DAC applications. These materials exhibit high CO₂ reactivity and selectivity,^21,31,32 high porosity,^33–37 and scalability for industrial deployment.^31,38–40

In this study, the used PDMAPAm-based block copolymers were developed via RAFT polymerization rather than conventional free-radical polymerization, as RAFT is a controlled radical polymerization technique that provides precise control over molecular weight, dispersity, and polymer composition, enabling the straightforward preparation of well-defined block copolymers.^40–42 Block copolymer architecture was selected to precisely tune the microenvironment around the CO₂ responsive amines and to control film mechanical stability, morphology, segmental mobility, and hydrophilicity factors that strongly influence adsorption behavior, especially under humid conditions.¹⁷ As mentioned in the previous publication,^17,40,41 for synthesizing the PDMAPAm-b-PMMA diblock copolymer, the lengths of the two blocks were deliberately chosen to achieve a balance between a high proportion of CO₂-responsive tertiary amines for effective sorption and a sufficiently long PMMA segment to provide the mechanical robustness required for membrane fabrication. This level of structural control is not achievable with free radical homopolymers.

As demonstrated in our previous publication,^17,40,41 an integrated computational and experimental unified model was developed to design acrylamide-based polymers with tailored CO₂ affinity and transport characteristics. Within this context, CO₂-responsive polymers such as PDMAPAm and PDMAPAm-b-PMMA were synthesized and their CO₂ uptake under dry conditions was experimentally quantified, allowing the measured uptake to be linked to the underlying solution–diffusion and adsorption mechanisms.^2,4 In parallel, our earlier work established a comprehensive understanding of CO₂ transport in PDMAPAm- and PDMAPAm-b-PMMA-coated membranes used as selective layers, showing that these materials can achieve CO₂/N₂ permeability selectivities of up to 10–15, indicative of their strong CO₂-responsive behavior.^40,41 SEM analyses confirmed that the selective layers form dense, continuous, and nonporous structures in which gas transport is governed by polymer–gas interactions rather than convective flow, consistent with the solution–diffusion mechanism in which gas molecules dissolve into the polymer matrix and subsequently diffuse through it.^40,43 Together, these findings highlight that these polymers exhibit both high CO₂ uptake and well-defined transport behaviour, providing a natural foundation for the development of membrane adsorbers that integrate dense-layer permeation with sorbent-like adsorption functionality.

A membrane adsorber is a flat sheet thin-film that combines the dense selective layer of a membrane with the functional adsorption sites of a sorbent, creating a material capable of both solution–diffusion-based permeation^40,41 and affinity-driven adsorption.¹⁷ This dual mechanism allows gases or solutes to dissolve and diffuse through the polymer matrix while simultaneously interacting with embedded adsorption sites, resulting in enhanced selectivity, higher uptake capacity, and faster mass-transfer performance compared to conventional membranes or sorbents alone.

This study primarily investigates the humid CO₂ sorption behavior of the CO₂-responsive PDMAPAm-based CO₂-responsive membrane adsorbers, with particular emphasis on their sorption kinetics. In addition to quantifying the contributions of physisorption and chemisorption under humid conditions that more closely resemble realistic atmospheric environments, the work clarifies how these sorption processes couple with the polymerization kinetics of the materials such as PDMAPAm and PDMAPAm-b-PMMA.^40,42 By integrating sorption kinetics and polymerization kinetics into a unified model, the study provides a unified model framework that links polymer structure formation to CO₂ uptake performance. Through systematic variation of temperature, pressure, and relative humidity of CO₂ capture conditions, polymer properties the CO₂ capture capacity of the materials is optimized, revealing how both material design and process conditions govern overall performance.

Experimental

Material and methods

The reagents and materials employed in the synthesis of the polymers in this study were the same as those previously described in our earlier publication,¹⁷ ensuring consistency in the experimental conditions and comparability of results.

Synthesis of PDMAPAm and PDMAPAm-b-PMMA

PDMAPAm and PDMAPAm-b-PMMA diblock copolymer used in this study were synthesized via RAFT polymerization following the procedure reported in our previous work.¹⁷ Detailed procedure and recipe of the synthesis were given in the SI.

The synthesis protocol of PMMA₇₀ can be found in our previous publication³⁸ and polymer properties is described in the Table S4 in the SI.¹⁷

Characterization

Gel permeation chromatography (GPC)

The molecular weight profiles of PDMAPAm homopolymers and PDMAPAm-b-PMMA diblock copolymers were determined using gel permeation chromatography (GPC) as shown in our previous work.¹⁷ Detailed information regarding the polymer characterization in the GPC was given in the SI.

Proton nuclear magnetic resonance (NMR)

¹H NMR spectroscopy experiments were conducted following the procedure described in a previous publication.¹⁷ A detailed description of the measurement protocol is provided in the SI.

DMAPAm conversion from macro-RAFT synthesis was estimated by comparing the integration of double-bond proton areas in the sample before and after the reaction, which was around 90%. Using the same method,⁴⁰ the conversion of methyl methacrylate in the second block synthesis, also measured in CDCl3, was calculated from the decrease in the integral of the monomer peaks, which was also approximately 90%.

InfraSORP device by Fraunhofer IWS

The INFRAsorp device developed by Fraunhofer IWS (Dresden, Germany) is an optical calorimeter that quantifies adsorption-induced heat release to characterize porous materials. During measurement, a test gas flows over the sample, initiating adsorption on its surface. The heat released from adsorption causes a temperature increase, which is detected by an infrared sensor positioned above the sample. The resulting thermal signal appears as a peak, and its area is directly proportional to the total heat of adsorption, reflecting the amount of gas adsorbed.^44–46 By knowing the specific heat capacity of the polymer (PDMAPAm) from the DSC measurement⁴⁰ and the integrated area under the temperature peak, the heat release arising from the gas adsorption can be estimated.

Open quartz crystal microbalance (openQCM Q⁻¹)

Adsorption measurement (chemisorption) of wet CO₂ has been conducted using the openQCM Q⁻¹ device (Novaetech Srl, Pompeii, Italy). The openQCM Q⁻¹ M is a Quartz Crystal Microbalance device that can simultaneously measure both frequency and dissipation changes of the quartz crystal at the same time. This allows for assessing variations in mass and the viscoelastic properties of the material on the quartz crystal's surface. The core sensing element of the QCM is a thin AT-cut quartz crystal equipped with electrodes on both sides. Prior to measurement, the crystal surface was uniformly coated with a PDMAPAm-based polymer film (≈130 µm thickness) by drop-casting a THF solution, followed by controlled solvent evaporation. During the measurements, the coated crystal was placed inside the QCM chamber and exposed to a continuous gas flow (CO₂ or N₂). For humid-gas experiments, the gas stream was bubbled through deionized water for 1 h, and the resulting relative humidity was monitored in real time using an inline humidity sensor. The flow rate, temperature, and pressure inside the chamber were kept constant throughout each experiment.

When the coated crystal is exposed to a gas stream, the polymer film interacts with the incoming gas molecules. Adsorption of gas onto the polymer increases the mass of the film, which in turn causes a measurable decrease in the resonant oscillation frequency of the quartz crystal. This frequency shift is detected through the electrodes.

The magnitude of the frequency change is directly proportional to the mass change on the crystal surface. This relationship is described by the Sauerbrey equation⁴⁸ shown below:

f₀ is the resonant frequency of the crystal (10 MHz), Δm is the mass change, A is the piezoelectrically active crystal area (0.320 cm²), ρ_q is the density of quartz (2.648 g cm⁻³), and µ_q is the shear modulus of an AT-cut crystal (2.947 × 10¹¹ g cm⁻¹ s⁻²).

By tracking the real-time frequency changes, a quartz crystal microbalance (openQCM Q⁻¹) can provide valuable insights into the amount of mass deposited and the rate at which these films are added or removed.^47,48

Fourier transform infrared spectroscopy (FTIR)

To investigate changes in functional groups following chemisorption, a film of PDMAPAm (thickness = 10 µm) coated onto the quartz crystal of openQCM Q⁻¹ device was examined using Fourier Transform Infrared (FTIR) spectroscopy. Spectra were recorded before and after exposing the film to dry N₂, humid N₂, and humid CO₂. However, this measurement was not carried out with dry CO₂, because in the absence of water, it does not chemically react with tertiary amines to form covalent bonds^49,50 that could be detected as characteristic peaks in the FTIR spectrum. The measurements were performed using a Bruker ALPHA FTIR spectrometer (Bruker, Ettlingen, Germany) in attenuated total reflectance (ATR) mode. Data were collected at room temperature over a spectral range of 600–4000 cm⁻¹, with a resolution of 4 cm⁻¹ and averaged over 64 scans.

Results and discussion

The synthesized polymers, PDMAPAm and its diblock copolymer, PDMAPAm-b-PMMA, were systematically characterized to evaluate their chemical and physical interactions with CO₂ under both dry and humid conditions. Comparative analyses were conducted using PDMAPAm homopolymers and PDMAPAm-b-PMMA copolymers featuring a constant PDMAPAm block and varying PMMA block lengths and measurements were conducted at different temperatures to follow Arrhenius parameters of reaction coefficients.

Mechanism of dry and humid CO₂ adsorption

As illustrated in Fig. 1, the diblock copolymer PDMAPAm-b-PMMA consists of two distinct polymer blocks: poly(N,N-dimethylaminopropylacrylamide) (PDMAPAm) and poly(methyl methacrylate) (PMMA). The PDMAPAm segment contains functional groups such as amides (comprising carbonyl and secondary amine functionalities) and tertiary amines. Upon exposure to dry CO₂, these functional groups are theoretically capable of interacting with CO₂ molecules, suggesting a potential for selective and efficient adsorption via chemical affinity.^51,52 The interaction of both PDMAPAm and PMMA blocks within the diblock copolymer with dry CO₂ has been discussed in greater detail in our previous publication.¹⁷ Given that the concentration of RAFT end groups is significantly lower than that of the functional groups present on the monomeric units, their interaction with dry or humid CO₂ can be considered negligible.

Fig. 1 Chemical structure of the diblock copolymer PDMAPAm-b-PMMA synthesized via RAFT polymerization.

In humid conditions, the amides on PDMAPAm block are relatively stable compounds due to resonance between the nitrogen lone pair and the carbonyl group. This makes them less reactive with humid CO₂ than amines.^53–56 Tertiary amines chemically interact with humid CO₂ via the following pathway shown in Fig. 2.

Fig. 2 Chemical interaction mechanism of tertiary amine with humid CO₂.

This mechanism, which involves the base-catalyzed hydration of CO₂, was initially documented by Donaldson⁵⁷ and later examined by Kenig⁵⁸ and involves a two-step reaction sequence. Initially, the tertiary amine reacts with water vapor to produce an ammonium ion and a hydroxide ion. The hydroxide ion subsequently reacts with CO₂ to form a bicarbonate ion. Finally, the resulting bicarbonate and ammonium ions associate to form a stable bicarbonate salt. In this scenario, CO₂ does not chemically react with tertiary amines in the absence of water (i.e., under dry conditions). For the chemical interaction between CO₂ and tertiary amine, the existence of water vapor is crucial.^49,50

Since the CO₂ uptake of PMMA homopolymer under dry conditions does not significantly differ from its uptake under humid conditions, the contribution of the PMMA block to the overall CO₂ adsorption capacity of the diblock copolymer in humid environments is considered negligible (see SI).

Validation of adsorption results from openQCM Q⁻¹

To start with, several adsorption measurements have been conducted to analyze the dry CO₂ capture performance of the synthesized CO₂-responsive polymer, PDMAPAm, in the two different devices, in a gravimetric adsorption device and in an openQCM Q⁻¹ for comparison of both results. The results of the comparison are represented in Fig. 3. It is crucial to note that the PDMAPAm sample was measured as film (30% w/w polymer in THF), both in the gravimetric adsorption device and openQCM Q⁻¹.

Fig. 3 Comparison of CO₂ uptake of PDMAPAm as film measured in openQCM Q⁻¹ with CO₂ uptake measured with the gravimetric adsorption device.

Fig. 3 presents a comparison of the dry CO₂ uptake capacities of PDMAPAm measured in film form using two different analytical devices: the open QCM Q⁻¹, which measures changes in resonance frequency corresponding to mass variation during CO₂ adsorption, and the gravimetric adsorption system, with data published elsewhere.¹⁷ As shown in Fig. 3, the CO₂ uptake values obtained between 0.6 and 1.5 bar are nearly identical across both measurement techniques. This consistency indicates that the adsorption results from the open QCM Q⁻¹ are in good agreement with those obtained from the gravimetric adsorption device. Therefore, in this study, an open QCM Q⁻¹ device was utilized to measure the adsorption capacity of polymers as a film in both dry and wet conditions.

Humid CO₂ adsorption–desorption

Furthermore, at atmospheric pressure, CO₂ uptake capacities of homopolymer (PDMAPAm₂₃₂) and diblock copolymer (PDMAPAm₂₃₂-b-PMMA₅₇) were measured in dry and humid conditions by building the following system (Fig. 4). For humid CO₂ (or similarly for humid N₂) measurements, the gas is bubbled into a closed Schott–Duran bottle, which is partially filled with water (20 mL of 1000 mL) for 1 hour at room temperature. Meanwhile, pressure and relative humidity of the wet gas going to the QCM Q⁻¹ device were measured using the manometer and the relative humidity measurement device connected to the bottle. The main part of the QCM Q⁻¹ device is the cell where the quartz crystal is located. The crystal is coated with polymer (10% w/w dissolved in THF). The thickness of the coating is around 130 micrometers. In the cell, a temperature sensor provides the temperature of the wet gas whereas the electrodes of the quartz crystal provide information regarding the resonance frequency change related to mass change as wet CO₂ is being adsorbed. For the dry gas measurement, the same measurement is conducted without water in the bottle.

Fig. 4 Sorption measurement using openQCM Q⁻¹ device. PI – Pressure indicator, RHI – relative humidity indicator, TI – temperature indicator, FI – frequency indicator.

Sorption measurements on the QCM Q⁻¹ device were conducted with dry and wet CO₂ and wet N₂, and the results are presented in Fig. 5.

Fig. 5 CO₂ and N₂ uptake of homopolymer PDMAPAm₂₃₂ in dry and humid conditions.

Fig. 5 represents the evolution of CO₂ and N₂ uptake by PDMAPAm₂₃₂ in dry and humid conditions (RH = 55%). This is clear from the figure that generally, in dry conditions, a small amount of CO₂ was captured by the PDMAPAm₂₃₂, which is almost the same amount as captured in another adsorption device mentioned before. In contrast, at RH = 55%, the PDMAPAm₂₃₂ shows quite a higher uptake for humid CO₂ and N₂ gases. As many other amine-based polymer sorbents exhibit higher CO₂ capacity in humid conditions than in dry conditions,^59,60 the PDMAPAm₂₃₂ shows the same trend. In other words, 8–9 times more CO₂ was captured in humid conditions than in dry conditions, and the difference in CO₂ capture amount between humid and dry conditions is around 2–4 times in other publications.^60–62 Another consideration is that the Fig. 5 shows that the weight of polymer is increased in the humid CO₂-exposure case more than in the humid N₂-exposure case under the same temperature, pressure and humidity conditions (55%). If dry CO₂ uptake and humid N₂ uptake are subtracted from humid CO₂ uptake of the polymer, the difference is obtained to be around 0.01 g g⁻¹. This difference increases up to 0.07 g g⁻¹ as the humidity turns to be 75% as shown in Table 1.

Table 1 CO₂ and N₂ uptake of homopolymer PDMAPAm₂₃₂ in dry and humid conditions (RH = 75%)

Conditions	Uptake (g g^−1)
Dry CO2	4.000 × 10^−3
Humid CO2	1.080 × 10^−1
Humid N2	3.747 × 10^−2

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There can be two reasons for the observed variation. First reason can be that monomeric units of PDMAPAm₂₃₂ have a tertiary amine on them that can chemically react with humid CO₂ and it can be chemisorbed onto the polymer, which can lead to the formation of ammonium bicarbonate.^57,58 The second reason could be that in dry environments, tertiary amines with bulky substituents (like two methyl groups) exhibit limited accessibility for CO₂ due to steric hindrance.^63–66 In the presence of water and CO₂, tertiary amines can become protonated^57,58 and this protonation may reduce steric hindrance, polarity and hydrogen bonding capacity of the nitrogen site, potentially opening up access for CO₂ molecules to interact via physical adsorption.⁶⁷ The protonation enhances hydration shells and facilitates CO₂ mass transfer.⁶⁸ However, if the homopolymer PMMA₇₀ is exposed to CO₂ in dry and humid conditions, there is no change in the CO₂ uptake of PMMA in humid conditions compared to in dry conditions (see Table S5 in SI). This is because there is no functional group that can be protonated, unlike in PDMAPAm.

To investigate where the difference exactly arises, additionally, before and after each openQCM Q⁻¹ measurement of the polymer films, they are washed with nitrogen gas for one day at atmospheric pressure and room temperature, and the polymer film mass is measured in a weight balance to see how the mass of polymer after the capturing process was changed. The results of the mass change of PDMAPAm₂₃₂ are illustrated in Table 2.

Table 2 Captured weight by polymer PDMAPAm₂₃₂ exposing to dry CO₂ and humid CO₂ (RH = 75%) and N₂

Conditions	Captured weight (g g^−1)
After dry CO2-exposure and N2 washing	1.008 × 10^−4
After humid CO2-exposure and N2 washing	1.175 × 10^−2
After humid N2-exposure and N2 washing	5.002 × 10^−4

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The theory behind is that if the polymer is washed with N₂ after each measurement, physically adsorbed gas molecules has to desorb easier than chemically adsorbed gas molecules because physisorption is a reversible process involving weak van der Waals interactions and the energy released during adsorption is comparable to the energy required for desorption^69,70 whereas in chemisorption case, desorption requires significantly more energy than physisorption due to the formed strong chemical bonds.^71,72 This can be clearly seen from the Table 2, which compared to the humid N₂ and dry CO₂ cases, the highest weight change, which is stable regardless of N₂ washing after exposure, occurs when the polymer film interacts with humid CO₂, which is around 1.175 × 10⁻² g g⁻¹ at RH = 75%. It means that more energy is required to desorb all the adsorbed gas molecules from the polymer. So, the reason for the remaining gas molecules inside the polymer can be chemically adsorbed CO₂ gas molecules that reacted with the tertiary amines of the polymer, leading to the formation of ammonium bicarbonate.^57,58 Considering that the polymer PDMAPAm (36 kDa) has approximately 230 monomeric units (in each monomeric unit, one tertiary amine) and a 1 : 1 reaction would occur between the tertiary amine and humid CO₂, theoretically, uptake of the polymer film via chemisorption had to be 0.280 g g⁻¹. This can mean that only some (about 7%) of the tertiary amines have reacted. As shown in our previous publication,^40,41 the film, which was fabricated, is thick and dense. The research group of J. R. Hoffman et al.^73,74 has reported that, in the thick-film regime, CO₂ capture is primarily limited by the accessibility of amine sites, and amine groups located deeper within the film are often inaccessible and therefore do not effectively participate in the reaction. In other words, when the polymer thickness is higher, interaction between CO₂ and the amine group occurs only on the surface. Hence, only a few percent of tertiary amines have reacted.

Table 2 shows that the chemisorbed CO₂ uptake of the polymer under humid conditions (RH = 75%) is approximately 1.175 × 10⁻² g g⁻¹ whereas Table 1 indicates that the difference in total uptake between samples exposed to humid CO₂ and humid N₂ at the same humidity level is about 0.07 g g⁻¹, which is five to six times greater than the chemisorbed CO₂ fraction. Overall, when the polymer is exposed to humid CO₂ at 75% RH, the total CO₂ uptake is 0.07 g g⁻¹, of which 1.175 × 10⁻² g g⁻¹ corresponds to chemisorption and 0.058 g g⁻¹ to physisorption. This clearly demonstrates that, under humid conditions, the dominant CO₂ capture mechanism in the polymer is physical adsorption rather than chemical adsorption.

Another noteworthy observation is that, under humid conditions, the amount of CO₂ physically adsorbed by the polymer (0.058 g g⁻¹) is an order of magnitude greater than its CO₂ uptake capacity under dry conditions. This means that in the presence of water and CO₂, tertiary amines can become protonated^57,58 and this protonation may reduce the steric hindrance mentioned before and it increases the polarity and hydrogen bonding capacity of the nitrogen site, which potentially opens up access for CO₂ molecules to interact via physical adsorption⁶⁷ and facilitates CO₂ mass transfer.⁶⁸ As a result, more CO₂ molecules are physically adsorbed.

To sum it all up, when the polymer is exposed to humid CO₂, the total adsorbed gas consists of physically adsorbed CO₂ and water vapor molecules, as well as chemically adsorbed CO₂ molecules.

Moreover, the openQCM Q⁻¹ quartz crystal can also measure dissipation values within the experiment. Dissipation (ΔD) reveals details about the viscoelastic nature of the adsorbed layer. A higher ΔD value suggests the layer is more viscoelastic—such as being soft, hydrated, or swollen—while a lower ΔD indicates a more rigid and less flexible film. Dissipation value changes of the adsorbed layer (which is polymer film) before and after exposures to dry CO₂, humid CO₂ and humid N₂ are observed and the increase percentage (%) of dissipation values were determined. At the same time, using the device, called Infrasorp, which is an optical calorimeter, the heat release from the polymer during adsorption of dry CO₂, humid CO₂ and humid N₂ was measured. Fig. 6 shows the increased percentage (%) of dissipation values and heat release after the polymer, PDMAPAm₂₃₂, is exposed to dry CO₂, humid CO₂ and humid N₂.

Fig. 6 Dissipation value change and heat release of adsorbed layer with exposure to dry CO₂, humid CO₂ and humid N₂.

It can be clear from the figure that the highest dissipation value change and highest heat release is observed when the polymer layer is exposed to humid CO₂ and the figures are relatively lower in humid N₂-exposure case which is followed by dry CO₂-exposure case.

Upon exposure to humid CO₂, the polymer film exhibits pronounced interactions, likely due to the synergistic effects of CO₂ and water vapor. These interactions may involve the formation of bicarbonate ions or enhanced polymer hydration, resulting in significant softening or swelling of the material. This hypothesis is supported by the observed heat release of approximately 90 kJ mol⁻¹, which closely aligns with literature values^{16,20,68,75,76} for the exothermic reaction that can potentially occur between tertiary amines and humid CO₂ leading to bicarbonate ion formation.

In contrast, exposure to humid N₂ results in a comparatively lower change in dissipation, likely attributable to water uptake alone. This can induce moderate swelling or plasticization of the polymer. The associated heat release, which is approximately 50 kJ mol⁻¹, during humid N₂ adsorption is consistent with values⁶⁸ typical of physisorption, likely driven by hydrogen bonding interactions. These findings indicate that humid N₂ is adsorbed onto PDMAPAm₂₃₂ primarily through physisorption mechanisms.

Simulation of humid CO₂ adsorption

Several kinetic models have been reported in the literature, including the Pseudo-First-Order (PFO),⁷⁷ Pseudo-Second-Order (PSO),^77–80 Elovich,¹⁴³ and Avrami⁸¹ models. Out of the models, only PSO and Avrami models were selected for fitting. The reason for this is that studies show PSO provides the best fit for CO₂ adsorption on amine-functionalized materials across various temperatures and concentrations^77,82 and also Avrami model can describe the system that involve both chemisorption and physisorption.⁸¹

The PSO model correlates the amount adsorbed with the square of the available sites.⁷⁸ It assumes that the interactions between the adsorbent and adsorbate arise from the strong binding of adsorbate molecules to the adsorbent's surface, making this model suitable for chemisorption-based CO₂ adsorption.^78–80 The model is represented as follows:

The Avrami model describes Fractional-order kinetics and multi-step adsorption considering complexity of dual chemisorption/physisorption.^80,81 This model is described by the following equation:
In these equations, q_t and q_e represent the adsorption capacity (mmol CO₂ per g) at time t (minutes) and at equilibrium, respectively. The constants k₂ and k_A correspond to the PSO and Avrami rate constants, respectively. The Avrami exponent (n_A) indicates the changes in the mechanism occurring during the adsorption process.⁸⁰

The impact of relative humidity on the kinetic studies of CO₂ adsorption onto PDMAPAm₂₃₂ was investigated at 25 °C using four different relative humidity levels (0%, 55%, 65%, 75 and 85%). Both kinetic models – Avrami and PSO models—were applied to analyze the experimental data. Using the two different models, the fitting has been done and the results of fitting are depicted in the Fig. 7 and Table 3.

Fig. 7 Fitting of two different models for description of adsorption of humid CO₂. Dashed lines (—) show Avrami model. Dot lines (…) show PSO model.

Table 3 R-Square (R²) values from fitting with the first and PSO model

Experiment	R-Square (avrami model)	R-Square (PSO model)
Dry CO2	0.98700	0.95416
Wet CO2, RH = 55%	0.99885	0.99879
Wet CO2, RH = 65%	0.99522	0.97413
Wet CO2, RH = 75%	0.99996	0.98533
Wet CO2, RH = 85%	0.99995	0.95401

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The Fig. 7 represents fitting of experimental CO₂ uptake data collected to two different adsorption models. It can be clearly seen from the graphs that both Avrami and PSO models predict adsorption of humid CO₂ precise. Compared to the PSO, the Avrami model for low humidity cases (such as RH = 55 and 65%) has relatively more accurate prediction. The Avrami model captures surface restructuring, nucleation, and growth of adsorbed layers, which are more pronounced under low humidity due to reduced water-mediated mobility of CO₂ and slower diffusion, making surface phenomena more dominant. Apart from that, under humid conditions, CO₂ undergoes both physical and chemical adsorption. As previously noted, at lower humidity levels, the extent of chemisorption decreases, resulting in a relatively higher contribution from physisorption. Given that the Avrami model accounts for both chemisorption and physisorption processes, unlike the pseudo-second-order model which primarily describes chemisorption, this may explain why the Avrami model tends to provide a better fit under conditions of lower humidity.

The Table 3 describes R-square (R²) values from fitting of experimental values with the Avrami model and PSO model. R-Square tells how much of the variation in the experimental data is captured by the model. It can be clearly seen from the Table 3, compared to R² values of PSO model, the values of the Avrami model are closer to 1. This also means that the Avrami model predicts adsorption in humid conditions better than the PSO model does. Considering the better fitting results, the Avrami model is chosen for the description of the adsorption of humid CO₂ onto the polymer.

The fitting of the Avrami model has been done for various humid CO₂ adsorption experiments and the kinetic parameters of the Avrami model at all these different relative humidities have been recorded. The calculated kinetic parameters of the Avrami model for humid CO₂ capture with variation of relative humidity is shown in the Fig. 8.

Fig. 8 Change of Avrami model kinetic parameters with relative humidity.

This is clear from Fig. 8 that q_e increases and k_A values decrease as relative humidity increases. Another critical point is that a big increase is observed for the q_e – values as the relative humidity changes from 65% to 75%. This kind of sudden increase in q_e value is observed for PEI film described in another publication.⁷³ This might be related to the fact that starting from RH = 75%, more chemisorption occurs between the tertiary amine group on each monomeric unit, leading to a huge mass rise, which increases the q_e value significantly in the end.

In summary, the adsorption of dry CO₂ onto the PDMAPAm polymer follows the Langmuir model,¹⁷ while adsorption in humid conditions is better described by the Avrami model. In both cases, the rate constants play a critical role, as they help assess the minimum energy barrier required for CO₂ adsorption under these distinct conditions. This energy barrier is quantified by the activation energy (E_a), which can be determined through the linearization of the Arrhenius equation described below and the result is demonstrated in Fig. 9.

where k is a rate constant, for Langmuir model is k_L and for Avrami model is k_A. E_a is the activation energy, R is the universal gas constant, A is an Arhenius pre-exponential factor and T is the absolute temperature.⁸³

Fig. 9 Arrhenius plots for rate coefficients of Langmuir model (k_L) and Avrami model (k_A).

Fig. 9 illustrates the natural logarithm of the rate constant (ln(k)) as a function of the inverse of the adsorption temperature under both dry and humid conditions. The activation energy determined for the system at 0% relative humidity is about 10 kJ mol⁻¹. In the presence of moisture, the activation energy increases to around 104 kJ mol⁻¹. The increase in activation energy can reflect a transition from physisorption to chemisorption, which is expected due to the involvement of chemical bonding in the presence of moisture. In dry conditions, physisorption involves weak van der Waals forces and typically has low activation energies, often below 40 kJ mol⁻¹,^69,84 and sometimes even close to zero because the process is not activated, but in humid conditions, chemisorption involves the formation of chemical bonds and is usually activated, requiring higher activation energies, often above 40 kJ mol⁻¹ (Table 4).⁸⁵

Table 4 Activation energies of Langmuir (k_L) and Avrami (k_A) constants

Conditions	Ea (kJ mol^−1)
kL of Langmuir model (dry CO2)	10.7
kA of Avrami model (humid CO2)	103.6

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FTIR measurement

Apart from the chemisorption experiments with wet CO₂, FTIR measurements have been conducted over the surface of the polymer film, which is made of PDMAPAm₂₃₂, to investigate the change on the surface of the film before and after exposing to wet CO₂ and N₂ and results are demonstrated in Fig. 10 and 11.

Fig. 10 FTIR spectrum of polymer PDMAPAm₂₃₂ exposed to N₂.

Fig. 11 FT-IR spectrum of polymer PDMAPAm₂₃₂ exposed to N₂, humid N₂ and humid CO₂ after drying them with N₂ for one night.

Fig. 10 illustrates the FTIR spectrum of polymer PDMAPAm₂₃₂ exposed to N₂. The characteristic transmittance bands associated with specific functional groups: a methyl (–CH₃) deformation at 1373 cm⁻¹, C–H bending at 1461 cm⁻¹, N–H bending (amide II) at 1535 cm⁻¹, C=O stretching (amide I) at 1641 cm⁻¹, symmetric and asymmetric stretching of the dimethylamino group (–N(CH₃)₂) at 2765 and 2816 cm⁻¹, C–H stretching vibrations at 2857 and 2939 cm⁻¹, and a broad N–H stretching band at 3298 cm⁻¹.

Fig. 11 represents FTIR spectrum of polymer PDMAPAm exposed to dry N₂, humid N₂ and humid CO₂. This is clear from the spectra that IR spectra of N₂-exposed PDMAPAm₂₃₂ serves as the baseline whereas humid N₂ shows slight intensity changes, indicating minor interactions with water. Compared to both cases, humid CO₂-exposed PDMAPAm₂₃₂ exhibits more pronounced vibration in the FTIR spectra results, suggesting stronger chemical interactions. Another important point is that as the humidity of CO₂ increases, intensity of peaks rises and especially over 75% of relative humidity, the intensity of peaks increases significantly. This is not coincidence that as shown in the Fig. 8, q_e-value (maximum uptake capacity of the polymer) also suddenly rises more than 75% of relative humidity. This may be due to formation of more bicarbonate ions at higher relative humidity conditions.^86,87

There are two big remarkable difference between spectra of humid CO₂ and humid N₂-exposed polymer films. The first one is that the intensity of some peaks get higher when the polymer interacts with humid CO₂ compared to humid N₂ as it was observed in another tertiary amine-based polymer.⁸⁸ The second one is that one new peak appears in the humid CO₂ case, which corresponds to (N–H) stretching vibrations from the ammonium ion (NH⁺) formation,⁸⁹ arising from the formation of ammonium bicarbonate salt. The reason for both differences is the reaction that occurs between the tertiary amine of the polymer and humid CO₂, which leads to the formation of ammonium bicarbonate.⁸⁸

Broad bands around 3300–3500 cm⁻¹ are typically associated with (N–H) stretching. Symmetric and asymmetric stretching of the dimethylamino group (–N(CH₃)₂) appear at 2766 cm⁻¹ and 2816 cm⁻¹ in the N₂-exposed case, but both peaks turn out to be intense, and the peak turns out to be sharper in the humid CO₂-exposed case. This may be because they are bound to a tertiary amine that potentially reacts with humid CO₂ for the formation of (NH⁺) and (HCO₃⁻). The 1650–1600 cm⁻¹ is a critical region for HCO₃⁻ asymmetric stretching. In dry N₂ and humid N₂-exposed cases, the peak at 1641 cm⁻¹ corresponding to (C=O) stretching of amide is overlapping. However, the intensity of the peak increases significantly as soon as the polymer interacts with the humid CO₂. Considering that (COO–) asymmetric stretching from bicarbonate^88,90 and (C–O) asymmetric stretch of bicarbonate^59,88 appear at 1657 cm⁻¹ and 1610 cm⁻¹, respectively. The reason for the higher intensity in the humid CO₂-case can be the formation of the bicarbonate.

Optimization of PDMAPAm polymer film thickness

In some other works, it is mentioned that altering the thickness of the polymeric amine film serves as a functional analogue to adjusting amine loadings within porous support material that can increase uptake capacity of material.^73,91 Therefore, three polymer solutions, 30% w/w, 10% w/w, and 2% w/w of PDMAPAm in THF were prepared and the polymer films with three different thickness were coated onto the quartz crystal as illustrated in previous publications.^40,41 Then, the CO₂ capture capacities of the polymer films were measured by changing the film thickness and are shown in Fig. 12.

Fig. 12 (a) Overall dry and wet CO₂ uptake (physisorption + chemisorption) and (b) CO₂ chemisorption uptake changing with polymer film thickness.

Fig. 12 illustrates the amount of gas adsorbed by the polymer film when exposed to both dry and humid CO₂, as well as the portion of gas uptake attributable specifically to chemisorption, across varying film thicknesses. It can be clearly seen from Fig. 12(a) that the CO₂ uptake capacity of the polymer film increases in both dry and humid conditions as the film thickness decreases, whereas Fig. 12(b) shows the same trend for chemisorption in humid conditions. This trend fits well with the findings shown in another publication⁷³ described in the literature. As shown in previous publication,^40,41 the film, which was fabricated, is thick and packed. The research group of J. R. Hoffman et al.^73,74 has mentioned that in the thick-film regime, CO₂ capture is primarily limited by the accessibility of amine sites and amine groups located deeper within the film are often inaccessible and therefore do not effectively participate in the reaction. In other words, when the polymer thickness is higher, interaction between CO₂ and the amine group only occurs on the surface in any way. Therefore, by making the polymer film thinner, the amount of polymer used for film fabrication decreases, and the surface area-to-volume ratio increases. As a result, using less polymer (thinner film), more CO₂ is captured. This is the reason why at thinner polymer films, CO₂ uptake capacity goes up in this case.

Using the impact of film thickness on the adsorption capacity, PDMAPAm and PDMAPAm-b-PMMA films were prepared with the smallest thickness (10 µm). CO₂ uptake capacity of the diblock copolymer was compared with the CO₂ uptake capacity of PDMAPAm polymer film. The result of comparison is demonstrated in the Fig. 13.

Fig. 13 CO₂ capture comparison of PDMAPAm₂₃₂ film with PDMAPAm₂₃₂-b-PMMA₅₇ film at dry and humid conditions.

This is clear from Fig. 13 that generally, a homopolymer shows a higher total CO₂ uptake capacity, which is the sum of adsorbed CO₂ via physisorption and chemisorption, than a diblock copolymer does in humid conditions. Alone, the homopolymer adsorbs more CO₂ via chemisorption than the diblock copolymer, and this is due to the fact that the homopolymer has more monomeric units with a tertiary amine group than the diblock copolymer has. Most of CO₂ is adsorbed via physisorption by both homopolymer and diblock copolymer. However, as for physisorption, the diblock copolymer adsorbs relatively more CO₂ at dry conditions than the homopolymer does, as it has been observed for the polymers in powder form. The reason for this higher CO₂ uptake capacity of diblock copolymer at dry conditions is the existence of the PMMA group on it, as mentioned before.

Unified model

In previous work,¹⁷ polymerization kinetics⁴² were integrated with the adsorption kinetics of CO₂ on the polymer material under dry conditions, yielding a unified model. Starting from molecular-level polymer design, the unified model approach establishes quantitative structure–property relationships linking polymer composition, molar mass, and block architecture to solution–diffusion-dominated CO₂ adsorption under dry conditions. The framework is subsequently extended to realistic DAC environments by explicitly incorporating humidity-dependent adsorption mechanisms, allowing simultaneous description of physisorption- and chemisorption-controlled CO₂ uptake within a single unified kinetic model. By resolving the distinct kinetic regimes, activation energies, and rate-limiting steps governing CO₂ capture in both dry and humid atmospheres, the model enables direct translation of polymer synthesis parameters and polymer properties into operational capture performance of CO₂ membrane adsorber made of the polymer. As a result, this unified methodology allows the rational design and fabrication of PDMAPAm-based polymer membrane adsorbers that achieve high CO₂ uptake capacities under dry and humid conditions, bridging the gap between polymer chemistry, adsorption science, and deployable direct air capture materials within a single coherent material-design strategy. Another important consideration is that humidity and temperature vary across different geographical locations, which implies that polymer materials can be tailored accordingly, for example by adjusting molar mass or block composition. Using the unified model, the CO₂ uptake capacity of these designed polymers can then be directly predicted under different humidity and temperature conditions without the need for extensive experimental screening, thereby significantly reducing time and experimental effort.

The unified model could predict polymer properties of the synthesized polymer PDMAPAm and the CO₂ uptake of it correctly in dry conditions. In this study, the kinetic model for CO₂ adsorption under humid conditions was developed and integrated into a unified framework to support digital-twin-assisted design of CO₂-responsive polymers. For consistency and comparative analysis, the same polymer, PDMAPAm₁₆₃, used in our previous work was selected as the case study material (SI).

The humid CO₂ adsorption isotherm of the polymer, PDMAPAm, was also simulated using the prediction line (Fig. 8), which describes how the kinetic parameters (q_e and k_A) change with relative humidity. To test whether the Avrami model predicts correctly, humid CO₂ adsorption isotherms of the homopolymer were experimentally measured and compared with the simulation shown in Fig. 14.

Fig. 14 A comparison between the kinetic model predictions and experimental data for CO₂ adsorption under humid conditions on the PDMAPAm163 homopolymer is presented. The measurements were conducted at room temperature, atmospheric pressure, and a relative humidity of 80%.

It can be clearly seen from Fig. 14 that the humid CO₂ adsorption model accurately predicted the polymer's uptake capacity, indicating that the model performs reliably under these conditions. With this, the unified model can simulate an optimal recipe of polymer synthesis and its properties and at the same time CO₂ uptake capacity of the polymer in dry and humid conditions.

The resulting unified model therefore functions as a materials design tool that can be universally applied to design CO₂-responsive polymers, starting from the design of a monomer that also enables to predict optimal polymer synthesis recipe, polymerization time, polymer properties and CO₂-capture process conditions for the polymers of interest and can also optimize CO₂ uptake capacity of developed polymers as a function of polymer properties and CO₂ capture process conditions.

Comparison of CO₂ uptake capacity of PDMAPAm and PDMAPAm-b-PMMA with polymer-based adsorbents

The adsorption performance of the developed polymer materials for CO₂ capture was assessed under identical conditions (25 °C, 1 bar) in both dry and humid environments. The Table 5 compares CO₂ uptake capacity of PDMAPAm₂₃₂ and PDMAPAm₂₃₂-b-PMMA₅₇ with other polymer-based adsorbers under different conditions.

Table 5 Comparison of CO₂ uptake capacity of PDMAPAm and PDMAPAm-b-PMMA with other polymer-based adsorbers

Polymer-based adsorbents	CO2 uptake capacity (mmol g^−1)	Conditions	Ref.
PDMAPAm232	0.05	25 °C, 1 bar, dry CO2	This study
PDMAPAm232-b-PMMA57	0.52	25 °C, 1 bar, dry CO2	This study
PDMAPAm232-b-PMMA57	5.60	25 °C, 1 bar, humid CO2, RH = 75%	This study
PDMAPAm232	6.00	25 °C, 1 bar, humid CO2, RH = 75%	This study
SBA-15-supported linear PEI	0.20–0.80	25 °C, 1 bar, dry CO2	92–94
SBA-15-supported branched PEI	0.50–1.50	25 °C, 1 bar, dry CO2	95–97
SBA-15-supported branched PEI	1.70–2.00	25 °C, 1 bar, humid CO2, RH = 50%	95–97
Al2O3-supported branched PEI	1.70–1.80	25 °C, 1 bar, dry CO2	94 and 98
Quaternized chitosan/poly(vinyl alcohol)	0.20	25 °C, 1 bar, dry CO2	94
Tetraethylenepentamine (TEPA) “ZS-T-60”	1.00–1.10	25 °C, 1 bar, dry CO2	99
SiO2-supported tetraethylenepentamine (TEPA)	1.00–2.50	25 °C, 1 bar, dry CO2	100
Polyacrylonitrile (PAN)	0.40	25 °C, 1 bar, dry CO2	101
PAN-PEI	0.20
PAN-DETA	1.80
MIL-101(Cr)-supported-polypropylenimine (PPI)	1.20–1.30	25 °C, 1 bar, dry CO2	93,94
MIL-101(Cr)-supported-polypropylenimine (PPI)	1.30–1.60	25 °C, 1 bar, humid CO2, RH = 50%	102
Lewatit® VP OC 1065	2.00–2.50	25 °C, 1 bar, humid CO2, RH = 40–80%	103

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Under dry conditions (25 °C, 1 bar), PDMAPAm₂₃₂ exhibited a modest uptake of 0.05 mmol g⁻¹, while its block copolymer PDMAPAm₂₃₂-b-PMMA₅₇ achieved a significantly higher uptake of 0.52 mmol g⁻¹. In comparison, polyethyleneimine (PEI)—a benchmark polymer for CO₂ adsorption—shows a dry uptake of 2.10 mmol g⁻¹, outperforming both polymers from this study. Another point: SBA-15-supported linear PEI ranges from 0.20–0.80 mmol g⁻¹, while branched PEI supported on SBA-15 ranges from 0.50–1.50 mmol g⁻¹, indicating that structural optimization and support materials play critical roles. Other polymers, such as quaternized chitosan/poly(vinyl alcohol) and polyacrylonitrile (PAN) show lower uptakes of 0.20 mmol g⁻¹ and 0.40 mmol g⁻¹, respectively, under dry conditions. tetraethylenepentamine (TEPA) supported on silica (SiO₂) performs better, with uptakes ranging from 1.00–2.50 mmol g⁻¹, depending on the support and formulation.

Under humid conditions, conventional polymer sorbents based on amine-functionalized polyacrylonitrile (PAN), and tetraethylenepentamine (TEPA), including PAN-DETA, PAN-PEI, and PAN-TEPA, exhibit relatively low CO₂ uptake capacities (typically ≤2 mmol g⁻¹).^99–101 Similarly, polymer–amine composites relying on the impregnation of low-molecular-weight amines or branched PEI onto polymeric or inorganic supports and Lewatit generally achieve moderate CO₂ uptake capacities in the range of 2–3 mmol g⁻¹.^94–98 In comparison, the PDMAPAm₂₃₂ membrane adsorber demonstrates a markedly higher CO₂ uptake of approximately 6 mmol g⁻¹, surpassing most reported polymer-based sorbents and underscoring the effectiveness of densely distributed tertiary amine groups within a thin, continuous polymer film. The diblock copolymer PDMAPAm₂₃₂-b-PMMA₅₇ maintains a comparably high CO₂ uptake capacity, with only a modest decrease relative to the PDMAPAm₂₃₂, demonstrating that incorporation of a PMMA block improves mechanical robustness without severely compromising adsorption performance.^38–40

Overall, the comparison demonstrates that both PDMAPAm and PDMAPAm-b-PMMA outperform a wide range of commercial polymer-based CO₂ sorbents, showing the new developed polymers as promising candidates for fabrication of CO₂ membrane adsorbers to implement direct air capture technology.

Conclusion

This study provides a comprehensive investigation into the CO₂ capture behavior of the CO₂-responsive homopolymer PDMAPAm and its diblock copolymer PDMAPAm-b-PMMA for fabrication of CO₂ membrane adsorbers, with a focus on their applicability as membrane adsorbers for direct air capture (DAC) technologies. Through a systematic approach, the adsorption mechanisms were delineated into physisorption and chemisorption processes, depending on the moisture content of the CO₂ stream and investigated.

As mentioned in previous publication,¹⁷ under dry conditions, CO₂ was found to undergo physisorption, interacting primarily with the tertiary amine groups of PDMAPAm and the carbonyl functionalities of PMMA. In contrast, in humid CO₂, chemisorption also occurs through bicarbonate formation at the tertiary amine sites, as confirmed by mass changes, calorimetry, and characteristic FTIR bands. Nevertheless, physisorption remains the dominant uptake pathway under humid conditions, with the physically adsorbed fraction exceeding the chemisorbed fraction by several-fold.

Beyond mechanistic characterization, the study explored the kinetics of CO₂ adsorption, incorporating both physisorption and chemisorption kinetics into the kinetics of polymer synthesis in a unified model for digital-twin supported design of CO₂-responsive polymers. The primary novelty of this work is the development of a unified kinetic model that, for the first time, integrates polymerization kinetics with adsorption kinetics, enabling direct prediction of CO₂ uptake capacity from the intrinsic polymer properties. A second key innovation is the application of this model to rationally design and fabricate a membrane adsorber that achieves a CO₂ uptake capacity of 6 mmol g⁻¹ significantly surpassing the performance of commercially available polymer-based sorbents. The results highlight the strong potential of PDMAPAm-based materials in addressing the pressing need for effective DAC solutions, contributing meaningfully to the broader scientific effort to mitigate atmospheric CO₂ levels through innovative material development.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data supporting this study are provided in the supplementary information (SI) and previous published dataset. Supplementary information: synthesis procedure, structural characterization, theoretical calculations, experimental methods, and spectral analyses. See DOI: https://doi.org/10.1039/d6mh00641h.

For access to the dataset, refer to DOI: https://doi.org/10.5281/zenodo.17963415.

Acknowledgements

The authors are grateful for financial support from Direct Air Capture and Storage (DACStorE) (KA2-HSC-12) offered by the Initiative and Networking Fund of the Helmholtz Association. Additionally, the authors thank Silvio Neumann and Maren Brinkmann for performing the NMR and GPC measurements as well as Dr. Felix Kandelhard for discussion on the polymerization kinetics. Scientific discussions with Prof. Dr. Volker Abetz are greatly acknowledged.

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