4.4. Gas Adsorption Measurements

The adsorptive properties of samples were measured using a high-pressure physical adsorption apparatus (3H-2000PH, Beishide). Two pressure sensors are placed in the high-pressure physical adsorption apparatus: one for the 200 bar model US381-2-200BA and the other for the 10 bar model US381-2-10BA. Before installing in the sample tube, all samples were dried in a vacuum drying oven at 423 K for about 6 h. Then, 1 g of the sample was placed in the sample tube. Before the measurements, the samples were heated to 573 K for 12 h to degas for accurate measurements.

In this paper, CO₂ adsorption isotherms of samples L-20, L-30, and L-40 were measured at temperatures of 273, 303, and 333 K in the pressure range of 0–15 bar. The Langmuir, Freundlich, and dual-site Langmuir models were used to carry out the fitting analysis with the measured data.

The Langmuir model was originally used to describe the gas–solid phase adsorption on activated carbon, which was traditionally used to quantify and compare the performance of different adsorbents.⁴⁷ The Langmuir isotherm refers to homogeneous adsorption, which means that each molecule has a constant enthalpy and adsorption activation energy and the adsorbate does not migrate onto the surface plane.⁴⁸ It is expressed by the following equations

where q is the adsorption quantity (mmol/g) at the absolute pressure p (bar), q_m is the complete monolayer adsorption constant (mmol/g), b_L is the Langmuir model constant (bar^–1), which is calculated by eq 2, Q is the same amount of adsorption heat that is required for physical adsorption (kJ/mol), T is the reaction temperature (K), and b_L,0 is a constant (bar^–1).

Compared to the Langmuir model, the Freundlich model is an empirical model applied to multilayer adsorption.⁴² It is expressed by the following equations⁴⁹

where q is the adsorption quantity (mmol/g) at the absolute pressure p (bar), k is the Freundlich model constant (mmol/(g·bar^1/n)), n is the heterogeneous adsorption surface coefficient calculated by eq 4, T is the reaction temperature (K), and n₁ and n₂ are constants.

The dual-site Langmuir model is a type of four-parameter model developed from the two-parameter Langmuir model, which is used to fit the adsorption isotherm. In the building of this model, it is considered that the heterogeneous surface of the adsorbent is a collection of different energy locations,⁵⁰ and it is expressed by the following equations

where q is the adsorption quantity (mmol/g) at the absolute pressure p (bar), q_m,A and q_m,B are the maximum saturated adsorption quantities of the two different adsorption sites considered (mmol/g), b_A and b_B are the Langmuir model constants of the two different adsorption sites (bar^–1), which are calculated by eqs 7 and 8, respectively, Q_A and Q_B are the same amount of adsorption heat that is required for physical adsorption (kJ/mol), T is the reaction temperature (K), and b_0,A and b_0,B are constants (bar^–1).

In this paper, the deviation index (D) is defined to express the adsorption quantity calculated by the model (q_c, mmol/g) and that measured practically (q_t, mmol/g) and is expressed as follows

To determine the selective adsorption capacity (S) of CO₂/N₂ and CO₂/O₂ of the three samples, we measured the adsorption isotherms of CO₂, O_2, and N₂ at 273 K. The obtained adsorption isotherms are fitted, and the fitting formula is used to calculate the selective adsorption capacity of CO₂/N₂ and CO₂/O₂ of the corresponding sample combined with the actual working conditions to predict the effect of the sample used in industrial flue gas separation. The industrial flue gas usually consists of N₂ and CO₂ in a volume ratio of 9:1.⁵¹ The selective adsorption capacity of CO₂/N₂ is calculated by the following equation

where q is the adsorption quantity (mmol/g) at the partial pressure p (bar), i represents CO₂, and j represents N₂ or O₂.

To measure the adsorption regeneration property, the CO₂ cyclic adsorption performance was measured at 273 K. The percentage of the regenerated adsorption amount and the initial adsorption amount was defined as the adsorption index.