971 resultados para Kinetic-analysis


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BACKGROUND: Acetate metabolism in skeletal muscle is regulated by acetylCoA synthetase (ACS). The main function of ACS is to provide cells with acetylCoA, a key molecule for numerous metabolic pathways including fatty acid and cholesterol synthesis and the Krebs cycle. METHODS: Hyperpolarized [1-(13)C]acetate prepared via dissolution dynamic nuclear polarization was injected intravenously at different concentrations into rats. The (13)C magnetic resonance signals of [1-(13)C]acetate and [1-(13)C]acetylcarnitine were recorded in vivo for 1min. The kinetic rate constants related to the transformation of acetate into acetylcarnitine were deduced from the 3s time resolution measurements using two approaches, either mathematical modeling or relative metabolite ratios. RESULTS: Although separated by two biochemical transformations, a kinetic analysis of the (13)C label flow from [1-(13)C]acetate to [1-(13)C]acetylcarnitine led to a unique determination of the activity of ACS. The in vivo Michaelis constants for ACS were KM=0.35±0.13mM and Vmax=0.199±0.031μmol/g/min. CONCLUSIONS: The conversion rates from hyperpolarized acetate into acetylcarnitine were quantified in vivo and, although separated by two enzymatic reactions, these rates uniquely defined the activity of ACS. The conversion rates associated with ACS were obtained using two analytical approaches, both methods yielding similar results. GENERAL SIGNIFICANCE: This study demonstrates the feasibility of directly measuring ACS activity in vivo and, since the activity of ACS can be affected by various pathological states such as cancer or diabetes, the proposed method could be used to non-invasively probe metabolic signatures of ACS in diseased tissue.

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A new synthetic pathway to analogues of the aglucones of naturally occurring cyclic hydroxamic acids (2,4-dihydroxy-l,4-benzoxazin-3-ones) has been developed. The new pathway involves the coupling of substituted nitrophenols wdth /-propyl-abromo- O-methoxymethylglycolate. These materials were reductively cyclised to reveal the hydroxamic acid functionality. Removal of the C-2 0-methoxymethyl protecting group was achieved chemoselectively using boron trichloride. The analogue 7-methoxy-2,4-dihydroxy-l,4-benzoxazin-3-one (DIMBOA) was assayed with papain and a semilog plot of activity of papain in the presence of excess DIMBOA was found to be linear. A single exponential equation was suggested as the model for kinetic analysis. '^ Nuclear magnetic resonance (NMR) spectra of a couple of hydroxamates were acquired as reference standards for future mechanistic studies of these compounds as thiol protease inhibitors. A 10% '^-labeled sample ofDIMBOA was also prepared for future mechanistic studies using NMR techniques.

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Lignocellulosic biomass is probably the best alternative resource for biofuel production and it is composed mainly of cellulose, hemicelluloses and lignin. Cellulose is the most abundant among the three and conversion of cellulose to glucose is catalyzed by the enzyme cellulase. Cellulases are groups of enzymes act synergistically upon cellulose to produce glucose and comprise of endoglucanase, cellobiohydrolase and β-glucosidase. β -glucosidase assumes great importance due to the fact that it is the rate limiting enzyme. Endoglucanases (EG) produces nicks in the cellulose polymer exposing reducing and non reducing ends, cellobiohydrolases (CBH) acts upon the reducing or non reducing ends to liberate cellobiose units, and β - glucosidases (BGL) cleaves the cellobiose to liberate glucose completing the hydrolysis. . β -glucosidases undergo feedback inhibition by their own product- β glucose, and cellobiose which is their substrate. Few filamentous fungi produce glucose tolerant β - glucosidases which can overcome this inhibition by tolerating the product concentration to a particular threshold. The present study had targeted a filamentous fungus producing glucose tolerant β - glucosidase which was identified by morphological as well as molecular method. The fungus showed 99% similarity to Aspergillus unguis strain which comes under the Aspergillus nidulans group where most of the glucose tolerant β -glucosidase belongs. The culture was designated the strain number NII 08123 and was deposited in the NII culture collection at CSIR-NIIST. β -glucosidase multiplicity is a common occurrence in fungal world and in A.unguis this was demonstrated using zymogram analysis. A total 5 extracellular isoforms were detected in fungus and the expression levels of these five isoforms varied based on the carbon source available in the medium. Three of these 5 isoforms were expressed in higher levels as identified by the increased fluorescence (due to larger amounts of MUG breakdown by enzyme action) and was speculated to contribute significantly to the total _- β glucosidase activity. These isoforms were named as BGL 1, BGL3 and BGL 5. Among the three, BGL5 was demonstrated to be the glucose tolerant β -glucosidase and this was a low molecular weight protein. Major fraction was a high molecular weight protein but with lesser tolerance to glucose. BGL 3 was between the two in both activity and glucose tolerance.121 Glucose tolerant .β -glucosidase was purified and characterized and kinetic analysis showed that the glucose inhibition constant (Ki) of the protein is 800mM and Km and Vmax of the enzyme was found to be 4.854 mM and 2.946 mol min-1mg protein-1respectively. The optimumtemperature was 60°C and pH 6.0. The molecular weight of the purified protein was ~10kDa in both SDS as well as Native PAGE indicating that the glucose tolerant BGL is a monomeric protein.The major β -glucosidase, BGL1 had a pH and temperature optima of 5.0 and 60 °C respectively. The apparent molecular weight of the Native protein is 240kDa. The Vmax and Km was 78.8 mol min-1mg protein-1 and 0.326mM respectively. Degenerate primers were designed for glycosyl hydrolase families 1, 3 and 5 and the BGL genes were amplified from genomic DNA of Aspergillus unguis. The sequence analyses performed on the amplicons results confirmed the presence of all the three genes. Amplicon with a size of ~500bp was sequenced and which matched to a GH1 –BGL from Aspergillus oryzae. GH3 degenerate primers producing amplicons were sequenced and the sequences matched to β - glucosidase of GH3 family from Aspergillus nidulans and Aspergillus acculateus. GH5 degenerate primers also gave amplification and sequencing results indicated the presence of GH5 family BGL gene in the Aspergillus unguis genomic DNA.From the partial gene sequencing results, specific as well as degenerate primers were designed for TAIL PCR. Sequencing results of the 1.0 Kb amplicon matched Aspergillus nidulans β -glucosidase gene which belongs to the GH1 family. The sequence mainly covered the N-Terminal region of the matching peptide. All the three BGL proteins ie. BGL1, BGL3 and BGL5 were purified by chromatography an electro elution from Native PAGE gels and were subjected to MALDI-TOF mass spectrometric analysis. The results showed that BGL1 peptide mass matched to . β -glucosidase-I of Aspergillus flavus which is a 92kDa protein with 69% protein coverage. The glucose tolerant β -glucosidase BGL5 mass matched to the catalytic C-terminal domain of β -glucosidase-F from Emericella nidulans, but the protein coverage was very low compared to the size of the Emericella nidulans protein. While comparing the size of BGL5 from Aspergillus unguis, the protein sequence coverage is more than 80%. BGL F is a glycosyl hydrolase family 3 protein.The properties of BGL5 seem to be very unique, in that it is a GH3 β -glucosidase with a very low molecular weight of ~10kDa and at the same time having catalytic activity and glucose 122 tolerance which is as yet un-described in GH β -glucosidases. The occurrence of a fully functional 10kDA protein with glucose tolerant BGL activity has tremendous implications both from the points of understanding the structure function relationships as well as for applications of BGL enzymes. BGL-3 showed similarity to BGL1 of Aspergillus aculateus which was another GH3 β -glucosidase. It may be noted that though PCR could detect GH1, GH3 and GH5 β-glucosidases in the fungus, the major isoforms BGL1 BGL3 and BGL5 were all GH3 family enzymes. This would imply that β-glucosidases belonging to other families may also co-exist in the fungus and the other minor isoforms detected in zymograms may account for them. In biomass hydrolysis, GT-BGL containing BGL enzyme was supplemented to cellulase and the performances of blends were compared with a cocktail where commercial β- glucosidase was supplemented to the biomass hydrolyzing enzyme preparation. The cocktail supplemented with A unguis BGL preparation yielded 555mg/g sugar in 12h compared to the commercial enzyme preparation which gave only 333mg/g in the same period and the maximum sugar yield of 858 mg/g was attained in 36h by the cocktail containing A. unguis BGL. While the commercial enzyme achieved almost similar sugar yield in 24h, there was rapid drop in sugar concentration after that, indicating probably the conversion of glucose back to di-or oligosaccharides by the transglycosylation activity of the BGl in that preparation. Compared this, the A.unguis enzyme containing preparation supported peak yields for longer duration (upto 48h) which is important for biomass conversion to other products since the hydrolysate has to undergo certain unit operations before it goes into the next stage ie – fermentation in any bioprocesses for production of either fuels or chemicals.. Most importantly the Aspergillus unguis BGL preparation yields approximately 1.6 fold increase in the sugar release compared to the commercial BGL within 12h of time interval and 2.25 fold increase in the sugar release compared to the control ie. Cellulase without BGL supplementation. The current study therefore leads to the identification of a potent new isolate producing glucose tolerant β - glucosidase. The organism identified as Aspergillus unguis comes under the Aspergillus nidulans group where most of the GT-BGL producers belong and the detailed studies showed that the glucose tolerant β -glucosidase was a very low molecular weight protein which probably belongs to the glycosyl hydrolase family 3. Inhibition kinetic studies helped to understand the Ki and it is the second highest among the nidulans group of Aspergilli. This has promoted us for a detailed study regarding the mechanism of glucose tolerance. The proteomic 123 analyses clearly indicate the presence of GH3 catalytic domain in the protein. Since the size of the protein is very low and still its active and showed glucose tolerance it is speculated that this could be an entirely new protein or the modification of the existing β -glucosidase with only the catalytic domain present in it. Hydrolysis experiments also qualify this BGL, a suitable candidate for the enzyme cocktail development for biomass hydrolysis

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La tesi doctoral presentada té com a objectius principals l'estudi de les etapes fonamentals de desintegració i flotació en un procés de destintatge de papers vell de qualitats elevades per a poder millorar l'eficàcia d'aquestes etapes clau. Conté una revisió teòrica completa i molt actualitzada del procés de desintegració i flotació tant a nivell macroscòpic com microscòpic. La metodologia de treball en el laboratori, la posada a punt dels aparells, així com les anàlisis efectuades per a valorar la resposta del procés (anàlisi de blancor, anàlisi d'imatge i anàlisi de la concentració efectiva de tinta residual) estan descrites en el capítol de material i mètodes. La posada en marxa permet obtenir unes primeres conclusions respecte la necessitat de treballar amb una matèria primera homogènia i respecte la no significació de la temperatura de desintegració dins l'interval de treball permès al laboratori (20-50°C). L'anàlisi de les variables mecàniques de desintegració: consistència de desintegració (c), velocitat d'agitació en la desintegració (N) i temps de desintegració (t), permet de discernir que la consistència de desintegració és una variable fonamental. El valor de consistència igual al 10% marca el límit d'existència de les forces d'impacte mecànic en la suspensió fibrosa. A consistències superiors, les forces viscoses i d'acceleració dominen l'etapa de desintegració. Existeix una interacció entre la consistència i el temps de desintegració, optimitzant-se aquesta darrera variable en funció del valor de la consistència. La velocitat d'agitació és significativa només per a valors de consistència de desintegració inferiors al 10%. En aquests casos, incrementar el valor de N de 800 a 1400 rpm representa una disminució de 14 punts en el factor de destintabilitat. L'anàlisi de les variables químiques de desintegració: concentració de silicat sòdic (% Na2SiO3), peròxid d'hidrogen (% H2O2) i hidròxid sòdic (% Na2OH), proporciona resultats força significatius. El silicat sòdic presenta un efecte altament dispersant corroborat per les corbes de distribució dels diàmetres de partícula de tinta obtingudes mitjançant anàlisi d'imatges. L'hidròxid sòdic també presenta un efecte dispersant tot i que no és tant important com el del silicat sòdic. Aquests efectes dispersants són deguts principalment a l'increment de les repulsions electrostàtiques que aporten a la suspensió fibrosa aquests reactius químics fent disminuir l'eficàcia d'eliminació de l'etapa de flotació. El peròxid d'hidrogen utilitzat generalment com agent blanquejant, actua en aquests casos com a neutralitzador dels grups hidroxil provinents tant del silicat sòdic com de l'hidròxid sòdic, disminuint la repulsió electrostàtica dins la suspensió. Amb l'anàlisi de les variables hidrodinàmiques de flotació: consistència de flotació (c), velocitat d'agitació durant la flotació (N) i cabal d'aire aplicat (q), s'aconsegueix la seva optimització dins el rang de treball permès al laboratori. Valors elevats tant de la velocitat d'agitació com del cabal d'aire aplicat durant la flotació permeten eliminar majors quantitats de tinta. La consistència de flotació assoleix valors òptims depenent de les condicions de flux dins la cel·la de flotació. Les metodologies d'anàlisi emprades permeten obtenir diferents factors de destintabilitat. Entre aquests factors existeix una correlació important (determinada pels coeficients de correlació de Pearson) que permet assegurar la utilització de la blancor com a paràmetre fonamental en l'anàlisi del destintatge de papers vells, sempre i quan es complementi amb anàlisis d'imatge o bé amb anàlisi de la concentració efectiva de tinta residual. S'aconsegueixen expressions empíriques tipus exponencial que relacionen aquests factors de destintabilitat amb les variables experimentals. L' estudi de les cinètiques de flotació permet calcular les constants cinètiques (kBlancor, kERIC, kSupimp) en funció de les variables experimentals, obtenint un model empíric de flotació que relacionant-lo amb els paràmetres microscòpics que afecten realment l'eliminació de partícules de tinta, deriva en un model fonamental molt més difícil d'interpretar. Mitjançant l'estudi d'aquestes cinètiques separades per classes, també s'aconsegueix determinar que l'eficàcia d'eliminació de partícules de tinta és màxima si el seu diàmetre equivalent és superior a 50 μm. Les partícules amb diàmetres equivalents inferiors a 15 μm no són eliminades en les condicions de flotació analitzades. Es pot dir que és físicament impossible eliminar partícules de tinta de diàmetres molt diferents amb la mateixa eficiència i sota les mateixes condicions de treball. El rendiment del procés analitzat en funció de l'eliminació de sòlids per l'etapa de flotació no ha presentat relacions significatives amb cap de les variables experimentals analitzades. Únicament es pot concloure que addicionar quantitats elevades de silicat sòdic provoca una disminució tant de sòlids com de matèria inorgànica presents en les escumes de flotació.

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Síntesi de nous complexos de Ruteni amb lligands no quirals que tenen per fórmula [Ru(phen)([9]aneS3)X] (on X = H2O, py i MeCN). Caracterització espectroscòpica electroquímica i estructural d'aquesta família de complexos. Estudi de les seves propietats catalítiques en front a l'oxidació de substrats orgànics com l'alcohol benzílic en reaccions d'electrocatàlisi. Avaluació cinètica dels mecanismes de substitució entre els complexos Ru-py i Ru-MeCN. Generació d'un interruptor molecular foto-induït. Síntesi de nous complexos quirals de Ru atropoisomèricament purs amb lligands oxazolínics que tenen per fórmula [Ru(trpy)(Ph-box-R)X] on (X = Cl, H2O, py, MeCN, 2-OH-py). Caracterització estructural exhaustiva en estat sòlid (Raig-X) en solució (RMN) i en fase gas (càlculs DFT). Avaluació de la seva activitat catalítica en reaccions asimmetriques d'epoxidació de substrats proquirals. Síntesi de nous lligands polipiridílics quirals amb simetria C3. Estudi de la seva química de coordinació i avaluació de la seva activitat catalítica en reaccions asimmetriques d'oxidació i reducció.

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Phosphorylation of the coronavirus nucleoprotein (N protein) has been predicted to play a role in RNA binding. To investigate this hypothesis, we examined the kinetics of RNA binding between nonphosphorylated and phosphorylated infectious bronchitis virus N protein with nonviral and viral RNA by surface plasmon resonance (Biacore). Mass spectroscopic analysis of N protein identified phosphorylation sites that were proximal to RNA binding domains. Kinetic analysis, by surface plasmon resonance, indicated that nonphospborylated N protein bound with the same affinity to viral RNA as phosphorylated N protein. However, phosphorylated N protein bound to viral RNA with a higher binding affinity than nonviral RNA, suggesting that phosphorylation of N protein determined the recognition of virus RNA. The data also indicated that a known N protein binding site (involved in transcriptional regulation) consisting of a conserved core sequence present near the 5' end of the genome (in the leader sequence) functioned by promoting high association rates of N protein binding. Further analysis of the leader sequence indicated that the core element was not the only binding site for N protein and that other regions functioned to promote high-affinity binding.

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A highly efficient process for oxidative degradation of 1,3-dialkylimidazolium ionic liquids in hydrogen peroxide/acetic acid aqueous medium assisted by ultrasonic chemical irradiation is, for the first time, described. It is shown that more than 93% of the 1,3-dialkylimidazolium cation with the corresponding Cl-, Br-, BF4- and PF6- counter-anions at a concentration of 2.5 mM can be degraded at 50 degrees C within 12 h while at 72 h the conversions approach 99%. A tentative mechanism for the degradation of these ILs is for the first time proposed through a detailed kinetic analysis of several characteristic transients and/or immediate products, which are identified during the ILs degradation using GC-MS. The results clearly indicate that three hydrogen atoms in the imidazolium ring are the first sites preferably oxidized, followed by cleavage of the alkyl groups attached to the N atoms from the ring. The nature of the alkyl chain length on the imidazolium ring and the type of counter anion do not seem to affect the degradation process. Further, selective fragmentations of C-N bonds of the imidazolium or derived ring lead to ring opening, forming degraded intermediates. It is also shown that acetoxyacetic acid and biurea are the final kinetically stable degraded products from the ILs under the degradation conditions.

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Thyroid hormones exert most of their physiological effects through two thyroid hormone receptor (TR) subtypes, TR alpha and TR beta, which associate with many transcriptional coregulators to mediate activation or repression of target genes. The search for selective TR beta ligands has been stimulated by the finding that several pharmacological actions mediated by TR beta might be beneficial in medical conditions such as obesity, hypercholesterolemia and diabetes. Here, we present a new methodology which employs surface plasmon resonance to investigate the interactions between TR beta ligand binding domain (LBD) complexes and peptides derived from the nuclear receptor interaction motifs of two of its coregulators, SRC2 and DAX1. The effect of several TR beta ligands, including the TR beta selective agonist GC-I and the TR beta selective antagonist NH-3, were investigated. We also determined the kinetic rate constants for the interaction of TR beta-T3 with both coregulators, and accessed the thermodynamic parameters for the interaction with DAX1. Our findings Suggest that flexibility plays an important role in the interaction between the receptor and its coregulators. and point out important aspects of experimental design that should be addressed when using TR beta LBD and its agonists. Furthermore, the methodology described here may be useful for the identification of new TR beta ligands. (C) 2008 Elsevier Ltd. All rights reserved.

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The relative contributions to the specificity and catalysis of aglycone, of residues E190, E194, K201 and M453 that form the aglycone-binding site of a beta-glycosidase from Spodoptera frugiperda (EC 3.2.1.21), were investigated through site-directed mutagenesis and enzyme kinetic experiments. The results showed that E190 favors the binding of the initial portion of alkyl-type aglycones (up to the sixth methylene group) and also the first glucose unit of oligosaccharidic aglycones, whereas a balance between interactions with E194 and K201 determines the preference for glucose units versus alkyl moieties. E194 favors the binding of alkyl moieties, whereas K201 is more relevant for the binding of glucose units, in spite of its favorable interaction with alkyl moieties. The three residues E190, E194 and K201 reduce the affinity for phenyl moieties. In addition, M453 favors the binding of the second glucose unit of oligosaccharidic aglycones and also of the initial portion of alkyl-type aglycones. None of the residues investigated interacted with the terminal portion of alkyl-type aglycones. It was also demonstrated that E190, E194, K201 and M453 similarly contribute to stabilize ES double dagger. Their interactions with aglycone are individually weaker than those formed by residues interacting with glycone, but their joint catalytic effects are similar. Finally, these interactions with aglycone do not influence glycone binding.

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An understanding of the rate and the mechanism of reaction is of fundamental importance in the many facets of chemistry. Electrochemical systems are further complicated by the heterogeneous boundary, between the solution and the electrode, that the electron passes through before any electrochemical reaction can take place. This thesis concerns the development of methods for analysing electrode kinetics. One part involves the further development of the Global Analysis procedure to include electrodes with a spherical geometry which are traditionally the most popular form of electrodes. Simulated data is analysed to ascertain the accuracy of the procedure and then the known artifacts of uncompensated solution resistance and charging current are added to the simulated data so that the effects can be observed. The experimental analysis of 2-methyl-2-nitropropane is undertaken and comparisons are made with the Marcus-Hush electrochemical theories concerning electrode kinetics. A related section explores procedures for the kinetic analysis of steady state voltammetric data obtained at microdisc electrodes. A method is proposed under the name of Normalised Steady State Voltammetry and is tested using data obtained from a Fast Quasi-Explicit Finite Difference simulation of diffusion to a microdisc electrode. In a second area of work using microelectrodes, the electrochemical behaviour of compounds of the general formula M(CO)3(η3 - P2P1) where M is either Cr, Mo or W and P2P' is bis(2-diphenylphosphinoethyl)phenylphosphine) is elucidated. The development of instrumentation and mathematical procedures relevant to the measurement and quantitation of these systems is also investigated. The tungsten compound represents the first examples where the 17-electronfac+ and mer+ isomers are of comparable stability.

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Thermal resistance is one of the most dominative properties for polymer materials. Thermal degradation mechanisms of epoxidized natural rubber (ENR) and NR are studied by thermogravimetric analysis (TGA) and differential thermal analysis (DTA). The results show that, the introduction of epoxy groups into the NR molecular main chain leads to a remarkable change in the degradation mechanism. The thermal stability of ENR is worse than that of NR. For the first thermooxidative degradation stage, the thermal decomposition mechanism of ENR is similar to that of NR, which corresponds to a mechanism involving one-dimensional diffusion. For the second stage, the thermal decomposition mechanism of ENR is a three-dimensional diffusion, which is more complex than that of NR. Kinetic analysis showed that activation energy (E?), activation entropy (?H) and activation Gibbs energy (?G) values are all positive, indicating that the thermooxidative degradation process of ENR is non-spontaneous.

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Composite LiFe0.4Mn0.6PO4/C microspheres are considered advanced cathode materials for electric vehicles and other high-energy density applications due to their advantages of high energy density and excellent cycling stability. LiFe0.4Mn0.6PO4/C microspheres have been produced using a double carbon coating process employing traditional industrial techniques (ball milling, spray-drying and annealing). The obtained LiFe0.4Mn0.6PO4 microspheres exhibit a high discharge capacity of around 166 mA h g-1 at 0.1 C and excellent rate capabilities of 132, 103, and 72 mA h g-1 at 5, 10, and 20 C, respectively. A reversible capacity of about 152 mA h g-1 after 500 cycles at a current density of 1 C indicates an outstanding cycling stability. The excellent electrochemical performance is attributed to the micrometer-sized spheres of double carbon-coated LiFe0.4Mn0.6PO4 nanoparticles with improved electric conductivity and higher Li ion diffusion coefficients, ensuring full redox reactions of all nanoparticles. The results show that the advanced high-energy density cathode materials can be produced using existing industry techniques.

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The present work aims at finding a relationship between kinetic models of thermal degradation process with the physiochemical structure of epoxy-clay nanocomposites in order to understand its service temperature. In this work, two different types of modified clays, including clay modified with (3-aminopropyl)triethoxysilane (APTES) and a commercial organoclay, were covalently and non-covalently incorporated into epoxy matrix, respectively. The effect of different concentrations of silanized clay on thermal behaviour of epoxy nanocomposites were first investigated in order to choose the optimum clay concentration. Afterwards, thermal characteristics of the degradation process of epoxy nanocomposites were obtained by TGA analysis and the results were employed to determine the kinetic parameters using model-free isoconversional and model-fitting methods. The obtained kinetic parameters were used to model the entire degradation process. The results showed that the incorporation of the different modified clay into epoxy matrix change the mathematical model of the degradation process, associating with different orientations of clay into epoxy matrix confirming by XRD results. The obtained models for each epoxy nanocomposite systems were used to investigate the dependence of degradation rate and degradation time on temperature and conversion degree. Our results provide an explanation as to how the life time of epoxy and its nanocomposites change in a wide range of operating temperatures as a result of their structural changes.

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The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

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