Autocatalytic Kinetic Model Research Articles

Hydrothermal stability of aromatic carboxylic acids

The chemical behavior of aromatic carboxylic acids in water at elevated temperatures has implications for industrial chemistry, fuel processing and waste treatment processes. Therefore, the hydrothermal reactions of six different aromatic carboxylic acids were investigated from 250–410 °C at times up to 240 min. Benzoic acid was the most stable of the six, showing negligible degradation after 1 h of hydrothermal treatment at 350 °C. Terephthalic acid, 2,6-naphthalene dicarboxylic acid and isophthalic acid were stable after 1 h at 300 °C, but they decarboxylated to form monoacids in 10–15% yields at 350 °C. Trimellitic anhydride decomposed completely after 30 min at 350 °C, but showed no appreciable decomposition after 30 min at 250 °C. Terephthalic acid and isophthalic acid were the main degradation products, but o-phthalic acid was also formed in small amounts at 350 °C. The o-phthalic acid conversion to benzoic acid was 73% after 60 min at 300 °C, but the diacid remained stable at 250 °C for 1 h. An autocatalytic kinetics model provided a good description of the trimellitic anhydride and terephthalic acid decomposition at 300 and 410 °C, respectively.

Water dispersion kinetics during starch gelatinization

The kinetics of water dispersion during the gelatinization of dilute suspensions of maize starch was studied by analyzing changes in electrical conductance data recorded continuously with time. Several analytical methods were compared for the preliminary study of the activation energy of gelatinization. The probable mechanism of the process was investigated by a number of homogeneous and heterogeneous reaction kinetic models. A modified composite methodology coupled with a reduced-plot method was employed to fit the kinetic data. Two simultaneous elementary reactions, expressed by an autocatalytic kinetic model and a 3D moving phase-boundary rate model, predicted the overall kinetic behavior with appreciable success.

Rheokinetic variations during curing of a tetrafunctional epoxy resin modified with two thermoplastics

The curing kinetics of an epoxy matrix based on tetraglycidyl diamino diphenyl methane polymerized with diamino diphenyl methane and those for its mixtures with poly(methyl methacrylate) and poly(ethersulfone) (PES) at compositions ranging from 0 to 15 wt.% were studied using differential scanning calorimetry in isothermal and dynamical conditions. Rheological properties were also measured to follow curing evolution. Apparent activation energies were calculated from the so obtained gelation times. Thermoplastic addition to the thermosetting resin delayed the polymerization, and above all in the PES case but it does not modify the cure kinetics of the thermosetting matrix. A modified autocatalytic kinetic model which contains the diffusional term was used. Satisfactory results were obtained as conversion curves fitted quite well the experimental data.

Investigation of the Non-isothermal Kinetics of the Formation of ZnFe2O4 and ZnCr2O4

Abstract The kinetics of ZnFe2 O4 and ZnCr2 O4 formation under non-isothermal conditions using DTA is discussed. It was determined activation energy and kinetic model for studied reactions in the case of used various sources of starting materials (ferric pigments, chromic oxides). The activation energies for ZnFe2 O4 are positioned in a range of 200–475 kJ mol−1 (in dependence of used ferric pigments) and in case of ZnCr2 O4 in a range of 130–160 kJ mol−1 . The autocatalytic kinetic model (Sestk-Berggren) was found to be the most convenient description of the studied processes.

Copolymerization kinetics of styrene/vinyl‐ester systms: Low temperature reactions

AbstractVinyl‐ester (VE), synthesized by the addition reaction of methacrylic acid and diglycidyl ether of bis‐phenol A (DGEBA) epoxy, and styrene react via bulk free radical chain growth copolymerization to form a crosslinked network polymer. Vital clues regarding the development and the structure of the network were obtained from the study of copolymerization kinetics of styrene/VE systems. Fourier transform infrared (FTIR) spectroscopy was used to obtain the individual fraction conversion rates of both the monomers. The conversion versus time data for both styrene and VE was fit to an autocatalytic kinetic model. The autocatalytic model was found to adequately replicate the kinetic data over the entire life of cure. In this investigation, the effects of styrene concentration, temperature, catalyst concentration, and initiator concentration on cure kinetics of styrene/VE systems were studied. The conversion profiles of both styrene and VE were used to obtain the reactivity ratios of the two monomers. The reactivity ratios were evaluated to be close to zero, suggesting that initially alternating copolymerization is favored over homopolymerization. The cure behavior of vinyl‐ester resins is affected not only by the chemical reactivity of the monomers toward the free radicals, but also by diffusion effects, phase separation, and microgel formation. The interplay of these factors controls the kinetics of cure, thereby affecting the physical and chemical properties of the resulting polymer.

Thermal decomposition of ethyl parathion

The thermal decomposition of ethyl parathion, an organophosphorus pesticide, has been studied by coupling calorimetric and chemical analysis. The decomposition process develops through two exothermic events with production of relevant amounts of uncondensible gases (final pressure 50 bar in an ARC run). A simple autocatalytic kinetic model has been adopted for simulating the first stage of the decomposition process.

Curing Behavior of Thick-Sectioned RTM Composites

The successful manufacture of thick-sectioned composites is challenging, since the highly exothermic nature of thermoset resins and limited temperature control make it difficult to avoid detrimental thermal and cure gradients within the composite. In order to make quality parts, it has been found experimentally that cure temperatures must be lowered as much as 50% from those suggested for thin parts. Differential Scanning Calorimetry (DSC) experiments of a vinyl-ester resin system at these lower temperatures revealed a significant dependence on temperature for the maximum extent of cure. If the resin is cured isothermally at 55°C, the final conversion of the resin was found to only reach 70%. When the maximum extent of cure parameter was incorporated into an empirical autocatalytic kinetic model, it was found to significantly improve the description of the cure kinetics. Inhibitors, added to the resin to improve shelf-life, disappear rapidly at higher cure temperatures but can double the time required to cure a thick composite processed at 55°C. A zeroth order kinetic relationship was developed to estimate the amount of inhibitor in the system during the resin's cure. The inhibitor relationship and the improved kinetic model were used in a finite difference cure simulation to successfully predict the thermal gradients during cure of a 2.54 cm thick composite manufactured by resin transfer molding (RTM).

The effects of cobalt promoter and glass fibers on the curing behavior of unsaturated polyester resin

AbstractIn this study, a phenomenological autocatalytic kinetic model is used to describe the cure of a polyester system containing a cobalt‐based promoter. The effect of including the promoter in the cure system is discussed regarding the changes in the kinetic parameters. It was found that the cure characteristics of the unsaturated polyester system were affected by the presence of the promoter. This effect resulted in a temperature dependency of the reaction exponents as well as in a significant increase of the Arrhenius frequency factor at low temperatures. The changes in cure characteristics of promoted polyester system caused by incorporation of chopped glass fibers were also investigated. The results indicate that unlike the promoter, the presence of glass fibers does not appreciably affect the reaction exponents. However, the presence of glass fibers results in some changes in the overall reaction rate of the cure system. To take into account the unrecorded extent of reaction at high cure temperatures, a new procedure was implemented. This procedure estimates a correction factor related to the total isothermal heat of cure obtained from DSC experiments at different isothermal cure temperatures.

Effects of liquid crystalline structure formation on the curing kinetics of an epoxy resin

The curing kinetics of a system containing 4,4′-diglycidyloxy-α-methylstilbene (DOMS) and different functionality amines, N-ethylaniline (NEA), aniline, benzenesulfonamide (BSA), and sulfanilamide (SAA), have been studied by differential scanning calorimetry (DSC) under isothermal conditions. The phase transformations during curing of the systems have been monitored by a crosspolarized optical microscope equipped with a hot-stage and photo detector. It has been found that the growth of a nematic liquid crystal structure does not cause a discrepancy from the autocatalytic model for the reactions between aniline and epoxy. There is no liquid crystalline structure formed for the systems containing NEA or BSA, which follow the autocatalytic kinetic models within the temperature range of 120–150°C. For the curing reactions between DOMS and SAA, there is a big deviation from the autocatalytic model when the liquid crystals transfer from a nematic structure to a smectic structure. Unlike the usual decrease of reaction rate resulting from diffusion in a heterogeneous reaction, the reaction rate is enhanced. A modified kinetic model has been constructed for this reaction system by introducing a pseudoconcentration term caused from the liquid crystalline structure formation. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 1105–1124, 1997

Modelling the Cure of a Commercial Epoxy Resin for Applications in Resin Transfer Moulding

An analytical procedure has been developed for modelling the kinetics of the cure process of a commercial epoxy resin for resin transfer moulding (RTM) applications, using differential scanning calorimetry (DSC) in the isothermal and dynamic modes to obtain the experimental database. The overall reaction rate of the epoxide groups with amines was determined and fitted by an autocatalytic kinetic model. An improvement of the model to allow for diffusion limitation effects results in a good agreement between experimentally determined and predicted reaction rates. A non-linear least squares regression analysis method based on Marquardt's algorithm was used to fit the DSC reaction rate data with an appropriate model and to evaluate the activation energies and the reaction orders for this particular resin system. The Di Benedetto equation was utilised to establish the relationship between conversion and glass transition temperature (T g ), required to develop the diffusion-dominated part of the model.

Cure Studies of a Benzoxazine-Based Phenolic Resin by Isothermal Experiment

Isothermal cure kinetics of newly synthesized benzoxazine-based phenolic resin were studied by differential scanning calorimetry. The cure reaction of benzoxazine-based pheolic resin follows an autocatalytic mechanism. The conversion at the maximum cure rate was independent of the cure temperature. Assuming that the overall reaction order was second, kinetic parameters of cure reaction for benzoxazine-based phenolic resin were determined from an autocatalytic kinetic model. The modified autocatalytic model has a good agreement with experimental results. In addition, the activation energy and the frequency factor were calculated by the Arrhenius plot.

Kinetics modeling and time‐temperature‐transformation diagram of microwave and thermal cure of epoxy resins

AbstractStoichimetric mixtures of a diglycidyl ether of bisphenol A (DGEBA)/ diaminodiphenyl sulfone (DDS) and a DGEBA/meta phenylene diamine (mPDA) were cured using both microwave and thermal energy. Fourier transform infrared (FTIR) was used for the measurement of the extent of cure and thermal mechanical analysis (TMA) was used for the determination of the glass transition temperature (Tg). The cure kinetics of the DGEBA/mPDA and DGEBA/DDS systems were described by an autocatalytic kinetic model up to vitrification in both the microwave and thermal cure. For the DGEBA/mPDA system, the reaction rate constants of the primary amine‐epoxy reaction are equal to those of the secondary amine‐epoxy reaction, and the etherification reaction is negligible for both microwave and thermal cure. For the DGEBA/DDS system, the reaction rate constants of the primary amine‐epoxy reaction are greater than those of the secondary amine‐epoxy reaction and the etherification reaction is only negligible at low cure temperatures for both microwave and thermal cure. Microwave radiation decreases the reaction rate constant ratio of the secondary amine‐epoxy reaction to the primary amine‐epxy reaction and the ratio of the etherification reaction to the primary amine‐epoxy reaction. Tg data were fitted to the DiBenedetto model. A master curve and a time‐temperature‐transformation (TTT) diagram were constructed. The vitrification time is shorter in microwave cure than in thermal cure, especially at higher isothermal cure temperatures. For the DGEBA/mPDA system, the minimum vitrification time is two to five times shorter in the microwave cure than in the thermal cure. For the DGEBA/DDS system, the minimum vitrification time is 44 times shorter in the microwave cure than in the thermal cure.

Rheokinetic studies for the reaction injection molding of polydicyclopentadiene

AbstractDicyclopentadiene (DCPD) based liquid engineered resins are emerging among the newest commercial reaction injection molding (RIM) systems. Since the filling stage is coupled with chemical reaction, an understanding of the chemorheological changes is critical for establishing moldability criteria. An adiabatic reactive viscometry technique which involves the simultaneous measurement of viscosity and temperature changes was used to investigate the chemorheological changes during the adiabatic copolymerization of a DCPD based RIM system. The influence of impingement mixing conditions and initial material temperature on the reaction kinetics, rheology, as well as the resulting final physical properties of the system were investigated. The “apparent gel time” under adiabatic conditions is estimated from the intersection of the tangents to the initial and final portions of the viscosity curve. An autocatalytic kinetic model with an Arrhenius rate constant was used to model the reaction kinetics.

Critical parameters for heat transfer and chemical reactions in thermosetting materials

AbstractThe equations of one‐dimensional heat transfer with chemical reactions with isothermal initial conditions and constant wall temperature are solved approximately for all types of kinetic models. The general solution is valid for low exothermal peaks and it is characterized explicitly by two dimensionless parameters. The first parameter is the ratio between the time scale for heat conduction and that for the chemical reaction; the second parameter is the ratio between the processing temperature and the adiabatic temperature rise. The number of additional parameters depends on the particular choice of kinetic model. The maximum temperature in the solution always occur at the center line and its magnitude is proportional to the maximum rate of reaction. For a second‐order autocatalytic kinetic model, closed from results can be obtained. The solution is in this case characterized by two additional dimensionless parameters. The analytical solution agrees excellently with numerical solutions for small exothermal temperature peaks (<10% of the adiabatic temperature rise), but the qualitative agreement is very good also for cases with significant exothermal peaks. The general solution can be used also for the case when the kinetic model is unknown and only experimental DSC results are available. © 1994 John Wiley & Sons, Inc.

Application of the kinetic composite methodology to autocatalytic‐type thermoset prepreg cures

AbstractUsing a commercial epoxy/carbon fiber prepreg as a model system, cure kinetics of an autocatalytic‐type reaction were analyzed by a general form of conversion‐dependent function first proposed for degradation kinetics of polymers and composites. The characteristic feature of conversion‐dependent function was determined using a reduced‐plot method where the temperature‐dependent reaction rate constant was analytically separated from the isothermal data. Assuming two elementary reaction mechanisms that were expressed by the nth order and autocatalytic kinetic models, they were combined with a composite methodology capable of predicting overall kinetic behavior. The activation energies were determined and favorably compared for both isothermal and dynamic‐heating differential scanning calorimetry experiments in the temperature region for standard epoxy cures at 177°C (350°F). Finally, the proposed model equation demonstrated excellent predictive capability and broad applicability in describing various types of thermoset polymer cure for both isothermal and dynamic heating conditions. © 1993 John Wiley & Sons, Inc.

Cure kinetics of elementary reactions of a diglycidyl ether of bisphenol A/diaminodiphenylsulfone epoxy resin: 2. Conversion versus time

The kinetics of the elementary reactions (primary amine-epoxy and secondary amine-epoxy) in addition to the overall reaction have been studied in a diglycidyl ether of bisphenol A (DGEBA) epoxy resin system, cured with diaminodiphenylsulfone (DDS) hardener. The conversion versus time data for the elementary reactions and for the overall reaction were obtained by monitoring the changes in concentration of epoxy, primary and secondary amine groups during cure using near-infra-red spectroscopy. The data were evaluated using nth-order and autocatalytic kinetic models. The primary amine-epoxy reaction (linear polymerization) was described well by the nth-order kinetic model over the whole range of conversion of the primary amine, whereas the secondary amine-epoxy reaction was described by both the nth-order kinetic and first-order autocatalytic models in the ranges of initial 30% conversion at 130°C cure, and 80% conversion at 205°C cure. The kinetic parameters for each reaction were also obtained. The reactivity ratio of the secondary amine to the primary amine for a non-catalysed reaction increased with increasing cure temperature, whereas the opposite trend was observed for the autocatalysed reaction.

A kinetic analysis of the curing reaction of an epoxy resin

The kinetics of a curing reaction under non-isothermal conditions using DSC is discussed. A simple, consistent method of kinetic analysis was applied. The method allows the correct determination of the most suitable kinetic model and the calculation of kinetic parameters. This method was used to study the kinetics of an epoxy resin based on diglycidyl ether of bisphenol A, cured by methyl tetrahydrophthalic anhydride with an accelerator. An activation energy of 73kJmol −1 was calculated and the autocatalytic kinetic model (Šesták-Berggren equation) was found to be the most covenient description of the studied curing process. The isothermal curves calculated for the kinetic parameters determined in non-isothermal conditions are in good agreement with experimental curves when the curing temperature T c is above the maximum glass-transition temperature of the system, T g∞ = 109°C. The influence of the vitrification phenomenon is discussed when T c is below T g∞. The temperature-time-transformation diagram of the studied epoxy system has been constructed and is discussed.

Thermogravimetry of WO 3 reduction in hydrogen: Kinetic characterization of autocatalytic effects

Chemical and autocatalytic events occurring during the hydrogen-reduction of WO 3 were observed and characterized by thermogravimetry, X-ray diffractometry and a kinetic analysis. The results indicated that WO 3 is completely reduced to W° near 800 °C, via the formation of WO 2.72 (at 520 °C) and WO 2 (at 600 °C) as intermediate products. Kinetically, the initial stage of the reduction was found to be dominated by the formation of WO 2, and to be influenced by strong autocatalytic effects associated with the commencement of formation of W°. These results fulfil the requirements of a consecutive autocatalytic kinetic model, whereby the dissociative adsorption of H 2 on freshly generated W° surfaces is considered the rate determining step. Arrhenius plot based on the initial rate as a function of temperature data resulted in an activation energy value of 118±5 kj mole −1.

Cure kinetics of dicyanate matrix polymers

AbstractThe cure kinetics of two dicyanate resins were investigated by differential scanning calorimetry under isothermal and nonisothermal conditions. An autocatalytic kinetic model was proposed and a set of general kinetic parameters was calculated from the isothermal experiments. Good agreement between experimental data and the kinetic model has been obtained under different processing conditions, which demonstrated the validity and the usefulness of the analytical procedure and of the kinetic expression employed. Consequently, in its current form, the modeling methodology is capable of describing the degree of cure during a typical processing cycle and has the potential for comparing different resin formulations as well as the manifestations of cure in property development. Specifically, in this work the modeling methodology was tested using two distinct dicyanate resin systems while the development of the cure was also observed through dielectric analysis (DEA).

The effect of reaction kinetics, mass transfer and flow pattern on non-catalytic and homogeneously catalyzed gas-liquid reactions in bubble columns

A bubble column model was implemented to simulate the performance of a gas-liquid reactor for selective chlorination of butanoic acid to α-chlorobutanoic acids in the presence of a homogeneous catalyst. The autocatalytic kinetic model of the chlorination reactions was found to be numerically very unstable. A homotopy approach was necessary to get viable solutions. High yields of α-monochlorobutanoic acid were obtained with all flow models ranging from complete backmixing to plug flow. The selectivity of α-monochlorobutanoic acid is favored by low chlorine concentrations in the liquid phase which can be achieved by cocurrent operation. Because of the autocatalytic reaction kinetics the formation of α-monochlorobutanoic acid is favored by backmixing.