2.1.1. Sample Preparation

The hardwood sawdust collected from a sawmill industry was prepared and characterized as suitable for pollution remediation [14]. The sawdust was washed with warm water to remove dirt, fungus, and other foreign materials, and then sun-dried for a full day. The sawdust was oven-dried at 110˚C until a constant drying weight was obtained. Afterwards, it was sieved to not more than 0.425 mm. The modification was performed using the method [15]. 10 g of the dried sample of sawdust was placed in a flat-bottomed flask, soaked, and mixed with 200 ml of a 0.5 M succinic acid solution. The mixture was continuously stirred and refluxed for 4 hours at 75˚C, then cooled to room temperature and filtered using Whatman No. 42 filter paper; the residue was washed with distilled water and dried at 120˚C until a constant drying weight was achieved.

2.1.2. Batch Adsorption of Xylene

The adsorption method used was batch adsorption, similar to that of [16]. The adsorption was carried out at a controlled laboratory temperature of 24˚C - 26˚C. Using a FA/JA-B series analytical balance manufactured by Tianjin Tianma Hengji Instrument Co., Ltd., 0.2 g of sawdust was weighed, then introduced into five 250 ml glass-stoppered conical flasks and placed on the IKA KS 260 Orbital Mechanical Shaker. 100 ml of five different concentrations (0.5, 0.4, 0.3, 0.2, and 0.1 M) xylene and water cosolvent were introduced into glass-stoppered conical flasks. The mechanical shaker was set to agitate at 300 rpm, and the process was run for 15, 30, 60, 90, and 120 min to assess the performance of the adsorption process.

2.1.3. Determination of the Amount of Xylene Adsorbed by the Modified Sawdust

UV/Vis spectrophotometric analysis was carried out to determine the concentration of xylene remaining after batch sorption at 15, 30, 60, 90, and 120 min, using the 1801 UV-VIS Spectrophotometer manufactured by Shanghai Yoke Instrument Co., Ltd. During the study, the filtrates after batch adsorption were collected in cuvettes and placed in a UV/Vis spectrophotometer at wavelengths of 267 - 307 nm. The xylene sample in the cuvette absorbs UV or visible radiation, and the xylene concentration in solution was determined. The amount of light absorbed by the xylene solution depended on the concentration of xylene in the solution, the path length of the cuvette, and how well the xylene absorbed the light at a specific wavelength. Transmittance indicates the concentration of the analyte in the sample [17].

2.2.1. Langmuir Isotherm

The Langmuir isotherm, which was originally designed to describe gas-solid phase adsorption, is also used to evaluate the adsorptive capacity of various adsorbents [18][19]. It accounts for the surface coverage by balancing the relative rates of adsorption and desorption [20]. It assumes that the rate at which adsorption sites are occupied is proportional to the number of unoccupied sites and that adsorption is limited to a monolayer. Equation (1) represents the Langmuir equation [21]:

where:

C_e: Concentration of adsorbate at equilibrium (mg/L).

q_e: Equilibrium monolayer adsorption capacity of the adsorbent (mg/g).

K_L: Langmuir adsorption constant (L/mg) related to the energy of adsorption, which quantitatively reflects the affinity between the adsorbent and the adsorbate.

q_m: Maximum monolayer adsorption capacity of the adsorbent (mg/g).

The linear plot of C_e/q_e as a function of C_e determines the q_m and K_L constants.

The separation factor (R_L) expresses the level of success of the adsorption technique in relation to the model [22][23]. R_L can be derived from the formula in Equation (2):

K_L: Langmuir constant in (mg/L).

C₀: Adsorbate's initial concentration (mg/L).

R_L: Values indicate that adsorption could be unfavourable when R_L > 1, linear when R_L = 1, favourable when 0 < R_L < 1, and irreversible when R_L = 0.

2.2.2. Freundlich Isotherm

The Freundlich isotherm is suitable for adsorption processes that occur on heterogeneous surfaces [24][25]. The linear form of the Freundlich isotherm is shown in Equation (3):

where:

q_e: Adsorption capacity at equilibrium (mg/g);

C_e: The concentration of adsorbate at equilibrium (mg/g);

K_F is the Freundlich constant indicative of adsorption capacity [(mg∙g⁻¹) (L∙mg⁻¹)^1/n];

1/n is the adsorption intensity; it is also indicative of the relative distribution of the energy and defines the heterogeneity of the adsorbate sites [26][27].

2.2.3. Adsorption Kinetic Models

The kinetics models basically measure the adsorption uptake with respect to time, which further provides useful information concerning the reaction pathways and the mechanism of the sorption reaction [28][29]. The following are examples of kinetic models: Lagergren pseudo-first order, pseudo-second order, intraparticle diffusion, and liquid film diffusion. In the course of this study, the two kinetic models used were the pseudo-first-order (PFO) and the pseudo-second-order kinetics (PSO). These were compared in this study.

2.2.4. Pseudo-first Order Kinetics

The Lagergren pseudo-first-order kinetic model is commonly applied to describe the rate of solute adsorption onto an adsorbent surface. It assumes that the rate of occupancy of adsorption sites is equal to the number of unoccupied sites. The pseudo-first-order kinetic model is shown in Equation (4):

where:

q_e = adsorption capacity at equilibrium (mg/g);

q_t = adsorption capacity at time t (min);

t = contact time (min);

K₁ = Lagergren rate constant for pseudo-first-order kinetics.

The plot of ln(q_e−q_t) as a function of t gives the slope and intercept, which are used to determine the rate constant (K₁) and adsorption capacity (q_e) [30][31].

2.2.5. Pseudo-Second-Order Kinetics

The formula for pseudo-second-order kinetics is represented in the form proposed by [27], as shown in Equation (5).

The pseudo-second order kinetic model is widely used to describe adsorption processes controlled by surface reaction or adsorption capacity. From the pseudo-second order kinetic model, it can be predicted that the adsorption rate is equal to the square of the number of unoccupied sites. The model is particularly useful in describing adsorption where chemical interactions, such as electron sharing or exchange, dominate.

The linear form of the pseudo-second-order equation is expressed as:

where:

q_e = adsorption capacity at equilibrium (mg/g);

q_t = adsorption capacity at time t (mg/g);

K₂ = pseudo-second-order rate constant (g/mg·min);

t = contact time (min).

From a plot of (t/q_t) versus t:

Slope = 1/q_e.

Intercept = t / ( k 2 ⋅ q e 2 ) was applied for determining their constants.

3.1.1. Descriptions of the Langmuir Isothermal Model from the Study

The Langmuir linear plots of C_e/q_e versus C_e, showing the removal of xylene from 0.1 - 0.5 M cosolvent solutions using hardwood sawdust modified with 0.5 M succinic acid, are shown in Figure 1. The abscissa spans approximately 1900 - 2700 mg/L, and the ordinate ranges from 0.05 to 0.70 g/L. Five series are colour- and marker-coded and listed in the legend (0.5 M, green circles; 0.4 M, blue diamonds; 0.3 M, orange squares; 0.2 M, grey triangles; 0.1 M, yellow crosses). Each series appears as a short linear segment with its least-squares fit equation and coefficient of determination annotated on the plot (R² = 0.9997 - 0.9999): y = 4 × 10⁻⁵x − 0.0047 (0.5 M), y = 5 × 10⁻⁵x − 0.007 (0.4 M),y = 7 × 10⁻⁵x − 0.0123 (0.3 M), y = 1 × 10⁻⁴x − 0.0283 (0.2 M), and y = 3 × 10⁻⁴x − 0.1383 (0.1 M). The vertical placement of the series increases from the 0.5 M data at the lowest C_e/q_e values to the 0.1 M data at the highest. Approximate data spans are as follows: 0.1 M, C_e ≈ 2050 - 2410 mg∙L⁻¹ and C_e/q_e ≈ 0.45–0.65 mg∙L⁻¹; 0.2 M, C_e ≈ 2120 - 2430 mmg∙L⁻¹ and C_e/q_e ≈ 0.22 - 0.27 mg∙L⁻¹; 0.3 M, C_e ≈ 2210 - 2420 mmg∙L⁻¹ and C_e/q_e ≈ 0.18 - 0.22 mg∙L⁻¹; 0.4 M, C_e ≈ 2280 - 2490 mmg∙L⁻¹ and C_e/q_e ≈ 0.11 - 0.14 mg∙L⁻¹; 0.5 M, C_e ≈ 2310 - 2600 mmg∙L⁻¹ and C_e/q_e ≈ 0.09 - 0.11 mg∙L⁻¹.

3.1.2. Descriptions of the Freundlich Isothermal Model from the Study

From the 0.1 - 0.5 M xylene cosolvent solution, the Freundlich linear plots in Figure 2 show the removal of the adsorbate from the solution using the 0.5 M

Figure 1. Langmuir isothermal model (C_e/q_e vs. C_e) for xylene removal from 0.1 M, 0.2 M, 0.3 M, 0.4 M, and 0.5 M solutions using 0.5 M succinic acid modified hardwood sawdust as the adsorbent.

Figure 2. Freundlich isothermal model (logarithmic linear plot) for xylene removal from 0.1 M, 0.2 M, 0.3 M, 0.4 M, and 0.5 M solutions using 0.5 M succinic‑acid‑modified hardwood sawdust as the adsorbent.

succinic acid modified sawdust; five data series corresponding to five plots display the five initial xylene concentrations, distinguished by different marker shapes and colours (legend row at the top). As shown in the figure, the axes are presented in the logarithmic form used for the Freundlich linearization. The abscissa is 7.00 - 7.35 and the ordinate 9.2 - 10.4. Each series appears as a short, nearly horizontal line segment with a superimposed least-squares fit. On the right-hand side of the plot are the fitted equations, showing small negative slopes with high linearity (R² ≈ 0.9997 - 0.9999); the reported slopes are −0.0482, −0.0591, −0.0783, −0.119, and −0.2631, with intercepts close to 10.xx as displayed. The five clusters are vertically separated, with their data points concentrated within a narrow x-range for each series.

3.1.3. Descriptions of the Lagergren Pseudofirst-Order Kinetics from the Study

The Lagergren pseudo-first-order linear plots of ln(q_e − q_t) versus time for xylene removal from 0.1 - 0.5 M cosolvent solutions are shown in Figure 3 using 0.5 M succinic-acid-modified hardwood sawdust. The abscissa is time (min), spanning approximately 0 - 140 min, and the ordinate is ln(q_e − q_t), spanning about 0 - 7. Five data series corresponding to the initial xylene concentrations of 0.1 M, 0.2 M, 0.3 M, 0.4 M, and 0.5 M are distinguished by different markers and colours, with the legend shown on the right of the plot. For each series, four measurement times are plotted (≈20, 40, 60, and 120 min). Least-squares fitted straight lines: 0.1 M, y = −0.0401x + 6.5937 (R² = 0.5729); 0.2 M, y = −0.0393x+ 6.4015 (R² =

Figure 3.Lagergren pseudo‑first‑order kinetics (ln(q_e−q_t) vs. time) for xylene removal from 0.1 M, 0.2 M, 0.3 M, 0.4 M, and 0.5 M solutions using 0.5 M succinic‑acid‑modified hardwood sawdust as an adsorbent

0.5922); 0.3 M, y = −0.0371x + 5.9133 (R² = 0.4295); 0.4 M, y= −0.0394x + 6.0172 (R² = 0.4144); and 0.5 M, y= −0.0443x + 6.3219 (R² = 0.8224), are overlaid and annotated on the right with their equations and coefficients of determination. The data points at 20 - 60 min cluster in the upper portion of the y-axis (≈4.3 - 5.2), and the 120-min points appear near the lower end of the y-axis, as displayed. Multiple black straight lines are visible across the figure, representing the linear fits.

3.1.4. Descriptions of Pseudosecond-Order Kinetics from the Study

Similarly, the pseudo-second-order linear plots (t/q_t versus time) for xylene removal from 0.1–0.5 M cosolvent solutions using hardwood sawdust modified with 0.5 M succinic acid as the adsorbent are shown in Figure 4. The abscissa is time (min), extending from 0 to approximately 140 min, and the ordinate is t/q_t, ranging from about 0.0000 to 0.0300. Five data series, with one for each initial concentration (0.1 M, 0.2 M, 0.3 M, 0.4 M, and 0.5 M), are distinguished by different marker shapes and colours as indicated in the legend at the right. For each series, four measurement times are shown (≈20, 40, 60, and 120 min). For each xylene concentration, the equations and coefficients of determination are shown on the straight line least squares fits that are superimposed in black as follows: 0.1 M, y = 0.0002x+ 0.0003 (R² = 0.9991); 0.2 M, y = 0.0001x+ 5E−05 (R² = 0.9999); 0.3 M,y = 7E−05x + 2E−05 (R² = 0.9999); 0.4 M, y= 5E−05x + 9E−06 (R² = 0.9999); and 0.5 M, y= 4E−05x + 7E−06 (R² = 0.9999). The data points for each concentration align closely with their respective fitted lines within a narrow x-range at each time point.

Figure 4.Pseudo‑second‑order kinetics (t/q_t vs. time) for xylene removal from 0.1 M, 0.2 M, 0.3 M, 0.4 M, and 0.5 M solutions using 0.5 M succinic‑acid‑modified hardwood sawdust as the adsorbent.

3.2.1. Deductions from the Langmuir Isothermal Model in the Study

Figure 1 shows the linearized Langmuir relationships for the investigated xylene concentration levels, and the corresponding regression and derived parameters are summarized in Table 1. Although the regressions exhibit near-unity linearity, the intercepts are consistently negative, which forces negative K_L values and consequently negative R_L values; this outcome is non-physical within the Langmuir framework and indicates that the Langmuir model assumptions are not satisfied for the present system. The derived Q_m values should therefore be interpreted only as apparent capacities from the linearization rather than true monolayer capacities. Non-Langmuir behaviour is traceable to the very high apparent uptake; this reflects heterogeneous sorption domains as well as contributions from non-ideal mechanisms (matrix partitioning and capillary retention). It may also be because the capacity approached the mass balance limit at the highest initial concentration [11][21][32][33].

3.2.2. Deductions from the Freundlich Isothermal Model from the Study

Figure 2 presents the Freundlich-type linear regressions for xylene uptake on succinic-acid-modified sawdust, and the corresponding regression and derived parameters are summarized in Table 2. For the dataset described by the trendline, the negative slope implies a non-physical process and is not typical for an adsorption isotherm, because it would correspond to a decrease in q_e with increasing C_e. Also, the R-square value near unity is not considered a validation of the Freundlich applicability, but rather an indication that linearization fits a narrow data band and yields parameters that are not physically interpretable under the Freundlich models.

Table 1. Langmuir Isotherm parameters.

Table 2. Freundlich isotherm parameters.

A negative 1/n commonly indicates that the points used in the fit do not represent a consistent equilibrium state and/or that non-ideal effects are influencing the calculated q_e values. Possible reasons for the process not aligning with true equilibrium typical of surface adsorption are: the inability of the dataset used for regression to attain equilibrium; distortion in mass balance; and non-single-phase behaviour of xylene in water. These signify more of sorption processes, such as partitioning into the lignocellulosic matrix and pore filling. The intercept (10.1) corresponds to lnK_F in the natural-log form, giving an apparent K_F ≈ e^10.1 ≈ 2.4 × 10⁴, but because 1/n is negative, this K_F value is an empirical outcome of the regression, not a reliable measure of adsorption capacity or favourability. Successes in removing xylene in the study could be attributed to non-specific interactions, such as hydrophobic and π-π interactions.

3.2.3. Deductions from Lagergren Pseudofirst-Order Kinetics from the Study

Figure 3 shows the pseudo-first-order kinetic plots for xylene at different concentrations with 0.5 M succinic acid-modified sawdust. For 0.5 M xylene concentration (orange square symbols):

Equation: y = −0.0443x + 6.3219 with R² = 0.8224

From the equation, the slope, intercept, and R² values are shown as −0.0443 = −k₁ → k₁ = 0.0443 min⁻¹, 6.3219 = ln(q_e) → q_e = exp(6.3219) ≈ 555 mg/g, and 0.8224, respectively. The slope represents the pseudo-first-order rate constant, which indicates a moderate adsorption rate for xylene onto 0.5 M succinic acid–modified sawdust. The equilibrium adsorption capacity q_e ≈ 555 mg/g demonstrates a high capacity for xylene removal.

The R² value indicates a fair correlation with the pseudo-first-order kinetic model, suggesting that the adsorption process may not be purely first-order and that other kinetic models (e.g., pseudo-second-order) could provide a better fit.

The kinetic analysis confirms that the adsorption of xylene onto 0.5 M succinic acid–modified sawdust occurs at a measurable rate that depends on the availability of active sites.

The modified sawdust shows significant potential for practical application, given its high q_e value and reasonable kinetic performance.

The deviation from perfect linearity (R² < 0.9) implies that multiple mechanisms, such as film diffusion and intra-particle diffusion, may influence the adsorption process.

3.2.4. Deductions from Pseudosecond-Order Kinetics in the Study

Figure 4 shows pseudo-second-order kinetic plots for succinic acid-modified sawdust at different concentrations. For the 0.5 M xylene concentration, which is indicated with light blue × symbols:

Equation: y= 4E−05x + 7E−06 with R² = 0.9999, showing a perfect fit to the model.

From the equation:

Slope = 1/q_e → q_e = 1/(4 × 10⁻⁵) = 25,000 mg/g

Intercept = 1 / ( k 2 ⋅ q e 2 )

Substituting q_e = 25,000 mg/g:

k₂ = 1/(intercept × q e 2 )

k₂ = 1/(7 × 10⁻⁶ × (25,000²))

k₂ ≈ 2.29 × 10⁻⁴ g/mg·min

The near-excellent fit R-square of 0.9991-0.9999 for the pseudo-second order model confirms that chemisorption is the dominant mechanism for xylene adsorption onto 0.5 M succinic acid-modified sawdust. It also validates pseudo-second-order kinetics as the most accurate descriptor for this adsorption system, compared to pseudo-first-order behaviour.

An efficient adsorption kinetics is indicated by the moderate rate constant k₂, which balances high uptake with steady reaction rates.

Succinic acid modification introduces carboxyl groups that strongly interact with aromatic xylene molecules, supporting a chemisorption-controlled process.

The high q_t value highlights the potential of 0.5 M modified sawdust for practical water treatment applications, where high pollutant removal efficiency is essential.