Equal Surface Oxygen, Different Adsorbent: Ammonium Persulfate Demineralises NaOH-Activated Plastic Pyrolytic Char While Hydrogen Peroxide Does Not

2.1 Materials

Pyrolytic char derived from mixed-plastic waste pyrolysis (PPC) was used as the carbon precursor; the char and its source facility have been described previously [14]. The characterisation and adsorption data for the untreated PPC (X-ray diffraction, thermogravimetry, XRF, EDS, FTIR, zeta potential and methylene blue uptake) were first reported in [41] and are reused here as the reference for the NaOH-activated series. Sodium hydroxide (NaOH, ≥ 97%, Merck), hydrochloric acid (HCl, 37%, Merck), hydrogen peroxide (H₂O₂, 30%, Merck), ammonium persulfate ((NH₄)₂S₂O₈, ≥ 98%, Merck), sulfuric acid (H₂SO₄, 96–98%, Merck), Triton X-100 (Sigma-Aldrich), and methylene blue (MB, CI 52015, Merck) were of analytical grade and used without further purification. Deionised water (resistivity ≥ 18.2 MΩ·cm) was used throughout.

2.2 NaOH Activation

PPC (2 g) was mixed with NaOH (2 g, mass ratio 1:1) in 15 mL of deionised water with 1.5 μL of Triton X-100 as a wetting agent. The slurry was stirred at 400 rpm for 15 min, then at 300 rpm and 60 °C for a further 30 min, then held at 100 °C until the water had evaporated (approximately 3 h). The solid was dried at 105 °C for 5 h and ground with a mortar and pestle.

The impregnated char was activated in a tube furnace under nitrogen (1 L/min), heated from room temperature to 600 °C at 5 °C/min and held for 2 h. After cooling under continuous N₂ flow, the product was washed with 250 mL of 0.5 M HCl under ultrasonication for 10 min to remove residual inorganic species and unreacted activating agent, vacuum-filtered, and rinsed with deionised water until the filtrate reached neutral pH. The washed solid was dried at 105 °C for 30 min and stored in a desiccator. This sample is denoted PPC-NaOH; the untreated precursor is denoted PPC.

2.3 Oxidative Post-Treatment

For H₂O₂ treatment, PPC-NaOH was dispersed in 100 mL of 30% H₂O₂ and ultrasonicated for 2 h. The suspension was vacuum-filtered, and the solid was washed three times with 100 mL of deionised water per cycle and dried at 80 °C for 1 h, yielding PPC-NaOH-H₂O₂.

For AP treatment, PPC-NaOH was dispersed in 50 mL of 2 M H₂SO₄, and 50 mL of 1 M (NH₄)₂S₂O₈ was added dropwise with stirring. The mixture was ultrasonicated for 2 h, vacuum-filtered, washed three times with 100 mL of deionised water, and dried at 80 °C for 1 h, yielding PPC-NaOH-AP.

Each route was applied under the conditions conventional for its oxidant rather than under conditions matched between the two. They differ in oxidant concentration, in reaction medium and in redox potential: the AP route is carried out in 2 M H₂SO₄ and the H₂O₂ route in water, and neither product received an acid wash after oxidation. The comparison drawn in this work is therefore between two treatments as they are commonly practised, not between two oxidants at equal strength, and it does not rank them. Demineralisation and sulfur retention are attributed throughout to the AP route as practised, not to the persulfate ion: without an acid-only control, neither can be partitioned between the oxidant and its medium (Sections 3.5 and 3.8). The full preparation route is shown in Figure 1.

2.4 Characterisation

Crystalline phases were identified by X-ray diffraction (XRD, SmartLab, Rigaku) with Cu Kα radiation (λ = 1.5406 Å) over 2θ = 5–80°. Phase fractions were quantified by Rietveld refinement (BGMN [42]) using a six-phase model (quartz, rutile, calcite, halite, muscovite 2M1 and hematite, each verified against its powder-diffraction card before inclusion) plus two broad Le Bail functions for the amorphous contribution. The PPC pattern [41] was refined here with the same model as the NaOH series. Fractions are reported on a crystalline basis only; no internal standard was added, so the absolute amorphous content is not quantified [43]. The refinement of PPC-NaOH did not yield usable fractions and is reported as rejected (Section 3.4). Surface functional groups were recorded by Fourier-transform infrared spectroscopy (FTIR, IRSpirit, Shimadzu) in attenuated total reflectance mode over 4000–400 cm⁻¹; spectra are displayed as transmittance, and band areas were computed on absorbance after convex-hull baseline correction. Morphology and local elemental composition were examined by field-emission scanning electron microscopy (FE-SEM, SU8000, Hitachi) with energy-dispersive X-ray spectroscopy (EDS, EMAX, Horiba); bulk inorganic composition was determined by energy-dispersive X-ray fluorescence (EDXRF, MESA-50, Horiba) at 15 kV and 200 μA using the fundamental parameter method. Thermal behaviour was measured by thermogravimetric analysis (TGA/DTG, DTG-60, Shimadzu) from room temperature to 800 °C at 10 °C/min under flowing air; the residue at 800 °C was taken as the ash content. Zeta potential was measured with a nanoparticle analyser (SZ-100, Horiba) at neutral pH with seven replicates per sample.

XRF and EDS both report weight percentages normalised to the quantified elements only, so leaching of one element raises the apparent content of all others, and neither technique reports the quantity of the mineral fraction. Element loadings were therefore obtained by scaling the XRF composition by the thermogravimetric ash content,

where c_i is the XRF weight fraction of element i and f_ash the ash fraction, giving grams of element per gram of product char. The scaling is semi-quantitative: XRF quantifies metals, chlorine and sulfur but not the oxygen, carbon or hydrogen that make up the remainder of the ash, so loadings are overestimated by a factor that varies with the phase assemblage. Changes between samples are therefore interpreted as fold-changes relative to the parent PPC-NaOH rather than as absolute inventories. Treatment yields were not recorded, so loadings are per gram of product and do not close a mass balance across the oxidation step. Sodium was not included in the EDS or XRF quantification lists and is not reported. It cannot be recovered from the raw EDS spectra, because Na Kα (1.041 keV) lies within one detector resolution width of Zn Lα and the Cu/Zn K lines are not excited at 15 kV.

2.5 Methylene Blue Adsorption

Batch experiments used 10 mg of adsorbent in 100 mL of MB solution (V/m = 10 L/g), agitated at 150 rpm in a thermostatic shaker at 25 °C. Isotherms were measured at initial concentrations of 2, 5, 8 and 10 mg/L at the natural solution pH. The effect of pH was examined at pH 3, 7 and 11, adjusted with 0.1 M HCl or 0.1 M NaOH, at an initial concentration of 10 mg/L. Aliquots were withdrawn at intervals over 120 min, filtered through a 0.45 μm syringe filter, and the residual MB concentration was measured at λ_max = 664 nm by UV–Vis spectrophotometry.

Uptake at time t was calculated as

where C₀ and C_t (mg/L) are the initial and time-dependent MB concentrations, V (L) the solution volume and m (g) the adsorbent mass.

2.6 Kinetic and Isotherm Models

Kinetic data were fitted with the pseudo-first-order (PFO) and pseudo-second-order (PSO) models [44,45,46],

and with the Weber–Morris intraparticle diffusion model [47],

where k_id (mg/g min^−11/2) is the intraparticle diffusion rate constant and C_i (mg/g) relates to the boundary-layer thickness. Weber–Morris plots were fitted as two-segment piecewise lines, with the breakpoint selected by least squares over all interior points with at least four points per segment. Isotherm data were fitted with the Langmuir model [48,49],

where q_m (mg/g) is the monolayer capacity and K_L (L/mg) the Langmuir constant. Because the uptake data are fixed-contact-time values rather than equilibrium values (Section 2.5.1), the fitted parameter is written q_m,120 throughout.

2.7 Replication

Zeta potential was measured with seven replicates per sample; it is the only axis on which a statistical test is possible. Differences between the two oxidised chars were assessed by equivalence testing rather than by a difference test, since failure to reject equality is not evidence of equivalence at this sample size. Two one-sided Welch tests were applied against an equivalence margin of ± 5 mV, declared before testing: the margin is approximately one standard deviation of either sample and lies inside the |ζ| = 30 mV boundary used to classify colloidal stability, so a difference smaller than the margin would not change how the surface charge is described. The Welch difference test, the Mann–Whitney test and Hedges’ g are also reported.

These measurements were made at the natural pH of the suspension. No potentiometric titration was performed, so neither a point of zero charge nor an isoelectric point was determined for these materials.

XRF, EDS, FTIR and TGA were each measured once per sample, so differences on those axes carry no error estimate, and no statistical test is applied to them.

3.1 Surface Oxygen: The Two Oxidants Are Matched

Activation and oxidation each raise the surface oxygen content (Figure 2). The atomic O/C ratio from EDS rises from 0.220 in the raw char to 0.329 after NaOH activation, and each oxidative treatment raises it further, to 0.457 for H₂O₂ and 0.455 for AP. The two oxidised values differ by 0.002, so by this measure the oxidants are indistinguishable between single determinations: each adds the same ≈0.13 of atomic O/C to the activated char. Because EDS was run once per sample (Section 2.7), this is a comparison of individual measurements rather than distributions, and no significance is claimed for it. What it shows is that the two chars do not differ in surface oxygen, so the mineral-matrix differences reported in Section 3.4 cannot be attributed to such a difference.

This ratio does not, however, measure oxidation of the carbon surface specifically. In a solid that is 52–61 wt% ash (Section 3.3), most of the oxygen EDS detects is bound in the oxide, carbonate and silicate phases rather than in functional groups on carbon. Oxygen was assigned stoichiometrically to the mineral-forming elements reported by EDS between two end-members: metals in their lowest plausible oxides with sulfur carrying no oxygen, and metals in their highest plausible oxides with calcium as carbonate where calcite is detected and sulfur as sulfate. On that bracket, the mineral share is 85–98% of detected oxygen in PPC-NaOH-H₂O₂ and 56–87% in PPC-NaOH-AP. The share is large in both and differs between them. Subtracting it leaves carbon-associated O/C ranges too wide to distinguish the two chars, and for PPC and PPC-NaOH the same assignment requires more oxygen than EDS detects. No corrected ratio is therefore reported. The atomic O/C used here is the quantity conventionally reported for an oxidised char, and it takes the same value for two solids that the following sections show are not the same material.

The FTIR spectra give the same qualitative picture (Figure 2a). After either oxidation, the carbonyl/carboxyl band at 1780–1650 cm⁻¹ intensifies relative to the parent char [50,51], and the carbonate band at 1480–1380 cm⁻¹, prominent in PPC and PPC-NaOH, weakens markedly, consistent with the calcite depletion resolved by XRD (Section 3.4). ATR band intensities are not quantitative across samples that differ in contact and scattering, so these changes are interpreted as directions, not magnitudes. The strongest feature in both oxidised spectra, the envelope at 950–1200 cm⁻¹, belongs to the mineral Si–O–Si framework (shaded in Figure 2a); silicon varies threefold across the series, and the band therefore carries no information about carbon–oxygen chemistry.

3.2 Surface Charge: The Two Oxidants Are Matched

Zeta potential separates the activation step from the oxidation steps (Figure 3). The raw char sits at −34.5 ± 10.0 mV at neutral pH (mean ± SD, n = 7). Activation does not so much shift this distribution as broaden it: the seven PPC-NaOH replicates span −44.7 to −0.2 mV (SD 19.0 mV), so the mean of −21.4 mV describes no single population. The spread is itself the observation: after activation, surface charge is heterogeneous on the scale sampled by individual replicate measurements [52,53].

Either oxidation collapses that heterogeneity onto the same value. The H₂O₂-treated char measures −35.0 ± 3.0 mV and the AP-treated char −36.7 ± 3.4 mV, and the spreads narrow about six-fold relative to PPC-NaOH. The two are equivalent within ± 5 mV: the difference is 1.70 mV with a 90% confidence interval of −1.33 to +4.73 mV, and both one-sided tests reject non-equivalence (p = 0.0010 and p = 0.038). The difference tests do not resolve them either (Welch t = 1.00, p = 0.34; Mann–Whitney p = 0.41; Hedges’ g = 0.50, 95% CI −0.57 to +1.57), though that on its own would not establish equivalence. The equivalence criterion is met narrowly: the upper confidence limit reaches 4.73 mV against the 5 mV bound. By the second descriptor conventionally used to characterise an oxidised carbon surface, the two oxidants are equivalent at a resolution finer than any distinction the descriptor is used to draw.

To this point the two treatments appear interchangeable. The sections that follow show they are not: what separates them lies in the inorganic matrix of the char (Sections 3.3 and 3.4), not on its carbon surface.

3.3 Ash Content: The Two Oxidants Separate

The residue after combustion gives the first quantitative separation of the two oxidants (Figure 4). The raw char leaves 41.5 wt% ash. Activation raises this to 60.7 wt%, as expected for a step that consumes carbon at 600 °C and removes soluble matter in the wash, concentrating the minerals left behind. It is on this ash-dominated solid that the two oxidants act, and here they no longer act alike. H₂O₂ treatment lowers the ash content by 8.6 percentage points, to 52.1 wt%; AP treatment removes most of the mineral load outright, leaving 16.8 wt%. Under the same contact time, temperature and washing (Section 2.3), one oxidant leaves an ash-rich solid and the other converts the char into a carbon-dominated one.

Elemental analysis resolves the same separation element by element (Table 2). Because XRF is normalised to its quantified elements, its weight percentages describe the composition of the mineral fraction and not its quantity: calcium, for instance, holds nearly constant at 6.7 and 6.5 wt% of quantified elements between PPC-NaOH and PPC-NaOH-AP, which would suggest it survives the treatment. Scaling by ash content (Equation (1)) shows it does not. Relative to the activated char, the AP route removes 88% of the potassium, 73% of the calcium and iron and 67% of the silicon; calcium falls from 4.08 to 1.10 g per 100 g of product. The H₂O₂ route removes 0 to 56% of the same elements. Depletion on the AP route is thus broad rather than selective: every major mineral element loses between two-thirds and nine-tenths of its loading. This is the pattern expected from an acidic medium acting on a mixed assemblage rather than from oxidative attack on a single phase.

Titanium is depleted along with the rest, and more than proportionately: its loading falls by 87% compared with 72% for the ash as a whole. It is therefore not a conserved reference in this series, and ratios normalised to it would overstate the enrichment of anything measured against it. Diffraction agrees in direction: rutile falls from the dominant crystalline phase after H₂O₂ treatment to a trace over the amorphous hump after AP treatment (Table 3). All elemental comparisons in this work are therefore made on the ash-scaled basis.

The shape of the mass-loss curves is consistent with this. In the combustion window (400–600 °C), the AP-treated char loses 50.2% of its initial mass, compared with 24.7% for PPC-NaOH and 28.6% for the H₂O₂-treated char, so combustible carbon is now its majority component. These are single thermograms, so the comparisons are between individual runs. The same ordering is, however, obtained independently from the diffraction results that follow (Section 3.4), which resolve the mineral loss phase by phase.

3.4 Crystalline Phases: The Two Oxidants Separate

The parent char carries a crystalline assemblage of quartz, rutile, calcite, halite and muscovite (Figure 5a,c). Rietveld refinement of the six-phase model converged at R_wp = 12.5% and distributed the crystalline fraction as 30.4 wt% quartz, 31.8 wt% rutile, 23.9 wt% calcite, 8.3 wt% halite and 5.5 wt% muscovite (Table 3). A weak hematite reflection at 33.0° passes card verification in this pattern, but the phase refines to zero; across the series, hematite never exceeds 2.6 wt% where it refines to a stable fraction. These fractions are relative to the crystalline part only: without an internal standard, neither the carbon nor any glassy silicate is quantified. Anatase is absent from all four patterns, and crystalline titanium occurs only as rutile.

Activation removes halite, as expected from the wash to neutral filtrate, and depletes calcite: the calcite 104 reflection at 29.4°, among the strongest lines of the parent pattern, falls below detection in PPC-NaOH (Figure 5b). The PPC-NaOH pattern itself, however, does not support quantification. Its mica 002 reflection at 8.85° is narrower than every other reflection in the same scan (FWHM 0.060° against 0.110° for quartz) and its basal-to-non-basal intensity ratio departs from the powder value by more than an order of magnitude, which is the signature of a coarse, basally oriented flake rather than of mica content. Two further sharp reflections, at 10.54° and 28.06° (d = 8.39 and 3.18 Å), match none of the candidate phases. With the dominant reflection an artefact of particle statistics and two others unassigned, the refinement converged only at R_wp = 22.8% (Figure 5d), and its fractions were rejected rather than reported.

The two oxidised chars separate (Figure 5e,f). After H₂O₂ treatment, the parent assemblage survives: quartz, rutile and muscovite persist at 31.2, 52.7 and 8.6 wt%, with residual calcite at 4.8 wt% (R_wp = 13.2%). After AP treatment, the crystalline remainder is reduced to two trace phases, quartz and rutile (84.6 and 15.4 wt% of what little remains), on a broad amorphous band; calcite, muscovite and hematite are below detection. Under the same contact time, temperature and washing, one oxidant leaves the mineral assemblage of the char intact and the other strips it to traces.

The routes differ in their medium as well as their oxidant, and the phase-by-phase pattern follows the medium at least as closely as the oxidant. Calcite is the phase lost most completely, and carbonate dissolves in 2 M H₂SO₄ without any oxidant, so its disappearance on the AP route does not require persulfate. Muscovite, the next most acid-susceptible phase of the assemblage, is likewise undetected, while quartz and rutile, the two most resistant, survive. Neither the ordering of the phases nor the breadth of the elemental depletion (Section 3.3) distinguishes the acid from the oxidant, and no acid-only control was run. Demineralisation is therefore reported as a property of the AP route as practised (Sections 2.3 and 3.8).

Loss of the calcite reflections does not by itself show that the calcium has dissolved. In a carbonate-bearing sludge char, activation with H₂SO₄ converts CaCO₃ to CaSO₄ rather than dissolving it [30], which removes the calcite reflections while the calcium stays in the solid. That is not what happens here: no gypsum or anhydrite reflection appears in the AP pattern, and the ash-scaled inventory places the calcium loading 73% below that of the activated char (Section 3.3), so the calcium leaves the solid rather than changing phase within it.

The band that dominates the PPC-NaOH-AP pattern is centred at 24.5–25.5°, corresponding to d₀₀₂ = 3.58 ± 0.07 Å, and is accompanied by a weaker two-dimensional (10) band near 42°. Together, the two bands are the signature of turbostratic carbon [54,55]. The band position argues against silica glass, whose halo falls at 21.5–22.5° [56], roughly 3° below the observed centre, and silica glass produces no counterpart to the 42° band. The band amplitude also rises across the series as the ash content (Section 3.3) falls, the opposite of what a silicate glass would produce. A minor sodium-silicate contribution nevertheless cannot be excluded on XRD evidence alone. The interlayer spacing, some 7% wider than that of graphite (3.354 Å), is consistent with turbostratic stacking disorder and falls within the 3.58–3.66 Å range reported for non-graphitising activated carbons prepared from tyre pyrolysis char [38]. Because the quartz–rutile–calcite cluster at 26–30° overlies the 002 window in every other sample, d₀₀₂ is reported for PPC-NaOH-AP only.

3.5 Sulfur Retention

Sulfur enters the char through the AP route alone (Figure 6). The native sulfur of the raw char (0.72 wt% by XRF) is largely removed by activation and washing (0.19 wt% in PPC-NaOH, 0.09 wt% after H₂O₂ treatment). The AP-treated char instead carries 11.25 wt%, two orders of magnitude more than its H₂O₂ counterpart. EDS shows the same direction at the surface (4.35 against 0.79 wt%). The two techniques disagree in magnitude because each normalises to its own quantified element set (Section 2.4), but they agree in direction and rank. Scaled by ash content (Equation (1)), the sulfur loading rises sixteen-fold from the activated char to the AP-treated char, from 0.12 to 1.89 g per 100 g of product.

The retained sulfur is amorphous to X-rays. The PPC-NaOH-AP pattern contains no reflection of thenardite, aphthitalite, arcanite or elemental S₈ (Section 3.4), which excludes crystalline sulfate salts. Given that the same sample retains almost no crystalline mineral of any kind, the sulfur most likely resides in or on the carbon-rich solid rather than in a discrete salt phase.

The present data cannot, however, assign that sulfur to the oxidant. The AP oxidation is carried out in 2 M H₂SO₄ and the product receives only a water wash (Section 2.3), so the retained sulfur has two candidate origins (sulfonate grafted during persulfate oxidation [25] or sulfate adsorbed from the acid medium), and nothing in this dataset separates them. The discriminating measurement is XPS S 2p, where sulfonate appears near 168 eV and adsorbed sulfate at 169–170 eV [57,58]; it was not performed here. The finding is therefore reported without assignment: the AP route leaves the char with about 11 wt% sulfur on a bulk basis, and its speciation remains unresolved.

3.6 Methylene Blue Uptake

The raw char takes up less than 4 mg/g of MB; every treated char exceeds it by an order of magnitude. At C₀ = 10 mg/L and natural pH (Figure 7a), the 120-min uptakes rank H₂O₂ (46.5) > NaOH (37.2) > AP (33.5 mg/g), but this ranking does not describe equilibrium. The pseudo-second-order model describes all three series, and its extrapolated capacities reorder the bottom of the list: 56.5, 37.1 and 47.5 mg/g, respectively. The AP-treated char is the furthest from equilibrium at 120 min (extrapolated q_e 42% above the 120-min value, compared with 21% for H₂O₂ and <1% for PPC-NaOH), so fixed-time uptake understates it most.

Langmuir fits of the 120-min isotherms (Figure 7b, Table 4) give an apparent capacity q_m,120 = 44.7 mg/g (K_L = 1.06, R² = 0.955) for PPC-NaOH and 57.6 mg/g (K_L = 0.66, R² = 0.866) for PPC-NaOH-H₂O₂, a 29% gain from the H₂O₂ step on a per-gram basis at fixed contact time. Two qualifications bound that number, and both work in the same direction.

The first is the contact time. All but one flask in Table 4 sit below their pseudo-second-order plateaus, which lie up to 42% above the measured values, and for the oxidised chars the gap is largest in the 5 and 10 mg/L flasks. The fitted values are therefore apparent capacities, not monolayer capacities.

The second is the basis. Ash accounts for 60.7 wt% of PPC-NaOH and 52.1 wt% of PPC-NaOH-H₂O₂ (Section 3.3), so a gram of each contains 0.39 and 0.48 g of non-mineral material, and the per-gram comparison is between unlike quantities. On an ash-free basis the same two fits give 113.7 and 120.2 mg/g, a gain of 6% rather than 29%. Most of the per-gram improvement from the H₂O₂ step is therefore the removal of mineral diluent. Per unit mass, the non-ash fraction of the oxidised char binds methylene blue at close to the same capacity as that of the activated char before oxidation. The direction is not particular to this series: demineralising a commercial activated carbon to 0.1 wt% ash raises its measured uptake, an increase attributed to reopening micropores that the mineral fraction had blocked [29]. The magnitudes are not comparable: that material was taken to near-zero ash, whereas these chars retain 52–61 wt%. In both cases, however, the ash content must be known before a per-gram capacity can be interpreted as a property of the carbon. The ash-free basis is not a carbon basis: the non-ash fraction is organic matter and moisture, and no elemental carbon determination was made on this series.

On a per-gram basis, these capacities fall where a filler-derived char would be expected to fall: an order of magnitude below optimised high-surface-area activated carbons, whose MB capacities reach 325–1000 mg/g [59,60,61], and of the same order as unactivated biochar and reduced graphene oxide [62,63]. The observation of interest is not the absolute capacity but the contrast between the two oxidative routes on the same activated char. For PPC-NaOH-AP, the four-point series is non-monotonic (13.6, 41.6, 48.1, then 33.5 mg/g at the highest C₀), which violates the premise of the Langmuir model, so no isotherm parameter is extracted. The kinetics offer a partial explanation: the 10 mg/L flask is the one furthest from equilibrium, and its extrapolated q_e of 47.5 mg/g would restore near-monotonicity. Extrapolation cannot substitute for a longer run, however, and the capacity of this sample is left unquantified. Nor does extrapolation help the other two series: on the plateau values of Table 4, all three samples become non-monotonic in C₀, so no Langmuir parameter is fitted to the plateaus.

3.7 pH Response

The two oxidised chars respond to pH with different shapes, not merely different sizes (Figure 8a,b). At 120 min, PPC-NaOH-AP peaks at pH 7 (36.8, 56.0, 50.9 mg/g at pH 3, 7, 11), while PPC-NaOH-H₂O₂ rises monotonically and six-fold across the same range (7.7, 26.2, 48.4 mg/g), the electrostatic pattern expected for a cationic adsorbate [24].

Because not every run had reached a plateau at 120 min, part of this contrast could in principle reflect rate rather than affinity. The kinetic fits constrain that possibility (Table 5). Three runs sit furthest from equilibrium, both pH-7 runs and the H₂O₂ run at pH 11 (PSO-extrapolated q_e 14–16% above q₁₂₀), and the other three lie within 3–6%. Extrapolating every run to its PSO plateau preserves both shapes (Figure 8c): the H₂O₂ response stays monotonic (8.0 → 29.7 → 55.3 mg/g) and the AP response stays peaked (38.9 → 64.7 → 52.9 mg/g). The point most exposed to this kinetic objection, the low H₂O₂ uptake at pH 3, is in fact the best-equilibrated run of the six (q_e within 3% of q₁₂₀, with the largest rate constant): that char takes up little MB at pH 3 because its capacity there is small, not because it is slow. Model extrapolation is not a substitute for longer contact times, and runs to plateau would settle the question. Within the data at hand, however, the shape difference survives the correction.

Ash dilution accounts for part of the size difference but not for the shapes. On an ash-free basis the H₂O₂ response is still monotonic (16.2, 54.6, 101.0 mg/g at pH 3, 7 and 11) and the AP response still peaked at pH 7 (44.2, 67.4, 61.2 mg/g); the AP-to-H₂O₂ ratio falls from 4.75, 2.14 and 1.05 to 2.74, 1.23 and 0.61, so at pH 11 the ranking reverses. Which char takes up more therefore depends on the basis chosen and on the pH; the difference in shape does not.

The mechanistic reading of these shapes is bounded by what was measured. Both chars are strongly negative at neutral pH, where a cationic dye is therefore electrostatically favoured. The zeta potential was, however, measured at a single pH rather than titrated (Section 2.7), so no point of zero charge is available and the pH at which either surface would change sign is unknown. Electrokinetic and titrimetric quantities report different properties, and a zeta potential measured at one pH substitutes for neither [64,65]. Within that limit, the monotonic H₂O₂ response is what protonation of surface oxygen groups at low pH and their deprotonation at high pH would produce. The AP maximum at pH 7 instead requires a contribution that declines at pH 11, such as competition from the Na⁺ introduced with the adjusting base, or dissolution and reprecipitation of residual mineral phases at the pH extremes, to which the two chars are not equally exposed. Distinguishing between these would require a titration and an ionic-strength series, neither of which was performed.

The Weber–Morris analysis (Figure 8d) separates the transport stages. Every run shows two stages, a fast initial segment breaking to a slower one at 20–35 min, and a single-line fit is clearly inferior (e.g. R² = 0.54 against 0.94 for PPC-NaOH-AP at pH 11). The intercepts are non-zero, indicating a boundary-layer contribution throughout. At pH 7, the AP-treated char diffuses faster than its H₂O₂ counterpart in both stages (k_id,1 = 6.6 against 3.3, k_id,2 = 3.9 against 1.7 mg/g min^−11/2), consistent with faster internal transport in the carbon-dominated, demineralised solid, although without textural data (Section 3.8) this interpretation remains kinetic rather than structural. The two chars enter these experiments with the same surface charge (Section 3.2). The pH response is where their difference first appears in application, and the matrix-level contrast of Sections 3.3 and 3.4 is the property that distinguishes them.

3.8 What the Surface Descriptors Miss

By the two descriptors conventionally used to characterise an oxidised carbon, the two treatments are interchangeable: atomic O/C of 0.457 against 0.455 (Section 3.1), zeta potential of −35.0 ± 3.0 against −36.7 ± 3.4 mV (Section 3.2). Yet the solids they leave behind are not the same material. One is half mineral (52.1 wt% ash) and retains the quartz–rutile–calcite–muscovite assemblage of its parent; the other is carbon-dominated (16.8 wt% ash), retains only traces of quartz and rutile over a turbostratic hump, and carries 11 wt% of X-ray-amorphous sulfur (Sections 3.3–3.5). The difference between the two products is larger than anything either surface descriptor registers.

This failure is structural rather than accidental. Both descriptors interrogate the carbon surface: O/C reports its composition, zeta potential the charge it presents to solution. In PPC-NaOH, which is 60.7 wt% ash, that surface belongs to the minority component, so two treatments can act very differently on most of the solid and still give the same values of both descriptors, as the AP and H₂O₂ treatments did. The consequences appear in application: two chars whose surface charge is equivalent within 5 mV respond to pH with different shapes (Figure 8c), and the intraparticle diffusion rate constants of the demineralised char are roughly twice those of its H₂O₂ counterpart in both Weber–Morris stages at pH 7 (Table 5).

The matrix also accounts for capacity that would otherwise be read as surface chemistry. The 29% rise in apparent Langmuir capacity from PPC-NaOH to PPC-NaOH-H₂O₂ falls to 6% once both are expressed per gram of ash-free material (Table 4): most of that gain is the removal of mineral diluent rather than an improvement in the non-mineral fraction. An uptake measured per gram of adsorbent inherits the ash content of whatever produced it.

Three limitations bound this reading. First, the textural link is unmeasured: removing 44 percentage points of ash from a solid would plausibly open porosity, and the faster intraparticle diffusion of the AP-treated char points the same way, but no surface-area or porosimetry measurement was made on this series, so the diffusion contrast is reported as kinetics and no textural claim is made. Second, the route-level caveat of Section 2.3 applies to the matrix as it does to the sulfur: the AP treatment differs from the H₂O₂ treatment in its 2 M H₂SO₄ medium as well as its oxidant, so the demineralisation belongs to the treatment as practised, not to the persulfate ion alone. An acid-only control, elemental analysis of the treatment filtrates (for example by ICP-OES) and a comparison at matched oxidant strength would partition the effect between oxidant and medium. None was performed, and the filtrates were not retained. Third, the surface chemistry is characterised by elemental ratio and by charge, not by speciation: no X-ray photoelectron spectra were recorded, so the functional groups behind the O/C parity are not resolved, and equal O/C does not establish that the two carbon surfaces carry the same functionality. Likewise, uptake was probed with a single cationic dye at 2–10 mg/L, which does not establish behaviour toward anionic, neutral or larger organic adsorbates. None of the three affects the methodological point. For a char whose inorganic fraction approaches or exceeds half its mass, the two standard surface descriptors together failed to register the largest change an oxidative treatment produced. Characterising such a treatment therefore requires a measurement of the mineral matrix alongside the surface chemistry, for which an ash determination and phase-resolved diffraction suffice. Reporting O/C alone leaves the larger structural change unrecorded.