Nylon wastes of LDPE were obtained from various refuse dump sites in Ile-Ife, Osun state, Nigeria. Plate 1 shows a piece of post-consumer LDPE waste used as a precursor in this study.

The precursor wastes were washed with water and dried at room temperature for 24 hrs. They were shredded into pieces and put into the reactor. All chemicals used for this work were of analytical grades and they include potassium hydroxide (KOH), hydrogen tetraoxosulphate (VI) acid (H₂SO₄), potassium iodide (KI), hydrochloric acid (HCl), starch soluble, iodine crystals, sodium thiosulphate (Na₂S₂O₃∙5H₂O), potassium per manganate (KMnO₄), cobalt (II) chloride (CoCl₂), and potassium dichromate (VI) (K₂Cr₂O₇).

Plate 1. A precursor waste of low-density polyethylene (LDPE).

The design of the experiment was performed using Design Expert software package, version 10.0.1 (Stat-Ease Inc., Minneapolis, MN, USA) and is used to evaluate the coefficients of the regression model equation and their statistical significance. The range of concentrations of the chemical activating agents, carbonization temperature and time were between 0.5 - 2.0 M [1], 400˚C - 500˚C [3], and 45 - 60 mins [26] respectively as shown in Table 1. The central composite design (CCD) was used to obtain (nineteen) 19 random experimental runs which include: five (5) centre points, six (6) axial points, and eight (8) factorial points.

Pyrolysis was carried out under a flow of nitrogen gas at the different corresponding temperatures and time. Samples (carbonized char) were removed from the reactor and crushed, followed by rinsing with large volume of distilled water. This is followed by sieving with a screen mesh of 106 µm in order to obtain smaller particles with increased and uniform surface area for efficient chemical activation of the raw materials. The carbonized char was then chemically activated using hydrogen tetraoxosulphate (vi) acid (H₂SO₄), and potassium hydroxide (KOH) at different concentrations depending on the factor levels as shown in the designed experiment. Chemical activation was carried out using a muffle furnace at 550˚C for a period of 30 mins. The chemically activated products were crushed and washed repeatedly with large volume of distilled water in order to remove excess activating agent and residual inorganic matter. Subsequently, they were dried and stored in a closed container for characterization.

Activated carbon yield of each sample was determined using the method adopted by [1].

The physico-chemical tests were done using standard procedures. The moisture content was obtained using the oven-drying test procedure [27]. The apparent density of each activated carbon sample was determined according to the method adopted by [28] using a graduated measuring cylinder. Ash content was determined according to standard procedure [29]. The iodine value experiment was also performed according to ASTM standard method [30]. The experiment was carried out in triplicates and their average values recorded.

50 ppm of potassium per manganate (KMnO₄), 50 ppm of potassium dichromate (VI) (K₂Cr₂O₇) and 100 ppm of cobalt (II) chloride (CoCl₂) solutions were separately prepared in 1 L volumetric flask using distilled water. About 0.25 g of AC sample was added with 50 mL of each simulated water solution and the resulting mixture was agitated with the rotary shaker at 150 rpm for 60 min. The mixture was subsequently filtered with Whatman No.1 (18.5 cm) filter paper, and the absorbance of the filtrate obtained for each of Mn²⁺, Cr²⁺, and Co²⁺ ions were determined using UV-Visible spectrophotometer at wavelengths 545.5 nm, 431 nm, and 351 nm respectively. The absorbance was used to obtain the remaining concentration (C_f) of the adsorbate in each case by means of the standard calibration curve.

The percentage removal is expressed in Equation (1) as:

% removal = C 0 − C f C 0 × 100 (1)

where C₀ and C_f are the initial and final concentrations of the adsorbate in solution respectively.

Statistical analysis for the optimization of AC obtained from LDPE wastes was carried out by setting yield and bulk density to be in a range, moisture content and ash content were set to be minimum, and iodine value and adsorption performance were set to be maximum. This was done in order to have both acid and base optimized AC.

Model validation was done by repeating the experimental procedure for both pyrolysis and chemical activation step at the optimized factor levels for concentration, temperature, and time. The physicochemical properties of the optimized AC produced were investigated and the error was obtained using Equation (2):

Error = Predicted − Actual Actual × 100 (2)

Fourier Transform Infrared (FTIR) analysis was used to determine the type of functional groups in the produced optimized carbon. About 0.1 g of the sample was mixed with 1 g of potassium bromide (KBr), spectroscopy grade (Merk, Darmstadt, Germany), in a mortar. Part of this mix was introduced in a cell connected to a piston of a hydraulic pump with a compression pressure of 15 kPa/cm². The mix was converted to a solid disc which was placed in an oven at 105˚C for 4 hours in order to prevent any interference with any existing carbondioxide or water vapour molecules. Subsequently, it was transferred to the FTIR analyzer (Nicolet: S5, thermo scientific, Helios Omega, USA) to obtain the spectrum [31]. The peaks were identified by comparing with those in literature.

Scanning Electron Microscopy (SEM) analysis was also used to study the surface morphology of the optimized carbons. The topographical images of the sample were captured by SEM machine (ASPEX 3020 Type-I, Japan). About 0.1 g sample was sticked to the mounting plate and was fastened to the stage using screw. Sample is below the top of the drawer. The sample drawer was held in snug with the right hand, the lever pulled down with the left hand and held snuggly for about 20 - 30 mins. At a pressure of approximately 5 × 10⁵ torr, vaccum pump starts and the drawer held up [32]. Magnification was increased to the desired factor. Moreover, brightness/contrast and spot size were adjusted for optimum resolution and signal. The images and spectra obtained were saved.

Batch adsorption studies were carried out to evaluate the adsorption capacity of the optimized AC. A weighed adsorbent sample (0.25 g) of optimized AC was added into 100 mL KMnO₄ aqeous solution having an initial concentration of 50 ppm, at pH 6.5 occurring at room temperature. The aqueous samples were put in the rotary shaker for continuous agitation at 150 rpm. Adsorption, equilibrium, and kinetic data were obtained by analyzing the remaining KMnO₄ concentration in the batch reactor at pre-set intervals of 15 mins using UV-visible spectrophotometer until equilibrium was achieved. The adsorbent dosage and initial KMnO₄ concentration adsorption uptake on the adsorbents were studied by varying the adsorbent dosage from 0.25 to 1.00 g and initial KMnO₄ concentration from 50 to 125 ppm. For reliability of results, the experiments were repeated for three times with an uncertainty value of about ±9% obtained.

The adsorption capacity was evaluated using Equation (3):

Adsorption capacity = C o − C t M × V (3)

where C_o (mg/L) is the initial concentration of KMnO₄ in contact with adsorbent, C_t (mg/g) is the final concentration of KMnO₄ after the batch adsorption procedure at any time t, M (g) is the mass of adsorbent and V (L) is the volume of the aqueous solution.

Four (4) two-parameter isotherm models were used in this study. These are Langmuir, Freundlich, Temkin and Dubnin-Radushkevich isotherm models. The linear forms of the isotherm models as shown in Table 2 were fitted into the adsorption data to obtain the adsorption parameters, correlation coefficients, and also used to explain the statistical significance of the parameters on the adsorption behaviour of the system.

Kinetic Studies

In liquid-solid adsorption process, the kinetic models help in describing the rate of solute uptake which is usually a function of the residence time. The kinetic study of metal ions on adsorbent is carried out using the pseudo-first and second order kinetics. The mechanism of diffusion of liquid-solid processes is explained using the intraparticle diffusion model [40]. The pseudo-first order model, pseudo-second order model, and the intraparticle diffusion models were employed in this study.

Source: Self. Where q_e represents the equilibrium adsorption capacity of solute per unit mass (mg/g), C_e the equilibrium concentration per unit mass of adsorbate in bulk solution (mg/L), k_L is the constant that relates to the free energy of adsorption (L/mg), q_m denotes the maximum adsorption capacity (mg/g); K_f is the Freundlich constants representing the adsorption capacity of the carbon, n represents the adsorption intensity which is a function of the system’s characteristics; A and B are the temkin parameter isotherm constants, B is the molecular interaction parameter, b relates to the heat of adsorption, T (K) is the absolute temperature, and R is the ideal gas constant (8314 J∙mol⁻¹∙K⁻¹); β is the free sorption energy per mole of the adsorbate as it moves to the surface of AC from an infinite distance within the solution (kJ²∙mol²), and ε is the polanyi potential (J∙mol⁻¹).

Pseudo-first order model: This is often expressed as:

d q d t = k 1 ( q e − q t ) (10)

where q_t represents the adsorption capacity per unit mass at any time t (mg/g) and k₁ is the pseudo-first order rate constant (1/min). Integrating Equation (10) and applying appropriate boundary conditions (att = 0, q_t = 0; and at t = t, q_t = q_t) gives:

ln ( q e − q t ) = ln q t − k 1 t (11)

Pseudo-second order model: The differential form is expressed by Equation (12):

d q t d t = k 2 ( q e − q t ) 2 (12)

Upon integration of Equation (12), and then applying boundary conditions leads to Equation (13):

t q t = 1 k 2 q e 2 + 1 q e t (13)

t q t = 1 h + 1 q e t (14)

where h = 1 k 2 q e 2 (mg∙g⁻¹∙min⁻¹) is defined as the initial adsorption rate as t → 0 and k₂ is the pseudo-second order rate constant (g/mg∙min).

Intraparticle diffusion model: One major assumption associated with this model is that the rate-controlling step is the process involving film diffusion. The amount adsorbed at time t is directly proportional to the square root of the time of contact. This is expressed in Equation (15):

q t = k d i f f t 1 2 + C (15)

where q_t represents the amount of adsorbate at time t and K_diff (mg∙g⁻¹∙min⁻¹) is the intraparticle diffusion constant. The interceptC provides information about the thickness of the boundary layer. Higher values of the intercept lead to stronger effect of the boundary layer.

The thermal decomposition of polymers involved both physical and chemical processes, the extent of which depends on the nature of the material, the degree of crystallinity (molecular packing) and the glass transition and crystalline melting temperature. LDPE is a carbonaceous polymer with no heteroatom, having about 60% crystallinity, glass transition temperature (T_g) of −25˚C, and a crystalline melting temperature in a range of 109˚C - 125˚C [25].

During pyrolysis of LDPE, there is a breaking of the main chain bond at a random location resulting in the formation of monomer units and free radicals. LDPE starts to cross-links at temperatures around 202˚C, and decomposes at around 292˚C. Consequently, the products of thermal decomposition of LDPE under inert atmosphere include a wide range of alkanes and alkenes such as ethane, ethene, propane, propene, butane, but-1-ene, and hex-1-ene.

The depolymerization process involves decomposition by random chain scission; a multistep radical chain reaction, which includes the initiation, depropagation, branching, and termination steps. Depolymerization of LDPE involves both the intramolecular and intermolecular hydrogen transfer and the unzipping reactions. The intramolecular hydrogen transfer involves the transfer of a hydrogen atom within a single polymer chain as illustrated in Equation (16).

The intermolecular hydrogen transfer involves the transfer of a hydrogen atom between polymer chains whereby a radical abstract a hydrogen atom from the polymer to form a new radical which breaks up to form an unsaturated polymer. This is illustrated in Equation (17):

The unzipping process usually does not require hydrogen transfer. The mechanism is shown in Equation (18).

The activated carbons produced from acid-activated and base-activated LDPE wastes were designated LDPE-H₂SO₄, and LDPE-KOH respectively. The chemical activating agents used on the carbon samples act as both oxidizing and dehydrating agents and help to promote the formation of both cross-linked and oxygen-containing carbon structures.

The various AC samples were characterized and their adsorption uptake was evaluated. The results obtained are shown in Table 3 and Table 4 for both acid- and base-activated precursors respectively.

The yield of AC from LDPE was found to significantly depend on the pyrolysis temperature and time. It was observed that both linear and quadratic terms of temperature and time of LDPE (B, C, B², C²) were found to be significant to the model due to their very low F-values of <0.0001, <0.0001, 0.0138, and 0.0195 respectively.

The overall model F-value of 17.57, its low standard deviation value of 0.58, and high R-Squared value of 0.9462 are a pointer to the high confidence level and significance of the model with respect to yield. This agrees with Betiku and Adepoju [41] where it was reported that the higher the F-value and the lower the P-value of any model term, the more significant will be the model. The coefficient of determination (R²) determines the goodness of fit of the model and a minimum value of 0.80 is required [41].

Figure 1 shows the 3D surface plot detailing the interactive effect of temperature and time on yield. It was observed that at temperature of about 410˚C and time of around 46 mins, an optimum yield of 26.38% is obtained. At higher temperatures and higher time, the yield was found to significantly decrease. An increase in pyrolysis temperature further enhances both elimination and dehydration reactions within the polymer molecules, thus leading to evolution of volatile matter. Thus, as both pyrolysis temperature and activation time increases, the % yield decreases as shown in Figure 1. This agrees with previous work done by Gonsalvesh et al., [26] whereby it was reported that an increase in activation time from 30 - 120 mins leads to a reduction in the yield of carbon synthesized from polystyrene (PS) precursor from 48% to 33%.

The obtained yield for LDPE was found to be higher than the values reported by Qiao et al., [42] where a carbon yield of 9% - 18% was obtained from resin polyvinyl chloride precursor. However, it falls within the range reported by László et al., [43] whereby carbon yield in the range of 17% - 21% were obtained from different PET samples at different temperatures and time.

The relatively low yield of LDPE can be attributed to its low-density in nature, and its relatively low molecular weight when compared to other polymers with higher molecular weights like PS, and PVC.

AC with a minimum amount of moisture content is generally desirable and this occurs at lower concentration of about 0.6 M and activation time of 58 mins as shown in Figure 2.

The ANOVA Tablefor the moisture content of LDPE-H₂SO₄ is shown in Table5. The linear terms A, B, and C and quadratic terms A², C² are quite significant due to their respective p-values of 0.0071, 0.0127, 0.0456, 0.0396, and 0.0466.

The model F-value of 4.24, low standard deviation value of 0.40 and adequate R-squared value of 0.8091 all points to the significance of the model and can be used to navigate the design space. The 3D surface plot shown in Figure 2 indicates that at lower concentrations and higher carbonization temperature, AC with low moisture content is obtained.

The moisture content values obtained for both acid and base-activated LDPE were found to be similar and increases as the concentration of the chemical activating increases. The values agree with previous work done by Adibfar et al. [44] where they reported that moisture content of AC produced from H₂SO₄-activated PET was 2.7%. However, the values are slightly higher than those reported by Al-Othman et al., [1] where carbons produced from agricultural and municipal solid wastes at different temperatures and concentrations of ZnCl₂ are reported to have moisture content values ranging between 0.16 and 0.76%. This higher moisture content value could be attributed to the nature of the activation agent.

The bulk densities of LDPE-H₂SO₄ and LDPE-KOH wastes were found to be within 0.411 - 0.481 and 0.401 - 0.476 g/cm³ respectively. These values were lower than those reported by László et al., [43] where the densities of PET-carbons produced at ambient temperatures but with different heat treatment ranges from 1.267 - 1.818 g/cm³. The obtained values are however, slightly higher than those of [44] where 0.20 - 0.33 g/cm³ were observed for different chemically activated samples. These differences in figures are a strong indication that the densities of carbons are largely influenced by factors such as particle size distribution, method of treatment/activation, the type and concentration of the chemical activating agents. Moreover, it was generally observed that the bulk density slightly increases as concentration of the chemical activating agent increases. That is to say, the higher the concentrations of activating agents used, the higher the moisture content of the produced carbons and the higher their bulk densities. However, an optimum value is reached such that a further increment in concentration of the activating agent does not affect the bulk density of the AC produced.

The interaction between concentration and temperature is shown in Figure 3. It

can be deduced that higher iodine values are obtained at concentrations > 1.0 M and temperatures > 440˚C.

At lower concentrations, the iodine value was relatively low due to insufficient amount of activating agent to react with the carbon to create the internal porosity. However, at higher reaction conditions, the microspore structure of the carbons is fully developed. The plot shows that iodine number increases as activation temperature and concentration increases. Moreover, it was observed that LDPE-KOH has higher iodine values than LDPE-H₂SO₄. This is in consonance with the findings carried out by Adibfar et al., [44] where it was reported that AC from KOH-activated PET has a relatively higher iodine value of 984 mg/g compared to H₂SO₄-activated PET sample reported to have 670 mg/g. In the study of heat effects on some synthesized carbon, László et al. [45] reported iodine value of 402 mg/g for AC obtained PET while Gonsalveshet al., [25] reported iodine adsorption capacities of 650 to 970 mg/g of AC produced from polystyrene (PS) precursor.

However, the reported values of [44] and other related works are relatively slightly lower than the obtained values in this study. The difference in values has to do with the nature of the polymeric precursor used in each study. Although, LDPE produced a low yield of AC, it was found to be highly porous as reflected in its iodine value determination.

The ANOVA Tables showed in Table 6 and Table 7 explains the statistical significance of the model terms on iodine value of AC produced from LDPE wastes. The linear terms A, B, C and quadratic terms A², B² are significant and can predict the model statistically. This implies that all three factors of concentration, temperature, and time play significant role in the surface chemistry and the development of the porosity of the carbons. The model F-values of 4.32 and 6.92 implies the models are significant, coupled with their good R-Squared values of

0.8120 and 0.8738 respectively. The precision values indicate an adequate representation of the model, and thus the model can be used to navigate the design space.

Table 8 represents a summary of the test of significance and final equations in terms of coded factors with respect to iodine value for the AC produced.

The relative impact of the factors is measured by comparing the factor coefficients and it is observed from the model equations of LDPE-H₂SO₄ and LDPE-KOH that the quadratic terms A² have higher co-efficient of 79.68 and 98.52 respectively. This indicates that A² is the most significant model term in the iodine value determination of AC. Thus, the concentration of the chemical activating agent used best predicts the iodine value.

The adsorption capacities of AC produced from LDPE-H₂SO₄ and LDPE-KOH using different simulated water solutions each containing manganese, chromium, and cobalt ions were investigated. Table 2 and Table 3 shows that carbons produced from LDPE has adsorption capacities ranging between 68% - 77%, 58% - 66%, 69% - 77% for Mn²⁺, Cr²⁺, and Co²⁺ respectively. The change in the initial purple colour of manganese, and bluish-pink colour of cobalt to both colourless solutions at equilibrium is as a result of the reduction of Mn⁷⁺ and Co²⁺ to Mn²⁺ and cobalt metal in their respective solutions. For the chromium ions, a mild change in colour from yellow to light yellow was visually observed; this reflects the relatively lower adsorption capacity of the carbon for the effective reduction of chromium (Cr⁶⁺ to Cr³⁺ ions) compared to manganese and cobalt ions.

In all cases, it was observed that AC produced at concentrations of 1.4 - 2.0 M and at temperatures above 450˚C have higher adsorption performance. In other words, increase in carbonization temperatures and concentration of chemical activating agent helps to develop and widen the pores of the carbon and makes its surface available for adsorption.

The interactive effect of concentration and time on the adsorption performance was investigated using the 2D contour plot shown in Figure 4. A maximum adsorption rate of 66% was seen to occur at the reaction conditions of 1.7 M KOH and 57 mins.

Table 9 shows the effects of the interactions of the model parameters on the adsorption uptake of the produced carbons.

It was shown that the linear terms A, B, and C, and all quadratic terms A², B², and C² are significant for the effective adsorption of ions from aqueous solutions.

Optimization studies were carried out and the model was validated using a set of experiment operated under optimized reaction conditions. The desirability of the models was very close to unity (1). Table 10 shows the conditions of optimization and obtained results used in the validation of the model. The optimized reaction conditions for LDPE-H₂SO₄ are 1.21 M, 478.90˚C, and 60 mins. Under these conditions, the yield was found to be 21.27%, 1.21% moisture content, 0.4118 g/cm³ bulk density, Iodine value of 814.98 mg/g; % removal of Mn, Cr, and Co were found to be 76%, 66%, and 77% respectively. On the other hand, the optimized conditions for LDPE-KOH are 1.00 M, 446.50˚C, and 51.09 mins. The results obtained under these conditions are a yield of 24.01%, moisture content of 1.01%, bulk density of 0.3862 g/cm³, iodine value of 988.69 mg/g, 76% Mn removal, 64% Cr removal, and 76% Co removal.

The error was obtained as the difference between the statistically predicted response and the actual response. The percentage error was calculated using Equation (3).

Figure 5(a) and Figure 5(b) show the FTIR spectra of both LDPE-H₂SO₄ and LDPE-KOH produced under optimized reaction conditions respectively. Measurements were done over the range of 4000 - 400 cm⁻¹ and peaks were assigned to the functional groups with reference to their respective wave numbers. In the functional group region (1500 - 3000 cm⁻¹), the sharp needle-like peaks between 1634 - 1651 cm⁻¹ represent the C=C stretching vibrations [46]. The bands at 2920 - 2997 cm⁻¹ are the sp³ -CH bonds. The peaks between the region 3258 - 3303 cm⁻¹ represent the sp² C-H stretching vibrations. It also suggests the presence of O-H stretching vibrations associated with intermolecular H-bonding [47] obtained as a result of chemical activation of the porous carbons.

In the fingerprint region (1500 - 600 cm⁻¹), the peaks at 1399 cm⁻¹ and 1408 cm⁻¹ from Figure 5(a) suggests the presence of a strong S=O stretching vibration associated with a sulphate group ( SO 4 2 ) and/or the presence of O-H bending vibrations associated with carboxylic acid [47]. Both of these bonds can be attributed to the sulphuric acid activation of the carbon. However, the peaks at 1101 cm⁻¹ and 1288 cm⁻¹ in Figure 5(b) suggest the presence of C-O bond which is likely as a result of base activation of the carbon. The FTIR analysis shows that the synthesized materials are purely rich in sp³ and sp² carbon bonds. It also reveals the presence of oxygen on the surface of the produced carbons.

SEM analysis was carried out on both LDPE-H₂SO₄ and LDPE-KOH optimized sample products in order to observe the surface physical morphology of the derived carbons. Plate 2 shows the visual carbon sample obtained from LDPE-H₂SO₄.

The micrographs of the carbons are shown in Figures 6(a)-(d).

The images show the presence of holes, cave openings and pores on the surface of the carbon. Moreover, there is extensive porosity introduced by chemical

Plate 2. AC produced from LDPE-H₂SO₄.

activation in both carbon structure. This leads to an increase in the number of sites that are available for adsorption; and thus, promoting the interfacial capacity of the carbons for adsorption of inorganic ions.

The isotherm data was analyzed and fitted to four different sorption models: Langmuir, Freundlich, Temkin, and Dubnin-Radushkevich isotherms. The characteristics parameters for each isotherm and their respective correlation coefficients were evaluated and represented in Table 10. The isotherm graphs are shown in Figures 7(a)-(d). From results obtained, the maximum adsorption monolayer capacity of the Langmuir isotherm model (Q_L) decreases from 53.1915 to −7.5873 mg/g as the adsorbent dosage is increased from 0.25 g to 1.00 g. When higher amount of mass of adsorbent is used, the model fits almost perfectly except in the case of the Langmuir adsorption of 0.50 g adsorbent mass where the R² was obtained to be 0.0443. In addition, the analysis of the equilibrium data shows that the adsorption process is a favourable one as the separation factor R_L values are between 0 and 1. Curko et al., [48] reports that for any adsorption process, the process can either be: irreversible at R_L = 0, favourable at 0< R_L < 1, or unfavourable at R_L > 1. The high values of the Langmuir constant K_L indicate that the AC has a large surface area and pore volume; thus, a high adsorption capacity.

The Freundlich model fits the data than the other isotherms due to its relatively higher R-squared values as shown in Table 11. It has higher correlation

coefficients of 0.9986 and 0.9969 at an adsorbent dosage of 0.25 and 0.75 g respectively, thus, suggesting that an optimum amount of adsorbent mass is needed for the adsorption study. Values obtained for (1/n) andK_f shows that there’s an energy distribution on the adsorption surfaces, and the interaction between manganese molecules and the adsorbent in the course of adsorption is sufficient.

The Temkin isotherms also fits the adsorption data with R² values ranging from 0.9944, 0.8454, 0.9808, and 0.8757 for 0.25, 0.50, 0.75, 1.0 g of adsorbent mass respectively. The positive value of constants A andB indicates that the interactions between carbon and manganese molecules involve an adequate distribution of binding energies and that the adsorption process reduces linearly with coverage [49].

The equilibrium values were also tested with the D-R model, and adsorption values were obtained for Q_m (mg/g), and E as shown in Table 11. The model was found to be a good fit with respect to the obtained correlation co-efficient.

Kinetic models were used to analyze the kinetic data generated from the experiment, and to explain the adsorption mechanisms. The kinetic conditions are: 0.75 g adsorbent dosage, pH 6.5, KMNO₄ adsorbate concentration of 100 mg/L, and a 150 revolution per minute (rpm) agitation rate. The data obtained are shown in Table 12.

The linearized forms of both the pseudo-first order (Equation (11)) and pseudo-second order models (Equation (14)) were used to obtain graphs shown in Figure 8(a) and Figure 8(b) respectively, and also to evaluate the rate law parameters. The kinetic rate constants K₁ and K₂ were found to be 0.0380 min⁻¹ and 0.0023; with correlation coefficients of 0.9548 and 0.9850 respectively. These high R-squared values confirm the possibility of the applicability of both models to the sorption process. The pseudo-second model helps in the evaluation of equilibrium amounts of manganese ions obtained at equilibrium and the initial adsorption rates (h) as t tends to zero. The relatively higher K₂ and R² values of the pseudo-second order reaction help to confirm that the adsorption of manganese ions onto the surface of the synthesized porous carbon follows a pseudo-second order kinetics.

Note: “-” denotes not applicable.

The intraparticle diffusion model illustrates the diffusion mechanisms involved during the sorption processes. The graph in Figure 9, represents a plot of the number of ions adsorbed as a function of t^1/2 under the conditions of reaction. It can be deduced from the plot that more than one step is involved in the diffusion process [49]. The first step is the external surface or instantaneous adsorption stage which lasted for a period of 36 mins. The next stage in the adsorption process occurs where intraparticle film diffusion determines the kinetics of the process. The carbon macropore structures are assumed to be relatively larger than the size of manganese molecules. Consequently, the adsorbate molecules experience film diffusion resistance on both the carbon surface and the large macropores. The intraparticle film diffusion model explains the kinetics of manganese adsorption on porous carbons and it shows that the kinetics occur from a period of 36 min up to approximately 120 mins. The diffusion rate constant Kp was obtained from the slope of the line in the second stage and was found to be 0.62 mg/g∙min^1/2, while the correlation coefficient was obtained as 0.9318. The third (final) stage is the equilibrium stage where intraparticle diffusion starts to slow down due to extremely low manganese concentrations in the solutions.