Preparation of urea-containing polysilsesquioxane membranes for CO₂ separation designed by model-based research

Abstract

Membrane separation has been extensively studied as a cost-effective CO₂ separation method, and polysilsesquioxane (PSQ)-based membranes are expected to be robust membranes with high thermal and mechanical stability and processability. In this study, a prediction model for CO₂ permeance and CO₂/N₂ permselectivity as target variables was generated by applying machine learning to experimental data collected in our previous studies as explanatory variables. On the basis of this model, two new urea-containing PSQ-based membranes were prepared, and their CO₂ separation performance was evaluated. Among them, a membrane synthesized through the 1:1 copolymerization of (3,6-dioxaoctane-1,8-diyl)bis-N-[N’-(triethoxysilylpropyl)urea] and bis(triethoxysilyl)ethane demonstrated high performance, achieving a CO₂ permeance of 1.3 × 10^–6mol m^–2s^–1Pa^–1 (4.0 × 10³ GPU) and a CO₂/N₂ permselectivity of 13. A membrane was also prepared using (triethylamine-2,2’,2”-triyl)tris-N-[N’-(triethoxysillylpropyl)urea] as a monomer, which resulted in inferior CO₂ separation performance. However, increasing the calcination temperature significantly increased the CO₂ permeance, whereas the CO₂/N₂ permselectivity slightly decreased, likely because of the thermal degradation of the urea units, resulting in the formation of void spaces.

Introduction

Reducing CO₂ emissions is crucial on a global scale, and membrane separation has been extensively studied as a cost-effective method for CO₂ separation. There are various categories of CO₂ separation membranes, including organic and inorganic membranes [1,2,3,4,5], mixed-matrix membranes (MMMs), and metal–organic framework (MOF) membranes [6, 7]. Several mechanisms have been recognized for CO₂ separation [8,9,10], such as molecular sieving effects, which allow smaller gas molecules to permeate the membrane more rapidly through a porous structure than larger molecules do. Additionally, the diffusion of gas molecules to the pore surface effectively enhances transport in porous membranes, particularly when the pore surface has an affinity for CO₂ molecules. For nonporous membranes, the dissolution permeation of CO₂ molecules through the membrane facilitates transport, where the CO₂ affinity influences membrane performance through its effect on the CO₂ dissolution capacity. Generally, the diffusivity and solubility of CO₂ molecules are enhanced by membrane CO₂ affinity. Therefore, diffusion- and solubility-based CO₂ transport accelerates with decreasing operation temperature, although reduced molecular mobility suppresses transport to some extent. However, an excessively high affinity may result in the tight capture of CO₂ molecules, which in turn inhibits their transport.

Polysilsesquioxanes (PSQs) have garnered significant attention as durable materials owing to their excellent thermal and mechanical stabilities and ease of processing. This is attributed to their inorganic siloxane network structure combined with organic groups attached to silicon atoms [11,12,13,14]. These materials are readily accessible via the hydrolysis condensation polymerization of trifunctional organosilicon monomers, such as trialkoxysilanes. PSQ-based CO₂ separation membranes have also been studied, and it has been demonstrated that their performance is significantly influenced by PSQ organic groups [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]. For example, a membrane prepared from a monomer with a primary amine unit (APTES in Fig. 1) exhibited CO₂ separation properties [17,18,19,20,21,22] with P_CO2 (CO₂ permeance) = 2.6 × 10^–8mol m^–2s^–1Pa^–1 and CO₂/N₂ (CO₂/N₂ permselectivity) = 22, whereas the use of a tertiary amine monomer (DMAPTES) improved the CO₂ permeance to a value of 1.72  × 10^–7mol m^–2s^–1Pa^–1, with CO₂/N₂ permselectivity remaining at a similar level (CO₂/N₂ = 21) [17, 18]. Employing secondary amine MAPTES as the monomer resulted in a decrease in both CO₂ permeance and CO₂/N₂ permselectivity (P_CO2 = 1.7 × 10^–8mol m^–2s^–1Pa^–1 and CO₂/N₂ = 11). Because DFT calculations indicated that the amine initially interacts with CO₂ as a base to form N--C(O₂) coordination rather than an acid with hydrogen bonding to CO₂ in the manner of NH--O(CO), tertiary amines would possess a higher CO₂ affinity than primary amines would. However, primary and secondary amines can form ionic complexes with CO₂ (RNHCO₂^- RNH₃⁺ and R₂NCO₂^- R₂NH₂⁺), which may hinder CO₂ transport [31]. Steric hindrance arising from the methyl group may also affect the performance; however, the reason for the lower performance of the MAPTES membrane than that of the APTES membrane is still unclear. A monomer (MOCMTES) containing an ester unit with a low affinity for CO₂ was also examined, and its copolymerization with TEOS provided a membrane with high CO₂ permeance (P_CO2 = 2.074 × 10^–6mol m^–2s^–1 Pa^–1) and a moderate level of permselectivity (CO₂/N₂ = 7.5) [23]. Aromatic rings were also investigated as rigid CO₂-philic units. Their rigidity was expected to enhance intramolecular void formation, thus facilitating gas permeation. The membranes obtained by the copolymerization of phenyl-, pyridyl-, and naphthyl-containing triethoxysilane monomers (TESEB, TESEPy, and TESENp) with BTESE at a ratio of 1:1 exhibited good performance depending on the CO₂ affinity of the aromatic units, and the TESEB–BTESE and TESEPy–BTESE membranes exhibited good performance, with P_CO2 = 1.36  × 10^–7mol m^–2s^–1Pa^–1 and 3.34 × 10^–7mol m^–2s^–1Pa^–1, respectively, and CO₂/N₂ = 16.5 and 27.9, respectively [24]. However, the performance of the TESENp–BTESE membrane was inferior (P_CO2 = 2.05 × 10^–8mol m^–2s^–1Pa^–1 and CO₂/N₂ = 14.4), presumably because the formation of a π-stacked naphthalene dimeric form reduced the CO₂ affinity and densified the membrane. Pinacol borate was also introduced as a nonaromatic rigid unit with moderate CO₂ affinity to yield a membrane characterized by high CO₂ permeance (P_CO2 = 2.10 × 10^–6mol m^–2s^–1Pa^–1) and relatively high permselectivity (CO₂/N₂ = 11.1) by 1:2 copolymerization with BTESE [25].

Fig. 1

Examples of precursors of PSQ-based CO₂ separation membranes

Bridged trialkoxysilanes have also been investigated as monomers, which may enhance the network structure of membranes. Among them, TTESMI and TTESPI, which contain a rigid CO₂-philic isocyanurate core, yielded good membranes with P_CO2 = 2.0 × 10^–7 and 3.2 × 10^–7mol m^–2s^–1Pa^–1 and CO₂/N₂ = 15 and 18, respectively [26]. When TTESPI and BTESE were copolymerized at a 1:1 ratio, the resulting membrane exhibited improved CO₂ permeance, although its permselectivity was slightly reduced. These values are slightly higher than those of less rigid BTESPU membranes with urea units [26]. In addition to the appropriately high CO₂ affinity of organic units, their rigidity, which enhances void formation, is important for enhancing gas permeation. Additionally, the copolymerization of BTESB and BTESBPh with BTESA resulted in high-performance membranes for CO₂ separation. Interestingly, the copolymerization of BTESA with BTESB resulted in an increase in CO₂/N₂ permselectivity compared with that of the BTESA homopolymer membrane (P_CO2 = 1.84 × 10^–6mol m^–2s^–1Pa^–1, CO₂/N₂ = 25), whereas the incorporation of BTESBPh increased the CO₂ permeance (P_CO2 = 3.25 × 10^–6mol m^–2s^–1Pa^–1, CO₂/N₂ = 12) [28]. This is likely due to the higher CO₂ affinity of the benzene ring than that of the acetylene bond and the rigid biphenylene linkage, which expands the silica network to enhance gas permeation.

These results indicate that the CO₂ affinity of the membranes plays a significant role in their performance. However, other characteristics of organic units, such as rigidity, steric bulkiness, and the number of reactive silicon sites, operate synergistically together with CO₂ affinity to affect membrane separation performance, and predicting membrane performance by simple molecular design seems difficult. In addition, membrane preparation processes seem to affect performance. Considering the complexity of the performance prediction of PSQ membranes, we examined machine learning using the experimental data collected in our previous studies to create a prediction model for PSQ-based CO₂ separation membranes. The resulting model was used to predict the performance of new urea-containing membranes. The prepared membranes exhibited good to high performance. The influence of the calcination temperature on the preparation of PSQ membranes was also studied, and a new method for enhancing CO₂ permeability by controlling the thermal decomposition of urea units was proposed.

Materials and methods

Machine learning for the prediction of membrane performance

To predict the performance of PSQ-based membranes with different organic groups, Gaussian process regression was employed with the experimental data collected in our previous studies. The prepared dataset consisted of 132 entries of PSQ-based membranes prepared by homo- and copolymerization of alkoxysilane precursors, as presented in Fig. S1. The CO₂ permeance and CO₂/N₂ permselectivity were defined as the target variables, and the raw data used to obtain the explanatory variables are listed in Table S1: the amount of HCl catalyst (hereafter denoted as HCl), the temperature of the measurement (temp), the molecular weight of the monomer (MW), the CO₂ coordination energy for each monomer (H) evaluated at the B3LYP/6-31 G level of calculation on Gaussian 16 revision C.01 (Gaussian, Inc., USA), the number of acidic and basic moieties (an and bn, respectively), the degree of unsaturation in the organic groups (un), and the average distance between Si atoms (Si–Si) evaluated by Chem3D 23.1.2 (PerkinElmer Informatics Inc., USA). The corresponding variables for copolymers were evaluated as weighted averages for composing monomers on the basis of their weight ratio (Table S2). In addition, three binary descriptors, SiNoOne, SiNoTwo, and SiNoThree, were introduced, which have a value of one when the number of Si atoms in the monomer was one/two/three, respectively.

Materials and characterization

BTESE was obtained from Gelest, Inc., and was used as received. Monomers, (3,6-dioxaoctane-1,8-diyl)bis-N-[N’-(triethoxysillylpropyl)urea] (BTESEgU) and (triethylamine-2,2’,2”-triyl)tris-N-[N’-(tri-ethoxysillylpropyl)urea] (TTESPUEA), were prepared as previously reported [29]. Ethanol used for the sol–gel reactions was distilled from magnesium ethoxide under an argon atmosphere and stored on activated molecular sieves in the dark until use. The sol particle sizes were measured by dynamic light scattering (DLS) using a Malvern Zetasizer Nano ZS analyzer at room temperature. Fourier transform infrared (FTIR) spectra were obtained using a Shimadzu IR Affinity-1 spectrometer. Thermogravimetric analysis (TGA) was performed using a Shimadzu DTG-60 thermal analyzer with a heating rate of 10 °C/min under a gentle nitrogen flow (100 mL/min).

Sol preparation

The sols were prepared according to a previously described method [26]. Water was added to stirred ethanol solutions of BTESEgU–BTESE and TTESPUEA–BTESE in a 1:1 weight ratio, and the mixtures were stirred further until the average sol particle sizes reached approximately 2 nm (Table 1). The resulting sols were diluted with ethanol to 0.25 wt% on the basis of the monomers used for the reactions. The sols were stored at 4 °C in tightly sealed screw vials until they were used. Drying the sols by heating at 60 °C in air provided the powders for TGA. For FTIR analysis, the sols were applied to a KBr plate and dried at 50 °C in air. The plates were subsequently heated at various temperatures for 10 min in nitrogen, and the spectra were collected in transmission mode.

Table 1 Conditions for sol formation

Membrane preparation

As described in a previous study [30], the support membrane was prepared using a commercially available porous tubular α-Al₂O₃ substrate (10 mm diameter, 1 μm average pore size). Initially, an aqueous colloidal α-Al₂O₃ sol was coated onto the tubular substrate, and the coated substrate was calcined. Subsequently, an intermediate layer with an approximate pore size of 1.5 nm was prepared by coating the substrate with silica-zirconia sols with different particle sizes, followed by calcination. Finally, a BTESEgU–BTESE or TTESPUEA–BTESE sol was coated onto the intermediate layer surface. The coated substrates were then calcined at 300 °C or 250 °C for 30 min in nitrogen for the preparation of a PSQ top layer (Fig. 2). The procedures of PSQ sol coating and subsequent calcination were conducted twice. Pure gases (He, H₂, CO₂, N₂, and SF₆) were fed into the membrane module at approximately 200 kPa. The gas permeance (P) was calculated using Eq. (1). The gas permeances that stabilized several hours after the gas permeation experiments were initiated are summarized in Table 2.

$$P=V/(22.4\times A\times \varDelta P)$$

(1)

ΔP: difference in pressure between the upstream and downstream sides of the membrane

Fig. 2

Preparation of the CO₂ separation membrane

Table 2 Predicted performance of the candidates by the Gaussian process model

V: flow rate of the permeated gas

A: effective membrane surface area

Results and discussion

Machine learning

There have been several reports on the construction of prediction models through machine learning for CO₂ separation in organic polymer membranes [32,33,34,35]. However, no studies have been conducted on PSQ-based membranes to date. In this study, a new model was created for PSQ-based membranes. The fivefold cross-validated values for CO₂ permeance and CO₂/N₂ permselectivity in the prepared dataset are plotted against the experimental values in Fig. 3. The corresponding R²_CV (cross‑validated R‑squared) values indicating the generalization of model performance are 0.763 for CO₂ permeance and 0.507 for CO₂/N₂ permselectivity. CO₂ permeance was better modeled than CO₂/N₂ permselectivity was, while both models tended to underestimate the experimental values in high-performance regions.

Fig. 3

Cross-validated values for (a) CO₂ permeance [10^–7mol m^–2s^–1Pa^–1] and b CO₂/N₂ permselectivity

With this trained Gaussian process model, the performance of the five monomer candidates of the precursors (Fig. 2 and Fig. 4) was predicted, as shown in Table 2. These candidates were designed on the basis of our previous study that indicated the potential of urea-based PSQ membranes for CO₂ separation [26, 27]. The high rigidity and moderate CO₂ affinity of urea were anticipated to enhance CO₂ permeation. In addition, the structural rigidity and CO₂ affinity of amine [17,18,19,20,21,22], arene [24], and ethylene glycol units [36] were considered in the design of monomer candidates. Compared with those of the training dataset, the CO₂ permeance and CO₂/N₂ permselectivity of the candidates were found to have moderate performance with a trade-off relationship. Given the worse R²_CV score for CO₂/N₂ permselectivity, TTESPUEA:BTESE and BTESEgU:BTESE were concluded to be the best choices among the five candidates.

Fig. 4

Chemical structures of the monomer candidates: HETESPU, BTESAU, and BTESUmX

When the experimental data obtained for the BTESEgU–BTESE and TTESPUEA–BTESE membranes (vide infra) were added, a revised model was obtained with an improved R²_CV score for CO₂/N₂ permselectivity (0.596), although the score for CO₂ permeance was not clearly affected (0.762). Shapley additive explanations (SHAP) were examined for the revised model, and the results are shown in Fig. 5. Interestingly, the CO₂ coordination energy (denoted as “H” in Fig. 5) strongly contributed to both the CO₂ permeance and CO₂/N₂ permeselectivity, which were positively correlated with the former and negatively correlated with CO₂/N₂ with the latter, indicating that the CO₂ coordination energy affected the performance as a trade-off factor for these parameters. Among the explanatory variables other than the CO₂ coordination energy, the degree of unsaturation of the organic unit (denoted as “un”) and the amount of HCl catalyst for PSQ preparation (denoted as “HCl”) strongly contributed to CO₂ permeance, whereas the measurement temperature, Si–Si distance (denoted as “Si–Si”), and degree of unsaturation influenced CO₂/N₂ permselectivity. The increased degree of unsaturation reflected the enhanced rigidity of the organic unit, which accelerated CO₂ permeation. However, the introduction of π-electron systems increased the CO₂ affinity to improve the CO₂/N₂ permselectivity and to suppress the permeation. HCl catalysts have been used for the preparation of amine-containing PSQ to enhance polymerization. However, HCl remains in the membrane as an ammonium salt, which improves the CO₂ permeance with reduced CO₂/N₂ permselectivity [21]. The origin of the HCl effects remains unclear but is in accordance with the SHAP results. The most significant feature for CO₂/N₂ selectivity was the operation temperature, whose influence was negative at higher temperatures, suggesting that higher molecular mobility could obscure molecular differences. Similar temperature effects have been reported for polyethylene glycol-based membranes [34].

Fig. 5

Results of SHAP analysis for (a) CO₂ permeance and b CO₂/N₂ permselectivity. The top 3 significant features for CO₂ permeance based on the mean absolute SHAP values are the degree of unsaturation in the organic groups (un), the amount of HCl catalyst (HCl), and the CO₂ coordination energy (H), whereas those for CO₂/N₂ permselectivity are the operation temperature (temp), CO₂ coordination energy, and the average distance between Si atoms (Si–Si). The other features are described in the Materials and methods section

Membrane preparation

The urea-containing monomers were copolymerized with BTESE in a 1:1 weight ratio with excess water in ethanol. The reaction mixtures were stirred until the resulting sol particles increased in size slightly beyond the pore size (1.5 nm) of the intermediate layer of the support membrane so that the sol did not penetrate the intermediate layer. The reaction of BTESEgU proceeded less rapidly than that of TTESPUEA did, and its reaction should be carried out at a higher temperature to complete the reaction within a reasonable time. The lower reactivity of BTESEgU is presumably due to the smaller number of reactive triethoxysilyl units and the lack of an amine unit that would catalyze hydrolysis/condensation. The obtained sols were applied to the intermediate layer of the support membrane, and the coated sols were dried and subjected to calcination in nitrogen to form a gel separation layer. To determine the calcination temperature, TGA was performed on the BTESEgU–BTESE and TTESPUEA–BTESE gels prepared by drying the sols (Fig. 6). FTIR spectra of the gels were also obtained after heating at various temperatures for 10 min in nitrogen (Fig. 7).

Fig. 6

TGA curves of BTESEgU–BTESE and TTESPUEA–BTESE gels in nitrogen

Fig. 7

IR spectra of (a) BTESEgU–BTESE and b TTESPUEA–BTESE gel films prepared on KBr plates after heating at different temperatures for 10 min in nitrogen

The TGA curves indicated that the BTESEgU–BTESE and TTESPUEA–BTESE gels underwent a two-step weight loss: the first occurred up to 250–300 °C, and the second occurred at higher temperatures extending up to 500–600 °C. Their FTIR spectra revealed that the intensities of the stretching peaks of O–H and Si–OH bonds at approximately 3350 cm^–1 and 950 cm^–1, respectively, weakened with increasing calcination temperature. An increase in the band at approximately 1000 cm^-1, ascribed to Si–O–Si stretching, was also observed, indicating that the dehydration condensation of silanols to form siloxanes occurred. For the TTESPUEA–BTESE gel, the Si–OH stretching band at approximately 950 cm^–1 remained even after heating at 250 °C, in contrast to the BTESEgU–BTESE gel, whose FTIR spectrum showed the disappearance of the Si–OH band after heating at the same temperature. This is likely due to the greater steric hindrance of TTESPUEA than BTESEgU, which suppresses silanol condensation. Two intense signals characteristic of urea C = O and N–H bonds were observed for each sample at approximately 1600 cm^–1 [37]. However, the urea signals weakened when the TTESPUEA–BTESE gel was heated to 300 °C, suggesting that thermal decomposition occurred at this temperature to some extent, whereas the spectrum of the BTESEgU–BTESE gel heated to 300 °C did not show significant changes in the urea signals. Notably, the Si–OH band at approximately 950 cm^-1 almost disappeared in the TTESPUEA–BTESE spectra after heating at 300 °C, including silanol condensation. On the basis of these results, the membranes were prepared by calcination at 300 °C and 250 °C in nitrogen for the preparation of the BTESEgU–BTESE and TTESPUEA–BTESE separation membranes, respectively. TTESPUEA–BTESE was also calcined at 300 °C to elucidate how the thermal degradation of urea units affects membrane performance.

Evaluation of CO₂ separation properties

Pure gas permeation experiments were conducted at 200 °C for the BTESEgU–BTESE (300 °C) and TTESPUEA–BTESE (250 and 300 °C) membranes, where the values in parentheses denote the respective calcination temperatures. The resulting gas permeances are plotted against the gas kinetic diameter in Fig. 8a. The normalized permeation data and theoretical Knudsen diffusion line are presented in Fig. 8b. Relative to the Knudsen line, the observed permeances were more significantly suppressed when the gas kinetic diameter increased from H₂ to SF₆. This trend clearly suggests that gas transport through the membranes is influenced by molecular size, which is indicative of molecular sieving effects. Notably, the CO₂ permeances of the BTESEgU–BTESE (300 °C) and TTESPUEA–BTESE (300 °C) membranes exceeded the values predicted by the Knudsen model, implying a preferential interaction between the CO₂ molecules and the membrane structures. The CO₂ permeance and CO₂/N₂ permselectivity determined at 50 °C are listed in Table 3. The literature data for membranes synthesized via the homopolymerization of BTESE [25] and the 1:1 copolymerization of BTESPU and BTESE are also presented [26].

Fig. 8

a Plots of pure gas permeances of urea-containing PSQ membranes measured at 200 °C versus gas kinetic diameter. b Normalized data and Knudsen prediction based on helium gas permeance

Table 3 Gas permeation properties of the urea-containing membranes

To further elucidate the gas transport mechanism, temperature-dependent gas permeation measurements were performed to determine the activation energies of CO₂ and N₂ permeation through the membranes (Fig. 9 and Table 3). Compared with N₂, all the present membranes demonstrated lower activation energies for the permeation of CO₂, which is consistent with an adsorption-controlled transport mechanism. Reduced operating temperatures increase CO₂ absorption by the membrane, thereby facilitating its permeation. Generally, lower activation energies are observed for inorganic membranes than for organic membranes because of the higher rigidity of inorganic structures, which are relatively unaffected by temperature. In contrast, the vibration of more flexible organic networks is readily enhanced at elevated temperatures compared with that of inorganic membranes to accelerate gas transport. The activation energy of N₂ permeation of the BTESEgU–BTESE (300 °C) membrane was nearly the same as that of the BTESPU–BTESE and BETSE membranes, indicating similar network rigidity. The higher activation energy of N₂ permeation for TTESPUEA–BTESE (250 °C) is likely due to the lower calcination temperature, leading to incomplete condensation, as indicated by the IR spectral analysis (vide supra). However, the value decreased for the TTESPUEA–BTESE (300 °C) membrane, indicating enhanced network formation by higher-temperature calcination. In terms of the CO₂ separation performance, the BTESEgU–BTESE (300 °C) membrane exhibited the best data, with the highest CO₂ permeance (P_CO2 = 1.3  × 10^–6mol m^–2s^–1Pa^–1) and moderately high CO₂/N₂ permselectivity (CO₂/N₂ = 13). This seems to be partly due to the enhanced siloxane network formation, as evidenced by the disappearance of the Si–OH bands in the IR spectrum after calcination at 300 °C (Fig. 7a). The presence of multiple CO₂-philic urea and ethylene glycol sites with appropriate CO₂ affinity could also explain the high performance of this membrane. Notably, the CO₂ permeance of the BTESEgU–BTESE (300 °C) membrane was much greater than that of the BTESPU–BTESE and BTESE membranes. In contrast, the TTESPUEA–BTESE (250 °C) membrane exhibited lower CO₂ permeance. As observed for the DMAPTES membrane, tertiary amine units have the potential to realize high CO₂ separation properties because of their appropriately high CO₂ affinity [17, 18]. However, the steric bulkiness of the tertiary amine unit in TTESPUEA overrides the effects of its CO₂ affinity, suppressing permeation (vide infra). Incomplete network formation is also a reason for the low CO₂ permeance. Interestingly, the permeation was markedly improved by calcination at 300 °C, and the P_CO2 value of the TTESPUEA–BTESE (300 °C) membrane was 27 times greater than that of TTESPUEA–BTESE (250 °C), although the permselectivity decreased from CO₂/N₂ = 11 to 8.1. It has been reported that N,N’-disubstituted urea undergoes thermal degradation to form primary amine and isocyanate units [38]. The isocyanate group reacts with moisture to provide another primary amine unit and CO₂ (Fig. 10). As the membrane contains hydrophilic urea units, it is not unexpected for the membrane to retain moisture even after calcination. Consequently, the membrane becomes looser, accelerating CO₂ permeation [39].

Fig. 9

Plots of gas permeances of (a) N₂ and b CO₂ versus operating temperatures for urea-containing membranes

Fig. 10

Thermal degradation of N,N’-disubstituted urea followed by hydrolysis

To compare the performance, the P_CO2 and CO₂/N₂ values of the presently and previously prepared PSQ-based membranes are plotted in Fig. 11. As shown in Fig. 11, the CO₂ separation performance of the BTESEgU–BTESE (300 °C) membrane was superior to that of most PSQ-based membranes reported thus far, approaching the highest level of performance achieved by the BPinTES–BTESE, BTESB–BTESA, and BTESBPh–BTESA membranes.

Fig. 11

Plots of P_CO2 versus CO₂/N₂ for PSQ-based membranes. Red plots indicate the data of the membranes prepared in this study

CO₂ affinity

To evaluate the CO₂ affinity of the BTESEgU- and TTESPUEA-based membranes, the coordination energies of CO₂ with the BTESEgU and TTESPUEA (BSEgU and TSPUEA) models were calculated at the B3LYP/6-31 G level. The optimized geometries of the complexes and their coordination energies are shown in Fig. 12, indicating that they possess appropriately high CO₂ affinity. For BSEgU, a geometry with NH--O intramolecular hydrogen bonding was found to be the most stable among those examined, and CO₂ coordinates either the urea or the ethylene glycol unit. The coordination to urea was calculated to be more favorable than that to ethylene glycol, and the heat of the former reaction was used as an explanatory variable for prediction by the model. However, in a real system, the presence of multiple coordination sites affects CO₂ permeation, as mentioned above. Further studies may be necessary to understand these effects in detail.

Fig. 12

Optimized geometries of CO₂ complexes of model compounds: a BSEgU coordinated at the urea site, b ethylene glycol unit site, and c TSPUEA, in which (triethoxysilyl)propyl groups of BTESEgU and TTESPUEA are replaced by methyl groups. The reaction heats for complex formation from the models and CO₂ molecules are also shown

For TSPUEA, two of the urea units were calculated to possess an intramolecular dimeric form by hydrogen bonding, making the coordination of CO₂ to this dimeric site difficult. Therefore, only the coordination to the unpaired urea site shown in Fig. 12c was considered, and the data were used as the explanatory variable. No stable CO₂ complexes coordinated to the tertiary amine unit of TSPUEA were obtained, likely because of steric repulsion between CO₂ and the substituents on the nitrogen atom.

Conclusions

In conclusion, two new urea-containing PSQ membranes were prepared, and their CO₂ separation performance was evaluated. Among them, the BTESEgU–BTESE (300 °C) membrane exhibited high performance, with P_CO2 = 1.3 × 10^–6mol m^–2s^–1Pa^–1 and a CO₂/N₂ = 13. In contrast, the TTESPUEA–BTESE (250 °C) membrane exhibited a significantly lower P_CO2 value. A prediction model for CO₂ permeance and CO₂/N₂ permselectivity as target variables was generated using machine learning based on experimental data collected in our previous studies as explanatory variables. The model has potential application for the design of the chemical structure of membranes, although the accuracy of the prediction model is not very high. The accuracy is improved by the addition of more experimental explanatory variables. Notably, the calcination of TTESPUEA–BTESE at higher temperatures resulted in a drastic improvement in membrane performance. This seems to be an effective methodology for optimizing the chemical structure of membranes. The CO_₂ separation performance of the BTESEgU–BTESE (300 °C) membranes ranks in the top tier of PSQ-based membranes. Given the high stability and facile film-forming properties of PSQ materials, these results merit significant attention. Optimizing the membrane preparation process, monomer ratio, and comonomer structure is in progress.

Supplementary information

Supplementary information is available at the Polymer Journal website, which includes structures of precursors (Fig. S1), lists of raw data, and explanatory and target variables (Tables S1 and S2) for machine learning.