Comparative Analysis of Linear and Nonlinear Methods of Estimating the Pseudo-Second-Order Kinetic Parameters for Sorption of Malachite Green onto Pretreated Rice Husk

Batch sorption experiments were carried out for removal of malachite green from aqueous solution using pretreated rice husk. The equilibrium kinetic data were analyzed using pseudo-second-order kinetic model. A comparison between linear and nonlinear methods of estimating the kinetic parameters was carried out. Four pseudo-second-order kinetic linear equations were discussed. The coefficient of determination (r ²) and chi-square (χ²) test were employed as error analysis methods to determine the best-fitting equation. The results show that nonlinear method is a better alternative to obtain the kinetic parameters. In addition, the chi-square test was a better method to determine the best-fitting model.     

Pseudo-Second-Order Kinetic Model for Biosorption of Methylene Blue onto Tamarind Fruit Shell: Comparison of Linear and Nonlinear Methods

In this study, the sorption of methylene blue, a basic dye, onto tamarind fruit shell was studied by performing batch kinetic sorption experiments. The equilibrium kinetic data were analyzed using the pseudo-second-order kinetic model. A comparison between linear least squares method and nonlinear regression method of estimating the kinetic parameters was examined. Four pseudo-second-order kinetic linear equations were discussed. The coefficient of determination (r ²), and the chi-square (χ²) test were employed as error analysis methods to determine the best-fitting equation. Kinetic parameters obtained from four kinetic linear equations using the linear method differed but they were the same when nonlinear method was used. Present investigation showed that by linear method a Type 1 expression very well represent the kinetic uptake of methylene blue onto tamarind fruit shell. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Nonlinear regression method was found to be the more appropriate method to determine the rate kinetic parameters.     

Exact and user-friendly kinetic analysis of the two-step rapid equilibrium Michaelis-Menten mechanism

Most enzyme kinetic experiments are carried out under pseudo-first-order conditions, that is, when one of the reactant species (the enzyme or the substrate) is in a large excess of the other species. More accurate kinetic information about the system can be gained without the restrictions of the pseudo-first-order conditions. We present a practical and general method of analysis of the common two-step rapid equilibrium Michaelis-Menten mechanism. The formalism is exact in that it does not involve any other approximations such as the steady-state, limitations on the reactant concentrations or on reaction times. We apply this method to the global analysis of kinetic progress curves for bovine alkaline phosphatase assays carried out under both pseudo-first-order and pseudo-second-order conditions.     

Adsorption of methylene blue from aqueous solution on pyrolyzed petrified sediment

The adsorption kinetics of methylene blue on pyrolyzed petrified sediment (PPS) has been performed using a batch-adsorption technique. The effects of various experimental parameters, such as initial dye concentration, contact time, and temperature were investigated. The pseudo-first-order and pseudo-second-order kinetic models were used to describe the kinetic data. The best correlation coefficient was obtained using the pseudo first-order kinetic model, which shows that the adsorption of methylene blue followed the pseudo-first-order rate expression and the rate constants were evaluated. The Langmuir and Freundlich adsorption isotherm models were applied to describe the equilibrium isotherms and the isotherm constants were determined. It was found that the data fitted well to Langmuir and Freundlich models. The activation energy of adsorption was also evaluated for the adsorption of methylene blue onto pyrolyzed sediment. It was found about 8.5 kJ mol(-1). Thermodynamics parameters DeltaG(o), DeltaH(o), DeltaS(o) were calculated, indicating that this process can be spontaneous and endothermic. The adsorption enthalpy and entropy were found as 14-18.5 kJ mol(-1) and 52.8-67 J mol(-1) K(-1), respectively. The results obtained from the adsorption process using PPS as adsorbent was subjected to student's t-test.     

Adsorption of gold(III), platinum(IV) and palladium(II) onto glycine modified crosslinked chitosan resin

The adsorption of Au(III), Pt(IV) and Pd(II) onto glycine modified crosslinked chitosan resin (GMCCR) has been investigated. The parameters studied include the effects of pH, contact time, ionic strength and the initial metal ion concentrations by batch method. The optimal pH for the adsorption of Au(III), Pt(IV) and Pd(II) was found to range from 1.0 to 4.0 and the maximum uptake was obtained at pH 2.0 for Au(III), Pt(IV) and Pd(II). The results obtained from equilibrium adsorption studies are fitted in various adsorption models such as Langmuir and Freundlich and the model parameters have been evaluated. The maximum adsorption capacity of GMCCR for Au(III), Pt(IV) and Pd(II) was found to be 169.98, 122.47 and 120.39mg/g, respectively. The kinetic data was tested using pseudo-first-order and pseudo-second-order kinetic models and an intraparticle diffusion model. The correlation results suggested that the pseudo-second-order model was the best choice among all the kinetic models to describe the adsorption behavior of Au(III), Pt(IV) and Pd(II) onto GMCCR. Various concentrations of HCl, thiourea and thiourea-HCl solutions were used to desorb the adsorbed precious metal ions from GMCCR. It was found that 0.7M thiourea-2M HCl solution provided effectiveness of the desorption of Au(III), Pt(IV) and Pd(II) from GMCCR. The modification of glycine on crosslinked chitosan resin (CCR) was studied by Fourier transform infrared spectrometry (FTIR) and scanning electron microscopy (SEM).     

Citric acid modified kenaf core fibres for removal of methylene blue from aqueous solution

Chemically modified kenaf core fibres were prepared via esterification in the presence of citric acid (CA). The adsorption kinetics and isotherm studies were carried out under different conditions to examine the adsorption efficiency of CA-treated kenaf core fibres towards methylene blue (MB). The adsorption capacity of the kenaf core fibres increased significantly after the citric acid treatment. The values of the correlation coefficients indicated that the Langmuir isotherm fitted the experimental data better than the Freundlich isotherm. The maximum adsorption capacity of the CA-treated kenaf core fibres was found to be 131.6 mg/g at 60 °C. Kinetic models, pseudo-first-order, pseudo-second-order and intraparticle diffusion, were employed to describe the adsorption mechanism. The kinetic data were found to fit pseudo-second-order model equation as compared to pseudo-first-order model. The adsorption of MB onto the CA-treated kenaf core fibres was spontaneous and endothermic.     

Biosorption of uranium by magnetically modified Rhodotorula glutinis

Adsorption of uranium from aqueous solution onto the magnetically modified yeast cell, Rhodotorula glutinis, was investigated in a batch system. Factors influencing sorption such as initial solution pH, biomass dosage, contact time, temperature, initial uranium concentration and other common cations were analyzed. Sorption isotherm, kinetic and thermodynamic studies of uranium on magnetically modified R. glutinis were also carried out. The temperature dependent equilibrium data agreed well with the Langmuir model. Kinetic data obtained at different temperatures were simulated using pseudo-first-order and pseudo-second-order kinetic models, the pseudo-second-order kinetic model was found to describe the data better with correlation coefficients near 1.0. The thermodynamic parameters, ΔH°, ΔS° and ΔG° were calculated from the sorption data gained at different temperatures. These thermodynamic parameters showed that the sorption process was endothermic and spontaneous. All results indicated that magnetically modified R. glutinis can be a potential sorbent for uranium wastewater treatment.     

Utilization of unconventional lignocellulosic waste biomass for the biosorption of toxic triphenylmethane dye malachite green from aqueous solution

Biosorption potential of novel lignocellulosic biosorbents Musa sp. peel (MSP) and Aegle marmelos shell (AMS) was investigated for the removal of toxic triphenylmethane dye malachite green (MG), from aqueous solution. Batch experiments were performed to study the biosorption characteristics of malachite green onto lignocellulosic biosorbents as a function of initial solution pH, initial malachite green concentration, biosorbents dosage, and temperature. Biosorption equilibrium data were fitted to two and three parameters isotherm models. Three-parameter isotherm models better described the equilibrium data. The maximum monolayer biosorption capacities obtained using the Langmuir model for MG removal using MSP and AMS was 47.61 and 18.86 mg/g, respectively. The biosorption kinetic data were analyzed using pseudo-first-order, pseudo-second-order, Elovich and intraparticle diffusion models. The pseudo-second-order kinetic model best fitted the experimental data, indicated the MG biosorption using MSP and AMS as chemisorption process. The removal of MG using AMS was found as highly dependent on the process temperature. The removal efficiency of MG showed declined effect at the higher concentrations of NaCl and CaCl₂. The regeneration test of the biosorbents toward MG removal was successful up to three cycles.     

Biosorption of Pb(II) and Cr(III) from aqueous solution by lichen (Parmelina tiliaceae) biomass

The biosorption characteristics of Pb(II) and Cr(III) ions from aqueous solution using the lichen (Parmelina tiliaceae) biomass were investigated. Optimum biosorption conditions were determined as a function of pH, biomass dosage, contact time, and temperature. Langmuir, Freundlich and Dubinin-Radushkevich (D-R) models were applied to describe the biosorption isotherm of the metal ions by P. tiliaceae biomass. Langmuir model fitted the equilibrium data better than the Freundlich isotherm. The monolayer biosorption capacity of P. tiliaceae biomass for Pb(II) and Cr(III) ions was found to be 75.8 mg/g and 52.1mg/g, respectively. From the D-R isotherm model, the mean free energy was calculated as 12.7 kJ/mol for Pb(II) biosorption and 10.5 kJ/mol for Cr(III) biosorption, indicating that the biosorption of both metal ions was taken place by chemical ion-exchange. The calculated thermodynamic parameters (delta G degrees , delta H degrees and delta S degrees ) showed that the biosorption of Pb(II) and Cr(III) ions onto P. tiliaceae biomass was feasible, spontaneous and exothermic under examined conditions. Experimental data were also tested in terms of biosorption kinetics using pseudo-first-order and pseudo-second-order kinetic models. The results showed that the biosorption processes of both metal ions followed well pseudo-second-order kinetics.     

Equilibrium and Kinetic Studies of Phosphate Removal from Solution onto a Hydrothermally Modified Oyster Shell Material

Phosphate removal to a hydrothermally modified fumed silica and pulverized oyster shell material for use in wastewater treatments were made. Sorption data modeling (pH’s 3–11, P concentrations of 3, 5, 10, 15, 20, & 25 mg/L, and at an ambient temperature of 23°C) indicate that an optimal removal of P occurs at pH 11. Three kinetic models were also applied (a pseudo-first-order Lagergren kinetic model, a pseudo-second-order (PSO) kinetic and Elovich) and indicate that a PSO model best describes P-removal. In addition, an application of the Weber and Morris intra-particle diffusion model indicates that external mass transfer and intra-particle diffusion were both involved in the rate-determining step. Langmuir, Freundlich modeling of the sorption data also indicate that the heterogeneous Freundlich sorption site model best describes the data although Langmuir data also fit with data tailing suggesting data are not linear. The data collected indicates that the hydrothermally modified fumed silica and pulverized oyster shell material is suitable for use in wastewater treatment, with P-removal to the solids being preferential and spontaneous.     

Preparation,Characterization and Application of Magnetic Fe3O4-CS for the Adsorption of Orange I from Aqueous Solutions

Fe₃O₄ (Fe₃O₄-CS) coated with magnetic chitosan was prepared as an adsorbent for the removal of Orange I from aqueous solutions and characterized by FTIR, XRD, SEM, TEM and TGA measurements. The effects of pH, initial concentration and contact time on the adsorption of Orange I from aqueous solutions were investigated. The decoloration rate was higher than 94% in the initial concentration range of 50–150 mg L⁻¹ at pH 2.0. The maximum adsorption amount was 183.2 mg g⁻¹ and was obtained at an initial concentration of 400 mg L⁻¹ at pH 2.0. The adsorption equilibrium was reached in 30 minutes, demonstrating that the obtained adsorbent has the potential for practical application. The equilibrium adsorption isotherm was analyzed by the Freundlich and Langmuir models, and the adsorption kinetics were analyzed by the pseudo-first-order and pseudo-second-order kinetic models. The higher linear correlation coefficients showed that the Langmuir model (R² = 0.9995) and pseudo-second-order model (R² = 0.9561) offered the better fits.     

Bioremediation potential of a widespread industrial biowaste as renewable and sustainable biosorbent for synthetic dye pollution

In this study, a model synthetic azo dye (Basic red 46) bioremoval by Carpinus betulus sawdust as inexpensive, eco-friendly, and sustainable biosorbent from aqueous solution was examined in a batch biosorption system. The effective environmental parameters on the biosorption process, such as the value of pH, amount of biosorbent, initial dye concentration and contact time were optimized using classical test design. The possible dye-biosorbent interaction was determined by Fourier Transform Infrared Spectroscopy (FTIR) and Scanning Electron Microscopy (SEM). The equilibrium, thermodynamic, and kinetic studies for the biosorption of Basic red 46 onto the sawdust biomass were performed. In addition, a single-stage batch dye biosorption system was also designed. The dye biosorption yield of biosorbent was significantly influenced by the change of operating variables. The experimental data were best described by the Freundlich isotherm model and both the pseudo-first-order kinetic and the pseudo-second-order kinetic models. Thermodynamic research indicated that the biosorption of dye was feasible and spontaneous. Based on the Langmuir isotherm model, the biosorbent was found to have a maximum biosorption potential higher than many other biosorbents in the literature (264.915?mg g^?1). Thus, this investigation presents a novel green option for the assessment of waste sawdust biomass as a cheap and effective biosorbent material.     

Biosorption of Nickel(II) from aqueous solution by the fungal mat of Trametes versicolor (rainbow) biomass: equilibrium, kinetics, and thermodynamic studies

This study investigates the equilibrium, kinetics and thermodynamics of Nickel(II) biosorption from aqueous solution by the fungal mat of Trametes versicolor (rainbow) biomass. The optimum biosorption conditions like pH, contact time, biomass dosage, initial metal ion concentration and temperaturewere determined in the batch method. The biosorbent was characterized by FTIR, SEM and BET surface area analysis. The experimental data were analyzed in terms of pseudo-first-order, pseudo-secondorder and intraparticle diffusion kinetic models, further it was observed that the biosorption process of Ni(II) ions closely followed pseudo-second-order kinetics. The equilibrium data of Ni(II) ions at 303, 313, and 323 K were fitted to the Langmuir and Freundlich isotherm models. Langmuir isotherm provided a better fit to the equilibrium data andthe maximum monolayer biosorption capacity of the T. versicolor(rainbow) biomass for Ni(II) was 212.5 mg/g at pH 4.0. The calculated thermodynamic parameters, ΔG^○, ΔH^○, and ΔS^○, demonstrated that the biosorption of Ni(II) ions onto the T. versicolor (rainbow) biomass was feasible, spontaneous and endothermic at 303 ～ 323 K. The performance of the proposed fungal biosorbent was also compared with that of many other reported sorbents for Nickel(II) removal and it was observed that the proposed biosorbent is effective in terms of its high sorption capacity.     

Adsorption of Basic violet 16 from aqueous solutions by waste sugar beet pulp: kinetic,thermodynamic, and equilibrium isotherm studies

Waste sugar beet pulp has been used as adsorbent for the removal of a hazardous cationic dye, Basic violet 16, from its aqueous solution. Adsorption of the dye was studied as function of time, pH of the solution, dosage of the adsorbent, sieve size of the particles, concentration of the dye, and temperature. The initial pH of the dye solution did not affect the chemistry of the dye molecule and the surface of beet pulp. Langmuir and Freundlich adsorption isotherms were successfully employed, and on the basis of these models, the thermodynamic parameters were evaluated. Adsorption of Basic violet 16 on beet pulp was found to be an exothermic reaction. Time contact studies showed that more than 80% adsorption of the dye is achieved in less than 1 h. Kinetics investigations confirmed both pseudo-first-order and pseudo-second-order behaviors; on the other hand, it shows that the intraparticle diffusion step is not the only rate-controlling step in all concentrations.     

Physical and chemical immobilization of choline oxidase onto different porous solid supports: Adsorption studies

This work carries out for the first time the comparison between the physical and chemical immobilization of choline oxidase onto aminated silica-based porous supports. The influence on the immobilization efficiency of concentration, pH, temperature and contact time between the support and choline oxidase, was evaluated. The immobilization efficiency was estimated taking into consideration the choline oxidase activity, which was assessed by using cadmium telluride (CdTe) quantum dots (QDs), obtained by hydrothermal synthesis, as photoluminescent probes. Hydrogen peroxide produced by enzyme activity was capable of quenching CdTe QDs photoluminescence. The magnitude of the PL quenching process was directly related with the enzyme activity.By comparing the chemical process with the physical adsorption, it was observed that the latter provided the highest choline oxidase immobilization. The equilibrium data were analyzed using Langmuir and Freundlich isotherms and kinetic data were fitted to the pseudo-first-order and pseudo-second-order models. Thermodynamic parameters, such as Gibbs free energy and entropy were also calculated. These results will certainly contribute to the development of new sensing schemes for choline, taking into account the growing demand for its quantification in biological samples.     

Desorption of Nitroaromatic Compounds From Explosive-contaminated Soil by Washing

The soil contaminated by explosive production wastewater was treated by washing using water as solvent. The effect of contact time and temperature, water/soil ratio and washing steps on desorption efficiency was investigated. Six kinetic models—parabolic diffusion model, zero-order equation, pseudo-first-order equation, pseudo-second-order equation, power function equation and Elovich equation—were used to study the desorption kinetics of nitroaromatic compounds from contaminated soil to water. The eluent of contaminated soil before and after washing was characterized by UV–vis analysis. The results showed that the removal rate was fast at the initial stage and then slowed down after 60 min. The desorption of contaminants from soil to water is endothermic. Washing with small quantities of water in high frequency is preferred when water volume is limited. The pseudo-second-order model can be used to describe the desorption process. Soil washing can remove most of the contaminants from the contaminated soil.     

Kinetic models of spike-timing dependent plasticity and their functional consequences in detecting correlations

Spike-timing dependent plasticity (STDP) is a type of synaptic modification found relatively recently, but the underlying biophysical mechanisms are still unclear. Several models of STDP have been proposed, and differ by their implementation, and in particular how synaptic weights saturate to their minimal and maximal values. We analyze here kinetic models of transmitter-receptor interaction and derive a series of STDP models. In general, such kinetic models predict progressive saturation of the weights. Various forms can be obtained depending on the hypotheses made in the kinetic model, and these include a simple linear dependence on the value of the weight (“soft bounds”), mixed soft and abrupt saturation (“hard bound”), or more complex forms. We analyze in more detail simple soft-bound models of Hebbian and anti-Hebbian STDPs, in which nonlinear spike interactions (triplets) are taken into account. We show that Hebbian STDPs can be used to selectively potentiate synapses that are correlated in time, while anti-Hebbian STDPs depress correlated synapses, despite the presence of nonlinear spike interactions. This correlation detection enables neurons to develop a selectivity to correlated inputs. We also examine different versions of kinetics-based STDP models and compare their sensitivity to correlations. We conclude that kinetic models generally predict soft-bound dynamics, and that such models seem ideal for detecting correlations among large numbers of inputs.     

Kinetic and equilibrium studies of copper biosorption onto <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis> base using direct determination of copper by a voltammetric method

This paper provided information on the use of linear sweep anodic stripping voltammetry for evaluating the process of copper biosorption onto Pseudomonas aeruginosa. This technique was suited to determine the concentration of free copper ion on site on the mercaptoethane sulfonate modified gold electrode surface without any pretreatment. It was in favor of the study of kinetic process as the fast changing kinetic data characteristic just after the beginning of biosorption could be accurately depicted. Based on the electrochemical results, the kinetics and equilibrium of biosorption were systematically examined. The pseudo-second-order kinetic model was used to correlate the kinetic experimental data and the kinetic parameters were evaluated. The Langmuir and Freundlich models were applied to describe the biosorption equilibrium. It was found that the Langmuir isotherm fitted the experimental data better than the Freundlich isotherm. Maximum adsorption capacity of copper ion onto Pseudomonas aeruginosa was 0.9355 μmol mg⁻¹ (about 59.4417 mg g⁻¹).     

Use of nonlinear regression to analyze enzyme kinetic data: application to situations of substrate contamination and background subtraction

In a recent publication, A. Lundin, P. Arner, and J. Hellmér [Anal. Biochem. 177, 125-131 (1989)] describe a method whereby kinetic substrate assays can be performed when the assay mixture includes a significant contaminating levels of substrate. Their method requires various rearrangements of the data, and involves three separate linear regression calculations. We show how the same data may be analyzed directly, and far more simply, by nonlinear regression. Unlike the linear regression method, nonlinear regression allows direct calculation of the actual values for Km, Vmax, and the concentration of contaminating substrate (as well as estimates of their standard errors); the former method gives only apparent values. The nonlinear regression technique is also statistically a more valid means of analysis, as the rearrangements required to give linearized equations will considerably distort the error distribution and render simple unweighted linear regression inappropriate. The ease of incorporating extra parameters into standard equations when nonlinear regression is used is further illustrated by fitting enzyme reaction data which describe a first-order process when a significant nonspecific background is present. For this equation no simple rearranged linear plot is possible, but nonlinear regression is easily applied to determine the kinetic parameters.     

Application of a new method of nonlinear dynamical system identification to biochemical problems

The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.