Relation between some two- and three-parameter isotherm models for the sorption of methylene blue onto lemon peel

Linear and Nonlinear Regression Analysis for the Adsorption of Remazol Dye by Romanian Brewery Waste By-Product, Saccharomyces cerevisiae

Earth’s water balance and economy are becoming increasingly fragile due to overpopulation, global warming, severe environmental pollution and both surface and groundwater pollution. Therefore, it is essential to find solutions to the problems of water scarcity and water pollution. In this research, an experiment was designed to optimize the technique for the adsorption of Remazol Red F3B (RR) dye by lyophilized brewery yeast waste from the fermentation process. Moreover, we proved that brewery yeast is a great adsorbent. Batch adsorption experiments were carried out for optimization of different initial parameters, such as initial dye concentration (5–1000 mg/L), amount of yeast (0.5–2.5 g), pH (3–11) and temperature (20 to 40 °C). Furthermore, the structure and elemental composition of the adsorbent were analyzed with SEM, EDS and FTIR before and after biosorption. The best fits for the mathematical isotherm models in the case of the linear form were the Langmuir I and Freundlich models (R² = 0.923 and R² = 0.921) and, for the nonlinear form, the Khan model (R² = 0.9996) was the best fit. The pseudo-second-order kinetic model showed the best fit for both linear (plotting t/q_t vs. t) and nonlinear forms, are the calculated q_e values were similar to the experimental data.

Phosphate group functionalized magnetic metal-organic framework nanocomposite for highly efficient removal of U(VI) from aqueous solution

The phosphate group functionalized metal-organic frameworks (MOFs) as the adsorbent for removal of U(VI) from aqueous solution still suffer from low adsorption efficiency, due to the low grafting rate of groups into the skeleton structure. Herein, a novel phosphate group functionalized metal-organic framework nanoparticles (denoted as Fe₃O₄@SiO₂@UiO-66-TPP NPs) designed and prepared by the chelation between Zr and phytic acid, showing fast adsorption rate and outstanding selectivity in aqueous media including 10 coexisting ions. The Fe₃O₄@SiO₂@UiO-66-TPP was properly characterized by TEM, FT-IR, BET, VSM and Zeta potential measurement. The removal performance of Fe₃O₄@SiO₂@UiO-66-TPP for U(VI) was investigated systematically using batch experiments under different conditions, including solution pH, incubation time, temperature and initial U(VI) concentration. The adsorption kinetics, isotherm, selectivity studies revealed that Fe₃O₄@SiO₂@UiO-66-TPP NPs possess fast adsorption rates (approximately 15 min to reach equilibrium), high adsorption capacities (307.8 mg/g) and outstanding selectivity (S_u = 94.4%) towards U(VI), which in terms of performance are much better than most of the other magnetic adsorbents. Furthermore, the adsorbent could be reused for U(VI) removal without obvious loss of adsorption capacity after five consecutive cycles. The research work provides a novel strategy to assemble phosphate group-functionalized MOFs.

Study on Optimum IUPAC Adsorption Isotherm Models Employing Sensitivity of Parameters for Rigorous Adsorption System Performance Evaluation

Adsorption cooling technologies driven by low-grade thermal or solar power are used as an energy-efficient alternative to conventional refrigeration and air conditioning systems. Explicit understanding of the adsorption cycles requires precise determination of the performance parameters, replication of the experimental data, and the rigorous study of the adsorption heat transformation method. Hence, the optimum adsorption isotherms model must be identified. Scientists often face difficulties in selecting the suitable isotherm model as there are many models for a particular form of adsorption isotherm. The present study introduces a novel approach for choosing the optimal models for each type of International Union of Pure and Applied Chemistry (IUPAC) classified adsorption isotherm using robust statistical methods. First, the box-and-whisker plots of error identification are employed. Tóth for Type-I(a) and Type-I(b), modified BET for Type-II, GAB for Type-III, Universal for Type-IV(a), and Type-IV(b), Sun Chakrabarty for Type-V, and Yahia et al. for Type-VI were found lower than the other candidate models in box-and-whisker plot. The optimality of our selected models was further verified using analysis of variance (ANOVA), pairwise Tukey honest significant difference (HSD) test, Kruskal–Wallis rank-sum test, and pairwise Wilcoxon rank-sum test. In short, rigorous statistical analysis was performed to identify the best model for each type of isotherm by minimizing error. Moreover, specific cooling effect (SCE) of Maxsorb III/ethanol and silica gel/water pairs were determined. Results showed that Tóth is the optimal isotherm model for the studied pairs, and the SCE values obtained from the model agree well with experimental data. The optimum isotherm model is indispensable for the precise designing of the next generation adsorption cooling cycles.

Preparation of a new magnetic ion-imprinted polymer and optimization using Box-Behnken design for selective removal and determination of Cu(II) in food and wastewater samples

A new magnetic Cu(II) IIP (Fe₃O₄@IIP-IDC) is synthesized by polymerization of Imidazole-4,5-dicarboxylic acid functionalized Allyl chloride, and significant improvement of its performance has been compared. SPE parameters were optimized using Box-Behnken design to achieve the twin objectives of quantitative determination and removal of Cu(II). FLPSO kinetic model and BS isotherm model fits well with the capacity of 175 mg g^-1. Analytical figures of merit includes a linearity range of 10-5,000 µg L^-1 (R² = 0.9986), preconcentration factor of 50 after eluting with 5 mL of 1 M HNO₃, LOD of 1.03 µg L^-1 and LOQ of 4.5 µg L^-1. Accuracy was assessed by analysis of SRM (Standard Reference Material) and recovery experiments after spiking in food samples (Tea, coffee, chocolate, spinach, infant milk substitute) and battery wastewater. Ease of use, reusability (15 cycles), rapid adsorption and high selectivity makes it a promising candidate for efficient and selective removal and trace determination.

Chromatography bioseparation technologies and in-silico modelings for continuous production of biotherapeutics

The potential of continuous bioprocessing is hindered by the bottlenecks of chromatography processing, which continues to be executed in batch mode. Highlighting the critical drawbacks of batch chromatography, this review underscores the transition that the industry has made by implementing continuous upstream process without devising a working model for downstream chromatography operations. Even though multitude of process development initiatives have commenced, the review emphasizes the first principle models of chromatography on which these initiatives are built. Various models of continuous chromatography, which are essential, but not limited to multi-column systems, employed to congeal a unified process are reviewed. Advancements made by several mechanistic models and simulations to maximize productivity and performance are described, in an attempt to provide the integral tools. The modeling tools can be used for development of a strong model based control strategy and can be embedded into the continuous chromatography framework. The review addresses the limitations and challenges of the current modeling methods for development of robust mechanistic modeling and efficient unit operation platform in continuous chromatography.

Corncob-derived activated carbon for roxarsone removal from aqueous solution: isotherms, kinetics, and mechanism

In this study, the adsorption of roxarsone (ROX) onto corncob-derived activated carbon (AC) was optimized using response surface methodology (RSM). Following this, the AC was comprehensively characterized by FT-IR, SEM, and EDS analysis. The results showed that the highest ROX adsorption efficiency of 304.34 mg/g was obtained at the contact time of 262 min, initial pH of 2.5, adsorbent dosage of 0.4 g/L, and initial concentration of 240 mg/L. Besides, it was found that the adsorption equilibrium data was fitted well to the Langmuir and Sips isotherm models. The thermodynamic parameters (e.g., ΔG, ΔH, and ΔS) revealed the spontaneous and exothermic nature of ROX adsorption. As indicated by pseudo second-order kinetics model, the adsorption of ROX onto AC could be achieved through the hydrogen bond, π-π adsorbate-adsorbent interaction, and electrostatic interaction between AC surface functional group and molecular species variations of ROX at different pH values. Overall, it can be concluded that corncob-derived AC is an alternative option for removing ROX from aqueous solution.

New insight into the removal of Cd(II) from aqueous solution by diatomite

Diatomite is an economical and environmentally friendly adsorbent, and its use has been applied widely for the treatment of water contaminated by heavy metals. Despite this, the mechanism for the removal of the heavy metal Cd(II) remains unclear. In this work, we explored the adsorption mechanism of Cd(II) by diatomite using batch experiment, and characterized the diatomite using scanning electron microscopy, energy-dispersive spectrometry, specific surface area, and pore size distribution analysis. Our results showed that, under the experimental conditions, the kinetic adsorption approached equilibrium within 5 min, and the Sips isotherm model was most suitable for data fitting. EDS characterization of the Cd-loaded diatomite indicated that Cd(II) was adsorbed onto the diatomite. Furthermore, desorption experiments showed that Ca²⁺ and Mg²⁺ in the diatomite caused an ion exchange interaction, and this was primarily responsible for Cd(II) adsorption. Moreover, we found that its contribution to the whole adsorption reaction could reach 80%, while the remainder of Cd(II) was probably trapped in the microporous structure of the diatomite. Additionally, our data indicated that the adsorption mechanism did not change significantly after regeneration. These results have provided special insight into the deep understanding of the mechanism of Cd(II) adsorption by diatomite, and could provide theoretical support and guidance for further development and application of diatomite in the treatment of Cd(II)-contaminated water. Graphical abstract.

Advanced TiO2-SiO2-Sulfur (Ti-Si-S) Nanohybrid Materials: Potential Adsorbent for the Remediation of Contaminated Wastewater

In this present work, TiO₂-SiO₂-sulfur (Ti-Si-S) nanohybrid material was successfully prepared using TiO₂ nano powder, TEOS sol-gel precursor, and elemental sulfur as raw material by sol-gel process and hydrothermal method at 120 °C temperature. Raman spectroscopy, XRD, SEM, TEM, and N₂ absorption-desorption characterized the synthesized nanohybrid material. The characterization results confirmed the homogeneous distribution of sulfur in the nanohybrid material. The size of the Ti-Si-S nanohybrid material is vary between 20 and 40 nm and the surface areas of the nanohybrid material was measured using N₂ absorption-desorption, which showed value of 57.2 m² g^-1. The potential of Ti-Si-S nanohybrid material as an adsorbent was further tested to adsorb methylene blue (MB) from aqueous solution. Adsorption performance of hybrid material was highly influenced by the solution pH and mass of adsorbent. The adsorption of MB using Ti-Si-S nanohybrid material was homogeneous monolayer adsorption, which followed the Langmuir adsorption isotherm with a q_e,max value of 804.80 mg g^-1 and pseudo-second-order rate equation. The dye diffusion mechanism partially followed both intraparticle and liquid film diffusion mechanisms. Thermodynamics studies predicted the spontaneous and endothermic nature of the whole adsorption process. The Ti-Si-S nanohybrid material was used for six repeated cycles of MB dye adsorption-desorption.

Targeted magnetic separation of biomolecules and cells using earthicle-based ferrofluids

Targeting specific molecular or cell populations within single tissues or multicomponent in vitro systems is a most sought goal in biomedicine. Here we report on targeted magnetic separation of cells and biomolecules using a ferrofluid comprising superparamagnetic iron-oxide/silicate/carbon core/shell/crust nanoparticles in combination with a handheld, 2.5 cm³ NdFeB magnet (≤180 mT) and one minute exposure time. Ferrofluids were highly effective at separating (i) biomolecules, (ii) bacteria and (iii) eukaryotic cells from solutions, and they also exhibited selectivity in the separation of all three families of entities. Specifically, they were more effective at separating the negatively charged protein, albumin in the presence of the external magnetic field, but were more effective at precipitating the positively charged protein, lysozyme without the application of the external field. Because of the more effective sorption of proteins than carbohydrates on carbon and the shielding of peptidoglycans by the transmembrane proteins and hydrophilic heads of the outer membrane amphiphiles in Gram-negative bacteria, they were separated more effectively than their Gram-positive counterparts. Ferrofluids were also more efficient at separating the clinical isolate, methicillin-resistant version of S. aureus (MRSA) than its regular, lab strain and the effect is thought to be due to structural changes to the cell envelope caused by the overexpression of efflux pumps or by the higher rate of conjugation conditioning horizontal gene transfer in MRSA than in the regular, nonresistant strain. Ferrofluids also displayed a greater affinity for the cancer cells than for the normal, primary cells and allowed for targeted separation of the former after the cells were allowed to uptake the nanoparticles for 24 h. This selectivity should allow for an effective separation of cancer cells interspersed within a healthy cell population. Interaction with bacterial and eukaryotic cells was driven neither by electrostatic attraction nor chemisorption, but by weaker, van der Waals and π-interactions. Adsorption was also endothermic, irreversible for the most part, and more favorable at high concentrations, as inferred by comparison with Langmuir, Freundlich, Temkin and Dubinin-Radushkevich isotherms. These targeted effects are relevant for numerous fields of biomedicine and biotechnologies and require further insight for optimization and translation.

Mechanistic insight into protein supported biosorption complemented by kinetic and thermodynamics perspectives

In this review, we discussed the micro-level aspects of protein supported biosorption. The mechanism, surface chemistry in terms of energy interactions and electron transfer process (ETP) of peptide systems within protein are three important areas that provide mechanistic insight into protein supported biosorption. The functional groups in proteinous material like hydroxyl (-OH), carbonyl (>C=O), carboxyl (-COOH) and sulfhydryl (-SH) play a significant role in the biosorption of variety of pollutants such as metal ions, metalloids, and organic matters in wastewaters. The mechanistic aspects of biosorption are crucial not only for the separation process but also they contribute towards stoichiometric considerations and mathematical modelling process. The surface chemistry of applied biosorbents relies on interfacial components whose interaction energies are estimated with help of classical Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory mathematically. Proteins are the fundamental molecules of many biomaterial used for the biosorption of contaminents and peptide bond is considered as the backbone of proteins. The charge variations on peptide bonding is the result of ETP whose discussion was made part of this review for understaning number of biological and technological processes of vital interests. In addition, this review was complemented by exhaustive overview of kinetic and thermodynamics perspectives of biosorption process.

A Highly Tunable Approach to Enhance CO2 Capture with Liquid Alkali/amines

A diverse range of alkali/amine infused hydrogels (AIHs) were generated by incorporating the liquids into a hydrogel particle for carbon capture application. As a consequence, the CO₂ uptake was significantly enhanced owing to the increased contact area. This AIHs technique was highly tunable as it could be applicable to varying species of alkali chemicals and it was found that their molecular structure and architectures could impact the CO₂ uptake. Compared to stirred bulk alkali/amine solutions, the CO₂ absorption capacity of AIHs was increased by 400% within 30 min with a low hydrogel loading (10 w/w%). In addition, the recyclability of various AIHs was assessed and was found to be extremely encouraging. The effect of salinity on the performance of AIHs was also investigated and high salinity was found to have a minimal effect on CO₂ absorption. Most importantly, the preparation of AIHs is fast and straightforward with few wastes and byproducts formed in the preparation process. In all, extensive investigations were presented and the AIHs were found to be a highly tunable and effective approach to enhance CO₂ capture with liquid alkali/amines.

Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: A critical review

In recent years, adsorption science and technology for water and wastewater treatment has attracted substantial attention from the scientific community. However, the number of publications containing inconsistent concepts is increasing. Many publications either reiterate previously discussed mistakes or create new mistakes. The inconsistencies are reflected by the increasing publication of certain types of article in this field, including "short communications", "discussions", "critical reviews", "comments", "letters to the editor", and "correspondence (comment/rebuttal)". This article aims to discuss (1) the inaccurate use of technical terms, (2) the problem associated with quantities for measuring adsorption performance, (3) the important roles of the adsorbate and adsorbent pK_a, (4) mistakes related to the study of adsorption kinetics, isotherms, and thermodynamics, (5) several problems related to adsorption mechanisms, (6) inconsistent data points in experimental data and model fitting, (7) mistakes in measuring the specific surface area of an adsorbent, and (8) other mistakes found in the literature. Furthermore, correct expressions and original citations of the relevant models (i.e., adsorption kinetics and isotherms) are provided. The authors hope that this work will be helpful for readers, researchers, reviewers, and editors who are interested in the field of adsorption studies.

Classification, processing and application of hydrogels: A review

This article aims to review the literature concerning the choice of selectivity for hydrogels based on classification, application and processing. Super porous hydrogels (SPHs) and superabsorbent polymers (SAPs) represent an innovative category of recent generation highlighted as an ideal mould system for the study of solution-dependent phenomena. Hydrogels, also termed as smart and/or hungry networks, are currently subject of considerable scientific research due to their potential in hi-tech applications in the biomedical, pharmaceutical, biotechnology, bioseparation, biosensor, agriculture, oil recovery and cosmetics fields. Smart hydrogels display a significant physiochemical change in response to small changes in the surroundings. However, such changes are reversible; therefore, the hydrogels are capable of returning to its initial state after a reaction as soon as the trigger is removed.

Indigo adsorption on a silicate surface: a theoretical density functional study

The applicability of naturally available low-cost and eco-friendly adsorbent materials for the removal of hazardous dyes from aqueous waste is of increasing environmental interest. Among the adsorption treatments available, clays seem to be economically attractive due to their abundance and adsorption capabilities. Indeed, many ancient coloring materials utilized clays mixed with natural dyes (e.g., indigo in Maya Blue). In this work, we performed a quantum-mechanical theoretical study of the adsorption of the indigo molecule onto the (001) surface of a phyllosilicate. Different methods and approaches were applied and compared. We found that the presence of a tetrahedral charge and a sodium counterion significantly increased the adsorption energy of the indigo molecule. The vibrational spectrum of the dye-surface system was also studied, and some interesting shifts in the frequencies of the main vibrational modes of indigo due to its interaction with the surface of the clay mineral were identified.

Recovery of Ga(III) by Raw and Alkali Treated Citrus limetta Peels

Alkali treated Citrus limetta peels were used for recovery of Ga(III) from its aqueous solution. The raw and alkali treated peels were characterized for functional groups. The efficiency of adsorption increased from 47.62 mg/g for raw peels to 83.33 mg/g for alkali treated peels. Between pH 1 and 3, the adsorption increased and thereafter decreased drastically. The adsorption followed pseudosecond order kinetics and Langmuir isotherm gave the best fit for the experimental data. Desorption studies showed 95.28% desorption after 3 cycles for raw peels while it was 89.51% for alkali treated peels. Simulated Bayer liquor showed 39.57% adsorption for gallium ions on raw peels which was enhanced to 41.13% for alkali treated peels.

Ultrasensitive detection of toxic cations through changes in the tunnelling current across films of striped nanoparticles

Although multiple methods have been developed to detect metal cations, only a few offer sensitivities below 1 pM, and many require complicated procedures and sophisticated equipment. Here, we describe a class of simple solid-state sensors for the ultrasensitive detection of heavy-metal cations (notably, an unprecedented attomolar limit for the detection of CH(3)Hg(+) in both standardized solutions and environmental samples) through changes in the tunnelling current across films of nanoparticles (NPs) protected with striped monolayers of organic ligands. The sensors are also highly selective because of the ligand-shell organization of the NPs. On binding of metal cations, the electronic structure of the molecular bridges between proximal NPs changes, the tunnelling current increases and highly conductive paths ultimately percolate the entire film. The nanoscale heterogeneity of the structure of the film broadens the range of the cation-binding constants, which leads to wide sensitivity ranges (remarkably, over 18 orders of magnitude in CH(3)Hg(+) concentration).

Biosorption of diesel and lubricating oil on algal biomass

Algae are widely used as biosorbent for the sorption of heavy metals, however sorption of oil on algae has not been explored. Algae in marine and fresh water environment may affect the fate and transport of spilled oil. Sorption of diesel and lubricating oil was studied using dead biomass of Spirulina sp. and Scenedesmus abundans. The rate and extent of sorption was studied in well mixed batch systems containing oil (0.1–2 %, v/v) and biomass (0.1 %) suspended in water. Sorption of diesel on Spirulina sp. was instantaneous. Rate limited sorption on algal biomass could be explained by the pseudo-second order model and equilibrium was established within 12 days. The Freundlich and Langmuir model could provide adequate fit for diesel sorption on algae but not for lubricating oil. A three parameter model, the Sips model, provided good fit for all the experimentally generated isotherms and yielded maximum sorption capacity of diesel and lubricating oil in the range of 12–14 g/g. Oil sorption on algae was comparable to other spill clean-up sorbents. Algae can be used for development of low cost sorbents and can facilitate removal of oil from contaminated water. Sorption is affected both by the type of oil and type of algae. This is the first study illustrating that the additives present in lubricating oil not only reduces the sorption rate but also alters sorption equilibrium such that two-parameter isotherms are inadequate.

A review on applicability of naturally available adsorbents for the removal of hazardous dyes from aqueous waste

The effluent water of many industries, such as textiles, leather, paper, printing, cosmetics, etc., contains large amount of hazardous dyes. There is huge number of treatment processes as well as adsorbent which are available for the processing of this effluent water-containing dye content. The applicability of naturally available low cast and eco-friendly adsorbents, for the removal of hazardous dyes from aqueous waste by adsorption treatment, has been reviewed. In this review paper, we have provided a compiled list of low-cost, easily available, safe to handle, and easy-to-dispose-off adsorbents. These adsorbents have been classified into five different categories on the basis of their state of availability: (1) waste materials from agriculture and industry, (2) fruit waste, (3) plant waste, (4) natural inorganic materials, and (5) bioadsorbents. Some of the treated adsorbents have shown good adsorption capacities for methylene blue, congo red, crystal violet, rhodamine B, basic red, etc., but this adsorption process is highly pH dependent, and the pH of the medium plays an important role in the treatment process. Thus, in this review paper, we have made some efforts to discuss the role of pH in the treatment of wastewater.

Basic dye adsorption onto an agro-based waste material--sesame hull (Sesamum indicum L.)

The aim of this project was to establish an economical and environmentally benign biotechnology for removing methylene blue (MB) from wastewater. The adsorption process of MB onto abandoned sesame hull (Sesamum indicum L.) (SH) was investigated in a batch system. The results showed that a wide range of pH (3.54-10.50) was favorable for the adsorption of MB onto SH. The Langmuir model displayed the best fit for the isothermal data. The exothermic adsorption process fits a pseudo-second-order kinetic model. The maximum monolayer adsorption capacity (359.88 mg g(-1)) was higher than most previously investigated low-cost bioadsorbents (e.g., peanut hull, wheat straw, etc.). This study indicated that sesame hull is a promising, unconventional, affordable and environmentally friendly bio-measure that is easily deployed for removing high levels of MB from wastewater.

Critical-point universality in adsorption: the effect of charcoal on a mixture of isobutyric acid and water near the consolute point

The mixture of isobutyric acid and water has a consolute point at a temperature of 25.75 °C and mole fraction 0.1148 isobutyric acid. When charcoal is added to this mixture, the concentration of isobutyric acid is reduced by adsorption. We have measured the action of charcoal on solutions of isobutyric acid and water as a function of isobutyric acid mole fraction at temperatures of 25.85 and 32.50 °C. At the higher temperature, the specific adsorption density (y(2)(α)/m) satisfies the Freundlich equation (y(2)(α)/m)=KX(2)(1/n), where y(2)(α) is the mass of isobutyric acid adsorbed, m is the mass of charcoal, X(2) is the equilibrium mole fraction of isobutyric acid, n is the Freundlich index, and K=K(T) is an amplitude that depends upon the temperature T. At 25.85 °C, a critical endpoint is located at an isobutyric acid mole fraction X(2)(ce)=0.09. When compared with the Freundlich equation at this temperature, a plot of the specific adsorption density as a function of X(2) in the vicinity of the critical-endpoint composition assumes a shape which is reminiscent of the derivative of a Dirac delta function. Using critical-point scaling theory, we show that this divergent pattern is consistent with the principle of critical point universality.

Adsorption of methylene blue on raw and MTZ/imogolite hybrid surfaces: effect of concentration and calorimetric investigation

The synthetic imogolite sample was used for organofunctionalization process with 2-mercaptothiazoline (MTZ). The compound 2-mercaptothiazoline was anchored onto imogolite surface by heterogeneous route. Due to the increment of basic centers attached to the pendant chains the dye adsorption capability of the final chelating material, was found to be higher than is precursor. The ability of these materials to remove methylene blue from aqueous solution was followed by a series of adsorption isotherms at room temperature and pH 4.0. The maximum number of moles adsorbed was determined to be 40.32×10(-2) and 65.13×10(-2) mmol g(-1) for IMO and IMO(MTZ), respectively. The energetic effects caused by dye cations adsorption were determined through calorimetric titrations. Thermodynamics indicated the existence of favorable conditions for such methylene blue-nitrogen and sulfur interactions.

Adsorption of methylene blue from aqueous solution by jackfruit (Artocarpus heteropyllus) leaf powder: A fixed-bed column study

Continuous fixed-bed studies were undertaken to evaluate the efficiency of jackfruit leaf powder (JLP) as an adsorbent for the removal of methylene blue (MB) from aqueous solution under the effect of various process parameters like bed depth (5-10cm), flow rate (30-50mL/min) and initial MB concentrations (100-300mg/L). The pH at point of zero charge (pH(PZC)) of the adsorbent was determined by the titration method and a value of 3.9 was obtained. A FTIR of the adsorbent was done before and after the adsorption to find the potential adsorption sites for interaction with methylene blue molecules. The results showed that the total adsorbed quantities and equilibrium uptake decreased with increasing flow rate and increased with increasing initial MB concentration. The longest breakthrough time and maximum MB adsorption were obtained at pH 10. The results showed that the column performed well at low flow rate. Also, breakthrough time and exhaustion time increased with increasing bed depth. The bed-depth service time (BDST) model and the Thomas model were applied to the adsorption of MB at different bed depths, flow rates, influent concentrations and pH to predict the breakthrough curves and to determine the characteristic parameters of the column that are useful for process design. The two model predictions were in very good agreement with the experimental results at all the process parameters studied indicating that they were very suitable for JLP column design.

Applicability of some statistical tools to predict optimum adsorption isotherm after linear and non-linear regression analysis

In any single component isotherm study, determining the best-fitting model is a key analysis to mathematically describe the involved sorption system and, therefore, to explore the related theoretical assumptions. Hence, several error calculation functions have been widely used to estimate the error deviations between experimental and theoretically predicted equilibrium adsorption values (Q(e,exp)vs.Q(e,theo) as X- and Y-axis, respectively), including the average relative error deviation, the Marquardt's percent standard error deviation, the hybrid fractional error function, the sum of the squares of the errors, the correlation coefficient and the residuals. In this study, five other statistical functions are analysed to investigate their applicability as suitable tools to evaluate isotherm model fitness, namely the Pearson correlation coefficient, the coefficient of determination, the Chi-square test, the F-test and the Student's T-test, using the commonly-used functions as references. The adsorption of textile dye onto Posidonia oceanica seagrass fibres was carried out, as study case, in batch mode at 20 degrees C. Besides, and in order to get an overall approach of the possible utilization of these statistical functions within the studied item, the examination was realized for both linear and non-linear regression analysis. The related results showed that, among the five studied statistical tools, the chi(2) and Student's T-tests were suitable to determine the best-fitting isotherm model for the case of linear modelling approach. On the other hand, dealing with the non-linear analysis, despite the Student's T-test, all the other functions gave satisfactorily results, by agreeing the commonly-used error functions calculation.

Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: comparison of various error functions

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon

A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

Equilibrium, kinetics and mechanism modeling and simulation of basic and acid dyes sorption onto jute fiber carbon: Eosin yellow, malachite green and crystal violet single component systems

Batch experiments were carried out for the sorption of eosin yellow, malachite green and crystal violet onto jute fiber carbon (JFC). The operating variables studied are the initial dye concentration, initial solution pH, adsorbent dosage and contact time. Experimental equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm by non-linear regression method. Langmuir isotherm was found to be the optimum isotherm for eosin yellow/JFC system and Freundlich isotherm was found to be the optimum isotherm for malachite green/JFC and crystal violet/JFC system at equilibrium conditions. The sorption capacities of eosin yellow, malachite green and crystal violet onto JFC according to Langmuir isotherm were found to 31.49 mg/g, 136.58 mg/g, 27.99 mg/g, respectively. A single stage batch adsorber was designed for the adsorption of eosin yellow, malachite green and crystal violet onto JFC based on the optimum isotherm. A pseudo second order kinetic model well represented the kinetic uptake of dyes studied onto JFC. The pseudo second order kinetic model successfully simulated the kinetics of dye uptake process. The dye sorption process involves both surface and pore diffusion with predominance of surface diffusion at earlier stages. A Boyd plot confirms the external mass transfer as the rate limiting step in the dye sorption process. The influence of initial dye concentration on the dye sorption process was represented in the form of dimensionless mass transfer numbers (Sh/Sc(0.33)) and was found to be agreeing with the expression: