The quantum calculation of 2,5-Furandicarboxylic acid (FDA) structure using the density functional theory is reported in this paper. Then, the physicochemical characteristics and the biological properties of the title compound are determined. The geometrical structure is optimized using B3LYP/6-311++G(d,p) level of theory. In this context, the structural parameters with and without dispersion correction are calculated and compared with X-ray data, showing good agreement. Besides, the FTIR spectrum is simulated in the range 0-4000cm-1 and compared with the experimental one. The strongest electrophilic (H14 and H15) and nucleophilic (O4 and O5) sites are identified using MEP analysis. The weak gap energy value (-4.98eV) demonstrates the high chemical reactivity and the easier electronic passage. In addition, the electrophile index (5.07eV) indicates that the investigated molecule is a good electrophile. Furthermore, the topological study shows the establishment of hydrogen bonding interactions (O-H & mldr;O) among the carboxylic acids. These bonds are associated with a -27.6 kcal/mol interaction energy value. The non-covalent C-H & mldr;O, O-H & mldr;O and O-H & mldr;C interactions responsible for the crystal stability and the pi & mldr;pi stacking interaction were discovered using Hirshfeld surface analysis. As a final point, docking analysis and ADME properties are presented to explore the pharmaceutical features of the title compound. The finding results show that the FDA presents good results with 1DQN, 1VZV, 4NZK, 9H9V and 2QGO, demonstrating their ability to be an anti-viral, anti-inflammatory and anti-microbial compound.

Humans perceived rosy odorants, as well as other odorant molecules, through olfactory receptors that belong to the family of seven-transmembrane GPCRs. However, characterizing olfactory receptors remains a major challenge, largely due to the lack of X-ray crystallographic structures with high resolution. In this work, a theoretical statistical physics simulation and analysis, validated with molecular docking calculations, was applied to obtain deeper insight into human olfactory perception function by reducing the docking process to an adsorption one. Fitting results showed that human OR2A25 responded selectively to rosy odorants such as phenyl alcohol, geraniol, and citronellol. From a microscopic perspective, an advanced statistical physics characterization, based on a monolayer model with one adsorption energy (MM1E), provided a high degree of precision in characterizing and understanding the docking mechanism that cannot be obtained by experimental methods. Indeed, docking simulations revealed that the adsorption process involves binding energies 12.13 kJ/mol for phenyl alcohol-OR2A25, 10.04 kJ/mol for geraniol-OR2A25, and 8.78 kJ/mol for citronellol-OR2A25. Thus, these docking energy values obtained by molecular docking simulation were found to be slightly close to molar adsorption energies obtained by statistical physics modeling. From a macroscopic perspective, four thermodynamic functions, governing the mechanism of adsorption, were examined. The evolution of disorder during the proposed adsorption process was assessed through analysis of the configurational entropy. Moreover, the adsorption process involved in the three tested olfactory systems was found to be exothermic and spontaneous, as indicated by the values of the internal energy, enthalpy, and Gibbs free energy.

Theoretical analysis of for aroma regulation of more-extended taste items (fruit, tea, etc.) can also be obtained by analyzing the formation mechanism of characteristic aroma. Hexanal, octanal, nonanal, and decanal were widely distributed in foods, particularly fruits, and citrus products, where they contributed green and citrus aroma notes. In this study, four aroma compounds were theoretically investigated and characterized. Indeed, molecular docking simulation was employed to reveal the interactions of hydrogen bonds and hydrophobic forces of the human olfactory receptor OR1A1 with the studied aroma compounds (i.e., decanal, nonanal, octanal, and hexanal). Hence, the binding energies of decanal, nonanal, octanal, and hexanal on OR1A1 were 25.52 kJ/mol, 16.73 kJ/mol, 14.64 kJ/mol, and 13.38 kJ/mol, respectively. The Asp180/Asn176/Thr273 (octanal), Tyr258 (nonanal), Asn292 (octanal), and Tyr258 (hexanal) were key amino acid residues, providing a theoretical basis for the regulation of food characteristic flavor. Additionally, the docking mechanism involved in the olfactory perception of the tested aroma compounds on OR1A1 was also studied via theoretical investigations through statistical physics approach using a new theoretical model. Finally, both statistical physics and molecular docking theories provided a consistent interpretation of the mechanism of adsorption putatively involved in the olfactory perception of four characteristic aroma compounds frequently used in food industries.

Olfactory receptors connected animals to airborne odorants. Interestingly, humans were able to detect the pheromones released by female flies. In this work, the study of the docking mechanism of the Zimbabwe fruit fly Drosophila melanogaster pheromone Z4-9Al ((Z)-4-nonenal) and the cosmopolitan fruit fly Drosophila melanogaster pheromone Z4-11Al ((Z)-4-undecenal) on the broadly tuned human olfactory receptor OR2W1 was theoretically performed to provide new insights into the complexes formed between the tested pheromones and the olfactory receptor. The two olfactory systems were investigated through the adjustment of the well-known in vitro concentration–response curves using two theoretical models. The adsorption of Z4-9Al on OR2W1, which presented a saturation level, was fitted using the ideal gas monolayer model, while the olfactory response of Z4-11Al, which showed a decline succeeding saturation, was fitted with the real gas monolayer model. Indeed, modeling results indicated that the Z4-9Al and Z4-11Al were adsorbed on OR2W1 via multi-molecular and mixed mechanisms, respectively. The downtrend observed in the olfactory response of Z4-11Al was attributed to the influence of van der Waals variables, which can describe the lateral interaction effects. The estimation of the molar adsorption energies revealed the formation of physical (weak) interactions between the pheromones and the human receptor binding sites. The thermodynamic analysis demonstrated that the disorder of the tested system was maximal at the level of the energetic parameters (C1/2 and X1/2) and the docking mechanism proceeded spontaneously toward saturation. For Z4-11Al, the Gibbs free energy behavior indicated that the lateral interactions between the pheromone molecules disfavored the adsorption process at high concentration. In addition the geometrical and MEP studies show that the Zimbabwe fruit fly Drosophila melanogaster pheromone was chemically more reactive than the other pheromone. Then, the topological analyses of pheromones in OR2W1 active sites suggest that Z4-9Al was easily absorbed by OR2W1 then Z4-11Al. Finally, docking simulation of OR2W1-Z4-9Al/Z4-11Al were consistent with results obtained with statistical study, and proved that Z4-9Al was better docked on OR2W1 than Z4-11Al.

Hydrogen adsorption on MOF-74/184-M (M = Mg2+, Ni2+) was investigated using a monolayer model with four types of site derived from statistical physics within the grand canonical ensemble. This work provides a novel multi-site statistical physics framework that enables a detailed molecular-level interpretation of hydrogen adsorption mechanisms in ligand-exchanged MOF systems. Key physicochemical parameters, including the number of adsorbed molecules per site, site density, and adsorption energy, were determined and analyzed as a function of temperature. The results reveal that hydrogen adsorption is exothermic and strongly dependent on the nature of the metal center. The adsorption energies range from 2 to 11 kJ.mol-1 for MOF-74/184-Mg and from 3 to 13 kJ.mol-1 for MOF-74/184-Ni, indicating that the process is governed by physisorption. Furthermore, the model enables the evaluation of thermodynamic functions such as Gibbs free energy, internal energy, and entropy, providing a consistent description of the adsorption behavior.

A monolayer model with three energies, developed based on statistical physics, was applied to analyze the adsorption mechanisms of sotolone and abhexone on the human olfactory receptor OR8D1. The first type of binding site played a dominant role in this food odorant mechanism, with OR8D1 binding sites arranged in non-parallel orientations, indicating a multimolecular process. Molar adsorption energies associated with the three types of binding sites, ranging from 23.75 to 32.97 kJ mol− 1, demonstrated that the food odorants were physically and exothermically adsorbed on the human OR8D1 receptor.

The recovery and upgrading of low-grade thermal energy has become an important challenge for improving industrial energy efficiency. Adsorption heat transformers (AdsHT) provide a viable solution by converting waste heat into higher-temperature heat streams exceeding 120 °C through reversible adsorption–desorption cycles. In this study, the thermodynamic performance of an AdsHT system was assessed using two post-synthetically modified MOF-808 materials, MOF-808NDS and MOF-808PDS, as adsorbents for water vapor. A statistical physics approach based on the grand canonical ensemble was applied to investigate the adsorption mechanism and to determine the key energetic and structural parameters governing the process. The modeling results reveal that water adsorption on both materials can be described by a monolayer model involving two distinct adsorption energy levels. Stereographic analysis suggests that water molecules interact with the adsorption sites mainly in a non-parallel orientation. The calculated adsorption energies, lower than 40 kJ mol⁻¹, indicate that the process is dominated by weak physical interactions such as hydrogen bonding and van der Waals forces. Furthermore, pore size distribution analysis confirms the microporous structure of the studied frameworks. The thermodynamic analysis of the adsorption cycle shows coefficients of performance (COPGCSP) of 0.764 for MOF-808NDS and 0.826 for MOF-808PDS, highlighting the superior efficiency of MOF-808PDS due to its higher water uptake and favorable pore characteristics. These findings demonstrate that functionalized MOF-808 materials are promising candidates for enhancing the performance of adsorption heat transformer systems dedicated to sustainable thermal energy utilization.

In this study, the critical magnetic behavior of PrSr1-xPbxMn2O6 (x = 0.4, 0.5, 0.6) double perovskite manganites was systematically investigated through experimental and theoretical approaches. Magnetization measurements near the paramagnetic-to-ferromagnetic (PM-FM) transition were analyzed using modified Arrott plots (MAPs) and the Kouvel-Fisher (KF) method to extract critical exponents (beta, gamma) and the Curie temperature $\lpar {{\rm T}_{\rm C}} \rpar$(TC). The couples (gamma; beta) are systematically optimized to attain (1.0865; 0.5324), (1.1242; 0.4206) and (0.8890; 0.5139) for the samples with x = 0.4, 0.5 and 0.6, respectively. The results show a consistent mean-field-like behavior in Pb04 and Pb06, with deviations in Pb05 indicating enhanced spin fluctuations. Landau theory was employed to model the Gibbs free energy, allowing for the simulation of isothermal magnetization ${\rm M}\lpar {{\rm H}\comma \; {\rm T}} \rpar$M(H,T) and magnetic entropy change $-\Delta {\rm S}_{\rm M}\lpar {\rm T} \rpar$-Delta SM(T) curves. Simulated $-\Delta {\rm S}_{\rm M}\lpar {\rm T} \rpar$-Delta SM(T) results showed a strong agreement with experimental values calculated via the Maxwell relation.

This study presents a comprehensive experimental and theoretical investigation of Catechol adsorption onto pinecone-derived activated carbon (PB600) for water remediation applications. Adsorption equilibrium data were modeled using four statistical physics-based isotherm formulations, systematically fitted to the experimental results. Convergence was evaluated through rigorous error analysis using reduced chi-square (χ2), residual sum of squares (RSS), coefficient of determination (R2), and adjusted R^2_adj . Among the tested scenarios, the monolayer adsorption model with a single energy level provided the best fit, revealing a maximum adsorption capacity (Qₘₐₓ) of 263.8 mg·g−1 at 298 K. The stereographic analysis showed that the occupation number (n) remained below unity across all temperatures, indicating a horizontal molecular orientation and a multi-point attachment mechanism on the adsorbent surface. The thermodynamic insights derived from the accurate model parameters revealed that surface accumulation is exothermic and spontaneous, as evidenced by the negative values of internal energy and Gibbs free energy. The adsorption energy values remained consistently below 40 kJ·mol−1, confirming that the process is driven by physisorption involving van der Waals forces, π–π interactions, and hydrogen bonding. Additionally, entropy increased with both temperature and concentration, suggesting enhanced molecular disorder at higher loading. A temperature-driven transition in adsorption behavior was observed around 302 K, beyond which the density of receptor sites (Nₘ) increased sharply, indicating thermally induced structural changes in the adsorbent and improved site accessibility. The outcomes demonstrate the potential of PB600 as a high-performance and renewable bio-adsorbent. Its strong adsorption capacity under moderate conditions, combined with low-energy binding characteristics, positions it as a promising material for scalable, eco-friendly treatment of phenolic pollutants. These findings support future development of hybrid or modular filtration systems tailored for real-world applications in industrial and decentralized water purification.

In this investigation, we deployed four advanced statistical physics models within the grand canonical ensemble to scrutinize the adsorption forces and thermodynamics governing the removal of hydroquinone (1,4-benzenediol, HYD) onto the biochar surface, contributing to advancements in water remediation. Our main findings demonstrated the effectiveness of a monolayer model with a single-site energy distribution for describing, at the molecular scale, the binding mechanism within biochar pores. By leveraging this framework, we successfully computed the key steric parameters and derived essential thermodynamic functions (molar entropy, molar internal energy, and Gibbs free energy). Thermodynamic analysis revealed that the microscopic docking of hydroquinone onto the adsorbent’s available sites is a spontaneous, endothermic (heat-consuming), and energetically favorable process. Furthermore, the magnitude of the internal energy confirms physisorption, in which weak physical interactions (van der Waals forces) primarily govern surface occupancy. Analysis of the pore size distribution (PSD) indicated that pine biochar is primarily composed of macropores, while the observed distribution of adhesion energies (AED) provided strong evidence supporting the physisorption mechanism.

The growing demand for efficient and sustainable thermal management technologies has intensified research on adsorption-based refrigeration systems. In this study, CO2 adsorption on two highly microporous activated carbons, Maxsorb III and ACF-A20, is investigated using a grand canonical statistical physics (GCSP) framework to provide a detailed thermodynamic and energetic description of the process. The monolayer model with a single effective energy provides an excellent representation of the experimental isotherms and allows the determination of key physicochemical parameters, including site occupancy, density of accessible adsorption sites, saturation capacity, and adsorption energy. The results indicate that CO2 adsorption is predominantly governed by physisorption within confined porous structures. The temperature dependence of the model parameters shows a systematic decrease in site occupancy, accompanied by enhanced site accessibility and reduced saturation capacity, reflecting the combined influence of thermal agitation and confinement effects. Based on the derived adsorption framework, thermodynamic functions such as internal energy, enthalpy, and Helmholtz free energy are evaluated as functions of pressure and temperature, confirming the spontaneous and exothermic nature of the adsorption process and its relevance for thermal energy storage and conversion applications. Furthermore, these thermodynamic insights are applied to assess the performance of two adsorption refrigeration cycle configurations. At 363 K, the predicted coefficients of performance (COP) are 0.59 and 0.89 for cycle I, and 0.79 and 0.64 for cycle II, for Maxsorb III and ACF-A20, respectively. Overall, this work highlights the capability of statistical physics modeling to bridge microscopic adsorption mechanisms with macroscopic thermal system performance, providing useful guidelines for the design and optimization of advanced adsorption cooling systems.

The effective removal of antibiotics and non-steroidal anti-inflammatory drugs and their combined pollutants is critical for both the aquatic environment and human health. This study evaluates the removal of pharmaceutical waste through the adsorption of aspirin and tetracycline hydrochloride (TC) onto the surface of a UiO-66/Polydopamine/Bacterial Cellulose composite (UiO-66/PDA/BC). Both theoretical and experimental approaches were considered to investigate the removal of aspirin and TC. The theoretical study, based on statistical physics theory, employs three analytical models to describe the adsorption phenomena of these drugs at the molecular level. According to the fitting results, the adsorption of both drugs onto the UiO-66/PDA/BC composite is an endothermic process and follows a monolayer adsorption mechanism with one type of site. Regarding the number of adsorbed molecules per site (n), the analysis indicates that both multi-docking (n < 1) and multi-molecular (n > 1) adsorption mechanisms are possible for aspirin and TC on UiO-66/PDA/BC. The adsorption capacities at saturation of the UiO-66/PDA/BC adsorbent deduced by the monolayer model are found to be 147.34-215.05 mg/g for aspirin and 193.72-246.66 mg/g for TC. Furthermore, adsorption energy calculations suggest that the removal of these pharmaceutical pollutants occurs primarily through physical interactions. The thermodynamic analysis confirms the spontaneous and feasible nature of the adsorption of both drugs onto the UiO-66/PDA/BC composite.

Herein, a novel dual metal (Nd3+/Zr4+) doped In2O3 structure integrated in reduced graphene nanolayers is prepared to rationally optimize charge carrier density, charge separation, and transfer dynamics along with pollutant-catalyst interaction to facilitate the photo-degradation of benzimidazole antibiotic. The opto-physical studies substantiate that Zr4+ trap sites and Nd3+ donor states improved charge carrier behavior, leading to improved electronic and surface redox properties. Under the UV light irradiation, the synergistic co-doping effect was significant: the Nd3+/Zr4+ co-doped In2O3 photocatalyst (at the optimal Nd-doping content, Nd-ZrINO3) achieved 62.9% benzimidazole degradation, outperforming Zr-In2O3 (36.2%). Notably, graphene nanolayers incorporated into an Nd-ZrINO3 composite delivered 91.8% degradation of benzimidazole within 40 min of light exposure, along with the highest pseudo-first-order kinetics (k = 0.061 min(-1)), signifying the role of graphene as an electron-accepting/transporting scaffold. Key operational parameters were systematically examined to ascertain the optimal catalyst content of 20 mg and maximum activity at pH 9. However, higher catalyst dosage and alkaline conditions reduced photocatalytic activity due to quenching and passivation effects. Scavenging studies corroborated a radical-driven photo-degradation pathway, where center dot OH radicals were the dominant active species with center dot O-2(-) contributing secondarily. The G-Nd-ZrINO3 heterostructure also exhibited high cyclic stability, retaining high activity up to five photocatalytic experiments (91.8% -> 85.5%). Inclusive of this, the study shows that Zr/Nd co-doping coupled with graphene integration is a viable approach to enhance the photodegradation of benzimidazole, offering a stable and efficient platform for wastewater treatment.

This work investigates the magnetocaloric effect, characterized by the magnetic entropy change - Δ S_M( H,T) , using isothermal magnetization data for PrSr1−xPbxMn2O6 (x = 0.4, 0.5, and 0.6), denoted as Pb04, Pb05, and Pb06. The analysis was performed using experimental magnetization isotherms, M(H, T), and mean-field theory (MFT). The exchange field, Hexch, spontaneous magnetization, MS, and saturation magnetization, M_0 , were determined through scaling analysis, Arrott plots, and entropy–magnetization correlations. Hexch exhibited a predominantly linear dependence on M, with negligible cubic contribution, yielding exchange parameter λ1 values of 1.71, 1.97, and 1.73 T·emu−1·g for Pb04, Pb05, and Pb06, respectively. Critical exponent β values obtained from both - Δ S_M versus M2 and H/M versus M2 were close to the MFT prediction (β ≈ 0.5), confirming second-order ferromagnetic–paramagnetic transitions. Numerical solutions of the MFT equation reproduced M(H, T) and - Δ S_M( H,T) curves in close agreement with experimental results, particularly at higher magnetic fields, validating the model’s applicability to these compounds.

The adsorption behavior of CO2 and N2 on zeolitic imidazolate frameworks (ZIF-8 and ZIF-67) is investigated using a statistical physics approach. Experimental adsorption isotherms are measured over a temperature range of 268–323 K and pressures up to 3000 kPa. To provide a detailed microscopic interpretation of the adsorption mechanism, an advanced model based on statistical physics (AMSP) is employed, enabling the determination of key adsorption parameters such as the number of gas molecules captured per site, adsorption site density, and total number of adsorbed layers. The results reveal that CO2 exhibits significantly higher affinity for ZIFs compared to N2, with maximum saturation adsorption capacities of 4.28 mmol g− 1 for CO2 on ZIF-8 and 5.13 mmol g− 1 for CO2 on ZIF-67, compared to 2.37 mmol g− 1 and 3.09 mmol g− 1 for N2, respectively. Most of the adsorption sites capture more than one molecule, indicating a multimolecular adsorption mechanism, with the total number of adsorbed layers ranging from 1.55 to 4.43 depending on gas type, temperature, and adsorbent. The adsorption process is found to be physical and exothermic, with adsorption energies below 10 kJ mol− 1 and capacity decreasing by up to 35

This study investigates magnetohydrodynamic (MHD) flow of a tangent hyperbolic nanofluid (HNF) over a stretching surface, incorporating thermal radiation, chemical reactions, and Soret-Dufour effects within a Darcy-Forchheimer porous medium. The governing partial differential equations (PDEs) are first converted into ordinary differential equations (ODEs) using appropriate similarity transformations. The MATLAB bvp4c algorithm is used to solve and generate a dataset for the Levenberg-Marquardt backpropagation artificial neural network (LMBP-ANN) numerically. The ANN model is trained, tested, and validated using comprehensive datasets generated for various fluid parameters, with accuracy assessed through regression analysis, error histograms, and curve fitting. The dataset was divided into three subsets, training, validation, and testing, 80%, 10%, and 10%. Key findings reveal that the velocity profile declines with increasing the value of the Hartmann number, Weissenberg number, and power-law index but rises with buoyancy parameters and the Deborah number. The temperature profile is enhanced by the Hartmann number, Brownian motion, power-law index, thermophoresis, Dufour number, and thermal radiation, while being reduced by the Prandtl number. The solute concentration profile decreases with the Schmidt number but increases with the Soret number. The numerical results for skin friction, Nusselt number, and Sherwood number are presented in tabular form.

The growing demand for sustainable cooling has renewed interest in adsorption-based refrigeration as a promising complement to conventional vapor-compression systems. In this study, CO2 adsorption on three activated carbon/graphene nanoplatelet (GNP) composites prepared using a polyvinyl alcohol (PVA) binder was analyzed using three grand canonical statistical physics (GCSP) models, with the best-performing model selected based on the highest coefficient of determination (R2). The results indicate that a dual-layer adsorption mechanism with two distinct energy levels provides the best description of CO2 uptake across all adsorbents. Steric analysis suggests that CO2 molecules preferentially adopt a parallel orientation relative to the substrate surface. Temperature-dependent adsorption parameters reveal variations in site occupancy, accessible site density, and adsorption strength. The low anchoring energies confirm that non-covalent interactions dominate the adsorption process. Internal energy and Helmholtz free energy derived from the selected GCSP model were applied to a pressure-swing adsorption (PSA) cooling cycle, yielding predicted coefficients of performance (COP) of 0.52, 0.64, and 0.68 at 343 K during the isothermal adsorption step for the three composites, respectively. These findings demonstrate that the GCSP framework effectively links microscopic adsorption behavior to macroscopic refrigeration performance and highlight the potential of PSA operation to enhance adsorption-based cooling systems.

This study investigates the development of a sustainable adsorbent, periwinkle-shell-derived activated carbon (PSAC), for the remediation of aqueous systems contaminated with thallium and antimony. Structural characterization (BET and FTIR) revealed that PSAC possesses a highly microporous architecture (SBET = 876 m2 g-1) and a chemically heterogeneous surface. Batch adsorption experiments demonstrated that removal efficiency is highly sensitive to pH, increasing as the solution pH approaches the point of zero charge (pHpzc = 6.8). Kinetic profiles followed the pseudo-second-order model, while intraparticle diffusion analysis confirmed a multi-stage mechanism governed by both surface film diffusion and internal pore transport. Equilibrium data were analyzed using advanced statistical physics formalisms. A monolayer model with lateral interactions provided the most accurate fit for single-component systems, whereas a dual-site model incorporating interaction parameters was statistically superior for the binary system, as confirmed by R2, RMSE, chi 2, and AIC testing. Steric parameters revealed that thallium exhibited higher receptor site densityand occupancy compared to Sb(iii), which was limited by the steric hindrance of the bulky Sb(iii)-tartrate complex. Adsorption energies for thallium were consistently higher than those for antimony, identifying a preferential uptake of thallium in competitive environments. FTIR analysis after adsorption suggested that the adsorption process is mainly governed by weak interactions, potentially including electrostatic attraction and pore filling rather than strong covalent bonding. Thermodynamic analysis derived from the statistical physics parameters confirmed the spontaneity and thermally-activated nature of the process, with configurational entropy profiles revealing greater flexibility for thallium species compared to the sterically constrained antimony-tartrate complex. These results highlight the efficacy of PSAC as a low-cost alternative to commercial carbons and demonstrate the power of statistical physics in decoding the non-ideal behavior of asymmetric binary adsorption systems.

To address the issue of wastewater decontamination, this meticulous study leverages the concepts of probabilistic physics formalism to depict the adsorptive equilibrium data of two widely used pesticides: 2,4-dichlorophenoxyacetic acid (2,4-D) and carbofuran on phosphoric acid-activated peach stone biochar. Numerically, we proposed three advanced modelsmonoenergetic linking monolayer scenario, bienergetic linking monolayer scenario, and multilayer linking with saturation scenarioto fit the experimental data. The analysis of data-theory accuracy through χred 2 and R adj 2 reveals that the adhesion of both toxic compounds occurs through a single monolayer at a single energy level. Based on the most probable scenario, our investigation demonstrates that an increase in temperature enhances retention on activated carbon, enabling a more optimized purification process. Regarding the equilibrium adsorption, a higher adsorption capacity is observed for 2,4-D (500 mg·g-1) compared to carbofuran (250 mg·g-1). Steric analysis further indicates that the number of adsorbate molecules per site, n, ranges from 2.46 to 1.65 for 2,4-D and from 1.29 to 1.68 for carbofuran over the temperature range of 25-65 °C. These values suggest multimolecular adsorption, in which a single binding site accommodates multiple adsorbate molecules, often with nonparallel anchoring orientations. As the temperature rises from 25 to 65 °C, the density of adsorption sites, n m, increases by a factor of 1.9 for 2,4-D and by a factor of 1.3 for carbofuran, reflecting a more pronounced temperature-dependent availability of active sites for 2,4-D and suggesting enhanced adsorption capacity at elevated temperatures. At 65 °C, energetic analysis indicates that the adsorption mechanism for both pesticides is primarily physisorption, with adsorption energies not exceeding 40 kJ·mol-1. Specifically, the adsorption energy for 2,4-D is approximately 17 kJ·mol-1, while for carbofuran, it is around 9 kJ·mol-1, reflecting weaker interactions with the adsorbent surface in the case of carbofuran. Pore size distribution characterization indicates that the smaller pore size ranges observed correspond to the microporous region (<2 nm) for both pesticides, while adsorption energy distribution confirms that van der Waals forces are the primary contributors to molecular adhesion. This study concludes that (2,4-D) is preferentially removed compared to carbofuran when in contact with activated carbon, highlighting its superior efficacy for wastewater treatment applications.

Banana peel-derived activated carbon (BPAC) was synthesized and evaluated for the ternary adsorption of Ni(ii), Cd(ii), and In(iii) from aqueous solutions at 30-50 °C. Experimental isotherms were interpreted using an extended statistical physics model that explicitly accounts for solution-phase interactions and excluded-volume effects, providing a physically consistent description of non-ideal multicomponent adsorption. Adsorption kinetics were best described by the pseudo-second-order model, and BPAC retained approximately 89% of its initial adsorption capacity after five adsorption-desorption cycles, demonstrating excellent reusability. Microscopic analysis revealed that BPAC possesses a high density of accessible receptor sites (R Mi ) together with low cohesion pressure (a i ) and covolume (b i ) parameters, thereby reducing lateral interactions and enhancing adsorption performance relative to commercial activated carbon (CAC). Adsorption energy distribution (AED) analysis revealed broader, higher-energy profiles for Ni(ii) and Cd(ii), indicating heterogeneous high-affinity sites and stronger adsorbate-surface interactions, whereas In(iii) exhibited lower-energy interactions consistent with predominantly physisorption. Thermodynamic analysis yielded negative Gibbs free energies for all ions (approximately -65.6 to -97.8 kJ mol-1 for Ni(ii), -54.6 to -83.6 kJ mol-1 for Cd(ii), and -42.3 to -21.4 kJ mol-1 for In(iii)), confirming the spontaneous nature of the adsorption process. Increasing temperature enhanced the adsorption of Ni(ii) and Cd(ii) but reduced that of In(iii). Overall, the explicit incorporation of lateral interaction parameters proved essential for accurately interpreting adsorption capacity, energetics, and selectivity, establishing BPAC as an efficient and sustainable adsorbent for multicomponent heavy-metal removal.