Thickness Dependent CO₂ Adsorption of Poly(ethyleneimine) Thin Films for Direct Air Capture

Abstract

Mesoporous silica impregnated with polyethyleneimine (PEI) has been shown to be a suitable material for the direct air capture (DAC) of CO₂. Factors such as CO₂ concentration, temperature, and amine loading impact overall capture capacity and amine efficiency by altering diffusional resistance and reaction kinetics. When studied in the impregnated 3-dimensional sorbent material, internal diffusion impacts the evaluation of the reaction kinetics at the air/amine interface. In this work, we designed a novel tandem quartz crystal microbalance with dissipation (QCM-D) and polarization modulation infrared reflective absorption spectroscopy (PM-IRRAS) instrument. CO₂ adsorption kinetics of the PEI-based amine layer in a 2-dimensional geometry were studied at a variety of film thicknesses (10 nm to 100 nm), temperatures (25 °C to 80 °C), and CO₂ concentrations (5 % and 0.04 % by mole fraction). Total CO₂ capture capacity increased with film thickness but decreased amine efficiency, as additional diffusional resistance for thicker films limits access to available amine sites. The capture capacity of thick films (>50 nm) is shown to be limited by amine availability, while capture of thin films (<50 nm) is limited by CO₂ availability. A 50 nm PEI film was shown to be optimal for capture of 0.04 % (400 ppm) CO_2. The adsorption profiles for these conditions were fitted to pseudo-first order and Avrami fractional order models. The reaction process switches between a diffusion limited reaction to a kinetic limited reaction at 80 °C when using 5 % CO₂ and 55 °C when using 0.04 % CO₂. These results offer accurate analysis of adsorption of CO₂ at the air/amine interface of PEI films which can be used for the design of future sorbent materials.

1. Introduction

CO₂ concentrations in the atmosphere have risen dramatically during the last century due to human activity [1]. Growing trends to decarbonize the global energy sector will reduce emissions [2], but there remains a need to achieve net negative emission strategies to reduce the impact of climate change from legacy emissions [3,4]. The removal of CO2 from the atmosphere using supported amines has shown promise as a platform for the direct air capture (DAC) of CO₂ [5,6]. The CO₂-amine reaction pathway forms carbamate and ammonium ions in dry conditions, shown in Scheme 1 [7,8]. These sorbent materials are designed to operate at low CO₂ concentrations found in the atmosphere, 0.04 % CO₂ (400 ppm), compared to other CO₂ capture conditions, such as capture from flue gas (≈10 % CO₂). The dilute nature of CO₂ in DAC applications requires high surface area sorbent materials to maximize amine loading and capture efficiency. There are many reviews which highlight the types of amines and materials studied for DAC [9–11], in which polymer-based amines can be introduced into porous materials via wet impregnation or chemical grafting techniques [12]. Wet impregnation can incorporate a high quantity of amine content, but excess polymer can result in pore blockage that decreases efficiency [13]. Chemical grafting of amines has more control on the functionalization process, but lower surface coverage can reduce overall capacity [12,14].

Scheme 1.

Reaction Mechanism of Dry CO₂ with Aqueous Amines

Physical impregnation of hyperbranched polyethyleneimine (PEI) within mesoporous silica is an attractive platform for DAC as a high quantity of amine groups can be incorporated and the high molecular mass of PEI allows for improved retention during cycling [15]. These physically impregnated PEI-amine materials undergo multiple diffusion and reaction steps to capture CO₂. These include external, film, and pore diffusion of CO₂ from the bulk to the amine layer, solid diffusion of CO₂ into the amine layer, and finally chemical reaction within the amine layer [16]. The extent of amine loading can drastically impact these diffusion and reaction steps, playing an important role in overall capture capacity and amine efficiency [17,18]. Lower loading values have been shown to exhibit a decreased capture capacity because there are less amine sites available for reaction; however, excess loading can make certain amine sites less accessible due to increased diffusional resistance.

Attempts have been made to model the capture system, evaluating the contributions of pore diffusion, solid diffusion, and chemical reaction over time [19]. Work by Ge, et al. modeled these contributions as a function of mass transfer resistance and determined that: (1) chemical reaction is the dominant step during the entire regime, (2) pore diffusion is important during the initial stages, and (3) solid diffusion resistance increases over time as the number of accessible amines decreases with capture [20]. These results highlight that further improvements of DAC materials requires maximizing the amount of available amines, while also understanding the mechanisms that drive capture at the air/amine interface.

Amine impregnated sorbent materials are commonly evaluated using thermogravimetric analysis (TGA) [9,21]. This technique monitors the change in mass of a sorbent material before and after CO₂ exposure to determine uptake capacity. Since this process utilizes a packed bed of 3-dimensional particles, there are additional diffusional resistances that impact the measurement of capture kinetics. This challenge has been overcome using a microfluidized bed TGA, which more accurately showed the rapid uptake of CO₂ within the amine layer compared to conventional TGA [22]. These results demonstrated that additional experimental techniques are needed in order to accurately measure adsorption kinetics within the amine layer.

The primary descriptor for amine impregnated sorbent materials is the PEI loading, which is simply the mass of PEI per mass of sorbent. However, this descriptor overlooks the 3D nature of PEI within the sorbent particle. Specifically, the tortuosity and variable length of the pores likely leads to heterogeneity within the particles (e.g., variable PEI coating thickness, plugs/domains of PEI, dead ends), as illustrated in Figure 1. This non-uniformity makes accurate depiction of the air/amine interface difficult. Here, we simplify the sample geometry by spin coating PEI into a planar thin film, which creates equal path lengths for CO₂ to diffuse into and react with the amine groups in PEI. A 2D planar geometry is an effective surrogate for the PEI coating within the porous sorbent, while allowing for quantification of coating thickness and thus diffusional path length. This approach also allows for a broader range of experimental techniques to be used to study CO₂ uptake in polymer-based sorbents, as there are numerous measurement platforms specifically designed to interrogate thin films.

Figure 1.

Diffusional pathways of a 3D particle vs a 2D planar (thin film) geometry. In the particle case, the arrows represent variations in CO₂ diffusional path length due to heterogeneity in PEI coating and tortuosity of the porous particle. Conversely, a planar (thin film) geometry results in uniform diffusional path lengths for CO₂ to enter the PEI and find available amine sites.

Here, we developed a tandem quartz crystal microbalance with dissipation (QCM-D) and polarization modulation infrared absorption spectroscopy (PM-IRRAS) platform to simultaneously measure the mass gain associated with CO₂ sorption into the PEI material and to explicitly monitor the chemical changes within the PEI, respectively. This tandem platform allows us to unambiguously correlate mass changes seen in QCM to reaction products (e.g., carbamate formation) within the sample under the exact same conditions (processing history, flow rate, temperature, etc). To mimic the PEI confined within a porous support, we studied film thicknesses ranging from 10 nm to 100 nm, where a 10 nm film is similar in length scale to the pore size of many sorbent materials [23–25]. While thickness values greater than 10 nm may not be feasible in current sorbent particles, the fundamental understanding of how thickness impacts capture in thicker films is useful for the design of future sorbent materials. 25 kDa PEI was chosen over the more commonly studied 800 Da PEI to ensure a stable and uniform film throughout testing. Capture capacity has been shown to increase with decreasing molecular mass, [17] but a higher molecular mass will prevent surface dewetting during testing. The kinetics of adsorption were measured for each film thickness at both 5 % and 0.04 % mole fraction CO₂ concentrations in N₂ balance across a range of temperatures. The changes in capture at these conditions offers vital insights into the impact of the CO₂ availability and diffusivity/reactivity within PEI on overall capture capacity.

2. Materials and Methods

Certain equipment, instruments, software, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement of any product or service by NIST, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

Quantitative ¹³C solution nuclear magnetic resonance (NMR) data of hyperbranched polyethyleneimine (PEI), (molecular mass = 25 kDa, Sigma-Aldrich) was obtained using a Bruker 600 MHz spectrometer following a previously reported method. [26] An inverse-gated ¹H-decoupled ¹³C experiment was performed using a 14 μs ¹³C detection pulse, a 1 s acquisition time, and a 5 s relaxation delay. The spectrum obtained from PEI in deuterated chloroform (CDCl₃), shown in Figure S1 was analyzed by summing peak areas of signals previously assigned to the carbon neighbor of primary, secondary, and tertiary amines in PEI and dividing by 1, 2, or 3, respectively, for each amine structure type. [26] The resulting values are represented by the fraction of the total amine-carbon population as listed in Table S1.

Tandem quartz crystal microbalance with dissipation (QCM-D) and polarization modulation-infrared reflection-adsorption spectroscopy (PM-IRRAS) measurements were performed using a custom QCM-D cell (AWSensors, Valencia, Spain) mounted within the PM-IRRAS accessory of a Nicolet iS50 IR spectrometer (Thermo Scientific, Waltham, MA). The QCM-D cell contains an enclosed environment which allows for controlled exposure to a desired feed gas. The cell was designed with two ZnSe windows that allow for the infrared (IR) beam to enter the QCM-D cell, reflect off the quartz crystal, and ultimately reach the PM-IRRAS detector. PM-IRRAS is a surface selective technique in which atmospheric absorption of CO₂ are eliminated from the IR spectra. This is achieved by ratioing the absorptions of s- and p- polarized light to isolate IR vibrational modes solely coming from the sample (film).

Measurements were made using 1” (25.4 mm) diameter gold coated AT-cut quartz crystals (AWSensors) with a resonant frequency of 5 MHz. Gold coated crystals provided the necessary IR reflective surface for PM-IRRAS measurements. QCM crystals were cleaned by sonicating for 10 min in acetone and 10 min in isopropanol. The crystals were dried using compressed nitrogen and exposed to ultraviolet-ozone (UVO) for 20 min prior to testing. QCM measurements were performed with the clean crystal at all tested temperatures to obtain the baseline frequency and dissipation values of each crystal.

25 kDa PEI was dissolved in ethanol at mass fractions between 0.5 % to 7.5 % and spin coated onto clean QCM crystals. The PEI solution concentration and spin rate were controlled to produce films of desired thickness. PEI films of 10 nm, 25 nm, 50 nm, 100 nm, and 500 nm thickness were prepared and confirmed using a M-2000XI variable angle spectroscopic ellipsometer (J.A. Woollam Co., Inc., Lincoln, NE). The coated crystals were placed within the QCM cell and heated to 60 °C under 750 standard cubic centimeters per minute (SCCM) N₂ flow to remove any adsorbed CO₂ and water prior to measurements. Once the cell temperature reached 60 °C, PM-IRRAS scans confirmed that all CO₂ was desorbed. Then, the sample was cooled/heated to the desired temperature (25 °C, 35 °C, 55 °C, or 80 °C) while maintaining a 750 SCCM N₂ flow for 1 h to allow the QCM frequency measurement to stabilize prior to exposure of the film to CO₂. The mass of PEI remained constant at each temperature and throughout testing.

The difference in frequency between the bare and PEI coated crystal was converted into mass of PEI by using the Sauerbrey equation:

$$\frac{\Delta F}{n}=-\frac{2f_0^2}{A\sqrt{{\rho }_q{\mu }_q}}\Delta m$$ (1)

where $f_0$ is the resonant frequency of the crystal (5 MHz), $\Delta m$ is the mass change, $A$ is the piezoelectrically active crystal area (0.32 cm²), ${\rho }_q$ is the density of quartz (2.648 g cm⁻³), and ${\mu }_q$ is the shear modulus of an AT-cut crystal (2.947×10¹¹ g cm⁻¹ s⁻²).

The experimental design for controlling the flow of gas into the QCM cell is shown schematically in Figure 2. Three mass flow controllers (Alicat Scientific, Tucson, AZ) were used to adjust the relative flow of N₂ and CO₂ into the cell. One flow controller was for the N₂ sweep gas and the other two flow controllers were used to vary the CO₂ concentration. The two lines were connected to a 4-way switching valve (VICI Valco Instruments, Houston, TX) which led into the QCM cell. The switching valve was utilized to achieve immediate switching between N₂ and CO₂, thereby minimizing the delay time that could persist if the flow rate was controlled solely through the on/off functions of the flow controllers. QCM and PM-IRRAS measurements were collected for 5 min prior to CO₂ exposure, after which CO₂ was exposed for controlled time periods. Long term equilibrium tests were performed for 15 h of CO₂ flow while short term tests were performed for 1 h. The normalized frequency shift, ΔF/n, and the dissipation, ΔD, were recorded for the n = 3, 5, 7, 9, and 11 harmonics. The mass of CO₂ gained was calculated using the Sauerbrey equation (Equation 1), using the difference between measured frequency and the PEI coated crystal frequency. Error bars for CO₂ capture represent one standard deviation of the data (n = 2) which is taken as the experimental uncertainty of the measurement. Some error bars are smaller than the symbols.

Figure 2.

Schematic of QCM/PM-IRRAS setup. Features of the QCM cell include inlet and outlet ports for controlled gas flow as well as ZnSe windows on both sides of the cell which allow the IR beam to pass through and interact with the sample before reaching the detector.

QCM-D allows for the monitoring of the dissipation of the film, which helps distinguish sample rigidity. The dissipation of each film thickness was measured prior to CO₂ exposure at each temperature to determine if a dissipation change occurred within the films.

The experimental data obtained via QCM were fit to a pseudo-first order and an Avrami’s fractional kinetic model, both of which have been utilized to model CO₂ adsorption of solid amine sorbents [27,28]. The integrated form of the pseudo-first order model is:

$$q_t=q_e\left(1-\text{exp}\left(-k_{f}t\right)\right)$$ (2)

where $q_t$ is the capacity at time $t,q_e$ is the equilibrium capacity, and $k_f$ is the pseudo-first order rate constant.

The integrated form of the Avrami kinetic model is:

$$q_t=q_e(1-\text{exp}\left(-{\left(k_{A}t\right)}^{n_A}\right))$$ (3)

where $k_A$ is the Avrami rate constant, and $n_A$ is the Avrami exponent.

In tandem with the QCM measurements, PM-IRRAS scans were collected. A wavelength of 2500 cm⁻¹ was used for the photoelastic modulator. Samples were scanned 62 times per measurement over a range of 1000 cm⁻¹ to 4000 cm⁻¹. Each measurement required 59 seconds to complete, with 1 second intervals being used between each measurement. Spectra were taken continuously for the duration of the experiment.

3. Results and Discussion

3.1. Validating tandem QCM/PM-IRRAS experiments

The exposure of PEI to CO₂ under dry conditions leads to the formation of carbamate via a reaction of primary and secondary amines with CO₂. This reaction produces a change in mass within the PEI due to the uptake of CO₂ both in terms of adsorption/carbamate formation, and physisorption of CO₂ on the polymer surface [29]. The nature of the tandem QCM/PM-IRRAS experiment allows for a complete understanding of this process. The QCM measurement encompasses both potential mass changes, while the IR spectra can differentiate between carbamate formation and physisorbed CO₂. To test this, a 100 nm film of 25 kDa PEI was prepared and exposed to CO₂ for 15 h at 25 °C. The results from the QCM/PM-IRRAS are shown in Figure 3. Prior to CO₂ exposure, the frequency was measured under dry N₂ flow and remained stable with a ΔF/n value near zero.

Figure 3.

QCM and PM-IRRAS data for a 100 nm, 25 kDa PEI film exposed to 5 % CO₂ at 25 °C. A) ΔF/n data shows good agreement between each harmonic, indicating that the Sauerbrey equation is valid to convert frequency to mass. B) CO₂ capture capacity as a function of time using ΔF/n data. C) PM-IRRAS scans of the PEI at the initial state (pre-CO₂), shown in the black spectrum, and after 15 h of CO₂ exposure, shown in the red spectrum. D) PM-IRRAS absorbance for the specific peak at 1305 cm⁻¹, which corresponds to carbamate formation. E) Normalizing the data from panel B and D results in similar uptake profiles, indicating that the mass uptake seen in the QCM results is directly linked to the formation of carbamate shown in the PM-IRRAS results.

Exposing the PEI film to CO₂ resulted in an immediate decrease in frequency, as the mass of the crystal increased during CO₂ adsorption. Five harmonics were measured, with all showing good agreement with each other, shown in Figure 3A. This indicates that the film can be modelled as a rigid film and the Sauerbrey equation was valid for converting ΔF/n to $\Delta m$ [30]. This metric is useful because bulk PEI is a viscous liquid at and above room temperature. This result suggests that when confined to a film of 100 nm and less, PEI can be considered a rigid and non-viscoelastic film. The frequency continued to decrease over the 15 h experiment. The mass of CO₂ captured was calculated and normalized by the mass of PEI on the crystal, as shown in Figure 3B. There was an initial rapid uptake of CO₂ at short times followed by a more gradual and continuous uptake of CO₂ at long times. This continuous mass change indicates that the sample does not reach equilibrium quickly, though 75 % of the total 15 h uptake occurs within 1 h after CO₂ introduction.

As equilibrium is not reached in this extended time, it is important to determine if the mass change measured in the QCM is due to carbamate formation or physisorbed CO₂ accumulating on the surface. The PM-IRRAS spectra collected during CO₂ exposure provides evidence of the reaction products. Shown in Figure 3C, the PM-IRRAS spectra before and after CO₂ exposure shows carbamate formation, due to the presence of peaks at 1305 cm⁻¹, 1470 cm⁻¹, and 1586 cm⁻¹ [8,31]. Gaseous CO₂ is shown in peak 2360 cm⁻¹. PM-IRRAS is a highly surface sensitive measurement, in which the head space environment is subtracted out of the scan, leaving only the surface measurement. The presence of the gaseous CO₂ peak may indicate physiosorbed CO₂ on the surface of the sample or on the cell windows. The 2360 cm⁻¹ peak grew in intensity during the first 15 min of CO₂ exposure before stabilizing with only random fluctuations in intensity during the 15 h experiment. This is shown in Figure S2. An additional measurement of a non-coated QCM crystal showed physiosorbed CO₂ on the surface. This is shown in Figure S3. The formation of specific carbamate peaks can be monitored in a similar way to QCM uptake by examining peak growth over time. The change in peak height of the 1305 cm⁻¹ peak is shown in Figure 3D. A similar profile is seen compared to the mass uptake plot. This indicates that the gradual increase in mass as measured by QCM is from continued carbamate formation, not physiosorbed CO₂ on the surface. When this data is normalized, in which mass and peak height at 15 h were set as the equilibrium point for both methods, the profiles from QCM and PM-IRRAS are nearly identical, as shown in Figure 3E. This result demonstrates the utility of the tandem QCM/PM-IRRAS system for evaluating CO₂ capture performance of amine containing polymers.

An equally important process for CO₂ capture is desorption of CO₂ for sequestration/storage. This is commonly done through temperature swing or pressure swing processes [6]. Desorption was not studied within this work as both changes in temperature and pressure affect the measured frequency of the QCM crystal, which occurs simultaneously with changes in frequency brought on by the loss of mass from the desorbing CO₂. Complete desorption of CO₂ was achieved immediately by heating the sample to 60 °C under 100 % N₂ flow.

3.2. Effect of film thickness on adsorption at 25 °C

PEI film thickness was varied to emulate the different amine loading levels seen in mesoporous silica materials [17,32]. It can be hypothesized that thicker PEI films add additional mass transport resistance to the system, making it more difficult for CO₂ to reach amine sites deep within impregnated sorbents. CO₂ sorption in PEI films with thicknesses ranging from 100 nm to 10 nm were measured to determine if this trend is maintained in films of a planar geometry. For these experiments, the CO₂ exposure time was reduced to 1 h as this time frame constitutes 75 % of the 15 h capture capacity. The results are shown in Figure 4.

Figure 4.

A) Amount of CO₂ captured and B) CO₂ capture normalized by PEI mass when exposed to 5 % CO₂. C) CO₂ capture normalized by PEI mass using 0.04 % CO₂. Samples consisted of 25 kDa PEI with thicknesses of 10 nm, 25 nm, 50 nm, and 100 nm. Measurement temperature was 25 °C. The error bars represent one standard deviation of the data (n = 2) which is taken as the experimental uncertainty of the measurement. Some error bars are smaller than the symbols.

The total mass of captured CO₂ using a feed concentration of 5 % CO₂ is shown in Figure 4A. The 100 nm film achieved the highest CO₂ uptake, and the 10 nm film exhibited the lowest. This observation can be attributed solely to thicker films having more PEI material (amine groups) than thinner films. However, the increase in capacity is not linear - increasing the thickness from 10 nm to 100 nm results in a 10× increase in the amount of amine-containing polymer but only a 5× increase in capture capacity. To further demonstrate this decrease in efficiency seen for thicker films, the amount of CO₂ captured was normalized by the mass of PEI on the QCM crystal. The CO₂ uptake relative to the mass of PEI of the film can be regarded as a metric of amine efficiency, as the ratio of amines per gram of PEI remains constant as thickness changes. This data is shown in Figure 4B. Thinner films exhibit greater CO₂ capture capacity per g of PEI, suggesting more amine sites are accessible due to lower diffusional resistance. This follows results shown in impregnated silica materials and studies of varied pore length, in which longer path lengths that CO₂ must travel resulted in decreased amine efficiency [33].

Additional experiments were performed at 0.04 % CO₂ to simulate DAC conditions. These results are shown in Figure 4C. The amount of CO₂ captured for the 10 nm film reduced dramatically, decreasing 44 % from 4.8 mmol CO₂ / g PEI at 5 % CO₂ to 2.7 mmol CO₂ / g PEI at 0.04 % CO₂. The 100 nm film only decreased 8 % from 2.5 mmol CO₂ / g PEI to 2.3 mmol CO₂ / g PEI. For thick films, in which diffusional resistance is the limiting factor for high adsorption, this result indicates that CO₂ concentration does not have much of an effect on capture capacity. As discussed in work by Sayari et al, in the instance of high amine loaded sorbents, CO₂ uptake is limited by amine accessibility rather than CO₂ availability [32]. The 100 nm film remains limited by accessible amines at both 5 % CO₂ and 0.04 % CO₂ as shown by the small difference in capture at the two conditions. The number of accessible amine sites remains lower than available CO₂ at both concentrations. The 100 nm film has less accessible amine sites relative to film thickness when compared to the 10 nm film. The 10 nm film has a large difference in capture at both CO₂ concentrations, indicating a transition from a regime limited by amine accessibility when challenged with 5 % CO₂ to a regime limited by CO₂ availability when challenged with 0.04 % CO₂. The decrease in capture shows that at 0.04 % CO₂, the available CO₂ value has reduced below the value of available amine sites. The 25 nm and 50 nm films exhibit similar performance, with capture decreasing from 5 % CO₂ to 0.04 % CO₂, and a final 0.04 % CO₂ capture value nearly identical with the 10 nm film. Figure 5 shows the final capture values from Figure 4B and 4C plotted on a log scale, with additional measurements of a 500 nm film included. The trend of this curve highlights the two regions that control CO₂ capture. Reducing the thickness below 100 nm reveals a transition from a reaction dominated by amine accessibility to one dominated by CO₂ availability.

Figure 5.

CO₂ capture after 1 h of exposure to 5 % and 0.04 % CO₂ at 25 °C as a function of film thickness. The error bars represent one standard deviation of the data (n = 2) which is taken as the experimental uncertainty of the measurement. Some error bars are smaller than the symbols.

Controlling the amine layer thickness for optimal capture performance is critical for the design on future DAC sorbent materials. A balance must be made between targeting total CO₂ capture (which increases with film thickness) or amine efficiency (which decreases with film thickness). Figure 5 shows that a film thickness of 50 nm is ideal for DAC conditions because it achieves the same amine efficiency as thinner films while achieving a higher total capture amount due to the increased amine content. Thicker films, which fall under the amine accessibility limited regime, have higher total capture amounts but begin to suffer with a less efficient capture process.

3.3. Effect of temperature on adsorption

The exothermic nature of the reaction between amines and CO₂ suggests that increasing temperature will favor the reverse reaction, reducing capture capacity. Concurrently, the increase in temperature can increase polymer mobility and CO₂ solubility, which determine the ability of CO₂ to diffuse to available amine sites. Therefore, a tradeoff exists in which decreased diffusional resistance and decreased reaction kinetics are balanced to provide either a net positive or net negative impact on capture capacity as a function of temperature [32,34]. For low amine loaded sorbents, increasing temperature can result in decreased capacity because the loss in reaction kinetics is not overcome by an increase in accessible amine sites brought on by the increased temperature. The opposite is true when amine loading is high, which often has an increase in capacity because the increase in accessible amines outweighs the decreased reaction kinetics. The effect that temperature has on capture capacity as a function of film thickness was evaluated by measuring capture at 35 °C, 55 °C, and 80 °C. Understanding how this effects capture is important for evaluating the performance of these materials in real-world conditions, as range of tropospheric conditions will most likely occur in direct air capture installations throughout the world.

Figure 6 shows the capture profiles for a 100 nm film using 5 % CO₂ and 0.04 % CO₂. For 5 % CO₂ experiments, there is an increase in capture capacity as the temperature increases. The capture capacity increased from 2.5 mmol CO₂ / g PEI at 25 °C to 4.7 mmol CO₂ / g PEI at 55 °C after 1 h of CO₂ exposure. This increase is attributed to decreased diffusional resistance brought on by a more mobile polymer at elevated temperatures. QCM-D measurements, shown in Figure S4, confirmed that the dissipation of the polymer films increased as temperature increased, indicating that the film is less rigid at higher temperatures.

Figure 6.

CO₂ capture as a function of temperature and thickness. QCM capture data for 1 h CO₂ exposure at 25 °C, 35 °C, 55 °C, and 80 °C for a 100 nm, 25 kDa PEI using A) 5 % CO₂ and B) 0.04 % CO₂. The error bars represent one standard deviation of the data (n = 2) which is taken as the experimental uncertainty of the measurement. Some error bars are smaller than the symbols.

The maximum CO₂ capture after 1 h of exposure was obtained at 55 °C, but due to the capture profile, the maximum CO₂ capture for the first 40 min of exposure was obtained at 80 °C. There is a distinguishable change in the capture profile between 80 °C and below, in which a gradual increase in capture is seen for lower temperatures and a step-like profile seen at 80 °C. This indicates a transition in the capture process occurs between these temperatures. At low temperatures, the film is diffusion limited, so that over time, capture increases as CO₂ diffuses into the film and finds available amine sites. Since the temperature is low, the reaction kinetics are still favorable. At 80 °C, it appears that the film is no longer diffusion limited, but rather reaction limited. The step-like profile indicates that CO₂ can immediately diffuse into the film and find all available amine sites, but at this temperature the reaction is less favorable. The reaction is now the limiting factor, and the capture amount does not change with time.

A similar trend is observed when a 0.04 % CO₂ feed stream is used. Here, a near identical increase is seen when increasing temperature from 25 °C to 35 °C with 0.04 % CO₂ to that seen using 5 % CO₂. At 35 °C, the benefit of decreased diffusion resistance compensates for a decrease in reaction and the 100 nm PEI film remains limited by amine accessibility. At 55 °C though, a similar step-like profile is observed to that seen when using 5 % CO₂ at 80 °C. This is thought to be due to a decrease in the available CO₂ capable of completing the carbamate reaction when the concentration is reduced from 5 % CO₂ to 0.04 % CO₂. There is no difference in available amines within the film at 55 °C for both CO₂ concentrations; the only reason for the observed change in capture profile is due to changes in CO₂ availability. The step-like capture profile seen using 0.04 % CO₂ suggests that the balancing of forward and reverse reaction rates occurs at a lower value of accessible amines when the CO₂ concentration is reduced. Further supporting this hypothesis, the 80 °C data does not show any capture of CO₂, with an actual decrease in mass obtained during this exposure test. This may be an artifact of the QCM data collection due to a change in pressure on the crystal which resulted in an increase in frequency. It is confirmed that no mass is lost, as it occurs during CO₂ exposure and not N₂ exposure. The IR spectrum further confirms that no carbamate is formed at 80 °C using 0.04 % CO₂. The IR spectra for capture at these temperatures and at both CO₂ concentrations are shown in Figure S5. At 80 °C, CO₂ can diffuse into the film and react with a maximum number of available amine sites, but at this temperature the reverse reaction is so favorable that no carbamate is formed over the 60 min.

Additional experiments were performed on films of 10 nm, 25 nm, and 50 nm. Capture profiles for these films are shown in Figure S6. The final capture amount after 60 min of CO₂ exposure for all films at each temperature are shown in Figure 7.

Figure 7.

CO₂ capture after 1 h exposure for 100 nm, 50 nm, 25 nm, and 10 nm films as a function of temperature using 5 % CO₂ from A) QCM and B) PM-IRRAS. Capture using 0.04 % CO₂ from C) QCM and D) PM-IRRAS is also shown. PM-IRRAS absorbance is measured for the specific peak at 1305 cm⁻¹ and normalized by film thickness. The error bars represent one standard deviation of the data (n = 2) which is taken as the experimental uncertainty of the measurement. Some error bars are smaller than the symbols.

The extent of CO₂ capture is highly dependent on temperature, film thickness, and CO₂ concentration. Figure 7A shows the final capture capacity after 1 h of exposure to 5 % CO₂. Unique capture profiles were observed depending on the sample thickness. The 10 nm film achieved the highest capture capacity at 25 °C and did not gain in capacity at elevated temperatures, with a maximum capacity of 5.1 mmol CO₂ / g PEI achieved at 25 °C and a minimum capacity of 2.2 mmol CO₂ / g PEI at 80 °C. Conversely, as previously shown in Figure 6A, the 100 nm increased in capacity with increasing temperature from 25 °C to 55 °C. The 25 nm and 50 nm film exhibited similar profiles to the 100 nm film, increasing in capacity from 3.7 mmol CO₂ / g PEI and 3.1 mmol CO₂ / g PEI at 25 °C, to 5.2 mmol CO₂ / g PEI and 5.3 mmol CO₂ / g PEI at 55 °C, respectively. A decrease was observed at 80 °C, with both films achieving capacities of 3.9 mmol CO₂ / g PEI.

Consistent with our previous discussion, thinner films have less diffusional resistance than thicker films at lower temperatures, which results in an increase in normalized CO₂ capture. Temperature plays a role in improving amine availability by increasing polymer mobility. The balance between higher amine availability and slower reaction kinetics determines if an elevated temperature is beneficial for capture. For the 10 nm film, elevating temperature is not beneficial, indicating that at this thickness the number of accessible amines does not increase. Rather, reduced reaction kinetics is what limits capture at this thickness. Thicker films, in comparison, can more than double in capacity with increasing temperature, due to the increase in accessible amines which overcome the slower reaction kinetics.

The extent of amine efficiency was calculated by converting the mass of PEI into mmol N. This analysis is detailed in the Supporting Information, and the values are plotted on the right-hand axis of Figure 7A. The maximum theoretical amine efficiency is equal to 1 if every amine within the film reacts with one CO₂ molecule. The formation of carbamate in the absence of water requires two amines. This limits the maximum amine efficiency from a value of 1 to 0.5 as now two amines are needed to react with one CO₂ molecule. Additionally, tertiary amines have been shown to minimally react to form carbamate and thus can be removed from the pool of available amines [35]. The composition of each amine type within the tested PEI was measured experimentally using quantitative ¹³C NMR. [26] A distribution of 32 % primary, 38 % secondary, and 30 % tertiary amines was calculated, further reducing the maximum amine efficiency to 0.35. The highest amine efficiency values obtained at 25 °C and 35 °C was 0.22 for the 10 nm film, at 55 °C was 0.23 for the 25 nm and 50 nm films, and at 80 °C was 0.19 for the 100 nm film.

The theoretical maximum amine efficiency was unable to be obtained due to limited amine accessibility, but the trend of higher amine efficiency with decreasing thickness suggests that films thinner than 10 nm may increase amine efficiency closer to the maximum. However, films thinner than 10 nm were not investigated because the mass of PEI on the crystal is very small at these length scales, and when testing at different temperatures, small fluctuations were detected in the measured mass value. These variabilities resulted in very large discrepancies in the observed capture value and could not be confidently reported. This is most likely the only pathway to encroach maximum efficiency, as the gains in capacity for thicker films at higher temperature likely include some loss in efficiency due to the decreased reaction kinetics.

The capture trend measured via PM-IRRAS is shown in Figure 7B. Absorbance of the carbamate peak at 1305 cm⁻¹ was measured before and after 60 minutes of CO₂ exposure. The total absorbance for each film was then normalized by film thickness. Very similar trends were seen for each film when comparing to the QCM mass uptake results. Larger error bars were seen in the 10 nm film case, likely due to the decreased overall detection and higher noise in the PM-IRRAS spectra compared to the 100 nm film.

When exposed to 0.04 % CO₂, capacity increased when the temperature increased from 25 °C to 35 °C, before decreasing to 0 mmol CO₂ / g PEI at 80 °C. This is shown in Figure 7C and 7D for the QCM and PM-IRRAS results, respectively. A similarly shaped profile was obtained for all film thicknesses across the measured temperature range. All films except for the 100 nm film decreased in capture capacity when exposed to 0.04 % CO₂ compared to 5 % CO₂ at 25 °C and 35 °C. As discussed in Figure 5, this decrease is attributed to a system which is limited by CO₂ availability. The 100 nm film capacity remains the same between 5 % CO₂ capture and 0.04 % CO₂ at both 25 °C and 35 °C, suggesting that limited accessible amines controls capture at these temperatures. Capacity decreased at 55 °C for all films and no capture was seen at 80 °C. Unfavorable reaction kinetics brought on by the increased temperature combine with the lower CO₂ concentrations to further reduce capture capacity.

3.4. Adsorption Kinetics

To better understand the adsorption characteristics as a function of film thickness, the adsorption profiles were fitted using a pseudo-first order (Equation 2) and the Avrami kinetic model (Equation 3). Fittings for data from one 100 nm film experiment are shown in Figure 8. These two models have been evaluated for CO₂ adsorption to try to account for the complexities of the adsorption process [27,28]. Additional dual kinetic models have been evaluated for PEI impregnated materials [36], due to the simplicity of the Avrami model, these other methods were not evaluated here. The complexities to the adsorption process include multiple reaction pathways [27], as well as competing physisorption and chemisorption processes [37]. The pseudo-first order fitting did not match well with experimental results at low temperatures. The model underestimates the capture within the first two minutes of exposure. The capture was then overestimated before levelling off at an equilibrium value below the final capture amount. This trend was observed at temperatures of 25 °C, 35 °C, and 55 °C. The pseudo-first order fitting did match the capture data at 80 °C, further suggesting that the capture process changes from diffusion limited to reaction limited.

Figure 8.

Kinetic model fitting of capture of a 100 nm film at each temperature using a A) pseudo-first order model and a B) Avrami kinetic model fitting. Model fittings are shown as the black dashed lines.

The Avrami model was developed to simulate phase transition and crystal growth and describes a kinetic system with a time-dependent rate coefficient [38]. The Avrami rate equation has been shown to offer good agreement with experimental data for CO₂ capture [39–41]. In this instance, the value of $k_A$ represents the overall sorption, reaction, and desorption steps of capture [27]. This model provided the best fitting during the entire adsorption process at all temperatures. The reaction rate constants, $k_f$ and $k_A$, the Avrami exponent, $n_A$, and the error for each fitting method are shown in Table 1.

Table 1.

Values of the kinetic model parameters for CO₂ adsorption of a 100 nm PEI film.

		25 °C	35 °C	55 °C	80 °C
Pseudo-first	kf (min−1)	0.120	0.208	0.512	6.060
	qe (mmol g−1)	2.351	2.903	4.400	4.553
	R2	0.893	0.859	0.668	0.984
Avrami	kA (min−1)	0.058	0.158	0.394	6.003
	qe (mmol g−1)	3.026	3.289	5.005	4.552
	n A	0.460	0.459	0.318	1.101
	R2	0.996	0.996	0.990	0.985

The value of $k_f$ and $k_A$ increased for all films as temperature increased. As temperature increases, the increased mobility within the PEI film reduces diffusional resistance of CO₂ to the amine sites. The CO₂ transfer rate is increased with higher $k$, which corresponds to the steepness of the capture profiles at higher temperatures. There are differences in the equilibrium capacity from each model, with the pseudo-first order underestimating the equilibrium capacity. Additionally, the $k$ values differ from each method, but are the same order of magnitude even though the error is much higher for the pseudo-first order fitting. This allows for direct comparison of $k_f$ values for each film thickness and CO₂ concentration. A comparison between $k_A$ cannot be done due to the different $n_A$ values for each $k_A$ [27].

The Avrami constant, $n_A$, is traditionally defined as the dimensionality of growth of adsorption [41], in which the $n_A$ values of 2, 3, and 4 account for one-dimensional, two-dimensional, and three-dimensional growth respectively. An $n_A$ value of 1 reduces the model to a pseudo-first order reaction and indicates that the probability of adsorption is equal at all sites [42]. Fractional values of the Avrami constant were seen at low temperatures, with $n_A$ values of 0.460 at 25 °C, 0.459 at 35 °C, and 0.318 at 55 °C. The fractional order of the Avrami constant suggests a complexity to the reaction process. Avrami constant values less than the integer value indicates that it follows the integer growth rate but that the adsorption rate decreases over time [43].

For the reaction to continue at the initial rate, the ability of CO₂ molecules to reach active sites must be constant. During the capture process, the dissipation of the PEI layer decreases due to a cross-linking affect occurring within the film. This is shown in Figure S7 using a 500 nm PEI film. As mentioned earlier, two amines are required (under dry conditions) to react to form one carbamate and the resultant stiffening of the polymer may play a role in the diffusion of CO₂ to further active sites. Figure S7 also shows a difference in rate occurs when comparing decreasing dissipation and frequency values, where the frequency change occurs more rapidly than the dissipation change.

An Avrami constant less than 1 at low temperatures suggests that the inhibition of CO₂ to amine sites plays an important role in the overall CO₂ capture. The $n_A$ value decreases as temperature increases. At 55 °C, the total capture increases because the PEI is more mobile, such that more CO₂ can penetrate and react with amine sites. A decreasing $n_A$ value with increasing temperature has been shown to indicate an adsorption process which is less dominated by diffusional processes [44]. A $n_A$ value of 1.101 was obtained at 80 °C. This indicates that the reaction process undergoes a change in adsorption mechanism. A value close to 1 matches the good fitting determined using the pseudo-first order model at this condition. At this temperature, the theory that the reaction transitions from a diffusion limited process to a kinetic limited process is affirmed because of this $n_A$ value, as it indicates equal chance to adsorb at all sites and this can only be achieved when diffusional limitations are removed.

The fittings for all other tested films using a 5 % CO₂ feed are shown in Figure S8 and using a 0.04 % CO₂ feed are shown in Figure S9. The model parameters for these fittings are shown in Table S2. Similar trends between pseudo-first order and Avrami fittings were seen at all testing conditions. A few trends were seen and are highlighted. Similar to the results shown for the 100 nm film, $k_f$ increased with temperature for all film thickness and both CO₂ concentrations. $k_f$ also increased as film thickness decreased at all temperatures and both CO₂ concentrations. This agrees with the analysis that as film thickness decreases, diffusional resistance also decreases. Increased ability of CO₂ to reach amine sites results in faster reaction rates, and $k_f$ values were predominately higher for capture using 0.04 % CO₂ than 5 % CO₂ for all film thicknesses, especially at 55 °C. This condition resulted in the step-like capture profile that was seen at 80 °C with the 5 % CO₂ feed.

4. Conclusions

The CO₂ capture capacity and efficiency of PEI thin films was evaluated as a function of film thickness, CO₂ concentration, and temperature. Tandem QCM and PM-IRRAS provided CO₂ capture capacity and IR spectra analysis which confirmed carbamate formation upon CO₂ exposure. Film thickness plays an important role in determining amine efficiency. Thicker PEI films (100 nm) achieved higher total CO₂ capture but lower amine efficiency than thinner films (10 nm). Thicker films have less accessible amines than thinner films due to added diffusional resistance. Two distinct capture regimes were measured by varying CO₂ concentration from 5 % CO₂ to 0.04 % (400 ppm) CO₂. Capture using films <50 nm is dependent on CO₂ concentration and is limited by CO₂ availability. At DAC conditions, these films had identical normalized capture at 25 °C. These results are beneficial for the design of future sorbent materials. Achieving a comparably uniform film thickness within an impregnated sorbent material will be challenging. The design principles outlined in this work extend beyond current supports and further the understanding of how controlling PEI impregnation can be utilized to enhance sorbent systems. A 50 nm film thickness is optimal if maximizing both total capture and amine efficiency is desired. As film thickness increases to 100 nm, capture is limited by amine accessibility, decreasing amine efficiency even though total capture increases. Temperature alters capture profiles as changes to both diffusion and reaction kinetics impact CO₂ capture capacity. At high temperatures (80 °C) capture matches first-order reaction kinetics when using a high CO₂ concentration feed (5 % CO₂). No capture was measured using DAC conditions at elevated temperatures as the exothermic nature of the carbamate reaction and the lower concentration of CO₂ resulted in unfavorable reaction conditions. Maximum capture was achieved at 35 °C for DAC CO₂ concentrations, suggesting that DAC installations in warm climates are suitable when using impregnated PEI sorbents. These results stress the importance of analyzing CO₂ capture at relevant testing conditions (5–10 % CO₂ for simulated flue gas and 0.04 % CO₂ for DAC) as concentration can greatly impact the evaluation of sorbent materials.