Molecular Simulation of Adsorption of CO₂ from a Combustion Exhaust Mixture of Zeolites with Different Topological Structures

Abstract

In this work, a molecular simulation method was used to study the adsorption of seven combustion products (CO₂, H₂O, SO₂, N₂, O₂, NO and NO₂) on three zeolites with different topological structures (4A, MIF and MOR). Adsorption isotherms of pure components and mixtures at a wide range of temperatures (253–333 K) were calculated using the Monte Carlo method, obtaining equilibrium parameters including the adsorption capacity, adsorption heat and energy distribution. The calculation results indicated that 4A zeolite with more micropores has a stronger adsorption performance for CO₂. The presence of water significantly reduced the CO₂ capture efficiency of the three zeolites, and the CO₂ adsorption amount decreased by more than 80%. Adsorption kinetics was studied using the molecular dynamic (MD) method, MFI and MOR, with channel-type pore structures exhibiting stronger gas diffusion performance, though their separation efficiency was not high. A 4A zeolite has the potential for kinetic separation of CO₂.

1. Introduction

Rising levels of CO₂ in the atmosphere have been a significant global concern in this century. CO₂ has a long lifetime (300–1000 years) in the atmosphere, leading to cumulative effects and persistent climate risks [1,2]. Among human activities that produce CO₂, industrial combustion processes, such as power generation and steel manufacturing, are huge emission sources that are hard to decarbonize because they are necessary for maintaining normal living standards. Besides developing carbon-free energy systems, carbon capture technology is an effective method for removal of CO₂ from a variety of source [3]. These technologies encompass post-combustion and pre-combustion capture methods from specific emission sources, biological carbon sequestration from atmospheric air and direct air capture [4]. In these technologies, solid adsorption is the most potential capture method because of its unique advantages, such as high capacity, high selectivity, long term chemical and physical stability, minimum energy requirements for regeneration process, low toxicity, low cost, etc. [5,6,7,8,9,10,11,12]. Hu et al. [13,14] enhanced the effectiveness of carbon capture by improving the structure of carbons. In industrial practice, dealing with complex components needs materials with strong robustness. Porous materials, in particular zeolites [15], are a class of promising adsorbent materials, which have been successfully commercialized for applications in separation under industrial conditions [16,17,18].

The structural framework of zeolites is mainly composed of Si-O and Al-O tetrahedra, in which the O atom is shared by two tetrahedra, forming a bridge connecting the two tetrahedra. The different topological structures formed by different constructions of tetrahedra are also known as skeleton configurations. Common zeolite skeleton configurations include MFI, CHA, FAU, MOR, etc. For example, FAU zeolites are 3D twelve-membered ring (12 MRs) pores with a larger super-cage structure, while MFI zeolites are 2D pores formed by the intersection of 10 MRs straight pores and 10 MRs sinusoidal pores. Most zeolites used as adsorbents belong to 3D crystal cell structures. The topological structure of zeolites has the characteristics of uniform pore size distribution, ordered pores and a large surface area. The features of different topological structures have similarities and differences, but each topological structure is unique. The structural features include ring size, pore channel dimension, porosity, structural type, etc.

Experimental results have confirmed that zeolites with different topological structures exhibit differences in the adsorption of adsorbates. Zhang et al. [19] studied the adsorption performance of NO in Cu-based molecular sieves with different topological structures using a fixed bed flow adsorption device, and found that the adsorption capacity order was MFI > OFF/ERI > MOR > LTL > FER > FAU. Pan et al. [20] studied the adsorption and catalytic performance of NO in Fe-based molecular sieves with different topological structures using a fixed bed reaction system, and found that the adsorption capacity order was MOR > FER > MFI > BEA. It is difficult to control the topological structure of the zeolites as the only variable (i.e., pure silicon zeolites) during the experimental process. Therefore, in order to explore the structure–activity relationship between topological structure and adsorption behavior, molecular simulation technology has gradually been applied by scholars in the design and research of adsorbents. With the development of this technology, its simulation efficiency has become increasingly efficient, and the simulation results have become more accurate.

Exploring the structure–activity relationship between topological structure and molecular adsorption to predict the diffusion behavior of molecules in pores is a complex and difficult task. For CO₂ adsorption, the interaction between the oxygen and carbon atoms of CO₂ molecules and the framework oxygen atoms of the zeolites dominates the adsorption strength [21]. The adsorption characteristics of zeolites are strongly influenced by their framework structure and the dimensions of their cages/pores [22]. Among the pure silica zeolites studied, dispersive interactions dominate, accounting for 90%, while electrostatic interactions contribute the remaining 10%. However, the proportion of electrostatic interactions varies considerably based on the framework structure. Notably, EDI, FER and ISV (for detailed framework information, refer to the IZA website) exhibit approximately 5% electrostatic interaction, whereas GIS, MER, MOR and RHO have more than 15%. Typically, smaller pore sizes result in higher adsorption heats due to stronger interactions between CO₂ and the zeolite framework.

Our previous work investigated the CO₂ capture ability of two commonly used commercial zeolites (13X and 5A) by GCMC and MD simulation method [23]. In this work, we continue to discuss three commercial zeolites with different topological structures. GCMC and MD simulation methods were used. The zeolites included cage-type zeolites (LTA), intersecting channel type zeolites (MFI) and channel type zeolites (MOR). We studied their adsorption properties during the process of CO₂ capture from combustion gas (CO₂, O₂, N₂, NO, NO₂, SO₂ and H₂O). Adsorption thermodynamics and kinetic parameters such as adsorption capacity, heat, electivity and the diffusion coefficients were calculated to establish the structure–activity relationship between topological structure and adsorption behavior, in order to reveal the influence of topological structure on the CO₂ capture ability.

2. Computational Methods and Details

2.1. Models

The models of 4A, MFI and MOR for molecular simulation are drawn by Material Studio (MS) 2019 software (Figure 1). Because the Al3⁺ position is unknown in the zeolite framework, a random allocation approach is employed, adhering to the Löwenstein rule. To guarantee that the dimensions in all three directions exceed twice the radius of the segment, we constructed a 2 × 2 × 2 supercell. The characteristics of single crystal cells are as follows: In 4A zeolite, the β cage is placed on the eight vertices of the cube, which are connected to each other through a four-membered ring, forming an α Cage. The α cage can be connected in three dimensions through an eight-membered ring, with a bore diameter of 4 Å. ZSM-5 is a typical MFI zeolite which belongs to the orthogonal system and has a special structure. MFI contains two perpendicular pore structures formed by ten-membered rings; one is a straight pore structure, and the other is a sinusoidal twisted pore structure. The pore sizes of both pore structures are approximately 5.4 Å. Pores of the same type are parallel to each other, while different types of pores intersect perpendicular to each other, forming an interconnected network of pores. MOR zeolite belongs to the orthogonal crystal system. The MOR framework mainly consists of two vertically intersecting channels, twelve-membered annular channels (12-MR) along the [001] direction and eight-membered annular channels (8-MR) along the [010] direction; 12-MR is elliptical in shape with a diameter of 6.5 Å × 7.0 Å, while 8-MR is located between 12-MR, is also elliptical in shape, with a diameter of 2.6 Å × 5.7 Å.

2.2. Adsorbate-Adsorbent Interaction Potential

In our calculations, we utilized the Dreiding force field in conjunction with the Lennard-Jones (L-J) potential function. The interaction parameters, ε and σ, were determined using the mixed calculation rule proposed by Lorentz–Berthelot, as outlined below:

$$\left\{\begin{array}{c}{\sigma }_{ij}=({\sigma }_i+{\sigma }_j)/2\\ {\epsilon }_{ij}=\sqrt{{\epsilon }_i{\epsilon }_j}\end{array}\right.$$

(1)

where σ_i and σ_j represent the diameters of the colliding species (in Ångstroms), while ε_i and ε_j denote the depths of their potential energy wells (in kcal/mol). The subscripts i and j distinguish between different types of atoms or molecules involved.

2.3. Molecular Simulation Methods

2.3.1. CGMC Simulation

For the predefined zeolite model unit cells, Grand Canonical Monte Carlo (GCMC) simulations were employed to determine the adsorption equilibria and isosteric heat of adsorbates under periodic boundary conditions. Each simulation iteration began with a zeolite framework devoid of adsorbents. Subsequently, configurations were generated using the Metropolis–Hastings algorithm, which either accepted or rejected the generation, disappearance, rotation, and translation of adsorbents based on energetic considerations.

In each GCMC simulation, the distribution of movements—exchange, conformation, rotation and translation—was set at 20%, 20%, 40% and 20%, respectively. Electrostatic interactions were treated using the Ewald summation method, ensuring an accuracy of 10⁻⁵ kcal/mol. The van der Waals interactions were calculated using the atomic summation method, with a cutoff value for the Lennard-Jones interaction energy set at 12.5 Å. The total simulation length was 1 × 10⁶ steps.

2.3.2. Isotherm Model and Adsorption Selectivity

The simulated conditions are characterized by a low-pressure environment, allowing fugacity to be approximated as equal to pressure, and the gas to behave according to the ideal gas state equation. In the context of zeolite adsorption of small gas molecules, the adsorption isotherm typically aligns with the Langmuir model:

$$q={\displaystyle \frac{q_m{K}_p}{1+K_p}}$$

(2)

The q_m represents the theoretical saturated adsorption capacity for a single molecule, measured in mmol/g, while K denotes the Langmuir constant, with units of L/mmol. The equilibrium selectivity, S, can be derived using the following formula:

$$S_{1/2}={\displaystyle \frac{q_1{K}_1}{q_2{K}_2}}$$

(3)

In a binary system, the selectivity can be determined as follows:

$$S_{1/2}={\displaystyle \frac{q_1{p}_2}{q_2{p}_1}}$$

(4)

where q is the saturated adsorption capacity of the gas, and p is the saturated adsorption pressures of the gas.

2.3.3. EMD Simulations

The molecular dynamics (MD) technique is employed to model the diffusion of gas within zeolites, aiming to ascertain the gas’s diffusion coefficient in the zeolite framework. Prior to conducting MD simulations, a gas molecule is introduced into the zeolite, and a low-energy configuration is obtained followed by structural optimization. During MD simulations, the NVT ensemble is utilized, assigning random initial velocities. The Nosé–Hoover thermostat method is applied, with a time step of 1 fs and a total simulation duration of 200 picoseconds (ps). The initial 50 ps are dedicated to achieving an equilibrium structure, whereas the subsequent 150 ps are used for computing the results. The self-diffusion coefficient of the gas is derived from the Einstein equation.

$$D_S=\underset{t\to \infty }{\lim }{\displaystyle \frac{1}{6t}}〈{\left|\overrightarrow{r}\left(t\right)-\overrightarrow{r}\left(0\right)\right|}^2〉$$

(5)

where $〈{\left|\overrightarrow{r}\left(t\right)-\overrightarrow{r}\left(0\right)\right|}^2〉$ is the mean squared displacement (MSD) of gas molecules. Convergence of the simulation results is indicated when the slope of the log MSD-log t curves reaches 1. At this stage, the self-diffusion coefficient can be determined as one-sixth of the slope of the MSD-t curve. In scenarios where the gas concentration is very low, the thermodynamic correction diffusion coefficient is roughly equivalent to the self-diffusion coefficient derived from the simulation.

3. Results

3.1. Validations of Model and Simulation

Our previous work [23] has discussed the CO₂ adsorption performance of two typical commercial molecular sieves (13X and 5A). The force field parameters have been well validated, and in this work, we continue to use the previous force field settings.

3.2. Adsorption Isotherms and Equilibrium Parameters of Pure Components

The adsorption isotherms of each component on 4A, MFI and MOR at different temperatures are shown in Figure 2, Figure 3 and Figure 4. The type of adsorption isotherm basically does not change with temperature. All of them belong to Langmuir-type isotherms. The Langmuir parameters are listed in Table 1, Table 2 and Table 3. As the temperature increases, the adsorption capacity of different zeolites decreases.

From the shape of the adsorption isotherms, it can be seen that the slopes of CO₂, H₂O and SO₂ adsorption isotherms are larger under low pressure, and gradually decrease with increasing pressure and temperature until a plateau appears. This is because—at low pressure—surface adsorption and molecular condensation of adsorbates in small pores occur in zeolites, resulting in a fast adsorption rate. As a result, the adsorption capacity increases sharply under low pressure, and then enters a multi-layer adsorption stage, where the adsorption rate slows down and finally reaches saturation.

For CO₂, H₂O and SO₂, which are easily adsorbed, 4A can provide more adsorption space due to its higher porosity and smaller cage topology of eight-membered ring pores. Therefore, the values of CO₂, H₂O, and SO₂ in 4A are higher than those in MFI and MOR. At 253 K, the order of CO₂ adsorption capacity for different types of zeolites is 4A > MFI > MOR. The ring size and pore dimension of molecular sieve pores are the main factors affecting NO adsorption. Compared with MOR and MFI, the cage-like structure of 4A has a high-dimensional pore structure, which is more conducive to the adsorption and diffusion of NO. From the data, it can also be seen that the topological structure of molecular sieves has a relatively small impact on O₂ adsorption capacity.

Figure 2. Adsorption isotherms (253–333 K) of six pure components for 4A.

Figure 2. Adsorption isotherms (253–333 K) of six pure components for 4A.

Table 1. Adsorption parameters of pure components for 4A zeolite fitted by Langmuir model.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	q (mmol·g−1)	7.72	7.38	7.11	6.80	6.59	6.28	6.07	5.80	5.50
	K (kPa−1)	3.00	3.50	2.72	2.38	1.91	1.79	1.39	1.15	1.02
	R2	0.99	0.98	0.97	0.98	0.98	0.98	0.99	0.99	0.97
H2O	q (mmol·g−1)	14.38	13.65	13.18	13.13	13.10	13.25	13.24	12.99	12.57
	K (kPa−1)	2380.2	2080.6	2207.9	1889.1	1808.0	1559.5	1593.2	1471.1	1434.7
	R2	0.66	0.67	0.78	0.79	0.70	0.87	0.89	0.87	0.86
SO2	q (mmol·g−1)	7.55	7.32	7.43	7.50	7.17	7.08	6.76	6.47	6.76
	K (kPa−1)	527.6	444.7	427.1	332.1	428.4	395.1	390.8	486.0	464.8
	R2	0.92	0.89	0.95	0.93	0.94	0.96	0.96	0.97	0.96
O2	q (mmol·g−1)	1.36	1.08	0.98	0.90	0.75	0.68	0.64	0.53	0.42
	K (kPa-1)	0.031	0.026	0.027	0.016	0.0018	0.013	0.0034	0.010	0.004
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99
NO	q (mmol·g−1)	0.85	0.77	0.50	0.31	0.20	0.12	0.11	0.10	0.06
	K (kPa−1)	1.06	0.37	0.26	0.15	0.31	0.58	0.96	0.32	0.27
	R2	0.99	0.99	0.98	0.98	0.98	0.99	0.99	0.99	0.99
N2	q (mmol·g−1)	3.67	2.78	2.53	2.14	2.10	2.09	1.92	1.87	1.84
	K (kPa−1)	0.019	0.017	0.013	0.010	0.008	0.005	0.005	0.003	0.002
	R2	0.99	0.99	0.99	0.98	0.98	0.99	0.99	0.99	0.99
NO2	q (mmol·g−1)	0.47	0.44	0.36	0.27	0.23	0.21	0.12	0.07	0.04
	K (kPa−1)	37.51	25.19	6.49	21.17	6.20	3.74	6.44	5.14	5.56
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99

Table 1. Adsorption parameters of pure components for 4A zeolite fitted by Langmuir model.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	q (mmol·g−1)	7.72	7.38	7.11	6.80	6.59	6.28	6.07	5.80	5.50
	K (kPa−1)	3.00	3.50	2.72	2.38	1.91	1.79	1.39	1.15	1.02
	R2	0.99	0.98	0.97	0.98	0.98	0.98	0.99	0.99	0.97
H2O	q (mmol·g−1)	14.38	13.65	13.18	13.13	13.10	13.25	13.24	12.99	12.57
	K (kPa−1)	2380.2	2080.6	2207.9	1889.1	1808.0	1559.5	1593.2	1471.1	1434.7
	R2	0.66	0.67	0.78	0.79	0.70	0.87	0.89	0.87	0.86
SO2	q (mmol·g−1)	7.55	7.32	7.43	7.50	7.17	7.08	6.76	6.47	6.76
	K (kPa−1)	527.6	444.7	427.1	332.1	428.4	395.1	390.8	486.0	464.8
	R2	0.92	0.89	0.95	0.93	0.94	0.96	0.96	0.97	0.96
O2	q (mmol·g−1)	1.36	1.08	0.98	0.90	0.75	0.68	0.64	0.53	0.42
	K (kPa-1)	0.031	0.026	0.027	0.016	0.0018	0.013	0.0034	0.010	0.004
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99
NO	q (mmol·g−1)	0.85	0.77	0.50	0.31	0.20	0.12	0.11	0.10	0.06
	K (kPa−1)	1.06	0.37	0.26	0.15	0.31	0.58	0.96	0.32	0.27
	R2	0.99	0.99	0.98	0.98	0.98	0.99	0.99	0.99	0.99
N2	q (mmol·g−1)	3.67	2.78	2.53	2.14	2.10	2.09	1.92	1.87	1.84
	K (kPa−1)	0.019	0.017	0.013	0.010	0.008	0.005	0.005	0.003	0.002
	R2	0.99	0.99	0.99	0.98	0.98	0.99	0.99	0.99	0.99
NO2	q (mmol·g−1)	0.47	0.44	0.36	0.27	0.23	0.21	0.12	0.07	0.04
	K (kPa−1)	37.51	25.19	6.49	21.17	6.20	3.74	6.44	5.14	5.56
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99

Figure 3. Adsorption isotherms (253–333 K) of six pure components for MFI.

Figure 3. Adsorption isotherms (253–333 K) of six pure components for MFI.

Table 2. Adsorption parameters of pure components for MFI zeolite fitted by Langmuir model.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	q (mmol·g−1)	5.90	5.55	5.48	4.55	4.42	4.30	3.72	3.56	3.22
	K (kPa−1)	5.54	5.64	5.34	5.54	5.17	5.97	5.69	5.95	5.27
	R2	0.89	0.97	0.96	0.97	0.98	0.97	0.97	0.98	0.99
H2O	q (mmol·g−1)	13.35	12.74	11.21	10.26	9.75	9.12	8.75	8.69	7.69
	K (kPa−1)	55.32	44.21	31.25	30.85	24.33	16.91	14.88	11.66	10.85
	R2	0.87	0.87	0.86	0.89	0.91	0.97	0.96	0.86	0.91
SO2	q (mmol·g−1)	8.35	7.75	7.25	6.76	6.15	5.92	5.75	5.69	5.31
	K (kPa−1)	0.341	0.406	0.305	0.371	0.315	0.359	0.379	0.315	0.620
	R2	0.78	0.89	0.79	0.78	0.84	0.88	0.87	0.89	0.88
O2	q (mmol·g−1)	1.96	1.58	1.41	1.37	1.30	1.25	1.13	1.02	0.93
	K (kPa−1)	0.0030	0.0096	0.0029	0.0016	0.0059	0.0018	0.0017	0.0030	0.0016
	R2	0.99	0.98	0.99	0.99	0.98	0.99	0.99	0.99	0.99
NO	q (mmol·g−1)	0.462	0.256	0.239	0.134	0.118	0.077	0.055	0.050	0.020
	K (kPa−1)	0.341	0.406	0.305	0.371	0.315	0.358	0.379	0.315	0.620
	R2	0.99	0.99	0.98	0.99	0.99	0.99	0.99	0.99	0.99
N2	q (mmol·g−1)	2.37	2.31	2.20	2.18	2.04	2.03	1.98	1.85	1.75
	K (kPa−1)	0.0091	0.0091	0.0049	0.0036	0.0092	0.0024	0.0016	0.0015	0.0013
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99
NO2	q (mmol·g−1)	0.76	0.67	0.62	0.55	0.45	0.38	0.33	0.27	0.24
	K (kPa−1)	32.38	19.85	11.48	7.07	4.02	2.84	1.49	0.71	0.48
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99

Table 2. Adsorption parameters of pure components for MFI zeolite fitted by Langmuir model.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	q (mmol·g−1)	5.90	5.55	5.48	4.55	4.42	4.30	3.72	3.56	3.22
	K (kPa−1)	5.54	5.64	5.34	5.54	5.17	5.97	5.69	5.95	5.27
	R2	0.89	0.97	0.96	0.97	0.98	0.97	0.97	0.98	0.99
H2O	q (mmol·g−1)	13.35	12.74	11.21	10.26	9.75	9.12	8.75	8.69	7.69
	K (kPa−1)	55.32	44.21	31.25	30.85	24.33	16.91	14.88	11.66	10.85
	R2	0.87	0.87	0.86	0.89	0.91	0.97	0.96	0.86	0.91
SO2	q (mmol·g−1)	8.35	7.75	7.25	6.76	6.15	5.92	5.75	5.69	5.31
	K (kPa−1)	0.341	0.406	0.305	0.371	0.315	0.359	0.379	0.315	0.620
	R2	0.78	0.89	0.79	0.78	0.84	0.88	0.87	0.89	0.88
O2	q (mmol·g−1)	1.96	1.58	1.41	1.37	1.30	1.25	1.13	1.02	0.93
	K (kPa−1)	0.0030	0.0096	0.0029	0.0016	0.0059	0.0018	0.0017	0.0030	0.0016
	R2	0.99	0.98	0.99	0.99	0.98	0.99	0.99	0.99	0.99
NO	q (mmol·g−1)	0.462	0.256	0.239	0.134	0.118	0.077	0.055	0.050	0.020
	K (kPa−1)	0.341	0.406	0.305	0.371	0.315	0.358	0.379	0.315	0.620
	R2	0.99	0.99	0.98	0.99	0.99	0.99	0.99	0.99	0.99
N2	q (mmol·g−1)	2.37	2.31	2.20	2.18	2.04	2.03	1.98	1.85	1.75
	K (kPa−1)	0.0091	0.0091	0.0049	0.0036	0.0092	0.0024	0.0016	0.0015	0.0013
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99
NO2	q (mmol·g−1)	0.76	0.67	0.62	0.55	0.45	0.38	0.33	0.27	0.24
	K (kPa−1)	32.38	19.85	11.48	7.07	4.02	2.84	1.49	0.71	0.48
	R2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99

Figure 4. Adsorption isotherms (253–333 K) of six pure components for MOR.

Figure 4. Adsorption isotherms (253–333 K) of six pure components for MOR.

Table 3. Adsorption parameters of pure components for MOR zeolite fitted by Langmuir model.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	q (mmol·g−1)	4.20	3.83	3.44	2.77	2.73	2.59	2.13	2.47	2.15
	K (kPa−1)	0.155	0.113	0.086	0.062	0.043	0.030	0.024	0.016	0.012
	R2	0.98	0.99	0.99	0.98	0.94	0.98	0.97	0.97	0.98
H2O	q (mmol·g−1)	12.34	11.78	11.04	10.67	10.21	9.78	9.31	9.14	8.89
	K (kPa−1)	0.130	0.412	0.855	0.109	0.228	0.178	0.398	0.091	0.697
	R2	0.87	0.87	0.86	0.89	0.91	0.97	0.96	0.86	0.91
SO2	q (mmol·g−1)	5.61	4.57	4.48	7.99	7.81	4.70	3.13	4.58	6.08
	K (kPa−1)	713.9	5.62	759.1	27.78	47.59	44.49	32.90	14.36	8.83
	R2	0.88	0.89	0.89	0.88	0.84	0.88	0.87	0.87	0.88
O2	q (mmol·g−1)	1.57	1.40	0.87	0.71	0.68	0.55	0.48	0.39	0.28
	K (kPa−1)	0.0017	0.0082	0.0115	0.0019	0.0015	0.0048	0.0017	0.0030	0.0014
	R2	0.99	0.99	0.99	0.98	0.99	0.98	0.97	0.97	0.98
NO	q (mmol·g−1)	0.541	0.373	0.230	0.137	0.066	0.053	0.033	0.030	0.016
	K (kPa−1)	0.396	1.14	0.373	0.161	1.51	1.08	0.308	0.292	0.787
	R2	0.99	0.99	0.99	0.98	0.99	0.98	0.98	0.98	0.98
N2	q (mmol·g−1)	2.37	2.34	2.32	2.30	2.23	2.30	2.18	1.81	1.79
	K (kPa−1)	0.0080	0.0055	0.0041	0.0031	0.0023	0.0014	0.0012	0.0012	0.00082
	R2	0.99	0.99	0.99	0.98	0.99	0.99	0.98	0.98	0.99
NO2	q (mmol·g−1)	0.337	0.279	0.170	0.107	0.091	0.089	0.085	0.010	0.009
	K (kPa−1)	80.32	3.305	7.021	1.097	13.73	1.45	3.62	43.95	2.26
	R2	0.99	0.99	0.99	0.98	0.99	0.99	0.99	0.98	0.99

Table 3. Adsorption parameters of pure components for MOR zeolite fitted by Langmuir model.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	q (mmol·g−1)	4.20	3.83	3.44	2.77	2.73	2.59	2.13	2.47	2.15
	K (kPa−1)	0.155	0.113	0.086	0.062	0.043	0.030	0.024	0.016	0.012
	R2	0.98	0.99	0.99	0.98	0.94	0.98	0.97	0.97	0.98
H2O	q (mmol·g−1)	12.34	11.78	11.04	10.67	10.21	9.78	9.31	9.14	8.89
	K (kPa−1)	0.130	0.412	0.855	0.109	0.228	0.178	0.398	0.091	0.697
	R2	0.87	0.87	0.86	0.89	0.91	0.97	0.96	0.86	0.91
SO2	q (mmol·g−1)	5.61	4.57	4.48	7.99	7.81	4.70	3.13	4.58	6.08
	K (kPa−1)	713.9	5.62	759.1	27.78	47.59	44.49	32.90	14.36	8.83
	R2	0.88	0.89	0.89	0.88	0.84	0.88	0.87	0.87	0.88
O2	q (mmol·g−1)	1.57	1.40	0.87	0.71	0.68	0.55	0.48	0.39	0.28
	K (kPa−1)	0.0017	0.0082	0.0115	0.0019	0.0015	0.0048	0.0017	0.0030	0.0014
	R2	0.99	0.99	0.99	0.98	0.99	0.98	0.97	0.97	0.98
NO	q (mmol·g−1)	0.541	0.373	0.230	0.137	0.066	0.053	0.033	0.030	0.016
	K (kPa−1)	0.396	1.14	0.373	0.161	1.51	1.08	0.308	0.292	0.787
	R2	0.99	0.99	0.99	0.98	0.99	0.98	0.98	0.98	0.98
N2	q (mmol·g−1)	2.37	2.34	2.32	2.30	2.23	2.30	2.18	1.81	1.79
	K (kPa−1)	0.0080	0.0055	0.0041	0.0031	0.0023	0.0014	0.0012	0.0012	0.00082
	R2	0.99	0.99	0.99	0.98	0.99	0.99	0.98	0.98	0.99
NO2	q (mmol·g−1)	0.337	0.279	0.170	0.107	0.091	0.089	0.085	0.010	0.009
	K (kPa−1)	80.32	3.305	7.021	1.097	13.73	1.45	3.62	43.95	2.26
	R2	0.99	0.99	0.99	0.98	0.99	0.99	0.99	0.98	0.99

As shown in Figure 5, Figure 7 and Figure 9, the adsorption heat at different adsorption capacities was calculated. The adsorption heat of each gas decreases slightly as the adsorption capacity increases. The adsorption heat of seven gases on three zeolites at 253 K is higher than that at 333 K, and lower temperature conditions are more favorable for the adsorption of zeolites. The adsorption heat reflects the adsorption strength, which corresponds to the pure component adsorption mentioned above, and the adsorption strengths of H₂O and SO₂ are higher.

Figure 6 shows the distribution of adsorption potential energy of seven gases in the 4A zeolite. The potential energy distribution of gas molecules in the zeolite is closely related to the spatial distribution of adsorption sites inside the zeolite. The intrinsic adsorption sites of O₂, N₂ and NO on the surface of cage-shaped microporous walls and the adsorption sites around cations in 4A zeolite result in a more concentrated distribution of adsorption potential energy, with a sharp bimodal distribution. The adsorption potential energy distribution of H₂O, SO₂, CO₂ and NO₂ is wider, and the adsorption effect is stronger, especially for H₂O and SO₂. For MFI and MOR (Figure 8 and Figure 10), due to the channel-shaped pore structure, the distribution of gas molecules is relatively uniform without specific adsorption sites. Therefore, the potential energy distribution of the two gas molecules on MFI and MOR is mostly unimodal. The interaction between cations loaded on special sites inside molecular sieves and gas molecules plays a very important role in adsorption separation. Therefore, the Van der Waals force and electrostatic force differences caused by the quadrupole moment of the adsorbate and the polarization of the cations are the main factors affecting adsorption separation.

Figure 5. Variations in adsorption heat of pure components for 4A with adsorption capacity.

Figure 5. Variations in adsorption heat of pure components for 4A with adsorption capacity.

Figure 6. Simulated distributions (a) and profiles (b) of potential energy for seven gases for 4A at 298 K, 100 kPa.

Figure 6. Simulated distributions (a) and profiles (b) of potential energy for seven gases for 4A at 298 K, 100 kPa.

Figure 7. Variations in adsorption heat of pure components for MFI with adsorption capacity.

Figure 7. Variations in adsorption heat of pure components for MFI with adsorption capacity.

Figure 8. Simulated distributions (a) and profiles (b) of potential energy for seven gases for MFI at 298 K, 100 kPa.

Figure 8. Simulated distributions (a) and profiles (b) of potential energy for seven gases for MFI at 298 K, 100 kPa.

Figure 9. Variations in adsorption heat of pure components for MOR with adsorption capacity.

Figure 9. Variations in adsorption heat of pure components for MOR with adsorption capacity.

Figure 10. Simulated distributions (a) and profiles (b) of potential energy for seven gases for MOR at 298 K, 100 kPa.

Figure 10. Simulated distributions (a) and profiles (b) of potential energy for seven gases for MOR at 298 K, 100 kPa.

3.3. Adsorption Isotherms and Equilibrium Parameters in Mixture

According to industrial conditions, the proportion of each component in mixture is 13.1% CO₂, 0.1% SO₂, 5.82% O₂, 0.0158% NO and 0.00158% NO₂. Using the saturated vapor pressure of H₂O at various temperatures between 253 and 333 K, it is found that H₂O comprises 0.6082% to 10% of the mixture, with the remainder being N₂. The co-adsorption process of flue gas components in three zeolites was evaluated. The adsorption isotherms for the gas mixture are depicted in Figure 11, Figure 12 and Figure 13. Notably, the adsorption capacity of all gases, except for H₂O molecules, exhibits a significant reduction.

When the adsorbate adsorbs on the surface, it exhibits energy heterogeneity. Molecular size, dipole moment, and quadrupole moment are important factors affecting the competitive adsorption of mixed components. The internal electrical distribution of CO₂ molecules is uniform, with 0 dipole moment. Compared to highly polar H₂O molecules, porous solid materials have weaker selectivity for CO₂ molecules. In addition, a large number of H₂O molecules occupying adsorption sites will form hydrogen bonds on the surface and separate the cations in the material from the skeleton, affecting the CO₂ adsorption performance.

Figure 11. Adsorption isotherms (253–333 K) of mixture for 4A.

Figure 11. Adsorption isotherms (253–333 K) of mixture for 4A.

Figure 12. Adsorption isotherms (253–333 K) of mixture for MFI.

Figure 12. Adsorption isotherms (253–333 K) of mixture for MFI.

Figure 13. Adsorption isotherms (253–333 K) of mixture for MOR.

Figure 13. Adsorption isotherms (253–333 K) of mixture for MOR.

3.4. Self-Diffusion from Mixture

The diffusion of gas in the adsorbent is crucial for the adsorption process. Excellent diffusion performance can reduce adsorption/desorption cycle time and improve processing capacity.

Table 4. Diffusion coefficients of seven gases for 4A zeolite at 253–333 K.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	Ds (×10−10 m2/s)	17.99	15.32	116.18	40.15	89.81	29.23	19.07	66.25	70.61
	R2	0.96	0.98	0.99	0.99	0.99	0.96	0.99	0.99	0.99
H2O	Ds (×10−10 m2/s)	-	-	-	-	-	-	-	-	-
	R2	-	-	-	-	-	-	-	-	-
SO2	Ds (×10−10 m2/s)	-	-	-	-	-	-	-	-	-
	R2	-	-	-	-	-	-	-	-	-
O2	Ds (×10−10 m2/s)	556.5	438.3	1365.2	2848.3	1026.7	746.3	135.1	3069.9	465.0
	R2	0.98	0.98	0.99	0.98	0.99	0.99	0.99	0.99	0.97
NO	Ds (×10−10 m2/s)	1070.4	2942.0	2711.1	724.4	4939.6	2196.4	1255.6	1331.0	1117.9
	R2	0.98	0.99	0.98	0.99	0.99	0.99	0.99	0.99	0.99
N2	Ds (×10−10 m2/s)	2163.6	1788.6	1295.8	5469.8	1256.0	2628.1	2628.8	5542.6	2742.4
	R2	0.98	0.99	0.98	0.98	0.99	0.99	0.99	0.99	0.99
NO2	Ds (×10−10 m2/s)	14.73	67.72	60.61	25.80	27.60	27.49	67.50	35.85	12.20
	R2	0.98	0.99	0.98	0.99	0.98	0.99	0.99	0.99	0.99

,

Table 5. Diffusion coefficients of seven gases for MFI zeolite at 253–333 K.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	Ds (×10−10 m2/s)	349	706	251	500	452	97	230	565	374
	R2	0.97	0.96	0.99	0.97	0.99	0.84	0.94	0.96	0.93
H2O	Ds (×10−10 m2/s)	865	991	556	581	294	1194	841	1346	315
	R2	0.99	0.98	0.99	0.99	0.92	0.99	0.99	0.98	0.96
SO2	Ds (×10−10 m2/s)	198	30.5	138	318	64	56.9	42.7	84	50.2
	R2	0.99	0.99	0.97	0.96	0.94	0.97	0.97	0.97	0.91
O2	Ds (×10−10 m2/s)	470	144	618	168	1525	273	185	563	1681
	R2	0.99	0.92	0.99	0.78	0.98	0.99	0.94	0.97	0.99
NO	Ds (×10−10 m2/s)	93.2	648	146	172	579	1167	345	1415	275
	R2	0.94	0.96	0.99	0.99	0.98	0.98	0.99	0.95	0.98
N2	Ds (×10−10 m2/s)	69.1	365	173	65.5	341	365	540	353	197
	R2	0.81	0.99	0.95	0.99	0.97	0.96	0.98	0.98	0.98
NO2	Ds (×10−10 m2/s)	2.56	0.66	0.73	0.27	4.13	0.50	4.06	17.1	17.3
	R2	0.96	0.44	0.87	0.42	0.94	0.30	0.92	0.99	0.99

and

Table 6. Diffusion coefficients of seven gases for MOR zeolite at 253–333 K.

Molecule		Temperatures (K)
		253	263	273	283	293	303	313	323	333
CO2	Ds (×10−10 m2/s)	243	1114	73.1	2431	189	405	1318	951	772
	R2	0.99	0.95	0.90	0.95	0.93	0.94	0.99	0.96	0.96
H2O	Ds (×10−10 m2/s)	0.72	1.99	2.20	0.86	1.35	0.32	0.13	10.7	3.24
	R2	0.85	0.96	0.95	0.82	0.90	0.49	0.14	0.94	0.95
SO2	Ds (×10−10 m2/s)	1.13	1.12	2.07	0.17	0.29	0.16	0.17	1.38	0.80
	R2	0.98	0.97	0.84	0.39	0.86	0.23	0.65	0.92	0.94
O2	Ds (×10−10 m2/s)	48.2	378	472	91.4	540	1578	535	434	443
	R2	0.96	0.93	0.98	0.97	0.93	0.96	0.97	0.88	0.95
NO	Ds (×10−10 m2/s)	1836	658	38.3	219	341	2439	1480	2259	2321
	R2	0.95	0.98	0.73	0.98	0.99	0.99	0.99	0.95	0.95
N2	Ds (×10−10 m2/s)	661	910	788	675	66	926	1595	1935	630
	R2	0.93	0.80	0.99	0.97	0.98	0.98	0.99	0.89	0.99
NO2	Ds (×10−10 m2/s)	1358	868	1504	1407	336	3370	483	1218	2511
	R2	0.99	0.99	0.95	0.99	0.96	0.96	0.99	0.97	0.96

lists the diffusion coefficients of each component on 4A, MFI and MOR. The MSD values of various gases in 4A zeolite is N₂ > NO > O₂ > CO₂ > NO₂, where SO₂ and H₂O failed to diffuse. This is because the pore size of 4A zeolite is smaller, which has a stronger binding force on gas molecules, making it difficult for SO2 and H₂O to diffuse. The MSD values of various gases in MFI zeolite is H₂O > CO₂ > O₂ > SO₂ > NO > N₂ > NO₂. For MOR zeolite, it is NO > NO₂ > O₂ > N₂ > CO₂ > SO₂ > H₂O. This is because the topological structures of MFI and MOR molecular sieves are different from those of 4A, with larger pores that are more conducive to molecular diffusion. For CO₂, the diffusion coefficient of CO₂ in 4A is lower than that in MFI and MOR. This is because MFI and MOR have long-range mesoporous channels in their structures, and adjacent mesopores are connected to each other through microporous walls, improving gas diffusion performance and having lower mass transfer resistance.

3.5. Adsorption Selectivity

The dynamic separation coefficient is much smaller than the thermodynamic separation coefficient, indicating that the molecular sieve mainly plays an adsorption equilibrium role in the separation of CO₂. However, the 4A molecular sieve exhibits good dynamic separation performance, but the presence of water makes the separation of CO₂ difficult.

The topology structure of 4A, MFI and MOR zeolites belong to the cage type, intersecting channel type, and the channel type, respectively. Studies have shown that with the increase in adsorption capacity, the diffusion coefficient of cage-type molecular sieves first increases and then decreases, while the diffusion coefficient of channel-type and intersecting channel-type molecular sieves decreases continuously. From the

Table 7. Adsorption selectivity for 4A zeolite at 253–333 K.

S/T (K)	H2O/CO2	SO2/CO2	CO2/N2	CO2/O2	CO2/NO	CO2/NO2
253	7.2	107.0	1045.4	3534.3	60.0	14.5
263	8.6	111.6	1018.5	4646.8	70.0	12.1
273	7.9	160.2	1211.5	4874.3	83.1	34.0
283	9.5	212.5	1280.0	5485.0	97.2	49.1
293	10.9	243.3	1336.8	5164.2	117.4	76.6
303	14.1	269.4	1252.2	4991.7	106.9	78.2
313	10.2	306.4	1262.2	4850.7	127.4	93.3
323	13.5	301.3	1177.6	4568.7	123.0	85.7
333	16.6	334.6	1129.0	4497.9	134.1	107.2

,

Table 8. Adsorption selectivity for MFI zeolite at 253–333 K.

S/T (K)	H2O/CO2	SO2/CO2	CO2/N2	CO2/O2	CO2/NO	CO2/NO2
253	3.6	96.4	2886.8	5019.2	43.1	39.7
263	3.7	147.5	3201.3	4785.4	39.1	83.5
273	8.7	198.0	1880.1	7489.7	79.5	56.6
283	9.9	232.9	2199.9	6014.3	56.1	26.9
293	9.5	280.3	1294.4	4988.0	91.3	73.5
303	10.3	339.4	1019.1	4947.4	64.8	83.51
313	11.1	401.6	1156.1	4420.9	133.5	137.5
323	12.6	440.8	944.9	3555.5	68.9	98.6
333	14.5	508.0	861.8	3877.5	76.4	33.5

and

Table 9. Adsorption selectivity for MOR zeolite at 253–333 K.

S/T (K)	H2O/CO2	SO2/CO2	CO2/N2	CO2/O2	CO2/NO	CO2/NO2
253	4.7	224.0	3224.5	3896.9	46.9	120.7
263	3.9	258.6	2905.0	4285.9	43.4	147.0
273	4.5	147.4	2862.1	9890.9	79.9	70.6
283	4.8	172.2	2613.0	5010.6	58.5	81.8
293	5.3	333.7	2219.7	4878.5	91.2	54.2
303	5.2	261.8	1567.1	3630.9	66.3	100.5
313	6.0	202.1	1457.3	3834.6	129.5	105.6
323	6.5	240.0	1240.6	5247.3	70.5	107.1
333	6.6	110.2	1151.0	3170.4	78.3	101.1

, it can be seen that compared to MFI and MOR, the separation coefficient of 4A has a stronger regularity with temperature variation, indicating that cage-type molecular sieves are more suitable for kinetic separation.

4. Conclusions

Utilizing well-validated models of gas-zeolite interactions, molecular simulations were conducted to compute the adsorption isotherms and self-diffusion coefficients of CO₂ and six combustion gases within 4A, MFI and MOR zeolites. The discussion focused on the adsorption selectivity of CO₂ relative to other gases. The findings reveal that the topological structure plays a crucial role in separating CO₂ from combustion gases. The adsorption capacities of CO₂, H₂O and SO₂ in 4A are higher than those in MFI and MOR. At 253 K, the order of CO₂ adsorption capacity for different types of zeolites is 4A > MFI > MOR. The ring size and pore dimension of molecular sieve pores are the main factors affecting NO adsorption. The diffusion coefficient of CO₂ in 4A is lower than that in MFI and MOR. The long-range mesoporous channels in their structures can improve gas diffusion performance. However, adsorption equilibrium is the main function of separation for CO₂. A 4A molecular sieve exhibits good dynamic separation performance. The presence of H₂O makes the separation of CO₂ difficult because of the competitive adsorption effect.