Nonlinear Analysis of the Kinetics and Equilibrium for Adsorptive Removal of Cd(II) by Starch Phosphate

In the present study, the nonlinear analysis method was used to evaluate the kinetics and equilibrium for Cd(II) adsorption on crosslinked starch phosphate (SP) from aqueous solution. The pseudo-first-order, pseudo-second-order and Elovich kinetic models were applied to test the kinetics experimental data, and the pseudo-first-order kinetic model provides a best correlation of the experimental data. Adsorption equilibrium data were fit by Langmuir, Freundlich, Dubinin-Radushkevich, and Sips isotherms. The results show that the data are best described by the Sips isotherms with a maximum adsorption capacity of 2.00 mmol/g. The effects of initial pH, and SP dose on the Cd(II) adsorption were also investigated. The adsorption capacities of Cd(II) on SP increase with the pH increasing from 2.0 to 8.0.     

Algorithm for error-compensated kinetic determinations without prior knowledge of reaction order or rate constant

The development and evaluation of a new algorithm for error-compensating predictive kinetic determinations are described. With the new algorithm it is possible to fit kinetic data without prior knowledge of the rate constant, reaction order or initial and final values of the detector signal. A curve-fitting method is used to obtain values of these parameters that give the best fit of the model to the data. Although intended to be used primarily to compute signal changes between t=0 and ∞, the method can also be used to determine reaction orders. Although the algorithm fails for reaction orders of zero and unity, it works well for orders between these values and orders greater than unity. Simulated data are used to evaluate the effects of reaction order, signal noise and data range on computed values of signal change and, to a lesser extent, reaction order.     

A new integral method for the kinetic analysis of thermogravimetric data

Methods for the calculation of activation energies, pre-exponential factors and reaction orders from thermogravimetric data are briefly reviewed. A new integral method is proposed for the determination of these kinetic parameters, using data from pairs of TG curves produced at different heating rates. Employing accurate values of the temperature integral of the Arrhenius equation, tabulated over a range ofE andT, and a simple graphical procedure, the method offers advantages of speed and accuracy over those previously reported. It is suggested that at least one of the kinetic parameters should be allowed to move freely in order to achieve the best possible fit between calculated and experimental traces.     

Discrimination between ethanol inhibition models in a continuous alcoholic fermentation process using flocculating yeast

Discrimination between different rival models for describing the inhibitory effect of ethanol both on yeast growth and on fermentation was studied for a continuous process of alcoholic fermentation in a tower reactor with recycling of flocculating cells. Models tested include linear, parabolic, hyperbolic, exponential, and generalized nonlinear power-law types. The best expressions were identified under the criteria that all the kinetic parameters should assume acceptable values in a feasible range and should result in the best fit of the experimental data. The kinetic parameters were estimated from steady-state data of several sugar concentrations in feeding stream (S₀ = 160, 170, 180, 190, 200 g/L), constant dilution rate (D = 0.2 h^-1), recycle ratio (α = 13.6), and temperature (T = 30°C). The best model for the yeast growth was of power-law type, whereas for the product formation the best model was of linear type. These models were able to reproduce the trends of the process variables satisfactorily.     

Combined kinetic analysis of solid-state reactions: a powerful tool for the simultaneous determination of kinetic parameters and the kinetic model without previous assumptions on the reaction mechanism

The combined kinetic analysis implies a simultaneous analysis of experimental data representative of the forward solid-state reaction obtained under any experimental conditions. The analysis is based on the fact that when a solid-state reaction is described by a single activation energy, preexponetial factor and kinetic model, every experimental T-alpha-dalpha/dt triplet should fit the general differential equation independently of the experimental conditions used for recording such a triplet. Thus, only the correct kinetic model would fit all of the experimental data yielding a unique activation energy and preexponential factor. Nevertheless, a limitation of the method should be considered; thus, the proposed solid-state kinetic models have been derived by supposing ideal conditions, such as unique particle size and morphology. In real systems, deviations from such ideal conditions are expected, and therefore, experimental data might deviate from ideal equations. In this paper, we propose a modification in the combined kinetic analysis by using an empirical equation that fits every f(alpha) of the ideal kinetic models most extensively used in the literature and even their deviations produced by particle size distributions or heterogeneities in particle morphologies. The procedure here proposed allows the combined kinetic analysis of data obtained under any experimental conditions without any previous assumption about the kinetic model followed by the reaction. The procedure has been verified with simulated and experimental data.     

Selection of the most effective kinetic model of lactase hydrolysis by immobilized Aspergillus niger and free β-galactosidase

The kinetic model of the hydrolysis of lactose by β-galactosidase from Aspergillus niger immobilized on a commercial ceramic monoliths was estimated in the attendance of lactose and its hydrolysis reaction products galactose and glucose. The aim of this work was to developing kinetic model of lactase hydrolysis by Aspergillus niger. The variables in this study are temperature, pH, enzyme concentration, substrate concentration and final product. The optimum temperature used to achieve the best hydrolysis performance in the kinetic model selection was 55 and 60 °C. The optimum pH used for enzyme activity was about 3.5 to 4. Five kinetic models were proposed to confirm experimental data the enzymatic reaction of the lactose hydrolysis by the β-galactosidase. The kinetics of lactose hydrolysis by both Immobilized and soluble lactases were scrutinized in a batch reactor system in the lack of any mass conduction restriction. In both instance the galactose inhibition kinetic models predicted the experimental data. The model is capable to fit the experimental data correctly in the extensive experimental span studied.     

An incremental isoconversional method for kinetic analysis based on the orthogonal distance regression

The parameters obtained from a kinetic analysis of thermoanalytical data often exhibit a conversion‐dependent behavior. A novel incremental isoconversional method able to deal with this phenomenon is proposed. The kinetic model is directly fitted to the experimental data using nonlinear orthogonal least squares procedure. The data are processed without transformations, so their error distribution is preserved. As the objective function is based on a maximum likelihood approach, reliable uncertainties of the parameters can be estimated. In contrast to other methods, the activation energy and the pre‐exponential factor are treated as equally important kinetic parameters and are estimated simultaneously. Validity of the method is verified on simulated data, including a dataset with local nonlinearity in the temperature variation. A practical application on the nonisothermal cold crystallization of polyethylene terephthalate is presented. © 2014 Wiley Periodicals, Inc.     

Application of soft- and hard-modelling approaches to resolution of kinetics of electron donor-acceptor complex formation of 2,3-dichloro-5,6-dicyano-1,4-benzoquinone with imipramine in different solutions

Kinetics of electron donor-acceptor (EDA) complex formation of imipramine and 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) was investigated spectrophotometrically in acetonitrile, 1,2-dichloroethane, and chloroform solutions using soft- and hard-modelling approaches. From the results of exploratory analysis of kinetic data and the spectral changes by soft-modelling approaches, evolving factor analysis (EFA) and orthogonal projection approach (OPA), a consecutive two-steps reaction with two intermediates was proposed for the process in acetonitrile and 1,2-dichloroethane media and one with a single intermediate in chloroform solution. Secondly, by applying, multivariate nonlinear least squares hard-modelling approach on the collected experimental kinetic data matrix, the nonlinear parameters (rate constants) as well as the linear parameters (spectral profiles) were obtained by fitting the collected experimental kinetic data matrix to the proposed model. Small values of standard deviation in the resulting parameters and sum of squares of the residuals (ssq) obtained showed the proper selection of the model. Furthermore, the values of lack of fit and percent of explained variance confirmed the correct identified models. Identification of the model with the aid of soft-modelling approaches followed by application of the hard-modelling approaches decreases significantly the rotational ambiguity associated with the obtained concentration and spectral profiles. Variations in the kinetic constants were in complete agreement with the model proposed and the solvent polarities.     

Automatic kinetic model generation and selection based on concentration versus time curves

The goal of the paper is to automatize the construction and parameterization of kinetic reaction mechanisms that can describe a set of experimentally measured concentration versus time curves. Using the framework and theorems of formal reaction kinetics, first, we build a set of possible mechanisms with a given number of measured and unmeasured (real or fictitious) species and reaction steps that fulfill some chemically reasonable requirements. Then we fit all the corresponding mass-action kinetic models and offer the best one to the chemist to help explain the underlying chemical phenomenon or to use it for predictions. We demonstrate the use of the method via two simple examples: on an artificial, simulated set of data and on a small real-life data set. The method can also be used to do a kind of lumping to generate a model that can reproduce the simulation results of a detailed mechanism with less species and thereby can largely accelerate spatially inhomogeneous simulations.     

Comparison of methods concerning the selection of a function describing the thermal decomposition of solids

Determination of the kinetic parameters of the thermal decomposition of solids usually requires a knowledge of the function describing the mechanism of decomposition. Research was made to obtain a method that enables the selection of one of the 16 functions used in the literature in such a way that it best describes experimental data in the isothermal measurements. The results obtained indicate that the best fit of experimental and calculated data is gained by using the weighted least-squares method with the equation g(α) = kt + b and using criteria based on the minimization of the difference between α_exp and α_calc     

Closed form numerical approach for a kinetic interpretation of high-cis polybutadiene rubber vulcanization with sulphur

A novel mathematical approach to predict the vulcanization degree of high-cis polybutadiene rubber vulcanized with sulphur is presented. The model has kinetic base, it is constituted by four reactions occurring in series and parallel and takes contemporarily into consideration, within a simplified but reliable scheme, the actual reactions occurring during polybutadiene sulphur curing, namely primary crosslinking and possible de-vulcanization. The first order differential equation system obtained is suitably rearranged and a closed form expression for the vulcanization degree is derived, depending the four kinetic constants characterizing the chemistry describing reactions. Instead of using classic least-squares optimization routines to characterize kinetic constants on experimental data, a simplified but reliable approach is proposed, where a system of four non-linear equations is solved with a recursive strategy, allowing estimating kinetic constants that proved to fit well normalized experimental data. The procedure is fast and its reliability is tested on a number of experimental data available, relying into a high-cis polybutadiene rubber cured under different temperatures and accelerators concentrations. Very good approximations of experimental data are obtained, also in comparison with a heuristic numerical approach where optimization is obtained interactively.     

Foldamer simulations: novel computational methods and applications to poly-phenylacetylene oligomers

We apply several methods to probe the ensemble kinetic and structural properties of a model system of poly-phenylacetylene (pPA) oligomer folding trajectories. The kinetic methods employed included a brute force accounting of conformations, a Markovian state matrix method, and a nonlinear least squares fit to a minimalist kinetic model used to extract the folding time. Each method gave similar measures for the folding time of the 12-mer chain, calculated to be on the order of 7 ns for the complete folding of the chain from an extended conformation. Utilizing both a linear and a nonlinear scaling relationship between the viscosity and the folding time to correct for a low simulation viscosity, we obtain an upper and a lower bound for the approximate folding time within the range 70 ns相似文献   

Shot-noise limited single-molecule FRET histograms: comparison between theory and experiments

We describe a simple approach and present a straightforward numerical algorithm to compute the best fit shot-noise limited proximity ratio histogram (PRH) in single-molecule fluorescence resonant energy transfer diffusion experiments. The key ingredient is the use of the experimental burst size distribution, as obtained after burst search through the photon data streams. We show how the use of an alternated laser excitation scheme and a correspondingly optimized burst search algorithm eliminates several potential artifacts affecting the calculation of the best fit shot-noise limited PRH. This algorithm is tested extensively on simulations and simple experimental systems. We find that dsDNA data exhibit a wider PRH than expected from shot noise only and hypothetically account for it by assuming a small Gaussian distribution of distances with an average standard deviation of 1.6 A. Finally, we briefly mention the results of a future publication and illustrate them with a simple two-state model system (DNA hairpin), for which the kinetic transition rates between the open and closed conformations are extracted.     

Combined kinetics and iterative target transformation factor analysis for spectroscopic monitoring of reactions

Obtaining rate constants and concentration profiles from spectroscopy is important in reaction monitoring. In this paper, we combined kinetic equations and Iterative Target Transformation Factor Analysis (ITTFA) to resolve spectroscopic data acquired during the course of a reaction. This approach is based on the fact that ITTFA needs a first guess (test vectors) of the parameters that will be estimated (target vectors). Three methods are compared. In the first, originally proposed by Furusj? and Danielsson, kinetic modelling is only used to provide the initial test vectors for ITTFA. In the second the rate constant used to provide the test vectors is optimised until a best fit is reached. In the third, a guess of the rate constant is used to provide the test vectors to ITTFA. The outcome of ITTFA is then used to fit the kinetic model and obtain a new guess of the rate constant. With this constant new concentration profiles are generated and provided to the ITTFA algorithm as new test vectors, in an iterative manner, minimising the residuals of the predicted dataset, until convergence. The second and third methods are new implementations of ITTFA and are compared to the first, established, method. First order (both one and two step) and second order reactions were simulated and instrumental noise was introduced. An experimental second order reaction was also employed to test the methods.     

A Branched Pore Model Analysis for the Adsorption of Acid Dyes on Activated Carbon

A new branched-pore adsorption model has been developed using an external mass transfer coefficient, K _f, an effective diffusivity, D _eff, a lumped micropore diffusion rate parameter, K _b, and the fraction of macropores, f, to describe sorption kinetic data from initial adsorbent-adsorbate contact to the long-term adsorption phase. This model has been applied to an environmental pollution problem—the removal of two dyes, Acid Blue 80 (AB80) and Acid Red 114 (AR114), by sorption on activated carbon. A computer program has been used to generate theoretical concentration-time curves and the four mass transfer kinetic parameters adjusted so that the model achieves a close fit to the experimental data. The best fit values of the parameters have been determined for different initial dye concentrations and carbon masses. Since the model is specifically applicable to fixed constant values of these four parameters, a further and key application of this project is to see if single constant values of these parameters can be used to describe all the experimental concentration-time decay curves for one dye-carbon system.The error analysis and best fit approach to modeling the decay curves for both dye systems show that the correlation between experimental and theoretical data is good for the fixed values of the four fitted parameters. A significantly better fit of the model predictions is obtained when K _f, K _b and f are maintained constant but D _eff is varied. This indicates that the surface diffusivity may vary as a function of surface coverage.     

Application of linear regression analysis for iron and copper removal process using natural zeolites

Natural zeolites (zeolitic volcanic tuffs) cropped out from three regions of Transilvania, Vultureni (V), Pagli?a (P) and M?cica? (M), were evaluated in the process of iron (V, P, M) and copper (M) removal from wastewaters. Iron and copper removal process was studied using a fixed bed column, when equilibrium and kinetic data were acquired. Four isotherms, Langmuir, Freundlich, Langmuir?CFreundlich and Redlich?CPeterson, were used to fit the experimental data obtained for each natural zeolite sample. Parameters of the adsorption isotherms were estimated from the experimental equilibrium data using MATLAB. Using these data the best fit with one of the chosen isotherm can be found. Isotherm constants were determined by linear regression analysis of the experimental data. We concluded that the mathematical model based on Freundlich isotherm is the most appropriate to describe the iron and copper exchange on our natural zeolite samples.     

Direct measurement of the end-to-end distance of individual polyfluorene polymer chains.

Wide-field imaging of individual multichromophoric molecules and successive photobleaching were used to determine, accurately, the relative position of the chromophores in such systems. First, a polyphenylene dendrimer with well-defined geometry was used to establish the accuracy in localization that can be obtained by this methodology. For a signal-to-noise ratio of 20, interchromophoric distances could be measured with 4 nm accuracy. Next, the method was used to determine the end-to-end distribution of an end-capped polyfluorene polymer. From comparison between the experimental and simulated distributions, information on the conformation of the polymer could be deduced. It was found that the polymer has a nonlinear conformation. A conjugation length of six monomer units gave the best fit of the experimental data to the proposed model.     

Adsorption of Basic Magenta II onto H2SO4 activated immature Gossypium hirsutum seeds: Kinetics,isotherms, mass transfer,thermodynamics and process design

The adsorption of Basic Magenta II onto H₂SO₄ activated immature Gossypium hirsutum seeds was analysed using Ho, modified Freundlich, Sobkowsk–Czerwi, Blanchard, Elovich, Avrami, and modified Ritchie kinetic models by nonlinear regression-sum of normalized errors analysis. The goodness of fit was evaluated with coefficient of determination and root mean square error. The good agreement of experimental data to Avrami second-order model indicated that the mechanism of adsorption followed multiple kinetic orders. The Avrami second-order mechanism was applied to predict the rate constant of sorption and the equilibrium capacity and subsequently the obtained equilibrium adsorption capacities were utilized to find the equilibrium concentrations. Langmuir, Freundlich, Temkin, Sips and Hill isotherms were investigated to understand the nature of adsorption with the help of nonlinear regression analysis. Both Sips and Hill isotherms were best fit to the adsorption equilibrium data showing the homogeneous adsorption on the heterogeneous surface of carbon and the positive co-operative manifestations of the Basic Magenta II molecules. The mass transfer study depicted the details such as mass transfer coefficient, intra-particle diffusion rate, pore diffusion coefficient, and film diffusion coefficient. The adsorption process was found to be controlled by film diffusion. The thermodynamic parameters like, Gibbs free energy change, enthalpy change, entropy change and isosteric heat of adsorption confirmed the endothermic, feasible and spontaneous nature of adsorption. A single stage batch adsorber was designed using Sips isotherm constants to estimate the amount of carbon required for desired purification.     

Kinetic study of the thermal decomposition of TEA<Superscript>+</Superscript>/SAPO-5

A silico alumino phosphate with AFI structure (SAPO-5) was prepared in a two-phase medium and characterized by XRD, followed by the addition of TEA⁺. The kinetics of the TEA⁺/SAPO-5 thermal decomposition reaction was studied by isothermal and dynamic thermogravimetry. Two kinetic models, D₃ and D₄ based on diffusion processes were found as best to fit the isothermal data. On the other hand, the best fit for the dynamic data is the F₁ first order reaction model. According to the apparent activation energy values, the use of the dynamic method indicates a higher temperature dependence than the isothermal method.     

Enzyme catalyzed reactions: From experiment to computational mechanism reconstruction

The traditional experimental practice in enzyme kinetics involves the measurement of substrate or product concentrations as a function of time. Advances in computing have produced novel approaches for modeling enzyme catalyzed reactions from time course data. One example of such an approach is the selection of appropriate chemical reactions that best fit the data. A common limitation of this approach resides in the number of chemical species considered. The number of possible chemical reactions grows exponentially with the number of chemical species, which makes difficult to select reactions that uniquely describe the data and diminishes the efficiency of the methods. In addition, a method’s performance is also dependent on several quantitative and qualitative properties of the time course data, of which we know very little. This information is important to experimentalists as it could allow them to setup their experiments in ways that optimize the network reconstruction. We have previously described a method for inferring reaction mechanisms and kinetic rate parameters from time course data. Here, we address the limitations in the number of chemical reactions by allowing the introduction of information about chemical interactions. We also address the unknown properties of the input data by determining experimental data properties that maximize our method’s performance. We investigate the following properties: initial substrate–enzyme concentration ratios; initial substrate–enzyme concentration variation ranges; number of data points; number of different experiments (time courses); and noise. We test the method using data generated in silico from the Michaelis–Menten and the Hartley–Kilby reaction mechanisms. Our results demonstrate the importance of experimental design for time course assays that has not been considered in experimental protocols. These considerations can have far reaching implications for the computational mechanism reconstruction process.