1. Introduction

The specific surface characteristics, porosity parameters, and specific pore volume of inorganic polymer sorbents derived from local raw materials are among the key factors determining their sorption properties [1]. While pore size and pore-size distribution govern the diffusion rate of substances within the porous structure, analysis of the specific pore volume is essential for evaluating the physicochemical properties of inorganic polymer sorbents [2].

To prepare the inorganic polymer sorbent, local clay was first treated with 1 M sulfuric acid at a solid-to-liquid ratio of 1:5 at room temperature for 2 h. The acid-treated clay was then washed with distilled water until neutral conditions were reached, followed by treatment with 3 M NaOH solution at a ratio of 1:3 at room temperature for 4 h [3]. The textural properties of the pristine clay and the resulting sorbent were investigated from nitrogen (N₂) adsorption–desorption isotherms measured at 77 K. Prior to analysis, a 0.0882 g sample was degassed under vacuum at 120 °C for 2 h 56 min. Adsorption and desorption isotherms were recorded over the relative-pressure range P/P₀ = 0.03–0.99.

The specific surface area (S_BET) was calculated using the Brunauer–Emmett–Teller (BET) equation from adsorption-branch data in the P/P₀ = 0.05–0.30 range [4]:

(1)

where V is the volume of nitrogen adsorbed at the relative pressure P/P₀, cm³ g⁻¹ (STP); Vₘ is the monolayer capacity, cm³ g⁻¹ (STP); and C is the BET constant related to the interaction energy between the adsorbate and the adsorbent. Taking the molecular cross-sectional area of nitrogen as 0.162 nm², the specific surface area is calculated as follows:

(2)

From the slope (s) and intercept (i) of the linear BET plot (Figure 3), the monolayer capacity and BET constant were determined as follows:

(3)

The specific surface area was calculated using the cross-sectional area of the nitrogen molecule (A_cs = 0.162 nm²):

(4)

where N_A is Avogadro’s constant, 6.022·10²³ mol⁻¹, and M is the molar mass of nitrogen, 28.013 g mol⁻¹.

The total pore volume (V_total) was determined by converting the volume of nitrogen adsorbed at the relative pressure P/P₀ = 0,99 to the equivalent volume of liquid nitrogen:

(5)

where 0.001547 is the conversion factor from the volume of gaseous nitrogen at STP to the volume of liquid nitrogen at 77 K. The average pore diameter was calculated assuming a cylindrical-pore model:

(6)

The pore-size distribution was determined by density functional theory (DFT) from the adsorption branch of the N₂ isotherm at 77 K using an NLDFT model for cylindrical/slit-shaped pores on the surface of the inorganic polymer sorbent [1,2]. The distribution was expressed as integral pore volume (V) and differential pore volume (dV/dr) as functions of the pore half-width.

2. Results and Discussion

The nitrogen adsorption–desorption isotherms of the inorganic polymer sorbent at 77 K are presented in Figure 1. The adsorption branch does not exhibit a sharp increase in the low-relative-pressure region (P/P₀ < 0,1); thus, no distinct stage characteristic of volumetric filling of micropores is observed. As the relative pressure increases, the adsorbed nitrogen volume increases almost linearly and approaches saturation at approximately 8 cm³ g⁻¹ at P/P₀ ≈ 0,9. The maximum adsorption value (≈8.1 cm³ g⁻¹) is relatively low, indicating limited overall porosity of the material.

Figure 1. Nitrogen adsorption (●) and desorption (○) isotherms of the inorganic polymer sorbent at 77 K

The saturation uptake at high relative pressures and the presence of a broad hysteresis loop make the isotherm close to Type IV according to the IUPAC classification [4]. The hysteresis loop extends over P/P₀ ≈ 0,1–0,9, and the desorption branch does not rejoin the adsorption branch even at low pressures (low-pressure hysteresis). This behavior is generally attributed to incomplete equilibration caused by slow diffusion of nitrogen molecules through narrow pore entrances, partial irreversible retention of nitrogen within the pores, or deformation of the material framework during adsorption [4].

The pore-size distribution determined by DFT is shown in Figure 2. The differential distribution curve exhibits a bimodal character: the principal and most intense peak corresponds to a pore half-width of approximately 9.5 Å (pore width ≈1.9 nm), whereas the second, less intense peak occurs at approximately 18 Å (≈3.6 nm). These results indicate that supermicropores and small mesopores predominate in the material.

Figure 2. Integral (●) and differential (□) pore-volume distributions of the inorganic polymer sorbent determined by DFT

The integral pore-volume curve increases sharply over the pore half-width range of 8–20 Å, within which approximately 70% of the total DFT pore volume is accumulated. The contribution of pores with half-widths greater than 40 Å (pore width >8 nm) is very small, and the curve becomes nearly horizontal. The integral pore volume determined by DFT is close to the total pore volume obtained at P/P₀ = 0,99, demonstrating good agreement between the two approaches.

The multipoint BET plot is presented in Figure 3, and the calculated parameters are summarized in Table 1. Within the selected range, the experimental points are distributed around a straight line (R² = 0.898); however, the point at P/P₀ = 0.25 deviates upward from the linear trend. Such a deviation indicates that the upper limit of applicability of the BET equation is being approached.

Table 1. BET analysis results, including linear fitting parameters, monolayer capacity, BET constant, and specific surface area of the material

Figure 3. Multipoint BET plot for the inorganic polymer sorbent

The calculated specific surface area was approximately 32 m² g⁻¹. The relatively low BET constant (C ≈ 4.2) indicates weak interactions between the adsorbate and the adsorbent surface, as well as substantial overlap between monolayer formation and multilayer adsorption. Therefore, the S_BET value should be regarded as an approximate estimate [4]. This result is consistent with the nitrogen adsorption isotherm and DFT analysis and confirms the limited porosity of the material.

3. Conclusions

Mesopores in the 15–20 nm range were retained most prominently, which is considered an optimal range for ion exchange and diffusion. The modification preserved the overall pore volume while promoting the formation of active sites for ion exchange. The predominance of mesopores in the 10–20 nm range provides a scientific basis for the high sorption performance of the inorganic polymer sorbent.