Materials, chemicals, and their sources are described in the Supplementary Material.

A double-beam UV-Vis spectrophotometer (T80+ UV/vis spectrometer, PG Instruments Ltd, UK) was used to measure the concentration of the dye at λ = 504 nm, while FT-IR spectra (FT-IR, KBr pellets; 3 mm thickness) were validated on a Perkin-Elmer FT-IR spectrophotometer (FT-IR 1650). Energy dispersive X-ray spectroscopy (EDX) FEI (QUANTA-250) was utilized to identify the chemical composition of the synthesized terpolymer. X-ray diffraction (XRD) analysis was used to determine the crystalline structure by (XRD-7000, Shimadzu, Japan) Cu kα radiation (λ = 1.54060 Å). The surface morphology was examined using a scanning electron microscope JEOL JSM-5300LV. The specific surface area of the adsorbents was calculated with the Brunauer–Emmett–Teller (BET) equation using a BELSORP-mini X (S/N: 149, Version 1.0.9.0). The zeta potential (ζ-potential) measurements of the diluted samples were determined using a Zetasizer (NANO, µV, APS) software v7.13.

The XRD spectrum of the amorphous structure of the nanocomposite CM-βCD:nChi:Glu is shown in Figure 1i. The spectral pattern reflects the amorphous nature of the cross-linked terpolymer (Mohamadi Zahedi and Mansourpanah, 2018; Yang et al., 2020).

The FTIR spectra of CM-βCD and CM-βCD:nChi:Glu terpolymer in the 400–4,000 cm⁻¹ wave number range are shown in Figure 1ii. The spectrum of CM-βCD exhibits bands at 3,330; 2,930; 1,634; and 1,405 cm⁻¹ attributed to ν_OH, ν_CH, ν_{asy C=O}, and ν_{sy C=O}, respectively. The bands at 1,060 and 1,040 cm⁻¹ are attributed to ν C–O. The spectrum of CM-βCD:nChi:Glu terpolymer shows a broadening in 3,100–3,550 cm⁻¹ that may be attributed to the cross-linkage bonding between nanochitosan and CM-βCD. The broad band appearing at 2,927 cm⁻¹ corresponds to the νCH that overlaps with the OH stretching peak (Chen and Park, 2003). The bonding between the carboxylic group of CM-βCD and the amino group of chitosan is evidenced in the shifts from 1,639 cm⁻¹ and 1,457 cm⁻¹ to 1,633 cm⁻¹ and 1,405 cm⁻¹, respectively (Wang et al., 2016).

The surface morphology of CM-βCD:nChi:Glu is determined by scanning electron microscopy, showing a heterogeneous surface due to the non-uniform cross-linking interactions. Figure 1Aiii shows an irregular surface structure with holes and high cavities increasing the surface area and can be the reason for the effective adsorption properties (Pu et al., 2020). The TEM image in Figure 1Biii shows the highly stable and well-dispersed spherical CM-βCD:nChi:Glu nanoparticles in the size range 30–72 nm.

CM-βCD:nChi:Glu was exposed to BET technique to determine the surface area and pore distribution via a nitrogen adsorption–desorption method. As can be predicted, this terpolymer shows the low specific surface area (2.903 m² g⁻¹), poor pore volume (0.002 cm³ g⁻¹), and average pore diameter (3.078 nm).

The surface charge density of the adsorbent is explained based on the point of zero charges, at which the charge on the adsorbent surface is zero (Behbahani et al., 2020; Elbadawy et al., 2021). Plotting the relationship between ΔpH and pH₀, the point of zero charges was found to be 4.5 after 48 h (Figure 2). Thus, a positive charge was formed on the CM-βCD:nChi:Glu surface when the solution pH was less than the calculated zero-point charge value (4.5), while a negative charge was developed when the pH was more than 4.5. The free negative charge on the CM-CD:nChi:Glu attracts the dye, promoting the adsorption process (Islam et al., 2019). Furthermore, the zeta potential was measured and showed a surface potential of 20.8 mV, confirming the positivity of the adsorbent’s surface. Also, this high positive charge reflects the electrical stability of CM-CD:nChi:Glu because the surface charge inhibits particle aggregation and becomes coagulation-resistant.

The adsorption behavior of the synthesized nano-composite CM-βCD:nChi:Glu toward acid red 37 dye was studied using batch adsorption techniques. The main parameters studied are i) pH, ii) contact time, iii) initial dye concentration, and iv) adsorbent dosage.

The adsorption kinetics of acid red 37 dye onto the surface of the synthesized adsorbent CM-βCD:nChi:Glu was investigated at a pH of 6.0°C and temperature of 29°C, applying the pseudo–first- and second-order, Elovich, and intraparticle diffusion kinetic models (Ho and Mckay, 1999; Yuh-Shan, 2004; Priscila et al., 2013; Wang et al., 2019). Supplementary Table S1 summarizes the examined adsorption kinetic models in Supplementary Equations S1–S4.

To determine whether the type of adsorption is physio-sorption or chemisorption, the pseudo–first-order and second-order kinetic models are applied. Figures 7A, B shows the experimentally determined values of rate constants K₁ and K₂ obtained from plotting the two models. The second-order model appears to be more favorable for the dye adsorption process, indicating its chemical adsorption by CM-βCD:nChi:Glu (Eltaweil et al., 2020). The K 1 and K 2 values for CM-βCD:nChi:Glu and the other parameters obtained from the linear form of pseudo–first-order and second-order are listed in Table 1.

In addition, the Elovich kinetic model is examined to identify if the adsorption mechanism is chemisorption. The chemisorption mechanism usually involves energetically heterogeneous adsorbent surfaces. The Elovich constants (initial adsorption rate, α: 115.9 mg g⁻¹ min⁻¹ and the surface coverage and activated energy, β: 0.0201 g mg⁻¹) give an insight into the energetic heterogeneity of the surface (Figure 7C).

Furthermore, the adsorption of the targeted material onto the active sites of the adsorbent, mass transfer across the liquid film surrounding the surface, and intra-particle diffusion onto the pores of the surface make up the three stages of the intra-particle diffusion model. The processes that make use of the active sites in the adsorbents are thought to go faster. Now, if the model fits, the plot of q_t versus t^0.5 should show a straight line, either i) passing through the origin, when the intra-particle diffusion is the only controlling step or ii) with an intercept with the y-axis (Figure 7C) (Özer et al., 2006; Singh et al., 2012; Haerifar and Azizian, 2013). However, after fitting the data to the intra-particle diffusion model, a multi-linear plot was seen, indicating that intra-particle diffusion and bulk-to-surface transit of acid red 37 dye interact together producing the observed response. Intra-particle diffusion is not the rate-limiting phase since the plot does not pass through the origin. k_id and C_i were found to be 2.514 mg g⁻¹ s^−0.5 and 155 mg g⁻¹, respectively.

The adsorption isotherm models are applied to relate the equilibrium and adsorbed concentrations of acid red 37 dye (Figure 8) and thus estimate the adsorption efficiency of the adsorbent CM-βCD:nChi:Glu. The linear equations of the applied isotherm models are given in Supplementary Table S2, expressed as Supplementary Equations S5–S9.

The values of the correlation coefficients R ² of the linear plots of the applied models are typically compared for the evaluation of the best fit (Table 2). The R ² values can be arranged as: Langmuir > Freundlich> Temkin > Flory–Huggins > Dubinin–Radushkevich.

From the Langmuir isotherm model, the values of the maximum adsorption capacity (q_m) and Langmuir isotherm constant (K_L) were calculated to be 370.37 mg g⁻¹ and 0.3068 L mg⁻¹, respectively. The equilibrium parameter R_L = (0.0390–0.0149) values postulate an advantageous adsorption behavior of the CM-βCD:nChi:Glu adsorbent toward the acid red 37 dye, leading to the assumption that sorption sites are energetically equivalent, and the acid dye removal occurs on a homogeneous surface by monolayer adsorption. The Freundlich model was also applied, and the experimental results revealed a linear association between log q_e and log C_e; the adsorption intensity (1/n) = 0.2345 < 1 (n = 4.264) and adsorption capacity (K_f) = 150.35 mg/g.

In order to examine if the adsorption possesses a uniform bond energy distribution, the Temkin isotherm model was applied (Tempkin and Pyzhev, 1940). With values of the Temkin isotherm constant (K_Te) and Temkin constant related to the heat of sorption (b_Te) being 10.77 L g⁻¹ and 44.61 J mol⁻¹, respectively, the Temkin isotherm fits the adsorption process well.

On the other hand, Dubinin–Radushkevich isotherm shows R ² is equal to 0.773, which is less fitting with the experimental data. While the Flory–Huggins model (Supplementary Equation S11) is better fitting with R ² equal to 0.9848, with the Flory–Huggins constants (n_FH, k_FH) being equal to −0.4766 and 0.0643 Lmol⁻¹, respectively, and the ΔG° value being −15863.91 Jmol⁻¹. The Flory–Huggins isotherm describes the adsorbate’s surface coverage patterns on the adsorbent.

The thermodynamic parameters such as the change in free energy ∆G^o, kJ/mole; change in enthalpy ∆H^o, kJ/mole; and change in entropy ∆S^o, kJ/mole/K) provide valued information about the type and mechanism of the adsorption process. The change in Gibbs free energy (∆G^o) of an adsorption process denotes its spontaneity. A negative ∆G^o value indicates spontaneous adsorption. Equations applied to deduce the thermodynamic parameters are given in Supplementary Table S3, expressed as Supplementary Equations S10–S12 (Dizge et al., 2008; Tanhaei et al., 2019).

By applying the Van 't Hoff equation (Supplementary Equation S13) in plotting ln K_d against 1/T as shown in Figure 9, a straight line is obtained with a slope equal to ΔH^o/R and an intercept of ΔS^o/R (Anush and Vishalakshi, 2019). Table 3 presents the thermodynamic parameters for acid red 37 dye adsorption onto the CM-βCD:nChi:Glu adsorbent studied at the temperature range 293–313 K. The negative values of ΔG° indicate the spontaneous nature of the adsorption processes, which are adjusted by chemical adsorption, whereas decreases in ΔG° with rising temperatures show more favorable adsorption at higher temperatures. Also, the positive values of ΔH^o and ΔS^o reflect endothermic adsorption with additional randomness states existing at the solid–liquid interfaces.

From the point of view of economical, ecological, and material science, the reusability of adsorbents is a fundamental issue. Consequently, it is desirable to adsorb pollutants and regenerate the adsorbent for many cycles. Desorption is accomplished by incubating the terpolymer adsorbent with a solution of 60% ethanol and 1 M NaCl for 20 min; the regenerated adsorbents are then washed many times with distilled water. The regenerated adsorbents were used for five successive adsorption–desorption cycles and are presented in Figure 10. It has been observed that the dye removal efficiency of CM-βCD:nChi:Glu after five cycles decreased from 97.2 to 92.4%. This decrease may be attributed to the possibility of breakage of the polymer chains as a result of repeated base treatment during the reusability process. Since the examined acid red 37 dye is of the anionic type, CM-βCD:nChi:Glu can be considered an efficient adsorbent for anionic dyes.

The adsorption mechanism of acid red 37 dye on the surface of CM-βCD:nChi:Glu is displayed in Scheme 1. A comparison between the FTIR analysis of the adsorbent before and after the adsorption process shows the interaction of acid red 37 dye with CM-βCD:nChi:Glu (Figures 1B, C, ii). The adsorbent band centered at 3425 cm⁻¹ corresponds to O-H and N-H stretching, showing different features with more broadening (3,000–3,600 cm⁻¹), indicating their interactions with the adsorbed dye. Moreover, a peak appears at 1,554 cm⁻¹ (Figure 1Cii), attributed to the vibration of the aromatic ring of the dye molecules. However, the adsorption mechanism could be explained by the synergistic effect of the electrostatic attraction of the amino groups from nanochitosan with host–guest interactions from β-cyclodextrin. Thus, cyclodextrin cavities are responsible for capturing organic pollutant molecules via the host–guest inclusion interaction (Zhao et al., 2017; Pu et al., 2020; Shi et al., 2022). Also, the negatively charged sulfonate groups (-SO₃ ⁻) of acid red 37 dye facilitate electrostatic attractions with the amino and hydroxyl groups of chitosan. Moreover, other interactions may take place, but with lesser opportunity, such as dipole–dipole bonds, hydrogen bonding, electrostatic, Van der Waals, hydrophobic, n–pi interactions, and porous network capture (Jiang et al., 2020; Galan et al., 2021). We also found that the adsorption process followed pseudo–second-order kinetics, suggesting chemical sorption. The affinity of CM-βCD:nChi:Glu as the adsorbent for the acid red 37 dye was verified by negative values of free energy change (ΔG°). The high adsorption efficiency may be attributed to the triple adsorption effect of CM-βCD:nChi:Glu (Jiang et al., 2020).