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.     

Linear and Nonlinear Regression Analyses for Binary Sorption Kinetics of Methylene Blue and Safranin onto Pretreated Rice Husk

This article extends the study of the comparison between linear and nonlinear forms of the two widely used kinetic models, namely, pseudo-first-order and pseudo-second-order, by considering the binary biosorption of the basic dyes methylene blue and safranin onto pretreated rice husk in a batch system. The present investigation showed that nonlinear forms of pseudo-first-order and pseudo-second-order models were more suitable than the linear forms for fitting the experimental data. The sorption process was found to follow the pseudo-second-order kinetics. The results suggest that it is not appropriate to use the linear method in determining the kinetic parameters of a particular kinetic model. The nonlinear method is a better way to obtain the kinetic parameters than the linear method and thus it should be primarily adopted to determine the kinetic parameters.     

Optimum Sorption Isotherm by Linear and Nonlinear Methods for Safranin onto Alkali-Treated Rice Husk

Rice husk, a lignocellulosic by-product of the agroindustry, was treated with alkali and used as a low-cost adsorbent for the removal of safranin from aqueous solution in batch adsorption procedure. In order to estimate the equilibrium parameters, the equilibrium adsorption data were analyzed using the following two-parameter isotherms: Freundlich, Langmuir, and Temkin. A comparison of linear and nonlinear regression methods in selecting the optimum adsorption isotherm was applied on the experimental data. Six linearized isotherm models (including four linearized Langmuir models) and three nonlinear isotherm models are thus discussed in this paper. In order to determine the best-fit isotherm predicted by each method, seven error functions namely, coefficient of determination (r ²), the sum of the squares of the errors (SSE), sum of the absolute errors (SAE), average relative error (ARE), hybrid fractional error-function (HYBRID), Marquardt's percent standard deviation (MPSD), and the chi-square test (χ²) were used. It was concluded that the nonlinear method is a better way to obtain the isotherm parameters and the data were in good agreement with the Langmuir isotherm model.     

Kinetics,Isotherms, and Thermodynamics of Hg(II) Biosorption onto Carica papaya

Carica papaya, a novel sorbent, was evaluated for sorption of Hg(II) from synthetic aqueous solutions using various pseudo-second order kinetic models as well as equilibrium sorption models. Batch kinetic and equilibrium experiments were carried out for the sorption of Hg(II) onto C. papaya at pH 6.5 and solid to liquid ratio (s/l) 1.0 g L^?1. The kinetic data were fitted to second order models of Sobkowsk and Czerwinski, Ritchie, Blanchard, Ho and McKay, whereas Langmuir, Freundlich, and Redlich-Peterson models were used for the equilibrium data. A comparative study on both linear and nonlinear regression showed that the Sobkowsk and Czerwinski and Ritchie's second order model were the same. Ho and McKay's pseudo-second order model fitted well to the experimental data when compared with the other second order kinetic expressions. Langmuir isotherm parameters obtained from the four Langmuir linear equations by using linear method were dissimilar, but were the same when nonlinear method was used. Additionally, various thermodynamic parameters, such as ΔG ⁰, ΔH ⁰, and ΔS ⁰, were calculated. The negative values of Gibbs free energy (ΔG ⁰) and ΔH ⁰ confirmed the intrinsic nature of biosorption process and exothermic, respectively. The negative value of ΔS ⁰ showed the decreased randomness at the solid-solution interface during biosorption.     

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).     

Kinetics and competitive modeling of cesium biosorption onto iron(III) hexacyanoferrate modified pine cone powder

This study looked at incorporation of iron(III) hexacyanoferrate onto chemically treated pine cone via iron(III) surface loading and its application for cesium (Cs) adsorption in the presence of alkali/alkali earth metals. The optimum iron(III) loading concentration was 2.50 mol l⁻¹ at pH 7, while optimum hexacyanoferrate (HCF) loading was achieved at a hexacyanoferrate concentration of 0.26 mol l⁻¹. The best-fitting kinetic model was confirmed using the closeness of the predicted equilibrium capacities to the experimentally determined capacity, three error determination methods, and the comparative plots of predictive and experimental uptake of Cs with time. The adsorption rate constants were reduced by alkali/alkali metal addition and the reduction was higher in the HCF-modified pine. The mechanism of Cs adsorption onto raw pine followed the pseudo-second-order model and involved stripping of the hydration water from the metal ion. The presence of Na⁺ did not alter the adsorption mechanism but Ca²⁺ addition changed the best-fitting model to pseudo-first-order. The diffusion-chemisorption model best fitted Cs adsorption onto HCF-modified pine and involved adsorption of Cs in its hydrated form, which migrated easily through the zeolite-like lattice of hexacyanoferrate. Addition of Na⁺ and Ca²⁺ changed the best-fitting model to a pseudo-first-order model.     

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.     

A comparison of methods for determining compartmental analysis parameters

The traditional method for determining compartmental analysis parameters relies on a visual selection of data points to be used for regression of data from each cellular compartment. This method is appropriate when the compartments are kinetically discrete and are easily discernible. However, where treatment effects on compartment parameters are being evaluated, a more objective method for determining initial parameters is desirable.

Three methods were examined for determining initial isotopic contents and half-times of ⁸⁶Rb elution from cellular compartments using theoretical data with known parameters. Experimental data from roots of Douglas fir (Pseudotsuga menziesii [Mirb.] Franco) and barley (Hordeum vulgare L.) intact seedlings were also used. The three methods were a visually assisted, linear regression on data of semilog plot of isotope elution versus time, a microcomputer-assisted, linear regression on semilog plot where maximization of the square of the correlation coefficient (r²) was the criterion to determine data points needed for each regression and a mainframe computer-assisted, direct nonlinear regression on elution data using a model of the sum of three exponential decay functions. The visual method resulted in the least accurate estimates of compartmental analysis parameters. The microcomputer-assisted and nonlinear regression methods calculated the parameters equally well.

     

QSAR studies on 4-anilino-3-quinolinecarbonitriles as Src kinase inhibitors using robust PCA and both linear and nonlinear models

Quantitative structure-activity relationship (QSAR) studies have been carried out on 4-anilino-3-quinolinecarbonitriles, a set of novel Src kinase inhibitors, with the aim of dissecting the structural requirements for Src inhibitory activities. After outlier identification using robust principal component analysis (robust PCA), linear models based on forward selection combined with multiple linear regression, (FS-MLR), enhanced replacement method followed by multiple linear regression (ERM) and a nonlinear model using support vector regression (SVR) were constructed and compared. All models were rigorously validated using leave-one-out cross-validation (LOOCV), 5-fold cross-validations (5-CV) and shuffling external validation (SEVs). ERM seems to outperform both FS-MLR and SVR evidenced by better prediction performance (n?=?35, R²_training?=?0.918, R²_pred?=?0.928). Robustness and predictive ability of ERM model were also evaluated. The generated QASR model revealed that the Src inhibitory activity of 4-anilino-3-quinolinecarbonitriles could be associated with the size of substituents in the C7 position and the steric hindrance effect. The results of the present study may be of great help in designing novel 4-anilino-3-quinolinecarbonitriles with more potent Src kinase inhibitory activity.     

Estimation of Kinetic Parameters for Bioremediation of Cr(VI) from Wastewater Using Pseudomonas taiwanensis,an Isolated Strain from Enriched Mixed Culture

An aerobic mixed culture collected in the form of activated sludge was enriched for Cr(VI) reduction. An indigenous microorganism was isolated from the enriched aerobic mixed culture and identified as Pseudomonas taiwanensis. Bioremediation studies were carried out for treating Cr(VI)-contaminated wastewater using the indigenous microorganism. The kinetic studies were carried out for initial Cr(VI) concentrations ranging from 20 to 200 mg L^?1. The maximum consumption of Cr(VI) obtained was 108.3 mg L^?1 for an initial Cr(VI) concentration of 150 mg L^?1 at a solution pH of 7.0. The effect of nutrient dosage and pH were studied to get their optimum values. The same isolated bacterial strain was also used to treat Cr(VI)-contaminated industrial wastewater collected from a local plating industry. Various growth kinetic models, such as Monod, Powell, Haldane, Luong, and Edward models, were fitted with the obtained experimental data. The obtained results for different growth kinetic models indicate that the growth kinetics of Pseudomonas taiwanensis for bioremediation of Cr(VI) can be better understood by the Luong model (R² = .913). The rate kinetic analysis was performed using zero-order and three-half-order kinetic models. The three-half-order kinetic model was found to be suitable for the present bioremediation study.     

Biosorption Behavior of Ciprofloxacin onto Enteromorpha prolifera: Isotherm and Kinetic Studies

The studies aimed at the feasibility of using Enteromorpha prolifera for the removal of ciprofloxacin from aqueous solutions. Batch experiments were carried out for the biosorption of ciprofloxacin onto Enteromorpha prolifera. The factors affecting the biosorption process such as the initial concentration, dosage, pH and the contact time were studied. Enteromorpha prolifera exhibited a maximum biosorption capacity of 21.7 mg/g. The pseudo-second-order kinetic model described the ciprofloxacin biosorption process with a good fitting. The optimum pH of ciprofloxacin adsorbed by Enteromorpha prolifera was 10. Biosorption equilibrium studies demonstrated that the biosorption followed Freundlich isotherm model, which implied a heterogeneous biosorption phenomenon.     

Chemical modification of chitosan by tetraethylenepentamine and adsorption study for anionic dye removal

To utilize the contribution of introduced amino groups to the adsorption of an anionic dye (eosin Y), a batch adsorption system was applied to study the adsorption of eosin Y from aqueous solution by tetraethylenepentamine (TEPA) modified chitosan (TEPA–CS). Experiments were carried out as a function of particle size, initial pH, agitation rate, adsorbent dosage, agitation period, temperature and initial concentration of eosin Y. The Langmuir and Freundlich models were used to fit the adsorption isotherms. From the values of correlation coefficients (R²), it was observed that the experimental data fit very well to the Langmuir model, giving a maximum sorption capacity of 292.4 mg/g at 298 K. Kinetic studies showed that the kinetic data were well described by the pseudo-second-order kinetic model. The thermodynamic study revealed negative value of enthalpy change (ΔH°) and free energy change (ΔG°), indicating spontaneous and endothermic nature of the adsorption of eosin Y on to TEPA–CS.     

Biodegradation kinetics of LAS in river water

This article reports the biodegradation kinetics of linear alkylbenzene sulfonates (LAS) in river water. The authors used the ‘river die-away' test method and high performance liquid chromatography to monitor LAS concentrations as functions of time in a series of tests systems. Controlled variables included initial LAS concentrations and incubation temperature. The kinetic parameters computed from the experimental data demonstrated strong correlations (r²>0.99) with theoretical values computed from the kinetic model presented in this paper. The proposed model accurately predicts concentrations of non-biodegradable substrate and the maximum specific microbial growth rate.     

Modeling individual leaf area of rose (<Emphasis Type="Italic">Rosa hybrida</Emphasis> L.) based on leaf length and width measurement

Accurate and nondestructive methods to determine individual leaf areas of plants are a useful tool in physiological and agronomic research. Determining the individual leaf area (LA) of rose (Rosa hybrida L.) involves measurements of leaf parameters such as length (L) and width (W), or some combinations of these parameters. Two-year investigation was carried out during 2007 (on thirteen cultivars) and 2008 (on one cultivar) under greenhouse conditions, respectively, to test whether a model could be developed to estimate LA of rose across cultivars. Regression analysis of LA vs. L and W revealed several models that could be used for estimating the area of individual rose leaves. A linear model having L×W as the independent variable provided the most accurate estimate (highest r ² , smallest MSE, and the smallest PRESS) of LA in rose. Validation of the model having L×W of leaves measured in the 2008 experiment coming from other cultivars of rose showed that the correlation between calculated and measured rose LA was very high. Therefore, this model can estimate accurately and in large quantities the LA of rose plants in many experimental comparisons without the use of any expensive instruments.     

Kinetic modeling of lipase‐catalyzed esterification reaction between oleic acid and trimethylolpropane: A simplified model for multi‐substrate multi‐product ping–pong mechanisms

Kinetic models are among the tools that can be used for optimization of biocatalytic reactions as well as for facilitating process design and upscaling in order to improve productivity and economy of these processes. Mechanism pathways for multi‐substrate multi‐product enzyme‐catalyzed reactions can become very complex and lead to kinetic models comprising several tens of terms. Hence the models comprise too many parameters, which are in general highly correlated and their estimations are often prone to huge errors. In this study, Novozym^®435 catalyzed esterification reaction between oleic acid (OA) and trimethylolpropane (TMP) with continuous removal of side‐product (water) was carried out as an example for reactions that follow multi‐substrate multi‐product ping‐pong mechanisms. A kinetic model was developed based on a simplified ping‐pong mechanism proposed for the reaction. The model considered both enzymatic and spontaneous reactions involved and also the effect of product removal during the reaction. The kinetic model parameters were estimated using nonlinear curve fitting through unconstrained optimization methodology and the model was verified by using empirical data from different experiments and showed good predictability of the reaction under different conditions. This approach can be applied to similar biocatalytic processes to facilitate their optimization and design. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:1422–1429, 2013     

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.     

Improving Mathematical Model in Biodegradation of PAHs Contaminated Soil Using Gram-Positive Bacteria

In published literature there are limited studies on the estimation of kinetic parameters of polycyclic aromatic hydrocarbons (PAHs) in soil. In addition, neither the kinetic studies were performed with Gram-positive bacteria nor conducted under non-indigenous condition in order to understand their removal performance. Thus, a mathematical model describing biodegradation of phenanthrene-contaminated soil by Corynebacterium urealyticum, bacterium isolated from municipal sludge, was developed in this study. The model includes three kinetic parameters that were determined using TableCurve 2D software, namely qmax (maximum substrate utilization rate per unit mass of bacteria), X (biomass concentration) and Ks (substrate concentration at one half the maximum substrate utilization rate). These parameters were evaluated and verified in five different initial phenanthrene concentrations. Highest degradation rate was determined to be 79.24 mg kg^?1 day^?1 at 500 mg kg^?1 initial phenanthrene concentrations. This high concentration shows that bacteria perform better in contaminated sand compared to liquid media. High r² values, ranging from 0.92 to 0.99, were obtained excluding 1000 mg/kg phenanthrene. The kinetic parameters, i.e., qmax and Ks, increased with the phenanthrene concentration and thus suggest that bacteria degrade at a higher degradation rate. This model successfully described the biodegradation profiles observed at different initial phenanthrene concentrations. The established model can be used to simulate the duration of phenanthrene degradation using only the value of the initial PAHs concentration.