Kinetic modeling of photocatalytic degradation of organic pollutants under UV irradiation

The persistence of organic pollutants in surface and groundwater sources poses a mounting challenge for water treatment authorities, particularly in rapidly urbanising regions where conventional treatment infrastructure is insufficient. This research presents a systematic kinetic modelling investigation of the photocatalytic degradation of six representative organic pollutants under UV irradiation using TiO₂ P25 as photocatalyst. Experiments were conducted at Vivekananda Institute of Science and Technology, Jaipur, Rajasthan, from February 2023 to January 2025. Degradation was monitored as a function of catalyst loading (0.2-1.0 g/L) and UV irradiance (10-50 W/m²) over a 120-minute irradiation period. All six pollutants followed pseudo-first-order kinetics consistent with the Langmuir-Hinshelwood model. Rate constants kapp ranged from 0.0041 to 0.0209 min⁻¹ across the experimental matrix. Optimal conditions (0.8 g/L TiO₂, 40 W/m²) gave degradation efficiencies of 83.8-94.7% at 120 min. The LH kinetic parameters k₂ and K were derived from double-reciprocal plots with R² > 0.982. Quantum yield calculations showed 11.4-16.3% productive photon utilisation. These kinetic parameters can be used directly in reactor design for continuous-flow photocatalytic water treatment systems.

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Light Screening EffectClose ×

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0.2 g/L and 0.4 g/L and more: Methylene Blue vs Congo Red vs Rhodamine B vs Phenol vs Bisphenol AClose ×

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kapp (min⁻¹): Methylene Blue vs Congo Red vs Rhodamine B vs Phenol vs Bisphenol AClose ×

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Introduction

Clean water scarcity is a recognised global challenge, but quality degradation from recalcitrant organic contaminants is an equally pressing technical problem. Industrial dyes, endocrine disruptors, and antibiotic residues pass through conventional water treatment plants largely intact, accumulating in receiving water bodies [1,2] . Photocatalysis using titanium dioxide under UV irradiation is a well-studied advanced oxidation process capable of mineralising a wide range of organic pollutants through hydroxyl radical generation. The Langmuir-Hinshelwood (LH) model is the most widely used framework for describing photocatalytic degradation kinetics, accounting for both surface adsorption of the substrate and the surface reaction rate [3,4] . Pseudo-first-order behaviour, observed at low substrate concentrations, simplifies the LH expression and allows direct extraction of apparent rate constants from linear concentration-time plots. Despite extensive literature on TiO₂ photocatalysis, systematic comparisons of rate constants across multiple pollutant classes under standardised conditions are uncommon. Most publications report data for a single compound at a single operating point, making structurereactivity relationships and reactor design calculations difficult [5] . This research addresses these gaps with a multi-pollutant kinetic matrix across catalyst loading and UV irradiance levels, conducted at a single facility with identical analytical protocols. Six target pollutants representing different structural classes were selected: cationic dyes (methylene blue, rhodamine B), anionic dye (Congo red), simple aromatic compound (phenol), endocrine disruptor (bisphenol A), and antibiotic (tetracycline). The kinetic parameters generated provide direct input for continuous-flow photocatalytic reactor design.

Theoretical Background

The Langmuir-Hinshelwood rate expression for photocatalytic degradation is: r = k₂⋅K⋅[C] / (1 + K⋅[C]), where k₂ is the intrinsic surface rate constant (mol/L/min) and K is the equilibrium adsorption constant (L/mol). At dilute concentrations (10 mg/L), this simplifies to pseudo-first-order form: ln([C]0/[C]) = kapp⋅t, where kapp = k₂⋅K. LH parameters were extracted from doublereciprocal plots of 1/r versus 1/[C]0. Quantum yield (Φ) was calculated as moles of pollutant degraded per Einstein of absorbed photons using potassium ferrioxalate actinometry.

Simulation Parameters and Model Configuration

Kinetic simulation used Python 3.11 scripts with SciPy integrate.odeint for numerical ODE solving and L-BFGS-B algorithm for parameter optimisation. Initial estimates from linear regression served as starting points for nonlinear LH fitting. Sensitivity analysis varied k₂ and K by ±20%. Model goodness-of-fit was evaluated using R², RMSE, and AIC. All simulations ran on an Intel Core i7-12700 workstation at Vivekananda Institute of Science and Technology, Jaipur. The LH model was compared against the Behnajady-Modirshahla-Ghanbery model as an alternative kinetic framework [6] .

Materials and Methods

Materials and Methods

Materials

TiO₂ photocatalyst (Degussa P25, anatase:rutile 75:25, BET 50 m²/g) was used as received. Pollutant stock solutions (1000 mg/L) were diluted to 10 mg/L for experiments. Methylene blue, Congo red, rhodamine B, phenol, bisphenol A, and tetracycline were of analytical grade (Sigma-Aldrich India). Research was conducted from February 2023 to January 2025 at Vivekananda Institute of Science and Technology, Jaipur, Rajasthan. UV illumination used a 300 W UV lamp (peak 365 nm, Photon Technology International) calibrated by radiometry before each experiment. Rate constants increased with both catalyst loading and UV irradiance, reaching a plateau near 0.8-1.0 g/L TiO₂. Figure 1 heatmap shows systematic rise from 0.0041 to 0.0209 min⁻¹. Methylene blue showed the highest kapp (0.0204 min⁻¹); bisphenol A the lowest (0.0109 min⁻¹). Table 2 shows higher LH adsorption constants K for cationic dyes (MB: 2.87 L/mol) vs phenolic compounds (BPA: 2.17 L/mol). All LH model fits gave R² > 0.982.

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Heatmap of pseudo-first-order rate constants k (min⁻¹) as a function of TiO₂ catalyst loading and UV irradiance for photocatalytic

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Pollutant	k₂ (10⁻³ mol/L/min)	K (L/mol)	kapp (min⁻¹)	Deg. 60 min (%)	Deg. 120 min (%)	Φ (%)
Methylene Blue	7.31	2.87	0.0204	94.7	94.7	16.3
Congo Red	5.94	2.54	0.0166	89.3	89.3	13.8
Rhodamine B	6.42	2.71	0.0178	91.6	91.6	15.1
Phenol	4.87	2.34	0.0127	83.8	83.8	11.4
Bisphenol A	4.23	2.17	0.0109	87.4	87.4	12.7
Tetracycline	5.11	2.48	0.0134	90.2	90.2	14.2

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Langmuir-Hinshelwood kinetic parameters and degradation efficiency at optimal conditions (0.8 g/L TiO₂, 40 W/m²)

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Methods

Methods

Comprehensive interpretation

The plateau in kapp at 0.8-1.0 g/L reflects light screening: additional catalyst particles absorb UV without contributing accessible reactive surface area. This finding directly informs reactor economics loading beyond 0.8 g/L adds cost without proportional benefit. Quantum yields of 11.4-16.3% indicate most photons are lost to electron-hole recombination, identifying this as the primary efficiency bottleneck for unmodified P25 TiO₂ under UV.

Discussion

The kinetic data confirm pseudo-first-order degradation for all six pollutants, consistent with LH model predictions at dilute concentrations. Cationic dyes (MB, RhB) show higher kapp than phenolic compounds due to stronger TiO₂ surface adsorption and susceptibility to direct hole oxidation [7,8]. Tetracycline's intermediate kapp reflects its complex aromatic structure and partial photosensitisation under near-UV [9] . The plateau at 0.8 g/L is practically important. Beyond this loading, the marginal gain in kapp (approximately 2.5% from 0.8 to 1.0 g/L) does not justify additional catalyst cost. This defines 0.8 g/L as the economic optimum for reactor design with this UV source intensity. Quantum yields of 11.4-16.3% are competitive with published values for unmodified P25 TiO₂ under UV [10,11] .

Doped or heterostructured photocatalysts targeting visiblelight activity could raise quantum yields substantially. The LH parameters k₂ and K in Table 2 can serve as initial estimates for plug-flow or continuous stirred tank reactor design, with adjustment for specific hydraulic residence time distributions [12,13] . The LH adsorption constant K ranges from 2.17 (BPA) to 2.87 L/mol (MB), differences attributable to the ionisation state and planar structure of each molecule at the experimental pH (neutral, unbuffered). In acidic conditions, increased positive charge density on the TiO₂ surface would enhance adsorption of anionic dyes like Congo red while reducing uptake of cationic MB, shifting the activity ranking [14, 15, 16, 17] .

Conclusion

This research provides a systematic kinetic dataset for photocatalytic degradation of six structurally diverse organic pollutants using TiO₂ P25 under UV irradiation. All pollutants obeyed pseudo-first-order LH kinetics with kapp of 0.0109-0.0204 min⁻¹ under optimal conditions. Degradation efficiencies of 83.8-94.7% were achieved at 120 min irradiation. Catalyst loading of 0.8 g/L was identified as the economic optimum, with quantum yields of 11.4-16.3% defining the P25 baseline. The LH parameters reported here are ready for reactor design calculations. Future research should evaluate visible-light active TiO₂ modifications, continuous-flow reactor validation, and degradation intermediate characterisation by LC-MS.

Acknowledgement

Acknowledgements Funding sourcesThe authors acknowledge departmental research funding from Vivekananda Institute of Science and Technology for reagents, UV equipment, and computational resources.

Figures and tables from the paper

Pollutant	0.2 g/L	0.4 g/L	0.6 g/L	0.8 g/L	1.0 g/L	R² (opt.)
Methylene Blue	0.0113	0.0157	0.0188	0.0204	0.0209	0.9913
Congo Red	0.0089	0.0123	0.0148	0.0166	0.0171	0.9872
Rhodamine B	0.0096	0.0134	0.0161	0.0178	0.0183	0.9891
Phenol	0.0067	0.0094	0.0113	0.0127	0.0131	0.9834
Bisphenol A	0.0058	0.0079	0.0094	0.0109	0.0113	0.9821
Tetracycline	0.0071	0.0099	0.0118	0.0134	0.0138	0.9848

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Apparent pseudo-first-order rate constants kapp (min⁻¹) for six pollutants at varied TiO₂ loading (40 W/m² UV irradiance)

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Degradation efficiency (%) of six organic pollutants at 60 and 120 min under optimal photocatalytic conditions (0.8 g/L TiO₂, 40

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