Adsorption of Pharmaceutical Formulations onto Non-Conventional Biocarbons
Abstract
1. Introduction
2. Materials and Methods
2.1. Materials
2.1.1. Pharmaceuticals
2.1.2. Calibration of Pharmaceuticals
2.2. Adsorbent Preparation
2.3. Characterization of the Adsorbents
2.4. Adsorption Process
3. Results
3.1. Pharmaceutical Adsorption
3.1.1. FTIR Spectroscopy Results for Pharmaceutical Adsorption
3.1.2. Results of Pharmaceuticals Adsorption by Raman Spectra Technology
3.2. Characterization of the Morphological Structure of Adsorbents
3.3. Textural Properties of the Adsorbents
3.4. Effect of the Operating Variables on the Adsorption Process of Pharmaceuticals
3.4.1. Effect of the pH
3.4.2. Effect of the Adsorbent Concentration
3.4.3. Effect of the Initial Adsorbate Concentration
3.4.4. Adsorbent Reutilization
3.4.5. Adsorption of Binary Mixtures
3.5. Adsorption Kinetics
3.6. Adsorption Isotherms
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
| 1/n | factor of heterogeneity of the Freundlich isotherm model (-) |
| a | adsorption constant of the Elovich kinetic model (mg g−1) |
| b | initial rate of adsorption of the Elovich kinetic model (mg g−1) |
| Ce, Co, C | concentration of the adsorbate at the equilibrium, initial concentration of the adsorbate and concentration of the adsorbate at the time t, respectively (mg L−1) |
| E | average free energy of adsorption (kJ mol−1) |
| I | value of the thickness of the boundary layer (mg g−1) |
| KD–R | the activity coefficient related to mean free energy of adsorption of the Dubinin–Radushkevich isotherm model (mol2 kJ−2) |
| KF | adsorbent–adsorbate equilibrium constant of the Freundlich isotherm model (mg1−1/n g−1L1/n) |
| KL | adsorbent–adsorbate equilibrium constant of the Langmuir isotherm model (l mg−1) |
| KS | adsorbent–adsorbate equilibrium constant of the Sips isotherm model (l mg−1) |
| k1 | equilibrium constant of the pseudo-first-order kinetic adsorption model (min−1) |
| k2 | equilibrium constant of the pseudo-second-order kinetic model (g mg−1 min−1) |
| ki | equilibrium constant of the intra-particle diffusion kinetic model (mg g−1/min−0.5) |
| q, qm, qe, qt | adsorption capacity, maximum adsorption capacity, adsorption capacities at the equilibrium and at any time, respectively (mg g−1) |
| R | universal gas constant (8.314 J mol−1 K−1) |
| S | mass of the adsorbent (g) |
| T | absolute temperature (K) |
| V | volume of the solution (mL) |
| Greek Letters | |
| ɛ | Polanyi potential (kJ mol−1) |
| η | adsorption efficiency (%) |
Abbreviations
| ASP | aspirin |
| CAC | commercial activated carbon |
| ENA | enantyum |
| IBU | ibuprofen |
| NOL | nolotil |
| OS | olive stones |
| OSPC | olive stones activated with H3PO4 and carbonized |
| PAR | paracetamol |
| PNS | pine nut shells |
| PNSPC | pine nut shells activated with H3PO4 and carbonized |
| TER | termalgin |
References
- Hogerzeil, H.V. The concept of essential medicines: Lessons for rich countries. BMJ 2004, 329, 1169–1172. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Lin, J.Y.; Zhang, Y.; Bian, Y.; Zhang, Y.X.; Du, R.Z.; Li, M.; Tan, Y.; Feng, X.S. Non-steroidal anti-inflammatory drugs (NSAIDs) in the environment: Recent updates on the occurrence, fate, hazards and removal technologies. Sci. Total Environ. 2023, 904, 166897. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Nand, S.; Singh, P.P.; Verma, S.; Mishra, S.; Patel, A.; Shukla, S.; Srivastava, P.K. Biochar for mitigating pharmaceutical pollution in wastewater: A sustainable solution. Sci. Total Environ. 2025, 966, 178743. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Huynh, N.C.; Nguyen, T.T.T.; Nguyen, D.T.C.; Tran, T.V. Occurrence, toxicity, impact and removal of selected non-steroidal anti-inflammatory drugs (NSAIDs): A review. Sci. Total Environ. 2023, 898, 165317. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Mlunguza, N.Y.; Ncube, S.; Mahlambi, P.N.; Chimuka, L.; Madikizela, L.M. Adsorbents and removal strategies of non-steroidal anti-inflammatory drugs from contaminated water bodies. J. Environ. Chem. Eng. 2019, 7, 103142. [Google Scholar] [CrossRef] [Scilit]
- Ahmed, M.J. Adsorption of non-steroidal anti-inflammatory drugs from aqueous solution using activated carbons. J. Environ. Manag. 2017, 190, 274–282. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Lillenberg, M.; Yurchenko, S.; Kipper, K.; Herodes, K.; Pihl, V.; Lõhmus, R.; Ivask, M.; Kuu, A.; Kutti, S.; Litvin, S.V.; et al. Presence of fluoroquinolones and sulfonamides in urban sewage sludge and their degradation as a result of composting. Int. J. Environ. Sci. Technol. 2010, 7, 307–312. [Google Scholar] [CrossRef] [Scilit]
- Ayati, A.; Tanhaei, B.; Beiki, H.; Krivoshapkin, P.; Krivoshapkina, E.; Tracey, C. Insight into the adsorptive removal of ibuprofen using porous carbonaceous materials: A review. Chemosphere 2023, 323, 138241. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Igwegbe, C.A.; Aniagor, C.O.; Oba, S.N.; Yap, P.S.; Iwuchukwu, F.U.; Liu, T.; Costa de Souza, E.; Ighalo, J.O. Environmental protection by the adsorptive elimination of acetaminophen from water: A comprehensive review. J. Ind. Eng. Chem. 2021, 104, 117–135. [Google Scholar] [CrossRef] [Scilit]
- Oba, S.N.; Ighalo, J.O.; Aniagor, C.O.; Igwegbe, C.A. Removal of ibuprofen from aqueous media by adsorption: A comprehensive review. Sci. Total Environ. 2021, 780, 146608. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Radovic, S.; Pap, S.; Niemi, L.; Prodanović, J.; Sekulic, M.T. A review on sustainable technologies for pharmaceutical elimination in wastewaters—A ubiquitous problem of modern society. J. Mol. Liq. 2023, 383, 122121. [Google Scholar] [CrossRef] [Scilit]
- Islam, M.A.; Nazal, M.K.; Sajid, M.; Suliman, M.A. Adsorptive removal of paracetamol from aqueous media: A review of adsorbent materials, adsorption mechanisms, advancements, and future perspectives. J. Mol. Liq. 2024, 396, 123976. [Google Scholar] [CrossRef] [Scilit]
- Zhan, D.; Ye, A.; Hou, T. Research progress on biochar-based material adsorption and removal of ibuprofen. Front. Environ. Sci. 2023, 11, 1327000. [Google Scholar] [CrossRef] [Scilit]
- Hoppen, M.I.; Carvalho, K.Q.; Ferreira, R.C.; Passig, F.H.; Pereira, I.C.; Rizzo-Domingues, R.C.P.; Lenzif, M.K.; Bottini, R.C.R. Adsorption and desorption of acetylsalicylic acid onto activated carbon of babassu coconut mesocarp. J. Environ. Chem. Eng. 2019, 7, 102862. [Google Scholar] [CrossRef] [Scilit]
- Kerkhoff, C.M.; Martinello, K.D.B.; Franco, D.S.; Netto, M.S.; Georgin, J.; Foletto, E.L.; Piccilli, D.G.A.; Silva, L.F.O.; Dotto, G.L. Adsorption of ketoprofen and paracetamol and treatment of a synthetic mixture by novel porous carbon derived from Butia capitata endocarp. J. Mol. Liq. 2021, 339, 117184. [Google Scholar] [CrossRef] [Scilit]
- Bouzidi, M.; Sellaoui, L.; Mohamed, M.; Franco, D.S.; Erto, A.; Badawi, M. A comprehensive study on paracetamol and ibuprofen adsorption onto biomass-derived activated carbon through experimental and theoretical assessments. J. Mol. Liq. 2023, 376, 121457. [Google Scholar] [CrossRef] [Scilit]
- Dilekoglu, M.F.; Yapici, M. Adsorption of naproxen pharmaceutical micropollutant from aqueous solutions on superior activated carbon synthesized from sheep manure: Kinetics, thermodynamics, and mechanism. J. Mol. Liq. 2023, 381, 121839. [Google Scholar] [CrossRef] [Scilit]
- Cabrita, I.; Ruiz, B.; Mestre, A.S.; Fonseca, I.M.; Carvalho, A.P.; Ania, C.O. Removal of an analgesic using activated carbons prepared from urban and industrial residues. Chem. Eng. J. 2010, 163, 249–255. [Google Scholar] [CrossRef] [Scilit]
- Ninh, P.T.T.; Dat, N.D.; Nguyen, M.L.; Dong, N.T.; Chao, H.P.; Tran, H.N. Two-stage preparation of highly mesoporous carbon for super-adsorption of paracetamol and tetracycline in water: Important contribution of pore filling and π-π interaction. Environ. Res. 2023, 218, 114927. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Georgin, J.; Salomón, Y.L.D.O.; Franco, D.S.; Netto, M.S.; Piccilli, D.G.; Perondi, D.; Silva, L.F.O.; Foletto, E.L.; Dotto, G.L. Development of highly porous activated carbon from Jacaranda mimosifolia seed pods for remarkable removal of aqueous-phase ketoprofen. J. Environ. Chem. Eng. 2021, 9, 105676. [Google Scholar] [CrossRef] [Scilit]
- Tomul, F.; Arslan, Y.; Kabak, B.; Trak, D.; Kendüzler, E.; Lima, E.C.; Tran, H.N. Peanut shells-derived biochars prepared from different carbonization processes: Comparison of characterization and mechanism of naproxen adsorption in water. Sci. Total Environ. 2020, 726, 137828. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Su, Q.; Ren, F.; Zhang, Y.; Wang, Y.; Cao, S.; Li, Z.; Shen, Y.; Li, H.; Su, Y.; Wang, Y.; et al. Adsorption of ibuprofen using biomass carbon derived from one-step pyrolysis of ginkgo leaves. Ind. Crops Prod. 2025, 226, 120739. [Google Scholar] [CrossRef] [Scilit]
- Czech, B.; Kończak, M.; Rakowska, M.; Oleszczuk, P. Engineered biochars from organic wastes for the adsorption of diclofenac, naproxen and triclosan from water systems. J. Clean. Prod. 2021, 288, 125686. [Google Scholar] [CrossRef] [Scilit]
- Guimarães, T.G.S.; Barros, L.A.; Silva, R.S.; Gonzalez, M.H.; Carrilhoc, E.N.V.M.; Labutoa, G. Synthesis and characterization of biochars modified with natural deep eutectic solvent (NADES) for dipyrone removal from aqueous medium. Sustain. Chem. Pharm. 2023, 35, 101205. [Google Scholar] [CrossRef] [Scilit]
- dos Reis Oliveira, M.; Paulino, I.M.R.; Resende, J.F.; Simão, L.; Vieira, M.F.; Bergamasco, R.; Vieira, A.M.S. Valorization of biomass ash for the effective removal of dipyrone from water: An efficient and low-cost option. J. Chem. Technol. Biotechnol. 2023, 98, 1690–1702. [Google Scholar] [CrossRef] [Scilit]
- Royal Decree 1/2001, of July 20, Which Approves the Consolidated Text of the Water Law. BOE. 2001. Available online: https://www.boe.es/eli/es/rdlg/2001/07/20/1 (accessed on 4 May 2026).
- Vyas, A.J.; Jha, S.A.; Patel, A.B.; Patel, A.I.; Shah, S.R.; Sheth, D.B. Review on simultaneous equation method (Vierodt’s Method). Asian J. Pharm. Anal. 2022, 12, 149–156. [Google Scholar] [CrossRef] [Scilit]
- San José, M.J.; López, R.; Alvarez, S.; Peñas, F.J. Bioadsorbents for the Removal of Pollutants in Wastewater: Adsorption Kinetics, Validation Test Using Methylene Blue and Methyl Orange. Appl. Sci. 2026, 16, 1512. [Google Scholar] [CrossRef] [Scilit]
- D3860-98; Standard Practice for Determination of Adsorptive Capacity of Activated Carbon by Aqueous Phase Isotherm Technique. ASTM International: West Conshohocken, PA, USA, 2020.
- Coates, J. Interpretation of Infrared Spectra, A Practical Approach. In Encyclopedia of Analytical Chemistry; Meyers, R.A., Ed.; Wiley: Chichester, UK, 2000; Volume 12, pp. 10815–10837. [Google Scholar]
- Silverstein, R.M.; Webster, F.X.; Kiemle, D.J.; Bryce, D.L. Infrared Spectroscopy. In Spectrometric Identification of Organic Compounds, 8th ed.; Wiley: Chichester, UK, 2014; pp. 71–125. [Google Scholar]
- Al-Ma’abreh, A.M.; Al-Essa, E.M.; Hmedat, D.A.; Edris, G.; Odeh, F.F.; Hamed, M. Green remediation: Casuarina equisetifolia fruit-based activated carbon for pharmaceutical removal. Sci. Prog. 2025, 108, 00368504251382003. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Cançado, L.G.; Takai, K.; Enoki, T.; Endo, M.; Kim, Y.A.; Mizusaki, H.; Jorio, A.; Coelho, L.N.; Magalhães-Paniago, R.; Pimenta, M.A. General equation for the determination of the crystallite size La of nanographite by Raman spectroscopy. Appl. Phys. Lett. 2006, 88, 163106. [Google Scholar] [CrossRef] [Scilit]
- Bouchelkia, N.; Benazouz, K.; Mameri, A.; Belkhiri, L.; Hamri, N.; Belkacemi, H.; Zoukel, A.; Amrane, A.; Aoulmi, F.; Mouni, L. Study and characterization of H3PO4 activated carbons prepared from jujube stones for the treatment of industrial textile effluents. Processes 2023, 11, 2694. [Google Scholar] [CrossRef] [Scilit]
- Delgado-Moreno, L.; Bazhari, S.; Gasco, G.; Ménde, A.; El Azzouzi, M.; Romero, E. New insights into the efficient removal of emerging contaminants by biochars and hydrochars derived from olive oil wastes. Sci. Total Environ. 2021, 752, 141838. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Wafaa, Y.; Akazdam, S.; Zyade, S.; Chafiq, M.; Ko, Y.G.; Chafi, M.; Tahiri, M.; Alrashdi, A.A.; Lgaz, H. Mechanistic insights into methylene blue removal via olive stone-activated carbon: A study on surface porosity and characterization. J. Saudi Chem. Soc. 2023, 27, 101692. [Google Scholar] [CrossRef] [Scilit]
- Ozcan, D.O.; Hendekcï, M.C.; Ovez, B. Enhancing the adsorption capacity of organic and inorganic pollutants onto impregnated olive stone derived activated carbon. Heliyon 2024, 10, e32792. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- García-Mateos, F.J.; Ruiz-Rosas, R.; Marqués, M.D.; Cotoruelo, L.M.; Rodríguez-Mirasol, J.; Cordero, T. Removal of paracetamol on biomass-derived activated carbon: Modeling the fixed bed breakthrough curves using batch adsorption experiments. Chem. Eng. J. 2015, 279, 18–30. [Google Scholar] [CrossRef] [Scilit]
- Naushad, M.; Khan, M.A.; Alothman, Z.A.; Khan, M.R.; Kuma, M. Adsorption of methylene blue on chemically modified pine nut shells in single and binary systems: Isotherms, kinetics, and thermodynamic studies. Desalin. Water Treat. 2016, 57, 15848–15861. [Google Scholar] [CrossRef] [Scilit]
- Hashemzadeh, F.; Ariannezhad, M.; Derakhshandeh, S.H. Sustainable removal of tetracycline and paracetamol from water using magnetic activated carbon derived from pine fruit waste. Sci. Rep. 2024, 14, 16346. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Kim, H.J.; Han, J.W.; Yu, J.H.; Jun, B.M.; Chon, K. Adsorption of charged synthetic organic dyes by pine nut husk biochars modified with hydroxyapatite: Adsorption mechanisms and reusability. Desalin. Water Treat. 2025, 321, 100970. [Google Scholar] [CrossRef] [Scilit]
- Al-sharify, Z.T.; Muhaisen, L.F.; Alsharify, T.A.; Al-sharify, N.; Faisa, F. Removal of Analgesic Paracetamol From Wastewater Using Dried Olive Stone. Int. J. Mech. Eng. Technol. 2018, 9, 293–299. [Google Scholar]
- Medjdoub, F.; Louhab, K.; Hamouche, A. Comparative study of the adsorption of paracetamol from aqueous solution on olive stones and date pits. Desalin. Water Treat. 2018, 10, 225–233. [Google Scholar] [CrossRef] [Scilit]
- Narloch, I.; Wejnerowska, G.; Wojewodzki, P. Biosorption of Aspirin, Salicylic Acid, Ketoprofen, and Naproxen in Aqueous Solution by Walnut Shell Biochar: Characterization, Equilibrium, and Kinetic Studies. Molecules 2025, 30, 4731. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Tanhaei, B.; Ayati, A.; Iakovleva, E.; Sillanpää, M. Efficient carbon interlayed magnetic chitosan adsorbent for anionic dye removal: Synthesis, characterization and adsorption study. Int. J. Biol. Macromol. 2020, 164, 3621–3631. [Google Scholar] [CrossRef] [Scilit] [PubMed]






































| Pharmaceutical (Format) | Active Principle | Structure | Molecular Weight (g/mol) | Density (kg/m3) | Solubility (mg/mL) | pKa | Excipients |
|---|---|---|---|---|---|---|---|
| Paracetamol (tablets) | Paracetamol C8H9NO2 (650 mg; 49.9%) | ![]() | 151.165 | 1293 | 12.78 | 9.5 | Pregelatinized maize starch, microcrystalline cellulose, sodium starch glycolate, povidone. |
| Ibuprofen (tablets) | Ibuprofen C13H18O2 (600 mg; 77.4%) | ![]() | 206.285 | 1030 | 0.021 | 4.45 | Core: croscarmellose sodium, hypromellose, lactose monohydrate, alline cellulose, pregelatinized corn starch, colloidal silica, magnesium stearate. Coating: hypromellose, titanium dioxide, talc. |
| Nolotil (capsules) | Nolotil (Metamizole Magnesium) C26H32MgN6O8S2 (575 mg; 95.8%) | ![]() | 645.001 | 680 | 10 | −1.4/−0.54 | Magnesium stearate, indigotine, erythrosine, titanium dioxide, gelatin. |
| Enantyum (tablets) | Enantyum (Dexketoprofen) C16H14O3 (25 mg; 9.4%) | ![]() | 254.28 | 1250 | 0.021 | 4.5 | Core: corn starch, microcrystalline cellulose, sodium starch glycolate, glycerol distearate. Coating: hypromellose, titanium dioxide, macrogol. |
| Termalgin (tablets) | Termalgin (Paracetamol, Phenylephrine bitartrate, Chlorphenamine maleate) C8H9NO2 (500 mg; 81.4%) C13H19NO8 C20H23ClN2O4 | ![]() ![]() ![]() ![]() | 151.165 317.29 90.86 | 1293 1122 1198 | 12.78 161 250 | 9.5 9.07 9.47 | Core: pregelatinized corn starch, calcium carbonate, alginic acid, crospovidone, povidone, magnesium stearate, colloidal silica. Coating: opadry white, carnauba wax. |
| Aspirin (effervescent granules) | Aspirin (Acetylsalicylic acid) C9H8O4 (500 mg; 14.6%) Phenylephrine C9H13NO2 (8.21 mg; 0.24%), Chlorphenamine C16H19N2Cl (1.41 mg; 0.04%) | ![]() ![]() ![]() | 180.16 167.21 274.79 | 1400 1200 1108 | 3.49 100 550 | 3.5 9.07 3.64 | Citric acid, sodium bicarbonate, lemon flavor, quinoline yellow dye. |
| Adsorbent | D-Band (cm−1) | G-Band (cm−1) | ID/IG Ratio | La (nm) |
|---|---|---|---|---|
| OSPC | 1351 | 1598 | 0.847 | 22.7 |
| OSPC/PAR | 1351 | 1590 | 0.861 | 22.3 |
| OSPC/IBU | 1349 | 1587 | 0.853 | 22.5 |
| OSPC/NOL | 1349 | 1590 | 0.889 | 21.6 |
| OSPC/ENA | 1347 | 1587 | 0.857 | 22.4 |
| OSPC/TER | 1347 | 1587 | 0.872 | 22.0 |
| OSPC/ASP | 1342 | 1586 | 0.871 | 22.1 |
| PNSPC | 1349 | 1597 | 0.827 | 23.2 |
| PNSPC/PAR | 1346 | 1587 | 0.867 | 22.2 |
| PNSPC/IBU | 1341 | 1590 | 0.875 | 22.0 |
| PNSPC/NOL | 1347 | 1587 | 0.897 | 21.4 |
| PNSPC/ENA | 1342 | 1587 | 0.835 | 23.0 |
| PNSPC/TER | 1342 | 1589 | 0.871 | 22.1 |
| PNSPC/ASP | 1347 | 1587 | 0.879 | 21.9 |
| Adsorbent | SBET (m2 g−1) | dp (nm) | VT (cm3 g−1) |
|---|---|---|---|
| OSPC | 1535 | 2.2264 | 0.854342 |
| PNSPC | 1076 | 1.6126 | 0.433962 |
| CAC | 921 | 2.9418 | 0.6775 |
| Adsorbent | Activating Method | Operating Conditions | Adsorption Capacity (mg/g) | Adsorption Efficiency (%) | Models | References |
|---|---|---|---|---|---|---|
| PAR | ||||||
| Olive stones | Washing | Co = 200 mg/L, S = 2.5 g/L, pH = 7, T = 25 °C, t = 3 h | 3.33 | 90 | [42] | |
| Olive stones | Hexane + thermal treatment | Co = 20–100 μm, S = 10 mg, V = 25 mL, pH = 6, T = 20 °C, t = 3 h | 37.12 | 98.19 | PSO Langmuir | [43] |
| Olive stones | H3PO4+ thermal treatment | Co = 0.3–10 mg/L, S = 100 mg/L, T = 15–35 °C, t = 10 h | 40–45 | - | Langmuir | [38] |
| Pine nut shells | Carbonization/H2SO4/co-precipitation | Co = 20 mg/L, S = 0.4–2 g/L, pH = 6, T = 25 °C, t = 2 h | 41.7 | PSO Langmuir | [40] | |
| IBU | ||||||
| Olive stones | Thermal treatment | Co = 4.7 g/L, S = 0.05 g, T = 20 °C | 6 10−3 | 43 | PSO Freundlich | [35] |
| NOL | ||||||
| Yeast/cork/coffee wastes | Thermal treatment | Co = 20–340 mg/L, S = 4 g/L, pH 6, t = 30 min | 30.9/52.1/47.08 | 31/52/47 | PFO, PSO Langmuir | [24] |
| Eucalyptus wood chips ash | Burning | Co = 20 mg/L, S = 0.4–40 g/L, V = 25 mL, T = 25, 35, 45 °C, pH 2–12, t = 24 h | 42 | 86 | PFO Langmuir | [25] |
| ASP | ||||||
| Walnut shell | Pyrolysis | Co = 25 mg/L, S = 1 g/L, T = room, pH 2–9, t = 1 h | 15.28 | 96.1–99.8 | PSO Freundlich | [44] |
| OSPC | ||||
|---|---|---|---|---|
| S = 5 g/L | S = 20 g/L | |||
| Cycle Number | η (%) | Removal (mg) | η (%) | Removal (mg) |
| 1 | 98.24 | 4.91 | 98.37 | 4.92 |
| 2 | 91.29 | 4.56 | 98.14 | 4.91 |
| 3 | 89.15 | 4.46 | 97.81 | 4.89 |
| 4 | 87.37 | 4.37 | 96.14 | 4.81 |
| 5 | 95.62 | 4.78 | ||
| 6 | 93.16 | 4.66 | ||
| 7 | 92.04 | 4.60 | ||
| 8 | 89.71 | 4.49 | ||
| 9 | 88.36 | 4.42 | ||
| 10 | 87.82 | 4.39 | ||
| 11 | 86.93 | 4.35 | ||
| 12 | 86.48 | 4.32 | ||
| 13 | 86.13 | 4.31 | ||
| 14 | 85.93 | 4.30 | ||
| 15 | 85.48 | 4.27 | ||
| 18.30 | 68.41 | |||
| qexp (mg/g) = | 36.61 | qexp (mg/g) = | 34.20 | |
| MIXTURE | NOL Removal (%) | IBU Removal (%) | ASP Removal (%) | PAR Removal (%) | ENA Removal (%) | TER Removal (%) |
|---|---|---|---|---|---|---|
| NOL+ASP | 41 | 55 | ||||
| NOL+IBU | 42 | 51 | ||||
| NOL+ENA | 23 | 97 | ||||
| PAR+IBU | 46 | 66 | ||||
| PAR+TER * | 78 * | 78 * |
| Model | Model Equation | Equation |
|---|---|---|
| Pseudo-first order | qt = qe (1 − e−k1·t) | (3) |
| Pseudo-second order | (4) | |
| Intra-particle diffusion | qt = ki·t0.5 + I | (5) |
| Elovich | qt = a + b lnt | (6) |
| Model | Model Equation | Equation |
|---|---|---|
| Langmuir | (7) | |
| Freundlich | (8) | |
| Sips | (9) | |
| Dubinin–Radushkevich | qe = qm exp(−KD–R ε2) | (10) |
| ε = RT ln (1 + 1/Ce) | (11) | |
| (12) |
| OSPC | PAR | IBU | NOL | ENA | TER | ASP | |
|---|---|---|---|---|---|---|---|
| Parameters | Langmuir | ||||||
| qm (mg/g) | 48.3 | 33.11 | 196.08 | 108.69 | 48.31 | 33.44 | |
| KL (L/mg) | 0.36 | 0.20 | 0.0098 | 0.102 | 0.29 | 0.46 | |
| R2 | 0.948 | 0.976 | 0.998 | 0.970 | 0.951 | 0.911 | |
| RMSE | 2.561 | 2.251 | 0.400 | 2.156 | 2.404 | 2.965 | |
| RSS | 32.787 | 25.344 | 0.799 | 23.234 | 28.893 | 43.942 | |
| AIC | 13.403 | 12.116 | −5.171 | 11.681 | 12.771 | 14.867 | |
| Parameters | Freundlich | ||||||
| KF (mg1−1/n g−1L1/n) | 13.59 | 8.30 | 2.12 | 10.59 | 12.19 | 12.81 | |
| n | 2.33 | 2.59 | 1.09 | 1.31 | 2.22 | 3.50 | |
| R2 | 0.982 | 0.992 | 0.996 | 0.982 | 0.988 | 0.966 | |
| RMSE | 1.523 | 0.661 | 0.592 | 1.749 | 1.266 | 1.821 | |
| RSS | 11.603 | 2.182 | 1.754 | 15.289 | 8.008 | 16.582 | |
| AIC | 8.209 | −0.146 | −1.238 | 9.588 | 6.355 | 9.994 | |
| Parameters | Sips | ||||||
| KS (L/mg) | 0.54 | 0.61 | 0.16 | 0.36 | 0.51 | 0.77 | |
| n | 2.60 | 3.03 | 1.34 | 1.41 | 2.46 | 3.79 | |
| R2 | 0.907 | 0.955 | 0.984 | 0.770 | 0.912 | 0.910 | |
| RMSE | 6.800 | 5.408 | 5.263 | 8.425 | 6.533 | 6.157 | |
| RSS | 231.22 | 146.228 | 138.516 | 354.928 | 213.390 | 189.519 | |
| AIC | 23.180 | 20.879 | 20.608 | 32.007 | 22.768 | 22.175 | |
| Parameters | Dubinin–Radushkevich | ||||||
| qm (mg/g) | 31.98 | 24.91 | 47.27 | 52.57 | 31.97 | 24.12 | |
| KD-R (mol2 kJ−2) | 0.0004 | 0.0008 | 0.0038 | 0.001 | 0.0005 | 0.0003 | |
| E (kJ mol−1) | 35.35 | 25.00 | 11.47 | 22.36 | 31.62 | 40.82 | |
| R2 | 0.811 | 0.855 | 0.988 | 0.918 | 0.825 | 0.749 | |
| RMSE | 5.254 | 2.631 | 0.928 | 4.071 | 4.836 | 4.050 | |
| RSS | 138.043 | 34.598 | 4.303 | 82.851 | 116.930 | 17.987 | |
| AIC | 20.591 | 13.672 | 3.249 | 18.038 | 19.761 | 0.749 | |
| PNSPC | PAR | IBU | NOL | ENA | TER | ASP | |
| Parameters | Langmuir | ||||||
| qm (mg/g) | 22.47 | 21.36 | 42.37 | 54.64 | 20.32 | 20.49 | |
| KL (L/mg) | 0.18 | 0.34 | 0.02 | 0.025 | 0.95 | 1.05 | |
| R2 | 0.976 | 0.941 | 0.993 | 0.993 | 0.921 | 0.855 | |
| RMSE | 0.589 | 1.161 | 0.331 | 0.421 | 2.103 | 2.394 | |
| RSS | 1.736 | 6.737 | 0.547 | 0.887 | 22.115 | 28.646 | |
| AIC | −1.289 | 5.491 | −7.065 | −4.648 | 11.434 | 12.728 | |
| Parameters | Freundlich | ||||||
| KF (mg1−1/n g−1L1/n) | 6.40 | 8.60 | 1.89 | 2.08 | 11.87 | 11.87 | |
| n | 3.02 | 4.00 | 1.47 | 1.38 | 6.24 | 6.14 | |
| R2 | 0.991 | 0.981 | 0.996 | 0.991 | 0.982 | 0.950 | |
| RMSE | 0.329 | 0.518 | 0.238 | 0.476 | 0.542 | 0.859 | |
| RSS | 0.541 | 1.342 | 0.282 | 1.133 | 1.470 | 3.689 | |
| AIC | −7.117 | −2.578 | −10.368 | −3.421 | −2.122 | 2.480 | |
| Parameters | Sips | ||||||
| KS (L/mg) | 1.00 | 1.21 | 0.001 | 0.28 | 1.48 | 3.22 | |
| n | 3.70 | 38.21 | 0.36 | 1.84 | 92.59 | 2.17 | |
| R2 | 0.988 | 0.979 | 0.962 | 0.999 | 0.984 | 0.994 | |
| RMSE | 3.384 | 5.676 | 7.851 | 4.494 | 3.521 | 3.628 | |
| RSS | 34.361 | 161.094 | 308.205 | 100.993 | 61.986 | 65.821 | |
| AIC | 13.315 | 21.363 | 24.607 | 19.028 | 16.587 | 16.888 | |
| Parameters | Dubinin–Radushkevich | ||||||
| qm (mg/g) | 20.36 | 18.38 | 25.41 | 29.76 | 18.90 | 18.01 | |
| KD-R (mol2 kJ−2) | 0.0014 | 0.0006 | 0.0043 | 0.004 | 0.0002 | 0.0002 | |
| E (kJ mol−1) | 18.90 | 28.87 | 10.78 | 11.18 | 50.00 | 50.00 | |
| R2 | 0.956 | 0.900 | 0.955 | 0.965 | 0.869 | 0.798 | |
| RMSE | 0.753 | 1.231 | 7.981 | 1.015 | 1.493 | 1.772 | |
| RSS | 2.835 | 7.573 | 318.520 | 5.147 | 11.148 | 15.700 | |
| AIC | 1.164 | 6.076 | 24.771 | 4.145 | 8.009 | 9.721 | |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
Share and Cite
López, R.; San José, M.J.; Alvarez, S.; Peñas, F.J. Adsorption of Pharmaceutical Formulations onto Non-Conventional Biocarbons. Appl. Sci. 2026, 16, 7157. https://doi.org/10.3390/app16147157
López R, San José MJ, Alvarez S, Peñas FJ. Adsorption of Pharmaceutical Formulations onto Non-Conventional Biocarbons. Applied Sciences. 2026; 16(14):7157. https://doi.org/10.3390/app16147157
Chicago/Turabian StyleLópez, Raquel, María J. San José, Sonia Alvarez, and Francisco J. Peñas. 2026. "Adsorption of Pharmaceutical Formulations onto Non-Conventional Biocarbons" Applied Sciences 16, no. 14: 7157. https://doi.org/10.3390/app16147157
APA StyleLópez, R., San José, M. J., Alvarez, S., & Peñas, F. J. (2026). Adsorption of Pharmaceutical Formulations onto Non-Conventional Biocarbons. Applied Sciences, 16(14), 7157. https://doi.org/10.3390/app16147157












