A new model for the kinetic analysis of thermal degradation of polymers driven by random scission

In this paper, a series of f(α) kinetic equations able to describe the random scission degradation of polymers is formulated in such a way that the reaction rate of the thermal degradation of polymers that go through a random scission mechanism can be directly related to the reacted fraction. The proposed equations are validated by a study of the thermal degradation of poly(butylene terephthalate) (PBT). The combined kinetic analysis of thermal degradation curves of this polymer obtained under different thermal pathways have shown that the proposed equation fits all these curves while other conventional models used in literature do not.     

Combined kinetic analysis of thermal degradation of polymeric materials under any thermal pathway

Combined kinetic analysis has been applied for the first time to the thermal degradation of polymeric materials. The combined kinetic analysis allows the determination of the kinetic parameters from the simultaneous analysis of a set of experimental curves recorded under any thermal schedule. The method does not make any assumptions about the kinetic model or activation energy and allows analysis even when the process does not follow one of the ideal kinetic models already proposed in the literature. In the present paper the kinetics of the thermal degradation of both polytetrafluoroethylene (PTFE) and polyethylene (PE) have been analysed. It has been concluded, without previous assumptions on the kinetic model, that the thermal degradation of PTFE obeys a first order kinetic law, while the thermal degradation of PE follows a diffusion-controlled kinetic model.     

Pyrolysis kinetics of ethylene–propylene (EPM) and ethylene–propylene–diene (EPDM)

The thermal degradation kinetics of several ethylene–propylene copolymers (EPM) and ethylene–propylene–diene terpolymers (EPDM), with different chemical compositions, have been studied by means of the combined kinetic analysis. Until now, attempts to establish the kinetic model for the process have been unsuccessful and previous reports suggest that a model other than a conventional nth order might be responsible. Here, a random scission kinetic model, based on the breakage and evaporation of cleavaged fragments, is found to describe the degradation of all compositions studied. The suitability of the kinetic parameters resulting from the analysis has been asserted by successfully reconstructing the experimental curves. Additionally, it has been shown that the activation energy for the pyrolysis of the EPM copolymers decreases by increasing the propylene content. An explanation for this behavior is given. A low dependence of the EPDM chemical composition on the activation energy for the pyrolysis has been reported, although the thermal stability is influenced by the composition of the diene used.     

Quantitative analysis of random scission and chain-end scission in the thermal degradation of polyethylene

The thermal degradation of polyethylene includes two different kinds of pathways. These are random and chain-end scissions which include β-scission on the chain end and radical transfer scission. We conducted a quantitative analysis on these pathways by Pyrolysis-GC/MS and computer simulation. Two different distributions of scission products of polyethylene were observed at different temperatures. They are determined by the relationship between rate of reaction and that of volatilisation. Furthermore, a characteristic distribution was observed in lower molecular weight. It could be explained by direct scission and one to five-step radical transfer scissions. The pathway possibilities calculated with the accumulated schemes showed that the direct scission and one-step-radical transfer increased with the temperature. This indicates that β-scission occurs on the chain end before the radical transfer because the rate of the β-scission becomes faster as the temperature rises.     

Thermal stability and degradation products analysis of benzocyclobutene-terminated imide polymers

Benzocyclobutene-terminated imides were prepared and fully characterized with ¹H NMR, MS, and FT-IR. The thermal degradation of polymers was investigated by using thermogravimetric analyzer (TGA) and high-resolution pyrolysis-gas chromatography–mass spectrometry (HR-Py-GC–MS). TGA showed that thermal degradation of the polymer was a single-stage process in N₂, whereas a three-stage degradation in air atmosphere. The major involved products were found to be CO₂, naphthalene and naphthalene derivatives. Degradation mechanism of the polymer was suggested and the relationship between structures of the polymer and degradation products was also discussed.     

Significant enhancement of thermal stability in the non-oxidative thermal degradation of bisphenol-A/aniline based polybenzoxazine aerogel

Previously we reported synthesis of a new type of organic aerogel from phenolic resins called polybenzoxazines and their transformation into carbon aerogels. Here, we further investigate the thermal degradation behaviors of both bulk polybenzoxazines and polybenzoxazine aerogels using Fourier transform infrared spectroscopy (FTIR), thermal gravimetric analysis (TGA)/FTIR, and gas chromatography/time of flight-mass spectroscopy (GC/TOF-MS). The activation energy (E_a) of the decomposition step was determined using the Kissinger method. It was found that the polybenzoxazine aerogels exhibit much higher degradation temperatures and char yields than the bulk. The decomposition temperatures at 10% weight loss and the char yields at 800 °C of the bisphenol-A/aniline based polybenzoxazine aerogel increased up to 24% and 97% higher, respectively, than the corresponding bulk values. Kinetic investigation indicated that the decomposition reaction of bulk polybenzoxazine exhibits three stages, whereas that of the polybenzoxazine aerogel features four stages with much higher overall activation energy. The enhanced thermal stability of the aerogel is ascribed to its highly porous structure, which increases the residence time of the primary decomposition products, and hence generates greater opportunity to form secondary reactions.     

Enhanced general analytical equation for the kinetics of the thermal degradation of poly(lactic acid) driven by random scission

An enhanced general analytical equation has been developed in order to evaluate the kinetic parameters of the thermal degradation of poly(lactic acid) (PLA) at various linear heating rates and at constant rate conditions. This improvement consisted of replacing the n-order conversion function by a modified form of the Sestak-Berggren equation f(α) = c(1?α)ⁿα^m, which led to better adjustment of experimental data, and also adequately represented the conventional mechanisms for solid-state processes. The kinetic parameters so obtained have been compared to those determined by conventional differential and isoconversional methods. Given that the thermal degradation of PLA has been argued to be caused by random chain scission reactions of ester groups, the conversion function (α) = 2(α^1/2?α), corresponding to a random scission mechanism, has been tested.     

Controlled rate thermal analysis of hydromagnesite

The reaction of magnesium minerals such as brucite with CO₂ is important in the sequestration of CO₂. The study of the thermal stability of hydromagnesite and diagenetically related compounds is of fundamental importance to this sequestration. The understanding of the thermal stability of magnesium carbonates and the relative metastability of hydrous carbonates including hydromagnesite, artinite, nesquehonite, barringtonite and lansfordite is extremely important to the sequestration process for the removal of atmospheric CO₂. This work makes a comparison of the dynamic and controlled rate thermal analysis of hydromagnesite and nesquehonite. The dynamic thermal analysis of synthetic hydromagnesite proves that dehydration takes place in two steps at 135 and 184°C, dehydroxylation at 412°C and decarbonation at 474°C. Controlled rate thermal analysis shows the first dehydration step is isothermal and the second quasi-isothermal at 108 and 145°C, respectively. In the CRTA experiment both water and carbon dioxide are evolved in an isothermal decomposition at 376°C. CRTA technology offers better resolution and a more detailed interpretation of the decomposition processes of magnesium carbonates such as nesquehonite via approaching equilibrium conditions of decomposition through the elimination of the slow transfer of heat to the sample as a controlling parameter on the process of decomposition. Constant-rate decomposition processes of non-isothermal nature reveal partial nesquehonite structure.     

Kinetics of the thermal degradation of poly(lactic acid) obtained by reactive extrusion: Influence of the addition of montmorillonite nanoparticles

A reactive extrusion-calendering process was used in order to manufacture sheets with a nominal thickness of 1 mm of poly(lactic acid) and its nanocomposite with 2.5% of an organo-modified montmorillonite. During processing, the properties of the melt were stabilized and enhanced by the addition of 0.5% of a styrene-acrylic multi-functional-epoxide oligomeric reactive agent. The general analytical equation has been used in order to evaluate the kinetic parameters of the thermal degradation of poly(lactic acid) obtained by reactive extrusion and its nanocomposite. Various empirical and theoretical solid-state mechanisms have been tested to elucidate the best kinetic model. In order to reach this goal, master plots have been constructed by means of standardized conversion functions. Given that it is not always easy to visualize the best accordance between experimental and theoretical values of standardized conversion functions, a new index has been developed to quantitatively discern the best mechanism. By doing that, it has been possible to determine the right activation energy of the thermal degradation. It has been demonstrated that the best theoretical mechanism was the random scission of macromolecular chains within the polymer matrix. This was also in accordance with an empirical kinetic model based on an autocatalytic kinetic model. The presence of montmorillonite nanoparticles has been beneficial and has enhanced the thermal stability of poly(lactic acid).     

Effect of metal compounds on thermal degradation behavior of aliphatic poly(hydroxyalkanoic acid)s

Effect of metal compounds on the thermal degradation behaviors of poly(3-hydroxybutyric acid) (P(3HB)), poly(4-hydroxybutyric acid) (P(4HB)), and poly(?-caprolactone) (PCL) was investigated by means of thermogravimetric and pyrolysis-gas chromatograph mass spectrometric analyses. Na and Ca compounds accelerated a random chain scission of P(3HB) molecules resulting in a decrease of thermal degradation temperature, whereas the contribution of Zn, Sn, Al compounds to the thermal degradation of P(3HB) was very small. In contrast to P(3HB), Zn, Sn and Al compounds induced the thermal degradation of PCL at lower temperature range by catalyzing the selective unzipping depolymerization from ω-hydroxyl chain end. Transesterification reaction of PCL molecules could be facilitated by the presence of Ca compound, while the gravimetric change was detected at almost identical temperature region regardless of the content of Ca compound. According to the lactonizing characteristic of monomer unit, the thermal degradation of P(4HB) progressed by the cyclic rupture via unzipping reaction from the ω-hydroxyl chain end or/and random intramolecular transesterification at the main chain with a release of γ-butyrolactone as volatile product. Each of metal compounds used in this study was effective to catalyze the cyclic rupture of P(4HB) molecules, and the degradation rate was accelerated by the presence of metal compounds.     

Dynamic and controlled rate thermal analysis of hydrozincite and smithsonite

The understanding of the thermal stability of zinc carbonates and the relative stability of hydrous carbonates including hydrozincite and hydromagnesite is extremely important to the sequestration process for the removal of atmospheric CO₂. The hydration-carbonation or hydration-and-carbonation reaction path in the ZnO-CO₂-H₂O system at ambient temperature and atmospheric CO₂ is of environmental significance from the standpoint of carbon balance and the removal of green house gases from the atmosphere. The dynamic thermal analysis of hydrozincite shows a 22.1% mass loss at 247°C. The controlled rate thermal analysis (CRTA) pattern of hydrozincite shows dehydration at 38°C, some dehydroxylation at 170°C and dehydroxylation and decarbonation in a long isothermal step at 190°C. The CRTA pattern of smithsonite shows a long isothermal decomposition with loss of CO₂ at 226°C. CRTA technology offers better resolution and a more detailed interpretation of the decomposition processes of zinc carbonate minerals via approaching equilibrium conditions of decomposition through the elimination of the slow transfer of heat to the sample as a controlling parameter on the process of decomposition. The CRTA technology offers a mechanism for the study of the thermal decomposition and relative stability of minerals such as hydrozincite and smithsonite.     

A model for thermal degradation of hybrid nanocomposites

A model is developed for thermal degradation of polymer nanocomposites. A composite is thought of as an equivalent network of linear chains with attached side-groups. Thermal degradation is treated as combination of (i) binary scission (fragmentation) of backbone chains, and (ii) detachment of side-groups and their subsequent annihilation (diffusion to the surface of a sample and desorption). An explicit solution is derived for the kinetic equation. This solution involves three adjustable parameters that are found by fitting observations on isotactic polypropylene reinforced with carbon nanofibres. Good agreement is demonstrated between the experimental data and the results of numerical simulation.     

Development of master curves for discriminating the mechanism of solid state reactions from experimental data obtained by using the cyclic and controlled rate thermal analysis

The cyclic and Controlled Rate Thermal Analysis method (CRTA) has been used. The two rates automatically selected in the cyclic curve are small enough to allow the two states of the sample to be compared have nearly the same reacted fraction. Thus, the activation energy can be calculated without previous knowledge of the actual reaction mechanism. Provided that the activation energy,E, is known, a procedure has been developed for determining the kinetic law obeyed by the reaction by means of master curves that represent the values of the reacted fraction, α, as a function of?E/R(1/T-1/T _0.5),T _0.5 being the temperature at which α=0.5. This procedure has been tested by studying the thermal decomposition reaction of BaCO₃.     

Study on thermal stability of poled non-linear optical polymers

A logarithmic expression is proposed to describe relaxation of the polar order in side chain polymers,together with a new way of plotting temperature dependent relaxation data.This results in a straight line extending even below the glass transition temperature in the case of poled nonlinear optics (NLO) side chain polymers.A simple procedure to determine the rotational diffusion constant Dr is given and Dr values of several polymer systems have been evaluated and compared with each other.It appears that,starting from the conventional and well known poled polymer system currently applied,a further lowering of Dr by about 3 orders of magnitude is necessary in order to reach an acceptable orientational stability or lifetime of poled polymers for practical applications.Attempts have been made to introduce electron push-pull substituents into high thermostable molecular frameworks and results of preliminary measurements are reported.     

Effects of silphenylene units on the thermal stability of silicone resins

A series of silicone resins containing silphenylene units were synthesized by a hydrolysis-polycondensation method, with methyltriethoxysilane, dimethyldiethoxysilane and 1,4-bis(ethoxydimethylsilyl)benzene. Their thermal degradation behaviours were studied by thermogravimetric analysis (TGA), differential thermogravimetry (DTG) and Fourier-transform infrared (FTIR) spectroscopy, and the effect of silphenylene units on the thermal stability of silicone resins was also investigated. Results showed that the thermal stability of silicone resins was improved by the introduction of silphenylene units into the backbone. Under nitrogen atmosphere, the temperature for maximum degradation rate of silicone resins with silphenylene units was lower compared to the pure methylsilicone resin. With the increase of silphenylene units, the amount of degradation residues increased under nitrogen atmosphere while it decreased under air atmosphere. Additionally, the short-term and long-term stability of silicone resins were also improved by the introduction of silphenylene units.     

The thermal degradation of poly(diethyl fumarate)

The kinetics and mechanism of the thermal degradation of poly(diethyl fumarate) (PDEF) were studied by thermogravimetry, as well as by analysis of the thermolysis volatiles and polymer residue. The characteristic mass loss temperatures were determined, as were the overall thermal degradation activation energies of three PDEF samples of varying molar mass. Ethylene and ethanol were present in the thermolysis volatiles at degradation temperatures below 300 °C, while diethyl fumarate was also evidenced at higher degradation temperatures. The amount of monomer increased with increasing degradation temperature. The dependence of the molar mass of the residual polymer on the degradation time and temperature was established and the number of main-chain scissions per monomer unit, s/P₀, calculated. A thermal degradation mechanism including de-esterification and random main-chain scission is proposed. The thermal degradation of PDEF was compared to the thermolysis of poly(ethyl methacrylate) (PEMA), poly(diethyl itaconate) (PDEI) and poly(ethyl acrylate) (PEA).     

On the kinetics of cellulose degradation: looking beyond the pseudo zero order rate equation

The kinetics of cellulose degradation was analysed by means of a two-stage model, characterised by an autoretardant and autocatalytic regime, later tempered by the consumption of glycosidic bonds in the amorphous regions. The proposed model explains the effects on the kinetic equations of different modes of ageing (acid hydrolysis, ageing in ventilated oven or sealed vessels), initial oxidation of cellulose and experimental procedures (with or without reduction of oxidised groups). The autoretardant branch can be analysed in a quantitative way, while the integration of the non-linear autocatalytic branch is allowed in some cases, characterised by the decrease of pH and/or emission of acid volatile organic compounds (VOCs). Most of the controversial results of the literature can be easily explained, but the proposed model offers also a guide for further studies on the kinetics of cellulose degradation.     

Constant Rate Thermal Analysis (CRTA) as a Tool for the Synthesis of Materials with Controlled Texture and Structure

Some examples of the use of the CRTA method for the synthesis of materials with controlled texture and structure are given. BaTiO₃ has been obtained from the thermal decomposition of Barium Titanyl Oxalate (BTO) and Barium Titanyl Citrate (BTC) by controlling the reaction temperature in such a way that the partial pressure of the gases generated in the reaction was maintained constant at a value close to 10^-2 mbar. It has been shown that this method allows getting BaTiO₃ with crystal sizes considerably lower than those obtained by decomposing the same precursors by conventional methods. This small crystal sizes lead to the stabilisation of the metastable cubic phase with regards to the tetragonal phase. It has been also shown that the control of the CO generated in the carbothermal reduction of silica allows tailoring the phase composition of the silicon nitride obtained as final product. This revised version was published online in August 2006 with corrections to the Cover Date.     

Global kinetics of thermal degradation of flame-retarded epoxy resin formulations

A predictive mathematical model to describe mass loss profiles of flame-retardant (FR) containing epoxy resin formulations is proposed. Mass loss is due to thermal degradation of the constituent components and can be described by a generic kinetic scheme with a given set of thermokinetic constants in the form of ordinary differential equations. The scope of this work is to determine the kinetic parameters of the thermal degradation of a known flame-retarded epoxy resin composition by using thermogravimetric analysis and using the acquired data to predict the degradation profiles for other formulations. The mass loss profiles of Visil and intumescent epoxy resin containing formulations were predicted by solving coupled systems of ordinary differential equations and then using Powell minimisation to find the optimal Arrhenius parameters, taking into account the mass ratio of the components in the mixture. The calculated kinetic constants for one formulation (85% resin-15% FR additives) are used to predict the mass loss profiles for other formulations (80% resin-20% FR additives and 90% resin-10% FR additives) with the assumption that the degradation mechanism does not change. The predicted thermal degradation profiles are compared with experimental data acquired using standard laboratory equipment in order to validate the proposed mechanisms. The kinetic parameters obtained adequately describe mass loss history of composite materials studied, even when extremely simplified kinetic schemes have been used.     

Silver sulfide/poly(3-hydroxybutyrate) nanocomposites: Thermal stability and kinetic analysis of thermal degradation

The non-isothermal degradation of poly(3-hydroxybutyrate) (PHB) and silver sulfide/poly(3-hydroxybutyrate) (Ag₂S/PHB) nanocomposites was investigated using thermogravimetric (TG) analysis. In the composite materials, Ag₂S caused the degradation of PHB at a lower temperature as opposed to that of neat PHB. Moreover, an increase Ag₂S loading in the PHB decreased the onset temperature (T_onset) of thermal degradation, whereas it was raised upon augmenting the heating rate. From Kissinger plots, the observed trend of the degradation activation energy, E_d, was attributed to polymer-particle surface interactions and the agglomeration of Ag₂S. The thermal degradation rate constant, k, was linearly related to the Ag₂S loading in PHB. Thus, the Ag₂S nanoparticles effectively catalyzed the thermal degradation of PHB in the Ag₂S/PHB nanocomposites. Differential scanning calorimetry (DSC) data also supported the catalytic property of Ag₂S.