Polyethylenimine-impregnated powdered activated carbon for efficient removal of Reactive Yellow 2 from aqueous solutions

Polyethylenimine-impregnated powdered activated carbon for efficient removal of Reactive Yellow 2 from aqueous solutions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Polyethylenimine-impregnated powdered activated carbon for efficient removal of Reactive Yellow 2 from aqueous solutions Sung Wook Won, Su Bin Kang, Byeong-Chan Min, Kwang-Il Go, Li Yong, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6780880/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Sep, 2025 Read the published version in Korean Journal of Chemical Engineering → Version 1 posted 4 You are reading this latest preprint version Abstract This study optimizes polyethylenimine (PEI) impregnation on powdered activated carbon (PAC) to maximize adsorption of the anionic dye Reactive Yellow 2 (RY2). Three factors, namely PEI molecular weight (600, 800, 1200, 10000 and 70000 g∙mol − 1 ), PEI content (0.1–10 wt.%), and impregnation stirring speed (0-200 rpm), were systematically evaluated in triplicate. Under optimal conditions (PEI Mw = 800 g mol − 1 , PEI content = 1.0 wt.%, stirring = 40 rpm), PEI-impregnated PAC achieved a maximum adsorption capacity of 477.02 mg g − 1 , which is 7.4-fold higher than raw PAC (64.13 mg g − 1 ). FTIR, BET, FESEM/EDS, and zeta potential analyses showed that although PEI impregnation reduced surface area, the introduced amine groups increased the surface charge by + 52.64 mV at pH 2, driving the enhanced adsorption. These results demonstrate that PEIimpregnated activated carbon is a strong and efficient adsorbent for RY2 removal in textile wastewater treatment. Polyethylenimine Activated carbon Reactive Yellow 2 Adsorption capacity Wastewater treatment Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction The textile dyeing industry is a major contributor to industrial water pollution, accounting for approximately 20% of global wastewater discharge and consuming nearly 10% of the world’s freshwater resources [ 1 , 2 ]. Among various dyes, reactive dyes such as Reactive Yellow 2 (RY2) are widely used due to their vivid color and strong bonding with textile fibers. However, their high solubility and chemical stability make them resistant to biodegradation, leading to persistent contamination in aquatic environments [ 3 , 4 ]. The discharge of dye-laden wastewater can cause eutrophication, oxygen depletion, and long-term ecological risks, including bioaccumulation and toxicity [ 5 , 6 ]. Even after conventional treatment, residual color often remains, necessitating additional treatment steps and increasing operational costs [ 7 ]. Various methods such as coagulation, biological degradation, and membrane separation have been employed for dye removal, but they often suffer from high energy consumption, low selectivity, and the generation of secondary pollutants such as sludge [ 8 – 10 ]. Adsorption has gained attention as an attractive alternative due to its simplicity, effectiveness, and minimal by-product formation [ 11 ]. Among adsorbents, powdered activated carbon (PAC) is widely used owing to its large surface area and broad adsorption range. However, raw PAC shows limited performance for anionic dyes due to its negatively charged surface under neutral to basic pH and the lack of electrostatically interactive functional groups [ 12 ]. Its fine particle size also hampers recovery and reuse, limiting its practical applicability in large-scale processes [ 13 ]. To address these limitations, surface modification of PAC with functional polymers has been widely investigated. Among numerous polymers, polyethylenimine (PEI), a highly branched polyamine, introduces amine-rich functional groups that become protonated under acidic conditions, generating positively charged sites for electrostatic interactions with anionic dyes [ 14 , 15 ]. While various studies have demonstrated the potential of PEI-modified adsorbents, many have used biomass-derived or non-powdered substrates, reported moderate adsorption capacities (< 300 mg g − 1 ), or required complex multi-step modifications that hinder scalability [ 16 – 18 ]. In addition, essential parameters such as PEI molecular weight, loading concentration, and mixing conditions during impregnation have rarely been systematically optimized. In this study, we report a simple, one-step impregnation method for fabricating PEI-impregnated PAC (PEI/PAC) using SPS-100, a commercially available powdered activated carbon. The modification was designed to enhance the electrostatic affinity of PAC toward anionic dyes by introducing amine functional groups. Key variables, including PEI molecular weight, PEI content, and stirring speed, were systematically optimized to obtain an effective adsorbent. The resulting material was evaluated in terms of dye adsorption performance, desorption efficiency, and reusability under batch-mode conditions. Overall, this work presents a practical and tunable surface modification strategy for PAC and aims to provide insights into the rational design of amine-functionalized adsorbents for enhanced dye removal in wastewater treatment systems. Experimental Materials SPS-100 was supplied by Samchully Activated Carbon Co., Ltd. (Geumsan, Korea). Branched PEI with a molecular weight (M w ) of 800 (98%) and RY2 (dye content ≥ 60%) were purchased by Sigma-Aldrich Korea Ltd. (Seoul, Korea). Branched PEIs of different molecular weights (M w = 600, 1200, 10000 and 70000, 98–100%) were provided by Nippon Shokubai Co. Ltd. (Osaka, Japan). HCl and NaOH were offered by Daejung Chemicals & Metals Co., Ltd. (Siheung, Korea). Fabrication of PEI-impregnated PAC Various PEI/PACs were prepared by a onestep impregnation of 2 g PAC in 50 mL aqueous PEI solution. All experiments were performed in triplicate (n = 3), and results are reported as mean ± standard error. Impregnation parameters were selected based on preliminary experiments to optimize polymer–carbon interactions. Three variables were investigated. First, the effect of PEI molecular weight was assessed by reacting PAC with 5 wt.% PEI solutions of different chain lengths (600, 800, 1200, 10000 and 70000 g mol − 1 ) at 160 rpm and 25°C for 72 h to determine how polymer chain length influences pore accessibility. Second, the impact of PEI content was evaluated by treating PAC with PEI (M w = 800 g mol − 1 ) solutions at 0.1, 1, 5, and 10 wt.% under the same stirring and temperature conditions for 72 h to establish the optimal polymer loading. Third, masstransfer effects were examined by impregnating PAC in a 1 wt.% PEI solution (M w = 800 g mol − 1 ) at 25°C for 72 h under stirring speeds of 0, 40, 80, 120, 160, and 200 rpm. After impregnation, each suspension was centrifuged at 2000 rpm for 10 min, washed three times with distilled water, and filtered. The wet solids were freezedried at − 50°C under 0.1 mbar for 24 h. Optimal conditions (PEI M w = 800 g mol − 1 , PEI content = 1 wt.%, stirring = 40 rpm) were selected based on the highest adsorption capacity in the evaluation of each influencing factor, and the sample prepared under this optimal condition was named 1% PEI/PAC-800 and was used for all subsequent adsorption experiments. Characterizations A Fourier transform infrared spectrometer (FT-IR, FT/IR-8X, Jasco, Japan) was used to record the FT-IR spectra of PAC and PEI/PAC in the range of 4000–500 cm − 1 . A 3Flex surface characterization analyzer (Micromeritics, USA) was used to collect the nitrogen adsorption-desorption isotherms of raw PAC and 1% PEI/PAC-800. A Field emission scanning electron microscope with energy dispersive spectroscopy (FE-SEM/EDS, JSM-7610F, Jeol, Japan) was used to record the surface morphologies of activated carbons. A zeta potential analyzer (ELSZ-2000, Otsuka, Japan) was used to analyze the zeta potential values of raw PAC and 1% PEI/PAC-100 at different pH values. Adsorption Experiments The stock solution of RY2 was prepared according to our previous method [ 19 ]. In all batch adsorption experiments, 30 mg of adsorbent and 30 mL of RY2 solution were mixed in a 50-mL conic tube and incubated in a shaker at 160 rpm. Unless otherwise noted, the pH, shaking speed, and temperature for all adsorption experiments were 2, 160 rpm, and 25°C. The pH edge experiments were conducted at pH 2–12 for 7 days with 485.59 mg L − 1 of RY2, and kinetic adsorption experiments were carried out at 504.25 mg L − 1 of RY2. The isothermal adsorption experiments were performed in the RY2 concentration range of 30 to 1000 mg L − 1 . The concentration of RY2 was measured using a UV-Vis spectrophotometer (X-ma 3000 pc, Human, Korea). The dye uptake, q (mg g − 1 ) was calculated using the following equation: $$\:q=\frac{{C}_{i}{V}_{i}-{C}_{f}{V}_{f}}{m}$$ 1 where C i , C f (mg L − 1 ) and V i , V f (L) are the RY2 concentration and the solution volume before and after adsorption, and m (g) is the weight of the adsorbent. Reusability Studies First, 30 mg of adsorbent and 30 mL of RY2 (100 mg L − 1 ) were mixed at 25°C for 4 h to obtain RY2-loaded adsorbent. After washing three times with distilled water, the RY2-loaded adsorbent was eluted with 30 mL of NaOH solution (0.01 mol L − 1 ) for 2 h, and the adsorption-desorption was repeated three times to confirm the recyclability in removing RY2. The RY2 concentration was measured by UV-Vis spectrophotometer, and the desorption rate was calculated by Eq. ( 2 ). $$\:\text{D}\text{e}\text{s}\text{o}\text{r}\text{p}\text{t}\text{i}\text{o}\text{n}\:\text{r}\text{a}\text{t}\text{e}\:\left(\text{%}\right)=\frac{\text{D}\text{e}\text{s}\text{o}\text{r}\text{b}\text{e}\text{d}\:\text{R}\text{Y}2\:\text{i}\text{n}\:\text{e}\text{a}\text{c}\text{h}\:\text{c}\text{y}\text{c}\text{l}\text{e}\:\left(\text{m}\text{g}\right)}{\text{A}\text{d}\text{s}\text{o}\text{r}\text{b}\text{e}\text{d}\:\text{R}\text{Y}2\:\text{i}\text{n}\:\text{e}\text{a}\text{c}\text{h}\:\text{c}\text{y}\text{c}\text{l}\text{e}\:\left(\text{m}\text{g}\right)}\times\:100$$ 2 Results and Discussion Optimization of PEI Impregnation for Maximum RY2 Adsorption To determine the optimal modification parameters for RY2 adsorption, raw PAC and various PEI/PACs were evaluated for three variables: PEI molecular weight, PEI content, and stirring speed during impregnation. Influence of PEI Molecular Weight The adsorption capacities of raw PAC and PAC modified with PEI of varying molecular weights (600, 800, 1200, 10000 and 70000 g mol − 1 ) are compared in Fig. 1 a. Modification enhanced RY2 uptake in all cases; the trend in capacity was: PEI/PAC-800 > PEI/PAC-600 > PEI/PAC-1200 > PEI/PAC-10000 ≈ PEI/PAC-70000 > raw PAC. The number following PEI/PAC indicates the PEI molecular weight. PEI of 800 g mol − 1 provides an optimal balance between chain length (enabling deep pore penetration) and amine-group density (maximizing electrostatic binding). Higher PEI molecular weights (≥ 1200 g mol − 1 ) are likely to be sterically hindered, which can limit pore access and reduce the surface area with amine groups available for binding to RY2 [ 20 ]. In contrast, PEI-600 is unhindered but has fewer functional groups than PEI-800, resulting in a slightly reduced adsorption capacity. These results indicate an optimal PEI molecular weight around 800 g mol − 1 for maximizing dye uptake. Influence of PEI Content Figure 1 b shows the effect of PEI content on the adsorption capacity of RY2, and the corresponding change in nitrogen content was also analyzed by EDS (Fig. S1 ). As the PEI loading increased from 0.1 to 1.0 wt.%, the RY2 uptake increased rapidly, reaching a maximum at 1.0 wt.%. This is attributed to the electrostatic interaction between the amine groups introduced by PEI and the anionic RY2 [ 21 , 22 ], as confirmed by the nitrogen content trend. However, when the PEI content exceeds 1.0 wt.%, the adsorption capacity tends to decrease, likely due to excessive PEI blocking micropores and mesopores, thereby reducing the effective surface area for dye adsorption [ 23 ]. This finding is consistent with the study by Hamdy et al. [ 24 ], which reported that an excess of high-molecular weight PEI can obstruct pore structures and active sites, resulting in reduced adsorption efficiency. Although the nitrogen content remains nearly constant beyond 1.0 wt.%, the adsorption capacity declines. This highlights the need for an optimal PEI content to prevent pore blockage and polymer aggregation [ 25 ]. Therefore, 1.0 wt.% PEI provides the optimal tradeoff between functional group availability and accessible surface area for RY2 adsorption. Influence of Stirring Speed The effect of stirring speed during the impregnation of 1% PEI/PAC-800 on RY2 adsorption capacity is shown in Fig. 1 c. The highest adsorption capacity was observed at 0 rpm; however, the overall impact of stirring speed on performance was limited. Static impregnation without mixing may lead to issues with reproducibility and non-uniform polymer distribution. In contrast, stirring at 40 rpm provided similar adsorption capacity while ensuring uniform dispersion, making it a more practical and reliable condition. Therefore, 40 rpm was selected as the optimal condition, considering adsorption performance, reproducibility, and experimental stability. Summary of Optimal Modification Conditions Under the conditions studied, the highest RY2 adsorption capacity was achieved with a PEI molecular weight of 800 g mol − 1 , a PEI content of 1.0 wt.%, and a stirring speed of 40 rpm. This optimal performance results from a well-balanced combination of sufficient functional group density (i.e., available amine groups), effective pore accessibility with minimal steric hindrance, and adequate mass-transfer efficiency due to proper mixing. The decline in adsorption observed at higher PEI molecular weights and contents highlights the importance of avoiding excessive steric hindrance and pore blockage during the design of polymer-modified adsorbents. Characterization The BET analysis results (Fig. 2 a–b) show that although the specific surface area of PAC decreased significantly after PEI impregnation, the adsorption capacity of 1% PEI/PAC-800 improved remarkably (Fig. 1 a). While activated carbon’s surface area typically governs its adsorption performance by providing accessible active sites, this outcome highlights that surface chemistry can also play a dominant role. A similar phenomenon has been reported by Bai et al. [ 25 ], who observed enhanced CO 2 capture using PEI-impregnated resins despite surface area reduction. The pore size distribution (Fig. 2 c–d) helps explain this behavior. For 1% PEI/PAC-800, pores in the 4–8 nm range nearly disappeared, likely due to blockage by the impregnated PEI. This is consistent with the molecular length of PEI (M w = 800 g mol − 1 ), whose longest segment is approximately 2.7 nm (Scheme 1 ). While smaller PEI chains may partially penetrate mesopores, their branched structure can cause pore constriction rather than complete occlusion, thereby altering the porous architecture. Nevertheless, the introduced amine groups serve as new active sites for dye uptake, enhancing adsorption through electrostatic attraction in addition to physical adsorption. Hence, the net effect of PEI loading is a trade-off: reduced surface area but increased functional group density. In summary, the decreased surface area caused by partial pore blockage is offset by the introduction of PEI-derived amine groups, which provide additional adsorption sites. The balance between structural modification and chemical functionality contributes to the superior performance of 1% PEI/PAC-800. These findings are in agreement with the work of Xu et al. [ 26 ] on PEI-modified mesoporous materials, where dual physical and chemical adsorption mechanisms were found to synergistically enhance performance. FTIR spectroscopy (Fig. 3 ) provides further evidence of successful PEI grafting. The raw PAC shows a broad O–H stretching band at 3000–3500 cm − 1 , corresponding to surface hydroxyl groups, along with peaks at 1613 cm − 1 (C = O stretching) and 1166 cm − 1 (C–O stretching) due to oxidation during activation [ 27 ]. After PEI modification, the broad band in the 3000–3500 cm − 1 region shifts and overlaps with N–H stretching vibrations, indicating the presence of amine groups. Additionally, a distinct peak at 1541 cm − 1 corresponds to N–H bending, further confirming PEI incorporation [ 28 ]. The reduced intensity of the O–H band suggests that some surface hydroxyls may have reacted with or been blocked by PEI. SEM and EDS analyses were conducted to examine changes in surface morphology and elemental composition (Fig. S2). Both raw PAC and 1% PEI/PAC-800 exhibit irregular, porous structures characteristic of wood-based activated carbon [ 29 ]. Following PEI impregnation, the surface became slightly smoother, though the overall morphology remained similar. EDS results showed that raw PAC consisted primarily of carbon with trace oxygen, while 1% PEI/PAC-800 exhibited clear nitrogen signals, attributed to amine groups from PEI (Fig. S3–S4), confirming successful chemical modification. After RY2 adsorption, the surface of the loaded 1% PEI/PAC-800 appeared rougher (Fig. 4 ), suggesting dye molecule attachment. EDS spectra of the RY2-loaded sample revealed the presence of sulfur and chlorine, alongside carbon, oxygen, and nitrogen. These elements originate from the RY2 dye, validating its successful adsorption onto the PEI-impregnated PAC. Collectively, these results demonstrate that PEI impregnation introduces functional groups that not only modify surface chemistry but also significantly enhance dye adsorption performance. Effect of pH Figure 5 a depicts the effect of pH on the adsorption of RY2 by raw PAC and 1% PEI/PAC-800. Compared to PAC, 1% PEI/PAC-800 showed a significant change in the adsorption of RY2 with pH. At pH 2, 1% PEI/PAC-800 has an adsorption capacity of 448.2 mg/g, approximately 5.6 times higher than that of raw PAC (79.5 mg/g). However, the adsorption capacity drops sharply to 130.1 mg/g at pH 4, and further decreases to 56.2 mg/g above pH 7. In contrast, raw PAC maintains a relatively stable adsorption capacity in the range of 60–80 mg/g across all pH levels, albeit at a lower performance. This strong pH sensitivity of 1% PEI/PAC-800 is closely related to its surface charge characteristics, as illustrated in the zeta potential analysis (Fig. 5 b). At pH 2, its surface exhibits a high positive zeta potential (+ 52.6 mV) due to the protonation of amine groups (–NH 3 + ), which facilitates strong electrostatic attraction with anionic dye molecules. As the pH increases, the surface charge decreases steadily, approaching neutrality at around pH 10 and becoming negative at pH 12 (–36.9 mV), indicating a reversal in surface charge. The point of zero charge (pH pzc ) is determined to be 10.1, which is similar to previous studies on PEI-based materials (~ 10.8) [ 30 ]. The diminished surface charge at higher pH levels weakens electrostatic interactions, resulting in lower dye adsorption efficiency. Raw PAC exhibits a pH-dependent surface charge behavior, being slightly positive under acidic conditions and increasingly negative with rising pH. However, its surface potential is significantly lower than that of 1% PEI/PAC-800, reflecting much weaker electrostatic interaction with anionic dye molecules. Consequently, RY2 adsorption by raw PAC is primarily driven by physical mechanisms such as π–π stacking, hydrophobic interactions, and micropore diffusion, which accounts for its relatively consistent adsorption capacity across the pH range [ 31 ]. In summary, 1% PEI/PAC-800 exhibits enhanced dye adsorption under acidic conditions due to strong electrostatic attraction from its highly positive surface charge. However, its performance diminishes at higher pH due to progressive deprotonation of surface amines. These results suggest that PEI-impregnated PAC is particularly effective for dye removal in acidic wastewater, although further surface modifications may be necessary to maintain performance under neutral or alkaline conditions. Adsorption Isotherms and Modeling Adsorption isotherms were conducted to evaluate the adsorption capacity and mechanism of raw PAC and 1% PEI/PAC-800 for RY2 removal. The experimental data were analyzed by fitting to both the Langmuir and Freundlich models, which represent different adsorption mechanisms based on surface homogeneity (Table 1 and Fig. 6 a). The Langmuir model assumes monolayer adsorption on homogeneous surface with identical binding sites and no interactions between adsorbed molecules [ 32 ]. The Langmuir equation is represented as: Table 1 Isotherm model parameters for RY2 adsorption onto activated carbons. Adsorbent Langmuir Freundlich q max (mg g − 1 ) b L (L mg − 1 ) R 2 K F (L g − 1 ) n R 2 Raw PAC 64.13 0.781 0.982 28.66 6.652 0.906 1% PEI/PAC-800 477.02 0.692 0.906 186.98 5.870 0.662 $$\:{q}_{e}=\frac{{q}_{max}{b}_{L}{C}_{e}}{1+{b}_{L}{C}_{e}}$$ 3 where q e (mg g − 1 ) is the amount of adsorbate adsorbed per unit weight of adsorbent, C e (mg L − 1 ) is the equilibrium concentration of the adsorbate, q max (mg g − 1 ) is the maximum adsorption capacity, and b L (L mg − 1 ) is the Langmuir constant related to the affinity of binding sites. In contrast, the Freundlich model describes multilayer adsorption on heterogeneous surfaces with varying adsorption energies. It is more applicable when the surface exhibits a non-uniform distribution of adsorption heat and site affinity. The Freundlich equation is expressed as: $$\:{q}_{e}={K}_{F}{C}_{e}^{1/n}$$ 4 where K F ((mg g − 1 ) (L mg − 1 ) 1/ n ) is the Freundlich constant indicative of adsorption capacity, and 1/ n is a measure of adsorption intensity or surface heterogeneity. For raw PAC, the Langmuir model provided an excellent fit ( R 2 = 0.982), yielding a maximum adsorption capacity ( q max ) of 64.13 mg g − 1 and a Langmuir constant ( b L ) of 0.781. The Freundlich model showed moderate agreement ( R 2 = 0.906), with K F = 28.66 and 1/ n = 0.1503, indicating relatively low adsorption intensity. In the case of 1% PEI/PAC-800, the Langmuir model demonstrated a superior fit ( R 2 = 0.906), with a significantly higher q max = 477.02 mg g − 1 and b L = 0.692, reflecting favorable and reversible binding. Although the Freundlich model showed a higher K F = 186.98, it was not suitable for fitting the 1% PEI/PAC-800 due to the low R 2 value (0.662). These results confirm that monolayer adsorption dominates both adsorbents and that the Langmuir model more accurately describes their behavior, particularly for the PEI-impregnated PAC. The enhanced adsorption performance of 1% PEI/PAC-800 can be attributed to introducing amine groups through PEI impregnation, which enables strong electrostatic and chemical interactions with anionic dye molecules. The notably higher q max and K F values of 1% PEI/PAC-800 reaffirm that PEI impregnation substantially enhances both the adsorption capacity and binding affinity by increasing the number of active sites and promoting stronger interactions with RY2. Notably, as shown in Table 2 , the maximum adsorption capacity of 1% PEI/PAC-800 (477.01 mg g − 1 ) outperforms many other reported adsorbents, including commercial activated carbon (Calgon, 209.5 mg g − 1 ) and a variety of biomass-based adsorbents [ 28 , 33 – 38 ]. While PEI/APTES-MWCNT demonstrates an even higher adsorption capacity (742.4 mg g − 1 ), the synthesis process is much more complex, requiring several steps [ 39 ]. In contrast, the simple PEI impregnation process employed here offers an efficient, cost-effective route to high-performance adsorbents suitable for large-scale wastewater remediation. Table 2 Comparison of maximum adsorption capacities ( q max ) for RY2 on various adsorbent materials. Adsorbent q max (mg g − 1 ) Ref. Polyethylenimine modified calcium silicate hydrate 235.0 Kang et al., 2023a Commercial activated carbon (Calgon) 209.5 Al-Degs et al., 2008 Activated sludge 333.3 Aksu, 2001 Corynebacterium glutamicum biomass 178.5 Won and Yun, 2008 Polysulfone/bacterial biomass composite fiber 153.2 Park et al., 2017 Magnetic carbon composite 112.6 Mello et al., 2024 Immobilized Gibberella fujikuroi on maize tassel biomatrix 90.0 Celik et al., 2024 Polyethylenimine-3-aminopropyltriethoxysilane-MWCNT 742.4 Wang and Won, 2023 Raw PAC 64.13 This study 1% PEI/PAC-800 477.02 This study Adsorption Kinetics and Modeling The adsorption kinetics of RY2 onto raw PAC and 1% PEI/PAC-800 were investigated to evaluate adsorption mechanisms and rate behaviors using pseudo-first-order and pseudo-second-order models (Table 3 and Fig. 6 b). The kinetic equations are expressed as follows: Table 3 Kinetic model parameters for RY2 adsorption onto activated carbons. Adsorbent Pseudo-first-order Pseudo-second-order q 1 (mg g − 1 ) k 1 (L min − 1 ) R 2 q 2 (mg g − 1 ) k 2 (g mg − 1 min − 1 ) h (mg g − 1 min − 1 ) R 2 Raw PAC 68.62 1.857 0.704 70.72 0.0374 187.02 0.774 1% PEI/PAC-800 376.18 0.105 0.767 397.39 0.0005 78.96 0.849 Pseudo-first-order model: \(\:{\text{l}\text{n}(q}_{e}-{q}_{t})=ln{q}_{e}-{k}_{1}t\) (5) Pseudo-second-order model: \(\:\frac{t}{{q}_{t}}=\frac{1}{{k}_{2}{q}_{e}^{2}}+\frac{t}{{q}_{e}}\) (6) where q e and q t (mg g − 1 ) are the amount of dye adsorbed at equilibrium and time t , respectively, k 1 (min − 1 ) is the pseudo-first-order rate constant, and k 2 (g mg − 1 min − 1 ) is the pseudo-second-order rate constant. Fitting to the pseudo-first-order model yielded an R 2 value of 0.704 for raw PAC with a theoretical capacity ( q e ) of 68.62 mg/g and k 1 = 1.857 min − 1 , while 1% PEI/PAC-800 showed a slightly higher R 2 of 0.767 with q e = 376.18 mg g − 1 and k 1 = 0.105 min − 1 . Although 1% PEI/PAC-800 exhibited significantly higher capacity, the lower rate constant suggests slower initial uptake. In contrast, the pseudo-second-order model provided better correlation, with R 2 values of 0.774 and 0.849 for raw PAC and 1% PEI/PAC-800, respectively. The estimated equilibrium capacities were 70.72 and 397.39 mg g − 1 , while the corresponding k 2 ​ values were 0.0374 and 0.0005 g mg − 1 min − 1 . These results indicate that the adsorption kinetics are better described by the pseudo-second-order model. Although pseudo-second-order kinetics are frequently linked to chemisorption, the dominant mechanism in this study is better attributed to site-specific electrostatic interactions between the anionic dye and the protonated amine groups introduced by PEI. The initial adsorption rate ( h ) was further evaluated using the following relation: $$\:h={k}_{2}{q}_{e}^{2}$$ 7 The calculated values of h were 187.02 mg g − 1 min − 1 for raw PAC and 78.96 mg g − 1 min − 1 for 1% PEI/PAC-800. Although raw PAC exhibited a higher initial uptake rate, its overall adsorption capacity remained low. In contrast, the PEI-modified adsorbent displayed a slower rate but substantially higher capacity, underscoring the trade-off between kinetic accessibility and binding affinity. A detailed comparison of kinetic behavior between raw PAC and 1% PEI/PAC-800 illustrates the interplay between pore structure and surface functionality. As shown in Table 4 , raw PAC, characterized by an extremely high specific surface area (1112.7 m 2 g − 1 ) and dominant microporous features (Horvath–Kawazoe median pore width = 0.77 nm), exhibited a rapid initial adsorption rate but limited overall uptake. This limitation can be attributed to the mismatch between the narrow micropores and the bulky molecular size of RY2 (Mw = 831.02 g mol − 1 ), which impedes internal diffusion and restricts adsorption to external surfaces or minor fraction of accessible mesopores. Notably, the external surface area of raw PAC was negligible, indicating that most of the surface was confined within micropores inaccessible to large dye molecules. On the other hand, 1% PEI/PAC-800 exhibited a markedly higher adsorption capacity despite a reduced adsorption rate. The enhancement is primarily ascribed to the incorporation of abundant protonated amine groups that enable strong electrostatic interactions with the anionic dye. Moreover, the external surface area of 1% PEI/PAC-800 (66.4 m 2 g − 1 ) was significantly greater than that of raw PAC, facilitating effective surface binding even in the absence of deep pore penetration. However, the impregnation of PEI also partially blocked or narrowed internal pore pathways, thereby hindering dye diffusion and leading to lower rate constants. This trade-off underscores the balance between surface functionality and pore accessibility in determining adsorption kinetics and capacity. Table 4 Comparison of BET surface area and pore structure parameters for raw PAC and 1% PEI/PAC-800. Property Raw PAC 1% PEI/PAC-800 BET surface area (m 2 g − 1 ) 1112.8 690.1 Langmuir surface area (m 2 g − 1 ) 1370.6 830.2 Micropore area (m 2 g − 1 ) 1261.5 623.7 Micropore volume (cm 3 g − 1 ) 0.4144 0.2569 External surface area (m 2 g − 1 ) - 66.4 BJH pore volume (1.7–300 nm, cm 3 g − 1 ) 0.0802 0.0534 BJH average pore diameter (nm) 3.27 3.26 H-K median pore width (nm) 0.77 0.7722 Adsorption average pore diameter (BET, nm) 1.78 1.75 In conclusion, kinetic modeling reveals that 1% PEI/PAC-800 achieves high adsorption capacity through electrostatically driven, site-specific uptake. While the adsorption rate is affected by physical diffusion barriers, the enhanced surface affinity compensates for this limitation. These findings demonstrate that PEI-functionalized activated carbon is a viable candidate for the efficient removal of bulky anionic dyes from aqueous media, despite diffusion limitations. Reusability and Desorption Behavior To evaluate the adsorption–desorption behavior of 1% PEI/PAC-800, three consecutive adsorption–desorption cycles were conducted using RY2 as a model anionic dye. As shown in Fig. 7 , the adsorbent exhibited excellent performance during the first cycle, with a maximum adsorption amount of approximately 12.8 mg and a desorption amount of 9.9 mg. The adsorption efficiency reached nearly 100%, and the desorption efficiency was as high as 83.0%, indicating strong electrostatic interactions and the presence of desorbable surface-bound species. In the second and third cycles, the adsorption capacity declined sharply to 1.85 mg and 1.23 mg, respectively. This decrease is attributed to the partial detachment or depletion of the PEI layer during the first desorption cycle. Despite this decline, such performance degradation is not a critical limitation for powdered activated carbon (PAC)-based systems, since PAC is primarily used in batch-mode processes and is typically discarded after a single use due to its fine particle size and low recoverability [ 40 ]. What is particularly noteworthy in this study is the high desorption efficiency observed in the first cycle. Unlike conventional PAC, which often shows poor desorption behavior, 1% PEI/PAC-800 enables the effective release of adsorbed species, thereby facilitating post-adsorption treatment. This feature is especially advantageous when targeting hazardous pollutants or valuable species such as precious metal ions, which may be recovered from the spent adsorbent through desorption prior to disposal. Therefore, although 1% PEI/PAC-800 may not be suitable for repeated reuse, its high single-use performance and desorption capability offer practical benefits for selective separation and recovery applications in environmental and resource management. Conclusions This study evaluated the adsorption performance of PEI-impregnated powdered activated carbon (PAC) for removing the anionic dye RY2 from aqueous solutions. The 1% PEI/PAC-800 sample achieved a maximum adsorption capacity of 477.02 mg/g, about 7.4 times higher than that of raw PAC. Despite a reduction in surface area after PEI modification, the introduced amine groups enhanced electrostatic interactions under acidic conditions, improving adsorption efficiency. Kinetic analysis showed that the process followed a pseudo-second-order model, indicating site-specific electrostatic interactions between the dye and protonated amine groups. Although adsorption capacity was significantly enhanced, the low rate constant suggests limited initial uptake due to diffusion constraints. Compared to microporous PAC like SPS-100, the PEI-modified adsorbent offered better dye accessibility and uptake. While reusability was limited after the first cycle, the high initial desorption efficiency and simple preparation process make the material suitable for batch-mode dye removal. In addition, the ability to release adsorbed species after use suggests potential for downstream treatment or selective separation before disposal. Declarations Conflict of Interest All the authors declared that there are no conflicts of interest. Author Contributions Su Bin Kang: Conceptualization, Investigation, Formal analysis, Methodology, Data curation, Writing – original draft; Byeong-Chan Min: Formal analysis, Methodology, Data curation, Writing – review & editing; Gwang-Il Ko: Formal analysis, Methodology; Li Yong: Formal analysis, Methodology; Yeoung-Sang Yun: Conceptualization, Funding acquisition, Supervision, Writing – review & editing; Sung Wook Won: Conceptualization, Funding acquisition, Supervision, Writing – review & editing. Acknowledgements This work was supported by the Technology Development Program (S3366606), funded by the Ministry of SMEs and Startups (MSS) and partly by the Technology development project to improve secondary battery circulation usability (Development of pollutants reduction technology generated in the lithium ion batteries recycling process) through the Korea Environmental Industry & Technology Institute funded by the Ministry of Environment (RS-2024-00345911). 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Molecular structure of branched polyethylenimine (M w = 800), highlighting the longest linear segment. Cite Share Download PDF Status: Published Journal Publication published 01 Sep, 2025 Read the published version in Korean Journal of Chemical Engineering → Version 1 posted Reviewers agreed at journal 09 Jun, 2025 Reviewers invited by journal 09 Jun, 2025 Editor assigned by journal 02 Jun, 2025 First submitted to journal 29 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6780880","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":468356363,"identity":"c7272039-5017-4f0a-beaf-c4e5cf2f14e5","order_by":0,"name":"Sung Wook Won","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYNCCAwxyMKYB0VqMSdeS2EC0FvkZuYdf85w5nD4/useA4UcNg7F5AwEtBjfy0qx5bhzO3XjnjAFjzzEGM5kDhLRI5JgZ83y4nbtxRo4BA28Dg40EYYdBtKQbArUw/iVGC8ONHOPHPDduJ8hL5BgwA20xI6jF4MwbM8Y5Z/4bbpBIKzgsc0zCmLDD2nOMP7w5liYvPyN548M3NTaGMwg6jIGBDWyuwQFQ9DAQ9gkIMH8AW9dAlOJRMApGwSgYiQAAYNQ+sCXLN3MAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-8858-233X","institution":"Gyeongsang National University College of Marine Science","correspondingAuthor":true,"prefix":"","firstName":"Sung","middleName":"Wook","lastName":"Won","suffix":""},{"id":468356364,"identity":"118a7097-efc7-490b-bce0-882aa4f658d1","order_by":1,"name":"Su Bin Kang","email":"","orcid":"","institution":"Jeonbuk National University","correspondingAuthor":false,"prefix":"","firstName":"Su","middleName":"Bin","lastName":"Kang","suffix":""},{"id":468356365,"identity":"15d4e5cf-5667-424b-b00f-fe05665cb056","order_by":2,"name":"Byeong-Chan Min","email":"","orcid":"","institution":"Gyeongsang National University","correspondingAuthor":false,"prefix":"","firstName":"Byeong-Chan","middleName":"","lastName":"Min","suffix":""},{"id":468356366,"identity":"23cb594e-86f0-4239-a9af-e299b2225f5e","order_by":3,"name":"Kwang-Il Go","email":"","orcid":"","institution":"Gyeongsang National University","correspondingAuthor":false,"prefix":"","firstName":"Kwang-Il","middleName":"","lastName":"Go","suffix":""},{"id":468356367,"identity":"1b9d650a-a674-4daf-9dd1-f1eae46a8fe4","order_by":4,"name":"Li Yong","email":"","orcid":"","institution":"Gyeongsang National University","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Yong","suffix":""},{"id":468356368,"identity":"8d2ae0ea-aece-4933-9f9e-44737dd3a37d","order_by":5,"name":"Yeoung-Sang Yun","email":"","orcid":"","institution":"Jeonbuk National University","correspondingAuthor":false,"prefix":"","firstName":"Yeoung-Sang","middleName":"","lastName":"Yun","suffix":""}],"badges":[],"createdAt":"2025-05-30 04:26:59","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6780880/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6780880/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11814-025-00548-4","type":"published","date":"2025-09-01T15:57:29+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":84369004,"identity":"289c1736-5e67-46a2-acfd-6ef7f249be92","added_by":"auto","created_at":"2025-06-11 06:49:43","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":58052,"visible":true,"origin":"","legend":"\u003cp\u003eEffects of (a) PEI molecular weight, (b) PEI content, and (c) stirring speed on the adsorption of RY2. The experimental conditions were: PEI/PAC-800, \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = 301.4 mg L\u003csup\u003e-1\u003c/sup\u003e, pH = 2, and contact time = 7 days.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/06e611c3817ca7ee24ee0aba.jpg"},{"id":84368815,"identity":"dc1fa81c-68e7-4635-9b7f-bbda1e63b91c","added_by":"auto","created_at":"2025-06-11 06:41:43","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":60902,"visible":true,"origin":"","legend":"\u003cp\u003e(a, b) Nitrogen adsorption-desorption isotherms and (c, d) pore size distributions of raw PAC and 1% PEI/PAC-800, respectively.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/44697da834cfdf7a5551e442.jpg"},{"id":84368855,"identity":"6d37e675-029e-4530-9ea3-345e01b565ed","added_by":"auto","created_at":"2025-06-11 06:41:46","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":40921,"visible":true,"origin":"","legend":"\u003cp\u003eFTIR spectra of raw PAC and 1% PEI/PAC-800, confirming the presence of functional groups introduced by PEI impregnation.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/65baee0971fd028c7f7ea1db.jpg"},{"id":84368816,"identity":"c523f830-31ed-49a3-9752-b7b9c5207cc6","added_by":"auto","created_at":"2025-06-11 06:41:43","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":131709,"visible":true,"origin":"","legend":"\u003cp\u003eSEM image and EDS analysis of RY2-loaded 1% PEI/PAC-800: (a) surface morphology; (b) EDS spectrum and elemental composition; (c–g) elemental mapping of C, N, O, S, and Cl.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/59341d2f7b32b3cdf17b1490.jpg"},{"id":84368822,"identity":"2585bc9c-7bdc-4431-9fdf-532aca1456f2","added_by":"auto","created_at":"2025-06-11 06:41:43","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":28377,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of pH on (a) RY2 adsorption capacity and (b) zeta potential of raw PAC and 1% PEI/PAC-800 (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = 485.59 mg L\u003csup\u003e-1\u003c/sup\u003e, contact time = 7 days).\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/c69525118989c64d6ce4ae9f.jpg"},{"id":84370088,"identity":"f97c20f0-7340-48a3-9783-c9de8dea245e","added_by":"auto","created_at":"2025-06-11 07:05:43","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":45008,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Adsorption isotherms of RY2 on raw PAC and 1% PEI/PAC-800 fitted to the Langmuir and Freundlich models (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = 30−1,000 mg L\u003csup\u003e-1\u003c/sup\u003e, pH = 2, contact time = 7 days). (b) Adsorption kinetics fitted to pseudo-first-order and pseudo-second-order models (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e = 504.25 mg L\u003csup\u003e-1\u003c/sup\u003e, pH = 2).\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/ccab76f201d51b83d8f423be.jpg"},{"id":84368824,"identity":"8f75eca4-7589-4c6e-9b01-6d8f9b9b57b9","added_by":"auto","created_at":"2025-06-11 06:41:44","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":45777,"visible":true,"origin":"","legend":"\u003cp\u003eReusability of 1% PEI/PAC-800 over three adsorption−desorption cycles: Comparison of adsorption/desorption amounts and corresponding efficiencies.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/c2d7c073eeff7430af3a9e02.jpg"},{"id":90828019,"identity":"08346f91-01cd-4ae4-a012-d13597a2af5d","added_by":"auto","created_at":"2025-09-08 16:05:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1396753,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/e8936b81-416d-4e8a-9a11-ee3415ec4184.pdf"},{"id":84368818,"identity":"9c2aaffb-f122-4973-9c3a-f398e6a34491","added_by":"auto","created_at":"2025-06-11 06:41:43","extension":"jpg","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":44821,"visible":true,"origin":"","legend":"","description":"","filename":"scheme1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/b76cd9f4c056837c03ec165d.jpg"},{"id":84369009,"identity":"86d177f6-23b1-47e1-8cc0-186994794746","added_by":"auto","created_at":"2025-06-11 06:49:44","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":2433262,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eScheme 1.\u003c/strong\u003e Molecular structure of branched polyethylenimine (M\u003csub\u003ew\u003c/sub\u003e = 800), highlighting the longest linear segment.\u003c/p\u003e","description":"","filename":"05.SupplementaryInformationforKJChE.docx","url":"https://assets-eu.researchsquare.com/files/rs-6780880/v1/ce5e9d83b65abb995a59c064.docx"}],"financialInterests":"","formattedTitle":"Polyethylenimine-impregnated powdered activated carbon for efficient removal of Reactive Yellow 2 from aqueous solutions","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe textile dyeing industry is a major contributor to industrial water pollution, accounting for approximately 20% of global wastewater discharge and consuming nearly 10% of the world\u0026rsquo;s freshwater resources [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Among various dyes, reactive dyes such as Reactive Yellow 2 (RY2) are widely used due to their vivid color and strong bonding with textile fibers. However, their high solubility and chemical stability make them resistant to biodegradation, leading to persistent contamination in aquatic environments [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The discharge of dye-laden wastewater can cause eutrophication, oxygen depletion, and long-term ecological risks, including bioaccumulation and toxicity [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Even after conventional treatment, residual color often remains, necessitating additional treatment steps and increasing operational costs [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eVarious methods such as coagulation, biological degradation, and membrane separation have been employed for dye removal, but they often suffer from high energy consumption, low selectivity, and the generation of secondary pollutants such as sludge [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Adsorption has gained attention as an attractive alternative due to its simplicity, effectiveness, and minimal by-product formation [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Among adsorbents, powdered activated carbon (PAC) is widely used owing to its large surface area and broad adsorption range. However, raw PAC shows limited performance for anionic dyes due to its negatively charged surface under neutral to basic pH and the lack of electrostatically interactive functional groups [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Its fine particle size also hampers recovery and reuse, limiting its practical applicability in large-scale processes [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo address these limitations, surface modification of PAC with functional polymers has been widely investigated. Among numerous polymers, polyethylenimine (PEI), a highly branched polyamine, introduces amine-rich functional groups that become protonated under acidic conditions, generating positively charged sites for electrostatic interactions with anionic dyes [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. While various studies have demonstrated the potential of PEI-modified adsorbents, many have used biomass-derived or non-powdered substrates, reported moderate adsorption capacities (\u0026lt;\u0026thinsp;300 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), or required complex multi-step modifications that hinder scalability [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. In addition, essential parameters such as PEI molecular weight, loading concentration, and mixing conditions during impregnation have rarely been systematically optimized.\u003c/p\u003e \u003cp\u003eIn this study, we report a simple, one-step impregnation method for fabricating PEI-impregnated PAC (PEI/PAC) using SPS-100, a commercially available powdered activated carbon. The modification was designed to enhance the electrostatic affinity of PAC toward anionic dyes by introducing amine functional groups. Key variables, including PEI molecular weight, PEI content, and stirring speed, were systematically optimized to obtain an effective adsorbent. The resulting material was evaluated in terms of dye adsorption performance, desorption efficiency, and reusability under batch-mode conditions.\u003c/p\u003e \u003cp\u003eOverall, this work presents a practical and tunable surface modification strategy for PAC and aims to provide insights into the rational design of amine-functionalized adsorbents for enhanced dye removal in wastewater treatment systems.\u003c/p\u003e"},{"header":"Experimental","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eMaterials\u003c/h2\u003e \u003cp\u003eSPS-100 was supplied by Samchully Activated Carbon Co., Ltd. (Geumsan, Korea). Branched PEI with a molecular weight (M\u003csub\u003ew\u003c/sub\u003e) of 800 (98%) and RY2 (dye content\u0026thinsp;\u0026ge;\u0026thinsp;60%) were purchased by Sigma-Aldrich Korea Ltd. (Seoul, Korea). Branched PEIs of different molecular weights (M\u003csub\u003ew\u003c/sub\u003e = 600, 1200, 10000 and 70000, 98\u0026ndash;100%) were provided by Nippon Shokubai Co. Ltd. (Osaka, Japan). HCl and NaOH were offered by Daejung Chemicals \u0026amp; Metals Co., Ltd. (Siheung, Korea).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eFabrication of PEI-impregnated PAC\u003c/h3\u003e\n\u003cp\u003eVarious PEI/PACs were prepared by a onestep impregnation of 2 g PAC in 50 mL aqueous PEI solution. All experiments were performed in triplicate (n\u0026thinsp;=\u0026thinsp;3), and results are reported as mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard error. Impregnation parameters were selected based on preliminary experiments to optimize polymer\u0026ndash;carbon interactions.\u003c/p\u003e \u003cp\u003eThree variables were investigated. First, the effect of PEI molecular weight was assessed by reacting PAC with 5 wt.% PEI solutions of different chain lengths (600, 800, 1200, 10000 and 70000 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) at 160 rpm and 25\u0026deg;C for 72 h to determine how polymer chain length influences pore accessibility. Second, the impact of PEI content was evaluated by treating PAC with PEI (M\u003csub\u003ew\u003c/sub\u003e = 800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) solutions at 0.1, 1, 5, and 10 wt.% under the same stirring and temperature conditions for 72 h to establish the optimal polymer loading. Third, masstransfer effects were examined by impregnating PAC in a 1 wt.% PEI solution (M\u003csub\u003ew\u003c/sub\u003e = 800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) at 25\u0026deg;C for 72 h under stirring speeds of 0, 40, 80, 120, 160, and 200 rpm.\u003c/p\u003e \u003cp\u003eAfter impregnation, each suspension was centrifuged at 2000 rpm for 10 min, washed three times with distilled water, and filtered. The wet solids were freezedried at \u0026minus;\u0026thinsp;50\u0026deg;C under 0.1 mbar for 24 h. Optimal conditions (PEI M\u003csub\u003ew\u003c/sub\u003e = 800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, PEI content\u0026thinsp;=\u0026thinsp;1 wt.%, stirring\u0026thinsp;=\u0026thinsp;40 rpm) were selected based on the highest adsorption capacity in the evaluation of each influencing factor, and the sample prepared under this optimal condition was named 1% PEI/PAC-800 and was used for all subsequent adsorption experiments.\u003c/p\u003e\n\u003ch3\u003eCharacterizations\u003c/h3\u003e\n\u003cp\u003eA Fourier transform infrared spectrometer (FT-IR, FT/IR-8X, Jasco, Japan) was used to record the FT-IR spectra of PAC and PEI/PAC in the range of 4000\u0026ndash;500 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. A 3Flex surface characterization analyzer (Micromeritics, USA) was used to collect the nitrogen adsorption-desorption isotherms of raw PAC and 1% PEI/PAC-800. A Field emission scanning electron microscope with energy dispersive spectroscopy (FE-SEM/EDS, JSM-7610F, Jeol, Japan) was used to record the surface morphologies of activated carbons. A zeta potential analyzer (ELSZ-2000, Otsuka, Japan) was used to analyze the zeta potential values of raw PAC and 1% PEI/PAC-100 at different pH values.\u003c/p\u003e\n\u003ch3\u003eAdsorption Experiments\u003c/h3\u003e\n\u003cp\u003eThe stock solution of RY2 was prepared according to our previous method [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In all batch adsorption experiments, 30 mg of adsorbent and 30 mL of RY2 solution were mixed in a 50-mL conic tube and incubated in a shaker at 160 rpm. Unless otherwise noted, the pH, shaking speed, and temperature for all adsorption experiments were 2, 160 rpm, and 25\u0026deg;C. The pH edge experiments were conducted at pH 2\u0026ndash;12 for 7 days with 485.59 mg L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e of RY2, and kinetic adsorption experiments were carried out at 504.25 mg L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e of RY2. The isothermal adsorption experiments were performed in the RY2 concentration range of 30 to 1000 mg L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The concentration of RY2 was measured using a UV-Vis spectrophotometer (X-ma 3000 pc, Human, Korea). The dye uptake, \u003cem\u003eq\u003c/em\u003e (mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) was calculated using the following equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:q=\\frac{{C}_{i}{V}_{i}-{C}_{f}{V}_{f}}{m}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e (mg L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e (L) are the RY2 concentration and the solution volume before and after adsorption, and \u003cem\u003em\u003c/em\u003e (g) is the weight of the adsorbent.\u003c/p\u003e\n\u003ch3\u003eReusability Studies\u003c/h3\u003e\n\u003cp\u003eFirst, 30 mg of adsorbent and 30 mL of RY2 (100 mg L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) were mixed at 25\u0026deg;C for 4 h to obtain RY2-loaded adsorbent. After washing three times with distilled water, the RY2-loaded adsorbent was eluted with 30 mL of NaOH solution (0.01 mol L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) for 2 h, and the adsorption-desorption was repeated three times to confirm the recyclability in removing RY2. The RY2 concentration was measured by UV-Vis spectrophotometer, and the desorption rate was calculated by Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\text{D}\\text{e}\\text{s}\\text{o}\\text{r}\\text{p}\\text{t}\\text{i}\\text{o}\\text{n}\\:\\text{r}\\text{a}\\text{t}\\text{e}\\:\\left(\\text{%}\\right)=\\frac{\\text{D}\\text{e}\\text{s}\\text{o}\\text{r}\\text{b}\\text{e}\\text{d}\\:\\text{R}\\text{Y}2\\:\\text{i}\\text{n}\\:\\text{e}\\text{a}\\text{c}\\text{h}\\:\\text{c}\\text{y}\\text{c}\\text{l}\\text{e}\\:\\left(\\text{m}\\text{g}\\right)}{\\text{A}\\text{d}\\text{s}\\text{o}\\text{r}\\text{b}\\text{e}\\text{d}\\:\\text{R}\\text{Y}2\\:\\text{i}\\text{n}\\:\\text{e}\\text{a}\\text{c}\\text{h}\\:\\text{c}\\text{y}\\text{c}\\text{l}\\text{e}\\:\\left(\\text{m}\\text{g}\\right)}\\times\\:100$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eOptimization of PEI Impregnation for Maximum RY2 Adsorption\u003c/h2\u003e \u003cp\u003eTo determine the optimal modification parameters for RY2 adsorption, raw PAC and various PEI/PACs were evaluated for three variables: PEI molecular weight, PEI content, and stirring speed during impregnation.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eInfluence of PEI Molecular Weight\u003c/h3\u003e\n\u003cp\u003eThe adsorption capacities of raw PAC and PAC modified with PEI of varying molecular weights (600, 800, 1200, 10000 and 70000 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) are compared in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea. Modification enhanced RY2 uptake in all cases; the trend in capacity was: PEI/PAC-800\u0026thinsp;\u0026gt;\u0026thinsp;PEI/PAC-600\u0026thinsp;\u0026gt;\u0026thinsp;PEI/PAC-1200\u0026thinsp;\u0026gt;\u0026thinsp;PEI/PAC-10000\u0026thinsp;\u0026asymp;\u0026thinsp;PEI/PAC-70000\u0026thinsp;\u0026gt;\u0026thinsp;raw PAC. The number following PEI/PAC indicates the PEI molecular weight. PEI of 800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e provides an optimal balance between chain length (enabling deep pore penetration) and amine-group density (maximizing electrostatic binding). Higher PEI molecular weights (\u0026ge;\u0026thinsp;1200 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) are likely to be sterically hindered, which can limit pore access and reduce the surface area with amine groups available for binding to RY2 [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In contrast, PEI-600 is unhindered but has fewer functional groups than PEI-800, resulting in a slightly reduced adsorption capacity. These results indicate an optimal PEI molecular weight around 800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e for maximizing dye uptake.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eInfluence of PEI Content\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb shows the effect of PEI content on the adsorption capacity of RY2, and the corresponding change in nitrogen content was also analyzed by EDS (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). As the PEI loading increased from 0.1 to 1.0 wt.%, the RY2 uptake increased rapidly, reaching a maximum at 1.0 wt.%. This is attributed to the electrostatic interaction between the amine groups introduced by PEI and the anionic RY2 [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], as confirmed by the nitrogen content trend. However, when the PEI content exceeds 1.0 wt.%, the adsorption capacity tends to decrease, likely due to excessive PEI blocking micropores and mesopores, thereby reducing the effective surface area for dye adsorption [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. This finding is consistent with the study by Hamdy et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], which reported that an excess of high-molecular weight PEI can obstruct pore structures and active sites, resulting in reduced adsorption efficiency. Although the nitrogen content remains nearly constant beyond 1.0 wt.%, the adsorption capacity declines. This highlights the need for an optimal PEI content to prevent pore blockage and polymer aggregation [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Therefore, 1.0 wt.% PEI provides the optimal tradeoff between functional group availability and accessible surface area for RY2 adsorption.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eInfluence of Stirring Speed\u003c/h2\u003e \u003cp\u003eThe effect of stirring speed during the impregnation of 1% PEI/PAC-800 on RY2 adsorption capacity is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec. The highest adsorption capacity was observed at 0 rpm; however, the overall impact of stirring speed on performance was limited. Static impregnation without mixing may lead to issues with reproducibility and non-uniform polymer distribution. In contrast, stirring at 40 rpm provided similar adsorption capacity while ensuring uniform dispersion, making it a more practical and reliable condition. Therefore, 40 rpm was selected as the optimal condition, considering adsorption performance, reproducibility, and experimental stability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eSummary of Optimal Modification Conditions\u003c/h2\u003e \u003cp\u003eUnder the conditions studied, the highest RY2 adsorption capacity was achieved with a PEI molecular weight of 800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, a PEI content of 1.0 wt.%, and a stirring speed of 40 rpm. This optimal performance results from a well-balanced combination of sufficient functional group density (i.e., available amine groups), effective pore accessibility with minimal steric hindrance, and adequate mass-transfer efficiency due to proper mixing. The decline in adsorption observed at higher PEI molecular weights and contents highlights the importance of avoiding excessive steric hindrance and pore blockage during the design of polymer-modified adsorbents.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eCharacterization\u003c/h2\u003e \u003cp\u003eThe BET analysis results (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea\u0026ndash;b) show that although the specific surface area of PAC decreased significantly after PEI impregnation, the adsorption capacity of 1% PEI/PAC-800 improved remarkably (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). While activated carbon\u0026rsquo;s surface area typically governs its adsorption performance by providing accessible active sites, this outcome highlights that surface chemistry can also play a dominant role. A similar phenomenon has been reported by Bai et al. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], who observed enhanced CO\u003csub\u003e2\u003c/sub\u003e capture using PEI-impregnated resins despite surface area reduction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe pore size distribution (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec\u0026ndash;d) helps explain this behavior. For 1% PEI/PAC-800, pores in the 4\u0026ndash;8 nm range nearly disappeared, likely due to blockage by the impregnated PEI. This is consistent with the molecular length of PEI (M\u003csub\u003ew\u003c/sub\u003e = 800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), whose longest segment is approximately 2.7 nm (Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). While smaller PEI chains may partially penetrate mesopores, their branched structure can cause pore constriction rather than complete occlusion, thereby altering the porous architecture. Nevertheless, the introduced amine groups serve as new active sites for dye uptake, enhancing adsorption through electrostatic attraction in addition to physical adsorption. Hence, the net effect of PEI loading is a trade-off: reduced surface area but increased functional group density.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn summary, the decreased surface area caused by partial pore blockage is offset by the introduction of PEI-derived amine groups, which provide additional adsorption sites. The balance between structural modification and chemical functionality contributes to the superior performance of 1% PEI/PAC-800. These findings are in agreement with the work of Xu et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] on PEI-modified mesoporous materials, where dual physical and chemical adsorption mechanisms were found to synergistically enhance performance.\u003c/p\u003e \u003cp\u003eFTIR spectroscopy (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) provides further evidence of successful PEI grafting. The raw PAC shows a broad O\u0026ndash;H stretching band at 3000\u0026ndash;3500 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, corresponding to surface hydroxyl groups, along with peaks at 1613 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (C\u0026thinsp;=\u0026thinsp;O stretching) and 1166 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (C\u0026ndash;O stretching) due to oxidation during activation [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. After PEI modification, the broad band in the 3000\u0026ndash;3500 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e region shifts and overlaps with N\u0026ndash;H stretching vibrations, indicating the presence of amine groups. Additionally, a distinct peak at 1541 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e corresponds to N\u0026ndash;H bending, further confirming PEI incorporation [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The reduced intensity of the O\u0026ndash;H band suggests that some surface hydroxyls may have reacted with or been blocked by PEI.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSEM and EDS analyses were conducted to examine changes in surface morphology and elemental composition (Fig. S2). Both raw PAC and 1% PEI/PAC-800 exhibit irregular, porous structures characteristic of wood-based activated carbon [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Following PEI impregnation, the surface became slightly smoother, though the overall morphology remained similar. EDS results showed that raw PAC consisted primarily of carbon with trace oxygen, while 1% PEI/PAC-800 exhibited clear nitrogen signals, attributed to amine groups from PEI (Fig. S3\u0026ndash;S4), confirming successful chemical modification.\u003c/p\u003e \u003cp\u003eAfter RY2 adsorption, the surface of the loaded 1% PEI/PAC-800 appeared rougher (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), suggesting dye molecule attachment. EDS spectra of the RY2-loaded sample revealed the presence of sulfur and chlorine, alongside carbon, oxygen, and nitrogen. These elements originate from the RY2 dye, validating its successful adsorption onto the PEI-impregnated PAC. Collectively, these results demonstrate that PEI impregnation introduces functional groups that not only modify surface chemistry but also significantly enhance dye adsorption performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eEffect of pH\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea depicts the effect of pH on the adsorption of RY2 by raw PAC and 1% PEI/PAC-800. Compared to PAC, 1% PEI/PAC-800 showed a significant change in the adsorption of RY2 with pH. At pH 2, 1% PEI/PAC-800 has an adsorption capacity of 448.2 mg/g, approximately 5.6 times higher than that of raw PAC (79.5 mg/g). However, the adsorption capacity drops sharply to 130.1 mg/g at pH 4, and further decreases to 56.2 mg/g above pH 7. In contrast, raw PAC maintains a relatively stable adsorption capacity in the range of 60\u0026ndash;80 mg/g across all pH levels, albeit at a lower performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis strong pH sensitivity of 1% PEI/PAC-800 is closely related to its surface charge characteristics, as illustrated in the zeta potential analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). At pH 2, its surface exhibits a high positive zeta potential (+\u0026thinsp;52.6 mV) due to the protonation of amine groups (\u0026ndash;NH\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e+\u003c/sup\u003e), which facilitates strong electrostatic attraction with anionic dye molecules. As the pH increases, the surface charge decreases steadily, approaching neutrality at around pH 10 and becoming negative at pH 12 (\u0026ndash;36.9 mV), indicating a reversal in surface charge. The point of zero charge (pH\u003csub\u003epzc\u003c/sub\u003e) is determined to be 10.1, which is similar to previous studies on PEI-based materials (~\u0026thinsp;10.8) [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. The diminished surface charge at higher pH levels weakens electrostatic interactions, resulting in lower dye adsorption efficiency.\u003c/p\u003e \u003cp\u003eRaw PAC exhibits a pH-dependent surface charge behavior, being slightly positive under acidic conditions and increasingly negative with rising pH. However, its surface potential is significantly lower than that of 1% PEI/PAC-800, reflecting much weaker electrostatic interaction with anionic dye molecules. Consequently, RY2 adsorption by raw PAC is primarily driven by physical mechanisms such as π\u0026ndash;π stacking, hydrophobic interactions, and micropore diffusion, which accounts for its relatively consistent adsorption capacity across the pH range [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn summary, 1% PEI/PAC-800 exhibits enhanced dye adsorption under acidic conditions due to strong electrostatic attraction from its highly positive surface charge. However, its performance diminishes at higher pH due to progressive deprotonation of surface amines. These results suggest that PEI-impregnated PAC is particularly effective for dye removal in acidic wastewater, although further surface modifications may be necessary to maintain performance under neutral or alkaline conditions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eAdsorption Isotherms and Modeling\u003c/h2\u003e \u003cp\u003eAdsorption isotherms were conducted to evaluate the adsorption capacity and mechanism of raw PAC and 1% PEI/PAC-800 for RY2 removal. The experimental data were analyzed by fitting to both the Langmuir and Freundlich models, which represent different adsorption mechanisms based on surface homogeneity (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea). The Langmuir model assumes monolayer adsorption on homogeneous surface with identical binding sites and no interactions between adsorbed molecules [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. The Langmuir equation is represented as:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eIsotherm model parameters for RY2 adsorption onto activated carbons.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAdsorbent\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eLangmuir\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eFreundlich\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e (mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e (L mg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003eF\u003c/em\u003e\u003c/sub\u003e (L g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRaw PAC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.781\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.982\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.652\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.906\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1% PEI/PAC-800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e477.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.692\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e186.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.870\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.662\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{q}_{e}=\\frac{{q}_{max}{b}_{L}{C}_{e}}{1+{b}_{L}{C}_{e}}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e (mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the amount of adsorbate adsorbed per unit weight of adsorbent, \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e (mg L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the equilibrium concentration of the adsorbate, \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e (mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the maximum adsorption capacity, and \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e (L mg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the Langmuir constant related to the affinity of binding sites. In contrast, the Freundlich model describes multilayer adsorption on heterogeneous surfaces with varying adsorption energies. It is more applicable when the surface exhibits a non-uniform distribution of adsorption heat and site affinity. The Freundlich equation is expressed as:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{q}_{e}={K}_{F}{C}_{e}^{1/n}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003eF\u003c/em\u003e\u003c/sub\u003e ((mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) (L mg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003csup\u003e1/\u003cem\u003en\u003c/em\u003e\u003c/sup\u003e) is the Freundlich constant indicative of adsorption capacity, and 1/\u003cem\u003en\u003c/em\u003e is a measure of adsorption intensity or surface heterogeneity.\u003c/p\u003e \u003cp\u003eFor raw PAC, the Langmuir model provided an excellent fit (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.982), yielding a maximum adsorption capacity (\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e) of 64.13 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and a Langmuir constant (\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e) of 0.781. The Freundlich model showed moderate agreement (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.906), with \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003eF\u003c/em\u003e\u003c/sub\u003e = 28.66 and 1/\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.1503, indicating relatively low adsorption intensity. In the case of 1% PEI/PAC-800, the Langmuir model demonstrated a superior fit (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.906), with a significantly higher \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e = 477.02 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e = 0.692, reflecting favorable and reversible binding. Although the Freundlich model showed a higher \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003eF\u003c/em\u003e\u003c/sub\u003e = 186.98, it was not suitable for fitting the 1% PEI/PAC-800 due to the low \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e value (0.662).\u003c/p\u003e \u003cp\u003eThese results confirm that monolayer adsorption dominates both adsorbents and that the Langmuir model more accurately describes their behavior, particularly for the PEI-impregnated PAC. The enhanced adsorption performance of 1% PEI/PAC-800 can be attributed to introducing amine groups through PEI impregnation, which enables strong electrostatic and chemical interactions with anionic dye molecules. The notably higher \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eK\u003c/em\u003e\u003csub\u003e\u003cem\u003eF\u003c/em\u003e\u003c/sub\u003e values of 1% PEI/PAC-800 reaffirm that PEI impregnation substantially enhances both the adsorption capacity and binding affinity by increasing the number of active sites and promoting stronger interactions with RY2.\u003c/p\u003e \u003cp\u003eNotably, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the maximum adsorption capacity of 1% PEI/PAC-800 (477.01 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) outperforms many other reported adsorbents, including commercial activated carbon (Calgon, 209.5 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and a variety of biomass-based adsorbents [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan additionalcitationids=\"CR34 CR35 CR36 CR37\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. While PEI/APTES-MWCNT demonstrates an even higher adsorption capacity (742.4 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), the synthesis process is much more complex, requiring several steps [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. In contrast, the simple PEI impregnation process employed here offers an efficient, cost-effective route to high-performance adsorbents suitable for large-scale wastewater remediation.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of maximum adsorption capacities (\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e) for RY2 on various adsorbent materials.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdsorbent\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e (mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRef.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePolyethylenimine modified calcium silicate hydrate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e235.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eKang et al., 2023a\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCommercial activated carbon (Calgon)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e209.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAl-Degs et al., 2008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eActivated sludge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAksu, 2001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCorynebacterium glutamicum\u003c/em\u003e biomass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e178.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWon and Yun, 2008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePolysulfone/bacterial biomass composite fiber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e153.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePark et al., 2017\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMagnetic carbon composite\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e112.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMello et al., 2024\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eImmobilized \u003cem\u003eGibberella fujikuroi\u003c/em\u003e on maize tassel biomatrix\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e90.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCelik et al., 2024\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePolyethylenimine-3-aminopropyltriethoxysilane-MWCNT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e742.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWang and Won, 2023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRaw PAC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThis study\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1% PEI/PAC-800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e477.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThis study\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eAdsorption Kinetics and Modeling\u003c/h2\u003e \u003cp\u003eThe adsorption kinetics of RY2 onto raw PAC and 1% PEI/PAC-800 were investigated to evaluate adsorption mechanisms and rate behaviors using pseudo-first-order and pseudo-second-order models (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb). The kinetic equations are expressed as follows:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eKinetic model parameters for RY2 adsorption onto activated carbons.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAdsorbent\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003ePseudo-first-order\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003ePseudo-second-order\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(L min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(g mg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eh\u003c/em\u003e\u003c/p\u003e \u003cp\u003e(mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRaw PAC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e68.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.857\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.704\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e70.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0374\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e187.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.774\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1% PEI/PAC-800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e376.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.767\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e397.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e78.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.849\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ePseudo-first-order model: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{l}\\text{n}(q}_{e}-{q}_{t})=ln{q}_{e}-{k}_{1}t\\)\u003c/span\u003e\u003c/span\u003e (5)\u003c/p\u003e \u003cp\u003ePseudo-second-order model: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{t}{{q}_{t}}=\\frac{1}{{k}_{2}{q}_{e}^{2}}+\\frac{t}{{q}_{e}}\\)\u003c/span\u003e\u003c/span\u003e (6)\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e (mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) are the amount of dye adsorbed at equilibrium and time \u003cem\u003et\u003c/em\u003e, respectively, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e (min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the pseudo-first-order rate constant, and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e (g mg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the pseudo-second-order rate constant.\u003c/p\u003e \u003cp\u003eFitting to the pseudo-first-order model yielded an \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e value of 0.704 for raw PAC with a theoretical capacity (\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e) of 68.62 mg/g and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.857 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, while 1% PEI/PAC-800 showed a slightly higher \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e of 0.767 with \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e = 376.18 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.105 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Although 1% PEI/PAC-800 exhibited significantly higher capacity, the lower rate constant suggests slower initial uptake. In contrast, the pseudo-second-order model provided better correlation, with \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e values of 0.774 and 0.849 for raw PAC and 1% PEI/PAC-800, respectively. The estimated equilibrium capacities were 70.72 and 397.39 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, while the corresponding \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e​ values were 0.0374 and 0.0005 g mg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. These results indicate that the adsorption kinetics are better described by the pseudo-second-order model. Although pseudo-second-order kinetics are frequently linked to chemisorption, the dominant mechanism in this study is better attributed to site-specific electrostatic interactions between the anionic dye and the protonated amine groups introduced by PEI.\u003c/p\u003e \u003cp\u003eThe initial adsorption rate (\u003cem\u003eh\u003c/em\u003e) was further evaluated using the following relation:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:h={k}_{2}{q}_{e}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe calculated values of \u003cem\u003eh\u003c/em\u003e were 187.02 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e for raw PAC and 78.96 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e for 1% PEI/PAC-800. Although raw PAC exhibited a higher initial uptake rate, its overall adsorption capacity remained low. In contrast, the PEI-modified adsorbent displayed a slower rate but substantially higher capacity, underscoring the trade-off between kinetic accessibility and binding affinity.\u003c/p\u003e \u003cp\u003eA detailed comparison of kinetic behavior between raw PAC and 1% PEI/PAC-800 illustrates the interplay between pore structure and surface functionality. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, raw PAC, characterized by an extremely high specific surface area (1112.7 m\u003csup\u003e2\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and dominant microporous features (Horvath\u0026ndash;Kawazoe median pore width\u0026thinsp;=\u0026thinsp;0.77 nm), exhibited a rapid initial adsorption rate but limited overall uptake. This limitation can be attributed to the mismatch between the narrow micropores and the bulky molecular size of RY2 (Mw\u0026thinsp;=\u0026thinsp;831.02 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), which impedes internal diffusion and restricts adsorption to external surfaces or minor fraction of accessible mesopores. Notably, the external surface area of raw PAC was negligible, indicating that most of the surface was confined within micropores inaccessible to large dye molecules. On the other hand, 1% PEI/PAC-800 exhibited a markedly higher adsorption capacity despite a reduced adsorption rate. The enhancement is primarily ascribed to the incorporation of abundant protonated amine groups that enable strong electrostatic interactions with the anionic dye. Moreover, the external surface area of 1% PEI/PAC-800 (66.4 m\u003csup\u003e2\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) was significantly greater than that of raw PAC, facilitating effective surface binding even in the absence of deep pore penetration. However, the impregnation of PEI also partially blocked or narrowed internal pore pathways, thereby hindering dye diffusion and leading to lower rate constants. This trade-off underscores the balance between surface functionality and pore accessibility in determining adsorption kinetics and capacity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of BET surface area and pore structure parameters for raw PAC and 1% PEI/PAC-800.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProperty\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRaw PAC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1% PEI/PAC-800\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBET surface area (m\u003csup\u003e2\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1112.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e690.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLangmuir surface area (m\u003csup\u003e2\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1370.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e830.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMicropore area (m\u003csup\u003e2\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1261.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e623.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMicropore volume (cm\u003csup\u003e3\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2569\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExternal surface area (m\u003csup\u003e2\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e66.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBJH pore volume (1.7\u0026ndash;300 nm, cm\u003csup\u003e3\u003c/sup\u003e g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0802\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0534\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBJH average pore diameter (nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH-K median pore width (nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.7722\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdsorption average pore diameter (BET, nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn conclusion, kinetic modeling reveals that 1% PEI/PAC-800 achieves high adsorption capacity through electrostatically driven, site-specific uptake. While the adsorption rate is affected by physical diffusion barriers, the enhanced surface affinity compensates for this limitation. These findings demonstrate that PEI-functionalized activated carbon is a viable candidate for the efficient removal of bulky anionic dyes from aqueous media, despite diffusion limitations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eReusability and Desorption Behavior\u003c/h2\u003e \u003cp\u003eTo evaluate the adsorption\u0026ndash;desorption behavior of 1% PEI/PAC-800, three consecutive adsorption\u0026ndash;desorption cycles were conducted using RY2 as a model anionic dye. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the adsorbent exhibited excellent performance during the first cycle, with a maximum adsorption amount of approximately 12.8 mg and a desorption amount of 9.9 mg. The adsorption efficiency reached nearly 100%, and the desorption efficiency was as high as 83.0%, indicating strong electrostatic interactions and the presence of desorbable surface-bound species.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the second and third cycles, the adsorption capacity declined sharply to 1.85 mg and 1.23 mg, respectively. This decrease is attributed to the partial detachment or depletion of the PEI layer during the first desorption cycle. Despite this decline, such performance degradation is not a critical limitation for powdered activated carbon (PAC)-based systems, since PAC is primarily used in batch-mode processes and is typically discarded after a single use due to its fine particle size and low recoverability [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhat is particularly noteworthy in this study is the high desorption efficiency observed in the first cycle. Unlike conventional PAC, which often shows poor desorption behavior, 1% PEI/PAC-800 enables the effective release of adsorbed species, thereby facilitating post-adsorption treatment. This feature is especially advantageous when targeting hazardous pollutants or valuable species such as precious metal ions, which may be recovered from the spent adsorbent through desorption prior to disposal. Therefore, although 1% PEI/PAC-800 may not be suitable for repeated reuse, its high single-use performance and desorption capability offer practical benefits for selective separation and recovery applications in environmental and resource management.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study evaluated the adsorption performance of PEI-impregnated powdered activated carbon (PAC) for removing the anionic dye RY2 from aqueous solutions. The 1% PEI/PAC-800 sample achieved a maximum adsorption capacity of 477.02 mg/g, about 7.4 times higher than that of raw PAC. Despite a reduction in surface area after PEI modification, the introduced amine groups enhanced electrostatic interactions under acidic conditions, improving adsorption efficiency. Kinetic analysis showed that the process followed a pseudo-second-order model, indicating site-specific electrostatic interactions between the dye and protonated amine groups. Although adsorption capacity was significantly enhanced, the low rate constant suggests limited initial uptake due to diffusion constraints. Compared to microporous PAC like SPS-100, the PEI-modified adsorbent offered better dye accessibility and uptake. While reusability was limited after the first cycle, the high initial desorption efficiency and simple preparation process make the material suitable for batch-mode dye removal. In addition, the ability to release adsorbed species after use suggests potential for downstream treatment or selective separation before disposal.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eConflict of Interest\u003c/strong\u003e \u003cp\u003eAll the authors declared that there are no conflicts of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contributions\u003c/h2\u003e \u003cp\u003eSu Bin Kang: Conceptualization, Investigation, Formal analysis, Methodology, Data curation, Writing \u0026ndash; original draft; Byeong-Chan Min: Formal analysis, Methodology, Data curation, Writing \u0026ndash; review \u0026amp; editing; Gwang-Il Ko: Formal analysis, Methodology; Li Yong: Formal analysis, Methodology; Yeoung-Sang Yun: Conceptualization, Funding acquisition, Supervision, Writing \u0026ndash; review \u0026amp; editing; Sung Wook Won: Conceptualization, Funding acquisition, Supervision, Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThis work was supported by the Technology Development Program (S3366606), funded by the Ministry of SMEs and Startups (MSS) and partly by the Technology development project to improve secondary battery circulation usability (Development of pollutants reduction technology generated in the lithium ion batteries recycling process) through the Korea Environmental Industry \u0026amp; Technology Institute funded by the Ministry of Environment (RS-2024-00345911).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eD.A. 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Barbeau, ACS ES\u0026amp;T Wat. \u003cstrong\u003e5\u003c/strong\u003e, 851 (2025).\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Scheme 1","content":"\u003cp\u003eScheme 1 is available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"korean-journal-of-chemical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"kjce","sideBox":"Learn more about [Korean Journal of Chemical Engineering](http://link.springer.com/journal/11814)","snPcode":"11814","submissionUrl":"https://www.editorialmanager.com/kjce/default2.aspx","title":"Korean Journal of Chemical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Subscription","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Polyethylenimine, Activated carbon, Reactive Yellow 2, Adsorption capacity, Wastewater treatment","lastPublishedDoi":"10.21203/rs.3.rs-6780880/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6780880/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study optimizes polyethylenimine (PEI) impregnation on powdered activated carbon (PAC) to maximize adsorption of the anionic dye Reactive Yellow 2 (RY2). Three factors, namely PEI molecular weight (600, 800, 1200, 10000 and 70000 g∙mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), PEI content (0.1\u0026ndash;10 wt.%), and impregnation stirring speed (0-200 rpm), were systematically evaluated in triplicate. Under optimal conditions (PEI Mw\u0026thinsp;=\u0026thinsp;800 g mol\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, PEI content\u0026thinsp;=\u0026thinsp;1.0 wt.%, stirring\u0026thinsp;=\u0026thinsp;40 rpm), PEI-impregnated PAC achieved a maximum adsorption capacity of 477.02 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, which is 7.4-fold higher than raw PAC (64.13 mg g\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e). FTIR, BET, FESEM/EDS, and zeta potential analyses showed that although PEI impregnation reduced surface area, the introduced amine groups increased the surface charge by +\u0026thinsp;52.64 mV at pH 2, driving the enhanced adsorption. These results demonstrate that PEIimpregnated activated carbon is a strong and efficient adsorbent for RY2 removal in textile wastewater treatment.\u003c/p\u003e","manuscriptTitle":"Polyethylenimine-impregnated powdered activated carbon for efficient removal of Reactive Yellow 2 from aqueous solutions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-11 06:41:39","doi":"10.21203/rs.3.rs-6780880/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2025-06-09T16:35:37+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-09T05:00:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-03T03:53:18+00:00","index":"","fulltext":""},{"type":"submitted","content":"Korean Journal of Chemical Engineering","date":"2025-05-30T00:26:24+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"korean-journal-of-chemical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"kjce","sideBox":"Learn more about [Korean Journal of Chemical Engineering](http://link.springer.com/journal/11814)","snPcode":"11814","submissionUrl":"https://www.editorialmanager.com/kjce/default2.aspx","title":"Korean Journal of Chemical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Subscription","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"757f0975-8723-4e7c-ae9d-5253f96cbc3c","owner":[],"postedDate":"June 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-09-08T16:02:21+00:00","versionOfRecord":{"articleIdentity":"rs-6780880","link":"https://doi.org/10.1007/s11814-025-00548-4","journal":{"identity":"korean-journal-of-chemical-engineering","isVorOnly":false,"title":"Korean Journal of Chemical Engineering"},"publishedOn":"2025-09-01 15:57:29","publishedOnDateReadable":"September 1st, 2025"},"versionCreatedAt":"2025-06-11 06:41:39","video":"","vorDoi":"10.1007/s11814-025-00548-4","vorDoiUrl":"https://doi.org/10.1007/s11814-025-00548-4","workflowStages":[]},"version":"v1","identity":"rs-6780880","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6780880","identity":"rs-6780880","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}