Kamal Autocatalytic Model Research Articles

Modeling the curing kinetics of two thermoset adhesives under varying temperature conditions

AbstractThis paper presents detailed curing kinetics models for two thermoset adhesives. The cure kinetics were characterized using differential scanning calorimetry in both anisothermal and isothermal modes. The Sestak–Berggren autocatalytic model was applied to describe the anisothermal cure kinetics of the two adhesives with the Malek and undetermined coefficients methods determining their kinetic parameters. The Kamal autocatalytic model was adopted for the isothermal curing processes with the Kenny analytical‐graphical method determining the kinetic parameters. A modified Kamal model was developed by introducing a concept of the maximum degree of cure (DOC) and temperature‐depended kinetic parameters to describe the isothermal cure kinetics of the adhesive with a typical exothermic peak, and an extended Kamal model was further proposed by adding an initial‐phase‐control term to the modified Kamal model to describe the isothermal cure kinetics of the adhesive with two exothermic peaks. The results showed that the presented curing kinetics models with the determined parameters can precisely predict the evolutions of the DOC of the two thermoset adhesives in both anisothermal and isothermal modes.

Investigation of the curing kinetics of polyurethane/nitrocellulose blends through FT‐IR measurements

AbstractPolyester (HTPS) based polyurethane (PU) elastomers were currently established to be effective binders for high‐energy composites with improved performances. Conventional PU binders are mostly non‐energetic materials, and consequently reduce the energy performance significantly. Nitrocellulose (NC), is an energetic polymer widely used as an ingredient in propellants, explosives, fireworks, and gas generators, it may be introduced in PU‐based compositions to overcome their performance drawback. Kinetic parameters must be specified in order to build PU binders with the most convenient and appropriate features. Therefore, the cure kinetics of polyester based polyurethane binder systems were investigated by Fourier transform infrared spectroscopy (FT‐IR) isothermal method. The polyester prepolymer (Desmophen® 1200) was cured with hexamethylene diisocyanate (HDI: Desmodur® N100) at various molar ratios (R[NCO]/[OH] = 0.6, 1, 1.25, and 1.5) and under different isothermal conditions (T = 60°C, 80°C, 100°C, and 120°C). In addition, the effect of the addition of nitrocellulose on the kinetics of polymerization of PU was investigated. The progression of the reaction was followed based on the decrease of the peak intensity of –NCO group at 2271 cm−1 as a function of the reaction time. The curing kinetic model and the apparent activation energy (Eα) were determined by the use of Kamal autocatalytic model and Friedman isoconversional method, respectively.

Polydimethylsiloxane crosslinking kinetics: A systematic study on Sylgard184 comparing rheological and thermal approaches

AbstractIn this work a systematic investigation of crosslinking kinetics of Sylgard184 polydimethylsiloxane is performed in both isothermal and dynamic conditions. The results are discussed in terms of two conversions, αC and αR determined by thermal and rheological analysis, respectively. Thermal analysis can well detect the first stage of the reaction, while rheological analysis starts being sensitive only at longer time. However, once the rheological response is observable, it changes with time faster than the calorimetric one. From rheology experiments it comes out that the gel point occurs at αR = 0.53, independently of the applied thermal history. At gel point, αC is around 0.30 indicating that about 30% of the bonds involved in the crosslinking process is enough to create an infinite network. A modified version of the Kamal's autocatalytic model allows to fit and predict the experimental findings from both the techniques; however, two distinct sets of parameters have been used. The results of this work may be a useful tool to design appropriate curing cycles for the preparation of Sylgard184.

Isothermal Curing Kinetics of Epoxidized Fatty Acid Methyl Esters and Triacylglycerols

AbstractPlant oil triacylglycerols are attractive renewable resources for biobased epoxy resins. We investigated the curing kinetics of three model epoxidized fatty acid methyl esters and representative epoxidized triacylglycerols with varied epoxide functionalities and distributions in the presence of a latent cationic initiator. Isothermal differential scanning calorimetry (DSC) was used to analyze the curing kinetics of the epoxy systems, and kinetic parameters (i.e., rate constants, reaction orders) were determined. Both epoxidized fatty esters and triacylglycerols followed the autocatalytic curing mechanism, and the DSC data were analyzed according to the Kamal autocatalytic model. Epoxidized methyl linoleate (EMLO) had the highest maximum curing rate, followed by epoxidized methyl linolenate (EMLON), and epoxidized methyl oleate (EMO) had the lowest maximum curing rate. We conclude that EMLO with two epoxide groups has the highest reactivity in this curing system, while the EMO with one epoxide group has the lowest reactivity. For epoxidized triacylglycerols, epoxidized camelina oil had the highest curing reactivity at higher temperatures, followed by epoxidized linseed oil and soybean oil.

Solvation effect of CO2 on accelerating the curing reaction process of epoxy resin

The solvation effect of compressed CO2 on the curing reaction process of epoxy resin was investigated by using the in-situ FTIR. The isothermal curing kinetic constant and activation energy of diglycidyl ether of bisphenol A (DGEBA) with m-xylylenediamine (MXDA) was calculated via Kamal autocatalytic model. The autocatalyzed rate constants and activation energy under 0.1 MPa CO2 are 0.7139 min−1 and 50.83 kJ/mol at 393 K, while those under 18 MPa CO2 are 1.0928 min−1 and 36.36 kJ/mol, respectively. The increased kinetic constant and reduced activation energy suggests that the plasticization effect of CO2 eases the chain movement, promotes the curing of epoxy resin, and increases the final conversion at relatively low temperature. Then, an amended Kamal model involving the diffusion factor was applied to better describe the curing process, which suggests that the high pressure CO2 plays an important role to reduce the mass transfer resistance and intensify the curing process. Meanwhile, the activation energy determined by the isoconversional method, also decreases with CO2 pressure at the same conversion. Especially, the activation energy at 90% conversion under 0.1 and 18 MPa CO2 are 46.52 and 36.19 kJ/mol, respectively, which further confirms the solvation effect of CO2 accelerates the curing of epoxy resin.

Modelling the kinetics and structural property evolution of a versatile reaction: aqueous HCN polymerization.

The kinetics of the reaction of the synthesis of HCN polymers in aqueous medium at high temperatures have been analysed to ascertain a suitable model for this material, for which it was recently demonstrated that prebiotic chemistry may now be adapted in the development of a new generation of high performance coatings and adhesives with biomedical applications. These experimental conditions were chosen for the simplicity of the reagents, being particularly convenient in regard to potential industrial scale-up of coating technology, where these polymers have revealed an interesting field of application. The kinetics of the precipitation polymerization of HCN in water were studied under isothermal conditions at four different temperatures between 75 °C and 90 °C throughout gravimetric measurements. The use of the Kamal-Sourour autocatalytic kinetic model was proposed, properly describing the overall formation process of this insoluble HCN polymer. All of the kinetic parameters, including reaction orders, kinetic constants and activation energy, were determined for the cross-linking polymerization reaction under study, and a relevant autocatalysis effect was observed. An isoconversion method was also used to analyse the variation of the global activation energy with conversion; and characterization by means of elemental analysis, Fourier transform infrared (FTIR) spectroscopy, and scanning electron microscopy (SEM) was carried out. This study demonstrates the autocatalytic, robust and straightforward character of this heterogeneous aqueous HCN polymerization, and to the best of our knowledge, this report describes the first time that a systematic and extended kinetic analysis has been conducted to obtain a more comprehensive and deeper understanding of this complex reaction, which is of great interest to the origin of life and, currently, to materials science.

Cure kinetics of epoxy/MWCNTs nanocomposites: Isothermal calorimetric and rheological analyses

Abstract A combinatorial route has been applied in cure kinetics study of epoxy nanocomposites containing multi-walled carbon nanotubes (MWCNTs) based on differential scanning calorimetry and rheokinetic analyses under isothermal conditions. Pristine and amine-modified MWCNTs bearing primary and secondary amines were used at very low concentrations (0.1 and 0.3 wt.% based on epoxy weight). Model-free and model-fitting methods were applied on calorimetric data, and Kamal autocatalytic model revealed good agreement with the experimental data. In case of epoxy filled with amine-modified MWCNTs, activation energy took a value lower than that obtained for sample containing pristine MWCNTs at an identical loading because of less hindrance brought about by curing. Isothermal rheokinetic studies supported formation of a filler network during processing, which hindered epoxy-anhydride cure reaction at higher MWCNTs loadings leading to a highly crosslinked epoxy network.

Isothermal kinetics and thermodynamics studies of curing reaction of epoxy-aromatic diamine reinforced with epoxy functional MWCNT

This study reports the cure kinetics and thermodynamics of an epoxy functional multiwall carbon nanotube-containing epoxy nanocomposite obtained by the polymerization of diglycidyl ether of bisphenol A with diaminodiphenyl sulfone as a curing agent through isothermal technique of differential scanning calorimetry. Isothermal kinetic parameters including reaction orders ( m, n), rate constants ( k1, k2), activation energy ( Ea), and pre-exponential factor ( A) were estimated using Kamal autocatalytic model. The model gives a good description of curing kinetics at various temperatures prior to the onset of vitrification. Thermodynamic parameters such as enthalpy (Δ H#), entropy (Δ S#), and Gibbs free energy (Δ G#) changes were also determined using the rate constants from the isothermal kinetic analysis and transition state theory. The thermodynamic functions were shown to be very sensitive parameters for the evaluation of the cure reaction.

Isothermal curing kinetics and mechanism of DGEBA epoxy resin with phthalide-containing aromatic diamine

The curing reaction of diglycidyl ether of bisphenol A (DGEBA) with a novel aromatic diamine containing phthalide structure (BAPP) was studied by differential scanning calorimetery (DSC). The optimal formulation of DGEBA/BAPP system was obtained in terms of the curing behavior and glass transition temperature determined by dynamic DSC. The nth-order reaction model and autocatalytic model were used to analyze the curing kinetics and mechanism based on the isothermal DSC technique. The results indicated that the Kamal autocatalytic model had a great agreement with the experimental data from the start of curing reaction to the initiation of diffusion control stage. Diffusion-controlled effect was also taken into account and then the extended Kamal model could describe precisely the curing reaction of BAPP/DGEBA in the entire conversion range.

Kinetics of multifunctional thiol-epoxy click reactions studied by differential scanning calorimetry: Effects of catalysis and functionality

Isothermal reaction kinetics of thiol-epoxy (multifunctional thiol-difunctional epoxy) reactions with and without external catalyst 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) were studied using differential scanning calorimetry (DSC). Autocatalytic behavior is observed both without DBU and with DBU, which is attributed to autocatalysis effects of hydroxyl products of the reaction. The isothermal curing kinetics are well described by the Kamal autocatalytic model, which is expressed as dα/dt=(k1 + k2αm)(1 − α)n (α: fractional conversion; dα/dt: apparent rate of reaction). Parameters of the reaction, including reaction orders m and n, apparent rate parameters k1 and k2, and activation energies are determined by fitting the experimental data to the Kamal model. For the thiol-epoxy reaction without DBU, the overall reaction order (m + n) is approximately 3 (with m ≈ 2 and n ≈ 1) but decreases to 2 (with m ≈ 1 and n ≈ 1) upon addition of DBU. Based on the most commonly described mechanism for nucleophilic thiol-epoxy reactions in the literature, new reaction schemes are proposed by incorporating the hydroxyl autocatalysis effect as well as the effect of external catalyst DBU on apparent reaction order. The proposed reaction schemes allow for excellent fits to reaction kinetics for thiol-epoxy reactions with and without DBU. In contrast to the strong effect of external DBU catalyst on reaction kinetics, changing the thiol monomer functionality leads to relatively small changes in apparent rate parameters and no change in the order of reaction or reaction mechanism.

Relationships of cure kinetics and processing for epoxidized soybean oil bio-thermoset

Epoxidized soybean oil (ESO) resin was thermally cured using methylhexahydrophthalic anhydride (MHHPA) curing agent, in the presence of 2-ethyl-4-methylimidazole (EMI) catalyst at different temperatures (i.e., 130, 135, 140, 145 and 150°C). Curing kinetics of the ESO/MHHPA systems was studied using Fourier Transform Infrared Spectroscopy (FTIR). The EMI-catalyzed ESO/MHHPA system showed autocatalytic behavior in the isothermal curing reaction. The kinetic parameters; reaction rate constants (k1 and k2) and reaction orders (m and n) of the ESO/MHHPA systems have been determined based on Kamal's autocatalytic model. EMI catalyst content and curing temperature showed significant effect on k1, k2, m and n. The overall reaction order (m+n) of the EMI-catalyzed ESO/MHHPA systems was about 1.5–3.0. The apparent activation energies (Ea1 and Ea2) were determined using the Arrhenius kinetic equation. As expected, the Ea1 and Ea2 had decreased with increasing EMI catalyst content. The critical conversion, αc was found to be in the range of 0.6–0.8. Curing reaction of ESO/MHHPA system as a function of EMI catalyst content can be well-described by introducing the diffusion factor, f(α) into Kamal's autocatalytic model.

Cure kinetics of an acrylated epoxidized hemp oil‐based bioresin system

AbstractIn this work, the cure kinetics of a novel acrylated epoxidized hemp oil (AEHO)‐based bioresin was investigated for the first time by differential scanning calorimetry (DSC) using both isothermal and nonisothermal conditions. This new bioresin was synthesized by the acrylation of a previously epoxidized hemp oil (EHO) bioresin. The curing of the AEHO bioresin showed an autocatalytic behavior with the vitrification phenomenon preventing the conversion reaching unity for all the temperatures studied. It was found that the curing behavior can be modeled with high accuracy using a modified Kamal autocatalytic model that takes into account the vitrification phenomenon. Dynamic activation energies were determined from the Kissinger and Ozawa–Flynn–Wall methods, resulting in 58.87 and 62.02 kJmol−1, respectively. In addition, activation energies associated with the autocatalytic model constants, k1 and k2, were established to be equal to 58.94 and 45.32 kJmol−1, respectively. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

Effect of nanoclay and carboxyl-terminated (butadiene-co-acrylonitrile) (CTBN) rubber on the reaction induced phase separation and cure kinetics of an epoxy/cyclic anhydride system

The effects of nano clay, carboxyl-terminated (butadiene-co-acrylonitrile) (CTBN) liquid rubber and the combination of both on the cure kinetics of diglycidyl ether of bisphenol-A (DGEBA)-based epoxy resin/nadic methyl anhydride were studied. Cure kinetics studies were carried out by performing dynamic and isothermal differential scanning calorimetric (DSC) experiments. The dynamic DSC experiments were carried out at four different heating rates. Dynamic kinetic modeling was performed using Kissinger and Ozawa approaches. Since these methods are based exclusively on the maximum rate of cure, which occurs approximately at the beginning of the cure reaction, the activation energy calculated using these methods is valid only for the initial stage of the cure. The clay (3 phr) filled epoxy system has an activation energy 24 % lower than the unfilled system. The role of the surfactant chemistry on the initial stage of the cure reaction was also studied. A plausible reaction mechanism which involves the effect of the nanoclay surfactant as an accelerator of the cure reaction was proposed. The phase separated CTBN rubber hindered the cure reaction and has 3 % higher activation energy for epoxy/CTBN system than the unfilled system. In the ternary epoxy/3 phr clay/15 phr CTBN system, the accelerating effect of clay on cure was highlighted. The cure activation observed in the presence of clay overshadows the hindrance created by the phase separated CTBN. Isothermal DSC scans were carried out at five different temperatures. The experimental datas showed an autocatalytic behavior of the reaction, and the isothermal modeling was carried out by Kamal autocatalytic model. The results showed a very good agreement within the whole conversion range for the unfilled and all the filled systems. The evolution of the morphology and phase separation was also studied using optical and scanning electron microscope. Faster cure reaction resulted in smaller phase-separated CTBN particles in epoxy/clay/CTBN ternary system as compared with those observed in epoxy/CTBN binary blend.

Study on curing kinetics of diallyl-bearing epoxy resin using sulfur as curing agent

In this paper the curing kinetics of diglycidyl ether of 4,4′-diallyl-bisphenol-A (DADGEBA) using sulfur (S) as curing agent was studied by non-isothermal and isothermal differential scanning calorimetry (DSC). The kinetic mechanism equations were determined using autocatalytic models and nth-order reaction model. DSC measurement showed that the curing process of DADGEBA/S system contains two steps because of the double exothermic peaks in DSC curve. The model data simulation results indicated that the Šesták-Berggren (SB) model had a great distinction with the experimental data. Isothermal DSC analysis showed that the curing reactions followed Kamal's autocatalytic model when the reaction temperature was below 210°C, and when the temperature was above 210°C the nth-order model can be used to describe the curing reaction process of the DADGEBA/S system perfectly. The two kinetic equations in the entire reaction process of DADGEBA/S system are consistent with the two-step reaction mechanisms of the same system.

Cure kinetics of an epoxidized hemp oil based bioresin system

AbstractA novel epoxidized hemp oil (EHO) based bioresin was synthesized by epoxidation in situ with peroxyacetic acid. In this research the cure kinetics of an EHO based bioresin system cured with triethylenetetramine (TETA) was studied by differential scanning calorimetry using both isothermal and nonisothermal data. The results show that the curing behavior can be modeled with a modified Kamal autocatalytic model that accounts for a shift to a diffusion‐controlled reaction postvitrification. The total order of the reaction was found to decrease with an increase in temperature from ∼ 5.2 at 110°C to ∼ 2.4 at 120°C. Dynamic activation energies were determined from the Kissinger (51.8 kJ/mol) and Ozawa‐Flynn‐Wall (56.3 kJ/mol) methods. Activation energies determined from the autocatalytic method were 139.5 kJ/mol and −80.5 kJ/mol. The observed negative activation energy is thought to be due to an unidentified competitive reaction that gives rise to the appearance of k2 decreasing with increasing temperature. The agreement of fit of the model predictions with experimental values was satisfactory for all temperatures. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Reaction kinetics and physical properties of unsaturated polyester modified with methylacyloxylpropyl-POSS

The polyhedral oligomeric silsesquioxanes which contains methylacryloylpropyl group (MAP-POSS) was synthesized and used to modify unsaturated polyester resin (UPR). The cure kinetics was investigated by isothermal DSC technique. The mechanical and electrical properties of fiberglass-reinforced laminate were determined. The result shows that the reaction can be described by a Kamal autocatalytic model which has two reaction rate constants k1 and k2, and two apparent activation energies Ea1 and Ea 2 are 98.12 kJ/mol and 74.01 kJ/mol, respectively. UPR and MAP-POSS can co-cure in free radical polymerization. When the MAP-POSS content is 5 wt%, the impact and tensile strength of fiberglass-reinforced laminate enhanced 10% and 6%, respectively, and has better electrical properties than no MAP-POSS. The dielectric constant e and dielectric loss tanδ are all decrease. The surface resistance ρs is 4.7 times higher than pure UPR laminates

Kinetics of cure for a coating system including DGEBA ( n = 0)/1,8-NDA and barium carbonate

The increasing demand for low-cost and high performance coatings has promoted the development of chip epoxy-based coatings using inert fillers. Attention has been paid here on employing mixtures of DGEBA with barium carbonate as novel ceramic-based filler to produce a coating using 1,8-naphthalene diamine (1,8-NDA) as the crosslinking agent. A substantial increase in the T g, from 85 to 100 °C, is observed for the optimum composition. The 1,8-NDA-cure of the epoxy composites showed an autocatalytic mechanism. At a specific conversion range the cure reaction of the composites will be controlled by a diffusion-control cure reaction rather than by Kamal autocatalytic model. Model-free isoconversional method is utilized to construct apparent activation energy dependence on conversion plot. The effect of diffusion control is described by an approach proposed by Chern and Poehlein. Greater diffusion control is observed as the cure temperature decreased.

Cure kinetics of epoxy resin used for advanced composites

AbstractThe cure kinetics of an epoxy resin used for the preparation of advanced polymeric composite structures was studied by isothermal differential scanning calorimetry (DSC). A series of isothermal DSC runs provided information about the kinetics of cure over a wide temperature range. According to the heat evolution behavior during the curing process, several influencing factors of isothermal curing reactions were evaluated. The results showed that the isothermal kinetic reaction of this epoxy resin followed an autocatalytic kinetic mechanism. In the latter reaction stage, the curing reaction became controlled mainly by diffusion. Cure rate was then modeled using a modified Kamal autocatalytic model that accounts for the shift from a chemically controlled reaction to a diffusion‐controlled reaction. The model parameters were determined by a nonlinear multiple regression method. Copyright © 2004 Society of Chemical Industry