Simulation of isothermal cure of A powder coating

The curing of a thermosetting powder coating was studied by means of differential scanning calorimetry (DSC). The isothermal cure was simulated by non-isothermal experiments. The results of the simulation were compared with experimental isothermal data. From non-isothermal isoconversional procedures (free model), it was concluded that these permit simulation of the isothermal cure but do not enable us to determine the complete kinetic triplet (A preexponential factor, E activation energy, f(a) and/or g(a) function of conversion). Non-isothermal procedures based on a single heating rate or on master curves present difficulties for determination of all the kinetic parameters, due to the compensation effect between preexponential factor and activation energy. The kinetic triplet can be determined by a combination of various non-isothermal methods or by using experimental isothermal data in addition to non-isothermal data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Model-free method for isothermal and non-isothermal decomposition kinetics analysis of PET sample

Pyrolysis, one possible alternative to recover valuable products from waste plastics, has recently been the subject of renewed interest. In the present study, the isoconversion methods, i.e., Vyazovkin model-free approach is applied to study non-isothermal decomposition kinetics of waste PET samples using various temperature integral approximations such as Coats and Redfern, Gorbachev, and Agrawal and Sivasubramanian approximation and direct integration (recursive adaptive Simpson quadrature scheme) to analyze the decomposition kinetics.The results show that activation energy (E_α) is a weak but increasing function of conversion (α) in case of non-isothermal decomposition and strong and decreasing function of conversion in case of isothermal decomposition. This indicates possible existence of nucleation, nuclei growth and gas diffusion mechanism during non-isothermal pyrolysis and nucleation and gas diffusion mechanism during isothermal pyrolysis. Optimum E_α dependencies on α obtained for non-isothermal data showed similar nature for all the types of temperature integral approximations.     

Addition effect of erbium(III) trifluoromethanesulfonate in the homopolymerization kinetics of a DGEBA resin

Solid bisphenol-A epoxy resin of medium molecular weight was cured using a Lewis acid initiator (erbium(III) trifluoromethanesulfonate) in three different proportions (0.5, 1 and 2 phr). A kinetic study was performed in a differential scanning calorimeter. The complete kinetic triplet was determined (activation energy, pre-exponential factor, and integral function of the degree of conversion) for each system. A kinetic analysis was performed with an integral isoconversional procedure (model-free), and the kinetic model was determined both with the Coats-Redfern method (the obtained isoconversional E value being accepted as the effective activation energy) and through the compensation effect. All the systems followed the same isothermal curing model simulated from non-isothermal ones. The “nucleation and growth” Avrami kinetic model A_3/2 has been proposed as the polymerization kinetic model. The addition of initiator accelerated the reaction having higher influence when low temperatures were applied.     

The deviation of the true heating rate with respect to the programmed one

The paper deals with the influence of the deviation of the true heating rate with respect to the programmed one on the values of non-isothermal kinetic parameters for the solid-gas thermal decompositions of CaC₂O₄.H₂O and [Ni(NH₃)₆]Br₂. An original method, based on integration over small ranges of the variables and making use of local heating rates, was applied in order to determine the non-isothermal kinetic parameter values. The results show significant differences between values of non-isothermal kinetic parameters obtained by using true local heating rates and those obtained by using the programmed heating rate.     

The thermal decomposition of alkaline earth formates

The thermal decomposition of alkaline earth formates has been studied. Experiments with single crystals, compacts and powders of strontium formate demonstrate that the method of sample presentation can affect the rate of decomposition.For anhydrous calcuim, strontium and barium formates, isothermal kinetic runs show that the decompositions follow the Erofeev law, In(l-α) = ktⁿ; the measured activation energies were 199.4, 228 and 270 kJ/mol respectively.     

High speed spinning of poly(ethylene terephthalate)—II: Orientation induced mechanism of cold crystallization in pre-orientated yarns

The kinetics of the “cold crystallization” of poly(ethylene terephthalate) (PET) pre-orientated yarns are investigated both in isothermal and in non-isothermal dynamic conditions. The amorphous-crystalline, solid-solid transformation is analyzed in terms of the Avrami equation and of Ozawa's theory. The nucleation and growth mechanism is a function of PET amorphous molecular orientation and changes from a three dimensional (n = 4) to a two dimensional and one dimensional disc-like or rod-like growth. The molecular orientation may be defined as the best “nucleating agent” for PET overall rate of crystallization in the low temperature region.     

Rational approach to thermodynamic rrocesses and constitutive equations in isothermal and non-isothermal kinetics

Isothermal and non-isothermal kinetics are classified according to the viewpoint of rational approach. The appropriate selection of basic quantities and constitutive equations is stressed. The extensive discussion recently focused to the meaning of the partial derivatives is reinvestigated and clarified considering the origin of following equation $$\alpha = f(T,t)$$ whereα is the extent of reaction,T andt are the temperature and time respectively, andf represents a function. The meaning of partial derivatives is demonstrated in details. The disagreement sometimes claimed between the data evaluated by means of isothermal and non-isothermal kinetics is also reviewed, but no fundamental differences are established.     

Kinetics of the thermal dehydration of trans-fluoroaquobis(ethylenediamine)chromium(III) tetracyanometallate(II) [metal(II) = Ni(II), Pd(II) and Pt(II)]

The solid phase thermal deaquation—anation of trans-[CrF(H₂O)(en)₂][M(CN)₄] (M = Ni, Pd, Pt; en = ethylenediamine) has been investigated by means of non-isothermal DSC and isothermal and non-isothermal TG measurements. The physical model for these reactions (nucleation, growth, diffusion or intermediates) has been found by comparison of the isothermal and non-isothermal TG data for all the principal g(α) expressions (0.2?α?0.8) and by the shape of the isothermal curves. The values found for activation energy are low (～ 130 kJ mol^?1 for the Ni compound, ～ 140 kJ mol^?1 for the Pd compound, and ～ 100 kJ mol^?1 for the Pt compound). These data permit the assignment of the deaquation—anation mechanism of the S_N1 type involving a square-base pyramid activated complex and elimination of water as Frenkel defects.     

Thermokinetic parameters and thermal hazard evaluation for three organic peroxides by DSC and TAM III

The thermokinetic parameters were investigated for cumene hydroperoxide (CHP), di-tert-butyl peroxide (DTBP), and tert-butyl peroxybenzoate (TBPB) by non-isothermal kinetic model and isothermal kinetic model by differential scanning calorimetry (DSC) and thermal activity monitor III (TAM III), respectively. The objective was to investigate the activation energy (E _a) of CHP, DTBP, and TBPB applied non-isothermal well-known kinetic equation to evaluate the thermokinetic parameters by DSC. We employed TAM III to assess the thermokinetic parameters of three liquid organic peroxides, obtained thermal runaway data, and then used the Arrhenius plot to obtain the E _a of liquid organic peroxides at various isothermal temperatures. In contrast, the results of non-isothermal kinetic algorithm and isothermal kinetic algorithm were acquired from a highly accurate procedure for receiving information on thermal decomposition characteristics and reaction hazard.     

Kinetic Analysis of Single or Multi-Step Decomposition Processes; Limits introduced by statistical analysis

A kinetic study on decomposition processes of some penicillin and some commercial drugs was carried out. As expected by the complex structures of penicillins, several steps with different activation energies occurred in their decomposition processes. Model-fitting and model-free kinetic approach were applied to non-isothermal and isothermal data. In the model-fitting methods the kinetic triplets (f(α), A and E _a) that defines a single reaction step resulted in being at variance with the multi-step nature of penicillins decomposition. The model-free approach represented by isothermal and non-isothermal isoconversional methods, gave dependences of the activation energies on the extent of conversion. The complex nature of the multi-step process of the studied compounds was more easily revealed using a broader temperature range in non-isothermal isoconversional method. The failure in the model fitting method did not allow calculating storage times. Model-fitting and model-free methods, both isothermal and non-isothermal, showed that F1 mechanism is able to describe decomposition processes for drugs (having Phosphomycin salts as active component) for which a single decomposition process occurs. Statistical analysis allowed us to select reliable kinetic parameters related to the decomposition processes for these last compounds. This procedure showed that the values obtained by extrapolation, outside the temperature range where the processes occurred must be used with caution. Indeed half-life and shelf-life values, commonly extrapoled at room temperature, seemed to be unrealistic. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis and cure kinetics of diphenyl(diphenylethynyl)silane monomer

Diphenyl(diphenylethynyl)silane ((ph–C≡C)₂–Si–ph₂) (DPDPES) was synthesized by the Grignard reaction. The corresponding isothermal and non-isothermal cure kinetics of DPDPES were analyzed by using differential scanning calorimetry (DSC), and the molecular structure was characterized by H-NMR. The results showed that all the cure curves were typically sigmoid shape and cure reactions could be described by an autocatalytic kinetic model by isothermal DSC. The kinetic data, for example, activation energy (E) and frequency factor (A), were 119.22 kJ/mol and 4.67 × 10⁷ (s^?1), respectively. The non-isothermal DSC analyses showed that E and A were 162.12 kJ/mol and 1.32 × 10⁹ (s^?1), respectively, and the reaction order was 0.94. Based on the research work of this paper, it can be said that the cure reaction of DPDPES monomer was of autocatalytic and diffusion-controlled characteristics, and the effect of the diffusion was more evident at low temperature. The cure reaction of DPDPES was a first-order kinetic reaction.     

Thermogravimetric studies on the reduction of hematite ore fines by a surrounding layer of coal or char fines: Part 1. Isothermal kinetic studies

Although there is a good deal of literature on the reduction of iron oxide by carbonaceous materials, it mostly covers systems where the oxide and reductant are thoroughly mixed. The present work concerns a system where the oxide and the reductant are not mixed.The kinetics of isothermal reduction of a central column of ore fines by a surrounding layer of coal fines have been studied by thermogravimetry. The course of reaction has been expressed in terms of a “degree of reaction” (f) defined as weight loss measured at a given time (t) with respect to the maximum possible weight loss. The kinetic data expressed in terms of f have been analysed using a kinetic law appropriate for diffusion-controlled processes and apparent activation energies have been calculated for reduction by coal and char. The results have been interpreted to identify carbon gasification as the rate-controlling step.     

Compensation effect in heterogeneous non-isothermal kinetics

A number of 1145 sets of kinetic parameters derived in our earlier papers from TG curves have been worked up. The apparent activation energy and pre-exponential factor values have been found to obey a linear compensation law (isokinetic relation) if the thermal decomposition begins in the same temperature interval, irrespective of the nature of the chemical reaction. The isokinetic temperatureT _i has been found to be very close to the mean value of the temperaturesT _0.1 at which the conversion becomes equal to 0.1 and atT _i the rate constant has been found to be approximately equal to 10^?3s^?1 in allT _0.1 intervals investigated. It is concluded that the kinetic compensation effect observed in heterogeneous non isothermal TG kinetics is not a true one.     

Mass spectrometric evolved gas analysis (MSEGA) study of the thermal decomposition of poly(1,2-acenaphthenediylidene) and poly(1,2-acenaphthylenylene) in vacuo

A mass spectrometric study of the thermal decompositions in vacuo of two polyene polymers, poly(1,2-acenaphthenediylidene)-I and poly(1,2-acenaphthylenylene)-II, was performed in order to establish the differences between their structures. Evolution of repeating units from a chain depropagation process of both polymers was observed. Annealing of the polymers prior to decomposition changed the temperature at which maxima were observed on the MSEGA ion current temperature profiles. These profiles of both polymers after annealing became more similar in shape and temperature location. These changes in MSEGA behaviour as a result of annealing can be attributed to an equalisation of the single and double bonds in the structure of the polymers. The kinetic study of the thermal decomposition of non-annealed polymers showed that the decomposition reaction for polymer I is isokinetic, i.e. of the same kinetic mechanism, when the fraction of sample decomposed “α” is in the range 0.4–0.7 with values of 127.8 ± 3.6 kJ mol^?1 for the activation energy and 2.6 ± 2.2 × l0⁷ s^?1 for the A factor. Polymer II did not show clearcut isokinetic behaviour, the activation energy increasing from 99.4 kJ mol^?1 at α = 0.4–113.5 kJ mol^?1 at α = 0.7. This change is attributed to the structure of the polymer altering during the course of the decomposition. The differences in the thermal properties lead to the conclusion that there is a bond alternation in the polyene chains of both polymers.     

Determination of the kinetic constants of endothermic decompositions of the type Asol f Bsol + Cgas

The present work describes the endothermic decompositions of calcium carbonate and nickel carbonate, recorded on a MOM derivatograph in the non-isothermal mode at different heating rates. The possibility and advantages of determining the kinetic parametersE, Z, andn for reactions proceeding in one step, as well as the detection of simultaneous (parallel or concurrent) reactions in the decomposition process, are discussed. The results obtained permit the conclusion that the thermal decomposition of calcite occurs in one step. In this case, the kinetic equation has the following form: $$\lg \left[ {\frac{{d\alpha }}{{(1 - \alpha )^n }}} \right] = \lg \frac{Z}{q} - \frac{E}{{2.3R}} \cdot \frac{1}{T}$$ where f(α)=(1?α)ⁿ,n=0.3, andE=176.8 kJ/mol. In the case of nickel carbonate the results of treating the experimental data have been obtained only in the graphical form. From the shape of the curves obtained, it is clearly seen that the decomposition of nickel carbonate in open air proceeds in several steps (i.e. several simultaneous reactions take place), which cannot be described by the equations for a one-step reaction.     

Support Effect in the Thermal Decomposition of Some Catalyst Precursors

The thermal decompositions of ammonium metavanadate, molybdic acid and ammonium phosphomolybdate supported on carborundum or silica were subjected to non-isothermal kinetic study. The compensation effect is discussed in connection with the quantitative estimation of the support effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-isothermal depolymerisation kinetics of poly(ethylene oxide)

The depolymerisation of low molecular weight poly(ethylene oxide) (PEO) under mild conditions was studied using a linear temperature ramped non-isothermal technique and the results compared with those obtained from a conventional isothermal technique. The analysis of the non-isothermal kinetic (NIK) data was performed using an original computer program incorporating an algorithm that systematically minimizes the sum of the squares of the residuals between the experimental data and the calculated theoretical kinetic profile in order to extract the kinetic parameters. The results revealed that the depolymerisation of PEO proceeds in accordance with the Ekenstam model and follows the Arrhenius equation over the temperature range of ca. 40-130 °C. The NIK analysis resulted in a two-dimensional convergence to produce a unique solution set for the kinetic parameters of E_a = 89.4 kJ mol⁻¹ and A = 9.6 × 10⁶ h⁻¹. These data are consistent with the results obtained from the isothermal experiments. It is proposed that NIK analysis is a quick and reliable means of obtaining kinetic parameters relevant to lifetime predictions in polymers whose degradation behaviour can be considered to be close to ideal.     

Thermal conductivity of Tetryl by modulated differential scanning calorimetry

An investigation of the use of modulated differential scanning calorimeter (MDSC) to measure thermal conductivity (κ) of the explosive Tetryl using isothermal and non-isothermal methods. Issues surrounding the use of silicone oil as a heat transfer aid are discussed. Using these methods the calculated isothermal and non-isothermal properties of specific heat capacity were observed to be 0.844 and 0.863 J/(g K) and the calculated thermal conductivity values were found to be 0.165 and 0.186 W/K. Calibration experiments using polystyrene indicate that the non-isothermal method is more reproducible but has a larger offset (35%) from the true value. Our corrected values for Tetryl fall in the middle of the considerable range of values reported in the literature.     

Kinetics and mechanism of the thermal degradation of polysulphide polymer cured with ammonium dichromate: Pyrolysis-gas chromatography and thermogravimetric studies

The kinetics and mechanism of the thermal degradation of thiol-terminated liquid polysulphide polymer cured with ammonium dichromate was studied by pyrolysis-gas chromatography and isothermal and dynamic thermogravimetry. Pyrolysis-gas chromatography showed that the nature and composition of the pyrolysates for the liquid and the cured elastomers were essentially the same. Isothermal measurements were made at 268, 280, 290 and 299°C and maxima in the rates of degradation occurred at 28% conversion (α). Isothermal rates calculated from a kinetic model based on random initiation followed by rapid termination by disproportionation were in good agreement with the experimental values. The dynamic experiments were run at several heating rates from 2 to 100°C/min. Analysis of the data based on the random initiation model gave kinetic parameters that agreed well with the isothermal values and with the values obtained by Ozawa's method, confirming the proposed kinetic model for the degradation. The overall activation energy for the degradation (E_d) was found to be 146.4, 144.1±7.6 and 145.6±7.6 kJ mole⁻¹ by isothermal, dynamic and Ozawa's methods, respectively. The Coats-Redfern method of analysis gave increasing values of E_d with increasing heating rates and showed a kinetic compensation effect.     

The effect of organoclay and graphene on the crystallization of PP in ABS/PP blends

In the present research, the isothermal and non-isothermal crystallization of polypropylene (PP) phase in PP-rich poly(acrylonitrile–butadiene–styrene)/polypropylene (ABS/PP) blends was studied. The effect of nanofillers’ incorporation and specialty of organically modified montmorillonite (OMMT) and graphene, into the prepared blends on the isothermal and non-isothermal crystallization of PP phase, were investigated. Moreover, kinetic study of their isothermal crystallization process was carried out, by applying the Avrami equation. The addition of ABS to the PP matrix increased the crystallization rate of PP at 130 °C. The incorporation of OMMT in pure PP accelerated slightly the crystallization process, whereas in ABS/PP blends, it seemed to retard crystallization, due to interactions between ABS phase and organoclay. The incorporation of graphene in pure PP accelerated impressively its isothermal crystallization, while the addition of ABS in graphene/PP nanocomposite slowed down the crystallization rate of PP. The effect of ABS and nanofillers, separately or in combination, on the crystallization of PP phase was reflected on the kinetic parameters of the Avrami equation. Regarding the non-isothermal crystallization, ABS/PP blends presented higher crystallization temperature (T _c) compared to pure PP. The organoclay reinforcement did not have any obvious effect on this temperature, whereas graphene caused significant increase, acting as nucleating agent. The presence of ABS to PP increased the concentration of the β-crystalline phase, reaching its maximum value at 30 mass% ABS content. The organoclay decreased the β-PP in ABS/PP blends, whereas graphene eliminated it.