Statistical Physics Models Research Articles

Fabricating nepheline syenite-chitosan composite for heavy metals uptake: Mechanism insight via statistical physics modeling

Given the substantial costs associated with conventional wastewater treatment methods, researchers are increasingly exploring mineral compounds for their cost-effectiveness, widespread availability, and efficiency. In this study, nepheline syenite, an alkaline igneous rock, was selected among these compounds. The research investigates the single and binary adsorption of heavy metals (Ni(II) and Cd(II)) from synthetic and electroplating industrial effluents using a nepheline syenite-chitosan composite (NS-CS). The physical and chemical properties of the adsorbents were characterized using XRD, XRF, FT-IR, BET, and SEM analyses. The study examined the effects of solution acidity, contact time, initial concentration, and adsorbent dosage to determine the optimal conditions for the uptake of Ni(II) and Cd(II). The isothermal data were best described by the Langmuir isotherm model, with NS-CS showing adsorption capacities of up to 40.48 mg/g for Ni(II) and 41.79 mg/g for Cd(II). Additionally, the competitive adsorption of nickel and cadmium in the binary system was more accurately described by the modified Freundlich equation. Kinetic data were best fitted by the pseudo-second-order model. Thermodynamic analysis indicated that the adsorption of both ions was endothermic and nonspontaneous. Statistical physics modeling was employed to elucidate the adsorption mechanism of heavy metals on the NS-CS composite. The single-layer model with one energy level provided the most precise fit to the experimental data. Using this model, key factors were calculated, revealing that the adsorption energies for both Ni(II) and Cd(II) ions were below 20 kJ/mol, suggesting that the adsorption process is likely physical in nature.

A statistical-physics approach for codon usage optimisation

The concept of “codon optimisation” involves adjusting the coding sequence of a target protein to account for the inherent codon preferences of a host species and maximise protein expression in that species. However, there is still a lack of consensus on the most effective approach to achieve optimal results. Existing methods typically depend on heuristic combinations of different variables, leaving the user with the final choice of the sequence hit. In this study, we propose a new statistical-physics model for codon optimisation. This model, called the Nearest-Neighbour interaction (NN) model, links the probability of any given codon sequence to the “interactions” between neighbouring codons. We used the model to design codon sequences for different proteins of interest, and we compared our sequences with the predictions of some commercial tools. In order to assess the importance of the pair interactions, we additionally compared the NN model with a simpler method (Ind) that disregards interactions. It was observed that the NN method yielded similar Codon Adaptation Index (CAI) values to those obtained by other commercial algorithms, despite the fact that CAI was not explicitly considered in the algorithm. By utilising both the NN and Ind methods to optimise the reporter protein luciferase, and then analysing the translation performance in human cell lines and in a mouse model, we found that the NN approach yielded the highest protein expression in vivo. Consequently, we propose that the NN model may prove advantageous in biotechnological applications, such as heterologous protein expression or mRNA-based therapies.

Deciphering BSA adsorption onto COL-BC: Interpretations from statistical physics modeling

In this current study, a single-energy double layer model was employed to inspect the adhesion mechanism of bovine serum albumin (BSA) on porous microsphere of cellulose (BC) collagen (COL) bacterium (COL-BC). Six physicochemical variables defining the retention mechanism, :the number of anchored BSA protein per site (n), the amount of (COL-BC) available pores (NM), the capacity of adsorbed quantity (Qa), the specific surface area (As), the concentrations at half saturation (C1/2) and the molar binding energy (ΔE1) are determined. Calculations revealed that n ≥ 1 indicating that an average of one BSA per site is linked to one (COL-BC) receptor site with forming two layers. The BSA/(COL-BC) docking system exhibits a weak binding affinity as evidenced by the computed molar adsorption energy (ΔE1) which is below 40 kJ/mol. This energetic observation aligns with the characteristics of a physical and exothermic binding mechanism. Analysis of the (COL-BC) surface using the Kelvin equation revealed a pore size distribution (PSDs) extending across 0.05 μm–2 μm, providing insights into the stereochemistry of its receptor sites. Discussion of the BSA/COL-BC adhesion reaction through Polanyi equation unveils an adsorption energy distribution (AED) localized between 0 and 15 kJ/mol, consistent with a weak interaction profile characteristic of a physisorption mechanism. Finally, three thermodynamic functions were estimated in order to macroscopically study the BSA/(COL-BC) adsorption systems.This work is involved to provide more information about the adsorption of BSA on the COL-BC microsphere and investigate a theorical approach for the application of the controlled release technology.

Structural dynamics of a model of amorphous silicon

We perform extensive simulations and systematic statistical analyses on the structural dynamics of a model of amorphous silicon. The simulations follow the dynamics introduced by Wooten, Winer and Weaire: the energy is obtained with the Keating potential, and the dynamics consists of bond transpositions proposed at random locations and accepted with the Metropolis acceptance ratio. The structural quantities we track are the variations in time of the lateral lengths (Lx, Ly, Lz) of the cuboid simulation cell. We transform these quantities into the volume V and two aspect ratios B1 and B2. Our analysis reveals that at short times, the mean squared displacement (MSD) for all of them exhibits normal diffusion. At longer times, they cross over to anomalous diffusion (AD), with a temperature-dependent anomalous exponent α<1. We analyze our findings in the light of two standard models in statistical physics that feature anomalous dynamics, viz., continuous time random walker (CTRW) and fractional Brownian motion (fBm). We obtain the distribution of waiting times, and find that the data are consistent with a stretched-exponential decay. We also show that the three quantities, V, B1 and B2 exhibit negative velocity autocorrelation functions. These observations together suggest that the dynamics of the material belong to the fBm class.

Arbeitsgemeinschaft: QFT and Stochastic PDEs

Quantum field theory (QFT) is a fundamental framework for a wide range of phenomena is physics. The link between QFT and SPDE was first observed by the physicists Parisi and Wu (1981), known as Stochastic Quantisation. The study of solution theories and properties of solutions to these SPDEs derived from the Stochastic Quantisation procedure has stimulated substantial progress of the solution theory of singular SPDE, especially the invention of the theories of regularity structures and paracontrolled distributions in the last decade. Moreover, Stochastic Quantisation allows us to bring in more tools including PDE and stochastic analysis to study QFT.This Arbeitsgemeinschaft starts by covering some background material and then explores some of the advances made in recent years. The focus of this Arbeitsgemeinschaft is QFT models such as the \Phi^{4} , sine-Gordon and Yang–Mills models as examples to discuss stochastic quantisation and SPDE methods and their applications in these models. We introduce the key ideas, results and applications of regularity structure and paracontrolled distributions, construction of solutions of the SPDEs corresponding to these models, and use the PDE method to study some qualitative behaviors of these QFTs, and connections with the corresponding lattice or statistical physical models. We also discuss some other topics of QFT, such as Wilsonian renormalisation group, log-Sobolev inequalities and their implications, and various connections between these topics and SPDEs.

Experimental and theoretical study of multiple active site-functionalized Spirulina residue-based porous carbon as an economical adsorbent for NH3 and SO2 adsorption: Micro- and macro-mechanistic investigations

Here, we successfully synthesized a cost-effective (7.88 USD/kg) multi-active site (CuCl2, CuO and KCl) functionalized Spirulina residue-based porous carbon (MMBC). This innovative synthesis method utilizes Spirulina residue, a sustainable and low-cost biomass source, making the production of MMBC economically viable and environmentally friendly. Under ambient conditions, MMBC exhibits competitive adsorption capacities for NH3 and SO2 compared to other adsorbents, reaching 3.01 mmol/g (i.e., 51.26 mg/g) and 0.70 mmol/g (i.e., 44.85 mg/g), respectively, and tolerable recoverability. These values are significant improvements over many existing adsorbents, highlighting MMBC's efficiency in removing toxic industrial chemicals (TICs). Additionally, even at low molar fractions of NH3 or SO2, such as 0.001, MMBC demonstrates significant ideal adsorption solution theory (IAST) selectivity for NH3/N2 and SO2/N2, with values of 12.02 and 4.19, respectively. This high selectivity at low concentrations underscores MMBC's potential for applications in environments with trace amounts of pollutants. Furthermore, extensive research has been conducted in this study to elucidate the microscopic and macroscopic adsorption mechanisms of NH3 and SO2 on MMBC. Specifically, investigations in statistical physics models and statistical thermodynamics reveal that the adsorption of NH3 and SO2 on MMBC adhere to a non-aggregative, multilayer, multi-anchorage, and spontaneous exothermic physicochemical behavior. And the adsorption orientation occurs either horizontally or both horizontally and non-horizontally, contingent upon the system and temperature. These findings provide a deeper understanding of the adsorption processes and provide innovative insights into the adsorption mechanisms at the molecular level and at the macroscopic scale. Besides, the material characterization results reveal that the above adsorption process involves both physical interactions (pore diffusion and van der Waals forces) and chemical interactions (CuCl2 with NH3, CuO and KCl with SO2), indicating a physicochemical adsorption mechanism. This dual mechanism of adsorption offers a comprehensive explanation of the high performance of MMBC. In summary, this study developed a cost-effective Spirulina residue-based adsorbent, exhibiting high removal efficiency and selectivity for TICs, and providing deep insights into adsorption mechanisms. The innovative use of Spirulina residue addresses waste management issues and promotes the development of sustainable materials in the field of environmental remediation, contributing to cleaner production.

Evaluation and analysis of the adsorption mechanism of three emerging pharmaceutical pollutants on a phosphorised carbon-based adsorbent: Application of advanced analytical models to overcome the limitation of classical models

The double layer adsorption of sulfamethoxazole, ketoprofen and carbamazepine on a phosphorus carbon-based adsorbent was analyzed using statistical physics models. The objective of this research was to provide a physicochemical analysis of the adsorption mechanism of these organic compounds via the calculation of both steric and energetic parameters. Results showed that the adsorption mechanism of these pharmaceuticals was multimolecular where the presence of molecular aggregates (mainly dimers) could be expected in the aqueous solution. This adsorbent showed adsorption capacities at saturation from 15 to 36 mg/g for tested pharmaceutical molecules. The ketoprofen adsorption was exothermic, while the adsorption of sulfamethoxazole and carbamazepine was endothermic. The adsorption mechanism of these molecules involved physical interaction forces with interaction energies from 5.95 to 19.66 kJ/mol. These results contribute with insights on the adsorption mechanisms of pharmaceutical pollutants. The identification of molecular aggregates, the calculation of maximum adsorption capacities and the characterization of thermodynamic behavior provide crucial information for the understanding of these adsorption systems and to optimize their removal operating conditions. These findings have direct implications for wastewater treatment and environmental remediation associated with pharmaceutical pollution where advanced adsorption technologies are required.

In-silico design of Metal oxide-Biochar composites for enhanced dibenzothiophene adsorption: DFT and statistical physics approach

This study proposes an efficient in-silico adsorbent material selection strategy for clean fuel combustion by leveraging Density Functional Theory (DFT) calculated reactivity parameters to optimize material configurations for enhanced dibenzothiophene (DBT) adsorption from model fuel oil (n-octane). A DFT screening identified TiO2 as the optimal material for DBT adsorption from biochar and four metal oxide (MOx) based on calculated adsorption energies (Eads). Further DFT optimization identified a 10 % TiO2 composition with biochar (TBC10) as the optimal material. This composite exhibited the strongest DBT interaction (−370.3 kcal mol−1) and a remarkably short sulfur-titanium bond (2.64 Å), indicative of an ideal adsorption geometry. Notably, TBC10 features a unique composite structure: TiO2 connected to BC via van der Waals forces, while DBT directly interacts with AC through π-π stacking and covalent sulfur-titanium bonds. To validate theoretical predictions, the designed composites were synthesized and experimentally evaluated. The excellent alignment between experimental adsorption performance and DFT-calculated adsorption energies corroborated TBC10′s superior DBT adsorption capacity. Employing a systematic optimization process, the most effective parameters for TBC10′s DBT removal from a 150 mL solution containing an initial DBT concentration of 45 mg L-1 were established as: a 30 min contact time, an adsorbent dosage of 13 mg, and a temperature of 25 °C. Under these conditions, TBC10 achieved a remarkable removal efficiency (RRDBT) of 99.82 % and a maximum DBT uptake capacity (qDBT) of 31.1 mg g−1. Kinetic and statistical physics modeling revealed a multi-molecular adsorption process with distinct binding sites, characterized by spontaneous endothermic interactions and involving both physical and chemical mechanisms. The in-silico methodology for adsorbent design reduces experimentation time, cost and identifies optimal candidates for DBT removal, enhancing fuel desulfurization and promoting sustainable combustion. This novel in-silico design paradigm holds immense potential for the development of next-generation adsorbents for various environmental remediation and industrial separation processes.

Statistical physical modeling insights for urinary analgesic drug adsorption on carbon nanomaterial derivative.

The presence of phenazopyridine in water is an environmental problem that can cause damage to human health and the environment. However, few studies have reported the adsorption of this emerging contaminant from aqueous matrices. Furthermore, existing research explored only conventional modeling to describe the adsorption phenomenon without understanding the behavior at the molecular level. Herein, the statistical physical modeling of phenazopyridine adsorption into graphene oxide is reported. Steric, energetic, and thermodynamic interpretations were used to describe the phenomenon that controls drug adsorption. The equilibrium data were fitted by mono, double, and multi-layer models, considering factors such as the numbers of phenazopyridine molecules by adsorption sites, density of receptor sites, and half saturation concentration. Furthermore, the statistical physical approach also calculated the thermodynamic parameters (free enthalpy, internal energy, Gibbs free energy, and entropy). The maximum adsorption capacity at the equilibrium was reached at 298 K (510.94 mg g-1). The results showed the physical meaning of adsorption, indicating that the adsorption occurs in multiple layers. The temperature affected the density of receptor sites and half saturation concentration. At the same time, the adsorbed species assumes different positions on the adsorbent surface as a function of the increase in the temperature. Meanwhile, the thermodynamic functions revealed increased entropy with the temperature and the equilibrium concentration.

Adsorptive features of cyclohexane carboxylic naphthenic acid on a novel cross-linked polymer developed from spent coffee grounds.

Naphthenic acids (NA) are organic compounds commonly found in crude oil and produced water, known for their recalcitrance and toxicity. This study introduces a new adsorbent, a polymer derived from spent coffee grounds (SCGs), through a straightforward cross-linking method for removing cyclohexane carboxylic acid as representative NA. The adsorption kinetics followed a pseudo-second-order model for the data (0.007gmin-1mg-1), while the equilibrium data fitted the Sips model ( = 140.55mgg-1). The process's thermodynamics indicated that the target NA's adsorption was spontaneous and exothermic. The localized sterical and energetic aspects were investigated through statistical physical modeling, which corroborated that the adsorption occurred indeed in monolayer, as suggested by the Sips model, but revealed the contribution of two energies per site ( ). The number of molecules adsorbed per site ) was highly influenced by the temperature as decreased with increasing temperature and increased. These results were experimentally demonstrated within the pH range between 4 and 6, where both C6H11COO-(aq.) and C6H11COOH(aq.) species coexisted and were adsorbed by different energy sites. The polymer produced was naturally porous and amorphous, with a low surface area of 20 to 30 m2g-1 that presented more energetically accessible sites than other adsorbents with much higher surface areas. Thus, this study shows that the relation between surface area and high adsorption efficiency depends on the compatibility between the energetic states of the receptor sites, the speciation of the adsorbate molecules, and the temperature range studied.

Experimental and theoretical investigation of water sorption on lemon leaves: New perspectives with statistical physical modeling

A deeper analysis of the water sorption isotherms on lemon leaves (40, 50, and 60 °C) was carried out using statistical physical modeling to obtain information about the sorption mechanism and better understand the process. For this, a theoretical model was developed based on the grand canonical potential to describe the experimental data, and the isotherms were analyzed using the finite multilayer sorption model. The experimental sorption isotherms obtained for lemon leaves are Type II. The model used to analyze the process showed excellent predictive capacity, with coefficient of determination values above 0.97 and root mean square error below 0.08. The interpretation of the estimated parameters indicated that the water molecules are parallel to the surface of the lemon leaves, which allows the formation of finite layers of water. The system is directly affected by temperature, where increasing temperature decreases the density of receptor sites. The process occurs through physisorption since the calculated sorption energies are less than 50 kJ mol−1. The thermodynamic analysis of the process shows that water sorption on leaves is exothermic and spontaneous. This work contributes to a better understanding the drying process through the results obtained.

Monolayer Adsorption of Ciprofloxacin on Magnetic Inulin/Mg-Zn-Al Layered Double Hydroxide: Advanced Interpretation of the Adsorption Process.

In this study, magnetic inulin/Mg-Zn-Al layered double hydroxide (MILDH) was synthesized for the adsorption of ciprofloxacin. The application of various analytical techniques confirmed the successful formation of MILDH. For the optimization of controllable factors, Taguchi design was applied and optimum values were obtained as equilibrium time─100 min, adsorbent dose─20 mg, and ciprofloxacin concentration─30 mg/L. The highest capacity of the material was recorded as 196.19 mg/g at 298 K. Langmuir model (R2 = 0.9669-0.9832) fitted best as compared to the Freundlich model (R2 = 0.9588-0.9657), concluded the monolayer adsorption of ciprofloxacin on MILDH. Statistical physics model M 2 was found to fit best to measured data (R2 = 0.9982-0.9989), indicating that the binding of ciprofloxacin took place on two types of receptor sites (n1 and n2). The multidocking mechanism with horizontal position was suggested on the first receptor site (n1 < 1), while multimolecular adsorption of ciprofloxacin lying vertically on the second receptor site (n2 > 1) at all temperatures. The adsorption energies (E1 = 22.79-27.20 kJ/mol; E2 = 18.00-19.46 kJ/mol) illustrated that the adsorption of ciprofloxacin onto MILDH occurred through physical forces. Best fitting of the fractal-like pseudo-first-order kinetic model (R2 = 0.9982-0.9992) indicated that the adsorption of ciprofloxacin happened on the MILDH surface having different energies. X-ray photoelectron spectroscopy analysis further confirmed the adsorption mechanism of ciprofloxacin onto MILDH.

Exploring diclofenac potassium adsorption on activated carbon: A comprehensive statistical physics and experimental approach

This study aims to contribute to understanding the removal processes of diclofenac potassium (DP) medicine in wastewater treatment systems, employing activated carbon (AC) as an adsorbent. To achieve this goal, a multidisciplinary approach was adopted, integrating experimental and theoretical analyses of equilibrium data regarding the adsorption of DP on AC. Five statistical physics models were applied to determine the model best for the adsorption process. The selection of the most appropriate model considered both the performance of the models and the analysis of the estimated parameters. Statistically, all models exhibited satisfactory results. However, when analyzing the estimated parameters, the double-layer model with single adsorption energy emerged as the most suitable model to describe the analyzed process. Based on the chosen model’s parameters, we observed that as the temperature increases, the number of active sites occupied during adsorption and their availability on the adsorbent also increases. However, the number of available adsorption sites decreases as the temperature rises. The half-saturation concentration, in turn, increases with increasing temperature, suggesting that the process is favored when temperatures above room temperature are used. Additionally, higher temperatures provide better removal results, indicating that DP molecules’ non-parallel and parallel orientations on the AC surface favor the adsorption process. Finally, our combined results led to the proposal of a mechanism for DP adsorption on AC, which is based on physical adsorption interactions between adsorbate-adsorbent and adsorbate–adsorbate.

Kinetics of the one-dimensional voter model with long-range interactions

The voter model is an extremely simple yet nontrivial prototypical model of ordering dynamics, which has been studied in great detail. Recently, a great deal of activity has focused on long-range statistical physics models, where interactions take place among faraway sites, with a probability slowly decaying with distance. In this paper, we study analytically the one-dimensional long-range voter model, where an agent takes the opinion of another at distance r with probability ∝r−α . The model displays rich and diverse features as α is changed. For α > 3 the behavior is similar to the one of the nearest-neighbor version, with the formation of ordered domains whose typical size grows as R(t)∝t1/2 until consensus (a fully ordered configuration) is reached. The correlation function C(r,t) between two agents at distance r obeys dynamical scaling with sizeable corrections at large distances r>r∗(t) , slowly fading away in time. For 2<α⩽3 violations of scaling appear, due to the simultaneous presence of two lengh-scales, the size of domains growing as t(α−2)/(α−1) , and the distance L(t)∝t1/(α−1) over which correlations extend. For α⩽2 the system reaches a partially ordered stationary state, characterised by an algebraic correlator, whose lifetime diverges in the thermodynamic limit of infinitely many agents, so that consensus is not reached. For a finite system escape towards the fully ordered configuration is finally promoted by development of large distance correlations. In a system of N sites, global consensus is achieved after a time T∝N2 for α > 3, T∝Nα−1 for 2<α⩽3 , and T∝N for α⩽2 .

EVALUATE NODE IMPORTANCE BY DECOMPOSING NETWORK WITH A RECURSIVE PERCOLATION PROCESS

Due to structural heterogeneity, the main function and structure of networked systems are significantly influenced by some important nodes rather than each member. In practical, the properties of important nodes could be different from network to network, and thus a variety of algorithms have been specially designed to identify important nodes of different networks and of different dynamics. In this paper we propose a widely applicable algorithm by employing the percolation model in statistical physics, which describes the behavior of connected clusters when nodes are connected randomly. This algorithm appropriately combines the local and global properties of a network, thus it stresses the significance of nodes that neither have a visibly local importance, such as degree and clustering, nor have a visibly global importance, such as betweenness. The effectiveness of our algorithm has been illustrated in a series of networks, including model networks with different degree distributions and different degree correlations, and empirical networks. As a shell decomposition process, the framework of our algorithm has extensive application prospects in analyzing network structure, such as community, core–periphery structure, and shell structures.

Adsorption of the rare earth elements cerium, lanthanum, and neodymium onto ZSM-5 zeolite: A statistical physics approach

The recovery of rare earth elements (REE) is essential to meet the growing demand for these resources and promote the reuse of available resources. This study investigated the potential of ZSM-5 zeolite in the recovery of trivalent ions of cerium, lanthanum and neodymium under conditions of pH 6 and temperatures between 298 and 328 K. REE equilibrium isotherms were analyzed using five statistical physics models. The results indicate that removing all REE occurs predominantly in monolayers, as these models showed better prediction performance (coefficient of determination > 0.97 and mean squared error < 18.0). The best model determined that lanthanum and neodymium have one adsorption energy, while cerium has two adsorption energies involved in the process. The predominant functional groups are those containing silicon. Increasing temperature causes an increase in the number of REE ions captured per functional group, which reduces the adsorption space available on the surface. The model parameters indicate that the adsorption of these ions implies a multi-ionic mechanism (number of ions adsorbed per site greater than 1) and is an exothermic process. Based on the calculated adsorption capacities at saturation, the order of preference in adsorption can be established: neodymium > cerium > lanthanum. The adsorption energies indicate that the process occurred mainly due to physical forces since all energy values are below 40 kJ mol−1. The study’s results led to the proposal of a mechanism for the adsorption of REE on ZSM-5 zeolite, which highlights the predominance of electrostatic interactions and complex formation, which result in the formation of a monolayer on the adsorbent’s surface.

A statistical physics approach to hydrogen sorption-desorption isotherms in LaNi4.3Fe0.7

This study explores experimental hydrogen sorption and desorption isotherms on LaNi4.3Fe0.7 at four temperatures, employing different statistical physics models based on the grand canonical ensemble. The choice of the most appropriate model considered statistical parameters and physical analysis of the estimated parameters, culminating in selecting the monolayer model with two types of energies. The detailed analysis of these parameters provides an improved understanding of the process, highlighting the presence of hysteresis in the H2sorption and desorption in the metallic alloy. The sorption and desorption energies determined for this model vary between 82 and 109 kJmol−1, indicating a predominant chemical mechanism. Calculations of thermodynamic potentials suggest that the processes are exothermic and spontaneous. When comparing with other alloys of the same base, we observed that adding Fe presents similar trends in the model parameters, contributing to subtle improvements in the process.

Physical Analysis and Mathematical Modeling of the Hydrogen Storage Process in the MmNi4.2Mn0.8 Compound.

The results of an experimental and mathematical study into the MmNi4.2Mn0.8 compound's hydrogen storage properties are presented in the present research. Plotting and discussion of the experimental isotherms (P-C-T) for different starting temperatures (288 K, 298 K, 308 K, and 318 K) were carried out first. Then, the enthalpy and entropy of formation (ΔH0, ΔS0) were deduced from the plot of van't Hoff. Following that, the P-C-T were contrasted with a mathematical model developed via statistical physics modeling. The steric and energetic parameters, such as the number of the receiving sites (n1, n2), their densities (Nm1, Nm2), and the energy parameters (P1, P2) of the system, were calculated thanks to the excellent agreement between the numerical and experimental results. Therefore, plotting and discussing these parameters in relation to temperature preceded their application in determining the amount of hydrogen in each type of site per unit of metal ([H/M]1, [H/M]2) as well as for the entire system [H/M] versus temperature and pressure besides the absorption energies associated with each kind of site (ΔE1, ΔE2) and the thermodynamic functions (free energy, Gibbs energy, and entropy) that control the absorption reaction.

Assessment of chromite ore wastes for methylene blue adsorption: Isotherm, kinetic, thermodynamic studies, ANN, and statistical physics modeling

This research investigates the adsorption potential of chrysotile and lizardite, two minerals derived from chromite ore wastes, for the uptake of Methylene Blue (MB) dye from waste streams. The characterization of these minerals involves XRD, XRF, FTIR, and SEM. Results confirm the dominance of polymorphic magnesium silicate minerals, specifically chrysotile and lizardite, in the samples. The FTIR spectra reveal characteristic vibration bands confirming the presence of these minerals. The SEM analysis depicts irregular surfaces with broken and bent edges, suggesting favorable morphologies for adsorption. N2 adsorption-desorption isotherms indicate mesoporous structures with Type IV pores in both adsorbents. The Central Composite Design approach is employed to optimize MB adsorption conditions, revealing the significance of contact time, adsorbent mass, and initial MB concentration. The proposed models exhibit high significance, with F-values and low p-values indicating the importance of the studied factors. Experimental validation confirms the accuracy of the models, and the optimum conditions for MB adsorption are determined. The influence of solution acidity on MB uptake is investigated, showing a significant enhancement at higher pH values. Isothermal studies indicate Langmuir and Freundlich models as suitable descriptions for MB adsorption onto chrysotile and lizardite. The maximum adsorption capacities of MB for chrysotile and lizardite were found to be 352.97 and 254.85, respectively. Kinetic studies reveal that the pseudo-first-order model best describes the adsorption process. Thermodynamic analysis suggests an exothermic and spontaneous process. Statistical physics models further elucidate the monolayer nature of adsorption. Additionally, an artificial neural network is developed, exhibiting high predictive capability during training and testing stages. The reusability of chrysotile and lizardite is demonstrated through multiple regeneration cycles, maintaining substantial adsorption potential. Therefore, this research provides comprehensive insights into the adsorption characteristics of chrysotile and lizardite, emphasizing their potential as effiective and reusable sorbents for MB uptake from wastewater.

Machine learning and statistical physics modeling of tetracycline adsorption using activated carbon derived from Cynometra ramiflora fruit biomass

The current investigation reports the usage of adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN), the two recognized machine learning techniques in modelling tetracycline (TC) adsorption onto Cynometra ramiflora fruit biomass derived activated carbon (AC). Many characterization methods utilized, confirmed the porous structure of synthesized AC. ANN and ANFIS models utilized pH, dose, initial TC concentration, mixing speed, time duration, and temperature as input parameters, whereas TC removal percentage was designated as the output parameter. The optimized configuration for the ANN model was determined as 6-8-1, while the ANFIS model employed trimf input and linear output membership functions. The obtained results showed a strong correlation, indicated by high R2 values (ANNR2: 0.9939 & ANFISR2: 0.9906) and low RMSE values (ANNRMSE: 0.0393 & ANFISRMSE: 0.0503). Apart from traditional isotherms, the dataset was fitted to statistical physics models wherein, the double-layer with a single energy satisfactorily explained the physisorption mechanism of TC adsorption. The sorption energy was 21.06 kJ/mol, and the number of TC moieties bound per site (n) was found to be 0.42, conclusive of parallel binding of TC molecules to the adsorbent surface. The adsorption capacity at saturation (Qsat) was estimated to be 466.86 mg/g – appreciably more than previously reported values. These findings collectively demonstrate that the AC derived from C. ramiflora fruit holds great potential for efficient removal of TC from a given system, and machine learning approaches can effectively model the adsorption processes.