Characteristics of Elovich equation used for the analysis of adsorption kinetics in dye-chitosan systems

The Elovich equation has been widely used in adsorption kinetics, which describes chemical adsorption (chemical reaction) mechanism in nature. The approaching equilibrium parameter of Elovich equation (R_E) was used here to describe the characteristic curves of adsorption kinetics. Of 64 adsorption systems surveyed in this work, 80% of the R_E values were between 0.1 and 0.3 with an adsorption curve belonging to “mild rising”. The results of three examples revealed that the characteristic curve of Elovich equation was between those of Lagergren's first-order equation and intraparticle diffusion model. Chitosans prepared from prawn, lobster, and crab shells were used for the adsorption of a reactive dye. The mean deviation obtained from the three kinetic models revealed that Elovich equation was the most suitable one. All the adsorption systems were in the “mild rising” zone. The R_E value was related to the type of raw material but not to the particle size of chitosan, which agreed with chemical adsorption nature of the Elovich equation. According to an optimal adsorbent consumption of 85% coupled with its corresponding operating time (t_0.85) proposed, these two parameters could be used for engineering design.     

Sorption kinetics for the removal of dyes from effluents onto chitosan

The ability of chitosan, a biosorbent obtained by the processing of waste seafood shells, to remove five acid dyes from effluents has been studied. Chitosan is a deacetylated bio‐polymer of chitin. The effect of varying initial dye concentration on the rate of adsorption has been investigated. The rate data have been analyzed using three kinetic models, namely, a pseudosecond order, the Ritchie modified second order, and the Elovich models. The sorption kinetics of Acid Green 25, Acid Orange 10, Acid Orange 12, Acid Red 18, and Acid Red 73 onto chitosan can be best correlated by the Elovich equation. The kinetic model was determined in accordance with the agreement between the rate equations and the differentiation of kinetic equations. The values of rate constants for the three models are in the range of 0.003–2.230, 0.004–0.237, and 0.0173–405 for the pseudosecond order, the Ritchie modified second order and the Elovich models, respectively. The sensitivity analysis, by plotting the reciprocal of the rate, Z_L = (d_q/d_t)^?1 against time, is used to identify the true kinetic model. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Adsorption of malachite green onto bentonite: Equilibrium and kinetic studies and process design

The adsorption of malachite green onto bentonite in a batch adsorber has been studied. The effects of contact time, initial pH and initial dye concentration on the malachite green adsorption by the bentonite have been studied. Malachite green removal was seen to increase with increasing contact time until equilibrium and initial dye concentration, and the adsorption capacity of bentonite was independent of initial pH in the range 3–11. Four kinetic models, the pseudo first- and second-order equations, the Elovich equation and the intraparticle diffusion equation, were selected to follow the adsorption process. Kinetic parameters; rate constants, equilibrium adsorption capacities and correlation coefficients, for each kinetic equation were calculated and discussed. It was shown that the adsorption of malachite green onto bentonite could be described by the pseudo second-order equation. The experimental isotherm data were analyzed using the Langmuir, Freundlich, Temkin and Dubinin–Radushkevich equations. Adsorption of malachite green onto bentonite followed the Langmuir isotherm. The thermodynamic parameters, such as ΔH, ΔS and ΔG, were also determined and evaluated. A single stage batch adsorber was designed for different adsorbent mass/treated effluent volume ratios using the Langmuir isotherm.     

Nonisothermal cure kinetics and diffusion effect of liquid-crystalline epoxy sulfonyl bis(1,4-phenylene)bis[4-(2,3-epoxypropyloxy)benzoate] resin with aromatic diamine

The curing kinetics of the liquid-crystalline epoxy resin sulfonyl bis(1,4-phenylene)bis[4-(2,3-epoxypropyloxy)benzoate] with 4,4′-diaminodiphenylsulfone was investigated by nonisothermal differential scanning calorimetry. The relationship between the apparent activation energy (E_a) and the conversion was determined, and the effects of the molecular structure and the order of liquid crystallinity on E_a are discussed in detail. Some parameters were evaluated with the autocatalytic kinetic model of the Šesták–Berggren (S–B) equation. The results show that there were some deviations of these simulation curves from the experimental curves at high heating rates and in the late stage of the curing reaction. The diffusion effect in the nonisothermal curing reaction is discussed, and a diffusion factor was proposed and introduced into the S–B equation. Then, a modified S–B equation was created, as follows: , where α is the conversion, t is the time, m and n are reaction orders, K is rate constant, C is the diffusion coefficient, and α_c is the critical conversion. The theoretical simulation curves agreed very well with the experimental data as determined with the modified S–B equation, which may be more useful for describing and predicting the nonisothermal curing reaction kinetics of epoxy resin. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Rheo‐kinetic evaluation on the formation of urethane networks based on hydroxyl‐terminated polybutadiene

Rheo‐kinetic studies on bulk polymerization reaction between hydroxyl‐terminated polybutadiene (HTPB) and di‐isocyanates such as toluene‐di‐isocyanate (TDI), hexamethylene‐di‐isocyanate (HMDI), and isophorone‐di‐isocyanate (IPDI) were undertaken by following the buildup of viscosity of the reaction mixture during the cure reaction. Rheo‐kinetic plots were obtained by plotting ln (viscosity) vs. time. The cure reaction was found to proceed in two stages with TDI and IPDI, and in a single stage with HMDI. The rate constants for the two stages k₁ and k₂ were determined from the rheo‐kinetic plots. The rate constants in both the stages were found to increase with catalyst concentration and decrease with NCO/OH equivalent ratio (r‐value). The ratio between the rate constants, k₁/k₂ also increased with catalyst concentration and r‐value. The extent of cure reaction at the point of stage separation (x_i) increased with catalyst concentration and r‐value. Increase in temperature caused merger of stages. Arrhenus parameters for the uncatalyzed HTPB‐isocyanate reactions were evaluated. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 1869–1876, 2001     

Thermal analysis of different cellulosic fabrics

Thermal behavior of different cellolusic fabrics was investigated in air and nitrogen by TG, DTG and DTA. Kinetic parameters based on weight loss for the initial and major stages of thermal degradation were determined. The weight loss in the TG curve for the cellulosic fabrics can be divided into four stages. In general, E_a values in air are lower than those in nitrogen, and the enthalpy changes as well as rates of degradation in air are much larger than those in nitrogen. This indicates that the thermal degradation of cellulosic fabric is promoted by oxygen. The E_a values of regenerated cellulose fabrics (viscose and modal) at the rapid weight loss stage are relatively higher than those of the cotton and linen fabrics. The raw cotton has the lowest E_a of all cellulosic fabrics, but its frequency factor and rate of weight loss are also the lowest. The thermal behavior of linen is similar to that of the raw cotton. Bleached, boiled and antibacterially finished cotton fabrics are also compared. Thermal behavior and kinetic parameters for the different cellulosic fabrics are discussed in the light of their structural characteristics, including degree of polymerization, crystallinity, crystalline form, orientation and morphology. Also the effects of the impurities and additives on the fabric are considered. © 1996 John Wiley & Sons, Inc.     

Modelling of the Hydrolysis of Benzylpenicillin to 6-Aminopenicillanic Acid and Phenyl Acetic Acid by an Immobilised Penicillin Amidase in a Small Pilot Plant Batch Recirculated Reactor

This paper deals with the modelling of the hydrolysis of benzylpenicillin to 6-aminopenicillanic acid (6-APA) and phenyl acetic acid (PAA) in a small pilot plant batch recirculated reactor by an immobilised penicillin amidase preparation. By using the following linearised form for an integrated Michaelis-Menten equation Et/V₀X=α+β| In (1-X)/X| where α and β are reaction kinetic parameters, good correlations are obtained of α and β with linear velocity across the reactor, substrate concentration and temperature of operation. A process to determine α and β from initial velocity measurements is outlined. The applicability of the above equation to published data is also analysed.     

Curing behavior of epoxy resins in two‐stage curing process by non‐isothermal differential scanning calorimetry kinetics method

In this research, a new thermal curing system, with two‐stage curing characteristics, has been designed. And the reaction behaviors of two different curing processes have been systematically studied. The non‐isothermal differential scanning calorimetry (DSC) test is used to discuss the curing reaction of two stages curing, and the data obtained from the curves are used to calculate the kinetic parameters. Kissinger‐Akahira‐Sunose (KAS) method is applied to determine activation energy (E_a) and investigate it as the change of conversion (α). Málek method is used to unravel the curing reaction mechanism. The results indicate that the curing behaviors of two different curing stages can be implemented successfully, and curing behavior is accorded with ?esták‐Berggren mode. The non‐isothermal DSC and Fourier transform infrared spectroscopy test results reveal that two different curing stages can be implemented successfully. Furthermore, the double x fitting method is used to determine the pre‐exponential factor (A), reaction order (m, n), and establish the kinetic equation. The fitting results between experiment curves and simulative curves prove that the kinetic equation can commendably describe the two different curing reaction processes. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40711.     

Thermal decomposition behavior of oligo(4‐hydroxyquinoline)

In this study, the kinetic parameters and reaction mechanism of decomposition process of oligo(4‐hydroxyquinoline) synthesized by oxidative polymerization were investigated by thermogravimetric analysis (TGA) at different heating rates. TGA‐derivative thermogravimetric analysis curves showed that the thermal decomposition occurred in two stages. The methods based on multiple heating rates such as Kissinger, Kim–Park, Tang, Flynn–Wall–Ozawa method (FWO), Friedman, and Kissinger–Akahira–Sunose (KAS) were used to calculate the kinetic parameters related to each decomposition stage of oligo(4‐hydroxyquinoline). The activation energies obtained by Kissinger, Kim–Park, Tang, KAS, FWO, and Friedman methods were found to be 153.80, 153.89, 153.06, 152.62, 151.25, and 157.14 kJ mol^?1 for the dehydration stage, 124.7, 124.71, 126.14, 123.75, 126.19, and 124.05 kJ mol^?1 for the thermal decomposition stage, respectively, in the conversion range studied. The decomposition mechanism and pre‐exponential factor of each decomposition stage were also determined using Coats–Redfern, van Krevelen, Horowitz–Metzger methods, and master plots. The analysis of the master plots and methods based on single heating rate showed that the mechanisms of dehydration and decomposition stage of oligo(4‐hydroxyquinoline) were best described by kinetic equations of A_n mechanism (nucleation and growth, n = 1) and D_n mechanism (dimensional diffusion, n = 6), respectively. POLYM. ENG. SCI., 54:992–1002, 2014. © 2013 Society of Plastics Engineers     

DSC curing study of catalytically synthesized maleic‐acid‐based unsaturated polyesters

Unsaturated polyesters were synthesized based on ethylene glycol and maleic acid as unsaturated dicarboxylic acid, using a variety of saturated acids in the initial acid mixture, without or with different catalysts. The curing of the polyesters produced with styrene was studied using differential scanning calorimetry (DSC) under dynamic‐ and isothermal‐heating conditions. The FTIR spectra of the initial polyesters and cured polyesters were also determined. Curing is not complete at the end of DSC scan and the unreacted bonds were quantitatively determined from the FTIR spectra and by estimation based on literature data. The value of the mean degree of conversion (α) of all double bonds (styrene unit and maleate unit) was approximately α = 0.40. Using an appropriate kinetic model for the curing exotherm of polyesters, the activation energy (E_a), the reaction order (x) and the frequency factor (k_o) were determined. Because the kinetic parameters (ie E_a, k, x) affect the kinetics in various different ways, the curves of degree of conversion versus time at various isothermal conditions are more useful to compare and characterize the curing of polyesters. The kinetic parameters are mainly influenced by the proportion of maleic acid in the polyesterification reaction mixture and secondarily by the residual polyesterification catalyst. The degree of conversion of already crosslinked polyesters is greatly increased by post‐curing them at elevated temperature and for a prolonged time. © 2002 Society of Chemical Industry     

Study of sawdust pyrolysis and its devolatilisation kinetics

Pyrolysis of sawdust was studied using a thermogravimetric analyser (TGA) to understand the devolatilisation process and to obtain its global kinetic parameters. The influences of particle size, initial weight of the sample and heating rate on the devolatilisation of sawdust particles have been studied. Results from proximate analysis show that smaller particle size has more ash content compared to larger particle size. The TG and derivative TG curve for variation in particle size and initial weight of the sample showed significant difference in the third stage of the pyrolysis. In addition, the pyrolysis of sawdust differed significantly for variation in heating rate. As the heating rates increased, the char yield also increased. The devolatilisation kinetics was studied considering different stages of pyrolysis. The kinetic parameters for thermal devolatilisation of the sawdust were determined through a nonlinear optimisation method of two independent parallel nth‐order reaction models. The kinetic parameters such as activation energy, frequency factor and order of the reaction for the two stages considered in the model were: E₂ = 79.53 (kJ/mol), E₃ = 60.71 (kJ/mol); k₀₂ = 1.90 × 10⁶ (1/min), k₀₃ = 1.01 × 10³ (1/min); n₂ = 0.91, n₃ = 1.78, respectively. The results show good agreement between the proposed model and the experimental data of the sawdust pyrolysis.     

A unified conjugate mass transfer model of VOC emission

This paper develops a unified conjugate mass transfer model for VOC (Volatile Organic Compound) emission, which implies conjugate boundary condition for mass transfer at the material-air interface. Thus, no special treatment is needed at the material-air interface and numerical methods for conjugate heat transfer problem can be applied directly. The material-air partition coefficient has been taken into account and its effect is the same as specific heat in the energy equation. The equivalent diffusion coefficient in the material K_maD_m instead of D_m characterizes the rate of mass transfer. The ratioK _ma D _m /D _a indicates whether VOC emission is controlled by the internal diffusion or not. The equivalent air-phase initial concentration C₀/K_ma determines the order of maximum concentration in the air. VOC emission contains two stages: the initial stage and the pseudo-steady stage when the emission rate nearly equals mass rate through the outlet of the air. Diffusion coefficient of VOC in the material has a significant effect on VOC emission in the two stages. The effect of partition coefficient on VOC emission depends on the value of K_maD_m/D_a.     

Investigation on the kinetics of the adsorption process of aliphatic amidpolyamine on cellulose

Investigation has been carried out on the kinetic dependences of the adsorption process of aliphatic amidpolyamine (lamide-1, L-1) on three kinds of bleached pulp (sulfate pulp of hard wood and sulfate and sulfite pulp of soft wood) at temperatures of 0, 20, 40, and 60°C within a concentration interval of 0.030 g/liter + 0.500 g/liter. It has been established that the kinetic process can be described by the Elovich–Tyomkin exponential kinetic equation. The activation energy is of the order of 4.12–4.42 kJ/mol and the entropy factors substantially affect the process speed. The coefficients of the correlations describing the effect of the L-1 solution concentrations on the coefficient of heterogeneity (α) and the initial adsorption speed (V₀) have been determined.     

Studies on thermal degradation of synthetic polymers. XV. Estimation of the product yield on the basis of intensity function for thermal gasification of isotactic and atactic polypropylenes

The kinetic equation for the pyrolysis gasification reaction of isotactic and atactic polypropylenes has been established. The difference in tacticity of the samples does not much affect the kinetic parameters. The exponent a of the intensity function I_F = Tδ^a (K·sec^a), concerning the severity of decomposition conditions, has been approximated as 0.039 (isotactic) and 0.040 (atactic), respectively from the kinetic parameters in this experiment. The calculated values of the product yield from Arrhenius equations, k = 2.0 × 10¹⁰ exp(?40.9 × 10³/RI_F) (isotactic) and k = 1.2 × 10¹⁰ exp(–41.4 × 10³/RI_F) (atactic), for the I_F standard agree with the experimental values.     

Kinetics of desorption of hydrogen from copper chromite catalyst

Isothermal desorption of hydrogen from copper chromite has been studied from 50 to 300°C. An empirical expression, β exp [—αq]= t, is found to fit the desorption data satisfactorily, while the application of the Elovich and the first order desorption rate expressions lead to the detection of three kinetic stages in the desorption process. The rate parameters obtained using these latter two models have a complex trend in their behaviour with temperature. The Elovich rate parameters are found to undergo undulatory changes with temperature like those of the adsorption isobar and their transition regions are very close to those of the adsorption isobar. Also, there seems to be a close relationship between the surface coverage at transition points and the adsorption isobars. The presence of the three kinetic stages in the desorption process may be accounted for by considering the three distinctly different types of adsorption sites on the reduced copper chromite.     

Anisotropy in activation energy of textured LiCoO2 for the initial stage of sintering

The anisotropic initial sintering of oriented LiCoO₂ green compacts prepared by slip casting in a strong magnetic field was studied. The activation energy and the mechanism of the initial stage of sintering were analyzed in order to understand the effect of the orientation. The analysis was carried out using constant rate heating (CRH). The activation energy of the initial stages of sintering for random, a, b-axes and c-axis direction was evaluated from the Arrhenius plots of the dilatometric measurements. It was confirmed that the activation energy of the c-axis direction was larger than that of the a, b-axes direction at the initial stage of sintering. The anisotropic shrinkage was attributed to the differences in the surface energies.     

Kinetics of hydroformylation of 1-decene using homogeneous HRh(CO)(PPh3)3 catalyst: a molecular level approach

The kinetics of hydroformylation of 1-decene using homogenous HRh(CO)(PPh₃)₃ catalyst has been reported in the temperature range of 50–70 °C. The effect of catalyst,P _{H 2},P _CO, and 1-decene concentration on the rate of hydroformylation has been studied. Based on the analysis of initial rate data, a rate equation has been proposed and kinetic parameters evaluated. The activation energy was found to be 11.76 kcal/mol. A molecular level approach to kinetic modelling has also been illustrated. The rate equation derived assuming oxidative addition of H₂ as a rate determining step, has been found to represent the data satisfactorily. The rate parameters for the mechanistic model have been evaluated for the data at 60 °C.NCL Communication No. 5735.     

Color Change Kinetics of Microwave-Dried Basil

The aim of this study was to investigate the effect of microwave output power and sample amount on color change kinetics of basil (Ocimum basilicum L.) during microwave drying. The color parameters for the color change of the materials were quantified by Hunter L (whiteness/darkness), a (redness/greenness), and b (yellowness/blueness) system. These values were also used for calculation of the total color change (ΔE), chroma, hue angle, and browning index. The microwave-drying process changed color parameters of L, a, and b, causing a color shift toward the darker region. The mathematical modeling study of color change kinetics showed that a and b fitted to a first-order kinetic model, while L and total color change (ΔE) followed a zero-order kinetic model. However, chroma and browning index (BI) followed a first-order kinetic model, whereas hue angle followed a zero-order kinetic model. For calculation of the activation energy for colour change kinetic parameters, the exponential expression based on Arrhenius equation was used.     

Comparative Study of the Kinetic Degradation of Differently Decrystallized Cotton Linters Using Nonisothermal DTA Curves

Cellulose samples of different degree of decrystallization were subjected to differential thermal analysis (DTA) technique under nonisothermal conditions. The samples were prepared by preswelling the cotton linters in 24-Baumé NaOH followed by the use of direct or indirect methods to dry the mercerized cotton. The thermal stabilities of the samples were estimated taking into account the values of initial decomposition temperature, maximum decomposition temperature, and activation energy. The activation energy preexponential constant, order of reaction, and other thermodynamic parameters (ΔH, ΔS, and ΔG) associated with each stage were derived by applying integrated peak areas (Satava and Skvara), the Borchart—Daniels general method, and the Prount—Tompkins equation. The results showed that the cellulose pyrolysis process cannot be described as having a single value of E _a over the entire pyrolysis range. Also, the decrystallization caused by destruction of the formed alkali cellulose complex with a isopropanol—water (WAN) system was found to be the most pronounced change in pyrolytic parameters (i.e., less thermal stability) compared with native and other decrystallized samples. The dependence of E _a on IR measurements is also discussed.