Marquardt's Percent Standard Deviation Research Articles

Fabrication of date palm kernel biochar-sulfur (DPKB-S) for super adsorption of methylene blue dye from water

A novel form of biochar was created by dehydration of Date palm kernel with 85% sulfuric acid. It was examined how the newly produced biochar (DPKB-S) affected the aqueous solution's capacity to extract Methylene Blue (MB) dye. The prepared DPKB-S was categorized by BET, BJH, FT-IR, SEM, EDX, DSC, and TGA analyses. The ideal pH for the MB dye adsorption by DPKB-S is 8. With 0.75 g L−1 of DPKB-S and an initial concentration of 50 ppm MB dye, Date Palm Kernel Biochar-Sulfur (DPKB-S) had the highest removal percentage of 100%. The Langmuir and Freundlich isotherm models were used to investigate the collected data. Freundlich model is the model that best covers MB dye adsorption in DPKB-S at low concentrations (0.75–1.25 g L−1) and the Langmuir model at high concentrations (1.5–1.75 g L−1). The Langmuir model maximum adsorption capacity (Qm) of the DPKB-S was 1512.30 mg g−1. Furthermore, a variety of error function models were applied to investigate the isotherm models derived data, including Marquardt’s percent standard deviation (MPSD), the sum of absolute errors (EABS), the sum of the errors squared (ERRSQ), root mean square errors (RMS), Chi-square error (X2), the average relative error (ARE), average percent errors (APE), and hybrid error function (HYBRID). Kinetic data were calculated by intraparticle diffusion (IPD), pseudo-second-order (PSO), pseudo-first-order (PFO), and film diffusion (FD) models. A PSO rate model with a strong correlation (R2 = 1.00) largely regulated the adsorption rate. The removal mechanism of MB dye by DPKB-S is based on the principle that these positively charged dyes are attracted by electrostatic attraction forces due to the growth in the number of negatively charged regions at basic pH value. According to the results, DPKB-S shows promise as an affordable and competent adsorbent for the adsorption of MB dye. It can be used frequently without experiencing a discernible decrease in adsorption efficiency.

Adsorption mechanism of nonsteroidal anti-inflammatories in wastewater using regenerable adsorbent (CCL): statistical modelling isotherm, kinetics and thermodynamic comparative studies

ABSTRACT The study was performed to investigate the biosorption mechanism of Diclofenac Sodium and Ketotifen Fumarate onto CCL biosorbent using isotherms models (Langmuir, Freundlich). Effects of parameters influencing the biosorption such as temperature, pH, biosorbent dose, contact time and biosorbate initial concentration were all investigated and optimised using a batch system. The comparison between various models indicates that the nonlinear form of Langmuir model was the best way to describe the equilibrium data that were approved using error functions: the coefficient of determination (R2), Average relative error (ARE), the sum of the squares of the errors (SSE), Marquardt’s percent standard deviation (MPSD), Hybrid fractional error function (HYBRID), Sum of the absolute errors (SAE) and ‘sum of the normalised errors (SNE)’ parameter. The kinetics experimental data was best predicted by the pseudo-second-order model. The adsorption mechanism identified external mass transfer as the principal measure of velocity control step. Thermodynamically, the process is spontaneous, exothermic and the adsorption was more favourable at lower temperatures. It was found that the regeneration is required as it changes the surface morphology of the biosorbent. Therefore, CCL biosorbent is considered as cost-effective and eco-efficient for removing Diclofenac and Ketotifen adsorbate from aqueous media by adsorption technique especially with its low cost preparation and regeneration.

Cost-Effective Natural Adsorbents for Remediation of Oil-Contaminated Water

Oil-contaminated water is among the most significant environmental challenges from various industries and manufacturing processes. Oily water poses a severe environmental threat and is toxic to many forms of life. This study aims to investigate the potential of natural adsorbents, namely animal bones (ABs) and anise residues (ARs), for removing oil from water using a batch adsorption process. The effects of adsorbent dosage (0.2–2 g), oil concentration (200–1000 mg/L), and contact time (30–120 min) on the adsorption process were evaluated. This study is the first to employ ABs and ARs as adsorbents for oil removal, and their efficacy for this purpose has not been previously reported. The results indicate that ABs exhibit superior oil removal capacity compared to ARs. Specifically, ABs removed 45 mg/g of oil from water, while ARs removed only 30 mg/g of oil. Furthermore, ABs achieved a percentage removal rate of 94%, whereas ARs had a percentage removal rate of 70%. The adsorbents were characterised using Fourier transform infrared (FTIR) spectrometry, contact angle measurements before and after adsorption, and thermogravimetric analysis (TGA). In addition to the experimental analysis, several kinetic and adsorption models were employed to investigate the adsorption process. The pseudo-first-order and pseudo-second-order models were used to represent the kinetics of the reaction, while the Langmuir and Freundlich isotherm models were used to represent the adsorption isotherm. Marquardt’s percent standard deviation (MPSD) error function was used to confirm the fit of the experimental data with the isotherm model, in addition to the correlation coefficient R2. The isotherm studies indicated that the experimental data of the two adsorbents used with the Langmuir isotherm model were consistent with one another. The kinetics study demonstrated that the adsorption process using the two adsorbents adheres to a pseudo-second-order kinetics model.

Isotherm and kinetic studies of acid yellow 11 dye adsorption from wastewater using Pisum Sativum peels microporous activated carbon

In this study, Pea Peels-Activated Carbon (PPAC), a novel biochar, was created from leftover pea peels (Pisum sativum) by wet impregnation with ZnCl2 and subsequent heating to 600, 700, and 800 °C in a CO2 atmosphere. Investigated how the newly acquired biochar affected the capacity to extract the AY11 dye from the aqueous solution. Through the use of FTIR, XRD, SEM, BJH, BET, DSC, EDX, and TGA studies, the prepared PPAC was identified. It was found that a pH of 2 is optimum for the AY11 dye elimination. The highest removal percentage of AY11 dye was 99.10% using a beginning AY11 dye concentration of 100 mg/L and a 1.0 g/L dose of PPAC. The highest adsorption capacity (Qm) of the PPAC was 515.46 mg/g. Freundlich (FIM), Halsey (HIM), Langmuir (LIM), Tempkin (TIM), and Gineralize (GIM) isotherm models were useful in examining the adsorption results. A variety of error functions, including the average percent errors (APE), root mean square errors (RMS), Marquardt's percent standard deviation (MPSD), hybrid error function (HYBRID), Chi-square error (X2) and a sum of absolute errors (EABS) equations, were also applied to test the isotherm models data. The PPAC experimental data were best suited by the HIM and FIM isotherm models. Elovich (EM), Pseudo-first-order (PFOM), Intraparticle diffusion (IPDM), Pseudo-second-order (PSOM), and Film diffusion (FDM) models were applied to study the kinetic adsorption results. The PSOM had a strong correlation coefficient (R2 > 0.99), and it was principally responsible for controlling the adsorption rate. Anions are typically absorbed during the adsorption mechanism of AY11 dye by PPAC owing to attractive electrostatic forces created with an increase in positively charged areas at acidic pH levels. The regenerated PPAC was used in six successive adsorption/desorption cycles. This study's outcomes show that PPAC successfully removes the AY11 dye from the aqueous solution; as a result, PPAC can be used repeatedly without experiencing considerable loss in effectiveness.

A comprehensive methodology for analysis of coagulation performance: Dosing approach, isotherm modelling, FTIR spectroscopy and floc characterization

Isolated studies for the evaluation of coagulation considering either microscopic or macroscopic dimensions have largely been discussed. However, comprehensive analysis of coagulation including various dimensions is imperative to design an optimal coagulation system. In this work, a comprehensive methodology has been described which includes dosing approach, mathematical modelling, chemical analysis by FTIR (Fourier Transform Infrared) spectroscopy, image analysis for floc properties and various analytical procedures. Jar tests were performed on simulated waters containing humic acid and kaolin using high basicity PACl (Poly Aluminium Chloride). A PODR (point of diminishing return) approach is used for the determination of coagulant dose corresponding to TOC (Total Organic Carbon), DOC (Dissolved Organic Carbon) and UV254 (Ultraviolet Absorbance at 254 nm). On average, PODR for UV254 was slightly greater than that of TOC followed by that of DOC. The correlation between the input TOC and PODR values was in the order: TOC (R2 = 0.84) > UV254 (R2 = 0.83) > DOC (R2 = 0.65). The isotherms are analyzed by non-linear error functions: RMSE (Root mean square error), HYBRID (Hybrid fractional error function), ARE (Average relative error), MPSD (Marquardt's percent standard deviation) and Chi-Square. It was observed that error functions RMSE, HYBRID and Chi-Square can be successfully used for non-linear analysis. However, ARE and MPSD cannot be used at low concentrations as they showed high residual values. Further, image processing is used to analyze floc size and fractal dimension. The interactions of species and the physical structure of flocs derived based on adsorption isotherms are corroborated by using the FTIR data.

Modelling the Kinetics of Tartrazine Sorption by Bottom Ash

Bottom ash is the solid residue left over from municipal waste combustion or incineration in a Municipal Waste Incineration Furnace. Its use as a sorption agent, particularly for dye sorption, is a new and important application. Linearized adsorption kinetics has drawbacks such as inaccurate representation of the parameters' 95 percent confidence interval output, unbalanced attention to potential outliers, and magnification of errors may result in inaccurate parameter values. In this study, we used nonlinear regression to investigate 16 adsorption kinetics models of tartrazine by bottom ash. The pseudo-second order was the best model based on the Bias and Accuracy factor near unity, but based on other error function analysis, this model performs equally well with the exponential and fractal-like pseudo-second order based other error functions such as Root-Mean-Square Error (RMSE), adjusted coefficient of determination (adjR2), Marquardt’s percent standard deviation (MPSD), Bayesian Information Criterion (BIC), Hannan-Quinn Information Criterion (HQC), and especially the corrected Akaike Information Criterion (AICc) function as the absolute difference is 5 absolute unit making discriminatory activity difficult. Furthermore, because the pseudo-second order and exponential models have only two parameters, they are less complicated according to Occam's razor. Because the pseudo-second order model is more popular and has more applications than the less well-known exponential model, we chose it as the best model for tartrazine sorption to bottom ash. Kinetic analysis using the PSO model gave a value of equilibrium adsorption capacity, qe of 21.88 mg g-1 (95% confidence interval (C.I.), 20.93 to 22.84) and k2 (g/(mg.sec)) of 0.00002 (95%, C.I., 0.00001 to 0.00002).

Selective removal of Cr (VI) from hydrometallurgical effluent using modified cellulose nanocrystals (CNCs) with succinic anhydride and ethylenediaminetetraacetic acid: Isotherm, kinetics, and thermodynamic studies

AbstractBiological sources are renewable basic resources that may be used for several purposes, including the development of green materials for the removal of heavy metal ions. Cellulose nanocrystals (CNCs) extracted from waste papers via acid hydrolysis were modified and utilized as adsorbents to remove Cr (VI) ions from metallurgical effluent in this work. X‐ray diffraction, scanning electron microscopy, Fourier‐transform infrared spectroscopy, thermogravimetric analysis, and zeta potentiometer were used to characterize the CNCs. The CNCs treated with succinic anhydride and ethylenediaminetetraacetic acid tetrasodium salt have thin particle sizes and are porous. The carboxylate functional group is primarily engaged in the coordination and selective removal of metal ions (–COO2−) and thermal degradation of 85%, observed at temperatures between 250–380°C. On the surface of the modified CNCs, the zeta potential data showed a decrease in negative value. The results revealed that the modified CNCs had a maximum adsorption capacity of 387.25 ± 0.88 mg L−1 at pH 5, at CNCs doses of 25 and 400 mg L−1 as starting concentrations. The adsorption equilibrium period was 300 min and the temperature was 313 K. The equilibrium results fit the Langmuir isotherm model with an R2 of 0.993 and a qmax of 340 ± 0.97. The Chi‐square (X2) and Marquardt's percent standard deviation tests confirmed that the adsorption process was pseudo‐second‐order with an R2 of 0.998, and the Elovich model revealed that Cr (VI) complexed with the adsorbent's functional groups. The reaction was endothermic due to positive ΔH and spontaneous due to negative ΔG. The positive ΔS indicates that the adsorption process enhances the unpredictability of the solid/liquid interface, according to thermodynamic analysis. After acid treatment, the CNCs may be effectively reused for six cycles with an adsorption capacity of 220 ± 0.78 mg g−1.

Multivariate modeling and optimization of Cr(VI) adsorption onto carbonaceous material via response surface models assisted with multiple regression analysis and particle swarm embedded neural network

Heavy metals especially Hexavalent chromium commonly known for its toxic effects. Herein we explore the efficacy of carbonaceous material derived from the domestic firework place for the adsorption of Cr(VI). The effects of significant variables including adsorption time, pH, Cr(VI) solution temperature and Cr(VI) initial concentration on the adsorption process were studied by batch experimental tests. These variables were further utilized as input to analyze, predict, and optimize the Cr(VI) adsorption process using response surface models (RSM) assisted with multiple regression analysis (MRA) and particle swarm embedded neural network (ANN-PSO) models. Regression parameters and analysis of variance (ANOVA) confirmed the validity of both models, and conditions for maximum & accelerated adsorption of 1.37 mg g−1 were predicted to be 94.7 min of adsorption time, Cr(VI) amount of 50.0 mg L−1, temperature of 33.6 °C and pH of 2.0. The statistical accuracy and prediction capability of both models were assessed using validation experiments and in terms of nonlinear statistical metrics such as R2, adju-R2, mean absolute error (MAE), root mean squared error (RMSE), absolute averaged error (AAD), Marquardt’s percent standard deviation (MPSD), sum of squared error (SSE), hybrid fractional error function (HYBRID), and Pearson chi-square measure (χ2), which revealed the superiority of ANN over MRA. Furthermore, the kinetic data revealed that the uptake of Cr(VI) by carbonaceous material favored pseudo 2nd order equation and adsorption phenomenon is better defined by the Langmuir isotherm, while the physisorption was the dominant governing mechanism. The thermodynamic assessment confirmed that adsorption was favorable, spontaneous, and endothermic in nature.

Investigation of hydrogen adsorption behavior of graphene under varied conditions using a novel energy-centered method

The adsorption of molecular hydrogen on the monolayer graphene sheet under varied temperature and pressure was studied using molecular dynamics simulations (MDS). A novel method for obtaining potential energy distributions (PEDs) of systems was developed to estimate the gravimetric density or weight percentage of hydrogen. The Tersoff and Lennard–Jones (LJ) potentials were used to describe interatomic interactions of carbon–carbon atoms in the graphene sheet and the interactions between graphene and hydrogen molecules, respectively. The results estimated by the use of novel method in conjunction with MDS developed herein were found to be in excellent agreement with the existing experimental results. The effect of pressure and temperature was studied on the adsorption energy and gravimetric density for hydrogen storage. In particular, we focused on hydrogen adsorption on graphene layer considering the respective low temperature and pressure in the range of 77–300 K and 1–10 MPa for gas storage purpose which indicate the combination of optimal extreme conditions. Adsorption isotherms were plotted at 77 K, 100 K, 200 K, and 300 K temperatures and up to 10 MPa pressure. The simulation results indicate that the reduction in temperature and increase in pressure favor the gravimetric density and adsorption energies. At 77 K and 10 MPa, the maximum gravimetric density of 6.71% was observed. Adsorption isotherms were also analyzed using Langmuir, Freundlich, Sips, Toth, and Fritz–Schlunder equations. Error analysis was performed for the determination of isotherm parameters using the sum of the squares of errors (SSE), the hybrid fractional error function (HYBRID), the average relative error (ARE), the Marquardt’s percent standard deviation (MPSD), and the sum of the absolute errors (SAE).

Optimum isotherm by linear and nonlinear regression methods for lead (II) ions adsorption from aqueous solutions using synthesized coconut shell–activated carbon (SCSAC)

Batch experiment was carried out to determine the optimum isotherm suitable to model the adsorption of Pb(II) ions onto synthesized coconut shell–activated carbon (SCSAC). In order to estimate the equilibrium parameters, the equilibrium adsorption data were analyzed using the following two-parameter isotherms: Langmuir, Freundlich, Temkin and Harkins–Jura by applying linear and nonlinear regression methods. In addition, seven linearized isotherm models (including four linearized Langmuir models) and four nonlinear isotherm models were discussed in this study. The specific surface areas of both nonsynthesized CSAC and synthesized SCSAC-activated carbon were estimated by Sears Method to be 650 m2g−1 and 768 m2g−1, respectively. Likewise other properties like bulk density, particle density, porosity, ash content, Scanning Electron Micrographs (SEM) analysis and Fourier Transform Infrared (FTIR) spectroscopy were also estimated. The error functions which includes the Sum of the Squares of the Errors (SSE), root mean square error (RMSE), Average relative error (ARE), Chi-square (X2), Marquardt’s Percent Standard Deviation (MPSD) and the correlation coefficient (R2) between the calculated and experimental data were also used to compare the suitability of different linearized and nonlinearized model parameters. In conclusion, Freundlich nonlinear isotherm was found to be in better agreement with optimum parameters having generated the maximum adsorption capacity Kf (110.10 Lmg−1), highest coefficient of determination R2 (0.9847) and lowest error functions. Hence, nonlinear isotherms of Freundlich and Harkin–Jura exibited greater performance than linear counterparts in the following order: Freundlich (nonlinear) > Harkin–Jura (nonlinear) > Freundlich (linear) > Harkins–Jura (linear) > Temkin (linear) > Temkin (nonlinear) isotherm models. This shows that transformation of nonlinear isotherm equations to linear forms implicitly alter their error structure.

Importance of estimation of optimum isotherm model parameters for adsorption of methylene blue onto biomass derived activated carbons: Comparison between linear and non-linear methods

A comparison of the linear and non-linear methods for the selection of optimum equilibrium isotherm for the adsorption of methylene blue onto the banana root (Musa acuminata) derived activated carbons was carried out. The adsorption equilibrium data were fitted to three isotherm models: Langmuir, Freundlich, and Temkin. The prediction of optimum isotherm was based on six error functions: the coefficient of determination (R2), the sum of the squares of the errors (SSE), the sum of the absolute errors (SAE), the average relative error (ARE), the hybrid fractional error function (HYBRID), and the Marquardt’s percent standard deviation (MPSD). The optimum isotherm achieved was the Temkin isotherm in non-linear and linear form followed by Freundlich and Langmuir based on the error functions. Non-linear pseudo-first-order and pseudo-second-order kinetic models analyzed the adsorption data. The present work demonstrated that the non-linear method is a more suitable method to estimate the isotherm parameters than the linear method, and the pseudo-first-order model best fitted the corresponding experimental data.

Linearized and nonlinearized modellings for comparative uptake assessment of metal-organic framework-derived nanocomposite towards sulfonamide antibiotics.

The emergent occurrence of sulfonamide species involving sulfadiazine (SDZ) and sulfamethazine (SMZ) in aquatic systems can cause a wide range of potential risks; hence, remediation strategies need to be necessary. Here, we develop the novel metal-organic framework-derived nanocomposite, and apply for the adsorption of SDZ and SMZ antibiotics. To assess the best-fitting kinetic (pseudo first-order, pseudo second-order) and isotherm (Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Redlich-Peterson, Sips, Toth, and Khan) models, a series of numerous statistical analysis was performed. Numerous error functions including squares of the errors (SSE), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), and mean relative error (MRE) were also analyzed to assess the linear and nonlinear models. The results indicated that both linear and nonlinear kinetic models were mostly fitted well with pseudo second-order models (Radj)2 > 0.97. Although linear kinetics gave better (Radj)2, error functions (MRE, SSE, HYBRID, and MPSD) were mostly higher than those of nonlinear kinetics. For adsorption isotherm, nonlinear Redlich-Peterson was the most compatible model with extremely high adjusted coefficients of determination (Radj)2 ~ 1.0000. While nonlinear Langmuir model gave relatively high (Radj)2 (0.9898-0.9960) and acceptable error functions, we found the considerable difference of error functions and parameters among four types of linear Langmuir (Types I, II, III, IV). The findings indicate potential errors as selecting one of linearized Langmuir types in equilibrium study. It is suggested that nonlinear models should be applied for better fitness.

Modeling and optimization of chromium adsorption onto clay using response surface methodology, artificial neural network, and equilibrium isotherm models

AbstractResponse surface methodology (RSM) was used for optimization of the adsorbent dosage, initial solution pH, initial ion concentration, and contact time in removal of Cr (III) with local nanoclay. The adsorption process was modeled by RSM and artificial neural network (ANN). The process was done in batch mode by central composite design (CCD) and the same design was applied for training ANN. The optimum condition was determined to be 500mg/L for adsorbent dosage, initial pH of 5, initial chromium concentration of 180mg/L and 20 min of contact time. In these conditions qRSM = 238.7780mg/g and qANN = 237.5152mg/g which indicate removal percentage of 72.45% and 72.07%, respectively. and indicate that the two models can predict the adsorption of Cr3+ properly. The two parameter Langmuir, Freundlich, Dubinin‐Radushkevich (D‐R), Temkin and three parameter Redlich‐Peterson (R‐PT), Sips and Toth isotherm models were applied to equilibrium data by minimizing the sum of squared errors (SSE), sum of the absolute errors (SAE), average relative errors (ARE), Hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), and nonlinear chi‐square test error functions. The results showed that the HYBRID error function gives the lowest value and the R‐PT model fits the data better than other isotherm models.

Comparison of Single, Binary and Temperature-Dependent Adsorption Models Based on Error Function Analysis

The choice of adsorption model to use when accounting for gas adsorption in shale gas reservoirs is critical especially for Gas in Place (OGIP) calculations since inaccurate predictions can affect reporting of overall gas reserves. To that end, different adsorption models would have to be compared and evaluated in order to select the model that fits experimental data accurately. In examining the effect of using different error criteria for determining parameters for shale gas adsorption models, a statistically robust error analysis has been performed based on the sum of normalised error (SNE). Most shale gas adsorption modelling are conducted without finding out the most appropriate error function to use which introduces adsorption prediction errors in calculations. Five different error analysis were used including Sum of squared error (SSE), average relative error (ARE), the sum of absolute error (SAE), Marquardt’s Percent standard Deviation (MPSD), and Hybrid fractional error (HYBRID). To account for the influence of temperature in adsorption capacities, the study also compares the use of temperature dependent models, such as Exponential and Bi-Langmuir models for gas adsorption. These models can be conducted at multiple temperatures and ensure adsorption data can be obtained at any temperature beyond laboratory conditions. This is particularly useful when conducting thermal stimulation as an enhanced gas recovery in both coal/shale gas reservoirs.

Development and validation of an adsorption kinetic model at solid-liquid interface using normalized Gudermannian function

In this article, a brief outlook of different kinetic models employed in batch adsorption study has been discussed. As the adsorption kinetic modeling has so far been inadequately addressed in the literature, therefore the equilibrium kinetic profiles of adsorption study were portrayed into an innovative sigmoidal expression qtqe=0.637tan−1sinh5.233×tteGnG, using the Gudermannian function with significant mathematical hypotheses. The kinetic data obtained from methylene blue and acridine orange dye adsorption studies using Abelmoschus esculentus seed powder were utilized to evaluate the adequacy of the proposed model. The extent of model compatibility was evaluated through six non-linear error functions represented as composite fractional error, residual root mean square error, Marquardt's percent standard deviation, average relative error, average percentage error and Chi-square error. This aforesaid three-parametric sigmoidal model was compared with pseudo-first-order, pseudo-second-order, intra-particle diffusion, Elovich, Bangham, modified-Freundlich and hyperbolic tangent model, which are known as the well-recognized kinetics. According to the comparison of different error functions and to the assessment of corrected Akaike information criterion, the developed model was ranked as the best fitting kinetic model illustrating the experimental data. It also demonstrated that the normalized Gudermannian kinetic equation has the ability to predict the equilibrium adsorption time at different initial dye concentrations, which can be exploited for configuring the large-scale industrial reactors.

Modeling and predicting total hydrogen adsorption in nanoporous carbon materials for advanced nuclear systems

The retention of hydrogen in a variety of disordered carbon materials including graphene nanoplatelets and amorphous carbon was measured by volumetric adsorption and modeled using thermodynamic methods. To date, high temperature hydrogen adsorption research in carbon has predominately focused on graphite used as plasma-facing materials in fusion systems, moderators in high temperature gas reactors, and fuel components in molten-salt cooled reactors. Tritium, a hydrogen isotope that is produced in these systems, adsorbs on carbon surfaces that could be used effectively as sinks to remove tritium. Since hydrogen has chemical similarity to tritium, it can be used as a surrogate to simplify experimental studies, greatly expediting materials exploration. Thus, an understanding and prediction of hydrogen behavior on carbon materials is essential for evaluation of performance and safety of present and future reactor designs. Chemisorption experiments were conducted on 9 different materials with a range of surface areas, pore volumes, and pore size distributions. The results showed that carbons with higher surface area and pore volume exhibit higher hydrogen adsorption, which is attributed to larger quantities of active sites. Further, hydrogen adsorption was found to increase in materials with greater micropore (<10 Å) surface area, which was interpreted as being a result of in-pore trapping. In contrast to previous studies that assumed a single isotherm, four isotherms were examined including two- and three-parameter methods and homo- and heterogeneous surface methods—the Langmuir, Temkin, Freundlich and Sips isotherms. Analyses of non-linear models by ordinary least squares and Marquardt's percent standard deviation minimization were performed. It was found that constant order homogeneous models that have been used in the past lack the ability to describe pathways and reactions steps that occur. Further, it was found that Sips isotherm consistently provided the best minimization of error and most accurate prediction.

A green approach for the removal of Sr(II) from aqueous media: Kinetics, isotherms and thermodynamic studies

Adsorption efficiency of native, NaOH-treated and immobilized peanut husk and sugarcane bagasse for Sr(II) removal was studied in batch mode. In view of promising adsorption efficiency of peanut husk versus sugarcane bagasse, the biosorption behaviour of the Sr(II) ions onto peanut husk (native and modified) was studied as a function of pH, biosorbent dose, contact time, initial metal ion concentration and temperature for the maximum removal of Sr(II) ions. Linear and non-linear pseudo-first and second-order kinetic models were applied and value of R2 and six non-linear regression error functions, namely hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), the sum of the errors squared (ERRSQ/SSE), the sum of the absolute errors (EABS) and Chi-square test (χ2) were used to predict the most optimum kinetic model. Sorbent-sorbate reaction nature was estimated by fitting equilibrium data by non-linear and transformed linear forms of the Langmuir, Freundlich and Redlich-Peterson isotherms and most optimum isothermal model was optimized by comparing linear and non-linear R2 value and non-linear regression error functions. HCl proved most successful eluating agents for sorbed Sr(II) ions. Biosorption characteristics and effectiveness of the process was also confirmed by Fourier transform infra-red spectroscopy (FTIR), scanning electron microscopy and energy dispersive X-ray spectroscopy (SEM-EDX). In view of promising efficiency of peanut husk as an adsorbent, it could possibly be used for the removal of Sr(II) ions from aqueous medium and is also extendable to other radionuclide.

Adsorption isotherm models and error analysis for single and binary adsorption of Cd(II) and Zn(II) using leonardite as adsorbent

Leonardite, a by-product from coal mines, was applied to adsorb Cd(II) and Zn(II) from aqueous solutions. Individual and simultaneous adsorptions of the two metal ions were investigated. In a single-component adsorption system, Langmuir and Freundlich isotherms were fitted to the adsorption data. Linear and nonlinear regression methods were used for the assessment of the optimum adsorption isotherm. Error functions including root-mean-square error, sum of the squares of the errors, mean absolute percentage error, Marquardt’s percent standard deviation (MPSD), and Chi-square were applied in the nonlinear regression. The most suitable model for the adsorption of Cd(II) and Zn(II) in the single system is the Freundlich isotherm. The isotherm parameters calculated by MPSD provided the lowest sum of normalized error (SNE) value. The adsorption capacity was found to be 23.89 mg/g for Cd(II) and 16.86 mg/g for Zn(II). It was observed that the adsorption of Cd(II) on leonardite is greater than that of Zn(II). For binary component adsorption systems, Cd(II) and Zn(II) showed antagonistic behavior. The presence of the other metal ions could decrease the amount of metal adsorbed. Binary adsorption of Cd(II) and Zn(II) was tested with regard to four multi-component isotherms: Extended Langmuir, Modified Langmuir, Sheindorf–Rebuhn–Sheintuch, and Extended Freundlich. The Extended Freundlich isotherm proved to be a good fit for the experimental data.

Comparison of linear and non-linear method for determination of optimum equilibrium isotherm for adsorption of copper(II) onto treated Martil sand

A comparison of linear and non-linear regression method for predicting the optimum isotherm was made using the experimental adsorption equilibrium data of Cu(II) onto treated Martil sand (TMS). For this, six error analysis methods were used: the coefficient of determination r2, the sum of the squares of the errors, the sum of the absolute errors, the average relative error, the hybrid fractional error function and the Marquardt's percent standard deviation. The error values indicated that non-linear method is a better way to obtain the isotherm parameters describing the Cu(II) adsorption onto TMS. The comparison between different models such as Langmuir, Freundlich, Dubinin-Radushkevich, Temkin, Redlich-Peterson, Koble-Corrigan and Fritz-Schlünder showed that Fritz-Schlünder model was more suitable to describe the equilibrium data. Based on this result and in order to optimize the equilibrium model results for more accurate parameters values, the Fritz-Schlünder equation was modified and called modified Fritz-Schlünder model. As a comparison of such developed modified model to existing mentioned ones, the results showed that the adsorption equilibrium of Cu(II) onto TMS was better described by the modified Fritz-Schlünder model than by others.

Batch growth kinetic studies for elimination of phenol and cyanide using mixed microbial culture

The efficiency of a mixed microbial culture to eliminate phenol and cyanide from aqueous solution was estimated in a batch process. The influence of initial concentration of phenol and cyanide on the microbial growth was calculated for the range of initial concentration between 50 and 1500mg/L of phenol and 5–150mg/L of cyanide. A maximum specific growth rate of 0.0663h−1 was observed at 250mg/L of phenol and 0.143h−1 at 25mg/L of cyanide concentration in the growth medium. The specific growth rate of the culture followed substrate inhibition kinetics. Monod, Haldane, Edward, Yano and Koga, Luong, Han-Levenspiel, and Powell growth kinetic models were used to determine the growth kinetics of mixed culture. Edward, Luong and Han and Levenspiel models were established as best fit to the specific growth rate data for phenol. However, for cyanide Haldane and Edward models were found to be best with lowest Marquardt’s percent standard deviation (MPSD) values. The degradation kinetics of phenol and cyanide was found to follow a three-half order model at all initial concentrations with lowest MPSD value.